Problem 60E

Fractional powers

Use the indicated substitution to convert the given integral to an integral of a rational function. Evaluate the resulting integral.

Problem 60E

Fractional powers Use the indicated substitution to convert the given integral to an integral of a rational function. Evaluate the resulting integral.

Solution:-

Step 1

Using the indicated substitution , and differentiating this we get

Substituting and , the integral becomes

=

=

=

= (Multiplying and dividing by 2)

=

=

=

Since

Putting in the final integral, we get

Thus, the value of the integral is