integral from 0 to a^{1/3 of}x^5sqrt(x^6+a^2)

Lösung

\int_{0}^{a^{\frac{1}{3}}} x^{5} x^{6} + a^{2} d x

\frac{( 2 2 - 1 ) a ^{3}}{9}

Schritte zur Lösung

\int_{0}^{a^{\frac{1}{3}}} x^{5} x^{6} + a^{2} d x

Wende U-Substitution an

= \int_{a^{2}}^{2 a^{2}} \frac{u}{6} d u

Entferne die Konstante:

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

= \frac{1}{6} \cdot \int_{a^{2}}^{2 a^{2}} u d u

Wende die Potenzregel an

= \frac{1}{6} [\frac{2}{3} u^{\frac{3}{2}}]_{a^{2}}^{2 a^{2}}

Berechne die Grenzen:

\frac{4 2 - 2}{3} a^{3}

= \frac{1}{6} \cdot \frac{4 2 - 2}{3} a^{3}

Vereinfache

= \frac{( 2 2 - 1 ) a ^{3}}{9}

\int_{- 5}^{5} x - 25 - x^{2} d x

\int_{\frac{1}{2}}^{1} (x^{- 3} - 19) d x

\int_{2}^{4} \frac{x}{x - 1} d x

\int_{1}^{5} \frac{1}{x ^{2} + 1} d x

\int_{0}^{1} 4 + 5 x d x