List of integrals of irrational functions

{{startplainlist|indent=1}}

• $\backslash int\; r\backslash ,dx\; =\; \backslash frac\{1\}\{2\}\backslash left(x\; r\; +a^2\backslash ,\backslash ln\backslash left(x+r\backslash right)\backslash right)$
• $\backslash int\; r^3\backslash ,dx\; =\; \backslash frac\{1\}\{4\}xr^3+\backslash frac\{3\}\{8\}a^2xr+\backslash frac\{3\}\{8\}a^4\backslash ln\backslash left(x+r\backslash right)$
• $\backslash int\; r^5\backslash ,dx\; =\; \backslash frac\{1\}\{6\}xr^5+\backslash frac\{5\}\{24\}a^2xr^3+\backslash frac\{5\}\{16\}a^4xr+\backslash frac\{5\}\{16\}a^6\backslash ln\backslash left(x+r\backslash right)$
• $\backslash int\; x\; r\backslash ,dx\; =\; \backslash frac\{r^3\}\{3\}$
• $\backslash int\; x\; r^3\backslash ,dx\; =\; \backslash frac\{r^5\}\{5\}$
• $\backslash int\; x\; r^\{2n+1\}\backslash ,dx\; =\; \backslash frac\{r^\{2n+3\}\}\{2n+3\}$
• $\backslash int\; x^2\; r\backslash ,dx\; =\; \backslash frac\{xr^3\}\{4\}-\backslash frac\{a^2xr\}\{8\}-\backslash frac\{a^4\}\{8\}\backslash ln\backslash left(x+r\backslash right)$
• $\backslash int\; x^2\; r^3\backslash ,dx\; =\; \backslash frac\{xr^5\}\{6\}-\backslash frac\{a^2xr^3\}\{24\}-\backslash frac\{a^4xr\}\{16\}-\backslash frac\{a^6\}\{16\}\backslash ln\backslash left(x+r\backslash right)$
• $\backslash int\; x^3\; r\backslash ,dx\; =\; \backslash frac\{r^5\}\{5\}\; -\; \backslash frac\{a^2\; r^3\}\{3\}$
• $\backslash int\; x^3\; r^3\backslash ,dx\; =\; \backslash frac\{r^7\}\{7\}-\backslash frac\{a^2r^5\}\{5\}$
• $\backslash int\; x^3\; r^\{2n+1\}\backslash ,dx\; =\; \backslash frac\{r^\{2n+5\}\}\{2n+5\}\; -\; \backslash frac\{a^2\; r^\{2n+3\}\}\{2n+3\}$
• $\backslash int\; x^4\; r\backslash ,dx\; =\; \backslash frac\{x^3r^3\}\{6\}-\backslash frac\{a^2xr^3\}\{8\}+\backslash frac\{a^4xr\}\{16\}+\backslash frac\{a^6\}\{16\}\backslash ln\backslash left(x+r\backslash right)$
• $\backslash int\; x^4\; r^3\backslash ,dx\; =\; \backslash frac\{x^3r^5\}\{8\}-\backslash frac\{a^2xr^5\}\{16\}+\backslash frac\{a^4xr^3\}\{64\}+\backslash frac\{3a^6xr\}\{128\}+\backslash frac\{3a^8\}\{128\}\backslash ln\backslash left(x+r\backslash right)$
• $\backslash int\; x^5\; r\backslash ,dx\; =\; \backslash frac\{r^7\}\{7\}\; -\; \backslash frac\{2\; a^2\; r^5\}\{5\}\; +\; \backslash frac\{a^4\; r^3\}\{3\}$
