** Final answer to the problem

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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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Rewrite the function $\cos\left(x^2\right)$ as it's representation in Maclaurin series expansion

Learn how to solve quotient rule of differentiation problems step by step online.

$\int\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^n}{\left(2n\right)!}\left(x^2\right)^{2n}dx$

Learn how to solve quotient rule of differentiation problems step by step online. Solve the trigonometric integral int(cos(x^2))dx. Rewrite the function \cos\left(x^2\right) as it's representation in Maclaurin series expansion. Simplify \left(x^2\right)^{2n} 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 2n. We can rewrite the power series as the following. Apply the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a number or constant function, such as 4n.

** Final answer to the problem

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