Final answer to the problem
$\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(7+8n\right)}}{\left(7+8n\right)\left(2n+1\right)!}+C_0$
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Step-by-step Solution
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- Integrate by partial fractions
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1
Rewrite the function $\sin\left(x^4\right)$ as it's representation in Maclaurin series expansion
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$\int x^2\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^n}{\left(2n+1\right)!}\left(x^4\right)^{\left(2n+1\right)}dx$
Learn how to solve problems step by step online. Find the integral int(x^2sin(x^4))dx. Rewrite the function \sin\left(x^4\right) as it's representation in Maclaurin series expansion. Simplify \left(x^4\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 4 and n equals 2n+1. Solve the product 4\left(2n+1\right). Bring the outside term x^2 inside the power serie.
Final answer to the problem
$\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(7+8n\right)}}{\left(7+8n\right)\left(2n+1\right)!}+C_0$
