integral of ((x+1)^3)/((x)^{10)}

Lösung

\int \frac{( x + 1 ) ^{3}}{( x ) ^{10}} d x

- \frac{1}{6 x ^{6}} - \frac{3}{7 x ^{7}} - \frac{3}{8 x ^{8}} - \frac{1}{9 x ^{9}} + C

Schritte zur Lösung

\int \frac{( x + 1 ) ^{3}}{x ^{10}} d x

Multipliziere aus

\frac{( x + 1 ) ^{3}}{x ^{10}} : \frac{1}{x ^{7}} + \frac{3}{x ^{8}} + \frac{3}{x ^{9}} + \frac{1}{x ^{10}}

= \int \frac{1}{x ^{7}} + \frac{3}{x ^{8}} + \frac{3}{x ^{9}} + \frac{1}{x ^{10}} 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{3}{x ^{8}} d x + \int \frac{3}{x ^{9}} d x + \int \frac{1}{x ^{10}} d x

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

\int \frac{3}{x ^{8}} d x = - \frac{3}{7 x ^{7}}

\int \frac{3}{x ^{9}} d x = - \frac{3}{8 x ^{8}}

\int \frac{1}{x ^{10}} d x = - \frac{1}{9 x ^{9}}

= - \frac{1}{6 x ^{6}} - \frac{3}{7 x ^{7}} - \frac{3}{8 x ^{8}} - \frac{1}{9 x ^{9}}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{6 x ^{6}} - \frac{3}{7 x ^{7}} - \frac{3}{8 x ^{8}} - \frac{1}{9 x ^{9}} + C