What is the integral of csc(a)ycot(a)y ?

The integral of csc(a)ycot(a)y is 1/3 y^3csc(a)cot(a)+C

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integral of csc(a)ycot(a)y

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

\frac{1}{3} y^{3} csc (a) cot (a) + C

Solution steps

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

Take the constant out:

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

= csc (a) cot (a) \cdot \int yy d y

Simplify

yy : y^{2}

= csc (a) cot (a) \cdot \int y^{2} d y

Apply the Power Rule

: \frac{y ^{3}}{3}

= csc (a) cot (a) \frac{y ^{3}}{3}

Simplify

csc (a) cot (a) \frac{y ^{3}}{3} : \frac{1}{3} y^{3} csc (a) cot (a)

= \frac{1}{3} y^{3} csc (a) cot (a)

Add a constant to the solution

= \frac{1}{3} y^{3} csc (a) cot (a) + C

\int \frac{4}{x ( x + 2 )} d x

\int_{0}^{4} \frac{1}{16 + x ^{2}} d x

\frac{1}{2 s ^{2} + 2}

\int \frac{x + 1}{x + 3} d x

\frac{\partial}{\partial y} (e^{x} \cdot sin (y))

What is the integral of csc(a)ycot(a)y ?
The integral of csc(a)ycot(a)y is 1/3 y^3csc(a)cot(a)+C