Step-by-step Solution

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Step-by-step explanation

Problem to solve:

$\int_0^{\infty}\left(\frac{1}{1+x^2}\right)dx$

Learn how to solve definite integrals problems step by step online.

$\lim_{c\to\infty }\:\int_{0}^{c}\frac{1}{1+x^2}dx$

Learn how to solve definite integrals problems step by step online. Integrate 1/(1+x^2) from 0 to \infty. Replace the integral's limit by a finite value. Solve the integral applying the formula \displaystyle\int\frac{x'}{x^2+a^2}dx=\frac{1}{a}\arctan\left(\frac{x}{a}\right). Evaluate the definite integral. Simplifying.

$\frac{\pi}{2}$$\,\,\left(\approx 1.5707963267948966\right)$
$\int_0^{\infty}\left(\frac{1}{1+x^2}\right)dx$