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

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

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integral of (sin(ln(x)))/x

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

- cos (ln (x)) + C

Solution steps

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

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 (x)

= - cos (ln (x))

Add a constant to the solution

= - cos (ln (x)) + C

\int \frac{x ^{2}}{( x ^{2} + 25 ) ^{\frac{3}{2}}} d x

\frac{d}{d x} (\frac{1}{- x ^{2}})

\frac{d y}{d x} = x + 2 y, y (0) = 6

x \to 0 lim (\frac{π x ^{2} + 2}{x})

\frac{\partial}{\partial x} (ln ∣ x ∣)

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