`int (4x - csc^2(x)) dx` Find the indefinite integral.

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Chapter 4, 4.1 - Problem 32 - Calculus of a Single Variable (10th Edition, Ron Larson).
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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to evaluate the indefinite integral, such that:

`int(4x - csc^2 x) dx= int 4x dx- int csc^2 x dx`

`int(4x - csc^2 x) dx= int 4x dx- int 1/(sin^2 x) dx`

You need to remember that `1/(sin^2 x) = -(cot x)'`

`int(4x - csc^2 x) dx= 4x^2/2 + cot x + c`

Hence, evaluating the indefinite integral yields `int(4x - csc^2 x) dx= 2x^2 + cot x + c.`

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