Further Integration (AQA A-Level Mathematics): Flashcards

Reverse Chain Rule

When integrand is a product of a function and its derivative

Choose $u$ as inner function whose derivative appears in integrand

Replace all x-terms with u-terms

$\ln |f(x)| + c$

$\frac{1}{n+1}(f(x))^{n+1} + c$

When denominator is factorised or can be factorised

$1 + \tan^2 x$

$\sec x \tan x$

By parts: product of unrelated functions; Substitution: derivative relationship exists