Question

How do you integrate `xlnx`?

Answer 1

It is

#int xlnxdx=int (x^2/2)'lnxdx=x^2/2*lnx-intx^2/2*lnx'dx= x^2/2*lnx-intx^2/2*1/xdx=x^2/2*lnx-intx/2dx=x^2/2*lnx-x^2/4+c#

Finally `int xlnxdx=x^2/2*lnx-x^2/4+c`

We used integration by parts

`intf'(x)*g(x)dx=f(x)g(x)-intf(x)*g'(x)dx`