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

Lösung

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

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

Schritte zur Lösung

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

Füge eine Konstante zur Lösung hinzu

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

\int \frac{1}{- x ^{2} + 2 x + 15} d x

in v erse l a pl a ce \frac{6}{s} + \frac{32}{s ^{2} + 16}

in v erse l a pl a ce \frac{8}{( s ^{2} + 1 ) ^{2}}

x^{2} \frac{d y}{d x} - y^{2} = 0

x \to 0 lim (x (ln (x))^{2})