Optimal. Leaf size=18 \[ -\frac{(1-2 x)^2}{22 (5 x+3)^2} \]
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Rubi [A] time = 0.0020572, 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} \[ -\frac{(1-2 x)^2}{22 (5 x+3)^2} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin{align*} \int \frac{1-2 x}{(3+5 x)^3} \, dx &=-\frac{(1-2 x)^2}{22 (3+5 x)^2}\\ \end{align*}
Mathematica [A] time = 0.0028611, size = 16, normalized size = 0.89 \[ \frac{20 x+1}{50 (5 x+3)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 20, normalized size = 1.1 \begin{align*} -{\frac{11}{50\, \left ( 3+5\,x \right ) ^{2}}}+{\frac{2}{75+125\,x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05051, size = 26, normalized size = 1.44 \begin{align*} \frac{20 \, x + 1}{50 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.40836, size = 50, normalized size = 2.78 \begin{align*} \frac{20 \, x + 1}{50 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.096869, size = 14, normalized size = 0.78 \begin{align*} \frac{20 x + 1}{1250 x^{2} + 1500 x + 450} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.26591, size = 19, normalized size = 1.06 \begin{align*} \frac{20 \, x + 1}{50 \,{\left (5 \, x + 3\right )}^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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