Optimal. Leaf size=92 \[ -\frac{135}{64} (1-2 x)^{15/2}+\frac{13905}{416} (1-2 x)^{13/2}-\frac{159111}{704} (1-2 x)^{11/2}+\frac{40453}{48} (1-2 x)^{9/2}-\frac{118993}{64} (1-2 x)^{7/2}+\frac{381073}{160} (1-2 x)^{5/2}-\frac{290521}{192} (1-2 x)^{3/2} \]
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Rubi [A] time = 0.0169372, antiderivative size = 92, normalized size of antiderivative = 1., 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} \[ -\frac{135}{64} (1-2 x)^{15/2}+\frac{13905}{416} (1-2 x)^{13/2}-\frac{159111}{704} (1-2 x)^{11/2}+\frac{40453}{48} (1-2 x)^{9/2}-\frac{118993}{64} (1-2 x)^{7/2}+\frac{381073}{160} (1-2 x)^{5/2}-\frac{290521}{192} (1-2 x)^{3/2} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \sqrt{1-2 x} (2+3 x)^4 (3+5 x)^2 \, dx &=\int \left (\frac{290521}{64} \sqrt{1-2 x}-\frac{381073}{32} (1-2 x)^{3/2}+\frac{832951}{64} (1-2 x)^{5/2}-\frac{121359}{16} (1-2 x)^{7/2}+\frac{159111}{64} (1-2 x)^{9/2}-\frac{13905}{32} (1-2 x)^{11/2}+\frac{2025}{64} (1-2 x)^{13/2}\right ) \, dx\\ &=-\frac{290521}{192} (1-2 x)^{3/2}+\frac{381073}{160} (1-2 x)^{5/2}-\frac{118993}{64} (1-2 x)^{7/2}+\frac{40453}{48} (1-2 x)^{9/2}-\frac{159111}{704} (1-2 x)^{11/2}+\frac{13905}{416} (1-2 x)^{13/2}-\frac{135}{64} (1-2 x)^{15/2}\\ \end{align*}
Mathematica [A] time = 0.0192108, size = 43, normalized size = 0.47 \[ -\frac{(1-2 x)^{3/2} \left (289575 x^6+1425600 x^5+3106755 x^4+3960500 x^3+3298140 x^2+1895832 x+734904\right )}{2145} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 40, normalized size = 0.4 \begin{align*} -{\frac{289575\,{x}^{6}+1425600\,{x}^{5}+3106755\,{x}^{4}+3960500\,{x}^{3}+3298140\,{x}^{2}+1895832\,x+734904}{2145} \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 = 1.28226, size = 86, normalized size = 0.93 \begin{align*} -\frac{135}{64} \,{\left (-2 \, x + 1\right )}^{\frac{15}{2}} + \frac{13905}{416} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{159111}{704} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{40453}{48} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{118993}{64} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{381073}{160} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{290521}{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 = 1.49514, size = 169, normalized size = 1.84 \begin{align*} \frac{1}{2145} \,{\left (579150 \, x^{7} + 2561625 \, x^{6} + 4787910 \, x^{5} + 4814245 \, x^{4} + 2635780 \, x^{3} + 493524 \, x^{2} - 426024 \, x - 734904\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.37245, size = 82, normalized size = 0.89 \begin{align*} - \frac{135 \left (1 - 2 x\right )^{\frac{15}{2}}}{64} + \frac{13905 \left (1 - 2 x\right )^{\frac{13}{2}}}{416} - \frac{159111 \left (1 - 2 x\right )^{\frac{11}{2}}}{704} + \frac{40453 \left (1 - 2 x\right )^{\frac{9}{2}}}{48} - \frac{118993 \left (1 - 2 x\right )^{\frac{7}{2}}}{64} + \frac{381073 \left (1 - 2 x\right )^{\frac{5}{2}}}{160} - \frac{290521 \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 = 2.43285, size = 143, normalized size = 1.55 \begin{align*} \frac{135}{64} \,{\left (2 \, x - 1\right )}^{7} \sqrt{-2 \, x + 1} + \frac{13905}{416} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} + \frac{159111}{704} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{40453}{48} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{118993}{64} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{381073}{160} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{290521}{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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