Question

if you go with the right substitution

∫[{(1-sin(x))/(1+sin(x))}{(2-sin(x))/(2+sin(x))}] dx
plz show me solution

Answer 1

wow Just looking at the answer at

http://www.wolframalpha.com/input/?i=%E2%88%AB%5B%7B(1-sin(x))%2F(1%2Bsin(x))%7D%7B(2-sin(x))%2F(2%2Bsin(x))%7D%5D+dx

I'd start with u = sinx
dx = 1/√(1-u^2) du

Then you are dealing with

(1-u)(2-u)
-------------- * 1/√(1-u^2) du
(1+u)(2+u)

= (1 + 6/(1-u) - 12/(2+u)) * 1/√(1-u^2) du

Those are marginally easier to deal with term by term, but it still gets nasty. The third term is the toughest, as in

http://www.wolframalpha.com/input/?i=%E2%88%AB(+12%2F(u%2B2))%2Fsqrt(1-u%5E2)+du