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Beliebt Rechnen >

integral from 1 to 3 of r^4ln(r)

Lösung

\int_{1}^{3} r^{4} ln (r) d r

Lösung

- \frac{242}{25} + \frac{243}{5} ln (3)

+1

Dezimale

43.71255 \dots

Schritte zur Lösung

\int_{1}^{3} r^{4} ln (r) d r

Wende die partielle Integration an

= [\frac{1}{5} r^{5} ln (r) - \int \frac{r ^{4}}{5} d r]_{1}^{3}

\int \frac{r ^{4}}{5} d r = \frac{r ^{5}}{25}

= [\frac{1}{5} r^{5} ln (r) - \frac{r ^{5}}{25}]_{1}^{3}

Berechne die Grenzen:

- \frac{242}{25} + \frac{243}{5} ln (3)

= - \frac{242}{25} + \frac{243}{5} ln (3)

Graph

Beliebte Beispiele

integral from 1 to 1 of 1/t

\int_{1}^{1} \frac{1}{t} d t

integral from 0 to 1 of 3e^x

\int_{0}^{1} 3 e^{x} d x

integral from 0 to pi/2 of 1 (sin^7(x))

\int_{0}^{\frac{π}{2}} \frac{d}{1} (sin^{7} (x)) d x

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\int_{0}^{6} x^{2} + x d x

integral from 1 to e^2 of sqrt(x)ln(x)

\int_{1}^{e^{2}} x ln (x) d x