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Beliebt Rechnen >

integral of (((x^3+1)^2)/(x^2))

Lösung

\int (\frac{( x ^{3} + 1 ) ^{2}}{x ^{2}}) d x

Lösung

- \frac{( x ^{3} + 1 ) ^{2}}{x} + 6 (\frac{x ^{5}}{5} + \frac{x ^{2}}{2}) + C

Schritte zur Lösung

\int \frac{( x ^{3} + 1 ) ^{2}}{x ^{2}} d x

Wende die partielle Integration an

= - \frac{( x ^{3} + 1 ) ^{2}}{x} - \int - 6 x (x^{3} + 1) d x

\int - 6 x (x^{3} + 1) d x = - 6 (\frac{x ^{5}}{5} + \frac{x ^{2}}{2})

= - \frac{( x ^{3} + 1 ) ^{2}}{x} - (- 6 (\frac{x ^{5}}{5} + \frac{x ^{2}}{2}))

Vereinfache

= - \frac{( x ^{3} + 1 ) ^{2}}{x} + 6 (\frac{x ^{5}}{5} + \frac{x ^{2}}{2})

Füge eine Konstante zur Lösung hinzu

= - \frac{( x ^{3} + 1 ) ^{2}}{x} + 6 (\frac{x ^{5}}{5} + \frac{x ^{2}}{2}) + C

Graph

Beliebte Beispiele

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\frac{\partial}{\partial x} (x y ln (x^{2} + y^{2}))

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\frac{d}{d x} (cos (2 x + 3 y))

y^{''}-16y^'+63y=240e^x

y^{^{''}} - 16 y^{^{'}} + 63 y = 240 e^{x}