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[h] IB Mathematics AA HL Flashcards -Integration by substitution
[q] More integration methods
[a]
INT. BY SUBSTITUTION
We will be looking at 2 more methods of integration so we can widen the variety of functions we can integrate significantly. The first method is called integration by substitution, also called \( u \)-substitution or reverse chain rule. If we recall that:
\[
\frac{d}{dx}f(g(x)) = f'(g(x))g'(x)
\]
[q]
Then, it follows that:
\[
\int f'(g(x))g'(x)dx = f(g(x)) + c
\]
This is a fairly complicated formula, so it needs unpacking. The following formula will become more clear after an example:
\[
\int f(g(x))g'(x)dx = \int f(u)du
\]
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