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Beliebt Rechnen >

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

Lösung

\int \frac{lo g _{10} ( x ^{3} )}{x} d x

Lösung

3 lo g_{10} (x) - \frac{1}{ln ( 10 )} (3 ln ∣ x ∣ - \frac{3}{2} ln^{2} (x)) + C

Schritte zur Lösung

\int \frac{lo g _{10} ( x ^{3} )}{x} d x

Wende die partielle Integration an

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

\int \frac{3 - ln ( x ^{3} )}{ln ( 10 ) x} d x = \frac{1}{ln ( 10 )} (3 ln ∣ x ∣ - \frac{3}{2} ln^{2} (x))

= lo g_{10} (x^{3}) - \frac{1}{ln ( 10 )} (3 ln ∣ x ∣ - \frac{3}{2} ln^{2} (x))

Wende log Regel an

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

angenommen

x \geq 0

= 3 lo g_{10} (x) - \frac{1}{ln ( 10 )} (3 ln ∣ x ∣ - \frac{3}{2} ln^{2} (x))

Füge eine Konstante zur Lösung hinzu

= 3 lo g_{10} (x) - \frac{1}{ln ( 10 )} (3 ln ∣ x ∣ - \frac{3}{2} ln^{2} (x)) + C

Graph

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