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Integrating a function of the form $\\frac{a}{x}$ using a table of integrals / anti-derivatives.

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Calculate the integral of $f(x)=\\frac{\\var{a}}{x}$

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From the Table of Integrals we see that a function of the form \\[ f(x)= \\frac{1}{x} \\] has the integral \\[ \\int \\frac{1}{x} dx  = \\ln |x|+ c,\\]

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and \\[ \\int kf(x) \\,dx = k \\int f(x) \\, dx.\\]

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So, for the function

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\\[f(x)=\\frac{\\var{{a}}}{x},\\]

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the integral is

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\\[ \\int \\frac{\\var{a}}{x} dx \\,= \\simplify[unitFactor]{{a}int(1/x,x)} \\,=\\simplify[unitFactor]{{a} ln(abs(x)) +c}.  \\]

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You forgot the constant of integration.

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You forgot the constant of integration.

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