Question

Question #07600

Answer 1

`int3/(x^2+4x+5)dx=3arctan(x+2)+C`

Explanation:

Using that `int1/(1+x^2)dx = arctan(x)`, we have

`int3/(x^2+4x+5)dx = 3int1/((x^2+4x+4)+1)dx`

`=3int1/((x+2)^2+1)dx`

Let `u = x+2 => du = dx`. Substituting, we have

`3int1/((x+2)^2+1)dx = 3int1/(u^2+1)du`

`=3(arctan(u)+C)`

`=3arctan(x+2)+C`