Optimal. Leaf size=26 \[ \log \left (3-e^5+e^x+\log \left (\frac {3}{x \left (1-x^2\right )}\right )\right ) \]
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Rubi [A]
time = 0.65, antiderivative size = 23, normalized size of antiderivative = 0.88, number of steps
used = 2, number of rules used = 2, integrand size = 72, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.028, Rules used = {6873, 6816}
\begin {gather*} \log \left (\log \left (\frac {3}{x-x^3}\right )+e^x-e^5+3\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6816
Rule 6873
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-1+3 x^2-e^x \left (-x+x^3\right )}{x \left (1-x^2\right ) \left (e^x+3 \left (1-\frac {e^5}{3}\right )+\log \left (\frac {3}{x-x^3}\right )\right )} \, dx\\ &=\log \left (3-e^5+e^x+\log \left (\frac {3}{x-x^3}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.32, size = 23, normalized size = 0.88 \begin {gather*} \log \left (3-e^5+e^x+\log \left (\frac {3}{x-x^3}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 3.13, size = 24, normalized size = 0.92
method | result | size |
default | \(\ln \left ({\mathrm e}^{5}-{\mathrm e}^{x}-\ln \left (-\frac {3}{x^{3}-x}\right )-3\right )\) | \(24\) |
norman | \(\ln \left ({\mathrm e}^{5}-{\mathrm e}^{x}-\ln \left (-\frac {3}{x^{3}-x}\right )-3\right )\) | \(24\) |
risch | \(\ln \left (\ln \left (x^{2}-1\right )-\frac {i \left (\pi \,\mathrm {csgn}\left (\frac {i}{x^{2}-1}\right ) \mathrm {csgn}\left (\frac {i}{x \left (x^{2}-1\right )}\right )^{2}-\pi \,\mathrm {csgn}\left (\frac {i}{x^{2}-1}\right ) \mathrm {csgn}\left (\frac {i}{x \left (x^{2}-1\right )}\right ) \mathrm {csgn}\left (\frac {i}{x}\right )+\pi \mathrm {csgn}\left (\frac {i}{x \left (x^{2}-1\right )}\right )^{3}-2 \pi \mathrm {csgn}\left (\frac {i}{x \left (x^{2}-1\right )}\right )^{2}+\pi \mathrm {csgn}\left (\frac {i}{x \left (x^{2}-1\right )}\right )^{2} \mathrm {csgn}\left (\frac {i}{x}\right )+2 i {\mathrm e}^{5}-2 i \ln \left (3\right )-2 i {\mathrm e}^{x}+2 i \ln \left (x \right )+2 \pi -6 i\right )}{2}\right )\) | \(164\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.51, size = 25, normalized size = 0.96 \begin {gather*} \log \left (e^{5} - e^{x} - \log \left (3\right ) + \log \left (x + 1\right ) + \log \left (x\right ) + \log \left (-x + 1\right ) - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 21, normalized size = 0.81 \begin {gather*} \log \left (-e^{5} + e^{x} + \log \left (-\frac {3}{x^{3} - x}\right ) + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.22, size = 19, normalized size = 0.73 \begin {gather*} \log {\left (e^{x} + \log {\left (- \frac {3}{x^{3} - x} \right )} - e^{5} + 3 \right )} \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 = 0.81 \begin {gather*} \log \left (-e^{5} + e^{x} + \log \left (-\frac {3}{x^{3} - x}\right ) + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 9.85, size = 21, normalized size = 0.81 \begin {gather*} \ln \left (\ln \left (\frac {3}{x-x^3}\right )-{\mathrm {e}}^5+{\mathrm {e}}^x+3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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