1+sinxsinx(1+cosx)dx ?

1 Answer
Apr 3, 2018

14(tan(x2))2+tan(x2)+12ln(tan(x2))+C

Explanation:

1+sinxsinx(1+cosx)dx

After using y=tan(x2), dx=2dyy2+1, sinx=2yy2+1 and cosx=1y2y2+1 transforms, this integral became

1+2yy2+12yy2+1(1+1y2y2+1)2dyy2+1

=y2+2y+1y2+12yy2+12y2+12dyy2+1

=(y2+2y+1)dy2y

=12ydy+dy+12dyy

=y24+y+12lny+C

=14(tan(x2))2+tan(x2)+12ln(tan(x2))+C