What is the integral of (csc(x)cot(x))/4 ?

The integral of (csc(x)cot(x))/4 is -1/4 csc(x)+C

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integral of (csc(x)cot(x))/4

\int \frac{csc ( x ) cot ( x )}{4} d x

- \frac{1}{4} csc (x) + C

Solution steps

\int \frac{csc ( x ) cot ( x )}{4} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{4} \cdot \int csc (x) cot (x) d x

Apply u-substitution

: \int - 1 d u

= \frac{1}{4} \cdot \int - 1 d u

Integral of a constant:

\int a d x = a x

= \frac{1}{4} (- 1) u

Substitute back

u = csc (x)

= \frac{1}{4} (- 1) csc (x)

Simplify

= - \frac{1}{4} csc (x)

Add a constant to the solution

= - \frac{1}{4} csc (x) + C

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What is the integral of (csc(x)cot(x))/4 ?
The integral of (csc(x)cot(x))/4 is -1/4 csc(x)+C