Optimal. Leaf size=25 \[ \frac {1}{4} \left (e^{6 x^2}+2 x (i \pi +\log (5))^2\right ) \]
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Rubi [A]
time = 0.02, antiderivative size = 27, normalized size of antiderivative = 1.08, number of steps
used = 3, number of rules used = 2, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {12, 2240}
\begin {gather*} \frac {e^{6 x^2}}{4}+\frac {1}{2} x (\log (5)+i \pi )^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2240
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \left (6 e^{6 x^2} x+(i \pi +\log (5))^2\right ) \, dx\\ &=\frac {1}{2} x (i \pi +\log (5))^2+3 \int e^{6 x^2} x \, dx\\ &=\frac {e^{6 x^2}}{4}+\frac {1}{2} x (i \pi +\log (5))^2\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 28, normalized size = 1.12 \begin {gather*} \frac {1}{2} \left (\frac {e^{6 x^2}}{2}+x (i \pi +\log (5))^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.18, size = 30, normalized size = 1.20
method | result | size |
default | \(-\frac {x \,\pi ^{2}}{2}+i \pi \ln \left (5\right ) x +\frac {x \ln \left (5\right )^{2}}{2}+\frac {{\mathrm e}^{6 x^{2}}}{4}\) | \(30\) |
norman | \(\left (i \pi \ln \left (5\right )-\frac {\pi ^{2}}{2}+\frac {\ln \left (5\right )^{2}}{2}\right ) x +\frac {{\mathrm e}^{6 x^{2}}}{4}\) | \(30\) |
risch | \(-\frac {x \,\pi ^{2}}{2}+i \pi \ln \left (5\right ) x +\frac {x \ln \left (5\right )^{2}}{2}+\frac {{\mathrm e}^{6 x^{2}}}{4}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 20, normalized size = 0.80 \begin {gather*} \frac {1}{2} \, {\left (i \, \pi + \log \left (5\right )\right )}^{2} x + \frac {1}{4} \, e^{\left (6 \, x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 28, normalized size = 1.12 \begin {gather*} -\frac {1}{2} \, \pi ^{2} x + i \, \pi x \log \left (5\right ) + \frac {1}{2} \, x \log \left (5\right )^{2} + \frac {1}{4} \, e^{\left (6 \, x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 27, normalized size = 1.08 \begin {gather*} x \left (- \frac {\pi ^{2}}{2} + \frac {\log {\left (5 \right )}^{2}}{2} + i \pi \log {\left (5 \right )}\right ) + \frac {e^{6 x^{2}}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 20, normalized size = 0.80 \begin {gather*} \frac {1}{2} \, {\left (i \, \pi + \log \left (5\right )\right )}^{2} x + \frac {1}{4} \, e^{\left (6 \, x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.12, size = 21, normalized size = 0.84 \begin {gather*} \frac {{\mathrm {e}}^{6\,x^2}}{4}+\frac {x\,{\left (\ln \left (5\right )+\Pi \,1{}\mathrm {i}\right )}^2}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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