integral of (a^{2/3}-x^{2/3})^2

Lösung

\int (a^{\frac{2}{3}} - x^{\frac{2}{3}})^{2} d x

a^{\frac{4}{3}} x - \frac{6}{5} a^{\frac{2}{3}} x^{\frac{5}{3}} + \frac{3}{7} x^{\frac{7}{3}} + C

Schritte zur Lösung

\int (a^{\frac{2}{3}} - x^{\frac{2}{3}})^{2} d x

Multipliziere aus

(a^{\frac{2}{3}} - x^{\frac{2}{3}})^{2} : a^{\frac{4}{3}} - 2 a^{\frac{2}{3}} x^{\frac{2}{3}} + x^{\frac{4}{3}}

= \int a^{\frac{4}{3}} - 2 a^{\frac{2}{3}} x^{\frac{2}{3}} + x^{\frac{4}{3}} 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 a^{\frac{4}{3}} d x - \int 2 a^{\frac{2}{3}} x^{\frac{2}{3}} d x + \int x^{\frac{4}{3}} d x

\int a^{\frac{4}{3}} d x = a^{\frac{4}{3}} x

\int 2 a^{\frac{2}{3}} x^{\frac{2}{3}} d x = \frac{6}{5} a^{\frac{2}{3}} x^{\frac{5}{3}}

\int x^{\frac{4}{3}} d x = \frac{3}{7} x^{\frac{7}{3}}

= a^{\frac{4}{3}} x - \frac{6}{5} a^{\frac{2}{3}} x^{\frac{5}{3}} + \frac{3}{7} x^{\frac{7}{3}}

Füge eine Konstante zur Lösung hinzu

= a^{\frac{4}{3}} x - \frac{6}{5} a^{\frac{2}{3}} x^{\frac{5}{3}} + \frac{3}{7} x^{\frac{7}{3}} + C

\int cos^{2} (6 x) sin^{3} (6 x) d x

\int \frac{10}{5 - x} d x

ma c l a u r in \frac{1}{( 1 - x ) ^{2}}

\frac{\partial}{\partial x} (x^{2} + x y + 5 y)

x \to 2 lim (6 x^{2})