integral of (1/(x^5)-x^5-1/4)

Lösung

\int (\frac{1}{x ^{5}} - x^{5} - \frac{1}{4}) d x

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

Schritte zur Lösung

\int \frac{1}{x ^{5}} - x^{5} - \frac{1}{4} 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 ^{5}} d x - \int x^{5} d x - \int \frac{1}{4} d x

\int \frac{1}{x ^{5}} d x = - \frac{1}{4 x ^{4}}

\int x^{5} d x = \frac{x ^{6}}{6}

\int \frac{1}{4} d x = \frac{1}{4} x

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

Füge eine Konstante zur Lösung hinzu

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

\int 2 y e^{- y^{2}} d y

in v erse l a pl a ce \frac{1}{s ^{2}} e^{- s}

x \to 2 lim (2 x + 1)

\frac{\partial}{\partial y} (2^{x} + 2^{y})

x \to 2 lim (\frac{x - 3}{x ^{2} - 9})