Optimal. Leaf size=41 \[ \frac {75 x^3}{4}+\frac {795 x^2}{8}+\frac {5119 x}{16}+\frac {5929}{32 (1-2 x)}+\frac {1309}{4} \log (1-2 x) \]
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Rubi [A] time = 0.02, antiderivative size = 41, 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 {75 x^3}{4}+\frac {795 x^2}{8}+\frac {5119 x}{16}+\frac {5929}{32 (1-2 x)}+\frac {1309}{4} \log (1-2 x) \end {gather*}
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^2 (3+5 x)^2}{(1-2 x)^2} \, dx &=\int \left (\frac {5119}{16}+\frac {795 x}{4}+\frac {225 x^2}{4}+\frac {5929}{16 (-1+2 x)^2}+\frac {1309}{2 (-1+2 x)}\right ) \, dx\\ &=\frac {5929}{32 (1-2 x)}+\frac {5119 x}{16}+\frac {795 x^2}{8}+\frac {75 x^3}{4}+\frac {1309}{4} \log (1-2 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 41, normalized size = 1.00 \begin {gather*} \frac {300 x^4+1440 x^3+4324 x^2-5554 x+2618 (2 x-1) \log (1-2 x)+15}{16 x-8} \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 {(2+3 x)^2 (3+5 x)^2}{(1-2 x)^2} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.36, size = 42, normalized size = 1.02 \begin {gather*} \frac {1200 \, x^{4} + 5760 \, x^{3} + 17296 \, x^{2} + 10472 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 10238 \, x - 5929}{32 \, {\left (2 \, x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.90, size = 57, normalized size = 1.39 \begin {gather*} \frac {1}{32} \, {\left (2 \, x - 1\right )}^{3} {\left (\frac {1020}{2 \, x - 1} + \frac {6934}{{\left (2 \, x - 1\right )}^{2}} + 75\right )} - \frac {5929}{32 \, {\left (2 \, x - 1\right )}} - \frac {1309}{4} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\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 = 32, normalized size = 0.78 \begin {gather*} \frac {75 x^{3}}{4}+\frac {795 x^{2}}{8}+\frac {5119 x}{16}+\frac {1309 \ln \left (2 x -1\right )}{4}-\frac {5929}{32 \left (2 x -1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.67, size = 31, normalized size = 0.76 \begin {gather*} \frac {75}{4} \, x^{3} + \frac {795}{8} \, x^{2} + \frac {5119}{16} \, x - \frac {5929}{32 \, {\left (2 \, x - 1\right )}} + \frac {1309}{4} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 29, normalized size = 0.71 \begin {gather*} \frac {5119\,x}{16}+\frac {1309\,\ln \left (x-\frac {1}{2}\right )}{4}-\frac {5929}{64\,\left (x-\frac {1}{2}\right )}+\frac {795\,x^2}{8}+\frac {75\,x^3}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 34, normalized size = 0.83 \begin {gather*} \frac {75 x^{3}}{4} + \frac {795 x^{2}}{8} + \frac {5119 x}{16} + \frac {1309 \log {\left (2 x - 1 \right )}}{4} - \frac {5929}{64 x - 32} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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