integral of (4-x^2)^{3/2}x

Lösung

\int (4 - x^{2})^{\frac{3}{2}} x d x

- \frac{1}{5} (4 - x^{2})^{\frac{5}{2}} + C

Schritte zur Lösung

\int (4 - x^{2})^{\frac{3}{2}} x d x

Wende U-Substitution an

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

Wende die Potenzregel an

= - \frac{1}{2} \cdot \frac{2}{5} u^{\frac{5}{2}}

Setze in

u = 4 - x^{2}

ein

= - \frac{1}{2} \cdot \frac{2}{5} (4 - x^{2})^{\frac{5}{2}}

Vereinfache

- \frac{1}{2} \cdot \frac{2}{5} (4 - x^{2})^{\frac{5}{2}} : - \frac{1}{5} (4 - x^{2})^{\frac{5}{2}}

= - \frac{1}{5} (4 - x^{2})^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{5} (4 - x^{2})^{\frac{5}{2}} + C

\frac{d}{d x} ((x) x^{2} cos (x))

x \to 0 lim ((1 + 2 x)^{\frac{6}{x}})

n = 2 \sum \infty ln (ln (n))

x \to 3 lim (3 x - 5)

\int + t ln (t + 5) d t