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Beliebt Rechnen >

integral from 1 to 5 of (ln(x))/(x^5)

Lösung

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

Lösung

\frac{39}{625} - \frac{1}{2500} ln (5)

+1

Dezimale

0.06175 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

= [- \frac{ln ( x )}{4 x ^{4}} - \int - \frac{1}{4 x ^{5}} d x]_{1}^{5}

\int - \frac{1}{4 x ^{5}} d x = \frac{1}{16 x ^{4}}

= [- \frac{ln ( x )}{4 x ^{4}} - \frac{1}{16 x ^{4}}]_{1}^{5}

Berechne die Grenzen:

\frac{39}{625} - \frac{1}{2500} ln (5)

= \frac{39}{625} - \frac{1}{2500} ln (5)

Graph

Beliebte Beispiele

derivative f(x)=4x^3-11x^2-14x+19

d er i v a t i v e f (x) = 4 x^{3} - 11 x^{2} - 14 x + 19

limit as x approaches 0 of ((1+tan(x))/(1+sin(x)))^{1/(sin(x))}

x \to 0 lim ((\frac{1 + tan ( x )}{1 + sin ( x )})^{\frac{1}{s i n ( x )}})

derivative of (2x-x^2^3)

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

integral of (x^4)/((x^4-1))

\int \frac{x ^{4}}{( x ^{4} - 1 )} d x

derivative y=x^{7/5}+e^{-4x}

d er i v a t i v e y = x^{\frac{7}{5}} + e^{- 4 x}