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Beliebt Rechnen >

integral of x(x^2+3)^4

Lösung

\int x (x^{2} + 3)^{4} d x

Lösung

\frac{1}{10} (x^{2} + 3)^{5} + C

Schritte zur Lösung

\int x (x^{2} + 3)^{4} d x

Wende U-Substitution an

= \int \frac{u ^{4}}{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^{4} d u

Wende die Potenzregel an

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

Setze in

u = x^{2} + 3

ein

= \frac{1}{2} \cdot \frac{( x ^{2} + 3 ) ^{5}}{5}

Vereinfache

\frac{1}{2} \cdot \frac{( x ^{2} + 3 ) ^{5}}{5} : \frac{1}{10} (x^{2} + 3)^{5}

= \frac{1}{10} (x^{2} + 3)^{5}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{10} (x^{2} + 3)^{5} + C

Graph

Beliebte Beispiele

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t an g e n t x y^{8} + 8 x y = 36, (4, 1)

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