Đáp án:
$A.\, 0$
Giải thích các bước giải:
$\quad \displaystyle\int\dfrac{1}{x^3 - x}dx$
$=\displaystyle\int\left[\dfrac{1}{2(x+1)} +\dfrac{1}{2(x-1)}-\dfrac1x\right]dx$
$=\dfrac12\displaystyle\int\dfrac{dx}{x+1} +\dfrac12\displaystyle\int\dfrac{dx}{x-1} - \displaystyle\int\dfrac{dx}{x}$
$=\dfrac12\displaystyle\int\dfrac{d(x+1)}{x+1} +\dfrac12\displaystyle\int\dfrac{d(x-1)}{x-1} - \displaystyle\int\dfrac{dx}{x}$
$=\dfrac12\ln|x+1| + \dfrac12\ln|x-1| - \ln|x| + C$
$=\dfrac12\ln|(x+1)(x-1)| -\ln|x| + C$
$\to \begin{cases}a =\dfrac12\\b = -1\end{cases}$
$\to 2a + b = 2\cdot \dfrac12 - 1$
$\to P = 0$
