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

The integral of csc(ay)cot(ay) is -1/a csc(ay)+C

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integral of csc(ay)cot(ay)

\int csc (a y) cot (a y) d y

- \frac{1}{a} csc (a y) + C

Solution steps

\int csc (a y) cot (a y) d y

Apply u-substitution

= \int \frac{csc ( u ) cot ( u )}{a} d u

Take the constant out:

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

= \frac{1}{a} \cdot \int csc (u) cot (u) d u

Apply u-substitution

= \frac{1}{a} \cdot \int - 1 d v

Integral of a constant:

\int a d x = a x

= \frac{1}{a} (- 1) v

Substitute back

= \frac{1}{a} (- 1) csc (a y)

Simplify

= - \frac{1}{a} csc (a y)

Add a constant to the solution

= - \frac{1}{a} csc (a y) + C

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