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Beliebt Rechnen >

integral of (2ysin(x)-x^3+ln(y))

Lösung

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

Lösung

y ln (y) - y - x^{3} y + y^{2} sin (x) + C

Schritte zur Lösung

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

Wende die Summenregel an:

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

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

\int ln (y) d y = y ln (y) - y

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

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

= y ln (y) - y - x^{3} y + y^{2} sin (x)

Füge eine Konstante zur Lösung hinzu

= y ln (y) - y - x^{3} y + y^{2} sin (x) + C

Graph

Beliebte Beispiele

y^{''}-9y^'=81t

y^{^{''}} - 9 y^{^{'}} = 81 t

derivative of (arccos(x)/x)

\frac{d}{d x} (\frac{arccos ( x )}{x})

derivative of tan(x+1/(x^2))

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

integral of 4-x

\int 4 - x d x

limit as x approaches-infinity of x^2+2

x \to - \infty lim (x^{2} + 2)