Optimal. Leaf size=92 \[ -\frac{81}{64} (1-2 x)^{15/2}+\frac{81}{4} (1-2 x)^{13/2}-\frac{97335}{704} (1-2 x)^{11/2}+\frac{4165}{8} (1-2 x)^{9/2}-\frac{74235}{64} (1-2 x)^{7/2}+\frac{12005}{8} (1-2 x)^{5/2}-\frac{184877}{192} (1-2 x)^{3/2} \]
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Rubi [A] time = 0.0180173, antiderivative size = 92, normalized size of antiderivative = 1., 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 = {77} \[ -\frac{81}{64} (1-2 x)^{15/2}+\frac{81}{4} (1-2 x)^{13/2}-\frac{97335}{704} (1-2 x)^{11/2}+\frac{4165}{8} (1-2 x)^{9/2}-\frac{74235}{64} (1-2 x)^{7/2}+\frac{12005}{8} (1-2 x)^{5/2}-\frac{184877}{192} (1-2 x)^{3/2} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \sqrt{1-2 x} (2+3 x)^5 (3+5 x) \, dx &=\int \left (\frac{184877}{64} \sqrt{1-2 x}-\frac{60025}{8} (1-2 x)^{3/2}+\frac{519645}{64} (1-2 x)^{5/2}-\frac{37485}{8} (1-2 x)^{7/2}+\frac{97335}{64} (1-2 x)^{9/2}-\frac{1053}{4} (1-2 x)^{11/2}+\frac{1215}{64} (1-2 x)^{13/2}\right ) \, dx\\ &=-\frac{184877}{192} (1-2 x)^{3/2}+\frac{12005}{8} (1-2 x)^{5/2}-\frac{74235}{64} (1-2 x)^{7/2}+\frac{4165}{8} (1-2 x)^{9/2}-\frac{97335}{704} (1-2 x)^{11/2}+\frac{81}{4} (1-2 x)^{13/2}-\frac{81}{64} (1-2 x)^{15/2}\\ \end{align*}
Mathematica [A] time = 0.0182522, size = 43, normalized size = 0.47 \[ -\frac{1}{33} (1-2 x)^{3/2} \left (2673 x^6+13365 x^5+29565 x^4+38220 x^3+32220 x^2+18696 x+7288\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 40, normalized size = 0.4 \begin{align*} -{\frac{2673\,{x}^{6}+13365\,{x}^{5}+29565\,{x}^{4}+38220\,{x}^{3}+32220\,{x}^{2}+18696\,x+7288}{33} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.07487, size = 86, normalized size = 0.93 \begin{align*} -\frac{81}{64} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} + \frac{81}{4} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{97335}{704} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{4165}{8} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{74235}{64} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{12005}{8} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{184877}{192} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.34584, size = 144, normalized size = 1.57 \begin{align*} \frac{1}{33} \,{\left (5346 \, x^{7} + 24057 \, x^{6} + 45765 \, x^{5} + 46875 \, x^{4} + 26220 \, x^{3} + 5172 \, x^{2} - 4120 \, x - 7288\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.30543, size = 82, normalized size = 0.89 \begin{align*} - \frac{81 \left (1 - 2 x\right )^{\frac{15}{2}}}{64} + \frac{81 \left (1 - 2 x\right )^{\frac{13}{2}}}{4} - \frac{97335 \left (1 - 2 x\right )^{\frac{11}{2}}}{704} + \frac{4165 \left (1 - 2 x\right )^{\frac{9}{2}}}{8} - \frac{74235 \left (1 - 2 x\right )^{\frac{7}{2}}}{64} + \frac{12005 \left (1 - 2 x\right )^{\frac{5}{2}}}{8} - \frac{184877 \left (1 - 2 x\right )^{\frac{3}{2}}}{192} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.78675, size = 143, normalized size = 1.55 \begin{align*} \frac{81}{64} \,{\left (2 \, x - 1\right )}^{7} \sqrt{-2 \, x + 1} + \frac{81}{4} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} + \frac{97335}{704} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{4165}{8} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{74235}{64} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{12005}{8} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{184877}{192} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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