I have been asked to find the definite integral, as described above, of a product of e, with a variable exponent, and a trigonometric function; an example would be the integral of e^x.cos(x). I have tried to use the integration by parts, or integration by reverse product rule differentiation (integral of udv/dx = uv - integral of vdu/dx), but have almost immediately realised that because both the differentiation and integration either of e with a variable exponent, or a trigonomnetric function, does not gradually cancel out the variables but increases the complexity of the function, the integral will simply increase to an infinite length. I therefore assumed this technique to be incorrect, and I want to ask if anyone can help me with the proper technique? Any help would be much appreciated!