Integrate the function $\frac{m^3n\sqrt{x}}{\sqrt[5]{2^4m^7n^6x}}$

Step-by-step Solution

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Final answer to the problem

$\frac{5\sqrt[5]{m^{8}}\sqrt[10]{x^{13}}}{4\sqrt[5]{16}\sqrt[5]{n}}+\frac{-25\sqrt[5]{m^{8}}\sqrt[10]{x^{13}}}{52\sqrt[5]{16}\sqrt[5]{n}}+C_0$
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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
  • Load more...
Can't find a method? Tell us so we can add it.
1

Find the integral

$\int\frac{m^3n\sqrt{x}}{\sqrt[5]{2^4m^7n^6x}}dx$

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$\int\frac{m^3n\sqrt{x}}{\sqrt[5]{2^4m^7n^6x}}dx$

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Unlock the first 3 steps of this solution

Learn how to solve problems step by step online. Integrate the function (m^3nx^(1/2))/((2^4m^7n^6x)^(1/5)). Find the integral. Rewrite the fraction \frac{m^3n\sqrt{x}}{\sqrt[5]{2^4m^7n^6x}} inside the integral as the product of two functions: \sqrt{x}\frac{m^3n}{\sqrt[5]{2^4m^7n^6x}}. We can solve the integral \int\sqrt{x}\frac{m^3n}{\sqrt[5]{2^4m^7n^6x}}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.

Final answer to the problem

$\frac{5\sqrt[5]{m^{8}}\sqrt[10]{x^{13}}}{4\sqrt[5]{16}\sqrt[5]{n}}+\frac{-25\sqrt[5]{m^{8}}\sqrt[10]{x^{13}}}{52\sqrt[5]{16}\sqrt[5]{n}}+C_0$

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Function Plot

Plotting: $\frac{5\sqrt[5]{m^{8}}\sqrt[10]{x^{13}}}{4\sqrt[5]{16}\sqrt[5]{n}}+\frac{-25\sqrt[5]{m^{8}}\sqrt[10]{x^{13}}}{52\sqrt[5]{16}\sqrt[5]{n}}+C_0$

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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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