Optimal. Leaf size=16 \[ -\frac {1}{4 \left (13+12 x+4 x^2\right )} \]
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Rubi [A]
time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {643}
\begin {gather*} -\frac {1}{4 \left (4 x^2+12 x+13\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 643
Rubi steps
\begin {align*} \int \frac {3+2 x}{\left (13+12 x+4 x^2\right )^2} \, dx &=-\frac {1}{4 \left (13+12 x+4 x^2\right )}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 16, normalized size = 1.00 \begin {gather*} -\frac {1}{4 \left (13+12 x+4 x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.90, size = 15, normalized size = 0.94
method | result | size |
risch | \(-\frac {1}{16 \left (x^{2}+3 x +\frac {13}{4}\right )}\) | \(13\) |
gosper | \(-\frac {1}{4 \left (4 x^{2}+12 x +13\right )}\) | \(15\) |
default | \(-\frac {1}{4 \left (4 x^{2}+12 x +13\right )}\) | \(15\) |
norman | \(-\frac {1}{4 \left (4 x^{2}+12 x +13\right )}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 14, normalized size = 0.88 \begin {gather*} -\frac {1}{4 \, {\left (4 \, x^{2} + 12 \, x + 13\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 3.38, size = 14, normalized size = 0.88 \begin {gather*} -\frac {1}{4 \, {\left (4 \, x^{2} + 12 \, x + 13\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 12, normalized size = 0.75 \begin {gather*} - \frac {1}{16 x^{2} + 48 x + 52} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.39, size = 14, normalized size = 0.88 \begin {gather*} -\frac {1}{4 \, {\left (4 \, x^{2} + 12 \, x + 13\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.16, size = 14, normalized size = 0.88 \begin {gather*} -\frac {1}{16\,x^2+48\,x+52} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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