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Beliebt Rechnen >

integral from 3 to 9 of 1/(xln(x))

Lösung

\int_{3}^{9} \frac{1}{x ln ( x )} d x

Lösung

ln (2)

+1

Dezimale

0.69314 \dots

Schritte zur Lösung

\int_{3}^{9} \frac{1}{x ln ( x )} d x

Wende U-Substitution an

= \int_{l n (3)}^{2 l n (3)} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{l n (3)}^{2 l n (3)}

Berechne die Grenzen:

ln (2 ln (3)) - ln (ln (3))

= ln (2 ln (3)) - ln (ln (3))

Vereinfache

= ln (2)

Graph

Beliebte Beispiele

tangent y=sqrt(2x+1),\at x= 1/2

t an g e n t y = 2 x + 1, at x = \frac{1}{2}

(\partial)/(\partial x)(2/((x-3t)^2+1))

\frac{\partial}{\partial x} (\frac{2}{( x - 3 t ) ^{2} + 1})

integral of (x-4)

\int (x - 4) d x

d/(dθ)(5/(2cos(θ)+7sin(θ)))

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tangent f(x)=3x^4-8x^3+2

t an g e n t f (x) = 3 x^{4} - 8 x^{3} + 2