Optimal. Leaf size=24 \[ e^{x^2}+e^{-3+5 x^2}+e^x (-1-x) \]
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Rubi [A] time = 0.03, antiderivative size = 26, normalized size of antiderivative = 1.08, number of steps used = 5, number of rules used = 3, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {2176, 2194, 2209} \begin {gather*} e^{x^2}+e^{5 x^2-3}-e^x (x+2)+e^x \end {gather*}
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rule 2209
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 \int e^{x^2} x \, dx+10 \int e^{-3+5 x^2} x \, dx+\int e^x (-2-x) \, dx\\ &=e^{x^2}+e^{-3+5 x^2}-e^x (2+x)+\int e^x \, dx\\ &=e^x+e^{x^2}+e^{-3+5 x^2}-e^x (2+x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 23, normalized size = 0.96 \begin {gather*} e^{x^2}+e^{-3+5 x^2}-e^x (1+x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 29, normalized size = 1.21 \begin {gather*} -{\left ({\left (x + 1\right )} e^{\left (x + 3\right )} - e^{\left (5 \, x^{2}\right )} - e^{\left (x^{2} + 3\right )}\right )} e^{\left (-3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 20, normalized size = 0.83 \begin {gather*} -{\left (x + 1\right )} e^{x} + e^{\left (5 \, x^{2} - 3\right )} + e^{\left (x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 22, normalized size = 0.92
method | result | size |
risch | \({\mathrm e}^{x^{2}}+{\mathrm e}^{5 x^{2}-3}+\left (-x -1\right ) {\mathrm e}^{x}\) | \(22\) |
default | \(-{\mathrm e}^{x} x -{\mathrm e}^{x}+{\mathrm e}^{5 x^{2}-3}+{\mathrm e}^{x^{2}}\) | \(23\) |
norman | \({\mathrm e}^{-3} {\mathrm e}^{5 x^{2}}-{\mathrm e}^{x} x -{\mathrm e}^{x}+{\mathrm e}^{x^{2}}\) | \(26\) |
meijerg | \(-{\mathrm e}^{-3} \left (1-{\mathrm e}^{5 x^{2}}\right )+{\mathrm e}^{x^{2}}+\frac {\left (-2 x +2\right ) {\mathrm e}^{x}}{2}-2 \,{\mathrm e}^{x}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 24, normalized size = 1.00 \begin {gather*} -{\left (x - 1\right )} e^{x} + e^{\left (5 \, x^{2} - 3\right )} + e^{\left (x^{2}\right )} - 2 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.11, size = 22, normalized size = 0.92 \begin {gather*} {\mathrm {e}}^{x^2}-{\mathrm {e}}^x+{\mathrm {e}}^{5\,x^2-3}-x\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.24, size = 26, normalized size = 1.08 \begin {gather*} \left (- x - 1\right ) e^{x} + \frac {e^{5 x^{2}} + e^{3} e^{x^{2}}}{e^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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