`int sin(2x)/sin(x) dx` Find the general indefinite integral.

Textbook Question

Chapter 5, 5.4 - Problem 18 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to find the indefinite integral, hence, you need to remember that sin `2x = 2sin x*cos x` , such that:

`int (sin 2x)(sin x) dx = int (2sin x*cos x)/(sin x) dx `

`int (sin 2x)(sin x) dx = int 2cos x dx = 2int cos x dx = 2sin x + c`

Hence, evaluating the indefinite integral, yields `int (sin 2x)(sin x) dx = 2sin x + c.`

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