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# Integrate $\int\sqrt{x}\left(x+\frac{1}{x}\right)dx$

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##  Final answer to the problem

$\frac{2\sqrt{x^{5}}}{5}+2\sqrt{x}+C_0$
Got another answer? Verify it here!

##  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
Can't find a method? Tell us so we can add it.
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Rewrite the integrand $\sqrt{x}\left(x+\frac{1}{x}\right)$ in expanded form

$\int\left(\sqrt{x^{3}}+x^{-\frac{1}{2}}\right)dx$

Learn how to solve integrals with radicals problems step by step online.

$\int\left(\sqrt{x^{3}}+x^{-\frac{1}{2}}\right)dx$

Learn how to solve integrals with radicals problems step by step online. Integrate int(x^(1/2)(x+1/x))dx. Rewrite the integrand \sqrt{x}\left(x+\frac{1}{x}\right) in expanded form. Expand the integral \int\left(\sqrt{x^{3}}+x^{-\frac{1}{2}}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\sqrt{x^{3}}dx results in: \frac{2\sqrt{x^{5}}}{5}. The integral \int x^{-\frac{1}{2}}dx results in: 2\sqrt{x}.

##  Final answer to the problem

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

##  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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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

###  Main Topic: Integrals with Radicals

Integrals with radicals are those integrals that contain a radical (square root, cubic, etc.) in the numerator or denominator of the integral.