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Beliebt Rechnen >

integral of (2x^3+5cos(x)+e^x)

Lösung

\int (2 x^{3} + 5 cos (x) + e^{x}) d x

Lösung

\frac{x ^{4}}{2} + 5 sin (x) + e^{x} + C

Schritte zur Lösung

\int 2 x^{3} + 5 cos (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 2 x^{3} d x + \int 5 cos (x) d x + \int e^{x} d x

\int 2 x^{3} d x = \frac{x ^{4}}{2}

\int 5 cos (x) d x = 5 sin (x)

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

= \frac{x ^{4}}{2} + 5 sin (x) + e^{x}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{4}}{2} + 5 sin (x) + e^{x} + C

Graph

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