CUET Mathematics 2026 30th May Shift 2 PYQs

$\int_0^1 x e^x dx$ is equal to

$\int \dfrac{e^{7\log x}-e^{6\log x}}{e^{5\log x}-e^{4\log x}}\,dx$, $x>0$ and $x\ne 1$ is equal to (consider $\log x = \log_e x$)

$\int e^x \left(\frac{1-x}{1+x^2}\right)^2 dx =$