Optimal. Leaf size=34 \[ \frac {6 x^2}{25}-\frac {92 x}{125}-\frac {121}{625 (5 x+3)}+\frac {319}{625} \log (5 x+3) \]
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Rubi [A] time = 0.01, antiderivative size = 34, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \begin {gather*} \frac {6 x^2}{25}-\frac {92 x}{125}-\frac {121}{625 (5 x+3)}+\frac {319}{625} \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (2+3 x)}{(3+5 x)^2} \, dx &=\int \left (-\frac {92}{125}+\frac {12 x}{25}+\frac {121}{125 (3+5 x)^2}+\frac {319}{125 (3+5 x)}\right ) \, dx\\ &=-\frac {92 x}{125}+\frac {6 x^2}{25}-\frac {121}{625 (3+5 x)}+\frac {319}{625} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 39, normalized size = 1.15 \begin {gather*} \frac {1500 x^3-3700 x^2-835 x+638 (5 x+3) \log (10 x+6)+913}{1250 (5 x+3)} \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)^2 (2+3 x)}{(3+5 x)^2} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.19, size = 37, normalized size = 1.09 \begin {gather*} \frac {750 \, x^{3} - 1850 \, x^{2} + 319 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 1380 \, x - 121}{625 \, {\left (5 \, x + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.89, size = 48, normalized size = 1.41 \begin {gather*} -\frac {2}{625} \, {\left (5 \, x + 3\right )}^{2} {\left (\frac {64}{5 \, x + 3} - 3\right )} - \frac {121}{625 \, {\left (5 \, x + 3\right )}} - \frac {319}{625} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 27, normalized size = 0.79 \begin {gather*} \frac {6 x^{2}}{25}-\frac {92 x}{125}+\frac {319 \ln \left (5 x +3\right )}{625}-\frac {121}{625 \left (5 x +3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 26, normalized size = 0.76 \begin {gather*} \frac {6}{25} \, x^{2} - \frac {92}{125} \, x - \frac {121}{625 \, {\left (5 \, x + 3\right )}} + \frac {319}{625} \, \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 = 0.03, size = 24, normalized size = 0.71 \begin {gather*} \frac {319\,\ln \left (x+\frac {3}{5}\right )}{625}-\frac {92\,x}{125}-\frac {121}{3125\,\left (x+\frac {3}{5}\right )}+\frac {6\,x^2}{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 27, normalized size = 0.79 \begin {gather*} \frac {6 x^{2}}{25} - \frac {92 x}{125} + \frac {319 \log {\left (5 x + 3 \right )}}{625} - \frac {121}{3125 x + 1875} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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