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Beliebt Rechnen >

integral from 1 to 4 of (ln(x))/(x^4)

Lösung

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

Lösung

\frac{7}{64} - \frac{1}{96} ln (2)

+1

Dezimale

0.10215 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int - \frac{1}{3 x ^{4}} d x = \frac{1}{9 x ^{3}}

= [- \frac{ln ( x )}{3 x ^{3}} - \frac{1}{9 x ^{3}}]_{1}^{4}

Berechne die Grenzen:

\frac{7}{64} - \frac{1}{96} ln (2)

= \frac{7}{64} - \frac{1}{96} ln (2)

Graph

Beliebte Beispiele

integral from 0 to 4-y^2 of 1

\int_{0}^{4 - y^{2}} 1

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

\int_{0}^{2 π} 2 sin (2 x) d x

integral from 10 to-6 of 1

\int_{10}^{- 6} 1

integral from 0 to 3 of x-3

\int_{0}^{3} x - 3 d x

integral from 0 to 4 of sqrt(4r^2+1)r

\int_{0}^{4} 4 r^{2} + 1 r d r