integral of x^7-1/(x^7)

Lösung

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

\frac{x ^{8}}{8} + \frac{1}{6 x ^{6}} + C

Schritte zur Lösung

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

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

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

= \frac{x ^{8}}{8} - (- \frac{1}{6 x ^{6}})

Vereinfache

= \frac{x ^{8}}{8} + \frac{1}{6 x ^{6}}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{8}}{8} + \frac{1}{6 x ^{6}} + C

\frac{\partial}{\partial x} (\frac{100}{6 x ^{2} + y ^{2}})

d er i v a t i v e \frac{1}{3 x}

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

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

\int_{- 1}^{3} 3 x^{2} d x