Honestly this doesn't surprise me. I don't have GPT-4 access, but I fed ChatGPT a simple calculus question as a sanity check.<p>Question: Calculate the integral of x arctan x dx. Show your work.<p>Answer: We can solve this integral using integration by parts:<p>Let u = arctan x and dv = x dx, then we have:<p>du/dx = 1/(1+x^2)
v = (1/2)x^2<p>Using the integration by parts formula, we get:<p>∫ x arctan x dx = uv - ∫ v du/dx dx
= (1/2)x^2 arctan x - (1/2)∫ x^2/(1+x^2) dx<p>To solve the second integral, we can use substitution. Letting u = 1+x^2, then du/dx = 2x, and dx = du/(2x). Substituting into the integral, we get:<p>∫ x^2/(1+x^2) dx = (1/2) ∫ du/u
= (1/2) ln|u| + C
= (1/2) ln|1+x^2| + C<p>Putting it all together, we get:<p>∫ x arctan x dx = (1/2)x^2 arctan x - (1/2) [(1/2) ln|1+x^2|] + C
= (1/2)x^2 arctan x - (1/4) ln|1+x^2| + C<p>Therefore, the integral of x arctan x dx is (1/2)x^2 arctan x - (1/4) ln|1+x^2| + C, where C is the constant of integration.<p>---<p>This is wrong, although it gets pretty damn close (see if you can spot the mistake.) I was an exceptionally kind grader when I taught and Landsburg seems like an exceptionally picky one. But either way ChatGPT wouldn't pass calculus 2, either.