Final answer to the problem
$3\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(7+6n\right)}}{\left(7+6n\right)\left(2n+1\right)!}+C_0$
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Step-by-step Solution
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- Integrate by partial fractions
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- Weierstrass Substitution
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- Product of Binomials with Common Term
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1
The integral of a function times a constant ($3$) is equal to the constant times the integral of the function
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$3\int x^3\sin\left(x^3\right)dx$
Learn how to solve problems step by step online. Find the integral int(3x^3sin(x^3))dx. The integral of a function times a constant (3) is equal to the constant times the integral of the function. Rewrite the function \sin\left(x^3\right) as it's representation in Maclaurin series expansion. Simplify \left(x^3\right)^{\left(2n+1\right)} 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+1. Solve the product 3\left(2n+1\right).
Final answer to the problem
$3\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(7+6n\right)}}{\left(7+6n\right)\left(2n+1\right)!}+C_0$
