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

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

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integral of-2csc^2(x)cot(x)

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

csc^{2} (x) + C

Solution steps

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

Apply u-substitution

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

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

Integral of a constant:

\int a d x = a x

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

Substitute back

u = csc^{2} (x)

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

Simplify

- 2 (- \frac{1}{2}) csc^{2} (x) : csc^{2} (x)

= csc^{2} (x)

Add a constant to the solution

= csc^{2} (x) + C

\frac{d}{d x} (\frac{5 x}{x + 3})

\frac{d}{d t} (t - \frac{t ^{3}}{3})

\int (sec^{2} (x)) (2 tan (x) + 1) d x

\frac{\partial}{\partial x} (\frac{1}{4} x^{2} \cdot y)

\frac{d y}{d x} - \frac{4 y}{x} = \frac{y ^{4}}{x ^{2}}

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