Optimal. Leaf size=20 \[ -x+\log \left (25 \log \left (\frac {16}{25} e^{-2 x} x^2\right )\right ) \]
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Rubi [A] time = 0.18, antiderivative size = 18, normalized size of antiderivative = 0.90, number of steps used = 3, number of rules used = 2, integrand size = 40, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {6742, 6684} \begin {gather*} \log \left (\log \left (\frac {16}{25} e^{-2 x} x^2\right )\right )-x \end {gather*}
Antiderivative was successfully verified.
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Rule 6684
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1-\frac {2 (-1+x)}{x \log \left (\frac {16}{25} e^{-2 x} x^2\right )}\right ) \, dx\\ &=-x-2 \int \frac {-1+x}{x \log \left (\frac {16}{25} e^{-2 x} x^2\right )} \, dx\\ &=-x+\log \left (\log \left (\frac {16}{25} e^{-2 x} x^2\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.15, size = 18, normalized size = 0.90 \begin {gather*} -x+\log \left (\log \left (\frac {16}{25} e^{-2 x} x^2\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.85, size = 15, normalized size = 0.75 \begin {gather*} -x + \log \left (\log \left (\frac {16}{25} \, x^{2} e^{\left (-2 \, x\right )}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 17, normalized size = 0.85 \begin {gather*} -x + \log \left (2 \, x - \log \left (\frac {16}{25} \, x^{2}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.11, size = 16, normalized size = 0.80
method | result | size |
norman | \(-x +\ln \left (\ln \left (\frac {16 x^{2} {\mathrm e}^{-2 x}}{25}\right )\right )\) | \(16\) |
default | \(-x +\ln \left (-\ln \left (\frac {16 x^{2} {\mathrm e}^{2 x} {\mathrm e}^{-4 x}}{25}\right )\right )\) | \(24\) |
risch | \(-x +\ln \left (\ln \left ({\mathrm e}^{x}\right )+\frac {i \left (\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}+\pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i {\mathrm e}^{-2 x}\right ) \mathrm {csgn}\left (i x^{2} {\mathrm e}^{-2 x}\right )-\pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x^{2} {\mathrm e}^{-2 x}\right )^{2}-\pi \mathrm {csgn}\left (i {\mathrm e}^{x}\right )^{2} \mathrm {csgn}\left (i {\mathrm e}^{2 x}\right )+2 \pi \,\mathrm {csgn}\left (i {\mathrm e}^{x}\right ) \mathrm {csgn}\left (i {\mathrm e}^{2 x}\right )^{2}-\pi \mathrm {csgn}\left (i {\mathrm e}^{2 x}\right )^{3}-\pi \,\mathrm {csgn}\left (i {\mathrm e}^{-2 x}\right ) \mathrm {csgn}\left (i x^{2} {\mathrm e}^{-2 x}\right )^{2}+\pi \mathrm {csgn}\left (i x^{2} {\mathrm e}^{-2 x}\right )^{3}+8 i \ln \relax (2)-4 i \ln \relax (5)+4 i \ln \relax (x )\right )}{4}\right )\) | \(214\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 19, normalized size = 0.95 \begin {gather*} -x + \log \left (-x - \log \relax (5) + 2 \, \log \relax (2) + \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.64, size = 15, normalized size = 0.75 \begin {gather*} \ln \left (\ln \left (\frac {16\,x^2}{25}\right )-2\,x\right )-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 15, normalized size = 0.75 \begin {gather*} - x + \log {\left (\log {\left (\frac {16 x^{2} e^{- 2 x}}{25} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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