What is ln(1/2 |x+2+sqrt(x^2+4x+8)|)+C ?

The solution to ln(1/2 |x+2+sqrt(x^2+4x+8)|)+C is ln|x+sqrt(x^2+4x+8)+2|+C-ln(2)

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simplify ln(1/2 |x+2+sqrt(x^2+4x+8)|)+C

simplify

ln (\frac{1}{2} x + 2 + x^{2} + 4 x + 8) + C

ln x + x^{2} + 4 x + 8 + 2 + C - ln (2)

Solution steps

ln (\frac{1}{2} x + 2 + x^{2} + 4 x + 8) + C

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (\frac{1}{2} x + 2 + x^{2} + 4 x + 8) = ln (\frac{1}{2}) + ln x + 2 + x^{2} + 4 x + 8

= ln (\frac{1}{2}) + ln x + x^{2} + 4 x + 8 + 2 + C

Apply log rule:

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

ln (\frac{1}{2}) = ln (1) - ln (2)

= ln (1) - ln (2) + ln x + x^{2} + 4 x + 8 + 2 + C

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (2) + ln x + x^{2} + 4 x + 8 + 2 + C

0 - ln (2) + ln x + 2 + x^{2} + 4 x + 8 + C = - ln (2) + ln x + 2 + x^{2} + 4 x + 8 + C

= ln x + x^{2} + 4 x + 8 + 2 + C - ln (2)

- 0.03 \cdot ln (\frac{( 1 - 4.1 )}{82})

lo g_{10} (4 θ^{4} (1 - θ)^{4} (1 - 2 θ)^{2})

ln (x (x + 6))

ln (\frac{3}{2}) + ln (\frac{1}{2})

5 lo g_{2} (A) - lo g_{2} (B) + 3

What is ln(1/2 |x+2+sqrt(x^2+4x+8)|)+C ?
The solution to ln(1/2 |x+2+sqrt(x^2+4x+8)|)+C is ln|x+sqrt(x^2+4x+8)+2|+C-ln(2)