What is the integral of (2x+1)/((x^2+x)^3) ?

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

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integral of (2x+1)/((x^2+x)^3)

\int \frac{2 x + 1}{( x ^{2} + x ) ^{3}} d x

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

Solution steps

\int \frac{2 x + 1}{( x ^{2} + x ) ^{3}} d x

Apply u-substitution

: \int \frac{1}{u ^{3}} d u

= \int \frac{1}{u ^{3}} d u

Apply the Power Rule

: - \frac{1}{2 u ^{2}}

= - \frac{1}{2 u ^{2}}

Substitute back

u = x^{2} + x

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

Add a constant to the solution

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

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