   Chapter 4.5, Problem 17E

Chapter
Section
Textbook Problem

# Evaluate the indefinite integral. ∫ sec 2 θ tan 3 θ   d θ

To determine

To evaluate:

The indefinite integral sec2θtan3θdθ

Explanation

1) Concept:

i) The substitution rule

If u=g(x) is a differentiable function whose range is an interval I and f is continuous on I, then f(gx)g'xdx=f(u)du.

ii) Indefinite integral

xn=xn+1n+1+C ( n  -1)

2) Given:

sec2θtan3θdθ

3) Calculation:

Here, use the substitution method because the differential of the function tanθ which is sec2θdθ is present in the integral.

Substitute u=tanθ

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