What is the integral of (sec^2(ln(x)))/x ?

The integral of (sec^2(ln(x)))/x is tan(ln(x))+C

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integral of (sec^2(ln(x)))/x

\int \frac{sec ^{2} ( ln ( x ) )}{x} d x

tan (ln (x)) + C

Solution steps

\int \frac{sec ^{2} ( ln ( x ) )}{x} d x

Apply u-substitution

: \int sec^{2} (u) d u

= \int sec^{2} (u) d u

Use the common integral:

\int sec^{2} (u) d u = tan (u)

= tan (u)

Substitute back

u = ln (x)

= tan (ln (x))

Add a constant to the solution

= tan (ln (x)) + C

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What is the integral of (sec^2(ln(x)))/x ?
The integral of (sec^2(ln(x)))/x is tan(ln(x))+C