Integrate the function 1/(1+x^2) from 3^(1/2) to infinity

 Exercise

$\int_{\sqrt{3}}^{\infty}\frac{1}{1+x^2}dx$

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Solve the integral by applying the formula $\displaystyle\int\frac{x'}{x^2+a^2}dx=\frac{1}{a}\arctan\left(\frac{x}{a}\right)$

$\arctan\left(x\right)$

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Add the initial limits of integration

$\left[\arctan\left(x\right)\right]_{\sqrt{3}}^{\infty }$

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Replace the integral's limit by a finite value

$\lim_{c\to\infty }\left(\left[\arctan\left(x\right)\right]_{\sqrt{3}}^{c}\right)$

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Evaluate the definite integral

$\lim_{c\to\infty }\left(\arctan\left(c\right)-\arctan\left(\sqrt{3}\right)\right)$

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Evaluate the resulting limits of the integral

$\frac{\pi }{2}-\arctan\left(\sqrt{3}\right)$

$\frac{\pi }{2}-\arctan\left(\sqrt{3}\right)$

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