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

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

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

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

tan (ln (z)) + C

Solution steps

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

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 (z)

= tan (ln (z))

Add a constant to the solution

= tan (ln (z)) + C

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