Integrate.

Answer

Take

*u* = *x*^{2}

*v'* = *e*^{2x}

so that *u'* will be simpler than *u*. Then

We apply the formula and get

Looks like we need to use integration by parts again to find

This is very much like our first example of integration by parts. Again, so that u' will be simpler than *u*, take

*u* = *x*

*v'* = *e*^{2x}

Then

We put everything in the formula and see what we get:

Wrap this up in parentheses (except for the + *C*), and put it back where we left off: