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# Integrate $\int\sqrt{x}\sqrt{1+x\sqrt{x}}dx$

## Step-by-step Solution

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###  Videos

$\frac{4}{9}\sqrt{\left(1+\sqrt{x^{3}}\right)^{3}}+C_0$
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##  Step-by-step Solution 

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When multiplying exponents with same base you can add the exponents: $x\sqrt{x}$

$\int\sqrt{x}\sqrt{1+\sqrt{x^{3}}}dx$

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

$\int\sqrt{x}\sqrt{1+\sqrt{x^{3}}}dx$

Learn how to solve integrals with radicals problems step by step online. Integrate int(x^1/2(1+xx^1/2)^1/2)dx. When multiplying exponents with same base you can add the exponents: x\sqrt{x}. We can solve the integral \int\sqrt{x}\sqrt{1+\sqrt{x^{3}}}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that \sqrt{x} it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Isolate dx in the previous equation.

$\frac{4}{9}\sqrt{\left(1+\sqrt{x^{3}}\right)^{3}}+C_0$

##  Explore different ways to solve this problem

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0
a
b
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m
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u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
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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.