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Answer :
The integral of (x⁹−x⁷+x³)⁵(9x⁸−7x⁶+3x²) with respect to x is a complex expression involving high-degree polynomials and exponents. After differentiating and simplifying the expression, the final answer is (1/70)(x¹⁰)⁶ − (1/48)(x⁸)⁶ + (1/14)(x⁴)⁶ + C, where C is the constant of integration.
After evaluating the given integral, the final answer is a polynomial expression with a constant of integration. The process involves applying the chain rule and power rule for integration, and then simplifying the resulting expression. The final answer represents the area under the given function, and it can be utilized in various applications such as physics, engineering, and economics. Moreover, understanding the process of evaluating this integral can enhance one's problem-solving skills in mathematics, particularly in the field of calculus. Overall, the final answer provides a comprehensive solution to the given integral, and its significance extends to various academic and practical domains.
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