We can write it as

Now let x² = t

2xdx = dt

Xdx = dt/2

Now

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 cost as the second function.

Replacing t with x²

=