Harder Substitution (AQA A-Level Mathematics): Quizzes

Derivative $2x$ is almost present as $x$

$dx = \frac{du}{2x}$

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

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

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

$x^2$ in exponent; derivative $2x$ present

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

$u = \ln(x)$

$x = \sec(\theta)$

$x = \tan(\theta)$