We can begin by using the fact that the derivative of tan(x) is sec^2(x). Using this derivative and the chain rule, we can rewrite the integral as:
∫sec^2 x dx = ∫1/cos^2 x dx = ∫(cos(x))^(-2) dx
Applying the power rule of integration, we can then obtain:
∫sec^2 x dx = tan(x) + C
Where C is the constant of integration. Therefore, the integral of sec^2 x dx is equal to the tangent function of x plus a constant.
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