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# Find the integral $\int\frac{u^2+\sqrt[3]{u}}{\sqrt{u}}du$

## Step-by-step Solution

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### Videos

$\frac{2}{5}\sqrt{u^{5}}+\frac{6\sqrt[6]{u^{5}}}{5}+C_0$
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## Step-by-step Solution

Problem to solve:

$\int\frac{u^2+u^{\frac{1}{3}}}{\sqrt{u}}du$

Specify the solving method

1

We can solve the integral $\int\frac{u^2+\sqrt[3]{u}}{\sqrt{u}}du$ 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 $v$), which when substituted makes the integral easier. We see that $\sqrt[6]{u}$ it's a good candidate for substitution. Let's define a variable $v$ and assign it to the choosen part

$v=\sqrt[6]{u}$

Learn how to solve integrals of rational functions problems step by step online.

$v=\sqrt[6]{u}$

Learn how to solve integrals of rational functions problems step by step online. Find the integral int((u^2+u^1/3)/(u^1/2))du. We can solve the integral \int\frac{u^2+\sqrt[3]{u}}{\sqrt{u}}du 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 v), which when substituted makes the integral easier. We see that \sqrt[6]{u} it's a good candidate for substitution. Let's define a variable v and assign it to the choosen part. Now, in order to rewrite du in terms of dv, we need to find the derivative of v. We need to calculate dv, we can do that by deriving the equation above. Isolate du in the previous equation. Substituting v and du in the integral and simplify.

$\frac{2}{5}\sqrt{u^{5}}+\frac{6\sqrt[6]{u^{5}}}{5}+C_0$
SnapXam A2

### beta Got another 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

$\int\frac{u^2+u^{\frac{1}{3}}}{\sqrt{u}}du$

### Main topic:

Integrals of Rational Functions

~ 0.14 s