Optimal. Leaf size=17 \[ \frac {e^{2 x} \log (x)}{25 \log \left (x^3\right )} \]
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Rubi [F]
time = 0.55, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {-\frac {3}{5} e^{2 x} \log (x)+\left (\frac {e^{2 x}}{5}+\frac {2}{5} e^{2 x} x \log (x)\right ) \log \left (x^3\right )}{5 x \log ^2\left (x^3\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {-\frac {3}{5} e^{2 x} \log (x)+\left (\frac {e^{2 x}}{5}+\frac {2}{5} e^{2 x} x \log (x)\right ) \log \left (x^3\right )}{x \log ^2\left (x^3\right )} \, dx\\ &=\frac {1}{5} \int \frac {e^{2 x} \left (\log \left (x^3\right )+\log (x) \left (-3+2 x \log \left (x^3\right )\right )\right )}{5 x \log ^2\left (x^3\right )} \, dx\\ &=\frac {1}{25} \int \frac {e^{2 x} \left (\log \left (x^3\right )+\log (x) \left (-3+2 x \log \left (x^3\right )\right )\right )}{x \log ^2\left (x^3\right )} \, dx\\ &=\frac {1}{25} \int \left (-\frac {3 e^{2 x} \log (x)}{x \log ^2\left (x^3\right )}+\frac {e^{2 x} (1+2 x \log (x))}{x \log \left (x^3\right )}\right ) \, dx\\ &=\frac {1}{25} \int \frac {e^{2 x} (1+2 x \log (x))}{x \log \left (x^3\right )} \, dx-\frac {3}{25} \int \frac {e^{2 x} \log (x)}{x \log ^2\left (x^3\right )} \, dx\\ &=\frac {1}{25} \int \left (\frac {e^{2 x}}{x \log \left (x^3\right )}+\frac {2 e^{2 x} \log (x)}{\log \left (x^3\right )}\right ) \, dx-\frac {3}{25} \int \frac {e^{2 x} \log (x)}{x \log ^2\left (x^3\right )} \, dx\\ &=\frac {1}{25} \int \frac {e^{2 x}}{x \log \left (x^3\right )} \, dx+\frac {2}{25} \int \frac {e^{2 x} \log (x)}{\log \left (x^3\right )} \, dx-\frac {3}{25} \int \frac {e^{2 x} \log (x)}{x \log ^2\left (x^3\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 17, normalized size = 1.00 \begin {gather*} \frac {e^{2 x} \log (x)}{25 \log \left (x^3\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 20, normalized size = 1.18
method | result | size |
default | \(\frac {\ln \left (x \right ) {\mathrm e}^{-\ln \left (5\right )+2 x}}{5 \ln \left (x^{3}\right )}\) | \(20\) |
risch | \(\frac {{\mathrm e}^{2 x}}{75}-\frac {\pi \,{\mathrm e}^{2 x} \left (\mathrm {csgn}\left (i x^{3}\right )^{3}-\mathrm {csgn}\left (i x^{3}\right )^{2} \mathrm {csgn}\left (i x \right )-\mathrm {csgn}\left (i x^{3}\right )^{2} \mathrm {csgn}\left (i x^{2}\right )+\mathrm {csgn}\left (i x^{3}\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )+\mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+\mathrm {csgn}\left (i x^{2}\right )^{3}\right )}{75 \left (\pi \mathrm {csgn}\left (i x^{3}\right )^{3}-\pi \mathrm {csgn}\left (i x^{3}\right )^{2} \mathrm {csgn}\left (i x \right )-\pi \mathrm {csgn}\left (i x^{3}\right )^{2} \mathrm {csgn}\left (i x^{2}\right )+\pi \,\mathrm {csgn}\left (i x^{3}\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )+\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}+6 i \ln \left (x \right )\right )}\) | \(239\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 6, normalized size = 0.35 \begin {gather*} \frac {1}{75} \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 11, normalized size = 0.65 \begin {gather*} \frac {1}{15} \, e^{\left (2 \, x - \log \left (5\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 5, normalized size = 0.29 \begin {gather*} \frac {e^{2 x}}{75} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 6, normalized size = 0.35 \begin {gather*} \frac {1}{75} \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.19, size = 14, normalized size = 0.82 \begin {gather*} \frac {{\mathrm {e}}^{2\,x}\,\ln \left (x\right )}{25\,\ln \left (x^3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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