• $\backslash int\; x^5\; r^3\backslash ,dx\; =\; \backslash frac\{r^9\}\{9\}\; -\; \backslash frac\{2\; a^2\; r^7\}\{7\}\; +\; \backslash frac\{a^4\; r^5\}\{5\}$
• $\backslash int\; x^5\; r^\{2n+1\}\backslash ,dx\; =\; \backslash frac\{r^\{2n+7\}\}\{2n+7\}\; -\; \backslash frac\{2a^2r^\{2n+5\}\}\{2n+5\}+\backslash frac\{a^4\; r^\{2n+3\}\}\{2n+3\}$
• $\backslash int\backslash frac\{r\backslash ,dx\}\{x\}\; =\; r-a\backslash ln\backslash left|\backslash frac\{a+r\}\{x\}\backslash right|\; =\; r\; -\; a\backslash ,\; \backslash operatorname\{arsinh\}\backslash frac\{a\}\{x\}$
• $\backslash int\backslash frac\{r^3\backslash ,dx\}\{x\}\; =\; \backslash frac\{r^3\}\{3\}+a^2r-a^3\backslash ln\backslash left|\backslash frac\{a+r\}\{x\}\backslash right|$
• $\backslash int\backslash frac\{r^5\backslash ,dx\}\{x\}\; =\; \backslash frac\{r^5\}\{5\}+\backslash frac\{a^2r^3\}\{3\}+a^4r-a^5\backslash ln\backslash left|\backslash frac\{a+r\}\{x\}\backslash right|$
• $\backslash int\backslash frac\{r^7\backslash ,dx\}\{x\}\; =\; \backslash frac\{r^7\}\{7\}+\backslash frac\{a^2r^5\}\{5\}+\backslash frac\{a^4r^3\}\{3\}+a^6r-a^7\backslash ln\backslash left|\backslash frac\{a+r\}\{x\}\backslash right|$
• $\backslash int\backslash frac\{dx\}\{r\}\; =\; \backslash operatorname\{arsinh\}\backslash frac\{x\}\{a\}\; =\; \backslash ln\backslash left(\; \backslash frac\{x+r\}\{a\}\; \backslash right)$
• $\backslash int\backslash frac\{dx\}\{r^3\}\; =\; \backslash frac\{x\}\{a^2r\}$
• $\backslash int\backslash frac\{x\backslash ,dx\}\{r\}\; =\; r$
• $\backslash int\backslash frac\{x\backslash ,dx\}\{r^3\}\; =\; -\backslash frac\{1\}\{r\}$
• $\backslash int\backslash frac\{x^2\backslash ,dx\}\{r\}\; =\; \backslash frac\{x\}\{2\}r-\backslash frac\{a^2\}\{2\}\backslash ,\backslash operatorname\{arsinh\}\backslash frac\{x\}\{a\}\; =\; \backslash frac\{x\}\{2\}r-\backslash frac\{a^2\}\{2\}\backslash ln\backslash left(\; \backslash frac\; \{x+r\}\{a\}\; \backslash right)$
• $\backslash int\backslash frac\{dx\}\{xr\}\; =\; -\backslash frac\{1\}\{a\}\backslash ,\backslash operatorname\{arsinh\}\backslash frac\{a\}\{x\}\; =\; -\backslash frac\{1\}\{a\}\backslash ln\backslash left|\backslash frac\{a+r\}\{x\}\backslash right|$

