How do you integrate x3x2+8x+16 using partial fractions?

1 Answer
Feb 1, 2017

12x28x+48ln|x+4|+64x+4+c

Explanation:

The denominator is a perfect square, so you don't use partial fractions. Instead, you substitute u=x+4. The integral becomes:
(u4)3u2du

=u312u2+48u64u2du

=u12+48u64u2du

=12u212u+48ln|u|+64u+k

=12(x+4)212(x+4)+48ln|x+4|+64x+4+k

=12x28x+48ln|x+4|+64x+4+c

(where c=848+k)