integral of (1/((x+1)^2)) — step-by-step solution

Let's integrate:

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

Let

u = x + 1

. Then

du = 1 \cdot dx

, so

dx = \frac{du}{1}

\int(\frac{1}{{(x + 1)}^{2}})dx = \int(u^{-2})du

Apply the power rule:

\int(u^{-2})du = - u^{-1}

Substitute

u

x + 1

back into the antiderivative

The antiderivative is valid on each interval where

x + 1!= 0

- \frac{1}{x + 1}

▶Indefinite integrals are defined up to an additive constant C, so this yields:

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