What is the integral of (csc^2(x)-sin(x)) ?

The integral of (csc^2(x)-sin(x)) is -cot(x)+cos(x)+C

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integral of (csc^2(x)-sin(x))

\int (csc^{2} (x) - sin (x)) d x

- cot (x) + cos (x) + C

Solution steps

\int csc^{2} (x) - sin (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int csc^{2} (x) d x - \int sin (x) d x

\int csc^{2} (x) d x = - cot (x)

\int sin (x) d x = - cos (x)

= - cot (x) - (- cos (x))

Simplify

= - cot (x) + cos (x)

Add a constant to the solution

= - cot (x) + cos (x) + C

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What is the integral of (csc^2(x)-sin(x)) ?
The integral of (csc^2(x)-sin(x)) is -cot(x)+cos(x)+C