Final answer to the problem
$\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(4n+1\right)}}{\left(4n+1\right)\left(2n\right)!}+C_0$
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Step-by-step Solution
Learn how to solve integration techniques 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
$\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(4n+1\right)}}{\left(4n+1\right)\left(2n\right)!}+C_0$
