What is the integral of cot(3s)csc^4(3s) ?

The integral of cot(3s)csc^4(3s) is -1/12 csc^4(3s)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cot(3s)csc^4(3s)

\int cot (3 s) csc^{4} (3 s) d s

- \frac{1}{12} csc^{4} (3 s) + C

Solution steps

\int cot (3 s) csc^{4} (3 s) d s

Apply u-substitution

: \int cot (u) csc^{4} (u) \frac{1}{3} d u

= \int cot (u) csc^{4} (u) \frac{1}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int cot (u) csc^{4} (u) d u

Rewrite using trig identities

= \frac{1}{3} \cdot \int \frac{cos ( u )}{sin ^{5} ( u )} d u

Apply u-substitution

: \int \frac{1}{v ^{5}} d v

= \frac{1}{3} \cdot \int \frac{1}{v ^{5}} d v

Apply the Power Rule

: - \frac{1}{4 v ^{4}}

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

Substitute back

= \frac{1}{3} (- \frac{1}{4 sin ^{4} ( 3 s )})

Simplify

\frac{1}{3} (- \frac{1}{4 sin ^{4} ( 3 s )}) : - \frac{1}{12} csc^{4} (3 s)

= - \frac{1}{12} csc^{4} (3 s)

Add a constant to the solution

= - \frac{1}{12} csc^{4} (3 s) + C

\int \frac{ln ( x )}{3 x ^{2}} d x

\int (x + 4)^{6} d x

\int \frac{y ^{2}}{y ^{3} + 4} d y

\int \frac{1}{x ^{4}} d x

\int \frac{- 4}{( x ^{2} + 4 ) ^{2}} d x

What is the integral of cot(3s)csc^4(3s) ?
The integral of cot(3s)csc^4(3s) is -1/12 csc^4(3s)+C