WEBVTT

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Here is the problem: the integral of 2x/(x squared plus 1) dx.

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Find the indefinite integral (antiderivative) of 2 x / (x squared plus 1) with respect to x.

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Start with the integral.

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Logarithm rule: the numerator is a constant multiple of the denominator prime s derivative, the integral of u prime /u dx equals ln|u|.

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Simplify and add the constant of integration.

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So the answer is ln(abs(x squared plus 1)) 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.