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# Integrate $\int\left(5\sqrt[3]{x}-x\right)dx$

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##  Final answer to the problem

$\frac{15\sqrt[3]{x^{4}}}{4}-\frac{1}{2}x^2+C_0$
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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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Expand the integral $\int\left(5\sqrt[3]{x}-x\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

$\int5\sqrt[3]{x}dx+\int-xdx$

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

$\int5\sqrt[3]{x}dx+\int-xdx$

Learn how to solve integrals of polynomial functions problems step by step online. Integrate int(5x^(1/3)-x)dx. Expand the integral \int\left(5\sqrt[3]{x}-x\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int5\sqrt[3]{x}dx results in: \frac{15\sqrt[3]{x^{4}}}{4}. The integral \int-xdx results in: -\frac{1}{2}x^2. Gather the results of all integrals.

##  Final answer to the problem

$\frac{15\sqrt[3]{x^{4}}}{4}-\frac{1}{2}x^2+C_0$

##  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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5
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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 Polynomial Functions

Integrals of polynomial functions.