I =

(x
2.cosx)/(1+sinx)
2 .dx
Integration by parts gives
I =
x2
cosx/(1+sinx)2 .dx -
(2x.integral(cosx/(1+sinx)2 ) .dx)
put (1+sinx) = t, then cosx dx = dt
I=(x^2)((-1)/(1+sinx)) + integral((2x/(1+sinx))dx
Now you can proceed by applyuing by pRTS ON SECOND PART AGAIN