What is the integral of x/((5x+2)^3) ?

The integral of x/((5x+2)^3) is -x/(10(5x+2)^2)-1/(50(5x+2))+C

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integral of x/((5x+2)^3)

\int \frac{x}{( 5 x + 2 ) ^{3}} d x

- \frac{x}{10 ( 5 x + 2 ) ^{2}} - \frac{1}{50 ( 5 x + 2 )} + C

Solution steps

\int \frac{x}{( 5 x + 2 ) ^{3}} d x

Apply Integration By Parts

= - \frac{x}{10 ( 5 x + 2 ) ^{2}} - \int - \frac{1}{10 ( 5 x + 2 ) ^{2}} d x

\int - \frac{1}{10 ( 5 x + 2 ) ^{2}} d x = \frac{1}{50 ( 5 x + 2 )}

= - \frac{x}{10 ( 5 x + 2 ) ^{2}} - \frac{1}{50 ( 5 x + 2 )}

Add a constant to the solution

= - \frac{x}{10 ( 5 x + 2 ) ^{2}} - \frac{1}{50 ( 5 x + 2 )} + C

What is the integral of x/((5x+2)^3) ?
The integral of x/((5x+2)^3) is -x/(10(5x+2)^2)-1/(50(5x+2))+C