To evaluate the integral ∫tan²(x)dx, we can use the identity:
tan²(x) = sec²(x) – 1
Substituting this identity in the integral, we get:
∫tan²(x)dx = ∫(sec²(x) – 1)dx
Integrating the right-hand side of the above equation, we get:
∫tan²(x)dx = tan(x) – x + C
where C is the constant of integration.
Therefore, the antiderivative of tan²(x) is tan(x) – x + C.
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