they are surely based on integration by parts, for q3, trig integration have formulas themself, use the "reduction formulas", this might help:

image

which is kinda what u did, except the (n-1)/n is missing

and to integrate (sin x)^2 use (sin x)^2=1/2(1-cos2x)



Q2, by "eye-ball differentiation" the answer, it seems to give out x^12e(x), so it is the integral of x^12e(x). But I am sure there is a more elegant answer than that:S