Optimal. Leaf size=27 \[ \frac {5}{6} (1-2 x)^{3/2}-\frac {11}{2} \sqrt {1-2 x} \]
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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 {5}{6} (1-2 x)^{3/2}-\frac {11}{2} \sqrt {1-2 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {3+5 x}{\sqrt {1-2 x}} \, dx &=\int \left (\frac {11}{2 \sqrt {1-2 x}}-\frac {5}{2} \sqrt {1-2 x}\right ) \, dx\\ &=-\frac {11}{2} \sqrt {1-2 x}+\frac {5}{6} (1-2 x)^{3/2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 18, normalized size = 0.67 \begin {gather*} -\frac {1}{3} \sqrt {1-2 x} (5 x+14) \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} (5 (1-2 x)-33) \sqrt {1-2 x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.96, size = 14, normalized size = 0.52 \begin {gather*} -\frac {1}{3} \, {\left (5 \, x + 14\right )} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.03, size = 19, normalized size = 0.70 \begin {gather*} \frac {5}{6} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {11}{2} \, \sqrt {-2 \, x + 1} \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 (5 x +14\right ) \sqrt {-2 x +1}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 19, normalized size = 0.70 \begin {gather*} \frac {5}{6} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {11}{2} \, \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 14, normalized size = 0.52 \begin {gather*} -\frac {\sqrt {1-2\,x}\,\left (10\,x+28\right )}{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.97, size = 88, normalized size = 3.26 \begin {gather*} \begin {cases} - \frac {\sqrt {5} i \left (x + \frac {3}{5}\right ) \sqrt {10 x - 5}}{3} - \frac {11 \sqrt {5} i \sqrt {10 x - 5}}{15} & \text {for}\: \frac {10 \left |{x + \frac {3}{5}}\right |}{11} > 1 \\- \frac {\sqrt {5} \sqrt {5 - 10 x} \left (x + \frac {3}{5}\right )}{3} - \frac {11 \sqrt {5} \sqrt {5 - 10 x}}{15} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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