What is the integral of 1/((x+8)^6) ?

The integral of 1/((x+8)^6) is x/((x+8)^6)+6(-1/(5(x+8)^5)+4/(3(x+8)^6))+C

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integral of 1/((x+8)^6)

\int \frac{1}{( x + 8 ) ^{6}} d x

\frac{x}{( x + 8 ) ^{6}} + 6 (- \frac{1}{5 ( x + 8 ) ^{5}} + \frac{4}{3 ( x + 8 ) ^{6}}) + C

Solution steps

\int \frac{1}{( x + 8 ) ^{6}} d x

Apply Integration By Parts

: \frac{x}{( x + 8 ) ^{6}} - \int - \frac{6 x}{( x + 8 ) ^{7}} d x

= \frac{x}{( x + 8 ) ^{6}} - \int - \frac{6 x}{( x + 8 ) ^{7}} d x

\int - \frac{6 x}{( x + 8 ) ^{7}} d x = - 6 (- \frac{1}{5 ( x + 8 ) ^{5}} + \frac{4}{3 ( x + 8 ) ^{6}})

= \frac{x}{( x + 8 ) ^{6}} - (- 6 (- \frac{1}{5 ( x + 8 ) ^{5}} + \frac{4}{3 ( x + 8 ) ^{6}}))

Simplify

= \frac{x}{( x + 8 ) ^{6}} + 6 (- \frac{1}{5 ( x + 8 ) ^{5}} + \frac{4}{3 ( x + 8 ) ^{6}})

Add a constant to the solution

= \frac{x}{( x + 8 ) ^{6}} + 6 (- \frac{1}{5 ( x + 8 ) ^{5}} + \frac{4}{3 ( x + 8 ) ^{6}}) + C

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What is the integral of 1/((x+8)^6) ?
The integral of 1/((x+8)^6) is x/((x+8)^6)+6(-1/(5(x+8)^5)+4/(3(x+8)^6))+C