Harder Substitution (AQA A-Level Mathematics): Flashcards

Integration requiring less obvious substitutions where you must recognize patterns (e.g., spotting derivative of inner function)

Derivative of inner function present in integrand

$\frac{1}{3} (1 + x^2)^{\frac{3}{2}} + C$

$u = 1 + \cos(2x)$

$-\frac{1}{2} \ln |1 + \cos(2x)| + C$

$u = x^2$

$\frac{1}{2} e^{x^2} + C$

$u = \ln(x)$

$\frac{(\ln(x))^2}{2} + C$

$\sec^2(\theta)$