What is the integral of csc(3/4 x)cot(3/4 x) ?

The integral of csc(3/4 x)cot(3/4 x) is -4/3 csc(3/4 x)+C

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integral of csc(3/4 x)cot(3/4 x)

\int csc (\frac{3}{4} x) cot (\frac{3}{4} x) d x

- \frac{4}{3} csc (\frac{3}{4} x) + C

Solution steps

\int csc (\frac{3}{4} x) cot (\frac{3}{4} x) d x

Apply u-substitution

: \int csc (u) cot (u) \frac{4}{3} d u

= \int csc (u) cot (u) \frac{4}{3} d u

Take the constant out:

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

= \frac{4}{3} \cdot \int csc (u) cot (u) d u

Apply u-substitution

: \int - 1 d v

= \frac{4}{3} \cdot \int - 1 d v

Integral of a constant:

\int a d x = a x

= \frac{4}{3} (- 1) v

Substitute back

= \frac{4}{3} (- 1) csc (\frac{3}{4} x)

Simplify

= - \frac{4}{3} csc (\frac{3}{4} x)

Add a constant to the solution

= - \frac{4}{3} csc (\frac{3}{4} x) + C

n = 1 \sum \infty \frac{3}{n ( n + 2 )}

\frac{\partial}{\partial x} (- 4 sin (3 x))

x \to \frac{3 π}{2} + lim (sec (x))

\frac{\partial}{\partial x} (\frac{x}{x ^{3} y ^{6}})

\frac{d}{d x} (x cos (x) + π)

What is the integral of csc(3/4 x)cot(3/4 x) ?
The integral of csc(3/4 x)cot(3/4 x) is -4/3 csc(3/4 x)+C