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Beliebt Rechnen >

integral from 1 to 2 of 3r^4ln(r)

Lösung

\int_{1}^{2} 3 r^{4} ln (r) d r

Lösung

3 (- \frac{31}{25} + \frac{32}{5} ln (2))

+1

Dezimale

9.58842 \dots

Schritte zur Lösung

\int_{1}^{2} 3 r^{4} ln (r) d r

Entferne die Konstante:

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

= 3 \cdot \int_{1}^{2} r^{4} ln (r) d r

Wende die partielle Integration an

= 3 [\frac{1}{5} r^{5} ln (r) - \int \frac{r ^{4}}{5} d r]_{1}^{2}

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

= 3 [\frac{1}{5} r^{5} ln (r) - \frac{r ^{5}}{25}]_{1}^{2}

Berechne die Grenzen:

- \frac{31}{25} + \frac{32}{5} ln (2)

= 3 (- \frac{31}{25} + \frac{32}{5} ln (2))

Graph

Beliebte Beispiele

integral of (3x)/(4-2x^2)

\int \frac{3 x}{4 - 2 x ^{2}} d x

derivative of-(25000/(x^2)+10)

\frac{d}{d x} (- \frac{25000}{x ^{2}} + 10)

derivative of (4x^5+5/(x^3))

\frac{d}{d x} (\frac{4 x ^{5} + 5}{x ^{3}})

integral from 2 to 7 of 1/(sqrt(x^2-4))

\int_{2}^{7} \frac{1}{x ^{2} - 4} d x

derivative (25)/(t^2)-5/t

d er i v a t i v e \frac{25}{t ^{2}} - \frac{5}{t}