integral of sqrt((x^2-2)/(x^8))

Lösung

\int \frac{x ^{2} - 2}{x ^{8}} d x

- \frac{x ^{2} - 2}{3 x ^{3}} + \frac{x ^{2} - 2}{6 x} + C

Schritte zur Lösung

\int \frac{x ^{2} - 2}{x ^{8}} d x

Vereinfache

\frac{x ^{2} - 2}{x ^{8}} : \frac{x ^{2} - 2}{x ^{4}}

= \int \frac{x ^{2} - 2}{x ^{4}} d x

Wende die partielle Integration an

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

\int - \frac{1}{3 x ^{2} x ^{2} - 2} d x = - \frac{x ^{2} - 2}{6 x}

= - \frac{x ^{2} - 2}{3 x ^{3}} - (- \frac{x ^{2} - 2}{6 x})

Vereinfache

= - \frac{x ^{2} - 2}{3 x ^{3}} + \frac{x ^{2} - 2}{6 x}

Füge eine Konstante zur Lösung hinzu

= - \frac{x ^{2} - 2}{3 x ^{3}} + \frac{x ^{2} - 2}{6 x} + C

\int \frac{cos ^{5} ( α )}{sin ( α )} d α

\frac{d}{d x} (3 sin (x))

x \to 1 lim (e^{2 x})

a re a f (x) = - 4 x^{2} - 4, g (x) = 2 x^{2} - 9

\frac{d}{d x} (- 3 ln (cos (\frac{x}{3})))