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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#