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

Lösung

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

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

Dezimale

- 1.85297 \dots

Schritte zur Lösung

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

Wende die Summenregel an:

\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)

Vereinfache

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

\int_{0}^{\frac{π}{6}} cos^{7} (2 x) d x

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

\int_{- 3}^{3} (\frac{x y ^{2}}{x ^{2} + 1}) d y

\int_{0}^{x} \frac{e ^{- x}}{x} d x

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