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Beliebt Rechnen >

integral from 1 to 5 of 4r^2ln(r)

Lösung

\int_{1}^{5} 4 r^{2} ln (r) d r

Lösung

4 (- \frac{124}{9} + \frac{125}{3} ln (5))

+1

Dezimale

213.12854 \dots

Schritte zur Lösung

\int_{1}^{5} 4 r^{2} ln (r) d r

Entferne die Konstante:

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

= 4 \cdot \int_{1}^{5} r^{2} ln (r) d r

Wende die partielle Integration an

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

\int \frac{r ^{2}}{3} d r = \frac{r ^{3}}{9}

= 4 [\frac{1}{3} r^{3} ln (r) - \frac{r ^{3}}{9}]_{1}^{5}

Berechne die Grenzen:

- \frac{124}{9} + \frac{125}{3} ln (5)

= 4 (- \frac{124}{9} + \frac{125}{3} ln (5))

Graph

Beliebte Beispiele

derivative f(x)= x/(x^2-x)

d er i v a t i v e f (x) = \frac{x}{x ^{2} - x}

integral of (x^3-6x-9)

\int (x^{3} - 6 x - 9) d x

derivative f(x)=(4x)/((x-9)^5)

d er i v a t i v e f (x) = \frac{4 x}{( x - 9 ) ^{5}}

taylor ln(4x),1

t a y l or ln (4 x), 1

integral of sqrt((2-x)/(2+x))

\int \frac{2 - x}{2 + x} d x