What is 3ln(x)+1/x+ln(x+1)+c ?

The solution to 3ln(x)+1/x+ln(x+1)+c is ln(x^3(x+1))+1/x+c

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simplify 3ln(x)+1/x+ln(x+1)+c

simplify

3 ln (x) + \frac{1}{x} + ln (x + 1) + c

ln (x^{3} (x + 1)) + \frac{1}{x} + c

Solution steps

3 ln (x) + \frac{1}{x} + ln (x + 1) + c

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 ln (x) = ln (x^{3})

= ln (x^{3}) + \frac{1}{x} + ln (x + 1) + c

Apply log rule:

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

ln (x^{3}) + ln (x + 1) = ln (x^{3} (x + 1))

= ln (x^{3} (x + 1)) + \frac{1}{x} + c

lo g_{10} (\frac{( 4 \cdot 1 0 ^{- 7} )}{( 1 0 ^{- 12} )})

ln (\frac{41}{140})

2 lo g_{10} (6) - 0.5 lo g_{10} (9)

lo g_{10} (60 e^{0.032 \cdot 5})

3 ln (x + 5) - ln (x + 2)

What is 3ln(x)+1/x+ln(x+1)+c ?
The solution to 3ln(x)+1/x+ln(x+1)+c is ln(x^3(x+1))+1/x+c