Optimal. Leaf size=24 \[ -\frac {3}{(-22-x) x}+\frac {1}{25} x^2 \log ^2(3) \]
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Rubi [A]
time = 0.07, antiderivative size = 28, normalized size of antiderivative = 1.17, number of steps
used = 5, number of rules used = 4, integrand size = 45, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.089, Rules used = {1608, 27, 12,
1634} \begin {gather*} \frac {1}{25} x^2 \log ^2(3)-\frac {3}{22 (x+22)}+\frac {3}{22 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 27
Rule 1608
Rule 1634
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-1650-150 x+\left (968 x^3+88 x^4+2 x^5\right ) \log ^2(3)}{x^2 \left (12100+1100 x+25 x^2\right )} \, dx\\ &=\int \frac {-1650-150 x+\left (968 x^3+88 x^4+2 x^5\right ) \log ^2(3)}{25 x^2 (22+x)^2} \, dx\\ &=\frac {1}{25} \int \frac {-1650-150 x+\left (968 x^3+88 x^4+2 x^5\right ) \log ^2(3)}{x^2 (22+x)^2} \, dx\\ &=\frac {1}{25} \int \left (-\frac {75}{22 x^2}+\frac {75}{22 (22+x)^2}+2 x \log ^2(3)\right ) \, dx\\ &=\frac {3}{22 x}-\frac {3}{22 (22+x)}+\frac {1}{25} x^2 \log ^2(3)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 32, normalized size = 1.33 \begin {gather*} \frac {2}{25} \left (\frac {75}{44 x}-\frac {75}{44 (22+x)}+\frac {1}{2} x^2 \log ^2(3)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.15, size = 23, normalized size = 0.96
method | result | size |
risch | \(\frac {x^{2} \ln \left (3\right )^{2}}{25}+\frac {3}{x \left (22+x \right )}\) | \(21\) |
default | \(\frac {x^{2} \ln \left (3\right )^{2}}{25}+\frac {3}{22 x}-\frac {3}{22 \left (22+x \right )}\) | \(23\) |
gosper | \(\frac {x^{4} \ln \left (3\right )^{2}+22 x^{3} \ln \left (3\right )^{2}+75}{25 x \left (22+x \right )}\) | \(30\) |
norman | \(\frac {3+\frac {22 x^{3} \ln \left (3\right )^{2}}{25}+\frac {x^{4} \ln \left (3\right )^{2}}{25}}{x \left (22+x \right )}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 21, normalized size = 0.88 \begin {gather*} \frac {1}{25} \, x^{2} \log \left (3\right )^{2} + \frac {3}{x^{2} + 22 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 27, normalized size = 1.12 \begin {gather*} \frac {{\left (x^{4} + 22 \, x^{3}\right )} \log \left (3\right )^{2} + 75}{25 \, {\left (x^{2} + 22 \, x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 17, normalized size = 0.71 \begin {gather*} \frac {x^{2} \log {\left (3 \right )}^{2}}{25} + \frac {3}{x^{2} + 22 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 21, normalized size = 0.88 \begin {gather*} \frac {1}{25} \, x^{2} \log \left (3\right )^{2} + \frac {3}{x^{2} + 22 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.01, size = 20, normalized size = 0.83 \begin {gather*} \frac {x^2\,{\ln \left (3\right )}^2}{25}+\frac {3}{x\,\left (x+22\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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