integral of (x-1)/(x^3)

Lösung

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

- \frac{1}{x} + \frac{1}{2 x ^{2}} + C

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

= - \frac{1}{x} - (- \frac{1}{2 x ^{2}})

Vereinfache

= - \frac{1}{x} + \frac{1}{2 x ^{2}}

Füge eine Konstante zur Lösung hinzu

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

f (y) = 2 e^{y}

x \to - 4 lim (\frac{\frac{4}{x} + 1}{x + 4})

\int_{0}^{1} 1 + (- 2 x)^{2} d x

t an g e n t f (x) = x^{2} + 5, (3, 14)

d er i v a t i v e \frac{x}{4} - \frac{4}{x}