integral of (x^6-1/(x^6))^2

Lösung

\int (x^{6} - \frac{1}{x ^{6}})^{2} d x

\frac{x ^{13}}{13} - 2 x - \frac{1}{11 x ^{11}} + C

Schritte zur Lösung

\int (x^{6} - \frac{1}{x ^{6}})^{2} d x

Vereinfache

(x^{6} - \frac{1}{x ^{6}})^{2} : x^{12} - 2 + \frac{1}{x ^{12}}

= \int x^{12} - 2 + \frac{1}{x ^{12}} 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^{12} d x - \int 2 d x + \int \frac{1}{x ^{12}} d x

\int x^{12} d x = \frac{x ^{13}}{13}

\int 2 d x = 2 x

\int \frac{1}{x ^{12}} d x = - \frac{1}{11 x ^{11}}

= \frac{x ^{13}}{13} - 2 x - \frac{1}{11 x ^{11}}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{13}}{13} - 2 x - \frac{1}{11 x ^{11}} + C

\int e^{\frac{x}{9}} d x

θ \to 0 lim (\frac{cos ( θ ) - 1}{sin ( θ )})

a re a y = x^{3} + x^{2}, y = 6 x

l a pl a ce t r an s f or m f (t) = 2 t^{4}

\frac{d}{d x} (\frac{e ^{x}}{5 x ^{2} + 1})