integral of (log_{4}(x))/x

Lösung

\int \frac{lo g _{4} ( x )}{x} d x

lo g_{4} (x) ln ∣ x ∣ - \frac{ln ∣ x ∣ ^{2}}{4 ln ( 2 )} + C

Schritte zur Lösung

\int \frac{lo g _{4} ( x )}{x} d x

Wende die partielle Integration an

= lo g_{4} (x) ln ∣ x ∣ - \int \frac{ln ∣ x ∣}{2 ln ( 2 ) x} d x

\int \frac{ln ∣ x ∣}{2 ln ( 2 ) x} d x = \frac{ln ∣ x ∣ ^{2}}{4 ln ( 2 )}

= lo g_{4} (x) ln ∣ x ∣ - \frac{ln ∣ x ∣ ^{2}}{4 ln ( 2 )}

Füge eine Konstante zur Lösung hinzu

= lo g_{4} (x) ln ∣ x ∣ - \frac{ln ∣ x ∣ ^{2}}{4 ln ( 2 )} + C

x \to - 2 lim ((2 - x)^{2})

\frac{d}{d x} (arctan (ln (4) x^{5}))

a re a y = 10 x, y = x^{2} - 11, x

x^{^{''}} + 2 x^{^{'}} + 2 x = 2

\frac{d}{d x} (- 2 ln (cos (x)))