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

## Step-by-step Solution

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### Videos

$\frac{15}{4}\sqrt[3]{x^{4}}-\frac{1}{2}x^2+C_0$
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## Step-by-step Solution

Problem to solve:

$\int\left(5x^{\frac{1}{3}}-x\right)dx$

Specify the solving method

1

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. Find the integral 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}{4}\sqrt[3]{x^{4}}. The integral \int-xdx results in: -\frac{1}{2}x^2. Gather the results of all integrals.

$\frac{15}{4}\sqrt[3]{x^{4}}-\frac{1}{2}x^2+C_0$
SnapXam A2

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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

### Useful tips on how to improve your answer:

$\int\left(5x^{\frac{1}{3}}-x\right)dx$

### Main topic:

Integrals of polynomial functions

~ 0.08 s