How do I find the integral x5ln(x)dx ?

1 Answer
Sep 24, 2014

By Integration by Parts,

x5lnxdx=x636(6lnx1)+C

Let us look at some details.

Let u=lnx and dv=x5dx.
du=dxx and v=x66

By Integration by Parts

udv=uvvdu,

we have

(lnx)x5dx=(lnx)x66x66dxx

by simplifying a bit,

=x66lnxx56dx

by Power Rule,

=x66lnxx636+C

by factoring out x636,

=x636(6lnx1)+C