integral of (x^3+x^2-x^5)/(x^6)

Lösung

\int \frac{x ^{3} + x ^{2} - x ^{5}}{x ^{6}} d x

- \frac{1}{2 x ^{2}} - \frac{1}{3 x ^{3}} - ln ∣ x ∣ + C

Schritte zur Lösung

\int \frac{x ^{3} + x ^{2} - x ^{5}}{x ^{6}} d x

Multipliziere aus

\frac{x ^{3} + x ^{2} - x ^{5}}{x ^{6}} : \frac{1}{x ^{3}} + \frac{1}{x ^{4}} - \frac{1}{x}

= \int \frac{1}{x ^{3}} + \frac{1}{x ^{4}} - \frac{1}{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 \frac{1}{x ^{3}} d x + \int \frac{1}{x ^{4}} d x - \int \frac{1}{x} d x

\int \frac{1}{x ^{3}} d x = - \frac{1}{2 x ^{2}}

\int \frac{1}{x ^{4}} d x = - \frac{1}{3 x ^{3}}

\int \frac{1}{x} d x = ln ∣ x ∣

= - \frac{1}{2 x ^{2}} - \frac{1}{3 x ^{3}} - ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{2 x ^{2}} - \frac{1}{3 x ^{3}} - ln ∣ x ∣ + C

\frac{d}{d x} (\frac{1}{4} (x^{4} + 8))

d er i v a t i v e g (x) = 3 x^{4} - 140 x^{3}

\int \frac{1}{t} d t

\frac{\partial}{\partial x} (- x)

d er i v a t i v e r