What is the integral of tanh(x/6) ?

The integral of tanh(x/6) is 6ln|cosh(x/6)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of tanh(x/6)

\int tanh (\frac{x}{6}) d x

6 ln cosh (\frac{x}{6}) + C

Solution steps

\int tanh (\frac{x}{6}) d x

Apply u-substitution

= \int tanh (u) \cdot 6 d u

Take the constant out:

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

= 6 \cdot \int tanh (u) d u

Rewrite using trig identities

= 6 \cdot \int \frac{sinh ( u )}{cosh ( u )} d u

Apply u-substitution

= 6 \cdot \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= 6 ln ∣ v ∣

Substitute back

= 6 ln cosh (\frac{x}{6})

Add a constant to the solution

= 6 ln cosh (\frac{x}{6}) + C

What is the integral of tanh(x/6) ?
The integral of tanh(x/6) is 6ln|cosh(x/6)|+C