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

The integral of cot^2(2x)csc^2(2x) is -1/6 cot^3(2x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cot^2(2x)csc^2(2x)

\int cot^{2} (2 x) csc^{2} (2 x) d x

- \frac{1}{6} cot^{3} (2 x) + C

Solution steps

\int cot^{2} (2 x) csc^{2} (2 x) d x

Apply u-substitution

: \int cot^{2} (u) csc^{2} (u) \frac{1}{2} d u

= \int cot^{2} (u) csc^{2} (u) \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int cot^{2} (u) csc^{2} (u) d u

Apply u-substitution

: \int - v^{2} d v

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

Take the constant out:

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

= \frac{1}{2} (- \int v^{2} d v)

Apply the Power Rule

: \frac{v ^{3}}{3}

= \frac{1}{2} (- \frac{v ^{3}}{3})

Substitute back

= \frac{1}{2} (- \frac{cot ^{3} ( 2 x )}{3})

Simplify

\frac{1}{2} (- \frac{cot ^{3} ( 2 x )}{3}) : - \frac{1}{6} cot^{3} (2 x)

= - \frac{1}{6} cot^{3} (2 x)

Add a constant to the solution

= - \frac{1}{6} cot^{3} (2 x) + C

\int \frac{1}{( x + 3 ) ( x - 2 )} d x

\int \frac{1}{2 sin ( x ) + 1} d x

\int x + x^{4} d x

\int (x + 1) e^{2 x + 1} d x

\int 48 x^{- \frac{1}{5}} tan (x^{\frac{4}{5}}) d x

What is the integral of cot^2(2x)csc^2(2x) ?
The integral of cot^2(2x)csc^2(2x) is -1/6 cot^3(2x)+C