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

The integral of (2sin(ln(x)))/x is -2cos(ln(x))+C

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integral of (2sin(ln(x)))/x

\int \frac{2 sin ( ln ( x ) )}{x} d x

- 2 cos (ln (x)) + C

Solution steps

\int \frac{2 sin ( ln ( x ) )}{x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int \frac{sin ( ln ( x ) )}{x} d x

Apply u-substitution

: \int sin (u) d u

= 2 \cdot \int sin (u) d u

Use the common integral:

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

= 2 (- cos (u))

Substitute back

u = ln (x)

= 2 (- cos (ln (x)))

Simplify

= - 2 cos (ln (x))

Add a constant to the solution

= - 2 cos (ln (x)) + C

y^{3} - x y^{2} + x^{3} = 5, (1, 2)

\int x cosh (x) d x

f (x) = x^{3} cos (x)

\frac{d}{d x} ((sin (x))^{\frac{1}{3}})

24 e^{- 7 t} - 5 e^{- 23 t}

What is the integral of (2sin(ln(x)))/x ?
The integral of (2sin(ln(x)))/x is -2cos(ln(x))+C