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Beliebt Rechnen >

integral of 3^x+x^3+3/x

Lösung

\int 3^{x} + x^{3} + \frac{3}{x} d x

Lösung

\frac{3 ^{x}}{ln ( 3 )} + \frac{x ^{4}}{4} + 3 ln ∣ x ∣ + C

Schritte zur Lösung

\int 3^{x} + x^{3} + \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^{x} d x + \int x^{3} d x + \int \frac{3}{x} d x

\int 3^{x} d x = \frac{3 ^{x}}{ln ( 3 )}

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

= \frac{3 ^{x}}{ln ( 3 )} + \frac{x ^{4}}{4} + 3 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{3 ^{x}}{ln ( 3 )} + \frac{x ^{4}}{4} + 3 ln ∣ x ∣ + C

Graph

Beliebte Beispiele

integral of (1/3 x^2+1/2 x)

\int (\frac{1}{3} x^{2} + \frac{1}{2} x) d x

integral of x^2(1-x^3)^3

\int x^{2} (1 - x^{3})^{3} d x

integral of sin(x/2)cos(nx)

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

integral of ln(x/(1-x))

\int ln (\frac{x}{1 - x}) d x

integral of sin^4(x/2)cos(x/2)

\int sin^{4} (\frac{x}{2}) cos (\frac{x}{2}) d x