Question Detail

We need to evaluate the indefinite integral ∫ a sec ax tan ax dx.Recall the derivative of sec(u) with respect to u is sec(u) tan(u).Using the chain rule, the derivative of sec(ax) with respect to x is d/dx [sec(ax)] = sec(ax) tan(ax) * d/dx(ax) = a sec(ax) tan(ax).Therefore, the antiderivative of a sec ax tan ax is sec ax + C.Option D matches this result (assuming the constant of integration C is implicit).