Homework Soursewhat is the indefinite integral of x2xsinxcosx2 I was able t
what is the indefinite integral of (x^2)/(xsin(x)+cos(x))^2. I was able to find the answer using wolfram alpha, but it was unable to provide me with steps on how it reached that answer. any help is greatly appreciated.
Solution
As sec(x)*cos(x) equals 1, the integrand can also be written as
( x sec(x) x cos(x)/(xsinx +cos(x))2 dx
integrating by parts
x sec(x) int ( xcos(x) /(xsin(x) +cos(x))2 dx) - int [(xsec(x)tan(x) + sec(x)) int(xsin(x) + cos(x))2 ]dx
= -xsec(x) / ( xsin(x) + cos(x)) + int (sec^(2x))dx
= -xsec(x) / ( xsin(x) + cos(x)) +tan(x) +c (Ans)
