What is the integral of xcoth(x^2) ?

The integral of xcoth(x^2) is 1/2 ln|sinh(x^2)|+C

Popular >

integral of xcoth(x^2)

\int x coth (x^{2}) d x

\frac{1}{2} ln sinh (x^{2}) + C

Solution steps

\int x coth (x^{2}) d x

Apply u-substitution

: \int \frac{coth ( u )}{2} d u

= \int \frac{coth ( u )}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int coth (u) d u

Rewrite using trig identities

= \frac{1}{2} \cdot \int \frac{cosh ( u )}{sinh ( u )} d u

Apply u-substitution

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

= \frac{1}{2} \cdot \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= \frac{1}{2} ln ∣ v ∣

Substitute back

= \frac{1}{2} ln sinh (x^{2})

Add a constant to the solution

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

\int x (x^{2} + 1)^{\frac{3}{4}} d x

\int x ln (\frac{1 + 2 x}{1 - 2 x}) d x

\int sinh (x) (cosh (x))^{2} d x

\int 2^{x} \cdot 2^{2^{x}} d x

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

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