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

Step-by-step Solution

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Final Answer

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

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Rewrite the integrand $\sqrt{x}\left(x+\frac{1}{x}\right)$ in expanded form

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

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

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Learn how to solve 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}.

Final Answer

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

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 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

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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

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