What is the integral of x/((x+b)^3) ?

The integral of x/((x+b)^3) is -x/(2(x+b)^2)-1/(2(x+b))+C

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integral of x/((x+b)^3)

integral

\frac{x}{( x + b ) ^{3}}

- \frac{x}{2 ( x + b ) ^{2}} - \frac{1}{2 ( x + b )} + C

Solution steps

\int \frac{x}{( x + b ) ^{3}} d x

Apply Integration By Parts

= - \frac{x}{2 ( x + b ) ^{2}} - \int - \frac{1}{2 ( x + b ) ^{2}} d x

\int - \frac{1}{2 ( x + b ) ^{2}} d x = \frac{1}{2 ( x + b )}

= - \frac{x}{2 ( x + b ) ^{2}} - \frac{1}{2 ( x + b )}

Add a constant to the solution

= - \frac{x}{2 ( x + b ) ^{2}} - \frac{1}{2 ( x + b )} + C

What is the integral of x/((x+b)^3) ?
The integral of x/((x+b)^3) is -x/(2(x+b)^2)-1/(2(x+b))+C