Optimal. Leaf size=22 \[ \frac {2 \sqrt {3+5 x}}{11 \sqrt {1-2 x}} \]
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Rubi [A]
time = 0.00, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {37}
\begin {gather*} \frac {2 \sqrt {5 x+3}}{11 \sqrt {1-2 x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x)^{3/2} \sqrt {3+5 x}} \, dx &=\frac {2 \sqrt {3+5 x}}{11 \sqrt {1-2 x}}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 22, normalized size = 1.00 \begin {gather*} \frac {2 \sqrt {3+5 x}}{11 \sqrt {1-2 x}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.07, size = 17, normalized size = 0.77
method | result | size |
gosper | \(\frac {2 \sqrt {3+5 x}}{11 \sqrt {1-2 x}}\) | \(17\) |
default | \(\frac {2 \sqrt {3+5 x}}{11 \sqrt {1-2 x}}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.52, size = 21, normalized size = 0.95 \begin {gather*} -\frac {2 \, \sqrt {-10 \, x^{2} - x + 3}}{11 \, {\left (2 \, x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.56, size = 23, normalized size = 1.05 \begin {gather*} -\frac {2 \, \sqrt {5 \, x + 3} \sqrt {-2 \, x + 1}}{11 \, {\left (2 \, x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [C] Result contains complex when optimal does not.
time = 0.47, size = 48, normalized size = 2.18 \begin {gather*} \begin {cases} \frac {\sqrt {10}}{11 \sqrt {-1 + \frac {11}{10 \left (x + \frac {3}{5}\right )}}} & \text {for}\: \frac {1}{\left |{x + \frac {3}{5}}\right |} > \frac {10}{11} \\- \frac {\sqrt {10} i}{11 \sqrt {1 - \frac {11}{10 \left (x + \frac {3}{5}\right )}}} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.64, size = 26, normalized size = 1.18 \begin {gather*} -\frac {2 \, \sqrt {5} \sqrt {5 \, x + 3} \sqrt {-10 \, x + 5}}{55 \, {\left (2 \, x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.49, size = 16, normalized size = 0.73 \begin {gather*} \frac {2\,\sqrt {5\,x+3}}{11\,\sqrt {1-2\,x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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