Optimal. Leaf size=40 \[ -\frac{25}{28} (1-2 x)^{7/2}+\frac{11}{2} (1-2 x)^{5/2}-\frac{121}{12} (1-2 x)^{3/2} \]
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Rubi [A] time = 0.0072807, antiderivative size = 40, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {43} \[ -\frac{25}{28} (1-2 x)^{7/2}+\frac{11}{2} (1-2 x)^{5/2}-\frac{121}{12} (1-2 x)^{3/2} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \sqrt{1-2 x} (3+5 x)^2 \, dx &=\int \left (\frac{121}{4} \sqrt{1-2 x}-\frac{55}{2} (1-2 x)^{3/2}+\frac{25}{4} (1-2 x)^{5/2}\right ) \, dx\\ &=-\frac{121}{12} (1-2 x)^{3/2}+\frac{11}{2} (1-2 x)^{5/2}-\frac{25}{28} (1-2 x)^{7/2}\\ \end{align*}
Mathematica [A] time = 0.0093514, size = 23, normalized size = 0.57 \[ -\frac{1}{21} (1-2 x)^{3/2} \left (75 x^2+156 x+115\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 20, normalized size = 0.5 \begin{align*} -{\frac{75\,{x}^{2}+156\,x+115}{21} \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 = 1.15597, size = 38, normalized size = 0.95 \begin{align*} -\frac{25}{28} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{11}{2} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{121}{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 = 1.52365, size = 73, normalized size = 1.82 \begin{align*} \frac{1}{21} \,{\left (150 \, x^{3} + 237 \, x^{2} + 74 \, x - 115\right )} \sqrt{-2 \, x + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.24947, size = 187, normalized size = 4.68 \begin{align*} \begin{cases} \frac{10 \sqrt{5} i \left (x + \frac{3}{5}\right )^{3} \sqrt{10 x - 5}}{7} - \frac{11 \sqrt{5} i \left (x + \frac{3}{5}\right )^{2} \sqrt{10 x - 5}}{35} - \frac{242 \sqrt{5} i \left (x + \frac{3}{5}\right ) \sqrt{10 x - 5}}{525} - \frac{2662 \sqrt{5} i \sqrt{10 x - 5}}{2625} & \text{for}\: \frac{10 \left |{x + \frac{3}{5}}\right |}{11} > 1 \\\frac{10 \sqrt{5} \sqrt{5 - 10 x} \left (x + \frac{3}{5}\right )^{3}}{7} - \frac{11 \sqrt{5} \sqrt{5 - 10 x} \left (x + \frac{3}{5}\right )^{2}}{35} - \frac{242 \sqrt{5} \sqrt{5 - 10 x} \left (x + \frac{3}{5}\right )}{525} - \frac{2662 \sqrt{5} \sqrt{5 - 10 x}}{2625} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.0016, size = 57, normalized size = 1.42 \begin{align*} \frac{25}{28} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{11}{2} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{121}{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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