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Beliebt Rechnen >

integral of 3e^x-5x^3+7+3/x

Lösung

\int 3 e^{x} - 5 x^{3} + 7 + \frac{3}{x} d x

Lösung

3 e^{x} - \frac{5 x ^{4}}{4} + 7 x + 3 ln ∣ x ∣ + C

Schritte zur Lösung

\int 3 e^{x} - 5 x^{3} + 7 + \frac{3}{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 3 e^{x} d x - \int 5 x^{3} d x + \int 7 d x + \int \frac{3}{x} d x

\int 3 e^{x} d x = 3 e^{x}

\int 5 x^{3} d x = \frac{5 x ^{4}}{4}

\int 7 d x = 7 x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

= 3 e^{x} - \frac{5 x ^{4}}{4} + 7 x + 3 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= 3 e^{x} - \frac{5 x ^{4}}{4} + 7 x + 3 ln ∣ x ∣ + C

Graph

Beliebte Beispiele

integral of x^2sqrt((5x^3-3)^5)

\int x^{2} (5 x^{3} - 3)^{5} d x

integral of x(x-5)^{1/2}

\int x (x - 5)^{\frac{1}{2}} d x

integral of 2/x-3e^x

\int \frac{2}{x} - 3 e^{x} d x

integral of bsin(x)cos(x)

\int b sin (x) cos (x) d x

integral of (x^2-3x)e^{(-x)/3}

\int (x^{2} - 3 x) e^{\frac{- x}{3}} d x