Optimal. Leaf size=18 \[ -\frac {(2 x+3)^2}{8 (6 x+7)^2} \]
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Rubi [A] time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 0.89 \[ -\frac {3 x+4}{9 (6 x+7)^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.38, size = 19, normalized size = 1.06 \[ -\frac {3 \, x + 4}{9 \, {\left (36 \, x^{2} + 84 \, x + 49\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.01, size = 14, normalized size = 0.78 \[ -\frac {3 \, x + 4}{9 \, {\left (6 \, x + 7\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 20, normalized size = 1.11 \[ -\frac {1}{18 \left (6 x +7\right )}-\frac {1}{18 \left (6 x +7\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.58, size = 19, normalized size = 1.06 \[ -\frac {3 \, x + 4}{9 \, {\left (36 \, x^{2} + 84 \, x + 49\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 14, normalized size = 0.78 \[ -\frac {3\,x+4}{9\,{\left (6\,x+7\right )}^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 15, normalized size = 0.83 \[ \frac {- 3 x - 4}{324 x^{2} + 756 x + 441} \]
Verification of antiderivative is not currently implemented for this CAS.
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