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

Lösung

integral

lo g_{10} (x^{2} + 1)

x lo g_{10} (x^{2} + 1) - \frac{2}{ln ( 10 )} (- arctan (x) + x) + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

= x lo g_{10} (x^{2} + 1) - \frac{2}{ln ( 10 )} (- arctan (x) + x)

Füge eine Konstante zur Lösung hinzu

= x lo g_{10} (x^{2} + 1) - \frac{2}{ln ( 10 )} (- arctan (x) + x) + C

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