What is the integral of (x^2+16x)/((x+8)^2) ?

The integral of (x^2+16x)/((x+8)^2) is -(x^2+16x)/(x+8)+2x+C

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integral of (x^2+16x)/((x+8)^2)

\int \frac{x ^{2} + 16 x}{( x + 8 ) ^{2}} d x

- \frac{x ^{2} + 16 x}{x + 8} + 2 x + C

Solution steps

\int \frac{x ^{2} + 16 x}{( x + 8 ) ^{2}} d x

Apply Integration By Parts

= - \frac{x ^{2} + 16 x}{x + 8} - \int - 2 d x

\int - 2 d x = - 2 x

= - \frac{x ^{2} + 16 x}{x + 8} - (- 2 x)

Simplify

= - \frac{x ^{2} + 16 x}{x + 8} + 2 x

Add a constant to the solution

= - \frac{x ^{2} + 16 x}{x + 8} + 2 x + C

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What is the integral of (x^2+16x)/((x+8)^2) ?
The integral of (x^2+16x)/((x+8)^2) is -(x^2+16x)/(x+8)+2x+C