{{endplainlist}}

Assume x² > a² (for x² < a², see next section):

{{startplainlist|indent=1}}

• $\backslash int\; s\backslash ,dx\; =\; \backslash frac\{1\}\{2\}\backslash left(xs-a^\{2\}\backslash ln\backslash left|x+s\backslash right|\backslash right)$
• $\backslash int\; xs\backslash ,dx\; =\; \backslash frac\{1\}\{3\}s^3$
• $\backslash int\backslash frac\{s\backslash ,dx\}\{x\}\; =\; s\; -\; |a|\backslash arccos\backslash left|\backslash frac\{a\}\{x\}\backslash right|$
• $\backslash int\backslash frac\{dx\}\{s\}\; =\; \backslash ln\backslash left|\backslash frac\{x+s\}\{a\}\backslash right|$

=\operatorname{sgn}(x)\,\operatorname{arcosh}\left|\frac{x}{a}\right|

=\frac{1}{2}\ln\left(\frac{x+s}{x-s}\right)\,, where the positive value of $\backslash operatorname\{arcosh\}\backslash left|\backslash frac\{x\}\{a\}\backslash right|$ is to be taken.

• $\backslash int\backslash frac\{dx\}\{xs\}\; =\; \backslash frac\{1\}\{a\}\backslash operatorname\{arcsec\}\backslash left|\backslash frac\{x\}\{a\}\backslash right|$
• $\backslash int\backslash frac\{x\backslash ,dx\}\{s\}\; =\; s$
• $\backslash int\backslash frac\{x\backslash ,dx\}\{s^3\}\; =\; -\backslash frac\{1\}\{s\}$
• $\backslash int\backslash frac\{x\backslash ,dx\}\{s^5\}\; =\; -\backslash frac\{1\}\{3s^3\}$
• $\backslash int\backslash frac\{x\backslash ,dx\}\{s^7\}\; =\; -\backslash frac\{1\}\{5s^5\}$
• $\backslash int\backslash frac\{x\backslash ,dx\}\{s^\{2n+1\}\}\; =\; -\backslash frac\{1\}\{(2n-1)s^\{2n-1\}\}$
• $\backslash int\backslash frac\{x^\{2m\}\backslash ,dx\}\{s^\{2n+1\}\}$

= -\frac{1}{2n-1}\frac{x^{2m-1}}{s^{2n-1}}+\frac{2m-1}{2n-1}\int\frac{x^{2m-2}\,dx}{s^{2n-1}}

• $\backslash int\backslash frac\{x^2\backslash ,dx\}\{s\}$

= \frac{xs}{2}+\frac{a^2}{2}\ln\left|\frac{x+s}{a}\right|

• $\backslash int\backslash frac\{x^2\backslash ,dx\}\{s^3\}$

= -\frac{x}{s}+\ln\left|\frac{x+s}{a}\right|

• $\backslash int\backslash frac\{x^4\backslash ,dx\}\{s\}$

= \frac{x^3s}{4}+\frac{3}{8}a^2xs+\frac{3}{8}a^4\ln\left|\frac{x+s}{a}\right|

• $\backslash int\backslash frac\{x^4\backslash ,dx\}\{s^3\}$

= \frac{xs}{2}-\frac{a^2x}{s}+\frac{3}{2}a^2\ln\left|\frac{x+s}{a}\right|

• $\backslash int\backslash frac\{x^4\backslash ,dx\}\{s^5\}$

= -\frac{x}{s}-\frac{1}{3}\frac{x^3}{s^3}+\ln\left|\frac{x+s}{a}\right|

• $\backslash int\backslash frac\{x^\{2m\}\backslash ,dx\}\{s^\{2n+1\}\}$

= (-1)^{n-m}\frac{1}{a^{2(n-m)}}\sum_{i=0}^{n-m-1}\frac{1}{2(m+i)+1}{n-m-1 \choose i}\frac{x^{2(m+i)+1}}{s^{2(m+i)+1}}\qquad\mbox{(}n>m\ge0\mbox{)}

• $\backslash int\backslash frac\{dx\}\{s^3\}\; =\; -\backslash frac\{1\}\{a^2\}\backslash frac\{x\}\{s\}$
• $\backslash int\backslash frac\{dx\}\{s^5\}\; =\; \backslash frac\{1\}\{a^4\}\backslash left[\backslash frac\{x\}\{s\}-\backslash frac\{1\}\{3\}\backslash frac\{x^3\}\{s^3\}\backslash right]$
• $\backslash int\backslash frac\{dx\}\{s^7\}$

=-\frac{1}{a^6}\left[\frac{x}{s}-\frac{2}{3}\frac{x^3}{s^3}+\frac{1}{5}\frac{x^5}{s^5}\right]

• $\backslash int\backslash frac\{dx\}\{s^9\}$

=\frac{1}{a^8}\left[\frac{x}{s}-\frac{3}{3}\frac{x^3}{s^3}+\frac{3}{5}\frac{x^5}{s^5}-\frac{1}{7}\frac{x^7}{s^7}\right]

• $\backslash int\backslash frac\{x^2\backslash ,dx\}\{s^5\}\; =\; -\backslash frac\{1\}\{a^2\}\backslash frac\{x^3\}\{3s^3\}$
• $\backslash int\backslash frac\{x^2\backslash ,dx\}\{s^7\}$

= \frac{1}{a^4}\left[\frac{1}{3}\frac{x^3}{s^3}-\frac{1}{5}\frac{x^5}{s^5}\right]

• $\backslash int\backslash frac\{x^2\backslash ,dx\}\{s^9\}$

= -\frac{1}{a^6}\left[\frac{1}{3}\frac{x^3}{s^3}-\frac{2}{5}\frac{x^5}{s^5}+\frac{1}{7}\frac{x^7}{s^7}\right]

