Optimal. Leaf size=21 \[ x+5 \left (3-\frac {e^{5+x^2}}{x}+2 x\right ) \]
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Rubi [A] time = 0.05, antiderivative size = 16, normalized size of antiderivative = 0.76, number of steps used = 3, number of rules used = 2, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {14, 2288} \begin {gather*} 11 x-\frac {5 e^{x^2+5}}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (11-\frac {5 e^{5+x^2} \left (-1+2 x^2\right )}{x^2}\right ) \, dx\\ &=11 x-5 \int \frac {e^{5+x^2} \left (-1+2 x^2\right )}{x^2} \, dx\\ &=-\frac {5 e^{5+x^2}}{x}+11 x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 16, normalized size = 0.76 \begin {gather*} -\frac {5 e^{5+x^2}}{x}+11 x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.97, size = 18, normalized size = 0.86 \begin {gather*} \frac {11 \, x^{2} - 5 \, e^{\left (x^{2} + 5\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 18, normalized size = 0.86 \begin {gather*} \frac {11 \, x^{2} - 5 \, e^{\left (x^{2} + 5\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 16, normalized size = 0.76
method | result | size |
risch | \(11 x -\frac {5 \,{\mathrm e}^{x^{2}+5}}{x}\) | \(16\) |
norman | \(\frac {11 x^{2}-5 \,{\mathrm e}^{x^{2}+5}}{x}\) | \(19\) |
default | \(11 x -5 \,{\mathrm e}^{5} \sqrt {\pi }\, \erfi \relax (x )+5 \,{\mathrm e}^{5} \left (-\frac {{\mathrm e}^{x^{2}}}{x}+\sqrt {\pi }\, \erfi \relax (x )\right )\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.60, size = 36, normalized size = 1.71 \begin {gather*} 5 i \, \sqrt {\pi } \operatorname {erf}\left (i \, x\right ) e^{5} - \frac {5 \, \sqrt {-x^{2}} e^{5} \Gamma \left (-\frac {1}{2}, -x^{2}\right )}{2 \, x} + 11 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 15, normalized size = 0.71 \begin {gather*} 11\,x-\frac {5\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^5}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 12, normalized size = 0.57 \begin {gather*} 11 x - \frac {5 e^{x^{2} + 5}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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