Optimal. Leaf size=25 \[ 3+e+x^2+(i \pi +\log (4))^2 \log ^2\left (4 e^x\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 23, normalized size of antiderivative = 0.92, number of steps
used = 3, number of rules used = 2, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {2188, 30}
\begin {gather*} x^2+(\log (4)+i \pi )^2 \log ^2\left (4 e^x\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 30
Rule 2188
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x^2+\left (2 (i \pi +\log (4))^2\right ) \int \log \left (4 e^x\right ) \, dx\\ &=x^2+\left (2 (i \pi +\log (4))^2\right ) \text {Subst}\left (\int x \, dx,x,\log \left (4 e^x\right )\right )\\ &=x^2+(i \pi +\log (4))^2 \log ^2\left (4 e^x\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 32, normalized size = 1.28 \begin {gather*} 2 \left (\frac {x^2}{2}+\frac {1}{2} (i \pi +\log (4))^2 \log ^2\left (4 e^x\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 43, normalized size = 1.72
method | result | size |
norman | \(\left (4 i \pi \ln \left (2\right )-\pi ^{2}+4 \ln \left (2\right )^{2}-1\right ) \ln \left (4 \,{\mathrm e}^{x}\right )^{2}+2 x \ln \left (4 \,{\mathrm e}^{x}\right )\) | \(37\) |
risch | \(2 \left (2 \ln \left (2\right )+i \pi \right )^{2} x \ln \left ({\mathrm e}^{x}\right )-\left (2 \ln \left (2\right )+i \pi \right )^{2} x \left (-4 \ln \left (2\right )+x \right )+x^{2}\) | \(42\) |
default | \(x^{2}-\pi ^{2} \ln \left (4 \,{\mathrm e}^{x}\right )^{2}+4 i \pi \ln \left (4 \,{\mathrm e}^{x}\right )^{2} \ln \left (2\right )+4 \ln \left (4 \,{\mathrm e}^{x}\right )^{2} \ln \left (2\right )^{2}\) | \(43\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 22, normalized size = 0.88 \begin {gather*} {\left (i \, \pi + 2 \, \log \left (2\right )\right )}^{2} \log \left (4 \, e^{x}\right )^{2} + x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 50, normalized size = 2.00 \begin {gather*} 16 \, x \log \left (2\right )^{3} - {\left (\pi ^{2} - 1\right )} x^{2} - 4 \, {\left (-4 i \, \pi x - x^{2}\right )} \log \left (2\right )^{2} - 4 \, {\left (\pi ^{2} x - i \, \pi x^{2}\right )} \log \left (2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 49, normalized size = 1.96 \begin {gather*} x^{2} \left (- \pi ^{2} + 1 + 4 \log {\left (2 \right )}^{2} + 4 i \pi \log {\left (2 \right )}\right ) + x \left (- 4 \pi ^{2} \log {\left (2 \right )} + 16 \log {\left (2 \right )}^{3} + 16 i \pi \log {\left (2 \right )}^{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 24, normalized size = 0.96 \begin {gather*} {\left (i \, \pi + 2 \, \log \left (2\right )\right )}^{2} {\left (x^{2} + 4 \, x \log \left (2\right )\right )} + x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.96, size = 50, normalized size = 2.00 \begin {gather*} \left (-\Pi ^2+4{}\mathrm {i}\,\ln \left (2\right )\,\Pi +4\,{\ln \left (2\right )}^2+1\right )\,x^2+\left (-2\,\ln \left (4\right )\,\Pi ^2+8{}\mathrm {i}\,\ln \left (2\right )\,\ln \left (4\right )\,\Pi +8\,{\ln \left (2\right )}^2\,\ln \left (4\right )\right )\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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