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Find the integral $\int\frac{1}{x^4\sqrt{x^{\left(2-3\right)}}}dx$

Step-by-step Solution

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Final answer to the problem

$-\frac{2}{5}x^{-\frac{5}{2}}+C_0$
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Step-by-step Solution

How should I solve this problem?

  • Integrate using trigonometric identities
  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using basic integrals
  • Product of Binomials with Common Term
  • FOIL Method
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1

Simplify the expression inside the integral

$\int\frac{1}{\sqrt{x^{7}}}dx$

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

$\int\frac{1}{\sqrt{x^{7}}}dx$

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Learn how to solve integrals of rational functions problems step by step online. Find the integral int(1/(x^4x^(2-3)^1/2))dx. Simplify the expression inside the integral. 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 -\frac{7}{2}. 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

$-\frac{2}{5}x^{-\frac{5}{2}}+C_0$

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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

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Function Plot

Plotting: $-\frac{2}{5}x^{-\frac{5}{2}}+C_0$

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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:

Main Topic: Integrals of Rational Functions

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

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