Ta có:
$\int\limits_0^1\dfrac{2xe^x-1}{1+x^2e^x}dx$
$=\int\limits_0^1\left(\dfrac{2xe^x+x^2e^x}{1+x^2e^x}-1\right)dx$
$=\int\limits_0^1\dfrac{d(1+x^2e^x)}{1+x^2e^x}-\int\limits_0^1dx$
$=\ln(1+x^2e^x)\left|\begin{array}{l}1\\0\end{array}\right.-x \left|\begin{array}{l}1\\0\end{array}\right.=\ln(1+e)-1$