Optimal. Leaf size=23 \[ -\frac {3 x^2}{5}+\frac {13 x}{25}+\frac {11}{125} \log (5 x+3) \]
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Rubi [A] time = 0.01, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {77} \[ -\frac {3 x^2}{5}+\frac {13 x}{25}+\frac {11}{125} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x) (2+3 x)}{3+5 x} \, dx &=\int \left (\frac {13}{25}-\frac {6 x}{5}+\frac {11}{25 (3+5 x)}\right ) \, dx\\ &=\frac {13 x}{25}-\frac {3 x^2}{5}+\frac {11}{125} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 22, normalized size = 0.96 \[ \frac {1}{125} \left (-75 x^2+65 x+11 \log (5 x+3)+66\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 17, normalized size = 0.74 \[ -\frac {3}{5} \, x^{2} + \frac {13}{25} \, x + \frac {11}{125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.22, size = 18, normalized size = 0.78 \[ -\frac {3}{5} \, x^{2} + \frac {13}{25} \, x + \frac {11}{125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 18, normalized size = 0.78 \[ -\frac {3 x^{2}}{5}+\frac {13 x}{25}+\frac {11 \ln \left (5 x +3\right )}{125} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 17, normalized size = 0.74 \[ -\frac {3}{5} \, x^{2} + \frac {13}{25} \, x + \frac {11}{125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 15, normalized size = 0.65 \[ \frac {13\,x}{25}+\frac {11\,\ln \left (x+\frac {3}{5}\right )}{125}-\frac {3\,x^2}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 20, normalized size = 0.87 \[ - \frac {3 x^{2}}{5} + \frac {13 x}{25} + \frac {11 \log {\left (5 x + 3 \right )}}{125} \]
Verification of antiderivative is not currently implemented for this CAS.
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