Optimal. Leaf size=25 \[ 4 \left (e^x+x-\left (2+e^x-x-\log \left (\frac {4}{3}\right )\right )^2\right ) \]
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Rubi [A] time = 0.03, antiderivative size = 45, normalized size of antiderivative = 1.80, number of steps used = 4, number of rules used = 2, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.061, Rules used = {2194, 2176} \begin {gather*} -4 x^2-8 e^x-4 e^{2 x}+4 x \left (5-2 \log \left (\frac {4}{3}\right )\right )-4 e^x \left (-2 x+1-2 \log \left (\frac {4}{3}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-4 x^2+4 x \left (5-2 \log \left (\frac {4}{3}\right )\right )-8 \int e^{2 x} \, dx+\int e^x \left (-4+8 x+8 \log \left (\frac {4}{3}\right )\right ) \, dx\\ &=-4 e^{2 x}-4 x^2+4 x \left (5-2 \log \left (\frac {4}{3}\right )\right )-4 e^x \left (1-2 x-2 \log \left (\frac {4}{3}\right )\right )-8 \int e^x \, dx\\ &=-8 e^x-4 e^{2 x}-4 x^2+4 x \left (5-2 \log \left (\frac {4}{3}\right )\right )-4 e^x \left (1-2 x-2 \log \left (\frac {4}{3}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 41, normalized size = 1.64 \begin {gather*} -4 e^{2 x}+20 x-4 x^2-8 x \log \left (\frac {4}{3}\right )+e^x \left (8 x+4 \left (-3+2 \log \left (\frac {4}{3}\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.76, size = 33, normalized size = 1.32 \begin {gather*} -4 \, x^{2} + 4 \, {\left (2 \, x - 2 \, \log \left (\frac {3}{4}\right ) - 3\right )} e^{x} + 8 \, x \log \left (\frac {3}{4}\right ) + 20 \, x - 4 \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.37, size = 33, normalized size = 1.32 \begin {gather*} -4 \, x^{2} + 4 \, {\left (2 \, x - 2 \, \log \left (\frac {3}{4}\right ) - 3\right )} e^{x} + 8 \, x \log \left (\frac {3}{4}\right ) + 20 \, x - 4 \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 42, normalized size = 1.68
method | result | size |
default | \(20 x +8 \,{\mathrm e}^{x} x -12 \,{\mathrm e}^{x}+16 \,{\mathrm e}^{x} \ln \relax (2)-8 \ln \relax (3) {\mathrm e}^{x}-4 x^{2}-4 \,{\mathrm e}^{2 x}+8 \ln \left (\frac {3}{4}\right ) x\) | \(42\) |
risch | \(-4 \,{\mathrm e}^{2 x}+\left (-12-8 \ln \relax (3)+16 \ln \relax (2)+8 x \right ) {\mathrm e}^{x}+8 x \ln \relax (3)-16 x \ln \relax (2)-4 x^{2}+20 x\) | \(42\) |
norman | \(\left (-12-8 \ln \relax (3)+16 \ln \relax (2)\right ) {\mathrm e}^{x}+\left (8 \ln \relax (3)-16 \ln \relax (2)+20\right ) x -4 x^{2}-4 \,{\mathrm e}^{2 x}+8 \,{\mathrm e}^{x} x\) | \(43\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 37, normalized size = 1.48 \begin {gather*} -4 \, x^{2} + 4 \, {\left (2 \, x - 2 \, \log \relax (3) + 4 \, \log \relax (2) - 3\right )} e^{x} + 8 \, x \log \left (\frac {3}{4}\right ) + 20 \, x - 4 \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 35, normalized size = 1.40 \begin {gather*} x\,\left (8\,\ln \left (\frac {3}{4}\right )+20\right )-4\,{\mathrm {e}}^{2\,x}-{\mathrm {e}}^x\,\left (8\,\ln \left (\frac {3}{4}\right )+12\right )+8\,x\,{\mathrm {e}}^x-4\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 42, normalized size = 1.68 \begin {gather*} - 4 x^{2} + x \left (- 16 \log {\relax (2 )} + 8 \log {\relax (3 )} + 20\right ) + \left (8 x - 12 - 8 \log {\relax (3 )} + 16 \log {\relax (2 )}\right ) e^{x} - 4 e^{2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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