What is the integral of sinh(3x) ?

The integral of sinh(3x) is 1/3 cosh(3x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of sinh(3x)

\int sinh (3 x) d x

\frac{1}{3} cosh (3 x) + C

Solution steps

\int sinh (3 x) d x

Apply u-substitution

= \int sinh (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 sinh (u) d u

Use the common integral:

\int sinh (u) d u = cosh (u)

= \frac{1}{3} cosh (u)

Substitute back

u = 3 x

= \frac{1}{3} cosh (3 x)

Add a constant to the solution

= \frac{1}{3} cosh (3 x) + C

\frac{\partial}{\partial y} (3.5 yz cos (x yz))

x y^{^{'}} + 45 y = 0

\frac{d}{d t} (sin^{3} (t))

\frac{d}{d x} (x^{2} tan (2 x^{5}))

f (x) = \frac{e ^{x}}{e ^{x} + 1}