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

The integral of (cosh(ln(x)))/x is -1/(2x)+1/2 x+C

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integral of (cosh(ln(x)))/x

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

- \frac{1}{2 x} + \frac{1}{2} x + C

Solution steps

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

Apply Integration By Parts

: cosh (ln (x)) - \int \frac{sinh ( ln ( x ) ) - cosh ( ln ( x ) )}{x} d x

= cosh (ln (x)) - \int \frac{sinh ( ln ( x ) ) - cosh ( ln ( x ) )}{x} d x

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

= cosh (ln (x)) - (cosh (ln (x)) + \frac{1}{2 x} - \frac{1}{2} x)

Simplify

= - \frac{1}{2 x} + \frac{1}{2} x

Add a constant to the solution

= - \frac{1}{2 x} + \frac{1}{2} x + C

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