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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int - \frac{1}{2} d u

= \int - \frac{1}{2} d u

Integral of a constant:

\int a d x = a x

= (- \frac{1}{2}) u

Substitute back

u = csc^{2} (y)

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

Simplify

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

Add a constant to the solution

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

x \to 3 - lim (\frac{3 - x}{x - 3})

e^{- 3.5 x^{2}}

\int (3 x - 1)^{2} (- 2 x) d x

7 y^{3} + 9 x^{8} = 5 y + 11 x

f (x) = cot (2 x)

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