1. Evaluate integral(e^(7x)cos(2x)dx)

I let u =e^(7x) and so du = 7e^(7x)dx. dv is cos(2x) so V= 1/2sin(2x). I did the procedure, but i cant get the answer. Please show me some intermediate steps please!

2. Evaluate I = integral(486cot(6x)/sin^2(6x)+18sin(6x)+81) dx

No exactly sure how to go about this problem. I can factor the bottom into (sin(6x)+9)^2. I am using partial fraction decomposition, but the numerator seems to confuse me.

Help is much appreciated!

Thanks to all who contribute.