Evaluate | tan (3x) sec*(3x) dx. EXAMPLE 5 If we separate one sec2(3x) factor, we can express the remaining sec?(3x) factor in terms of tangent using the identity sec2(3x) = 1 + tan?(3x). SOLUTION We can then evaluate the integral by substituting u = tan(3x) so that du = dx. | = | tan (3x) sec*(3x) dx tan (3x) sec²(3x) sec²(3x) dx tan°(3x)(1 + tan?(3x)) sec²(3x) dx du 1 + du 27 + C + + 27 긁 tan®(3x) + C -|3. II

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