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

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

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integral of-csc(x)cot(x)

\int - csc (x) cot (x) d x

csc (x) + C

Solution steps

\int - csc (x) cot (x) d x

Take the constant out:

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

= - \int csc (x) cot (x) d x

Apply u-substitution

: \int - 1 d u

= - \int - 1 d u

Integral of a constant:

\int a d x = a x

= - (- 1) u

Substitute back

u = csc (x)

= - (- 1) csc (x)

Simplify

= csc (x)

Add a constant to the solution

= csc (x) + C

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

(x + 6)^{2}

\frac{d}{d x} (\frac{5}{x ^{5}} + \frac{3}{x ^{2}})

n = 1 \sum \infty 9 e^{- n}