integral of (1/(x^9)-x^9-1/8)

Lösung

\int (\frac{1}{x ^{9}} - x^{9} - \frac{1}{8}) d x

- \frac{1}{8 x ^{8}} - \frac{x ^{10}}{10} - \frac{1}{8} x + C

Schritte zur Lösung

\int \frac{1}{x ^{9}} - x^{9} - \frac{1}{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 ^{9}} d x - \int x^{9} d x - \int \frac{1}{8} d x

\int \frac{1}{x ^{9}} d x = - \frac{1}{8 x ^{8}}

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

\int \frac{1}{8} d x = \frac{1}{8} x

= - \frac{1}{8 x ^{8}} - \frac{x ^{10}}{10} - \frac{1}{8} x

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{8 x ^{8}} - \frac{x ^{10}}{10} - \frac{1}{8} x + C

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

\int x^{2} (4 - x) d x

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

\frac{d}{d x} (20 x - x^{2})

\frac{d x}{d t} = \frac{3}{2} t cos^{2} (x), x (0) = - 1.4