Optimal. Leaf size=21 \[ \frac {1}{11} \log (5 x+3)-\frac {1}{11} \log (1-2 x) \]
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Rubi [A] time = 0.00, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {36, 31} \[ \frac {1}{11} \log (5 x+3)-\frac {1}{11} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 31
Rule 36
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x) (3+5 x)} \, dx &=\frac {2}{11} \int \frac {1}{1-2 x} \, dx+\frac {5}{11} \int \frac {1}{3+5 x} \, dx\\ &=-\frac {1}{11} \log (1-2 x)+\frac {1}{11} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 21, normalized size = 1.00 \[ \frac {1}{11} \log (5 x+3)-\frac {1}{11} \log (1-2 x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 17, normalized size = 0.81 \[ \frac {1}{11} \, \log \left (5 \, x + 3\right ) - \frac {1}{11} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.85, size = 19, normalized size = 0.90 \[ \frac {1}{11} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {1}{11} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 18, normalized size = 0.86 \[ -\frac {\ln \left (2 x -1\right )}{11}+\frac {\ln \left (5 x +3\right )}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.79, size = 17, normalized size = 0.81 \[ \frac {1}{11} \, \log \left (5 \, x + 3\right ) - \frac {1}{11} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.13, size = 16, normalized size = 0.76 \[ \frac {\ln \left (\frac {5\,x+3}{2\,x-1}\right )}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 15, normalized size = 0.71 \[ - \frac {\log {\left (x - \frac {1}{2} \right )}}{11} + \frac {\log {\left (x + \frac {3}{5} \right )}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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