Optimal. Leaf size=40 \[ -\frac{15}{28} (1-2 x)^{7/2}+\frac{17}{5} (1-2 x)^{5/2}-\frac{77}{12} (1-2 x)^{3/2} \]
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Rubi [A] time = 0.0084678, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ -\frac{15}{28} (1-2 x)^{7/2}+\frac{17}{5} (1-2 x)^{5/2}-\frac{77}{12} (1-2 x)^{3/2} \]
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) \, dx &=\int \left (\frac{77}{4} \sqrt{1-2 x}-17 (1-2 x)^{3/2}+\frac{15}{4} (1-2 x)^{5/2}\right ) \, dx\\ &=-\frac{77}{12} (1-2 x)^{3/2}+\frac{17}{5} (1-2 x)^{5/2}-\frac{15}{28} (1-2 x)^{7/2}\\ \end{align*}
Mathematica [A] time = 0.0100952, size = 23, normalized size = 0.57 \[ -\frac{1}{105} (1-2 x)^{3/2} \left (225 x^2+489 x+373\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 20, normalized size = 0.5 \begin{align*} -{\frac{225\,{x}^{2}+489\,x+373}{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 = 1.08022, size = 38, normalized size = 0.95 \begin{align*} -\frac{15}{28} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{17}{5} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{77}{12} \,{\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 = 1.35289, size = 76, normalized size = 1.9 \begin{align*} \frac{1}{105} \,{\left (450 \, x^{3} + 753 \, x^{2} + 257 \, x - 373\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.57053, size = 34, normalized size = 0.85 \begin{align*} - \frac{15 \left (1 - 2 x\right )^{\frac{7}{2}}}{28} + \frac{17 \left (1 - 2 x\right )^{\frac{5}{2}}}{5} - \frac{77 \left (1 - 2 x\right )^{\frac{3}{2}}}{12} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.71598, size = 57, normalized size = 1.42 \begin{align*} \frac{15}{28} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{17}{5} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{77}{12} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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