integral of x(4-2x^2)

Lösung

\int x (4 - 2 x^{2}) d x

- \frac{1}{8} (4 - 2 x^{2})^{2} + C

Schritte zur Lösung

\int x (4 - 2 x^{2}) d x

Wende U-Substitution an

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

Entferne die Konstante:

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

= - \frac{1}{4} \cdot \int u d u

Wende die Potenzregel an

= - \frac{1}{4} \cdot \frac{u ^{2}}{2}

Setze in

u = 4 - 2 x^{2}

ein

= - \frac{1}{4} \cdot \frac{( 4 - 2 x ^{2} ) ^{2}}{2}

Vereinfache

- \frac{1}{4} \cdot \frac{( 4 - 2 x ^{2} ) ^{2}}{2} : - \frac{1}{8} (4 - 2 x^{2})^{2}

= - \frac{1}{8} (4 - 2 x^{2})^{2}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{8} (4 - 2 x^{2})^{2} + C

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