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Beliebt Rechnen >

integral from 0 to 3 of sqrt(x^4+1)x^3

Lösung

\int_{0}^{3} x^{4} + 1 x^{3} d x

Lösung

\frac{82 82 - 1}{6}

+1

Dezimale

123.59026 \dots

Schritte zur Lösung

\int_{0}^{3} x^{4} + 1 x^{3} d x

Wende U-Substitution an

= \int_{1}^{82} \frac{u}{4} d u

Entferne die Konstante:

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

= \frac{1}{4} \cdot \int_{1}^{82} u d u

Wende die Potenzregel an

= \frac{1}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{82}

Berechne die Grenzen:

\frac{164 82}{3} - \frac{2}{3}

= \frac{1}{4} (\frac{164 82}{3} - \frac{2}{3})

Vereinfache

= \frac{82 82 - 1}{6}

Graph

Beliebte Beispiele

integral of (x^2+8x+1)/(x^3+12x^2+3x+6)

\int \frac{x ^{2} + 8 x + 1}{x ^{3} + 12 x ^{2} + 3 x + 6} d x

integral of (-4y-1)/(y+1)

\int \frac{- 4 y - 1}{y + 1} d y

derivative f(x)=sqrt(x)(3x-1)

d er i v a t i v e f (x) = x (3 x - 1)

derivative of (3x+4^6)

\frac{d}{d x} ((3 x + 4)^{6})

derivative of-e^{7x}

\frac{d}{d x} (- e^{7 x})