What is the integral of 5+cot^2(x) ?

The integral of 5+cot^2(x) is 4x-cot(x)+C

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integral of 5+cot^2(x)

\int 5 + cot^{2} (x) d x

4 x - cot (x) + C

Solution steps

\int 5 + cot^{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 5 d x + \int cot^{2} (x) d x

\int 5 d x = 5 x

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

= 5 x - x - cot (x)

Simplify

= 4 x - cot (x)

Add a constant to the solution

= 4 x - cot (x) + C

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