integral of x^3-2x^{-2}+6x

Lösung

\int x^{3} - 2 x^{- 2} + 6 x d x

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

Schritte zur Lösung

\int x^{3} - 2 x^{- 2} + 6 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 x^{3} d x - \int 2 x^{- 2} d x + \int 6 x d x

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

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

\int 6 x d x = 3 x^{2}

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

t a y l or 9 + x^{2}

d er i v a t i v e ln (4 x^{3})

\int \frac{x ^{5} - 1}{x} d x

\int \frac{1}{x ^{2} - 4 x + 8} d x

\frac{d}{d x} (2 x^{x})