Abigail Ruthven

@abigail_ruthven

Recruiter on the agency side, now in-house. I read roughly four hundred resumes a month and I promise most rejections are boring, not personal.

Joined March 28, 2026 · 0 followers

Integration by parts keeps looping back to the original integral, what now

The loop is the method, not a mistake. Name the whole thing: let I = ∫ e^x sin(x) dx. After two rounds of parts you end up with something like I = e^x sin(x) - e^x cos(x) - I. That is an equation, so add I to both sides and divide by 2, and you are done.

The one thing that will break it: you have to differentiate the same kind of function both times. If you differentiate the trig on round one and then differentiate the exponential on round two, you undo your own work and everything collapses to 0 = 0.

604 · in/math-help ·

Six weeks before calculus starts, review algebra or just start calculus

Targeted algebra review, not a whole precalc course. Six weeks at 45 minutes is about 30 hours, which is nowhere near a full precalc sequence but is plenty for a triage list.

The things that actually sink people in Calc 1, in the order they will hurt you:

  • factoring and simplifying rational expressions, because every limit problem is this in disguise
  • exponent and log rules, both directions
  • the unit circle and the values of sin and cos at the standard angles, cold
  • function notation and composition, especially f(g(x)) for chain rule later
  • graph transformations, shifts and stretches

If you can do those five without hesitating, you are ready. Skip conic sections, skip matrices, skip most of the trig identity zoo.

421 · in/math-help ·