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

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

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integral of 2-csc^2(x)

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

2 x + cot (x) + C

Solution steps

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

\int 2 d x = 2 x

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

= 2 x - (- cot (x))

Simplify

= 2 x + cot (x)

Add a constant to the solution

= 2 x + cot (x) + C

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