What is the integral of-(csc(x)cot(x))/5 ?

The integral of-(csc(x)cot(x))/5 is 1/5 csc(x)+C

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integral of-(csc(x)cot(x))/5

\int - \frac{csc ( x ) cot ( x )}{5} d x

\frac{1}{5} csc (x) + C

Solution steps

\int - \frac{csc ( x ) cot ( x )}{5} d x

Take the constant out:

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

= - \frac{1}{5} \cdot \int csc (x) cot (x) d x

Apply u-substitution

: \int - 1 d u

= - \frac{1}{5} \cdot \int - 1 d u

Integral of a constant:

\int a d x = a x

= - \frac{1}{5} (- 1) u

Substitute back

u = csc (x)

= - \frac{1}{5} (- 1) csc (x)

Simplify

= \frac{1}{5} csc (x)

Add a constant to the solution

= \frac{1}{5} csc (x) + C

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What is the integral of-(csc(x)cot(x))/5 ?
The integral of-(csc(x)cot(x))/5 is 1/5 csc(x)+C