MHT-CET Maths — Teaching Notes

Indefinite Integration is one of the densest MHT-CET Maths chapters — 121 PYQs across 2021–2025, and the HARDEST by difficulty mix (about 60% are HARD). It is pure technique: there is no theory to memorise, only a toolbox of methods and the judgement to pick the right one. The chapter teaches in six movements, easiest tool first: (1) Foundations — what an antiderivative is, the +C, the standard-formula table, and the algebra you do BEFORE integrating; (2) Substitution — the single highest-yield method (44 PYQs), built on the f'(x)/f(x) → log pattern; (3) Trigonometric Integrals I — power-reduction and identity simplification; (4) Rational Functions and Partial Fractions — standard quadratic forms, completing the square, and decomposition (the arctan-quadratic machinery the next movement leans on); (5) Trigonometric Integrals II — rational-in-sin/cos, the half-angle (Weierstrass) substitution, and the fractional-power tan trick, the chapter's hard core; (6) Integration by Parts — LIATE, the cyclic integrals, and the recurring eˣ[f(x)+f'(x)] family. Every PYQ is tagged — learn the pattern, drill the bank, recover the marks.

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