Optimal. Leaf size=23 \[ 5-e-e^{3 x+\left (2+4 x^2\right )^2}+x \]
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Rubi [A]
time = 0.03, antiderivative size = 21, normalized size of antiderivative = 0.91, number of steps
used = 2, number of rules used = 1, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.033, Rules used = {6838}
\begin {gather*} x-e^{16 x^4+16 x^2+3 x+4} \end {gather*}
Antiderivative was successfully verified.
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Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x+\int e^{4+3 x+16 x^2+16 x^4} \left (-3-32 x-64 x^3\right ) \, dx\\ &=-e^{4+3 x+16 x^2+16 x^4}+x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 21, normalized size = 0.91 \begin {gather*} -e^{4+3 x+16 x^2+16 x^4}+x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 21, normalized size = 0.91
method | result | size |
default | \(x -{\mathrm e}^{16 x^{4}+16 x^{2}+3 x +4}\) | \(21\) |
norman | \(x -{\mathrm e}^{16 x^{4}+16 x^{2}+3 x +4}\) | \(21\) |
risch | \(x -{\mathrm e}^{16 x^{4}+16 x^{2}+3 x +4}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 20, normalized size = 0.87 \begin {gather*} x - e^{\left (16 \, x^{4} + 16 \, x^{2} + 3 \, x + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 20, normalized size = 0.87 \begin {gather*} x - e^{\left (16 \, x^{4} + 16 \, x^{2} + 3 \, x + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 17, normalized size = 0.74 \begin {gather*} x - e^{16 x^{4} + 16 x^{2} + 3 x + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 20, normalized size = 0.87 \begin {gather*} x - e^{\left (16 \, x^{4} + 16 \, x^{2} + 3 \, x + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.09, size = 22, normalized size = 0.96 \begin {gather*} x-{\mathrm {e}}^{3\,x}\,{\mathrm {e}}^4\,{\mathrm {e}}^{16\,x^2}\,{\mathrm {e}}^{16\,x^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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