   Chapter 7.2, Problem 47E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ 1 − tan 2 x sec 2 x   d x

To determine

To evaluate: The trigonometric integral 1tan2xsec2xdx

Explanation

Trigonometric integral can be solved using the various trigonometric identities which simplifies the integrand.

Formula used:

The identity cos2x=2cos2x1

and the identity sec2xtan2x=1

Given:

The integral, 1tan2xsec2xdx.

Calculation:

Rewrite the given integral by using the identity sec2xtan2x=1:

1tan2xsec2xdx=1(sec2x1)sec2xdx=2sec2xsec2

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