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

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

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integral of 1/((u+1)^2)

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

- \frac{1}{u + 1} + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{v ^{2}} d v

= \int \frac{1}{v ^{2}} d v

Apply the Power Rule

: - \frac{1}{v}

= - \frac{1}{v}

Substitute back

v = u + 1

= - \frac{1}{u + 1}

Add a constant to the solution

= - \frac{1}{u + 1} + C

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\int_{- 1}^{1} x + 2 d x