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# Improper Integrals Calculator

## Get detailed solutions to your math problems with our Improper Integrals step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

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###  Difficult Problems

1

Here, we show you a step-by-step solved example of improper integrals. This solution was automatically generated by our smart calculator:

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

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

$\frac{1}{\sqrt{1}}\arctan\left(\frac{x}{\sqrt{1}}\right)$

Calculate the power $\sqrt{1}$

$\frac{1}{1}\arctan\left(\frac{x}{\sqrt{1}}\right)$

Any expression divided by one ($1$) is equal to that same expression

$1\arctan\left(\frac{x}{\sqrt{1}}\right)$

Any expression multiplied by $1$ is equal to itself

$\arctan\left(\frac{x}{\sqrt{1}}\right)$

Calculate the power $\sqrt{1}$

$\arctan\left(\frac{x}{1}\right)$

Any expression divided by one ($1$) is equal to that same expression

$\arctan\left(x\right)$
2

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

$\arctan\left(x\right)$
3

Add the initial limits of integration

$\left[\arctan\left(x\right)\right]_{0}^{\infty }$
4

Replace the integral's limit by a finite value

$\lim_{c\to\infty }\left(\left[\arctan\left(x\right)\right]_{0}^{c}\right)$
5

Evaluate the definite integral

$\lim_{c\to\infty }\left(\arctan\left(c\right)-\arctan\left(0\right)\right)$

Evaluate the arctangent of $0$

$\lim_{c\to\infty }\left(\arctan\left(c\right)-1\cdot 0\right)$

Multiply $-1$ times $0$

$\lim_{c\to\infty }\left(\arctan\left(c\right)+0\right)$

$x+0=x$, where $x$ is any expression

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

Apply the limit $\lim_{x\to\infty}\arctan(x)=\frac{\pi}{2}$

$\frac{\pi }{2}$
6

Evaluate the resulting limits of the integral

$\frac{\pi }{2}$

##  Final answer to the problem

$\frac{\pi }{2}$

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