Find the integral $\int\frac{1}{x^3}dx$

Step-by-step Solution

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Final answer to the problem

$\frac{1}{-2x^{2}}+C_0$
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Step-by-step Solution

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  • Integrate by partial fractions
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  • Product of Binomials with Common Term
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1

Rewrite the exponent using the power rule $\frac{a^m}{a^n}=a^{m-n}$, where in this case $m=0$

$\int x^{-3}dx$

Learn how to solve integrals of rational functions problems step by step online.

$\int x^{-3}dx$

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Learn how to solve integrals of rational functions problems step by step online. Find the integral int(1/(x^3))dx. 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 -3. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration C.

Final answer to the problem

$\frac{1}{-2x^{2}}+C_0$

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Function Plot

Plotting: $\frac{1}{-2x^{2}}+C_0$

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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

How to improve your answer:

Main Topic: Integrals of Rational Functions

Integrals of rational functions of the form R(x) = P(x)/Q(x).

Used Formulas

See formulas (1)

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