What is the integral of (sin(ln(t)))/t ?

The integral of (sin(ln(t)))/t is -cos(ln(t))+C

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integral of (sin(ln(t)))/t

\int \frac{sin ( ln ( t ) )}{t} d t

- cos (ln (t)) + C

Solution steps

\int \frac{sin ( ln ( t ) )}{t} d t

Apply u-substitution

: \int sin (u) d u

= \int sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= - cos (u)

Substitute back

u = ln (t)

= - cos (ln (t))

Add a constant to the solution

= - cos (ln (t)) + C

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What is the integral of (sin(ln(t)))/t ?
The integral of (sin(ln(t)))/t is -cos(ln(t))+C