Integration by substitution (as seen in SL 5.10) simplifies complex integrals into a form with which we can integrate.
The general method can be seen as.
$$\int kf(g(x))g'(x)dx$$
where we make $u = g(x)$ such that $du = g'(x)dx$ and $dx = \frac{du}{g'(x)}$.
Therefore the integral becomes
$$k\int f(u)g'(x)\,\frac{du}{g'(x)} = k \int f(u)\,du$$
where $k$ is a constant.
Of course we would not want to do this if $f(x)$ is a function that's even more difficult to integrate since it is a method to simplify! Choose $u=g(x)$ wisely.
In IB examinations, if the integral is not in the form $\int kg'(x)f(g(x))dx$, the substitution will be provided.
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