integral of (x+4)/(x^8)

Lösung

\int \frac{x + 4}{x ^{8}} d x

- \frac{1}{6 x ^{6}} - \frac{4}{7 x ^{7}} + C

Schritte zur Lösung

\int \frac{x + 4}{x ^{8}} d x

Multipliziere aus

\frac{x + 4}{x ^{8}} : \frac{1}{x ^{7}} + \frac{4}{x ^{8}}

= \int \frac{1}{x ^{7}} + \frac{4}{x ^{8}} 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 ^{7}} d x + \int \frac{4}{x ^{8}} d x

\int \frac{1}{x ^{7}} d x = - \frac{1}{6 x ^{6}}

\int \frac{4}{x ^{8}} d x = - \frac{4}{7 x ^{7}}

= - \frac{1}{6 x ^{6}} - \frac{4}{7 x ^{7}}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{6 x ^{6}} - \frac{4}{7 x ^{7}} + C

x \to 0 lim (\frac{1}{e ^{2 x} - 1})

x \to 2 lim (\frac{4 x}{x - 4})

\frac{d}{d x} (\frac{x + 2}{2 - x})

\frac{\partial}{\partial k} (ln (sin (\frac{x}{k})))

\int \frac{x ^{2}}{4 x ^{3} + 7} d x