Evaluate the following integrals.

Solution:-

Step 1</p>

We have to integrate

To evaluate this integral we use the method of integration by parts.

I =

Multiplying and dividing the integrand by ,we get

I =

=

Now, taking I1 = and I2 =

I = 36I1 I2

Step 2</p>

To solve for I1 = ,we go ahead with the method of integration by substitution.

But first let’s arrange the integral,

Going ahead with the method of integration by substitution, put Differentiating , we get

Changing the variable in the integral, we get

I1 =

The integral we have now, we use the formula

Putting in the value for t , we obtain the integral

I1 =