# 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.

$\left[\frac{1}{\sqrt{1}}\arctan\left(\frac{x}{\sqrt{1}}\right)\right]_{0}^{\infty }$

Learn how to solve definite integrals problems step by step online. Integrate 1/(1+x^2) from 0 to \infty. Solve the integral applying the formula \displaystyle\int\frac{x'}{x^2+a^2}dx=\frac{1}{a}\arctan\left(\frac{x}{a}\right). Calculate the power \sqrt{1}. Any expression divided by one (1) is equal to that same expression. Replace the integral's limit by a finite value.

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