We can write Sin2x = 2sinx.cosx

Let Sinx = t

Cosxdx = dt

Using BY PART METHOD. Using the superiority list as ILATE (Inverse Logarithm Algebra Trigonometric Exponential). Taking the first function to the one which comes first in the list.

Here t is the first function and e^t as the second function.

Replacing t with sin x

= 2e^sinx(sinx - 1) + c