What is the integral of sinh(1+4x) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of sinh(1+4x)

\int sinh (1 + 4 x) d x

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

Solution steps

\int sinh (1 + 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 = 1 + 4 x

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

Add a constant to the solution

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

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