Optimal. Leaf size=22 \[ \frac{2 (5 x+3)^{3/2}}{33 (1-2 x)^{3/2}} \]
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Rubi [A] time = 0.0017861, antiderivative size = 22, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0051132, size = 22, normalized size = 1. \[ \frac{2 (5 x+3)^{3/2}}{33 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 17, normalized size = 0.8 \begin{align*}{\frac{2}{33} \left ( 3+5\,x \right ) ^{{\frac{3}{2}}} \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 [B] time = 3.42917, size = 65, normalized size = 2.95 \begin{align*} \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 )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.44495, size = 74, normalized size = 3.36 \begin{align*} \frac{2 \,{\left (5 \, x + 3\right )}^{\frac{3}{2}} \sqrt{-2 \, x + 1}}{33 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.52727, size = 82, normalized size = 3.73 \begin{align*} \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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.52549, size = 35, normalized size = 1.59 \begin{align*} \frac{2 \, \sqrt{5}{\left (5 \, x + 3\right )}^{\frac{3}{2}} \sqrt{-10 \, x + 5}}{165 \,{\left (2 \, x - 1\right )}^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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