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Beliebt Rechnen >

integral of (y^3-y^2sin(x)-x)

Lösung

\int (y^{3} - y^{2} sin (x) - x) d x

Lösung

y^{3} x - \frac{x ^{2}}{2} + y^{2} cos (x) + C

Schritte zur Lösung

\int y^{3} - y^{2} sin (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 y^{3} d x - \int x d x - \int sin (x) y^{2} d x

\int y^{3} d x = y^{3} x

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

\int sin (x) y^{2} d x = - y^{2} cos (x)

= y^{3} x - \frac{x ^{2}}{2} - (- y^{2} cos (x))

Vereinfache

= y^{3} x - \frac{x ^{2}}{2} + y^{2} cos (x)

Füge eine Konstante zur Lösung hinzu

= y^{3} x - \frac{x ^{2}}{2} + y^{2} cos (x) + C

Graph

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