Evaluate the following integrals:

∫ e^2x sin (3x + 1) dx

Let I = ∫ e^2x sin (3x + 1) dx

Now Integrating by parts choosing sin (3x + 1) as first function and e^2x as second function we get,

Now again integrating by parts by taking cos(3x + 1) as first function and e^2x as second function we get,

Therefore,