CUET Mathematics 2022 10 Aug Shift 1 PYQs

$\int_{\pi/6}^{\pi/3} \frac{tan x}{tan x + cot x} dx$ is equal to

$\int e^x \left(\frac{1}{x} - \frac{2}{x^3}\right) dx =$

For $x \neq -1$, if $\int \frac{xe^x dx}{(1+x)^2} = \frac{ae^x}{(1+x)^b} + c$, where a, b are fixed numbers and c is the integration constant, then $a + b$ is equal to