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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

sin (x) - sin (1)

Solution steps

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

Apply u-substitution

: \int_{1}^{x} cos (u) d u

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

Use the common integral:

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

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

Compute the boundaries:

sin (x) - sin (1)

= sin (x) - sin (1)

\int_{T}^{T^{^{'}}} 1 d T

\int_{1}^{2} x x d x

\int_{0}^{1} 2 - x^{2} - x^{4} d x

\int_{0}^{y} \frac{1}{4} (x + y) d x

\int_{1}^{5} (2 x) d x

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