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

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