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Integrating a function of the form $\\frac{a}{x}$ using a table of integrals / anti-derivatives.
", "licence": "None specified"}, "statement": "Calculate the integral of $f(x)=\\frac{\\var{a}}{x}$
\n", "advice": "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,\\]
\nand \\[ \\int kf(x) \\,dx = k \\int f(x) \\, dx.\\]
\nSo, for the function
\n\\[f(x)=\\frac{\\var{{a}}}{x},\\]
\nthe integral is
\n\\[ \\int \\frac{\\var{a}}{x} dx \\,= \\simplify[unitFactor]{{a}int(1/x,x)} \\,=\\simplify[unitFactor]{{a} ln(abs(x)) +c}. \\]
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