1. The problem statement, all variables and given/known data Hi could anyone please help me to solve the following integrals? x and z are the only variable in all of the following integrals. Others are just constants. (a) Integrate sin(2x) * [(sinx)^2] with limits [0,a] or with limits [-a, +a] (b) Integrate sin(3x) * [(sinx)^2] with limits [0,a] Does it require the same method for cos, for example cos(5x) * (cosx)^3 (c) Integrate the indefinite integral 1/((x^2)+4) I guess this one has something to do with arctan, but I don't know how to start with it. Could anyone please show me the steps? Okay, I promise this is the last question.... (d) Integrate the indefinite integral exp(-kz)/(z+iL) where k is a positive constant, such that z=iL is the singularity inside any simple closed contour C(R). I try to find the residue at z=-iL = (exp(-kz) / first derivative of x+iL and then evaluate everything at z=-iL which gives = exp(-ikL) Then the required integral is 2*pi*exp(ikL). But the question is, is that right or have I done anything fundamentally wrong? 2. Relevant equations 3. The attempt at a solution Thanks a lot, that's it from me!