What is the integral of [(tan(x))^2+(cot(x))^2] ?

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

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integral of [(tan(x))^2+(cot(x))^2]

\int [(tan (x))^{2} + (cot (x))^{2}] d x

- 2 x + tan (x) - cot (x) + C

Solution steps

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

Simplify

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

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

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

= - x + tan (x) - x - cot (x)

Simplify

= - 2 x + tan (x) - cot (x)

Add a constant to the solution

= - 2 x + tan (x) - cot (x) + C

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