What is the integral of x/((x+1)^5) ?

The integral of x/((x+1)^5) is -x/(4(x+1)^4)-1/(12(x+1)^3)+C

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integral of x/((x+1)^5)

\int \frac{x}{( x + 1 ) ^{5}} d x

- \frac{x}{4 ( x + 1 ) ^{4}} - \frac{1}{12 ( x + 1 ) ^{3}} + C

Solution steps

\int \frac{x}{( x + 1 ) ^{5}} d x

Apply Integration By Parts

: - \frac{x}{4 ( x + 1 ) ^{4}} - \int - \frac{1}{4 ( x + 1 ) ^{4}} d x

= - \frac{x}{4 ( x + 1 ) ^{4}} - \int - \frac{1}{4 ( x + 1 ) ^{4}} d x

\int - \frac{1}{4 ( x + 1 ) ^{4}} d x = \frac{1}{12 ( x + 1 ) ^{3}}

= - \frac{x}{4 ( x + 1 ) ^{4}} - \frac{1}{12 ( x + 1 ) ^{3}}

Add a constant to the solution

= - \frac{x}{4 ( x + 1 ) ^{4}} - \frac{1}{12 ( x + 1 ) ^{3}} + C

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What is the integral of x/((x+1)^5) ?
The integral of x/((x+1)^5) is -x/(4(x+1)^4)-1/(12(x+1)^3)+C