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Beliebt Rechnen >

integral of x^5sqrt(11+x^6)

Lösung

\int x^{5} 11 + x^{6} d x

Lösung

\frac{1}{9} (11 + x^{6})^{\frac{3}{2}} + C

Schritte zur Lösung

\int x^{5} 11 + x^{6} d x

Wende U-Substitution an

= \int \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 u d u

Wende die Potenzregel an

= \frac{1}{6} \cdot \frac{2}{3} u^{\frac{3}{2}}

Setze in

u = 11 + x^{6}

ein

= \frac{1}{6} \cdot \frac{2}{3} (11 + x^{6})^{\frac{3}{2}}

Vereinfache

\frac{1}{6} \cdot \frac{2}{3} (11 + x^{6})^{\frac{3}{2}} : \frac{1}{9} (11 + x^{6})^{\frac{3}{2}}

= \frac{1}{9} (11 + x^{6})^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{9} (11 + x^{6})^{\frac{3}{2}} + C

Graph

Beliebte Beispiele

integral of u/(1+u^2)

\int \frac{u}{1 + u ^{2}} d u

limit as x approaches ln(2) of e^{2x}

x \to l n (2) lim (e^{2 x})

inverselaplace 1/((s+65))

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derivative f(x)=5x^3+8

d er i v a t i v e f (x) = 5 x^{3} + 8

limit as x approaches 0 of (-1)/(x^3)

x \to 0 lim (\frac{- 1}{x ^{3}})