Optimal. Leaf size=66 \[ -\frac{225}{176} (1-2 x)^{11/2}+\frac{85}{6} (1-2 x)^{9/2}-\frac{3467}{56} (1-2 x)^{7/2}+\frac{1309}{10} (1-2 x)^{5/2}-\frac{5929}{48} (1-2 x)^{3/2} \]
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Rubi [A] time = 0.01326, antiderivative size = 66, 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} \[ -\frac{225}{176} (1-2 x)^{11/2}+\frac{85}{6} (1-2 x)^{9/2}-\frac{3467}{56} (1-2 x)^{7/2}+\frac{1309}{10} (1-2 x)^{5/2}-\frac{5929}{48} (1-2 x)^{3/2} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \sqrt{1-2 x} (2+3 x)^2 (3+5 x)^2 \, dx &=\int \left (\frac{5929}{16} \sqrt{1-2 x}-\frac{1309}{2} (1-2 x)^{3/2}+\frac{3467}{8} (1-2 x)^{5/2}-\frac{255}{2} (1-2 x)^{7/2}+\frac{225}{16} (1-2 x)^{9/2}\right ) \, dx\\ &=-\frac{5929}{48} (1-2 x)^{3/2}+\frac{1309}{10} (1-2 x)^{5/2}-\frac{3467}{56} (1-2 x)^{7/2}+\frac{85}{6} (1-2 x)^{9/2}-\frac{225}{176} (1-2 x)^{11/2}\\ \end{align*}
Mathematica [A] time = 0.0142711, size = 33, normalized size = 0.5 \[ -\frac{(1-2 x)^{3/2} \left (23625 x^4+83650 x^3+125115 x^2+102714 x+48098\right )}{1155} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 30, normalized size = 0.5 \begin{align*} -{\frac{23625\,{x}^{4}+83650\,{x}^{3}+125115\,{x}^{2}+102714\,x+48098}{1155} \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 = 1.01038, size = 62, normalized size = 0.94 \begin{align*} -\frac{225}{176} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{85}{6} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{3467}{56} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{1309}{10} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{5929}{48} \,{\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 = 1.60726, size = 122, normalized size = 1.85 \begin{align*} \frac{1}{1155} \,{\left (47250 \, x^{5} + 143675 \, x^{4} + 166580 \, x^{3} + 80313 \, x^{2} - 6518 \, x - 48098\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.92181, size = 58, normalized size = 0.88 \begin{align*} - \frac{225 \left (1 - 2 x\right )^{\frac{11}{2}}}{176} + \frac{85 \left (1 - 2 x\right )^{\frac{9}{2}}}{6} - \frac{3467 \left (1 - 2 x\right )^{\frac{7}{2}}}{56} + \frac{1309 \left (1 - 2 x\right )^{\frac{5}{2}}}{10} - \frac{5929 \left (1 - 2 x\right )^{\frac{3}{2}}}{48} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.39782, size = 100, normalized size = 1.52 \begin{align*} \frac{225}{176} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{85}{6} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{3467}{56} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{1309}{10} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{5929}{48} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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