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Beliebt Rechnen >

integral from 0 to 7 of 2x\sqrt[3]{x+1}

Lösung

\int_{0}^{7} 2 x 3 x + 1 d x

Lösung

\frac{1209}{14}

+1

Dezimale

86.35714 \dots

Schritte zur Lösung

\int_{0}^{7} 2 x 3 x + 1 d x

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{7} x 3 x + 1 d x

Wende U-Substitution an

= 2 \cdot \int_{1}^{8} (u - 1) 3 u d u

Multipliziere aus

(u - 1) 3 u : u^{\frac{4}{3}} - 3 u

= 2 \cdot \int_{1}^{8} u^{\frac{4}{3}} - 3 u d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 2 (\int_{1}^{8} u^{\frac{4}{3}} d u - \int_{1}^{8} 3 u d u)

\int_{1}^{8} u^{\frac{4}{3}} d u = \frac{381}{7}

\int_{1}^{8} 3 u d u = \frac{45}{4}

= 2 (\frac{381}{7} - \frac{45}{4})

Vereinfache

2 (\frac{381}{7} - \frac{45}{4}) : \frac{1209}{14}

= \frac{1209}{14}

Graph

Beliebte Beispiele

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\int \frac{1}{sin ^{5} ( x )} d x

derivative f(x)=sqrt(x)+1/(sqrt(x^3))

d er i v a t i v e f (x) = x + \frac{1}{x ^{3}}

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a re a x = 2 y, x = y^{2} - 3

integral of 2x^2+5x

\int 2 x^{2} + 5 x d x

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