Optimal. Leaf size=33 \[ -e^4+e^{x^2}-x+3 \left (\frac {5}{9}+x\right )-\frac {e^x+3 x}{x} \]
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Rubi [A]
time = 0.04, antiderivative size = 17, normalized size of antiderivative = 0.52, number of steps
used = 6, number of rules used = 3, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.103, Rules used = {14, 2240, 2228}
\begin {gather*} e^{x^2}+2 x-\frac {e^x}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2228
Rule 2240
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (2 e^{x^2} x+\frac {e^x-e^x x+2 x^2}{x^2}\right ) \, dx\\ &=2 \int e^{x^2} x \, dx+\int \frac {e^x-e^x x+2 x^2}{x^2} \, dx\\ &=e^{x^2}+\int \left (2-\frac {e^x (-1+x)}{x^2}\right ) \, dx\\ &=e^{x^2}+2 x-\int \frac {e^x (-1+x)}{x^2} \, dx\\ &=e^{x^2}-\frac {e^x}{x}+2 x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 17, normalized size = 0.52 \begin {gather*} e^{x^2}-\frac {e^x}{x}+2 x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.17, size = 16, normalized size = 0.48
method | result | size |
default | \(2 x -\frac {{\mathrm e}^{x}}{x}+{\mathrm e}^{x^{2}}\) | \(16\) |
risch | \(2 x -\frac {{\mathrm e}^{x}}{x}+{\mathrm e}^{x^{2}}\) | \(16\) |
norman | \(\frac {{\mathrm e}^{x^{2}} x +2 x^{2}-{\mathrm e}^{x}}{x}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [C] Result contains higher order function than in optimal. Order 4 vs. order
3.
time = 0.29, size = 17, normalized size = 0.52 \begin {gather*} 2 \, x - {\rm Ei}\left (x\right ) + e^{\left (x^{2}\right )} + \Gamma \left (-1, -x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 20, normalized size = 0.61 \begin {gather*} \frac {2 \, x^{2} + x e^{\left (x^{2}\right )} - e^{x}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 12, normalized size = 0.36 \begin {gather*} 2 x + e^{x^{2}} - \frac {e^{x}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 20, normalized size = 0.61 \begin {gather*} \frac {2 \, x^{2} + x e^{\left (x^{2}\right )} - e^{x}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.21, size = 15, normalized size = 0.45 \begin {gather*} 2\,x+{\mathrm {e}}^{x^2}-\frac {{\mathrm {e}}^x}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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