Optimal. Leaf size=34 \[ \frac {\sqrt [8]{e} \sqrt {\pi } \text {erf}\left (\frac {5+4 x}{2 \sqrt {2}}\right )}{2 \sqrt {2}} \]
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Rubi [A]
time = 0.01, antiderivative size = 34, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {2266, 2236}
\begin {gather*} \frac {\sqrt [8]{e} \sqrt {\pi } \text {erf}\left (\frac {4 x+5}{2 \sqrt {2}}\right )}{2 \sqrt {2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 2236
Rule 2266
Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=\sqrt [8]{e} \int e^{-\frac {1}{8} (-5-4 x)^2} \, dx\\ &=\frac {\sqrt [8]{e} \sqrt {\pi } \text {erf}\left (\frac {5+4 x}{2 \sqrt {2}}\right )}{2 \sqrt {2}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 34, normalized size = 1.00 \begin {gather*} \frac {\sqrt [8]{e} \sqrt {\pi } \text {erf}\left (\frac {5+4 x}{2 \sqrt {2}}\right )}{2 \sqrt {2}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 23, normalized size = 0.68
method | result | size |
default | \(\frac {\sqrt {\pi }\, {\mathrm e}^{\frac {1}{8}} \sqrt {2}\, \erf \left (\sqrt {2}\, x +\frac {5 \sqrt {2}}{4}\right )}{4}\) | \(23\) |
risch | \(\frac {\sqrt {\pi }\, {\mathrm e}^{\frac {1}{8}} \sqrt {2}\, \erf \left (\sqrt {2}\, x +\frac {5 \sqrt {2}}{4}\right )}{4}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.47, size = 22, normalized size = 0.65 \begin {gather*} \frac {1}{4} \, \sqrt {2} \sqrt {\pi } \operatorname {erf}\left (\sqrt {2} x + \frac {5}{4} \, \sqrt {2}\right ) e^{\frac {1}{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.58, size = 21, normalized size = 0.62 \begin {gather*} \frac {1}{4} \, \sqrt {2} \sqrt {\pi } \operatorname {erf}\left (\frac {1}{4} \, \sqrt {2} {\left (4 \, x + 5\right )}\right ) e^{\frac {1}{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.34, size = 32, normalized size = 0.94 \begin {gather*} \frac {\sqrt {2} \sqrt {\pi } e^{\frac {1}{8}} \operatorname {erf}{\left (\sqrt {2} x + \frac {5 \sqrt {2}}{4} \right )}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.48, size = 21, normalized size = 0.62 \begin {gather*} \frac {1}{4} \, \sqrt {2} \sqrt {\pi } \operatorname {erf}\left (\frac {1}{4} \, \sqrt {2} {\left (4 \, x + 5\right )}\right ) e^{\frac {1}{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.08, size = 22, normalized size = 0.65 \begin {gather*} \frac {\sqrt {2}\,\sqrt {\pi }\,{\mathrm {e}}^{1/8}\,\mathrm {erf}\left (\sqrt {2}\,x+\frac {5\,\sqrt {2}}{4}\right )}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Chatgpt [F] Failed to verify
time = 1.00, size = 10, normalized size = 0.29 \begin {gather*} -\frac {{\mathrm e}^{-2 \left (x +\frac {5}{4}\right )^{2}}}{4} \end {gather*}
Warning: Unable to verify antiderivative.
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