Evaluate the following integrals:

We can write it as

Let x² = t

2xdx = dt

Using the relation in the above condition, we get

Integrating with respect to t

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 is the second function.

Replacing t with x²,we get