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Beliebt Rechnen >

integral of (x+5)sqrt(10x+x^2)

Lösung

\int (x + 5) 10 x + x^{2} d x

Lösung

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

Schritte zur Lösung

\int (x + 5) 10 x + x^{2} d x

Wende U-Substitution an

= \int u^{2} d u

Wende die Potenzregel an

= \frac{u ^{3}}{3}

Setze in

u = 10 x + x^{2}

ein

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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