Optimal. Leaf size=28 \[ 5 \left (5-\frac {3}{625 \left (5+e^{x^2}-x-16 e^{2 x} x\right )}\right ) \]
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Rubi [A] time = 0.23, antiderivative size = 24, normalized size of antiderivative = 0.86, number of steps used = 3, number of rules used = 3, integrand size = 87, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.034, Rules used = {6688, 12, 6686} \begin {gather*} -\frac {3}{125 \left (e^{x^2}-16 e^{2 x} x-x+5\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-3+6 e^{x^2} x-48 e^{2 x} (1+2 x)}{125 \left (5+e^{x^2}-x-16 e^{2 x} x\right )^2} \, dx\\ &=\frac {1}{125} \int \frac {-3+6 e^{x^2} x-48 e^{2 x} (1+2 x)}{\left (5+e^{x^2}-x-16 e^{2 x} x\right )^2} \, dx\\ &=-\frac {3}{125 \left (5+e^{x^2}-x-16 e^{2 x} x\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.05, size = 24, normalized size = 0.86 \begin {gather*} -\frac {3}{125 \left (5+e^{x^2}-x-16 e^{2 x} x\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.06, size = 20, normalized size = 0.71 \begin {gather*} \frac {3}{125 \, {\left (16 \, x e^{\left (2 \, x\right )} + x - e^{\left (x^{2}\right )} - 5\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.28, size = 20, normalized size = 0.71 \begin {gather*} \frac {3}{125 \, {\left (16 \, x e^{\left (2 \, x\right )} + x - e^{\left (x^{2}\right )} - 5\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 21, normalized size = 0.75
method | result | size |
risch | \(\frac {3}{125 \left (16 x \,{\mathrm e}^{2 x}+x -{\mathrm e}^{x^{2}}-5\right )}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 20, normalized size = 0.71 \begin {gather*} \frac {3}{125 \, {\left (16 \, x e^{\left (2 \, x\right )} + x - e^{\left (x^{2}\right )} - 5\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.55, size = 22, normalized size = 0.79 \begin {gather*} \frac {3}{125\,\left (x-{\mathrm {e}}^{x^2}+16\,x\,{\mathrm {e}}^{2\,x}-5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 22, normalized size = 0.79 \begin {gather*} - \frac {3}{- 2000 x e^{2 x} - 125 x + 125 e^{x^{2}} + 625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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