What is the integral of sinh(4x) ?

The integral of sinh(4x) is 1/4 cosh(4x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of sinh(4x)

\int sinh (4 x) d x

\frac{1}{4} cosh (4 x) + C

Solution steps

\int sinh (4 x) d x

Apply u-substitution

= \int sinh (u) \frac{1}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int sinh (u) d u

Use the common integral:

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

= \frac{1}{4} cosh (u)

Substitute back

u = 4 x

= \frac{1}{4} cosh (4 x)

Add a constant to the solution

= \frac{1}{4} cosh (4 x) + C

t a y l or (1 + (\frac{1}{2}) \cdot x) - 4

t \to 0 lim (e^{5 t})

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

\frac{d}{d t} (10 sin (t))

\frac{d ^{2} y}{d t ^{2}} + 4 \frac{d y}{d t} + 4 y = 0