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# Find the integral $\int\frac{e^{\left(\sqrt[3]{x^{5}}\right)}}{x^4}dx$

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##  Final answer to the problem

$\sum_{n=0}^{\infty } \frac{x^{\left(\frac{5}{3}n-3\right)}}{\left(\frac{5}{3}n-3\right)\left(n!\right)}+C_0$
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##  Step-by-step Solution 

How should I solve this problem?

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• Integrate by partial fractions
• Integrate by substitution
• Integrate by parts
• Integrate using tabular integration
• Integrate by trigonometric substitution
• Weierstrass Substitution
• Integrate using trigonometric identities
• Integrate using basic integrals
• Product of Binomials with Common Term
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1

Rewrite the exponent using the power rule $\frac{a^m}{a^n}=a^{m-n}$, where in this case $m=0$

$\int e^{\left(\sqrt[3]{x^{5}}\right)}x^{-4}dx$

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

$\int e^{\left(\sqrt[3]{x^{5}}\right)}x^{-4}dx$

Learn how to solve integrals of exponential functions problems step by step online. Find the integral int((e^x^(5/3))/(x^4))dx. Rewrite the exponent using the power rule \frac{a^m}{a^n}=a^{m-n}, where in this case m=0. Rewrite the function e^{\left(\sqrt[3]{x^{5}}\right)} as it's representation in Maclaurin series expansion. Simplify \left(\sqrt[3]{x^{5}}\right)^n using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{5}{3} and n equals n. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number.

##  Final answer to the problem

$\sum_{n=0}^{\infty } \frac{x^{\left(\frac{5}{3}n-3\right)}}{\left(\frac{5}{3}n-3\right)\left(n!\right)}+C_0$

##  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

SnapXam A2

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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: Integrals of Exponential Functions

Those are integrals that involve exponential functions. Recall that an exponential function is a function of the form f(x)=a^x.

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