integral of 3x^3+4x^2-2x^{-1}+13

Lösung

\int 3 x^{3} + 4 x^{2} - 2 x^{- 1} + 13 d x

\frac{3 x ^{4}}{4} + \frac{4 x ^{3}}{3} - 2 ln ∣ x ∣ + 13 x + C

Schritte zur Lösung

\int 3 x^{3} + 4 x^{2} - 2 x^{- 1} + 13 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 x^{3} d x + \int 4 x^{2} d x - \int 2 x^{- 1} d x + \int 13 d x

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

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

\int 2 x^{- 1} d x = 2 ln ∣ x ∣

\int 13 d x = 13 x

= \frac{3 x ^{4}}{4} + \frac{4 x ^{3}}{3} - 2 ln ∣ x ∣ + 13 x

Füge eine Konstante zur Lösung hinzu

= \frac{3 x ^{4}}{4} + \frac{4 x ^{3}}{3} - 2 ln ∣ x ∣ + 13 x + C

\int - y^{3} d y

\frac{d}{d x} (2 e^{x} - 5 cos (x) + 3)

d er i v a t i v e 4 e^{x} + \frac{4}{3 x}

\frac{\partial}{\partial x} (- 6 y^{3} + 10 x^{2} - 4 x y)

a re a y = 7 - 2 x^{2}, y = x^{2} + 4