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Beliebt Rechnen >

integral of x^4e(1-x^5)

Lösung

\int x^{4} e (1 - x^{5}) d x

Lösung

e (\frac{x ^{5}}{5} - \frac{x ^{10}}{10}) + C

Schritte zur Lösung

\int x^{4} e (1 - x^{5}) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= e \cdot \int x^{4} (1 - x^{5}) d x

Multipliziere aus

x^{4} (1 - x^{5}) : x^{4} - x^{9}

= e \cdot \int x^{4} - x^{9} 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

= e (\int x^{4} d x - \int x^{9} d x)

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

\int x^{9} d x = \frac{x ^{10}}{10}

= e (\frac{x ^{5}}{5} - \frac{x ^{10}}{10})

Füge eine Konstante zur Lösung hinzu

= e (\frac{x ^{5}}{5} - \frac{x ^{10}}{10}) + C

Graph

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

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\int \frac{x ^{3}}{x ^{8} - 2} d x

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\int \frac{3 x}{5 x ^{2} + 7} d x