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

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

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

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

tan (ln (t)) + C

Solution steps

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

Apply u-substitution

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

Use the common integral:

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

= tan (u)

Substitute back

u = ln (t)

= tan (ln (t))

Add a constant to the solution

= tan (ln (t)) + C

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