7.2. Integration Techniques
Example 7.2.4(d): Applying the Substitution Rule
Find tan(x) dx and cot(x) dxThis will be a relief because it is easy: tan(x) = sin(x)/cos(x) so that the top function is the derivative of the bottom function (except for a minus sign).
Therefore we can apply a previous example (or make the substitution u = cos(x)) to determine the answer right away:
tan(x) dx = -ln(cos(x))To find cot(x) dx is left as an (easy) exercise.