Optimal. Leaf size=66 \[ -\frac{25}{16} (1-2 x)^{9/2}+\frac{255}{14} (1-2 x)^{7/2}-\frac{3467}{40} (1-2 x)^{5/2}+\frac{1309}{6} (1-2 x)^{3/2}-\frac{5929}{16} \sqrt{1-2 x} \]
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Rubi [A] time = 0.012597, 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} \[ -\frac{25}{16} (1-2 x)^{9/2}+\frac{255}{14} (1-2 x)^{7/2}-\frac{3467}{40} (1-2 x)^{5/2}+\frac{1309}{6} (1-2 x)^{3/2}-\frac{5929}{16} \sqrt{1-2 x} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^2 (3+5 x)^2}{\sqrt{1-2 x}} \, dx &=\int \left (\frac{5929}{16 \sqrt{1-2 x}}-\frac{1309}{2} \sqrt{1-2 x}+\frac{3467}{8} (1-2 x)^{3/2}-\frac{255}{2} (1-2 x)^{5/2}+\frac{225}{16} (1-2 x)^{7/2}\right ) \, dx\\ &=-\frac{5929}{16} \sqrt{1-2 x}+\frac{1309}{6} (1-2 x)^{3/2}-\frac{3467}{40} (1-2 x)^{5/2}+\frac{255}{14} (1-2 x)^{7/2}-\frac{25}{16} (1-2 x)^{9/2}\\ \end{align*}
Mathematica [A] time = 0.0119313, size = 33, normalized size = 0.5 \[ -\frac{1}{105} \sqrt{1-2 x} \left (2625 x^4+10050 x^3+17391 x^2+19574 x+23354\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 30, normalized size = 0.5 \begin{align*} -{\frac{2625\,{x}^{4}+10050\,{x}^{3}+17391\,{x}^{2}+19574\,x+23354}{105}\sqrt{1-2\,x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.18494, size = 62, normalized size = 0.94 \begin{align*} -\frac{25}{16} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{255}{14} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{3467}{40} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{1309}{6} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{5929}{16} \, \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.40504, size = 103, normalized size = 1.56 \begin{align*} -\frac{1}{105} \,{\left (2625 \, x^{4} + 10050 \, x^{3} + 17391 \, x^{2} + 19574 \, x + 23354\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 30.7771, size = 58, normalized size = 0.88 \begin{align*} - \frac{25 \left (1 - 2 x\right )^{\frac{9}{2}}}{16} + \frac{255 \left (1 - 2 x\right )^{\frac{7}{2}}}{14} - \frac{3467 \left (1 - 2 x\right )^{\frac{5}{2}}}{40} + \frac{1309 \left (1 - 2 x\right )^{\frac{3}{2}}}{6} - \frac{5929 \sqrt{1 - 2 x}}{16} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.54153, size = 90, normalized size = 1.36 \begin{align*} -\frac{25}{16} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{255}{14} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{3467}{40} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{1309}{6} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{5929}{16} \, \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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