What is the integral from 1 to e of (sin(ln(x)))/x ?

The integral from 1 to e of (sin(ln(x)))/x is -cos(1)+1

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integral from 1 to e of (sin(ln(x)))/x

\int_{1}^{e} \frac{sin ( ln ( x ) )}{x} d x

- cos (1) + 1

Decimal

0.45969 \dots

Solution steps

\int_{1}^{e} \frac{sin ( ln ( x ) )}{x} d x

Apply u-substitution

: \int_{0}^{1} sin (u) d u

= \int_{0}^{1} sin (u) d u

Use the common integral:

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

= [- cos (u)]_{0}^{1}

Compute the boundaries:

- cos (1) + 1

= - cos (1) + 1

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What is the integral from 1 to e of (sin(ln(x)))/x ?
The integral from 1 to e of (sin(ln(x)))/x is -cos(1)+1