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

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

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

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

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

Solution steps

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

Take the constant out:

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

= \frac{1}{2} \cdot \int csc (x) cot (x) d x

Apply u-substitution

: \int - 1 d u

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

Integral of a constant:

\int a d x = a x

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

Substitute back

u = csc (x)

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

Simplify

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

Add a constant to the solution

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

\int \frac{( x ^{2} + 1 )}{( x - 1 ) ^{3}} d x

\int e^{t} - e^{- t} d t

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

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