What is sqrt(x^2+1)-ln((1+sqrt(x^2+1))/x) ?

The solution to sqrt(x^2+1)-ln((1+sqrt(x^2+1))/x) is sqrt(x^2+1)-ln(1+sqrt(x^2+1))+ln(x)

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simplify sqrt(x^2+1)-ln((1+sqrt(x^2+1))/x)

simplify

x^{2} + 1 - ln (\frac{1 + x ^{2} + 1}{x})

x^{2} + 1 - ln (1 + x^{2} + 1) + ln (x)

Solution steps

x^{2} + 1 - ln (\frac{1 + x ^{2} + 1}{x})

Apply log rule:

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

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

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

- (ln (1 + x^{2} + 1) - ln (x)) : - ln (1 + x^{2} + 1) + ln (x)

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

\frac{1}{2} ln ∣ x - 3 ∣ - \frac{1}{x - 3} + \frac{1}{2} ln ∣ x + 3 ∣ + C

ln (5) + 3 ln (4) - ln (8)

- lo g_{10} (8.41 \cdot 1 0^{- 4})

ln (\frac{p}{x})

lo g_{10} (\frac{x ^{3} y}{x ^{3}})

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