Integration by Substitution (Edexcel A-Level Further Mathematics): Flashcards

Simplifies integrals by substituting part with a simpler variable

$x = a \sin \theta$

$dx = a \cos \theta \, d\theta$

$x = a \sec \theta$

$dx = a \sec \theta \tan \theta \, d\theta$

$x = a \tan \theta$

$\arcsin\left(\frac{x}{a}\right) + C$

$\ln\left|x + \sqrt{x^2 - a^2}\right| + C$

$\frac{1}{a} \arctan\left(\frac{x}{a}\right) + C$

$\sec^2 \theta$