What is the integral of csc^2(6θ)cot(6θ) ?

The integral of csc^2(6θ)cot(6θ) is -1/12 cot^2(6θ)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of csc^2(6θ)cot(6θ)

\int csc^{2} (6 θ) cot (6 θ) d θ

- \frac{1}{12} cot^{2} (6 θ) + C

Solution steps

\int csc^{2} (6 θ) cot (6 θ) d θ

Apply u-substitution

: \int - \frac{u}{6} d u

= \int - \frac{u}{6} d u

Take the constant out:

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

= - \frac{1}{6} \cdot \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= - \frac{1}{6} \cdot \frac{u ^{2}}{2}

Substitute back

u = cot (6 θ)

= - \frac{1}{6} \cdot \frac{cot ^{2} ( 6 θ )}{2}

Simplify

- \frac{1}{6} \cdot \frac{cot ^{2} ( 6 θ )}{2} : - \frac{1}{12} cot^{2} (6 θ)

= - \frac{1}{12} cot^{2} (6 θ)

Add a constant to the solution

= - \frac{1}{12} cot^{2} (6 θ) + C

x \to \infty lim (x \cdot x)

x \to 0 lim (\frac{sin ( 15 x )}{x})

\int e^{- 0.1 x} d x

x^{3} + y^{3} = 9, (1, 2)

\int (a^{2} - x^{2}) d x

What is the integral of csc^2(6θ)cot(6θ) ?
The integral of csc^2(6θ)cot(6θ) is -1/12 cot^2(6θ)+C