Optimal. Leaf size=18 \[ -\frac{(2 x+3)^2}{8 (6 x+7)^2} \]
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Rubi [A] time = 0.0015898, 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} \[ -\frac{(2 x+3)^2}{8 (6 x+7)^2} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin{align*} \int \frac{3+2 x}{(7+6 x)^3} \, dx &=-\frac{(3+2 x)^2}{8 (7+6 x)^2}\\ \end{align*}
Mathematica [A] time = 0.003006, size = 16, normalized size = 0.89 \[ -\frac{3 x+4}{9 (6 x+7)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 20, normalized size = 1.1 \begin{align*} -{\frac{1}{126+108\,x}}-{\frac{1}{18\, \left ( 7+6\,x \right ) ^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.958868, size = 26, normalized size = 1.44 \begin{align*} -\frac{3 \, x + 4}{9 \,{\left (36 \, x^{2} + 84 \, x + 49\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.407813, size = 50, normalized size = 2.78 \begin{align*} -\frac{3 \, x + 4}{9 \,{\left (36 \, x^{2} + 84 \, x + 49\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.095918, size = 15, normalized size = 0.83 \begin{align*} - \frac{3 x + 4}{324 x^{2} + 756 x + 441} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07244, size = 19, normalized size = 1.06 \begin{align*} -\frac{3 \, x + 4}{9 \,{\left (6 \, x + 7\right )}^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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