Optimal. Leaf size=22 \[ \frac {2 (5 x+3)^{3/2}}{33 (1-2 x)^{3/2}} \]
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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} \[ \frac {2 (5 x+3)^{3/2}}{33 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin {align*} \int \frac {\sqrt {3+5 x}}{(1-2 x)^{5/2}} \, dx &=\frac {2 (3+5 x)^{3/2}}{33 (1-2 x)^{3/2}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 22, normalized size = 1.00 \[ \frac {2 (5 x+3)^{3/2}}{33 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.00, size = 28, normalized size = 1.27 \[ \frac {2 \, {\left (5 \, x + 3\right )}^{\frac {3}{2}} \sqrt {-2 \, x + 1}}{33 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.93, size = 26, normalized size = 1.18 \[ \frac {2 \, \sqrt {5} {\left (5 \, x + 3\right )}^{\frac {3}{2}} \sqrt {-10 \, x + 5}}{165 \, {\left (2 \, x - 1\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 17, normalized size = 0.77 \[ \frac {2 \left (5 x +3\right )^{\frac {3}{2}}}{33 \left (-2 x +1\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.20, size = 48, normalized size = 2.18 \[ \frac {\sqrt {-10 \, x^{2} - x + 3}}{3 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac {5 \, \sqrt {-10 \, x^{2} - x + 3}}{33 \, {\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.36, size = 35, normalized size = 1.59 \[ -\frac {\sqrt {5\,x+3}\,\left (\frac {5\,x}{33}+\frac {1}{11}\right )}{x\,\sqrt {1-2\,x}-\frac {\sqrt {1-2\,x}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.88, size = 82, normalized size = 3.73 \[ \begin {cases} \frac {250 i \left (x + \frac {3}{5}\right )^{\frac {3}{2}}}{330 \left (x + \frac {3}{5}\right ) \sqrt {10 x - 5} - 363 \sqrt {10 x - 5}} & \text {for}\: \frac {10 \left |{x + \frac {3}{5}}\right |}{11} > 1 \\- \frac {250 \left (x + \frac {3}{5}\right )^{\frac {3}{2}}}{330 \sqrt {5 - 10 x} \left (x + \frac {3}{5}\right ) - 363 \sqrt {5 - 10 x}} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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