integral of \sqrt[3]{1-x^2}x

Lösung

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

- \frac{3}{8} (1 - x^{2})^{\frac{4}{3}} + C

Schritte zur Lösung

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

Wende U-Substitution an

= \int - \frac{3 u}{2} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \frac{1}{2} \cdot \int 3 u d u

Wende die Potenzregel an

= - \frac{1}{2} \cdot \frac{3}{4} u^{\frac{4}{3}}

Setze in

u = 1 - x^{2}

ein

= - \frac{1}{2} \cdot \frac{3}{4} (1 - x^{2})^{\frac{4}{3}}

Vereinfache

- \frac{1}{2} \cdot \frac{3}{4} (1 - x^{2})^{\frac{4}{3}} : - \frac{3}{8} (1 - x^{2})^{\frac{4}{3}}

= - \frac{3}{8} (1 - x^{2})^{\frac{4}{3}}

Füge eine Konstante zur Lösung hinzu

= - \frac{3}{8} (1 - x^{2})^{\frac{4}{3}} + C

\int cos (x) sin (x) d x

x \to - 5 lim (\frac{∣ x + 5 ∣}{x + 5})

a re a y = \frac{4}{x}, y = \frac{4}{x ^{2}}, x = 5

\int 1 + \frac{1}{x} d x

\frac{d}{d x} (6 e^{5 x} + e^{- x^{2}})