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Beliebt Rechnen >

integral of (1+x)(2x+x^2)^5

Lösung

\int (1 + x) (2 x + x^{2})^{5} d x

Lösung

\frac{1}{12} (2 x + x^{2})^{6} + C

Schritte zur Lösung

\int (1 + x) (2 x + x^{2})^{5} d x

Wende U-Substitution an

= \int \frac{u ^{5}}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int u^{5} d u

Wende die Potenzregel an

= \frac{1}{2} \cdot \frac{u ^{6}}{6}

Setze in

u = 2 x + x^{2}

ein

= \frac{1}{2} \cdot \frac{( 2 x + x ^{2} ) ^{6}}{6}

Vereinfache

\frac{1}{2} \cdot \frac{( 2 x + x ^{2} ) ^{6}}{6} : \frac{1}{12} (2 x + x^{2})^{6}

= \frac{1}{12} (2 x + x^{2})^{6}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{12} (2 x + x^{2})^{6} + C

Graph

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