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Beliebt Rechnen >

(dy)/(dx)=x^3(1-x^4)^4

Lösung

\frac{d y}{d x} = x^{3} (1 - x^{4})^{4}

Lösung

y = \frac{x ^{4}}{4} - \frac{x ^{8}}{2} + \frac{x ^{12}}{2} - \frac{x ^{16}}{4} + \frac{x ^{20}}{20} + c_{1}

Schritte zur Lösung

\frac{d y}{d x} = x^{3} (1 - x^{4})^{4}

Ersetze

\frac{d y}{d x}

mit

y^{'} (x)

y^{^{'}} (x) = x^{3} (1 - x^{4})^{4}

Wenn

f^{^{'}} (x) = g (x)

dann

f (x) = \int g (x) d x

y = \int x^{3} (1 - x^{4})^{4} d x

\int x^{3} (1 - x^{4})^{4} d x = \frac{x ^{4}}{4} - \frac{x ^{8}}{2} + \frac{x ^{12}}{2} - \frac{x ^{16}}{4} + \frac{x ^{20}}{20} + c_{1}

y = \frac{x ^{4}}{4} - \frac{x ^{8}}{2} + \frac{x ^{12}}{2} - \frac{x ^{16}}{4} + \frac{x ^{20}}{20} + c_{1}

Graph

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