What is the integral of (cosh(x))/(2+3sinh(x)) ?

The integral of (cosh(x))/(2+3sinh(x)) is 1/3 ln|2+3sinh(x)|+C

Popular >

integral of (cosh(x))/(2+3sinh(x))

\int \frac{cosh ( x )}{2 + 3 sinh ( x )} d x

\frac{1}{3} ln ∣ 2 + 3 sinh (x) ∣ + C

Solution steps

\int \frac{cosh ( x )}{2 + 3 sinh ( x )} d x

Apply u-substitution

: \int \frac{1}{3 u} d u

= \int \frac{1}{3 u} 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 \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} ln ∣ u ∣

Substitute back

u = 2 + 3 sinh (x)

= \frac{1}{3} ln ∣ 2 + 3 sinh (x) ∣

Add a constant to the solution

= \frac{1}{3} ln ∣ 2 + 3 sinh (x) ∣ + C

\frac{d}{d x} (\frac{sec ( x )}{1 + sec ( x )})

\frac{d}{d x} (\frac{6 x + 2}{x + 1})

x \to 1 lim ((a - x) (a + x))

\frac{d}{d x} (3 (sin (x + \frac{π}{2})))

\frac{d}{d x} ((x + 2) 2 x - 3)

What is the integral of (cosh(x))/(2+3sinh(x)) ?
The integral of (cosh(x))/(2+3sinh(x)) is 1/3 ln|2+3sinh(x)|+C