Integration by parts is the product rule reversed, and it trades one integral for another. The skill is choosing u so that the new integral is simpler than the one you started with — otherwise you go in circles. This is the real knowscape from knowhere, not a picture of one. Drag it. Watch what actually changes.
You can't integrate what you're handed — so you rewrite it into something you can. Partial fractions splits one hostile quotient into a sum of standard logs; product-to-sum turns a product of trig functions into terms you already know how to integrate. Every technique here is the same move: reshape the integrand until it's a form you've already beaten.
Integration by parts uses the formula ∫u dv = uv − ∫v du, converting a product into a boundary term minus a new integral that should be easier to evaluate.
knowhere maps every concept to what it rests on and what rests on it — 1 underneath this one, 0 built on top. Each one says why, in a sentence, not as an arrow on a diagram.
Each one is its own knowscape in the app — built for how a particular student takes things in, not one explanation handed to everybody.
Every HSC and VCE concept in knowhere is built like this one — mapped to your curriculum, never capped by it. Free for a week. No card tricks, no lecture.
Free for a week, then $49 once — the 2026 exam pass ends itself after the last exam. 0 days of the pass left.
Free for a week, then a plan you can stop any time.
not your card? send it to whoever's is.