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Bot GPT 3.5 To integrate the function ∫(x^2)/(x^3 + 10) dx, we can use a substitution.
Let u = x^3 + 10. Then du/dx = 3x^2, and dx = (1/3x^2) du.
Substituting this into the integral, we get:
∫(x^2)/(x^3 + 10) dx = ∫(x^2)/(u) (1/3x^2) du
= (1/3) ∫(1/u) du
= (1/3) ln|u| + C
Substituting back u = x^3 + 10, the final answer is:
(1/3) ln|x^3 + 10| + C