integral 1/(x^2)log_{10}(x)

Lösung

integral

\frac{1}{x ^{2}} lo g_{10} (x)

\frac{lo g _{10} ( x )}{x} - \frac{2 ln ( x ) + 1}{ln ( 10 ) x} + C

Schritte zur Lösung

\int \frac{1}{x ^{2}} lo g_{10} (x) d x

Vereinfache

\frac{1}{x ^{2}} lo g_{10} (x) : \frac{lo g _{10} ( x )}{x ^{2}}

= \int \frac{lo g _{10} ( x )}{x ^{2}} d x

Wende die partielle Integration an

= \frac{lo g _{10} ( x )}{x} - \int \frac{1 - 2 ln ( x )}{ln ( 10 ) x ^{2}} d x

\int \frac{1 - 2 ln ( x )}{ln ( 10 ) x ^{2}} d x = \frac{2 ln ( x ) + 1}{ln ( 10 ) x}

= \frac{lo g _{10} ( x )}{x} - \frac{2 ln ( x ) + 1}{ln ( 10 ) x}

Füge eine Konstante zur Lösung hinzu

= \frac{lo g _{10} ( x )}{x} - \frac{2 ln ( x ) + 1}{ln ( 10 ) x} + C

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