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

To integrate composite functions effectively.

Identify the inner function in the integrand.

Set $u = g(x)$ where $g(x)$ is the inner function.

Differentiate $u$ with respect to $x$ to find $du/dx$.

Replace $g(x)$ with $u$ and $dx$ with $du/(du/dx)$.

The integral should now be in terms of $u$ and $du$.

Substitute back $u = g(x)$ into the integral's result.

Inner function is $x^2$, with $g'(x) = 2x$.

Integral of $\cos(u)$ is $\sin(u) + C$.

The integral is $e^{x^2} + C$ by u-substitution.