Question

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Answer 1

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$\frac{\pi}{12} \: \: ans...$

Answer 2

$\color{purple}\Large\bold\star\mathcal{Hey\:There}\star$

Integration of dx/(a^2 + x^2) is given by the formula

$\int \frac{dx}{ {a}^{2} + {x}^{2} } = \frac{1}{a} {tan }^{ - 1} ( \frac{x}{a} )$

Thus, integration of dx/(1+x^2) is tan^-1 (x).

Now, putting the limits we get,

tan^-1 (√3) - tan^-1 (1)

=> π/3 - π/4

=> π/12

Thus, integration of dx/(1 + x^2) under the limits from 1 to √3 is π/12.