Optimal. Leaf size=10 \[ \frac {\operatorname {ExpIntegralEi}\left (e^{x^2}\right )}{2} \]
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Rubi [A]
time = 0.02, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {6847, 2320,
2209} \begin {gather*} \frac {\operatorname {ExpIntegralEi}\left (e^{x^2}\right )}{2} \end {gather*}
Antiderivative was successfully verified.
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Rule 2209
Rule 2320
Rule 6847
Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=\frac {1}{2} \text {Subst}\left (\int e^{e^x} \, dx,x,x^2\right )\\ &=\frac {1}{2} \text {Subst}\left (\int \frac {e^x}{x} \, dx,x,e^{x^2}\right )\\ &=\frac {\operatorname {ExpIntegralEi}\left (e^{x^2}\right )}{2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 10, normalized size = 1.00 \begin {gather*} \frac {\operatorname {ExpIntegralEi}\left (e^{x^2}\right )}{2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 11, normalized size = 1.10
method | result | size |
derivativedivides | \(-\frac {\expIntegral _{1}\left (-{\mathrm e}^{x^{2}}\right )}{2}\) | \(11\) |
default | \(-\frac {\expIntegral _{1}\left (-{\mathrm e}^{x^{2}}\right )}{2}\) | \(11\) |
risch | \(-\frac {\expIntegral _{1}\left (-{\mathrm e}^{x^{2}}\right )}{2}\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.35, size = 7, normalized size = 0.70 \begin {gather*} \frac {1}{2} \, {\rm Ei}\left (e^{\left (x^{2}\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.57, size = 7, normalized size = 0.70 \begin {gather*} \frac {1}{2} \, {\rm Ei}\left (e^{\left (x^{2}\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.92, size = 7, normalized size = 0.70 \begin {gather*} \frac {\operatorname {Ei}{\left (e^{x^{2}} \right )}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 7, normalized size = 0.70 \begin {gather*} \frac {1}{2} \, {\rm Ei}\left (e^{\left (x^{2}\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 7, normalized size = 0.70 \begin {gather*} \frac {\mathrm {ei}\left ({\mathrm {e}}^{x^2}\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Chatgpt [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {not solved} \end {gather*}
Warning: Unable to verify antiderivative.
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