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

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

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integral from e to 2e of (cos(x)-1/x)

\int_{e}^{2 e} (cos (x) - \frac{1}{x}) d x

sin (2 e) - sin (e) - ln (2 e) + 1

Decimal Notation

- 1.85297 \dots

Solution steps

\int_{e}^{2 e} cos (x) - \frac{1}{x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{e}^{2 e} cos (x) d x - \int_{e}^{2 e} \frac{1}{x} d x

\int_{e}^{2 e} cos (x) d x = sin (2 e) - sin (e)

\int_{e}^{2 e} \frac{1}{x} d x = ln (2 e) - 1

= sin (2 e) - sin (e) - (ln (2 e) - 1)

Simplify

= sin (2 e) - sin (e) - ln (2 e) + 1

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