What is the integral from e to e^2 of (cos(ln(x)))/x ?

The integral from e to e^2 of (cos(ln(x)))/x is sin(2)-sin(1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from e to e^2 of (cos(ln(x)))/x

\int_{e}^{e^{2}} \frac{cos ( ln ( x ) )}{x} d x

sin (2) - sin (1)

Decimal

0.06782 \dots

Solution steps

\int_{e}^{e^{2}} \frac{cos ( ln ( x ) )}{x} d x

Apply u-substitution

= \int_{1}^{2} cos (u) d u

Use the common integral:

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

= [sin (u)]_{1}^{2}

Compute the boundaries:

sin (2) - sin (1)

= sin (2) - sin (1)

What is the integral from e to e^2 of (cos(ln(x)))/x ?
The integral from e to e^2 of (cos(ln(x)))/x is sin(2)-sin(1)