Optimal. Leaf size=92 \[ -\frac{1215}{832} (1-2 x)^{13/2}+\frac{1053}{44} (1-2 x)^{11/2}-\frac{10815}{64} (1-2 x)^{9/2}+\frac{5355}{8} (1-2 x)^{7/2}-\frac{103929}{64} (1-2 x)^{5/2}+\frac{60025}{24} (1-2 x)^{3/2}-\frac{184877}{64} \sqrt{1-2 x} \]
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Rubi [A] time = 0.0167062, 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} \[ -\frac{1215}{832} (1-2 x)^{13/2}+\frac{1053}{44} (1-2 x)^{11/2}-\frac{10815}{64} (1-2 x)^{9/2}+\frac{5355}{8} (1-2 x)^{7/2}-\frac{103929}{64} (1-2 x)^{5/2}+\frac{60025}{24} (1-2 x)^{3/2}-\frac{184877}{64} \sqrt{1-2 x} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x)^5 (3+5 x)}{\sqrt{1-2 x}} \, dx &=\int \left (\frac{184877}{64 \sqrt{1-2 x}}-\frac{60025}{8} \sqrt{1-2 x}+\frac{519645}{64} (1-2 x)^{3/2}-\frac{37485}{8} (1-2 x)^{5/2}+\frac{97335}{64} (1-2 x)^{7/2}-\frac{1053}{4} (1-2 x)^{9/2}+\frac{1215}{64} (1-2 x)^{11/2}\right ) \, dx\\ &=-\frac{184877}{64} \sqrt{1-2 x}+\frac{60025}{24} (1-2 x)^{3/2}-\frac{103929}{64} (1-2 x)^{5/2}+\frac{5355}{8} (1-2 x)^{7/2}-\frac{10815}{64} (1-2 x)^{9/2}+\frac{1053}{44} (1-2 x)^{11/2}-\frac{1215}{832} (1-2 x)^{13/2}\\ \end{align*}
Mathematica [A] time = 0.016173, size = 43, normalized size = 0.47 \[ -\frac{1}{429} \sqrt{1-2 x} \left (40095 x^6+208251 x^5+488925 x^4+698580 x^3+707436 x^2+597464 x+638648\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 40, normalized size = 0.4 \begin{align*} -{\frac{40095\,{x}^{6}+208251\,{x}^{5}+488925\,{x}^{4}+698580\,{x}^{3}+707436\,{x}^{2}+597464\,x+638648}{429}\sqrt{1-2\,x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.37661, size = 86, normalized size = 0.93 \begin{align*} -\frac{1215}{832} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} + \frac{1053}{44} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} - \frac{10815}{64} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{5355}{8} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{103929}{64} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{60025}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{184877}{64} \, \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.42338, size = 144, normalized size = 1.57 \begin{align*} -\frac{1}{429} \,{\left (40095 \, x^{6} + 208251 \, x^{5} + 488925 \, x^{4} + 698580 \, x^{3} + 707436 \, x^{2} + 597464 \, x + 638648\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 54.7853, size = 82, normalized size = 0.89 \begin{align*} - \frac{1215 \left (1 - 2 x\right )^{\frac{13}{2}}}{832} + \frac{1053 \left (1 - 2 x\right )^{\frac{11}{2}}}{44} - \frac{10815 \left (1 - 2 x\right )^{\frac{9}{2}}}{64} + \frac{5355 \left (1 - 2 x\right )^{\frac{7}{2}}}{8} - \frac{103929 \left (1 - 2 x\right )^{\frac{5}{2}}}{64} + \frac{60025 \left (1 - 2 x\right )^{\frac{3}{2}}}{24} - \frac{184877 \sqrt{1 - 2 x}}{64} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.31124, size = 134, normalized size = 1.46 \begin{align*} -\frac{1215}{832} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} - \frac{1053}{44} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} - \frac{10815}{64} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{5355}{8} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{103929}{64} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{60025}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{184877}{64} \, \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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