Optimal. Leaf size=16 \[ \frac {11}{25} \log (5 x+3)-\frac {2 x}{5} \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {43} \begin {gather*} \frac {11}{25} \log (5 x+3)-\frac {2 x}{5} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {1-2 x}{3+5 x} \, dx &=\int \left (-\frac {2}{5}+\frac {11}{5 (3+5 x)}\right ) \, dx\\ &=-\frac {2 x}{5}+\frac {11}{25} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.06 \begin {gather*} \frac {1}{25} (-10 x+11 \log (5 x+3)-6) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1-2 x}{3+5 x} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.39, size = 12, normalized size = 0.75 \begin {gather*} -\frac {2}{5} \, x + \frac {11}{25} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.24, size = 13, normalized size = 0.81 \begin {gather*} -\frac {2}{5} \, x + \frac {11}{25} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.81 \begin {gather*} -\frac {2 x}{5}+\frac {11 \ln \left (5 x +3\right )}{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.63, size = 12, normalized size = 0.75 \begin {gather*} -\frac {2}{5} \, x + \frac {11}{25} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 10, normalized size = 0.62 \begin {gather*} \frac {11\,\ln \left (x+\frac {3}{5}\right )}{25}-\frac {2\,x}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 14, normalized size = 0.88 \begin {gather*} - \frac {2 x}{5} + \frac {11 \log {\left (5 x + 3 \right )}}{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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