   Chapter 8.3, Problem 54E

Chapter
Section
Textbook Problem

Finding an Indefinite Integral In Exercises 49–58, find the indefinite integral. Use a computer algebra system to confirm your result. ∫ cot 3 t csc t   d t

To determine

To calculate: The indefinite integral cot3tcosectdt and verify the result using computer algebra system.

Explanation

Given: cot3tcosectdt

Formula used:

xndx=xn+1n+1+C

Calculation:

Consider the integral,

cot3tcosectdt

Rewrite as an integral,

cot3tcosectdt=cos3tsin3tcosectdt=cos2tcostsin2tdt=(1sin2t)costsin2tdt

Substitute,

u=sintdu=costdt

Therefore,

cot3tcosectdt=(1u2)u2du

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