Final answer:
The student's question to evaluate a complex integral seems to contain typographical errors, making it difficult to solve without additional context. Usually, methods like partial fraction decomposition or substitution are used to solve such integrals.
Step-by-step explanation:
The student has asked to evaluate the integral ∫_0¹(x²x)/(x+1)²(x+2) dx. The function within the integral is quite complex, and proper integration techniques must be used to solve it. Without proper context or additional information, the provided function seems to contain typographical errors, and hence it's challenging to provide a definitive answer. Typically, to solve such integrals, we would use methods such as partial fraction decomposition or substitution if applicable. After simplifying the expression, we would then integrate term by term.
However, considering the information provided about odd and even functions, it appears there could be a discussion on the function's symmetry. If indeed the function is odd and we are integrating over symmetric limits around the origin, then the integral would evaluate to zero. Otherwise, we would have to use the appropriate integration techniques to find the exact value of the integral.