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# Find the integral $\int\frac{x+x^2}{\sqrt{x}}dx$

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##  Final answer to the problem

$\frac{2\sqrt{x^{3}}}{3}+\frac{2\sqrt{x^{5}}}{5}+C_0$
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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 fraction $\frac{x+x^2}{\sqrt{x}}$ into $2$ simpler fractions with common denominator $\sqrt{x}$

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

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

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

Learn how to solve integrals of rational functions problems step by step online. Find the integral int((x+x^2)/(x^(1/2)))dx. Expand the fraction \frac{x+x^2}{\sqrt{x}} into 2 simpler fractions with common denominator \sqrt{x}. Simplify the resulting fractions. Simplify the expression. The integral \int\sqrt{x}dx results in: \frac{2\sqrt{x^{3}}}{3}.

##  Final answer to the problem

$\frac{2\sqrt{x^{3}}}{3}+\frac{2\sqrt{x^{5}}}{5}+C_0$

##  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
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

###  Main Topic: Integrals of Rational Functions

Integrals of rational functions of the form R(x) = P(x)/Q(x).