ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

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

Step-by-step Solution

Go!
Math mode
Text mode
Go!
1
2
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

 Videos

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

 Step-by-step Solution 

Specify the solving method

We could not solve this problem by using the method: Integration by Trigonometric Substitution

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 parts

SnapXam A2

beta Got a different answer? Verify it!

Go!
1
2
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

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

 Join 500k+ students in problem solving.

Without automatic renewal.
Create an Account