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Beliebt Rechnen >

integral of (4y-x^2)^2

Lösung

\int (4 y - x^{2})^{2} d x

Lösung

\frac{x ^{5}}{5} - \frac{8 y x ^{3}}{3} + 16 y^{2} x + C

Schritte zur Lösung

\int (4 y - x^{2})^{2} d x

Multipliziere aus

(- x^{2} + 4 y)^{2} : x^{4} - 8 y x^{2} + 16 y^{2}

= \int x^{4} - 8 y x^{2} + 16 y^{2} 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^{4} d x - \int 8 y x^{2} d x + \int 16 y^{2} d x

\int x^{4} d x = \frac{x ^{5}}{5}

\int 8 y x^{2} d x = \frac{8 y x ^{3}}{3}

\int 16 y^{2} d x = 16 y^{2} x

= \frac{x ^{5}}{5} - \frac{8 y x ^{3}}{3} + 16 y^{2} x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{5}}{5} - \frac{8 y x ^{3}}{3} + 16 y^{2} x + C

Graph

Beliebte Beispiele

integral of (x^2)/(sqrt(25-16x^2))

\int \frac{x ^{2}}{25 - 16 x ^{2}} d x

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

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\int 0.5 e^{t} d t

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\int x + \frac{1}{x} d x