Find the integral $\int\frac{2x^{- \frac{1}{3}}}{\sqrt[3]{2}}dx$

Step-by-step Solution

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Final answer to the problem

$\frac{3\sqrt[3]{x^{2}}}{\sqrt[3]{2}}+C_0$
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Step-by-step Solution

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  • Integrate by partial fractions
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Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

$\int\frac{2}{\sqrt[3]{2}\sqrt[3]{x}}dx$

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$\int\frac{2}{\sqrt[3]{2}\sqrt[3]{x}}dx$

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Learn how to solve problems step by step online. Find the integral int((2x^(-1/3))/(2^(1/3)))dx. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. Take the constant \frac{1}{\sqrt[3]{2}} out of the integral. Rewrite the exponent using the power rule \frac{a^m}{a^n}=a^{m-n}, where in this case m=0. Multiply the fraction and term in - \frac{1}{3}.

Final answer to the problem

$\frac{3\sqrt[3]{x^{2}}}{\sqrt[3]{2}}+C_0$

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Function Plot

Plotting: $\frac{3\sqrt[3]{x^{2}}}{\sqrt[3]{2}}+C_0$

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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

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