Substitution (Reverse Chain Rule) (Edexcel A-Level Mathematics): Flashcards

It's the Reverse Chain Rule for simplifying integrals.

Choose a substitution $u$ for part of the integrand.

Differentiate $u$ to express $du$ in terms of $dx$.

Rewrite the integral with $u$ and $du$, replacing $x$ terms.

Integrate with respect to $u$ to solve the integral.

Substitute back the initial expression for $u$ in $x$.

Only for functions where a part's derivative is present.

Products of functions that are differentiable.

When integrating rational functions with polynomial denominators.

$\sin^2 x + \cos^2 x = 1$, useful in integration.