What is the integral of 3cot^2(x) ?

The integral of 3cot^2(x) is 3(-x-cot(x))+C

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integral of 3cot^2(x)

\int 3 cot^{2} (x) d x

3 (- x - cot (x)) + C

Solution steps

\int 3 cot^{2} (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int cot^{2} (x) d x

Rewrite using trig identities

= 3 \cdot \int - 1 + 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

= 3 (- \int 1 d x + \int csc^{2} (x) d x)

\int 1 d x = x

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

= 3 (- x - cot (x))

Add a constant to the solution

= 3 (- x - cot (x)) + C

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