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

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

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integral of 5csc(x)cot(x)

\int 5 csc (x) cot (x) d x

- 5 csc (x) + C

Solution steps

\int 5 csc (x) cot (x) d x

Take the constant out:

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

= 5 \cdot \int csc (x) cot (x) d x

Apply u-substitution

: \int - 1 d u

= 5 \cdot \int - 1 d u

Integral of a constant:

\int a d x = a x

= 5 (- 1) u

Substitute back

u = csc (x)

= 5 (- 1) csc (x)

Simplify

= - 5 csc (x)

Add a constant to the solution

= - 5 csc (x) + C

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