Question

Solve integral

Answer 1

\[\int\limits (x+1) / (x^2+4x+5)^2 dx\]

Answer 2

Notice that
\[
\frac{x+1}{\left(x^2+4
x+5\right)^2}=\frac{x+2}{\left(x^2+4
x+5\right)^2}-\frac{1}{\left(
x^2+4 x+5\right)^2}
\]
The first integral is easy with u= x^2 + 4x + 5

Answer 3

For the second one
click on
http://www.wolframalpha.com/input/?i=integrate1%2F%28x^2+%2B+4+x+%2B+5%29^2
or copy and paste in your browser, then click show steps.

Answer 4

If you combine both, your final answer should look lke
\[
\int \frac{x+1}{\left(x^2+4
x+5\right)^2} \,
dx=\frac{-x-3}{2 \left(x^2+4
x+5\right)}-\frac{1}{2} \tan
^{-1}(x+2) + C
\]