integral of x^3log_{10}(x)

Lösung

\int x^{3} lo g_{10} (x) d x

\frac{1}{4} x^{4} lo g_{10} (x) - \frac{x ^{4}}{16 ln ( 10 )} + C

Schritte zur Lösung

\int x^{3} lo g_{10} (x) d x

Wende die partielle Integration an

= \frac{1}{4} x^{4} lo g_{10} (x) - \int \frac{x ^{3}}{4 ln ( 10 )} d x

\int \frac{x ^{3}}{4 ln ( 10 )} d x = \frac{x ^{4}}{16 ln ( 10 )}

= \frac{1}{4} x^{4} lo g_{10} (x) - \frac{x ^{4}}{16 ln ( 10 )}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{4} x^{4} lo g_{10} (x) - \frac{x ^{4}}{16 ln ( 10 )} + C

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