Optimal. Leaf size=53 \[ \frac{25}{24} (1-2 x)^{9/2}-\frac{505}{56} (1-2 x)^{7/2}+\frac{1133}{40} (1-2 x)^{5/2}-\frac{847}{24} (1-2 x)^{3/2} \]
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Rubi [A] time = 0.0104894, antiderivative size = 53, 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} \[ \frac{25}{24} (1-2 x)^{9/2}-\frac{505}{56} (1-2 x)^{7/2}+\frac{1133}{40} (1-2 x)^{5/2}-\frac{847}{24} (1-2 x)^{3/2} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \sqrt{1-2 x} (2+3 x) (3+5 x)^2 \, dx &=\int \left (\frac{847}{8} \sqrt{1-2 x}-\frac{1133}{8} (1-2 x)^{3/2}+\frac{505}{8} (1-2 x)^{5/2}-\frac{75}{8} (1-2 x)^{7/2}\right ) \, dx\\ &=-\frac{847}{24} (1-2 x)^{3/2}+\frac{1133}{40} (1-2 x)^{5/2}-\frac{505}{56} (1-2 x)^{7/2}+\frac{25}{24} (1-2 x)^{9/2}\\ \end{align*}
Mathematica [A] time = 0.0117169, size = 28, normalized size = 0.53 \[ -\frac{1}{105} (1-2 x)^{3/2} \left (875 x^3+2475 x^2+2817 x+1569\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 25, normalized size = 0.5 \begin{align*} -{\frac{875\,{x}^{3}+2475\,{x}^{2}+2817\,x+1569}{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 = 2.59278, size = 50, normalized size = 0.94 \begin{align*} \frac{25}{24} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{505}{56} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{1133}{40} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{847}{24} \,{\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 = 1.51547, size = 95, normalized size = 1.79 \begin{align*} \frac{1}{105} \,{\left (1750 \, x^{4} + 4075 \, x^{3} + 3159 \, x^{2} + 321 \, x - 1569\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.73868, size = 46, normalized size = 0.87 \begin{align*} \frac{25 \left (1 - 2 x\right )^{\frac{9}{2}}}{24} - \frac{505 \left (1 - 2 x\right )^{\frac{7}{2}}}{56} + \frac{1133 \left (1 - 2 x\right )^{\frac{5}{2}}}{40} - \frac{847 \left (1 - 2 x\right )^{\frac{3}{2}}}{24} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.63176, size = 78, normalized size = 1.47 \begin{align*} \frac{25}{24} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{505}{56} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{1133}{40} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{847}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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