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Beliebt Rechnen >

integral from 1/3 to 5 of 16xln(3x)

Lösung

\int_{\frac{1}{3}}^{5} 16 x ln (3 x) d x

Lösung

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

+1

Dezimale

442.05448 \dots

Schritte zur Lösung

\int_{\frac{1}{3}}^{5} 16 x ln (3 x) d x

Entferne die Konstante:

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

= 16 \cdot \int_{\frac{1}{3}}^{5} x ln (3 x) d x

Wende die partielle Integration an

= 16 [\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}

= 16 [\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)

= 16 (- \frac{56}{9} + \frac{25}{2} ln (15))

Graph

Beliebte Beispiele

tangent f(x)=x^2+4x-5,\at x=2

t an g e n t f (x) = x^{2} + 4 x - 5, at x = 2

integral of 1/(25-81x^2)

\int \frac{1}{25 - 81 x ^{2}} d x

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

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

integral from 0 to pi/8 of (sin(2x))

\int_{0}^{\frac{π}{8}} (sin (2 x)) d x

derivative of x/(x^{-1+5})

\frac{d}{d x} (\frac{x}{x ^{- 1} + 5})