Let x = sin t ; t = sin- 1x
dx = cos t 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 sin 2t as the second function.
We know that cos 2t = 1 - 2 sin2t , sin2t = 2 sin t × cos t and cos t = √1 - sin2t
Replacing in above equation