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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(<em>x</em>). This integral is possible if we realise that tan(<em>x</em>) is equal to sin(<em>x</em>)/cos(<em>x</em>). Because sin(<em>x</em>) is very closely related to the derivative of cos(<em>x</em>). In fact, the derivative of cos(<em>x</em>) is equal to -sin(<em>x</em>).

This means we can use a <em>u</em>-substitution, by letting <em>u</em> = cos(<em>x</em>) to find the result.

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