integral of (-4xy+2x^3-2y+3)

Lösung

\int (- 4 x y + 2 x^{3} - 2 y + 3) d x

3 x - 2 y x + \frac{x ^{4}}{2} - 2 y x^{2} + C

Schritte zur Lösung

\int - 4 x y + 2 x^{3} - 2 y + 3 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 3 d x - \int 2 y d x + \int 2 x^{3} d x - \int 4 y x d x

\int 3 d x = 3 x

\int 2 y d x = 2 y x

\int 2 x^{3} d x = \frac{x ^{4}}{2}

\int 4 y x d x = 2 y x^{2}

= 3 x - 2 y x + \frac{x ^{4}}{2} - 2 y x^{2}

Füge eine Konstante zur Lösung hinzu

= 3 x - 2 y x + \frac{x ^{4}}{2} - 2 y x^{2} + C

\int (sin (wt))^{2} d t

\int (2^{x} + e^{x}) d x

\int_{- 3}^{3} \frac{14}{x ^{2} - 6 x - 40} d x

\frac{\partial}{\partial x} (\frac{( y ^{3} )}{x})

t an g e n t y = x^{2} + x, (0, 0)