What is the integral of 1/((tan(x))^2) ?

The integral of 1/((tan(x))^2) is -x-cot(x)+C

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integral of 1/((tan(x))^2)

\int \frac{1}{( tan ( x ) ) ^{2}} d x

- x - cot (x) + C

Solution steps

\int \frac{1}{( tan ( x ) ) ^{2}} d x

Rewrite using trig identities

= \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)

Add a constant to the solution

= - x - cot (x) + C

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What is the integral of 1/((tan(x))^2) ?
The integral of 1/((tan(x))^2) is -x-cot(x)+C