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

Lösung

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

- \frac{2}{5 x ^{5}} + \frac{5}{4 x ^{4}} + C

Schritte zur Lösung

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

Multipliziere aus

\frac{2 - 5 x}{x ^{6}} : \frac{2}{x ^{6}} - \frac{5}{x ^{5}}

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

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

\int \frac{5}{x ^{5}} d x = - \frac{5}{4 x ^{4}}

= - \frac{2}{5 x ^{5}} - (- \frac{5}{4 x ^{4}})

Vereinfache

= - \frac{2}{5 x ^{5}} + \frac{5}{4 x ^{4}}

Füge eine Konstante zur Lösung hinzu

= - \frac{2}{5 x ^{5}} + \frac{5}{4 x ^{4}} + C

\frac{d y}{d x} + \frac{2 x y}{x ^{2} + 1} = x

t an g e n t \frac{3}{x ^{2}}

\int \frac{1}{x ^{2} x ^{2} + 9} d x

x \to 3 lim (7 x + ∣ x - 3 ∣)

\frac{\partial}{\partial x} (e^{y} + x e^{x y})