Final answer to the problem
$2\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(6n+2\right)}}{\left(6n+2\right)\left(2n\right)!}+C_0$
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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
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- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
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1
The integral of a function times a constant ($2$) is equal to the constant times the integral of the function
$2\int x\cos\left(x^3\right)dx$
Learn how to solve integral calculus problems step by step online.
$2\int x\cos\left(x^3\right)dx$
Learn how to solve integral calculus problems step by step online. Find the integral int(2xcos(x^3))dx. The integral of a function times a constant (2) is equal to the constant times the integral of the function. Rewrite the function \cos\left(x^3\right) as it's representation in Maclaurin series expansion. Simplify \left(x^3\right)^{2n} 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 2n. Bring the outside term x inside the power serie.
Final answer to the problem
$2\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(6n+2\right)}}{\left(6n+2\right)\left(2n\right)!}+C_0$
