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

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Solution

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Final answer to the problem

$1$
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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 1/(x^2) from 1 to infinity. Rewrite the exponent using the power rule \frac{a^m}{a^n}=a^{m-n}, where in this case m=0. Apply the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a number or constant function, such as -2. Simplify the expression. Add the initial limits of integration.

Final answer to the problem

$1$

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Function Plot

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

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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
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:

Similar Problems Solved

Evaluate the integral

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

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$\int_1^{\infty}\left(\frac{ln\left(x\right)}{x}\right)dx$

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$\int_1^{\infty}\left(\frac{lnx}{x}\right)dx$

Evaluate the integral

$\int_1^{\infty}\left(\frac{1}{x^3}\right)dx$

Evaluate the integral

$\int_{-\infty}^0\left(\frac{1}{\sqrt{3-x}}\right)dx$

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

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