Afellow calculus enthusiast was working through some practice problems.

they come to you asking if the following problem is correct: ∫ [(3x^2 + 1) / 2x] dx = [(x^3 + x) / x^2] + c

determine if they are correct. explain how you know if they are correct without integrating the function (i. e. find another method using calculus).

Integrating this gives

so the enthusiast's antiderivative is incorrect.

Without integrating, you can show the enthusiast's solution is incorrect by taking the derivative:

but this is not the same as the original integrand.

the enthusiast's antiderivative is incorrect

Step-by-step explanation:

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