Preliminary steps The following integrals

Chapter 4, Problem 55E

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QUESTION:

Preliminary steps The following integrals require a preliminary step such as long division or a change of variables before using partial fractions. Evaluate these integrals.

\(\int \frac{\sec \theta}{1+\sin \theta} d \theta\)

Questions & Answers

QUESTION:

Preliminary steps The following integrals require a preliminary step such as long division or a change of variables before using partial fractions. Evaluate these integrals.

\(\int \frac{\sec \theta}{1+\sin \theta} d \theta\)

ANSWER:

Solution:-

Step1

Apply integral substitution

 ,    u=g(x)

=

Step2

Apply integral substitution

 ,    u=g(x)

                =

                =

Step3

Take the partial fraction of

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