# Examples of Integration by Substitution

__Example__**:** Evaluate the integral

with respect to .

We have integral

Putting and differentiating

Now the above integral of the form

We observe that the derivation of given function is in the given problem, so using the general power formula of integration

Here implies that

Now using the original substitution again in the result of the integration, we have

__Example__**: **Integrate with respect to .

Consider the function to be integrate

Putting and differentiating implies

Now by using these values, equation (i) becomes

Using the formula of integration , we have