How do you find the integral of f(x)=x^5lnx using integration by parts?

1 Answer
Oct 31, 2015

I = x^6/6(lnx - 1/6) +C

Explanation:

lnx=u => dx/x=du

x^5dx=dv => v=x^6/6

int udv = uv - int vdu

I = int x^5lnxdx = x^6/6lnx - int x^6/6dx/x = x^6/6lnx - 1/6int x^5dx

I = x^6/6lnx - 1/6x^6/6 +C

I = x^6/6(lnx - 1/6) +C