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

## Step-by-step Solution

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###  Videos

$\frac{2}{3}\sqrt{x^{3}}+\frac{2}{5}\sqrt{x^{5}}+C_0$
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##  Step-by-step Solution 

Problem to solve:

$\int\frac{x+x^2}{\sqrt{x}}dx$

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1

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 inside the integral. The integral \int\sqrt{x}dx results in: \frac{2}{3}\sqrt{x^{3}}.

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

##  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

Solve int((x+x^2)/(x^1/2))dx using partial fractionsSolve int((x+x^2)/(x^1/2))dx using basic integralsSolve int((x+x^2)/(x^1/2))dx using u-substitutionSolve int((x+x^2)/(x^1/2))dx using integration by partsSolve int((x+x^2)/(x^1/2))dx using trigonometric substitution

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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

### Main topic:

Integrals of Rational Functions

~ 0.05 s

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