integral of (ax^3-bx^2-cx+

Lösung

\int (a x^{3} - b x^{2} - c x + d) d x

\frac{a x ^{4}}{4} - \frac{b x ^{3}}{3} - \frac{c x ^{2}}{2} + d x + C

Schritte zur Lösung

\int a x^{3} - b x^{2} - c x + dd 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 a x^{3} d x - \int b x^{2} d x - \int c x d x + \int dd x

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

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

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

\int dd x = d x

= \frac{a x ^{4}}{4} - \frac{b x ^{3}}{3} - \frac{c x ^{2}}{2} + d x

Füge eine Konstante zur Lösung hinzu

= \frac{a x ^{4}}{4} - \frac{b x ^{3}}{3} - \frac{c x ^{2}}{2} + d x + C

\int_{- 2}^{4} ∣ x ∣ d x

\frac{d y}{d x} = x e^{y}

d er i v a t i v e f (x) = \frac{2 + x + 8 x ^{3}}{x ^{4}}

\int \frac{y}{1 + y ^{2}} d y

\frac{\partial}{\partial x} (20 sin (4 x) cos (2 y))