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

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

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

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

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

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

: - \frac{1}{u}

= - \frac{1}{u}

Substitute back

u = x + 1

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

Add a constant to the solution

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

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