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# Find the integral $\int\frac{7\sqrt[3]{x^{2}}}{\sqrt{x^3\sqrt{x}}}dx$

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##  Final answer to the problem

$-84x^{-\frac{1}{12}}+C_0$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Integrate by partial fractions
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
• Integrate by trigonometric substitution
• Weierstrass Substitution
• Integrate using trigonometric identities
• Integrate using basic integrals
• Product of Binomials with Common Term
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Simplify the expression

$7\int x^{\left(\frac{2}{3}-\frac{7}{4}\right)}dx$

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

$7\int x^{\left(\frac{2}{3}-\frac{7}{4}\right)}dx$

Learn how to solve integrals of rational functions problems step by step online. Find the integral int((7x^(2/3))/((x^3x^(1/2))^(1/2)))dx. Simplify the expression. 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{2}{3}-\frac{7}{4}. As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration C. Simplifying.

##  Final answer to the problem

$-84x^{-\frac{1}{12}}+C_0$

##  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

SnapXam A2

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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

###  Main Topic: Integrals of Rational Functions

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