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Q: Evaluate the integral of 2x(x^2+1)^5 dx. Let u = x^2+1. Then du = 2x dx, which matches the integrand. Integral becomes: integral of u^5 du = u^6/6 + C. Back-substitute: (x^2+1)^6/6 + C. Check: differentiating gives 2x(x^2+1)^5. Correct!