What is $\int \frac{x}{{(x + 1)}^{3}} d x$ $int (x)/(x+1)^3 dx$ ?

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What is $\int \frac{x}{{(x + 1)}^{3}} d x$ $int (x)/(x+1)^3 dx$ ?

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Answer 1 · 2018-03-03T11:09:12

$\int \frac{x}{{(x + 1)}^{3}} d x = - \frac{1}{x + 1} + \frac{1}{2 {(x + 1)}^{2}} + C$ $int x/(x+1)^3 dx = -1/(x+1)+1/(2(x+1)^2)+C$

Explanation:

$\int \frac{x}{{(x + 1)}^{3}} d x = \int \frac{1}{{(x + 1)}^{2}} - \frac{1}{{(x + 1)}^{3}} d x$ $int x/(x+1)^3 dx = int 1/(x+1)^2-1/(x+1)^3 dx$

$\int \frac{x}{{(x + 1)}^{3}} d x = - \frac{1}{x + 1} + \frac{1}{2 {(x + 1)}^{2}} + C$ $color(white)(int x/(x+1)^3 dx) = -1/(x+1)+1/(2(x+1)^2)+C$

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