integral of y+y^2cos(x)

Lösung

\int y + y^{2} cos (x) d x

y x + y^{2} sin (x) + C

Schritte zur Lösung

\int y + y^{2} cos (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 d x + \int cos (x) y^{2} d x

\int y d x = y x

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

= y x + y^{2} sin (x)

Füge eine Konstante zur Lösung hinzu

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

d er i v a t i v e \frac{8 x ^{2} + 8 + 4}{x}

\int (x + 5) 10 x + x^{2} d x

t an g e n t f (x) = x + \frac{4}{x}, (4, 5)

\frac{\partial}{\partial x} (y sin (x y))

\frac{d y}{d x} = \frac{9 x ^{2} - 6}{x ^{2}}