WEBVTT

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Here is the problem: integrate 1/(x(x plus 1)) dx.

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

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Start with the integral.

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Partial fractions: split 1/((x minus r₁)(x minus r₂)) into A/(x minus r₁) plus B/(x minus r₂).

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Simplify and add the constant of integration.

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So the answer is ln(abs(x)) minus ln(abs(x 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.