How do you integrate int 3 xln x^2 dx 3xlnx2dx using integration by parts?

1 Answer
Feb 12, 2017

The answer is =3x^2ln(|x|)-3/2x^2+C

Explanation:

Integration by parts is

intu'vdx=uv-intuv'dx

Here, we have

int3xln(x^2)dx=6intxlnxdx

v=lnx, =>, v'=1/x

u'=x, =>, u=x^2/2

Therefore,

int3xln(x^2)dx=6(1/2x^2lnx-int1/2xdx)

=3x^2lnx-3*1/2*x^2

=3x^2ln(|x|)-3/2x^2+C