Question

integrals e^(2x) cos(3x) dx

Answer 1

\[\int\limits e^{2x} \cos(3x) dx\]

do by parts, u = cos 3x, u' = - 3 sin 3x

this will lead to an integral in sin 3x and just do the same. insert correct coeffcients but basically u = sin 3x u' = cos 3x, so you back to the integral you started with.

do the book keeping and you are done.

basically you toggle between cos and sin and cos until you are back where you started, thematic .