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Here is the problem: integrate sec(x) to the power 2tan(x).

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Find the indefinite integral (antiderivative) of sec(x) squared tan(x) with respect to x.

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Start with the integral.

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Substitute u equals sec(x), so du equals (sec(x) times tan(x)) dx.

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Power rule: the integral of x to the power n dx equals x to the power n plus 1/(n plus 1).

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Substitute back u equals sec(x).

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Simplify and add the constant of integration.

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So the answer is sec(x) squared/2 plus C.

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An antiderivative F satisfies F prime of x equals f(x). Because the derivative of any constant is 0, every antiderivative differs by a constant C.

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Differentiated the answer and compared it with the integrand at 8 sample points, which checks out.