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Integrate the function $\frac{6}{x^2+1}$ from 0 to $\infty $

Step-by-step Solution

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Solution

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Final answer to the problem

$3\pi $
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Step-by-step Solution

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Learn how to solve improper integrals problems step by step online. Integrate the function 6/(x^2+1) from 0 to infinity. The integral of a function times a constant (6) is equal to the constant times the integral of the function. 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). Add the initial limits of integration. Replace the integral's limit by a finite value.

Final answer to the problem

$3\pi $

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Function Plot

Plotting: $\frac{6}{x^2+1}$

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0
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m
n
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x
y
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.
(◻)
+
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×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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:

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Main Topic: Improper Integrals

An improper integral is the limit of a definite integral as an endpoint of the interval(s) of integration approaches either a specified real number that is not part of the function's domain, or infinity.

Used Formulas

See formulas (1)

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