Evaluate the integral.e3x dxSolutionAccording to the following statement, we substituteu =3x.Ifnax + boccurs, we use the rationalizing substitutionu =nax + b.More generally, this sometimes works forng(x).Then3x =,sodx =duande3x dx =23ueu du.The integrand is now a product of u and the transcendental function eu so it can be integrated by parts. Choosingu=u dv=eu dudu=du v=,we have the following.e3x dx=23eu du=23eu + C=23e3x + C.