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Answer 1 · 2016-01-03T12:35:27

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

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:

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