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Beliebt Rechnen >

integral of x^{11}e^{x^{12}}

Lösung

\int x^{11} e^{x^{12}} d x

Lösung

\frac{1}{12} e^{x^{12}} + C

Schritte zur Lösung

\int x^{11} e^{x^{12}} d x

Wende U-Substitution an

= \int \frac{e ^{u^{\frac{12}{11}}} u ^{\frac{1}{11}}}{11} d u

Entferne die Konstante:

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

= \frac{1}{11} \cdot \int e^{u^{\frac{12}{11}}} u^{\frac{1}{11}} d u

Wende U-Substitution an

= \frac{1}{11} \cdot \int \frac{11 e ^{v}}{12} d v

Entferne die Konstante:

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

= \frac{1}{11} \cdot \frac{11}{12} \cdot \int e^{v} d v

Nutze das gemeinsame Integral :

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

= \frac{1}{11} \cdot \frac{11}{12} e^{v}

Ersetze zurück

= \frac{1}{11} \cdot \frac{11}{12} e^{(x^{11})^{\frac{12}{11}}}

Vereinfache

\frac{1}{11} \cdot \frac{11}{12} e^{(x^{11})^{\frac{12}{11}}} : \frac{1}{12} e^{x^{12}}

= \frac{1}{12} e^{x^{12}}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{12} e^{x^{12}} + C

Graph

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