{{endplainlist}}

{{startplainlist|indent=1}}

• $\backslash int\; u\backslash ,dx\; =\; \backslash frac\{1\}\{2\}\backslash left(xu+a^2\backslash arcsin\backslash frac\{x\}\{a\}\backslash right)\; \backslash qquad\backslash mbox\{(\}|x|\backslash leq|a|\backslash mbox\{)\}$
• $\backslash int\; xu\backslash ,dx\; =\; -\backslash frac\{1\}\{3\}\; u^3\; \backslash qquad\backslash mbox\{(\}|x|\backslash leq|a|\backslash mbox\{)\}$
• $\backslash int\; x^2u\backslash ,dx\; =\; -\backslash frac\{x\}\{4\}\; u^3+\backslash frac\{a^2\}\{8\}(xu+a^2\backslash arcsin\backslash frac\{x\}\{a\})\; \backslash qquad\backslash mbox\{(\}|x|\backslash leq|a|\backslash mbox\{)\}$
• $\backslash int\backslash frac\{u\backslash ,dx\}\{x\}\; =\; u-a\backslash ln\backslash left|\backslash frac\{a+u\}\{x\}\backslash right|\; \backslash qquad\backslash mbox\{(\}|x|\backslash leq|a|\backslash mbox\{)\}$
• $\backslash int\backslash frac\{dx\}\{u\}\; =\; \backslash arcsin\backslash frac\{x\}\{a\}\; \backslash qquad\backslash mbox\{(\}|x|\backslash leq|a|\backslash mbox\{)\}$
• $\backslash int\backslash frac\{x^2\backslash ,dx\}\{u\}\; =\; \backslash frac\{1\}\{2\}\backslash left(-xu+a^2\backslash arcsin\backslash frac\{x\}\{a\}\backslash right)\; \backslash qquad\backslash mbox\{(\}|x|\backslash leq|a|\backslash mbox\{)\}$
• $\backslash int\; u\backslash ,dx\; =\; \backslash frac\{1\}\{2\}\backslash left(xu-\backslash sgn\; x\backslash ,\backslash operatorname\{arcosh\}\backslash left|\backslash frac\{x\}\{a\}\backslash right|\backslash right)\; \backslash qquad\backslash mbox\{(for\; \}|x|\backslash ge|a|\backslash mbox\{)\}$
• $\backslash int\; \backslash frac\{x\}\{u\}\backslash ,dx\; =\; -u\; \backslash qquad\backslash mbox\{(\}|x|\backslash leq|a|\backslash mbox\{)\}$

{{endplainlist}}

Assume (ax² + bx + c) cannot be reduced to the following expression (px + q)² for some p and q.

