What is ln(x/((x^2+1)^{1/2)})+x ?

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

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simplify ln(x/((x^2+1)^{1/2)})+x

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

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

\frac{1}{2} ln (\frac{110}{125})

lo g_{8} (\frac{9 x ^{2}}{y ^{3}})

\frac{1}{3} ln (n^{2} + 8) - \frac{1}{3} ln (7 n^{2} + 5)

lo g_{2} (\frac{s ^{5}}{7 t ^{2}})

ln (\frac{e x + 1}{e x - 1})

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