What is the integral of csc(8x)cot(8x) ?

The integral of csc(8x)cot(8x) is -1/8 csc(8x)+C

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integral of csc(8x)cot(8x)

\int csc (8 x) cot (8 x) d x

- \frac{1}{8} csc (8 x) + C

Solution steps

\int csc (8 x) cot (8 x) d x

Rewrite using trig identities

= \int \frac{cot ( 8 x )}{sin ( 8 x )} d x

Apply u-substitution

: \int \frac{cot ( u )}{8 sin ( u )} d u

= \int \frac{cot ( u )}{8 sin ( u )} d u

Take the constant out:

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

= \frac{1}{8} \cdot \int \frac{cot ( u )}{sin ( u )} d u

Rewrite using trig identities

= \frac{1}{8} \cdot \int \frac{cos ( u )}{sin ^{2} ( u )} d u

Apply u-substitution

: \int \frac{1}{v ^{2}} d v

= \frac{1}{8} \cdot \int \frac{1}{v ^{2}} d v

Apply the Power Rule

: - \frac{1}{v}

= \frac{1}{8} (- \frac{1}{v})

Substitute back

= \frac{1}{8} (- \frac{1}{sin ( 8 x )})

Simplify

\frac{1}{8} (- \frac{1}{sin ( 8 x )}) : - \frac{1}{8} csc (8 x)

= - \frac{1}{8} csc (8 x)

Add a constant to the solution

= - \frac{1}{8} csc (8 x) + C

ln (4 x)

\frac{d}{d x} (e^{c o s (x)} sin (x))

\int_{0}^{a} x sin^{2} (\frac{π x}{a}) d x

\int_{1}^{9} 9 x^{2} d x

y = \frac{88 t}{99 t - 88}

What is the integral of csc(8x)cot(8x) ?
The integral of csc(8x)cot(8x) is -1/8 csc(8x)+C