Optimal. Leaf size=27 \[ \frac {1}{2} (1-2 x)^{5/2}-\frac {11}{6} (1-2 x)^{3/2} \]
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Rubi [A] time = 0.01, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {43} \begin {gather*} \frac {1}{2} (1-2 x)^{5/2}-\frac {11}{6} (1-2 x)^{3/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \sqrt {1-2 x} (3+5 x) \, dx &=\int \left (\frac {11}{2} \sqrt {1-2 x}-\frac {5}{2} (1-2 x)^{3/2}\right ) \, dx\\ &=-\frac {11}{6} (1-2 x)^{3/2}+\frac {1}{2} (1-2 x)^{5/2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 18, normalized size = 0.67 \begin {gather*} -\frac {1}{3} (1-2 x)^{3/2} (3 x+4) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 22, normalized size = 0.81 \begin {gather*} \frac {1}{6} (3 (1-2 x)-11) (1-2 x)^{3/2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.43, size = 19, normalized size = 0.70 \begin {gather*} \frac {1}{3} \, {\left (6 \, x^{2} + 5 \, x - 4\right )} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.26, size = 26, normalized size = 0.96 \begin {gather*} \frac {1}{2} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - \frac {11}{6} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 15, normalized size = 0.56 \begin {gather*} -\frac {\left (3 x +4\right ) \left (-2 x +1\right )^{\frac {3}{2}}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 19, normalized size = 0.70 \begin {gather*} \frac {1}{2} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - \frac {11}{6} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 12, normalized size = 0.44 \begin {gather*} -{\left (1-2\,x\right )}^{3/2}\,\left (x+\frac {4}{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 1.02, size = 138, normalized size = 5.11 \begin {gather*} \begin {cases} \frac {2 \sqrt {5} i \left (x + \frac {3}{5}\right )^{2} \sqrt {10 x - 5}}{5} - \frac {11 \sqrt {5} i \left (x + \frac {3}{5}\right ) \sqrt {10 x - 5}}{75} - \frac {121 \sqrt {5} i \sqrt {10 x - 5}}{375} & \text {for}\: \frac {10 \left |{x + \frac {3}{5}}\right |}{11} > 1 \\\frac {2 \sqrt {5} \sqrt {5 - 10 x} \left (x + \frac {3}{5}\right )^{2}}{5} - \frac {11 \sqrt {5} \sqrt {5 - 10 x} \left (x + \frac {3}{5}\right )}{75} - \frac {121 \sqrt {5} \sqrt {5 - 10 x}}{375} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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