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Beliebt Rechnen >

integral of x^{12}e^{x^{13}}

Lösung

\int x^{12} e^{x^{13}} d x

Lösung

\frac{1}{13} e^{x^{13}} + C

Schritte zur Lösung

\int x^{12} e^{x^{13}} d x

Wende U-Substitution an

= \int \frac{e ^{u^{\frac{13}{12}}} u ^{\frac{1}{12}}}{12} d u

Entferne die Konstante:

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

= \frac{1}{12} \cdot \int e^{u^{\frac{13}{12}}} u^{\frac{1}{12}} d u

Wende U-Substitution an

= \frac{1}{12} \cdot \int \frac{12 e ^{v}}{13} d v

Entferne die Konstante:

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

= \frac{1}{12} \cdot \frac{12}{13} \cdot \int e^{v} d v

Nutze das gemeinsame Integral :

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

= \frac{1}{12} \cdot \frac{12}{13} e^{v}

Ersetze zurück

= \frac{1}{12} \cdot \frac{12}{13} e^{(x^{12})^{\frac{13}{12}}}

Vereinfache

\frac{1}{12} \cdot \frac{12}{13} e^{(x^{12})^{\frac{13}{12}}} : \frac{1}{13} e^{x^{13}}

= \frac{1}{13} e^{x^{13}}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{13} e^{x^{13}} + C

Graph

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