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Beliebt Rechnen >

integral from 1 to 5 of (ln(x))/(x^7)

Lösung

\int_{1}^{5} \frac{ln ( x )}{x ^{7}} d x

Lösung

\frac{434}{15625} - \frac{1}{93750} ln (5)

+1

Dezimale

0.02775 \dots

Schritte zur Lösung

\int_{1}^{5} \frac{ln ( x )}{x ^{7}} d x

Wende die partielle Integration an

= [- \frac{ln ( x )}{6 x ^{6}} - \int - \frac{1}{6 x ^{7}} d x]_{1}^{5}

\int - \frac{1}{6 x ^{7}} d x = \frac{1}{36 x ^{6}}

= [- \frac{ln ( x )}{6 x ^{6}} - \frac{1}{36 x ^{6}}]_{1}^{5}

Berechne die Grenzen:

\frac{434}{15625} - \frac{1}{93750} ln (5)

= \frac{434}{15625} - \frac{1}{93750} ln (5)

Graph

Beliebte Beispiele

derivative of 3/2 x^{5/3}-(\sqrt[5]{x}/4+7x^2-6/(x^5)+6)

\frac{d}{d x} (\frac{3}{2} x^{\frac{5}{3}} - \frac{5 x}{4} + 7 x^{2} - \frac{6}{x ^{5}} + 6)

y=(3x-2x^2)^3(dy)/(dx)

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

(dy)/(dx)=x^7e^{x^8}

\frac{d y}{d x} = x^{7} e^{x^{8}}

limit as x approaches 0 of xe^{1/x}

x \to 0 lim (x e^{\frac{1}{x}})

integral of 3/(x^2+10x+29)

\int \frac{3}{x ^{2} + 10 x + 29} d x