Optimal. Leaf size=66 \[ -\frac {25}{16} (1-2 x)^{9/2}+\frac {255}{14} (1-2 x)^{7/2}-\frac {3467}{40} (1-2 x)^{5/2}+\frac {1309}{6} (1-2 x)^{3/2}-\frac {5929}{16} \sqrt {1-2 x} \]
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Rubi [A] time = 0.01, antiderivative size = 66, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {88} \begin {gather*} -\frac {25}{16} (1-2 x)^{9/2}+\frac {255}{14} (1-2 x)^{7/2}-\frac {3467}{40} (1-2 x)^{5/2}+\frac {1309}{6} (1-2 x)^{3/2}-\frac {5929}{16} \sqrt {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}{\sqrt {1-2 x}} \, dx &=\int \left (\frac {5929}{16 \sqrt {1-2 x}}-\frac {1309}{2} \sqrt {1-2 x}+\frac {3467}{8} (1-2 x)^{3/2}-\frac {255}{2} (1-2 x)^{5/2}+\frac {225}{16} (1-2 x)^{7/2}\right ) \, dx\\ &=-\frac {5929}{16} \sqrt {1-2 x}+\frac {1309}{6} (1-2 x)^{3/2}-\frac {3467}{40} (1-2 x)^{5/2}+\frac {255}{14} (1-2 x)^{7/2}-\frac {25}{16} (1-2 x)^{9/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 33, normalized size = 0.50 \begin {gather*} -\frac {1}{105} \sqrt {1-2 x} \left (2625 x^4+10050 x^3+17391 x^2+19574 x+23354\right ) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 60, normalized size = 0.91 \begin {gather*} \frac {-2625 (1-2 x)^{9/2}+30600 (1-2 x)^{7/2}-145614 (1-2 x)^{5/2}+366520 (1-2 x)^{3/2}-622545 \sqrt {1-2 x}}{1680} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.42, size = 29, normalized size = 0.44 \begin {gather*} -\frac {1}{105} \, {\left (2625 \, x^{4} + 10050 \, x^{3} + 17391 \, x^{2} + 19574 \, x + 23354\right )} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.96, size = 67, normalized size = 1.02 \begin {gather*} -\frac {25}{16} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} - \frac {255}{14} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {3467}{40} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} + \frac {1309}{6} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {5929}{16} \, \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 30, normalized size = 0.45 \begin {gather*} -\frac {\left (2625 x^{4}+10050 x^{3}+17391 x^{2}+19574 x +23354\right ) \sqrt {-2 x +1}}{105} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 46, normalized size = 0.70 \begin {gather*} -\frac {25}{16} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} + \frac {255}{14} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {3467}{40} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} + \frac {1309}{6} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {5929}{16} \, \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 46, normalized size = 0.70 \begin {gather*} \frac {1309\,{\left (1-2\,x\right )}^{3/2}}{6}-\frac {5929\,\sqrt {1-2\,x}}{16}-\frac {3467\,{\left (1-2\,x\right )}^{5/2}}{40}+\frac {255\,{\left (1-2\,x\right )}^{7/2}}{14}-\frac {25\,{\left (1-2\,x\right )}^{9/2}}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 47.64, size = 58, normalized size = 0.88 \begin {gather*} - \frac {25 \left (1 - 2 x\right )^{\frac {9}{2}}}{16} + \frac {255 \left (1 - 2 x\right )^{\frac {7}{2}}}{14} - \frac {3467 \left (1 - 2 x\right )^{\frac {5}{2}}}{40} + \frac {1309 \left (1 - 2 x\right )^{\frac {3}{2}}}{6} - \frac {5929 \sqrt {1 - 2 x}}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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