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

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

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Find the Antiderivative csc(x)cot(x)

integral

csc (x) cot (x)

- csc (x) + C

Solution steps

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

Apply u-substitution

: \int - 1 d u

= \int - 1 d u

Integral of a constant:

\int a d x = a x

= (- 1) u

Substitute back

u = csc (x)

= (- 1) csc (x)

Simplify

= - csc (x)

Add a constant to the solution

= - csc (x) + C

- \frac{d}{d x} (\frac{x}{( x + 1 )})

\frac{- 1}{u}

\frac{d y}{d x} y = 2 x

- \frac{d}{d x} (x^{\frac{1}{2}})

- \frac{d}{d x} y = sin (x)

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