设f（x方-1）=ln(x方/x方-2),且f[φ（x）]=lnx,求∫φ（x）dx

设f（x方-1）=ln(x方/x方-2),且f[φ（x）]=lnx,求∫φ（x）dx
设f（x方-1）=ln(x方/x方-2),且f[φ（x）]=lnx,求∫φ（x）dx

设f（x方-1）=ln(x方/x方-2),且f[φ（x）]=lnx,求∫φ（x）dx
f(x² - 1) = ln[x²/(x² - 2)] = ln[(x² - 1 + 1)/(x² - 1 - 1)]
f(x) = ln[(x + 1)/(x - 1)]
f[φ(x)] = lnx
ln{[φ(x) + 1]/[φ(x) - 1]} = lnx
[φ(x) + 1]/[φ(x) - 1] = x
φ(x) + 1 = xφ(x) - x
φ(x) * (x - 1) = x + 1
φ(x) = (x + 1)/(x - 1)
∫ φ(x) dx = ∫ (x + 1)/(x - 1) dx = ∫ (x - 1 + 2)/(x - 1) dx = x + 2ln|x - 1| + C