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Beliebt Rechnen >

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

Lösung

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

Lösung

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

+1

Dezimale

87.42511 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die partielle Integration an

= 2 [\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}

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

Berechne die Grenzen:

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

= 2 (- \frac{242}{25} + \frac{243}{5} ln (3))

Graph

Beliebte Beispiele

steigung (-4,-4),(2,5)

s l o p e (- 4, - 4), (2, 5)

integral of (4x-3)(2x-1)

\int (4 x - 3) (2 x - 1) d x

(\partial)/(\partial x)(x^3y+xy^2-2x^2-y^2)

\frac{\partial}{\partial x} (x^{3} y + x y^{2} - 2 x^{2} - y^{2})

integral of (x-1)/(x+2)

\int \frac{x - 1}{x + 2} d x

derivative f(x)=8x^3

d er i v a t i v e f (x) = 8 x^{3}