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

Step-by-step Solution

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Final Answer

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

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We could not solve this problem by using the method: Integration by Trigonometric Substitution

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Simplify the expression inside the integral

$7\int\frac{1}{\sqrt[12]{x^{13}}}dx$

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

$7\int\frac{1}{\sqrt[12]{x^{13}}}dx$

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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 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{13}{12}. Simplify the expression inside the integral.

Final Answer

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

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

Solve integral of (7x^0.6667/(x^3x^0.5^0.5))dx using partial fractionsSolve integral of (7x^0.6667/(x^3x^0.5^0.5))dx using basic integralsSolve integral of (7x^0.6667/(x^3x^0.5^0.5))dx using u-substitutionSolve integral of (7x^0.6667/(x^3x^0.5^0.5))dx using integration by parts

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Function Plot

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

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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

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