Question

Question #a1ef7

Answer 1

`1/14(ln(x+1)-ln(x+15))+c`

Explanation:

Start by ignoring the fact that we will be integrating, and let

`f(x)=1/(x^2+16x+15)`

Factorise the denominator:

`f(x)=1/((x+15)(x+1))`

Use partial fractions to put this in an easy form for integration.

`f(x)=1/(14(x+1))-1/(14(x+15))`

This is what we will integrate.

`int(1/(14(x+1))-1/(14(x+15)))dx`

We can take the constant `1/14` out to the front:

`1/14int(1/(x+1)-1/(x+15))dx`

and solve:

`1/14(ln(x+1)-ln(x+15))+c`