integral of (log_{10}(x))^2

Lösung

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

x lo g_{10} (x)^{2} - \frac{2}{ln ^{2} ( 10 )} (x ln (x) - x) + C

Schritte zur Lösung

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

Vereinfache

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

Wende die partielle Integration an

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

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

= x lo g_{10} (x)^{2} - \frac{2}{ln ^{2} ( 10 )} (x ln (x) - x)

Füge eine Konstante zur Lösung hinzu

= x lo g_{10} (x)^{2} - \frac{2}{ln ^{2} ( 10 )} (x ln (x) - x) + C

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