What is the integral of csc((v-pi)/2)cot((v-pi)/2) ?

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

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integral of csc((v-pi)/2)cot((v-pi)/2)

\int csc (\frac{v - π}{2}) cot (\frac{v - π}{2}) d v

- 2 csc (\frac{1}{2} (v - π)) + C

Solution steps

\int csc (\frac{v - π}{2}) cot (\frac{v - π}{2}) d v

\frac{v - π}{2} = \frac{1}{2} (v - π - 2) + 1

= \int csc (\frac{1}{2} (v - π - 2) + 1) cot (\frac{v - π}{2}) d v

Apply u-substitution

: \int csc (\frac{u}{2}) cot (\frac{u}{2}) d u

= \int csc (\frac{u}{2}) cot (\frac{u}{2}) d u

Apply u-substitution

: \int csc (w) cot (w) \cdot 2 d w

= \int csc (w) cot (w) \cdot 2 d w

Take the constant out:

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

= 2 \cdot \int csc (w) cot (w) d w

Apply u-substitution

: \int - 1 d t

= 2 \cdot \int - 1 d t

Integral of a constant:

\int a d x = a x

= 2 (- 1) t

Substitute back

= 2 (- 1) csc (\frac{v - π}{2})

Simplify

2 (- 1) csc (\frac{v - π}{2}) : - 2 csc (\frac{1}{2} (v - π))

= - 2 csc (\frac{1}{2} (v - π))

Add a constant to the solution

= - 2 csc (\frac{1}{2} (v - π)) + C

\frac{d y}{d x} + (\frac{4}{x}) y = - 4 x - 5

\int_{0}^{1} \frac{1}{x ( x + 1 )} d x

\frac{\partial}{\partial x} (4 x^{4} y^{5} - 3 x^{2})

\frac{\partial}{\partial x} (x - y^{2} + 3 x y)

\int (\frac{1}{x ^{2} + 9}) d x

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