vereinfachen 1/3 ln((|3x+sqrt(16+9x^2)|)/4)+C

Lösung

vereinfachen

\frac{1}{3} ln (\frac{3 x + 16 + 9 x ^{2}}{4}) + C

\frac{1}{3} (ln 3 x + 16 + 9 x^{2} - 2 ln (2)) + C

Schritte zur Lösung

\frac{1}{3} ln (\frac{3 x + 16 + 9 x ^{2}}{4}) + C

Wende die log Regel an:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{3 x + 16 + 9 x ^{2}}{4}) = ln 3 x + 16 + 9 x^{2} - ln (4)

= \frac{1}{3} (ln 3 x + 9 x^{2} + 16 - ln (4)) + C

ln (4) = 2 ln (2)

= \frac{1}{3} (ln 3 x + 9 x^{2} + 16 - 2 ln (2)) + C

s im pl i f y ln ((0.5 + \frac{0.044315}{2}) (1.05))

s im pl i f y 3 (- \frac{1}{6} ln ∣ x + 2 ∣ + \frac{1}{6} ln ∣ x - 4 ∣) + C

e x p an d lo g_{3} ((2 x)^{2})

e x p an d ln ((\frac{2}{a ^{3}})^{4})

e x p an d lo g_{10} (\frac{a ^{4}}{b ^{2} c ^{3}})