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Beliebt Rechnen >

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

Lösung

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

Lösung

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

+1

Dezimale

213.12854 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die partielle Integration an

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

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

= 4 [\frac{1}{3} x^{3} ln (x) - \frac{x ^{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

f^'(x)=2sin(6x),f(pi/6)=-5/2

f^{^{'}} (x) = 2 sin (6 x), f (\frac{π}{6}) = - \frac{5}{2}

limit as x approaches 1 of sin(5pix)

x \to 1 lim (sin (5 p i x))

limit as x approaches 1+of (x^2+1)/(x-1)

x \to 1 + lim (\frac{x ^{2} + 1}{x - 1})

derivative 8x^3+2x+7x^{1/3}

d er i v a t i v e 8 x^{3} + 2 x + 7 x^{\frac{1}{3}}

integral of e^x+xe^x

\int e^{x} + x e^{x} d x