Integration by Parts (AQA A-Level Mathematics): Flashcards

Product of two functions unrelated by differentiation

$\int u \frac{dv}{dx} dx = uv - \int v \frac{du}{dx} dx$

Product rule: $(uv)' = uv' + vu'$

$-x \cos x + \sin x + c$

$xe^x - e^x + C$

No, use integration by parts

$u$ (not $\frac{dv}{dx}$)

$x \ln x - x + c$

$\frac{x^2}{2}\ln x - \frac{x^2}{4} + c$

Substitution