Optimal. Leaf size=18 \[ \frac{(5 x+3)^2}{22 (1-2 x)^2} \]
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Rubi [A] time = 0.0022027, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {37} \[ \frac{(5 x+3)^2}{22 (1-2 x)^2} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin{align*} \int \frac{3+5 x}{(1-2 x)^3} \, dx &=\frac{(3+5 x)^2}{22 (1-2 x)^2}\\ \end{align*}
Mathematica [A] time = 0.0035941, size = 16, normalized size = 0.89 \[ \frac{20 x+1}{8 (1-2 x)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 20, normalized size = 1.1 \begin{align*}{\frac{11}{8\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{5}{8\,x-4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.16529, size = 26, normalized size = 1.44 \begin{align*} \frac{20 \, x + 1}{8 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.22962, size = 46, normalized size = 2.56 \begin{align*} \frac{20 \, x + 1}{8 \,{\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 = 0.098572, size = 14, normalized size = 0.78 \begin{align*} \frac{20 x + 1}{32 x^{2} - 32 x + 8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 7.60148, size = 19, normalized size = 1.06 \begin{align*} \frac{20 \, x + 1}{8 \,{\left (2 \, x - 1\right )}^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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