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

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

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integral of-cot^2(x)

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

x + cot (x) + C

Solution steps

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

Take the constant out:

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

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

Rewrite using trig identities

= - \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

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

\int 1 d x = x

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

= - (- x - cot (x))

Simplify

= x + cot (x)

Add a constant to the solution

= x + cot (x) + C

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