1. The problem statement, all variables and given/known data Integral ( cos(x)/(1+cos(x))^.5 dx) 2. Relevant equations 3. The attempt at a solution Integral ( cos(x)/(1+cos(x))^.5 dx) Square it Integral ( cos(x)^2/(1+cos(x) dx) Multiply by the Conjugate Integral ( cos(x)^2/(1+cos(x) * (1 - cos(x))/(1 - cos(x)) dx) Take the square root and then multiply by sin(x)/sin(x) Integral ( cos(x)(1-cos(x))^.5/(sin(x) * sin(x)/sin(x) dx ) Convert sin(x)^2 in denom to 1-cos(x)^2 then use u-sub, u= cos(x) du=-sin(x) Integral -( u(1-u)^.5/(1-u^2) du ) w substitution w= (1-u)^.5 u = 1-w^2 du = -2w Integral (1-w^2)w^2/(1-(1-2w^2+w^4) dw) Reduce down to Integral 2((1-w^2)/(2-w^2) dw ) I have more done but am leaving to go out to dinner now. Will post more of my work later if needed. Thanks in advance.