MathCS.org - Real Analysis: Example 7.2.4(d): Applying the Substitution Rule

Example 7.2.4(d): Applying the Substitution Rule

Find tan(x) dx and cot(x) dx

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This 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.

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Example 7.2.4(d): Applying the Substitution Rule