Problem 76E

Rational functions of trigonometric functions

An integrand with trigonometric functions in the numerator and denominator can often be converted to a rational integrand using the substitution u =tan (x/2) or x = 2 tan−1 u. The following relations are used in making this change of variables.

A:

B:

C:

Evaluate .

Problem 76E

Rational functions of trigonometric functions

An integrand with trigonometric functions in the numerator and denominator can often be converted to a rational integrand using the substitution or

The following relations are used in making this change of variables:

A:

B:

C:

Evaluate

Solution:-

Step 1

(Making the indicated substitutions in the integral)

=

=

=

=

=

Since , the integral now becomes,

Thus, the value of the integral is