{{startplainlist|indent=1}}

• $\backslash int\backslash frac\{dx\}\{R\}\; =\; \backslash frac\{1\}\{\backslash sqrt\{a\}\}\backslash ln\backslash left|2\backslash sqrt\{a\}R+2ax+b\backslash right|\; \backslash qquad\; \backslash mbox\{(for\; \}a>0\backslash mbox\{)\}$
• $\backslash int\backslash frac\{dx\}\{R\}\; =\; \backslash frac\{1\}\{\backslash sqrt\{a\}\}\backslash ,\backslash operatorname\{arsinh\}\backslash frac\{2ax+b\}\{\backslash sqrt\{4ac-b^2\}\}\; \backslash qquad\; \backslash mbox\{(for\; \}a>0\backslash mbox\{,\; \}4ac-b^2>0\backslash mbox\{)\}$
• $\backslash int\backslash frac\{dx\}\{R\}\; =\; \backslash frac\{1\}\{\backslash sqrt\{a\}\}\backslash ln|2ax+b|\; \backslash quad\; \backslash mbox\{(for\; \}a>0\backslash mbox\{,\; \}4ac-b^2=0\backslash mbox\{)\}$
• $\backslash int\backslash frac\{dx\}\{R^3\}\; =\; \backslash frac\{4ax+2b\}\{(4ac-b^2)R\}$
• $\backslash int\backslash frac\{dx\}\{R^5\}\; =\; \backslash frac\{4ax+2b\}\{3(4ac-b^2)R\}\backslash left(\backslash frac\{1\}\{R^2\}+\backslash frac\{8a\}\{4ac-b^2\}\backslash right)$
• $\backslash int\backslash frac\{dx\}\{R^\{2n+1\}\}\; =\; \backslash frac\{2\}\{(2n-1)(4ac-b^2)\}\backslash left(\backslash frac\{2ax+b\}\{R^\{2n-1\}\}+4a(n-1)\backslash int\backslash frac\{dx\}\{R^\{2n-1\}\}\backslash right)$
• $\backslash int\backslash frac\{x\}\{R\}\backslash ,dx\; =\; \backslash frac\{R\}\{a\}-\backslash frac\{b\}\{2a\}\backslash int\backslash frac\{dx\}\{R\}$
• $\backslash int\backslash frac\{x\}\{R^3\}\backslash ,dx\; =\; -\backslash frac\{2bx+4c\}\{(4ac-b^2)R\}$
• $\backslash int\backslash frac\{x\}\{R^\{2n+1\}\}\backslash ,dx\; =\; -\backslash frac\{1\}\{(2n-1)aR^\{2n-1\}\}-\backslash frac\{b\}\{2a\}\backslash int\backslash frac\{dx\}\{R^\{2n+1\}\}$
• $\backslash int\backslash frac\{dx\}\{xR\}\; =\; -\backslash frac\{1\}\{\backslash sqrt\{c\}\}\backslash ln\; \backslash left|\backslash frac\{2\backslash sqrt\{c\}R+bx+2c\}\{x\}\backslash right|,\; ~\; c\; >\; 0$
• $\backslash int\backslash frac\{dx\}\{xR\}\; =\; -\backslash frac\{2\}\{bx\}\backslash left(\backslash sqrt\{ax^2+bx\}\backslash right),\; ~\; c\; =\; 0$
• $\backslash int\backslash frac\{x^2\}\{R\}\backslash ,dx\; =\; \backslash frac\{2ax-3b\}\{4a^2\}R+\backslash frac\{3b^2-4ac\}\{8a^2\}\backslash int\backslash frac\{dx\}\{R\}$
• $\backslash int\; \backslash frac\{dx\}\{x^\{2\}\; R\}\; =\; -\backslash frac\{\; R\}\{cx\}-\backslash frac\{b\}\{2c\}\; \backslash int\; \backslash frac\{dx\}\{x\; R\}$
• $\backslash int\; R\backslash ,dx\; =\; \backslash frac\{2ax+b\}\{4a\}\; R\; +\; \backslash frac\{4ac-b^\{2\}\}\{8a\}\; \backslash int\; \backslash frac\{dx\}\{\; R\}$
• $\backslash int\; x\; R\backslash ,dx\; =\; \backslash frac\{R^3\}\{3a\}-\backslash frac\{b(2ax+b)\}\{8a^\{2\}\}\; R\; -\; \backslash frac\{b(4ac-b^\{2\})\}\{16a^\{2\}\}\; \backslash int\; \backslash frac\{dx\}\{\; R\}$
• $\backslash int\; x^\{2\}\; R\backslash ,dx\; =\; \backslash frac\{6ax-5b\}\{24a^\{2\}\}R^3+\backslash frac\{5b^\{2\}-4ac\}\{16a^\{2\}\}\; \backslash int\; R\backslash ,dx$
• $\backslash int\; \backslash frac\{\; R\}\{x\}\backslash ,dx\; =\; R\; +\; \backslash frac\{b\}\{2\}\; \backslash int\; \backslash frac\{dx\}\{\; R\}+c\; \backslash int\; \backslash frac\{dx\}\{x\; R\}$
• $\backslash int\; \backslash frac\{\; R\}\{x^\{2\}\}\backslash ,dx\; =\; -\backslash frac\{\; R\}\{x\}+a\; \backslash int\; \backslash frac\{dx\}\{R\}+\; \backslash frac\{b\}\{2\}\; \backslash int\; \backslash frac\{dx\}\{\; xR\}$
• $\backslash int\; \backslash frac\{x^\{2\}\backslash ,dx\}\{R^3\}\; =\; \backslash frac\{(2b^\{2\}-4ac)x+2bc\}\{a(4ac-b^\{2\})\; R\}+\; \backslash frac\{1\}\{a\}\; \backslash int\; \backslash frac\{dx\}\{\; R\}$

{{endplainlist}}

{{startplainlist|indent=1}}

• $\backslash int\; S\backslash ,dx\; =\; \backslash frac\{2\; S^\{3\}\}\{3\; a\}$
• $\backslash int\; \backslash frac\{dx\}\{S\}\; =\; \backslash frac\{2S\}\{a\}$
• $\backslash int\; \backslash frac\{dx\}\{x\; S\}\; =$

\begin{cases}

-\dfrac{2}{\sqrt{b}} \operatorname{arcoth}\left( \dfrac{S}{\sqrt{b}}\right) & \mbox{(for }b > 0, \quad a x > 0\mbox{)} \\

