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

Step-by-step Solution

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$\frac{x^{3}}{3}-4\sqrt{x}+C_0$
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Step-by-step Solution

Problem to solve:

$\int\frac{x^3-2\sqrt{x}}{x}dx$

Specify the solving method

1

Expand the fraction $\frac{x^3-2\sqrt{x}}{x}$ into $2$ simpler fractions with common denominator $x$

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

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

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

Learn how to solve integrals of rational functions problems step by step online. Find the integral int((x^3-2x^1/2)/x)dx. Expand the fraction \frac{x^3-2\sqrt{x}}{x} into 2 simpler fractions with common denominator x. Simplify. Expand the integral \int\left(x^{2}-2x^{-\frac{1}{2}}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int x^{2}dx results in: \frac{x^{3}}{3}.

$\frac{x^{3}}{3}-4\sqrt{x}+C_0$
SnapXam A2

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Go!
1
2
3
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

$\int\frac{x^3-2\sqrt{x}}{x}dx$

Main topic:

Integrals of Rational Functions

~ 0.07 s