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Beliebt Rechnen >

integral of sqrt(x)(x^3-1/x)

Lösung

\int x (x^{3} - \frac{1}{x}) d x

Lösung

\frac{2}{9} x^{4} x - 2 x + C

Schritte zur Lösung

\int x (x^{3} - \frac{1}{x}) d x

Wende die partielle Integration an

= x^{4} x - x - \int \frac{x ^{4} + 6 x x ^{\frac{7}{2}} + 1}{2 x ^{\frac{1}{2}}} d x

\int \frac{x ^{4} + 6 x x ^{\frac{7}{2}} + 1}{2 x ^{\frac{1}{2}}} d x = \frac{1}{9} x (7 x^{4} + 9)

= x^{4} x - x - \frac{1}{9} x (7 x^{4} + 9)

Vereinfache

x^{4} x - x - \frac{1}{9} x (7 x^{4} + 9) : \frac{2}{9} x^{4} x - 2 x

= \frac{2}{9} x^{4} x - 2 x

Füge eine Konstante zur Lösung hinzu

= \frac{2}{9} x^{4} x - 2 x + C

Graph

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