Problem 82AE

Challenge Show that with the change of variables , the integral can be converted to an integral amenable to partial fractions. Evaluate .

Problem 82AE

Challenge Show that with the change of variables , the integral can be converted to an integral amenable to partial fractions. Evaluate .

Solution

Step 1

In this problem we have to check whether with the change of variables , the integral can be converted to an integral amenable to partial fractions or not. And then we have to evaluate

Consider

Take

Differentiating we get

Thus which is an integral amenable to partial fractions.

Hence we have showed that with the change of variables , the integral can be converted to an integral amenable to partial fractions.