Table of Integrals, Series, and Products, 8th Edition

${\displaystyle \int \frac{x^6}{u^5}\text{d}x=\frac{1}{2}\frac{x^5}{c{u}^3}+\frac{10a{x}^3}{3c^2{u}^3}+\frac{5}{2}\frac{a^{2}x}{c^3{u}^3}-\frac{5}{2}\frac{a}{c^3}{I}_1}$

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6. 

${\displaystyle \int \frac{x^6}{u^7}\text{d}x}=-\frac{23}{15}\frac{x^5}{c{u}^5}-\frac{7}{3}\frac{a{x}^3}{c^2{u}^5}-\frac{a^{2}x}{c^3{u}^5}+\frac{1}{c^3}{I}_1$

DW

7. 

${\displaystyle \int \frac{x^6}{u^9}\text{d}x=\frac{1}{7}\frac{x^7}{a{u}^7}}$

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8. 

${\displaystyle \int \frac{x^6\text{d}x}{u^{2n+1}}}=\frac{1}{a^{n-3}}{\displaystyle \sum _{k=0}^{n-4}\frac{{(-1)}^k}{2k+7}\left(\begin{array}{c}n-4\hfill \\ k\hfill \end{array}\right)\frac{c^k{x}^{2k+7}}{u^{2k+7}}}$

9. 

${\displaystyle \int \frac{x^7\text{d}x}{x^{2n+1}}}=-\frac{1}{(2n-7)c^4{u}^{2n-7}}+\frac{3a}{(2n-5)c^4{u}^{2n-5}}-\frac{3a^2}{(2n-3)c^4{u}^{2n-3}}+\frac{a^3}{(2n-1)c^4{u}^{2n-1}}$

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2.275

1. 

${\displaystyle \int \frac{u^5}{x}\text{d}x=}\frac{u^5}{5}+\frac{1}{3}a{u}^3+a^{2}u+a^3{I}_2$

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2. 

${\displaystyle \int \frac{u^3}{x}\text{d}x}=\frac{u^3}{3}+au+a^2{I}_2$

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3. ...