Optimal. Leaf size=25 \[ 5 \left (2+2 \left (\frac {5 x}{36 \left (3-x^2\right )}-\log (4)\right )\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 14, normalized size of antiderivative = 0.56, number of steps used = 2, number of rules used = 2, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {28, 383} \begin {gather*} \frac {25 x}{18 \left (3-x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 28
Rule 383
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=18 \int \frac {75+25 x^2}{\left (-54+18 x^2\right )^2} \, dx\\ &=\frac {25 x}{18 \left (3-x^2\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 12, normalized size = 0.48 \begin {gather*} -\frac {25 x}{18 \left (-3+x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.07, size = 10, normalized size = 0.40 \begin {gather*} -\frac {25 \, x}{18 \, {\left (x^{2} - 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 10, normalized size = 0.40 \begin {gather*} -\frac {25 \, x}{18 \, {\left (x^{2} - 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 11, normalized size = 0.44
method | result | size |
gosper | \(-\frac {25 x}{18 \left (x^{2}-3\right )}\) | \(11\) |
default | \(-\frac {25 x}{18 \left (x^{2}-3\right )}\) | \(11\) |
norman | \(-\frac {25 x}{18 \left (x^{2}-3\right )}\) | \(11\) |
risch | \(-\frac {25 x}{18 \left (x^{2}-3\right )}\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 10, normalized size = 0.40 \begin {gather*} -\frac {25 \, x}{18 \, {\left (x^{2} - 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.98, size = 12, normalized size = 0.48 \begin {gather*} -\frac {25\,x}{18\,\left (x^2-3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 10, normalized size = 0.40 \begin {gather*} - \frac {25 x}{18 x^{2} - 54} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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