osteoblogda

2021-12-30

Evaluate the integral.

$\int {({x}^{6}-7x)}^{4}dx$

Thomas Lynn

Beginner2021-12-31Added 28 answers

Step 1

Consider the integral

$\int {({x}^{6}-7x)}^{4}dx$

Step 2

let $I=\int {({x}^{6}-7x)}^{4}dx$

remove x from the bracket

$I=\int {x}^{4}{({x}^{5}-7)}^{4}dx$

put $u={x}^{5}-7$

differentiating it wrt x we have

$du=5{x}^{4}dx$

$\frac{du}{5}={x}^{4}dx$

Replace it with the integral

$I=\int {u}^{4}\frac{du}{5}$

$I=\frac{1}{5}\int {u}^{4}du$

$I=\frac{1}{5}\left(\frac{{u}^{5}}{5}\right)+c$

$I=\frac{{({x}^{5}-7)}^{5}}{25}+c$

Foreckije

Beginner2022-01-01Added 32 answers

karton

Expert2022-01-04Added 613 answers

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