Optimal. Leaf size=16 \[ \left (28+e^{5+x^2}\right ) \left (-5+\frac {1}{e^4}+x\right ) \]
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Rubi [A] time = 0.09, antiderivative size = 28, normalized size of antiderivative = 1.75, number of steps used = 8, number of rules used = 5, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.139, Rules used = {12, 2226, 2204, 2209, 2212} \begin {gather*} e^{x^2+5} x+\left (1-5 e^4\right ) e^{x^2+1}+28 x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2204
Rule 2209
Rule 2212
Rule 2226
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (28 e^4+e^{5+x^2} \left (2 x+e^4 \left (1-10 x+2 x^2\right )\right )\right ) \, dx}{e^4}\\ &=28 x+\frac {\int e^{5+x^2} \left (2 x+e^4 \left (1-10 x+2 x^2\right )\right ) \, dx}{e^4}\\ &=28 x+\frac {\int \left (e^{9+x^2}-2 e^{5+x^2} \left (-1+5 e^4\right ) x+2 e^{9+x^2} x^2\right ) \, dx}{e^4}\\ &=28 x-\left (2 \left (5-\frac {1}{e^4}\right )\right ) \int e^{5+x^2} x \, dx+\frac {\int e^{9+x^2} \, dx}{e^4}+\frac {2 \int e^{9+x^2} x^2 \, dx}{e^4}\\ &=-\left (\left (5-\frac {1}{e^4}\right ) e^{5+x^2}\right )+28 x+e^{5+x^2} x+\frac {1}{2} e^5 \sqrt {\pi } \text {erfi}(x)-\frac {\int e^{9+x^2} \, dx}{e^4}\\ &=-\left (\left (5-\frac {1}{e^4}\right ) e^{5+x^2}\right )+28 x+e^{5+x^2} x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 28, normalized size = 1.75 \begin {gather*} e^{1+x^2} \left (1-5 e^4\right )+28 x+e^{5+x^2} x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.91, size = 24, normalized size = 1.50 \begin {gather*} {\left (28 \, x e^{4} + {\left ({\left (x - 5\right )} e^{4} + 1\right )} e^{\left (x^{2} + 5\right )}\right )} e^{\left (-4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.31, size = 25, normalized size = 1.56 \begin {gather*} {\left (28 \, x e^{4} + {\left (x - 5\right )} e^{\left (x^{2} + 9\right )} + e^{\left (x^{2} + 5\right )}\right )} e^{\left (-4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 22, normalized size = 1.38
method | result | size |
risch | \(28 x +\left (x \,{\mathrm e}^{4}-5 \,{\mathrm e}^{4}+1\right ) {\mathrm e}^{x^{2}+1}\) | \(22\) |
norman | \(x \,{\mathrm e}^{x^{2}+5}+28 x -\left (5 \,{\mathrm e}^{4}-1\right ) {\mathrm e}^{-4} {\mathrm e}^{x^{2}+5}\) | \(31\) |
default | \({\mathrm e}^{-4} \left (\frac {{\mathrm e}^{4} {\mathrm e}^{5} \sqrt {\pi }\, \erfi \relax (x )}{2}+{\mathrm e}^{5} {\mathrm e}^{x^{2}}-5 \,{\mathrm e}^{x^{2}} {\mathrm e}^{5} {\mathrm e}^{4}+2 \,{\mathrm e}^{4} {\mathrm e}^{5} \left (\frac {{\mathrm e}^{x^{2}} x}{2}-\frac {\sqrt {\pi }\, \erfi \relax (x )}{4}\right )+28 x \,{\mathrm e}^{4}\right )\) | \(61\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.41, size = 31, normalized size = 1.94 \begin {gather*} {\left (28 \, x e^{4} + x e^{\left (x^{2} + 9\right )} - 5 \, e^{\left (x^{2} + 9\right )} + e^{\left (x^{2} + 5\right )}\right )} e^{\left (-4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.92, size = 23, normalized size = 1.44 \begin {gather*} 28\,x+x\,{\mathrm {e}}^{x^2+5}+{\mathrm {e}}^{x^2+5}\,\left ({\mathrm {e}}^{-4}-5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 24, normalized size = 1.50 \begin {gather*} 28 x + \frac {\left (x e^{4} - 5 e^{4} + 1\right ) e^{x^{2} + 5}}{e^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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