How do you integrate int 4 x^2 ln x^2 dx using integration by parts?
1 Answer
Apr 19, 2016
Explanation:
First, rewrite
This gives us the integral
For this, recalling that integration by parts takes the form
u=lnx" "=>" "(du)/dx=1/xdx" "=>" "du=1/xdx
dv=x^2dx" "=>" "intdv=intx^2dx" "=>" "v=x^3/3
This gives us:
8intx^2lnx=8[(x^3/3)lnx-intx^3/3(1/x)dx]
=(8x^3lnx)/3-8intx^2/3dx
=(8x^3lnx)/3-(8x^3)/9+C
Which can also be written as
int4x^2ln(x^2)dx=(8x^3(3lnx-1))/9+C