Optimal. Leaf size=92 \[ -\frac{225}{64} (1-2 x)^{9/2}+\frac{13905}{224} (1-2 x)^{7/2}-\frac{159111}{320} (1-2 x)^{5/2}+\frac{40453}{16} (1-2 x)^{3/2}-\frac{832951}{64} \sqrt{1-2 x}-\frac{381073}{32 \sqrt{1-2 x}}+\frac{290521}{192 (1-2 x)^{3/2}} \]
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Rubi [A] time = 0.0167298, 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} \[ -\frac{225}{64} (1-2 x)^{9/2}+\frac{13905}{224} (1-2 x)^{7/2}-\frac{159111}{320} (1-2 x)^{5/2}+\frac{40453}{16} (1-2 x)^{3/2}-\frac{832951}{64} \sqrt{1-2 x}-\frac{381073}{32 \sqrt{1-2 x}}+\frac{290521}{192 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^4 (3+5 x)^2}{(1-2 x)^{5/2}} \, dx &=\int \left (\frac{290521}{64 (1-2 x)^{5/2}}-\frac{381073}{32 (1-2 x)^{3/2}}+\frac{832951}{64 \sqrt{1-2 x}}-\frac{121359}{16} \sqrt{1-2 x}+\frac{159111}{64} (1-2 x)^{3/2}-\frac{13905}{32} (1-2 x)^{5/2}+\frac{2025}{64} (1-2 x)^{7/2}\right ) \, dx\\ &=\frac{290521}{192 (1-2 x)^{3/2}}-\frac{381073}{32 \sqrt{1-2 x}}-\frac{832951}{64} \sqrt{1-2 x}+\frac{40453}{16} (1-2 x)^{3/2}-\frac{159111}{320} (1-2 x)^{5/2}+\frac{13905}{224} (1-2 x)^{7/2}-\frac{225}{64} (1-2 x)^{9/2}\\ \end{align*}
Mathematica [A] time = 0.0190011, size = 43, normalized size = 0.47 \[ -\frac{23625 x^6+137700 x^5+402489 x^4+915492 x^3+3294996 x^2-6731112 x+2238664}{105 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 40, normalized size = 0.4 \begin{align*} -{\frac{23625\,{x}^{6}+137700\,{x}^{5}+402489\,{x}^{4}+915492\,{x}^{3}+3294996\,{x}^{2}-6731112\,x+2238664}{105} \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 = 1.83664, size = 81, normalized size = 0.88 \begin{align*} -\frac{225}{64} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{13905}{224} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{159111}{320} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{40453}{16} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{832951}{64} \, \sqrt{-2 \, x + 1} + \frac{3773 \,{\left (1212 \, x - 529\right )}}{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 = 1.53935, size = 173, normalized size = 1.88 \begin{align*} -\frac{{\left (23625 \, x^{6} + 137700 \, x^{5} + 402489 \, x^{4} + 915492 \, x^{3} + 3294996 \, x^{2} - 6731112 \, x + 2238664\right )} \sqrt{-2 \, x + 1}}{105 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 24.8006, size = 82, normalized size = 0.89 \begin{align*} - \frac{225 \left (1 - 2 x\right )^{\frac{9}{2}}}{64} + \frac{13905 \left (1 - 2 x\right )^{\frac{7}{2}}}{224} - \frac{159111 \left (1 - 2 x\right )^{\frac{5}{2}}}{320} + \frac{40453 \left (1 - 2 x\right )^{\frac{3}{2}}}{16} - \frac{832951 \sqrt{1 - 2 x}}{64} - \frac{381073}{32 \sqrt{1 - 2 x}} + \frac{290521}{192 \left (1 - 2 x\right )^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.07236, size = 119, normalized size = 1.29 \begin{align*} -\frac{225}{64} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{13905}{224} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{159111}{320} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{40453}{16} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{832951}{64} \, \sqrt{-2 \, x + 1} - \frac{3773 \,{\left (1212 \, x - 529\right )}}{192 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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