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

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

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integral of cot^2(2x)

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

- x - \frac{1}{2} cot (2 x) + C

Solution steps

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

Rewrite using trig identities

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

\int 1 d x = x

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

= - x - \frac{1}{2} cot (2 x)

Add a constant to the solution

= - x - \frac{1}{2} cot (2 x) + C

in v erse l a pl a ce \frac{1}{s ^{2} + 1}

\frac{d}{d t} (2 cos (t))

\frac{\partial}{\partial z} (ln (z))

d er i v a t i v e f (x) = cos (x) + sin (x)

\frac{d x}{d y} = 4 (x^{2} + 1), x (\frac{π}{4}) = 1

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