What is the integral of coth(x/5) ?

The integral of coth(x/5) is 5ln|sinh(x/5)|+C

Popular >

integral of coth(x/5)

\int coth (\frac{x}{5}) d x

5 ln sinh (\frac{x}{5}) + C

Solution steps

\int coth (\frac{x}{5}) d x

Apply u-substitution

: \int coth (u) \cdot 5 d u

= \int coth (u) \cdot 5 d u

Take the constant out:

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

= 5 \cdot \int coth (u) d u

Rewrite using trig identities

= 5 \cdot \int \frac{cosh ( u )}{sinh ( u )} d u

Apply u-substitution

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

= 5 \cdot \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= 5 ln ∣ v ∣

Substitute back

= 5 ln sinh (\frac{x}{5})

Add a constant to the solution

= 5 ln sinh (\frac{x}{5}) + C

\int 2 R e (z) d z

\int \frac{x ^{2} - 1}{x ^{2} - 4} + a d x

\int \frac{x}{( 1 + x y ) ^{2}} d y

\int x^{2} (4 - 2 x + x^{3}) d x

\int \frac{1}{x ^{2} - 2 a x} d x

What is the integral of coth(x/5) ?
The integral of coth(x/5) is 5ln|sinh(x/5)|+C