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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (cosh(x))/(1+sinh(x))

\int \frac{cosh ( x )}{1 + sinh ( x )} d x

ln ∣ 1 + sinh (x) ∣ + C

Solution steps

\int \frac{cosh ( x )}{1 + sinh ( x )} d x

Apply u-substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = 1 + sinh (x)

= ln ∣ 1 + sinh (x) ∣

Add a constant to the solution

= ln ∣ 1 + sinh (x) ∣ + C

\int \frac{1}{( e ^{x} + 1 )} d x

\frac{d}{d x} (\frac{1 + sin ( x )}{cos ( x )})

y^{^{'}} - \frac{4 y}{x} = - \frac{2}{x ^{2}}

\frac{- 6 x}{x ^{2} + 1}

\frac{d}{d y} (2 y^{3})

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