Final answer to the problem
$\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(3+4n\right)}}{\left(3+4n\right)\left(2n\right)!}+C_0$
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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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1
When multiplying two powers that have the same base ($x$), you can add the exponents
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$\int x^2\cos\left(x^2\right)dx$
Learn how to solve problems step by step online. Find the integral int(xxcos(x^2))dx. When multiplying two powers that have the same base (x), you can add the exponents. 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. Bring the outside term x^2 inside the power serie.
Final answer to the problem
$\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(3+4n\right)}}{\left(3+4n\right)\left(2n\right)!}+C_0$
