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

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

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integral of csc(2x)cot(2x)

\int csc (2 x) cot (2 x) d x

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

Solution steps

\int csc (2 x) cot (2 x) d x

Apply u-substitution

: \int - \frac{1}{2} d u

= \int - \frac{1}{2} d u

Integral of a constant:

\int a d x = a x

= (- \frac{1}{2}) u

Substitute back

u = csc (2 x)

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

Simplify

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

Add a constant to the solution

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

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t \frac{d y}{d t} + 3 y = 3 t

\frac{\partial}{\partial x} (4 x y + yz + 5 x z - 40)

\int - 5 e^{2 x} d x

\int (e^{2 x} - 3)^{2} d x

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