化简 2ln|x|-ln|x^2+1|+arctan(x)+1/(x^2+1)

解答

化简

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

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

求解步骤

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

使用对数计算法则:

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

2 ln ∣ x ∣ = ln (∣ x ∣^{2})

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

使用对数计算法则:

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

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

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

∣ x ∣^{2} = x^{2}

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

s im pl i f y ln (x) - 3 ln (y) - ln (4)

s im pl i f y ln (6 + x^{2}) - ln (3 + x)

s im pl i f y lo g_{10} (4 x^{4} \cdot (1 - x)^{4} \cdot (1 - 2 x)^{2})

s im pl i f y ln ∣ x ∣ - ln (x^{2} + 1)

e x p an d ln (\frac{( x + 3 ) ^{3}}{4 x})^{- 2}