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Integration is always more difficult than differentiation as the rules for integration are much more open, and less apparent than for derivatives.
A good example is the anti-derivative of tan(x). This integral is possible if we realise that tan(x) is equal to sin(x)/cos(x). Because sin(x) is very closely related to the derivative of cos(x). In fact, the derivative of cos(x) is equal to -sin(x).
This means we can use a u-substitution, by letting u = cos(x) to find the result.
