What is the integral of-2csc^2(x) ?

The integral of-2csc^2(x) is 2cot(x)+C

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integral of-2csc^2(x)

\int - 2 csc^{2} (x) d x

2 cot (x) + C

Solution steps

\int - 2 csc^{2} (x) d x

Take the constant out:

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

= - 2 \cdot \int csc^{2} (x) d x

Use the common integral:

\int csc^{2} (x) d x = - cot (x)

= - 2 (- cot (x))

Simplify

= 2 cot (x)

Add a constant to the solution

= 2 cot (x) + C

x \to 0 lim (x^{3} \cdot csc^{2} (x))

f (x) = sin^{5} (2 x) cos^{3} (2 x)

(x^{2} - 1) y^{^{'}} = 2 y

y = \frac{x ^{2} + 1}{3 x + 1}, at x = 0

\frac{\partial}{\partial y} (A x + B y^{2} + C x^{2} y)