Optimal. Leaf size=24 \[ 3-3 \left (2+\frac {20}{x^2}\right ) \left (-2-\frac {3}{2} (-5+x)+\log \left (x^2\right )\right ) \]
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Rubi [A]
time = 0.03, antiderivative size = 27, normalized size of antiderivative = 1.12, number of steps
used = 5, number of rules used = 2, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {14, 2341}
\begin {gather*} -\frac {330}{x^2}-\frac {60 \log \left (x^2\right )}{x^2}+9 x+\frac {90}{x}-12 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2341
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {3 \left (180-30 x-4 x^2+3 x^3\right )}{x^3}+\frac {120 \log \left (x^2\right )}{x^3}\right ) \, dx\\ &=3 \int \frac {180-30 x-4 x^2+3 x^3}{x^3} \, dx+120 \int \frac {\log \left (x^2\right )}{x^3} \, dx\\ &=-\frac {60}{x^2}-\frac {60 \log \left (x^2\right )}{x^2}+3 \int \left (3+\frac {180}{x^3}-\frac {30}{x^2}-\frac {4}{x}\right ) \, dx\\ &=-\frac {330}{x^2}+\frac {90}{x}+9 x-12 \log (x)-\frac {60 \log \left (x^2\right )}{x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 27, normalized size = 1.12 \begin {gather*} -\frac {330}{x^2}+\frac {90}{x}+9 x-12 \log (x)-\frac {60 \log \left (x^2\right )}{x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.37, size = 28, normalized size = 1.17
method | result | size |
norman | \(\frac {-330+90 x +9 x^{3}-60 \ln \left (x^{2}\right )}{x^{2}}-12 \ln \left (x \right )\) | \(26\) |
default | \(9 x +\frac {90}{x}-12 \ln \left (x \right )-\frac {330}{x^{2}}-\frac {60 \ln \left (x^{2}\right )}{x^{2}}\) | \(28\) |
risch | \(-\frac {60 \ln \left (x^{2}\right )}{x^{2}}-\frac {3 \left (4 x^{2} \ln \left (x \right )-3 x^{3}-30 x +110\right )}{x^{2}}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 27, normalized size = 1.12 \begin {gather*} 9 \, x + \frac {90}{x} - \frac {60 \, \log \left (x^{2}\right )}{x^{2}} - \frac {330}{x^{2}} - 12 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 26, normalized size = 1.08 \begin {gather*} \frac {3 \, {\left (3 \, x^{3} - 2 \, {\left (x^{2} + 10\right )} \log \left (x^{2}\right ) + 30 \, x - 110\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 26, normalized size = 1.08 \begin {gather*} 9 x - 12 \log {\left (x \right )} + \frac {90 x - 330}{x^{2}} - \frac {60 \log {\left (x^{2} \right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 27, normalized size = 1.12 \begin {gather*} 9 \, x + \frac {30 \, {\left (3 \, x - 11\right )}}{x^{2}} - \frac {60 \, \log \left (x^{2}\right )}{x^{2}} - 12 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.46, size = 26, normalized size = 1.08 \begin {gather*} 9\,x-6\,\ln \left (x^2\right )-\frac {60\,\ln \left (x^2\right )-90\,x+330}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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