Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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The integral of sec(x)tan(x) is equal to?

tan(x)
sec(x)
ln|sec(x) + tan(x)|
sec²(x)

The correct answer is: sec(x)

To determine the integral of sec(x)tan(x), we start by considering the derivatives of common trigonometric functions. The derivative of sec(x) is sec(x)tan(x). Therefore, when we integrate sec(x)tan(x), we essentially find the function whose derivative gives us sec(x)tan(x), which leads us directly to conclude that the integral is sec(x). This relationship is fundamental in calculus, linking the operations of differentiation and integration. When applying this to sec(x), it confirms that the integration process yields the correct result of the integral being equal to sec(x) plus a constant of integration. Thus, the statement about the integral of sec(x)tan(x) equaling sec(x) is accurate based on these well-established principles of calculus. The other options, while they may involve related trigonometric functions or logarithmic expressions, do not accurately represent the integral of sec(x)tan(x) or correspond to its derivative.