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# Integrate the function $\frac{x^3}{\sqrt{x}}$ from 0 to $4$

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##  Final answer to the problem

$\frac{256}{7}$
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##  Step-by-step Solution 

How should I solve this problem?

• Integrate by parts
• Integrate by partial fractions
• Integrate by substitution
• Integrate using tabular integration
• Integrate by trigonometric substitution
• Weierstrass Substitution
• Integrate using trigonometric identities
• Integrate using basic integrals
• Product of Binomials with Common Term
• FOIL Method
Can't find a method? Tell us so we can add it.
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Rewrite the fraction $\frac{x^3}{\sqrt{x}}$ inside the integral as the product of two functions: $x^3\frac{1}{\sqrt{x}}$

$\int_{0}^{4} x^3\frac{1}{\sqrt{x}}dx$

Learn how to solve integral calculus problems step by step online.

$\int_{0}^{4} x^3\frac{1}{\sqrt{x}}dx$

Learn how to solve integral calculus problems step by step online. Integrate the function (x^3)/(x^(1/2)) from 0 to 4. Rewrite the fraction \frac{x^3}{\sqrt{x}} inside the integral as the product of two functions: x^3\frac{1}{\sqrt{x}}. We can solve the integral \int x^3\frac{1}{\sqrt{x}}dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify or choose u and calculate it's derivative, du. Now, identify dv and calculate v.

##  Final answer to the problem

$\frac{256}{7}$

##  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

SnapXam A2

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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

###  Main Topic: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.