Question

Solve $\int \frac{-3}{{(x+2)}^2}dx$

Answer 1

Consider the given integral.

$I=\int \frac{-3}{{(x+2)}^2}dx$

Let $t=x+2$

$dt=dx$

Therefore,

$I=\int \frac{-3}{{\left(t\right)}^2}dt$

$I=\frac{-3}{-t}+C$

$I=\frac{3}{t}+C$

On putting the value of $t$, we get

$I=\frac{3}{(x+2)}+C$

Hence, this is the answer.