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Integrate the function $\frac{1}{1+x^2}$ from 0 to $\infty $

Step-by-step Solution

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Final Answer

$\frac{\pi}{2}$
Got another answer? Verify it here!

Step-by-step Solution

Problem to solve:

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

Specify the solving method

1

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

$\left[\arctan\left(x\right)\right]_{0}^{\infty }$
2

Replace the integral's limit by a finite value

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

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

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

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Learn how to solve definite integrals problems step by step online. Integrate the function 1/(1+x^2) from 0 to \infty. 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). Replace the integral's limit by a finite value. Evaluate the definite integral. Simplifying.

Final Answer

$\frac{\pi}{2}$

Numeric Answer

$1.570796$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve int(1/(1+x^2))dx&0&\infty using partial fractionsSolve int(1/(1+x^2))dx&0&\infty using basic integralsSolve int(1/(1+x^2))dx&0&\infty using u-substitutionSolve int(1/(1+x^2))dx&0&\infty using integration by partsSolve int(1/(1+x^2))dx&0&\infty using trigonometric substitution
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7
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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

How to improve your answer:

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

Main topic:

Definite Integrals

Time to solve it:

~ 0.04 s