What is the integral of csc(pix)cot(pix) ?

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

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integral of csc(pix)cot(pix)

\int csc (π x) cot (π x) d x

- \frac{1}{π} csc (π x) + C

Solution steps

\int csc (π x) cot (π x) d x

Apply u-substitution

: \int csc (u) cot (u) \frac{1}{π} d u

= \int csc (u) cot (u) \frac{1}{π} d u

Take the constant out:

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

= \frac{1}{π} \cdot \int csc (u) cot (u) d u

Apply u-substitution

: \int - 1 d v

= \frac{1}{π} \cdot \int - 1 d v

Integral of a constant:

\int a d x = a x

= \frac{1}{π} (- 1) v

Substitute back

= \frac{1}{π} (- 1) csc (π x)

Simplify

= - \frac{1}{π} csc (π x)

Add a constant to the solution

= - \frac{1}{π} csc (π x) + C

e^{- t} \cdot cos (2 t)

\int e^{2 x + 2} d x

\int x^{\frac{3}{4}} + 6 d x

y^{^{'''}} - 6 y^{^{''}} - 7 y^{^{'}} = 0

\int t^{3} d t

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