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

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

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

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

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

Solution steps

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

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} (x)

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

Simplify

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

Add a constant to the solution

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

\frac{d}{d x} (2 x cos (2 x))

\frac{d}{d x} (4 x^{3} + 3 x^{2} - 6 x)

y - x \frac{d y}{d x} = a (1 + x^{2} \frac{d y}{d x})

f (x) = (5 x - 9) (x + 5), (2, 7)

x^{^{''}} + 10 x^{^{'}} + 21 x = 0

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