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

## Step-by-step Solution

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

Problem to solve:

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

Specify the solving method

1

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}{5}\sqrt{x^{5}}. The integral \int x^{-\frac{1}{2}}dx results in: 2\sqrt{x}.

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

##  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

Solve integral of x^0.5(x+1/x)dx using partial fractionsSolve integral of x^0.5(x+1/x)dx using basic integralsSolve integral of x^0.5(x+1/x)dx using u-substitutionSolve integral of x^0.5(x+1/x)dx using integration by partsSolve integral of x^0.5(x+1/x)dx using trigonometric substitution

SnapXam A2

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a
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u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
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

~ 0.23 s

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