   Chapter 4.5, Problem 7E

Chapter
Section
Textbook Problem

Recognizing Patterns In Exercises 5-8, complete the table by identifying u and du for the integral. ∫ f ( g ( x ) ) g ' ( x ) d x                   u = g ( x )                       d u = g ' ( x ) d x ∫ tan 2 x sec 2 x   d x

To determine

To calculate: The value of u and du of the integral tan2xsec2xdx.

Explanation

Given:

The provided integral is:

tan2xsec2xdx

Formula used:

Differentiation of tanx is given by:

ddx(tanx)=sec2x

Calculation:

According to theorem for change of variable for indefinite integrals,

If u=g(x) then du=g'(x)dx

Then integral will take the following form

f(g(x))g'(x)dx=f(u)du

Since, sec2x is derivative of tanx

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