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Beliebt Rechnen >

integral from 1/3 to 5 of 8xln(3x)

Lösung

\int_{\frac{1}{3}}^{5} 8 x ln (3 x) d x

Lösung

8 (- \frac{56}{9} + \frac{25}{2} ln (15))

+1

Dezimale

221.02724 \dots

Schritte zur Lösung

\int_{\frac{1}{3}}^{5} 8 x ln (3 x) d x

Entferne die Konstante:

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

= 8 \cdot \int_{\frac{1}{3}}^{5} x ln (3 x) d x

Wende die partielle Integration an

= 8 [\frac{1}{2} x^{2} ln (3 x) - \int \frac{x}{2} d x]_{\frac{1}{3}}^{5}

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

= 8 [\frac{1}{2} x^{2} ln (3 x) - \frac{x ^{2}}{4}]_{\frac{1}{3}}^{5}

Berechne die Grenzen:

- \frac{56}{9} + \frac{25}{2} ln (15)

= 8 (- \frac{56}{9} + \frac{25}{2} ln (15))

Graph

Beliebte Beispiele

derivative of ln(sin(x^2))

\frac{d}{d x} (ln (sin (x^{2})))

derivative of 1/(f(x^2(x)))

\frac{d}{d x} (\frac{1}{f ( x ) ^{2} ( x )})

steigung-10x^3+6x^{40}y+y^4=3

s l o p e - 10 x^{3} + 6 x^{40} y + y^{4} = 3

integral of (x^3)/(1-x^2)

\int \frac{x ^{3}}{1 - x ^{2}} d x

limit as x approaches 4-of 2-x-x^2

x \to 4 - lim (2 - x - x^{2})