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# Find the integral $\int e^{-x^3}dx$

## Step-by-step Solution

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Solving: $\int e^{-x^3}dx$

##  Final answer to the problem

$\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(3n+1\right)}}{\left(3n+1\right)\left(n!\right)}+C_0$
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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 function $e^{-x^3}$ as it's representation in Maclaurin series expansion

$\int\sum_{n=0}^{\infty } \frac{\left(-x^3\right)^n}{n!}dx$

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

$\int\sum_{n=0}^{\infty } \frac{\left(-x^3\right)^n}{n!}dx$

Learn how to solve integrals of exponential functions problems step by step online. Find the integral int(e^(-x^3))dx. Rewrite the function e^{-x^3} as it's representation in Maclaurin series expansion. The power of a product is equal to the product of it's factors raised to the same power. Simplify \left(x^3\right)^n using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 3 and n equals n. We can rewrite the power series as the following.

##  Final answer to the problem

$\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(3n+1\right)}}{\left(3n+1\right)\left(n!\right)}+C_0$

##  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

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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

###  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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