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

Lösung

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

\frac{x ^{3}}{3} + \frac{2}{7} x^{\frac{7}{2}} + C

Schritte zur Lösung

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

Multipliziere aus

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

= \int x^{2} + x^{\frac{5}{2}} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x^{2} d x + \int x^{\frac{5}{2}} d x

\int x^{2} d x = \frac{x ^{3}}{3}

\int x^{\frac{5}{2}} d x = \frac{2}{7} x^{\frac{7}{2}}

= \frac{x ^{3}}{3} + \frac{2}{7} x^{\frac{7}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} + \frac{2}{7} x^{\frac{7}{2}} + C

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