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)

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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

= \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)

\int_{- 1}^{4} 4 x (1 - x^{2}) d x

\int_{0}^{1} 4 y^{2} + 1 d y

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

\int_{0}^{1} (x^{2} - 3 x + 4) d x

\int_{0}^{r} r^{2} d r

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)