Optimal. Leaf size=55 \[ \frac {324 x^5}{125}+\frac {189 x^4}{125}-\frac {1809 x^3}{625}-\frac {3621 x^2}{3125}+\frac {5459 x}{3125}-\frac {121}{78125 (5 x+3)}+\frac {1408 \log (5 x+3)}{78125} \]
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Rubi [A] time = 0.03, antiderivative size = 55, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {88} \begin {gather*} \frac {324 x^5}{125}+\frac {189 x^4}{125}-\frac {1809 x^3}{625}-\frac {3621 x^2}{3125}+\frac {5459 x}{3125}-\frac {121}{78125 (5 x+3)}+\frac {1408 \log (5 x+3)}{78125} \end {gather*}
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (2+3 x)^4}{(3+5 x)^2} \, dx &=\int \left (\frac {5459}{3125}-\frac {7242 x}{3125}-\frac {5427 x^2}{625}+\frac {756 x^3}{125}+\frac {324 x^4}{25}+\frac {121}{15625 (3+5 x)^2}+\frac {1408}{15625 (3+5 x)}\right ) \, dx\\ &=\frac {5459 x}{3125}-\frac {3621 x^2}{3125}-\frac {1809 x^3}{625}+\frac {189 x^4}{125}+\frac {324 x^5}{125}-\frac {121}{78125 (3+5 x)}+\frac {1408 \log (3+5 x)}{78125}\\ \end {align*}
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Mathematica [A] time = 0.05, size = 56, normalized size = 1.02 \begin {gather*} \frac {5062500 x^6+5990625 x^5-3881250 x^4-5655000 x^3+2054000 x^2+3698835 x+7040 (5 x+3) \log (6 (5 x+3))+990421}{390625 (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)^4}{(3+5 x)^2} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.16, size = 52, normalized size = 0.95 \begin {gather*} \frac {1012500 \, x^{6} + 1198125 \, x^{5} - 776250 \, x^{4} - 1131000 \, x^{3} + 410800 \, x^{2} + 1408 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 409425 \, x - 121}{78125 \, {\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 = 75, normalized size = 1.36 \begin {gather*} -\frac {1}{390625} \, {\left (5 \, x + 3\right )}^{5} {\left (\frac {3915}{5 \, x + 3} - \frac {8775}{{\left (5 \, x + 3\right )}^{2}} - \frac {26850}{{\left (5 \, x + 3\right )}^{3}} - \frac {30050}{{\left (5 \, x + 3\right )}^{4}} - 324\right )} - \frac {121}{78125 \, {\left (5 \, x + 3\right )}} - \frac {1408}{78125} \, \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 = 42, normalized size = 0.76 \begin {gather*} \frac {324 x^{5}}{125}+\frac {189 x^{4}}{125}-\frac {1809 x^{3}}{625}-\frac {3621 x^{2}}{3125}+\frac {5459 x}{3125}+\frac {1408 \ln \left (5 x +3\right )}{78125}-\frac {121}{78125 \left (5 x +3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 41, normalized size = 0.75 \begin {gather*} \frac {324}{125} \, x^{5} + \frac {189}{125} \, x^{4} - \frac {1809}{625} \, x^{3} - \frac {3621}{3125} \, x^{2} + \frac {5459}{3125} \, x - \frac {121}{78125 \, {\left (5 \, x + 3\right )}} + \frac {1408}{78125} \, \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 = 39, normalized size = 0.71 \begin {gather*} \frac {5459\,x}{3125}+\frac {1408\,\ln \left (x+\frac {3}{5}\right )}{78125}-\frac {121}{390625\,\left (x+\frac {3}{5}\right )}-\frac {3621\,x^2}{3125}-\frac {1809\,x^3}{625}+\frac {189\,x^4}{125}+\frac {324\,x^5}{125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 48, normalized size = 0.87 \begin {gather*} \frac {324 x^{5}}{125} + \frac {189 x^{4}}{125} - \frac {1809 x^{3}}{625} - \frac {3621 x^{2}}{3125} + \frac {5459 x}{3125} + \frac {1408 \log {\left (5 x + 3 \right )}}{78125} - \frac {121}{390625 x + 234375} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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