What is the integral of (sinh(ln(x)))/x ?

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

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integral of (sinh(ln(x)))/x

\int \frac{sinh ( ln ( x ) )}{x} d x

cosh (ln (x)) + C

Solution steps

\int \frac{sinh ( ln ( x ) )}{x} d x

Apply u-substitution

: \int sinh (u) d u

= \int sinh (u) d u

Use the common integral:

\int sinh (u) d u = cosh (u)

= cosh (u)

Substitute back

u = ln (x)

= cosh (ln (x))

Add a constant to the solution

= cosh (ln (x)) + C

x \to + 0 lim (\frac{∣ x - 3 ∣}{x - 3})

\int \frac{y ^{2} + 28 y + 196}{( y ^{2} + 196 ) ^{2}} d y

x \to - 4 lim (\frac{x ^{2} - 1}{4 - x})

\int_{0}^{1} cos (\frac{π x}{2}) d x

y^{^{''}} + 4 y^{^{'}} = (4 t - 4) sin (3 t)

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