1. The problem statement, all variables and given/known data Hi, I'm trying to evaluate the integration of (e^x)cos3x dx, by using integration by parts. I've already done a couple of similar questions on integration by parts but this one seems to puzzle me. 2. Relevant equations The answer is supposed to be (e^x/10)*(cos3x + 3sin3x), I can't seem to get to it. 3. The attempt at a solution I've basically taken the same approach to this question as the other couple of integration by parts questions I've done but the answer is never right. I let u=cos3x and dv/dx=e^x. And basically just subbed back into the formula uv - integ.v*(du/dx). I suspect I may be anti-differentiating the second part wrong, which I think is (e^x)*3sin3x. I get 3e^x(3cos3x+sin3x). Any idea where I went wrong? I'm also having trouble finding the integral of (x^2)/[2(1+x^2)]. Any advice or help would be appreciated. Thanks in advance.