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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

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\int x^{3} (7 + x^{4})^{6} d x

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\int \frac{6 ^{x} + 1}{2 ^{x}} d x

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\int \frac{cos ( 4 x )}{sin ( 4 x )} d x