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Beliebt Rechnen >

integral of \sqrt[7]{x^2}+xsqrt(x)

Lösung

\int 7 x^{2} + x x d x

Lösung

\frac{7}{9} x^{\frac{9}{7}} + \frac{2}{5} x^{\frac{5}{2}} + C

Schritte zur Lösung

\int 7 x^{2} + x x d x

7 x^{2} = x^{\frac{2}{7}},

angenommen

x \geq 0

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

\int x^{\frac{2}{7}} d x = \frac{7}{9} x^{\frac{9}{7}}

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

= \frac{7}{9} x^{\frac{9}{7}} + \frac{2}{5} x^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{7}{9} x^{\frac{9}{7}} + \frac{2}{5} x^{\frac{5}{2}} + C

Graph

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