Optimal. Leaf size=9 \[ c \text {Ei}(-\log (c x)) \]
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Rubi [A] time = 0.02, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {2309, 2178} \[ c \text {Ei}(-\log (c x)) \]
Antiderivative was successfully verified.
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Rule 2178
Rule 2309
Rubi steps
\begin {align*} \int \frac {1}{x^2 \log (c x)} \, dx &=c \operatorname {Subst}\left (\int \frac {e^{-x}}{x} \, dx,x,\log (c x)\right )\\ &=c \text {Ei}(-\log (c x))\\ \end {align*}
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Mathematica [A] time = 0.01, size = 9, normalized size = 1.00 \[ c \text {Ei}(-\log (c x)) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 10, normalized size = 1.11 \[ c \operatorname {log\_integral}\left (\frac {1}{c x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^{2} \log \left (c x\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 10, normalized size = 1.11 \[ -c \Ei \left (1, \ln \left (c x \right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.71, size = 9, normalized size = 1.00 \[ c {\rm Ei}\left (-\log \left (c x\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.11 \[ \int \frac {1}{x^2\,\ln \left (c\,x\right )} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^{2} \log {\left (c x \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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