What is the integral of ycsc^2(y)cot(y) ?

The integral of ycsc^2(y)cot(y) is -1/2 ycsc^2(y)-1/2 cot(y)+C

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integral of ycsc^2(y)cot(y)

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

- \frac{1}{2} y csc^{2} (y) - \frac{1}{2} cot (y) + C

Solution steps

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

Apply Integration By Parts

: - \frac{1}{2} y csc^{2} (y) - \int - \frac{1}{2} csc^{2} (y) d y

= - \frac{1}{2} y csc^{2} (y) - \int - \frac{1}{2} csc^{2} (y) d y

\int - \frac{1}{2} csc^{2} (y) d y = \frac{1}{2} cot (y)

= - \frac{1}{2} y csc^{2} (y) - \frac{1}{2} cot (y)

Add a constant to the solution

= - \frac{1}{2} y csc^{2} (y) - \frac{1}{2} cot (y) + C

2 e^{3 t} - e^{2 t}

\int_{e^{x}}^{0} sin^{3} (t) d t

\int \frac{32}{x ( x ^{2} + 4 ) ^{2}} d x

y = x^{2}, y = x, 0.25, 1

\frac{x ^{2} - 3 x + 8}{x ^{2} + 9}

What is the integral of ycsc^2(y)cot(y) ?
The integral of ycsc^2(y)cot(y) is -1/2 ycsc^2(y)-1/2 cot(y)+C