ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

# 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.

Go!
Math mode
Text mode
Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

###  Difficult Problems

1

Solved example of improper integrals

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

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

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

Calculate the power $\sqrt{1}$

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

Simplify the fraction $\frac{1}{1}$ by $1$

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

Calculate the square root of $1$

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

Any expression multiplied by $1$ is equal to itself

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

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

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

Simplify the expression inside the integral

$\arctan\left(x\right)$

4

Add the initial limits of integration

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

Replace the integral's limit by a finite value

$\lim_{c\to\infty }\left(\left[\arctan\left(x\right)\right]_{0}^{c}\right)$
6

Evaluate the definite integral

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

Evaluate the arctangent of $0$

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

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

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

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

$\frac{\pi }{2}$

Divide $\pi$ by $2$

$\frac{\pi}{2}$
7

Evaluate the resulting limits of the integral

$\frac{\pi}{2}$

$\frac{\pi}{2}$