** Final answer to the problem

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** Step-by-step Solution **

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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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Rewrite the function $e^{-x^2}$ as it's representation in Maclaurin series expansion

Learn how to solve definite integrals problems step by step online.

$\int\sum_{0}^{2}_{n=0}^{\infty } \frac{\left(-x^2\right)^n}{n!}dx$

Learn how to solve definite integrals problems step by step online. Integrate the function e^(-x^2) from 0 to 2. Rewrite the function e^{-x^2} 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^2\right)^n using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals n. We can rewrite the power series as the following.

** Final answer to the problem

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