integral of-2cos(x)+3x^2-5x+4

Lösung

\int - 2 cos (x) + 3 x^{2} - 5 x + 4 d x

- 2 sin (x) + x^{3} - \frac{5 x ^{2}}{2} + 4 x + C

Schritte zur Lösung

\int - 2 cos (x) + 3 x^{2} - 5 x + 4 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 2 cos (x) d x + \int 3 x^{2} d x - \int 5 x d x + \int 4 d x

\int 2 cos (x) d x = 2 sin (x)

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

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 4 d x = 4 x

= - 2 sin (x) + x^{3} - \frac{5 x ^{2}}{2} + 4 x

Füge eine Konstante zur Lösung hinzu

= - 2 sin (x) + x^{3} - \frac{5 x ^{2}}{2} + 4 x + C

\frac{d}{d x} (x e^{\frac{y}{z}})

d er i v a t i v e 7 x - 6 x

\int_{1}^{5} \frac{ln ( x )}{x ^{2}} d x

d er i v a t i v e 3 e^{3 e^{x} + x}

\int (e - x - e^{3}) (e x + e - 5) d x