Question

How do you find the indefinite integral of `int [(x + 2)/(x^2 + 4 x +5)] dx`?

Answer 1

`(1/2)*ln(x^2+4*x+5)+c`

Explanation:

take `x^2+4*x+5` as `t`
`(2*x+4)dx=dt`
the equation becomes
`int((1/2)*(1/t)dt)`
=`(1/2)*ln(t)+c`
replacing t back
`(1/2)*ln(x^2+4*x+5)+c`