What is the integral of (x^2)/((5x+7)^3) ?

The integral of (x^2)/((5x+7)^3) is -(x^2)/(10(5x+7)^2)+1/5 (-x/(5(5x+7))+1/25 ln|5x+7|)+C

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integral of (x^2)/((5x+7)^3)

\int \frac{x ^{2}}{( 5 x + 7 ) ^{3}} d x

- \frac{x ^{2}}{10 ( 5 x + 7 ) ^{2}} + \frac{1}{5} (- \frac{x}{5 ( 5 x + 7 )} + \frac{1}{25} ln ∣ 5 x + 7 ∣) + C

Solution steps

\int \frac{x ^{2}}{( 5 x + 7 ) ^{3}} d x

Apply Integration By Parts

: - \frac{x ^{2}}{10 ( 5 x + 7 ) ^{2}} - \int - \frac{x}{5 ( 5 x + 7 ) ^{2}} d x

= - \frac{x ^{2}}{10 ( 5 x + 7 ) ^{2}} - \int - \frac{x}{5 ( 5 x + 7 ) ^{2}} d x

\int - \frac{x}{5 ( 5 x + 7 ) ^{2}} d x = - \frac{1}{5} (- \frac{x}{5 ( 5 x + 7 )} + \frac{1}{25} ln ∣ 5 x + 7 ∣)

= - \frac{x ^{2}}{10 ( 5 x + 7 ) ^{2}} - (- \frac{1}{5} (- \frac{x}{5 ( 5 x + 7 )} + \frac{1}{25} ln ∣ 5 x + 7 ∣))

Simplify

= - \frac{x ^{2}}{10 ( 5 x + 7 ) ^{2}} + \frac{1}{5} (- \frac{x}{5 ( 5 x + 7 )} + \frac{1}{25} ln ∣ 5 x + 7 ∣)

Add a constant to the solution

= - \frac{x ^{2}}{10 ( 5 x + 7 ) ^{2}} + \frac{1}{5} (- \frac{x}{5 ( 5 x + 7 )} + \frac{1}{25} ln ∣ 5 x + 7 ∣) + C

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What is the integral of (x^2)/((5x+7)^3) ?
The integral of (x^2)/((5x+7)^3) is -(x^2)/(10(5x+7)^2)+1/5 (-x/(5(5x+7))+1/25 ln|5x+7|)+C