Optimal. Leaf size=18 \[ e^{\left (1+2 e^5+4 x\right )^2}-x \]
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Rubi [A]
time = 0.06, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.051, Rules used = {2259, 2240}
\begin {gather*} e^{\left (4 x+2 e^5+1\right )^2}-x \end {gather*}
Antiderivative was successfully verified.
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Rule 2240
Rule 2259
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-x+\int e^{1+4 e^{10}+8 x+16 x^2+e^5 (4+16 x)} \left (8+16 e^5+32 x\right ) \, dx\\ &=-x+\int e^{\left (1+2 e^5+4 x\right )^2} \left (8+16 e^5+32 x\right ) \, dx\\ &=e^{\left (1+2 e^5+4 x\right )^2}-x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 18, normalized size = 1.00 \begin {gather*} e^{\left (1+2 e^5+4 x\right )^2}-x \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 4 vs. order
3.
time = 0.11, size = 161, normalized size = 8.94
method | result | size |
risch | \(-x +{\mathrm e}^{16 x \,{\mathrm e}^{5}+16 x^{2}+4 \,{\mathrm e}^{5}+4 \,{\mathrm e}^{10}+8 x +1}\) | \(29\) |
norman | \(-x +{\mathrm e}^{4 \,{\mathrm e}^{10}+\left (16 x +4\right ) {\mathrm e}^{5}+16 x^{2}+8 x +1}\) | \(30\) |
default | \(-x -i \sqrt {\pi }\, {\mathrm e}^{4 \,{\mathrm e}^{5}+4 \,{\mathrm e}^{10}+1-\frac {\left (16 \,{\mathrm e}^{5}+8\right )^{2}}{64}} \erf \left (4 i x +\frac {i \left (16 \,{\mathrm e}^{5}+8\right )}{8}\right )+{\mathrm e}^{16 x^{2}+\left (16 \,{\mathrm e}^{5}+8\right ) x +4 \,{\mathrm e}^{5}+4 \,{\mathrm e}^{10}+1}+\frac {i \left (16 \,{\mathrm e}^{5}+8\right ) \sqrt {\pi }\, {\mathrm e}^{4 \,{\mathrm e}^{5}+4 \,{\mathrm e}^{10}+1-\frac {\left (16 \,{\mathrm e}^{5}+8\right )^{2}}{64}} \erf \left (4 i x +\frac {i \left (16 \,{\mathrm e}^{5}+8\right )}{8}\right )}{8}-2 i \sqrt {\pi }\, {\mathrm e}^{4 \,{\mathrm e}^{5}+4 \,{\mathrm e}^{10}+6-\frac {\left (16 \,{\mathrm e}^{5}+8\right )^{2}}{64}} \erf \left (4 i x +\frac {i \left (16 \,{\mathrm e}^{5}+8\right )}{8}\right )\) | \(161\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 28, normalized size = 1.56 \begin {gather*} -x + e^{\left (16 \, x^{2} + 4 \, {\left (4 \, x + 1\right )} e^{5} + 8 \, x + 4 \, e^{10} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 28, normalized size = 1.56 \begin {gather*} -x + e^{\left (16 \, x^{2} + 4 \, {\left (4 \, x + 1\right )} e^{5} + 8 \, x + 4 \, e^{10} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 26, normalized size = 1.44 \begin {gather*} - x + e^{16 x^{2} + 8 x + \left (16 x + 4\right ) e^{5} + 1 + 4 e^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 28, normalized size = 1.56 \begin {gather*} -x + e^{\left (16 \, x^{2} + 16 \, x e^{5} + 8 \, x + 4 \, e^{10} + 4 \, e^{5} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.14, size = 33, normalized size = 1.83 \begin {gather*} {\mathrm {e}}^{4\,{\mathrm {e}}^5}\,{\mathrm {e}}^{4\,{\mathrm {e}}^{10}}\,{\mathrm {e}}^{8\,x}\,\mathrm {e}\,{\mathrm {e}}^{16\,x^2}\,{\mathrm {e}}^{16\,x\,{\mathrm {e}}^5}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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