Question

int cos^3(x)sin^4(x), dx

Answer 1

do this by substitution method so first what you do you let u=sinx then you break cos^3(x) into cosx(cos^2(x)). Then after you know cos^2(x) = 1 - sin^2(x). Therefore you got u = sinx, du=cosx and if u = sinx then sin^2(x) = u^2.

So now our equation becomes integrate u^4(1 - u^2) du

and now that is simple integration so no you got integrate u^4 - u^6 which is u^5/5 - u^7/7 + c and now substituting u back final answer is (sinx)5/5 + (sinx)^7/7 + C

Answer 2

thx