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Beliebt Rechnen >

integral of x^{-1}+sin(x)+e^x

Lösung

\int x^{- 1} + sin (x) + e^{x} d x

Lösung

ln ∣ x ∣ - cos (x) + e^{x} + C

Schritte zur Lösung

\int x^{- 1} + sin (x) + e^{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 x^{- 1} d x + \int sin (x) d x + \int e^{x} d x

\int x^{- 1} d x = ln ∣ x ∣

\int sin (x) d x = - cos (x)

\int e^{x} d x = e^{x}

= ln ∣ x ∣ - cos (x) + e^{x}

Füge eine Konstante zur Lösung hinzu

= ln ∣ x ∣ - cos (x) + e^{x} + C

Graph

Beliebte Beispiele

(dy)/(dx)+2xy=1

\frac{d y}{d x} + 2 x y = 1

limit as h approaches 0-of (-ln(1+6h))/h

h \to 0 - lim (\frac{- ln ( 1 + 6 h )}{h})

derivative 2t^3

d er i v a t i v e 2 t^{3}

integral of 2/(cos(2x))

\int \frac{2}{cos ( 2 x )} d x

derivative of (sqrt(x^2+y-1)/(x+1))

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