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

The solution to 1/3 ln((|3x+sqrt(16+9x^2)|)/4)+C is 1/3 (ln|3x+sqrt(16+9x^2)|-2ln(2))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

simplify

\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

Solution steps

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

Apply log rule:

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

ln ((0.5 + \frac{0.044315}{2}) (1.05))

3 (- \frac{1}{6} ln ∣ x + 2 ∣ + \frac{1}{6} ln ∣ x - 4 ∣) + C

lo g_{3} ((2 x)^{2})

ln (\frac{1}{a b ^{3}})

ln ((\frac{2}{a ^{3}})^{4})

What is 1/3 ln((|3x+sqrt(16+9x^2)|)/4)+C ?
The solution to 1/3 ln((|3x+sqrt(16+9x^2)|)/4)+C is 1/3 (ln|3x+sqrt(16+9x^2)|-2ln(2))+C