Optimal. Leaf size=21 \[ -3+\left (\frac {1}{2 e^3 x}+x\right ) \left (-3+\log \left (x^2\right )\right ) \]
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Rubi [A] time = 0.05, antiderivative size = 35, normalized size of antiderivative = 1.67, number of steps used = 7, number of rules used = 3, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.086, Rules used = {12, 14, 2334} \begin {gather*} \frac {\left (2 e^3 x+\frac {1}{x}\right ) \log \left (x^2\right )}{2 e^3}-3 x-\frac {3}{2 e^3 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2334
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {5-2 e^3 x^2+\left (-1+2 e^3 x^2\right ) \log \left (x^2\right )}{x^2} \, dx}{2 e^3}\\ &=\frac {\int \left (\frac {5-2 e^3 x^2}{x^2}+\frac {\left (-1+2 e^3 x^2\right ) \log \left (x^2\right )}{x^2}\right ) \, dx}{2 e^3}\\ &=\frac {\int \frac {5-2 e^3 x^2}{x^2} \, dx}{2 e^3}+\frac {\int \frac {\left (-1+2 e^3 x^2\right ) \log \left (x^2\right )}{x^2} \, dx}{2 e^3}\\ &=\frac {\left (\frac {1}{x}+2 e^3 x\right ) \log \left (x^2\right )}{2 e^3}+\frac {\int \left (-2 e^3+\frac {5}{x^2}\right ) \, dx}{2 e^3}-\frac {\int \left (2 e^3+\frac {1}{x^2}\right ) \, dx}{e^3}\\ &=-\frac {3}{2 e^3 x}-3 x+\frac {\left (\frac {1}{x}+2 e^3 x\right ) \log \left (x^2\right )}{2 e^3}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 34, normalized size = 1.62 \begin {gather*} -\frac {3}{2 e^3 x}-3 x+\frac {\log \left (x^2\right )}{2 e^3 x}+x \log \left (x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.72, size = 31, normalized size = 1.48 \begin {gather*} -\frac {{\left (6 \, x^{2} e^{3} - {\left (2 \, x^{2} e^{3} + 1\right )} \log \left (x^{2}\right ) + 3\right )} e^{\left (-3\right )}}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 31, normalized size = 1.48 \begin {gather*} \frac {{\left (2 \, x^{2} e^{3} \log \left (x^{2}\right ) - 6 \, x^{2} e^{3} + \log \left (x^{2}\right ) - 3\right )} e^{\left (-3\right )}}{2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 35, normalized size = 1.67
method | result | size |
default | \(\frac {{\mathrm e}^{-3} \left (2 x \,{\mathrm e}^{3} \ln \left (x^{2}\right )-6 x \,{\mathrm e}^{3}+\frac {\ln \left (x^{2}\right )}{x}-\frac {3}{x}\right )}{2}\) | \(35\) |
norman | \(\frac {x^{2} \ln \left (x^{2}\right )-3 x^{2}-\frac {3 \,{\mathrm e}^{-3}}{2}+\frac {{\mathrm e}^{-3} \ln \left (x^{2}\right )}{2}}{x}\) | \(35\) |
risch | \(\frac {{\mathrm e}^{-3} \left (2 x^{2} {\mathrm e}^{3}+1\right ) \ln \left (x^{2}\right )}{2 x}-\frac {3 \,{\mathrm e}^{-3} \left (2 x^{2} {\mathrm e}^{3}+1\right )}{2 x}\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 37, normalized size = 1.76 \begin {gather*} \frac {1}{2} \, {\left (2 \, {\left (x \log \left (x^{2}\right ) - 2 \, x\right )} e^{3} - 2 \, x e^{3} + \frac {\log \left (x^{2}\right )}{x} - \frac {3}{x}\right )} e^{\left (-3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.42, size = 22, normalized size = 1.05 \begin {gather*} \frac {{\mathrm {e}}^{-3}\,\left (\ln \left (x^2\right )-3\right )\,\left (2\,{\mathrm {e}}^3\,x^2+1\right )}{2\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.14, size = 37, normalized size = 1.76 \begin {gather*} \frac {- 6 x e^{3} - \frac {3}{x}}{2 e^{3}} + \frac {\left (2 x^{2} e^{3} + 1\right ) \log {\left (x^{2} \right )}}{2 x e^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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