integral of (x^3-5x^2-sqrt(x))/(x^2)

Lösung

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

\frac{x ^{2}}{2} - 5 x + \frac{2}{x} + C

Schritte zur Lösung

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

Multipliziere aus

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

= \int x - 5 - \frac{1}{x ^{\frac{3}{2}}} 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 d x - \int 5 d x - \int \frac{1}{x ^{\frac{3}{2}}} d x

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

\int 5 d x = 5 x

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

= \frac{x ^{2}}{2} - 5 x - (- \frac{2}{x})

Vereinfache

= \frac{x ^{2}}{2} - 5 x + \frac{2}{x}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} - 5 x + \frac{2}{x} + C

\int \frac{x}{144 x ^{2} - 1} d x

\int \frac{x}{x ^{2} - 4 x + 7} d x

n = 0 \sum \infty 3^{n} x^{n}

- 2 x^{\frac{3}{2}}

d er i v a t i v e y = 9 x^{3}