-\dfrac{2}{\sqrt{b}} \operatorname{artanh}\left( \dfrac{S}{\sqrt{b}}\right) & \mbox{(for }b > 0, \quad a x < 0\mbox{)} \\

\dfrac{2}{\sqrt{-b}} \arctan\left( \dfrac{S}{\sqrt{-b}}\right) & \mbox{(for }b < 0\mbox{)} \\

\end{cases}

• $\backslash int\backslash frac\{S\}\{x\}\backslash ,dx\; =$

\begin{cases}

2 \left( S - \sqrt{b}\,\operatorname{arcoth}\left( \dfrac{S}{\sqrt{b}}\right)\right) & \mbox{(for }b > 0, \quad a x > 0\mbox{)} \\

2 \left( S - \sqrt{b}\,\operatorname{artanh}\left( \dfrac{S}{\sqrt{b}}\right)\right) & \mbox{(for }b > 0, \quad a x < 0\mbox{)} \\

2 \left( S - \sqrt{-b} \arctan\left( \dfrac{S}{\sqrt{-b}}\right)\right) & \mbox{(for }b < 0\mbox{)} \\

\end{cases}

• $\backslash int\; \backslash frac\{x^\{n\}\}\{S\}\backslash ,dx\; =\; \backslash frac\{2\}\{a\; (2\; n\; +\; 1)\}\; \backslash left(\; x^\{n\}\; S\; -\; b\; n\; \backslash int\; \backslash frac\{x^\{n\; -\; 1\}\}\{S\}\backslash ,dx\backslash right)$
• $\backslash int\; x^\{n\}\; S\backslash ,dx\; =\; \backslash frac\{2\}\{a\; (2\; n\; +\; 3)\}\; \backslash left(x^\{n\}\; S^\{3\}\; -\; n\; b\; \backslash int\; x^\{n\; -\; 1\}\; S\backslash ,dx\backslash right)$
• $\backslash int\; \backslash frac\{1\}\{x^\{n\}\; S\}\backslash ,dx\; =\; -\backslash frac\{1\}\{b\; (n\; -\; 1)\}\; \backslash left(\; \backslash frac\{S\}\{x^\{n\; -\; 1\}\}\; +\; \backslash left(\; n\; -\; \backslash frac\{3\}\{2\}\backslash right)\; a\; \backslash int\; \backslash frac\{dx\}\{x^\{n\; -\; 1\}\; S\}\backslash right)$

{{endplainlist}}

• {{cite book |editor1-last= Abramowitz |editor1-first= Milton |editor2-last= Stegun |editor2-first= Irene A. |date= 1972 |title= Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables |publisher= Dover |location= New York |chapter= Chapter 3 |chapter-url= http://www.math.sfu.ca/~cbm/aands/page_13.htm }}
• {{cite book |author-first1=Izrail Solomonovich |author-last1=Gradshteyn |author-link1=Izrail Solomonovich Gradshteyn |author-first2=Iosif Moiseevich |author-last2=Ryzhik |author-link2=Iosif Moiseevich Ryzhik |author-first3=Yuri Veniaminovich |author-last3=Geronimus |author-link3=Yuri Veniaminovich Geronimus |author-first4=Michail Yulyevich |author-last4=Tseytlin |author-link4=Michail Yulyevich Tseytlin |author-first5=Alan |author-last5=Jeffrey |editor-first1=Daniel |editor-last1=Zwillinger |editor-first2=Victor Hugo |editor-last2=Moll |editor-link2=Victor Hugo Moll |translator=Scripta Technica, Inc. |title=Table of Integrals, Series, and Products |publisher=Academic Press, Inc. |date=2015 |orig-year=October 2014 |edition=8 |language=en |isbn=978-0-12-384933-5 |lccn=2014010276 |title-link=Gradshteyn and Ryzhik}} (Several previous editions as well.)
• {{cite book |last=Peirce |first=Benjamin Osgood |title=A Short Table of Integrals |orig-year=1899 |edition=3rd revised |date=1929 |publisher=Ginn and Co |location=Boston |pages=16–30 |chapter=Chapter 3 }}

{{Lists of integrals}}

Irrational functions