integral of (5e^x+(10)/x-4x^3+2^x)

Lösung

\int (5 e^{x} + \frac{10}{x} - 4 x^{3} + 2^{x}) d x

5 e^{x} + 10 ln ∣ x ∣ - x^{4} + \frac{2 ^{x}}{ln ( 2 )} + C

Schritte zur Lösung

\int 5 e^{x} + \frac{10}{x} - 4 x^{3} + 2^{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 5 e^{x} d x + \int \frac{10}{x} d x - \int 4 x^{3} d x + \int 2^{x} d x

\int 5 e^{x} d x = 5 e^{x}

\int \frac{10}{x} d x = 10 ln ∣ x ∣

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

\int 2^{x} d x = \frac{2 ^{x}}{ln ( 2 )}

= 5 e^{x} + 10 ln ∣ x ∣ - x^{4} + \frac{2 ^{x}}{ln ( 2 )}

Füge eine Konstante zur Lösung hinzu

= 5 e^{x} + 10 ln ∣ x ∣ - x^{4} + \frac{2 ^{x}}{ln ( 2 )} + C

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