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Beliebt Rechnen >

integral from 1/7 to 3 of 8xln(7x)

Lösung

\int_{\frac{1}{7}}^{3} 8 x ln (7 x) d x

Lösung

8 (- \frac{110}{49} + \frac{9}{2} ln (21))

+1

Dezimale

91.64362 \dots

Schritte zur Lösung

\int_{\frac{1}{7}}^{3} 8 x ln (7 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}{7}}^{3} x ln (7 x) d x

Wende die partielle Integration an

= 8 [\frac{1}{2} x^{2} ln (7 x) - \int \frac{x}{2} d x]_{\frac{1}{7}}^{3}

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

= 8 [\frac{1}{2} x^{2} ln (7 x) - \frac{x ^{2}}{4}]_{\frac{1}{7}}^{3}

Berechne die Grenzen:

- \frac{110}{49} + \frac{9}{2} ln (21)

= 8 (- \frac{110}{49} + \frac{9}{2} ln (21))

Graph

Beliebte Beispiele

tangent y=3x+6cos(x),\at (pi/3)

t an g e n t y = 3 x + 6 cos (x), at (\frac{π}{3})

inverselaplace s/(s^2+2s+3)

in v erse l a pl a ce \frac{s}{s ^{2} + 2 s + 3}

derivative f(x)=(2x^3-3x+1)/x

d er i v a t i v e f (x) = \frac{2 x ^{3} - 3 x + 1}{x}

steigung y=x^2-2

s l o p e y = x^{2} - 2

laplacetransform e^{-t}(t^2)

l a pl a ce t r an s f or m e^{- t} (t^{2})