Optimal. Leaf size=27 \[ \frac{11}{6 (1-2 x)^{3/2}}-\frac{5}{2 \sqrt{1-2 x}} \]
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Rubi [A] time = 0.005132, antiderivative size = 27, normalized size of antiderivative = 1., 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} \[ \frac{11}{6 (1-2 x)^{3/2}}-\frac{5}{2 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{3+5 x}{(1-2 x)^{5/2}} \, dx &=\int \left (\frac{11}{2 (1-2 x)^{5/2}}-\frac{5}{2 (1-2 x)^{3/2}}\right ) \, dx\\ &=\frac{11}{6 (1-2 x)^{3/2}}-\frac{5}{2 \sqrt{1-2 x}}\\ \end{align*}
Mathematica [A] time = 0.0068459, size = 18, normalized size = 0.67 \[ \frac{15 x-2}{3 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 15, normalized size = 0.6 \begin{align*}{\frac{-2+15\,x}{3} \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 [A] time = 2.19352, size = 19, normalized size = 0.7 \begin{align*} \frac{15 \, x - 2}{3 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.5908, size = 66, normalized size = 2.44 \begin{align*} \frac{{\left (15 \, x - 2\right )} \sqrt{-2 \, x + 1}}{3 \,{\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 [B] time = 0.568682, size = 48, normalized size = 1.78 \begin{align*} - \frac{15 x}{6 x \sqrt{1 - 2 x} - 3 \sqrt{1 - 2 x}} + \frac{2}{6 x \sqrt{1 - 2 x} - 3 \sqrt{1 - 2 x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.2528, size = 28, normalized size = 1.04 \begin{align*} -\frac{15 \, x - 2}{3 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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