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Beliebt Rechnen >

integral of sqrt(x)(2x+7)

Lösung

\int x (2 x + 7) d x

Lösung

\frac{2}{3} x^{\frac{3}{2}} (2 x + 7) - \frac{8}{15} x^{\frac{5}{2}} + C

Schritte zur Lösung

\int x (2 x + 7) d x

Wende die partielle Integration an

= \frac{2}{3} x^{\frac{3}{2}} (2 x + 7) - \int \frac{4}{3} x^{\frac{3}{2}} d x

\int \frac{4}{3} x^{\frac{3}{2}} d x = \frac{8}{15} x^{\frac{5}{2}}

= \frac{2}{3} x^{\frac{3}{2}} (2 x + 7) - \frac{8}{15} x^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{3} x^{\frac{3}{2}} (2 x + 7) - \frac{8}{15} x^{\frac{5}{2}} + C

Graph

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