Final answer to the problem
$x^3\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^ny^{\left(6n+4\right)}}{\left(6n+4\right)\left(2n+1\right)!}+C_0$
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Step-by-step Solution
Learn how to solve integrals of polynomial functions problems step by step online. Find the integral int(x^3sin(y^3))dy. The integral of a function times a constant (x^3) is equal to the constant times the integral of the function. Rewrite the function \sin\left(y^3\right) as it's representation in Maclaurin series expansion. Simplify \left(y^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
$x^3\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^ny^{\left(6n+4\right)}}{\left(6n+4\right)\left(2n+1\right)!}+C_0$
