# Examples of Integration by Substitution

__Example__**:** Evaluate the integral

with respect to

We have integral

Putting and differentiate

Now the above integral of the form, we have

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

Here implies that

Using the formula

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

__Example__**: **Integrate with respect to .

Consider the function to be integrate

Putting and differentiate implies

Now equation (i) becomes, by putting the values

Using the formula of integration , we have