What is the integral of cosh(2x)sinh^2(2x) ?

The integral of cosh(2x)sinh^2(2x) is 1/6 sinh^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 cosh(2x)sinh^2(2x)

\int cosh (2 x) sinh^{2} (2 x) d x

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

Solution steps

\int cosh (2 x) sinh^{2} (2 x) d x

Apply u-substitution

: \int cosh (u) sinh^{2} (u) \frac{1}{2} d u

= \int cosh (u) sinh^{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 cosh (u) sinh^{2} (u) d u

Apply u-substitution

: \int v^{2} d v

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

Apply the Power Rule

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

= \frac{1}{2} \cdot \frac{v ^{3}}{3}

Substitute back

= \frac{1}{2} \cdot \frac{sinh ^{3} ( 2 x )}{3}

Simplify

\frac{1}{2} \cdot \frac{sinh ^{3} ( 2 x )}{3} : \frac{1}{6} sinh^{3} (2 x)

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

Add a constant to the solution

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

\int \frac{x ^{2} - x + 1}{x ^{2}} d x

\int 5 sec^{2} (x) e^{t a n (x)} d x

\int x e^{- c x} d x

\int (x^{2} + 3) e^{- 2 x} d x

\int \frac{9}{3 + x ^{2}} d x

What is the integral of cosh(2x)sinh^2(2x) ?
The integral of cosh(2x)sinh^2(2x) is 1/6 sinh^3(2x)+C