What is the integral of (sec(ln(x))tan(ln(x)))/x ?

The integral of (sec(ln(x))tan(ln(x)))/x is sec(ln(x))+C

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integral of (sec(ln(x))tan(ln(x)))/x

\int \frac{sec ( ln ( x ) ) tan ( ln ( x ) )}{x} d x

sec (ln (x)) + C

Solution steps

\int \frac{sec ( ln ( x ) ) tan ( ln ( x ) )}{x} d x

Apply u-substitution

= \int sec (u) tan (u) d u

Apply u-substitution

= \int 1 d v

Integral of a constant:

\int a d x = a x

= 1 \cdot v

Substitute back

= 1 \cdot sec (ln (x))

Simplify

= sec (ln (x))

Add a constant to the solution

= sec (ln (x)) + C

What is the integral of (sec(ln(x))tan(ln(x)))/x ?
The integral of (sec(ln(x))tan(ln(x)))/x is sec(ln(x))+C