Optimal. Leaf size=21 \[ 2+\left (1-e^{16+2 e^2-x}+x\right )^2 \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(51\) vs. \(2(21)=42\).
time = 0.03, antiderivative size = 51, normalized size of antiderivative = 2.43, number of steps
used = 4, number of rules used = 2, integrand size = 34, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {2225, 2207}
\begin {gather*} x^2-2 e^{2 \left (8+e^2\right )-x} x+2 x+e^{4 \left (8+e^2\right )-2 x}-2 e^{2 \left (8+e^2\right )-x} \end {gather*}
Antiderivative was successfully verified.
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Rule 2207
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 x+x^2-2 \int e^{32+4 e^2-2 x} \, dx+2 \int e^{16+2 e^2-x} x \, dx\\ &=e^{4 \left (8+e^2\right )-2 x}+2 x-2 e^{2 \left (8+e^2\right )-x} x+x^2+2 \int e^{16+2 e^2-x} \, dx\\ &=e^{4 \left (8+e^2\right )-2 x}-2 e^{2 \left (8+e^2\right )-x}+2 x-2 e^{2 \left (8+e^2\right )-x} x+x^2\\ \end {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(57\) vs. \(2(21)=42\).
time = 0.06, size = 57, normalized size = 2.71 \begin {gather*} 2 \left (\frac {1}{2} e^{32+4 e^2-2 x}+x+\frac {x^2}{2}+e^{-x} \left (-e^{16+2 e^2}-e^{16+2 e^2} x\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(49\) vs.
\(2(20)=40\).
time = 0.60, size = 50, normalized size = 2.38
method | result | size |
risch | \({\mathrm e}^{-2 x +32+4 \,{\mathrm e}^{2}}+2 \left (-x -1\right ) {\mathrm e}^{2 \,{\mathrm e}^{2}+16-x}+x^{2}+2 x\) | \(35\) |
norman | \(x^{2}+{\mathrm e}^{-2 x +32} {\mathrm e}^{4 \,{\mathrm e}^{2}}+2 x -2 \,{\mathrm e}^{2 \,{\mathrm e}^{2}} {\mathrm e}^{16-x}-2 x \,{\mathrm e}^{16-x} {\mathrm e}^{2 \,{\mathrm e}^{2}}\) | \(49\) |
default | \(x^{2}+2 x +{\mathrm e}^{-2 x +32} {\mathrm e}^{4 \,{\mathrm e}^{2}}+2 \,{\mathrm e}^{2 \,{\mathrm e}^{2}} \left ({\mathrm e}^{16-x} \left (16-x \right )-17 \,{\mathrm e}^{16-x}\right )\) | \(50\) |
derivativedivides | \(\left (16-x \right )^{2}-544+34 x +{\mathrm e}^{-2 x +32} {\mathrm e}^{4 \,{\mathrm e}^{2}}-2 \,{\mathrm e}^{2 \,{\mathrm e}^{2}} \left (-{\mathrm e}^{16-x} \left (16-x \right )+17 \,{\mathrm e}^{16-x}\right )\) | \(56\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 40 vs.
\(2 (19) = 38\).
time = 0.33, size = 40, normalized size = 1.90 \begin {gather*} x^{2} - 2 \, {\left (x e^{\left (2 \, e^{2} + 16\right )} + e^{\left (2 \, e^{2} + 16\right )}\right )} e^{\left (-x\right )} + 2 \, x + e^{\left (-2 \, x + 4 \, e^{2} + 32\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 32, normalized size = 1.52 \begin {gather*} x^{2} - 2 \, {\left (x + 1\right )} e^{\left (-x + 2 \, e^{2} + 16\right )} + 2 \, x + e^{\left (-2 \, x + 4 \, e^{2} + 32\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 44 vs.
\(2 (17) = 34\).
time = 0.05, size = 44, normalized size = 2.10 \begin {gather*} x^{2} + 2 x + \left (- 2 x e^{2 e^{2}} - 2 e^{2 e^{2}}\right ) e^{16 - x} + e^{32 - 2 x} e^{4 e^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 48 vs.
\(2 (19) = 38\).
time = 0.40, size = 48, normalized size = 2.29 \begin {gather*} x^{2} - 2 \, {\left (x - 2 \, e^{2} + 1\right )} e^{\left (-x + 2 \, e^{2} + 16\right )} + 2 \, x - 4 \, e^{\left (-x + 2 \, e^{2} + 18\right )} + e^{\left (-2 \, x + 4 \, e^{2} + 32\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.07, size = 42, normalized size = 2.00 \begin {gather*} 2\,x-2\,{\mathrm {e}}^{2\,{\mathrm {e}}^2-x+16}+{\mathrm {e}}^{4\,{\mathrm {e}}^2-2\,x+32}-2\,x\,{\mathrm {e}}^{2\,{\mathrm {e}}^2-x+16}+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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