Optimal. Leaf size=25 \[ x+\left (1+e^x\right ) \left (-2+2 e^{-x} x \left (3-5 x^2\right )\right ) \]
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Rubi [A] time = 0.12, antiderivative size = 32, normalized size of antiderivative = 1.28, number of steps used = 15, number of rules used = 4, integrand size = 46, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.087, Rules used = {14, 2194, 2196, 2176} \begin {gather*} -10 e^{-x} x^3-10 x^3+6 e^{-x} x+7 x-2 e^x \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2176
Rule 2194
Rule 2196
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (7-2 e^x-30 x^2+2 e^{-x} \left (3-3 x-15 x^2+5 x^3\right )\right ) \, dx\\ &=7 x-10 x^3-2 \int e^x \, dx+2 \int e^{-x} \left (3-3 x-15 x^2+5 x^3\right ) \, dx\\ &=-2 e^x+7 x-10 x^3+2 \int \left (3 e^{-x}-3 e^{-x} x-15 e^{-x} x^2+5 e^{-x} x^3\right ) \, dx\\ &=-2 e^x+7 x-10 x^3+6 \int e^{-x} \, dx-6 \int e^{-x} x \, dx+10 \int e^{-x} x^3 \, dx-30 \int e^{-x} x^2 \, dx\\ &=-6 e^{-x}-2 e^x+7 x+6 e^{-x} x+30 e^{-x} x^2-10 x^3-10 e^{-x} x^3-6 \int e^{-x} \, dx+30 \int e^{-x} x^2 \, dx-60 \int e^{-x} x \, dx\\ &=-2 e^x+7 x+66 e^{-x} x-10 x^3-10 e^{-x} x^3-60 \int e^{-x} \, dx+60 \int e^{-x} x \, dx\\ &=60 e^{-x}-2 e^x+7 x+6 e^{-x} x-10 x^3-10 e^{-x} x^3+60 \int e^{-x} \, dx\\ &=-2 e^x+7 x+6 e^{-x} x-10 x^3-10 e^{-x} x^3\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.15, size = 30, normalized size = 1.20 \begin {gather*} -2 e^x+7 x-10 x^3+2 e^{-x} \left (3 x-5 x^3\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 53, normalized size = 2.12 \begin {gather*} -{\left ({\left (10 \, x^{3} - 7 \, x\right )} e^{\left (-x + \log \left (2 \, x\right )\right )} + {\left (5 \, x^{2} - 3\right )} e^{\left (-2 \, x + 2 \, \log \left (2 \, x\right )\right )} + 4 \, x\right )} e^{\left (x - \log \left (2 \, x\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 28, normalized size = 1.12 \begin {gather*} -10 \, x^{3} - 2 \, {\left (5 \, x^{3} - 3 \, x\right )} e^{\left (-x\right )} + 7 \, x - 2 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 28, normalized size = 1.12
method | result | size |
risch | \(-10 x^{3}+7 x -2 \,{\mathrm e}^{x}+\left (-10 x^{3}+6 x \right ) {\mathrm e}^{-x}\) | \(28\) |
default | \(7 x -10 x^{3}-2 \,{\mathrm e}^{x}+6 x \,{\mathrm e}^{-x}-10 x^{3} {\mathrm e}^{-x}\) | \(30\) |
norman | \(\left (6 x -10 x^{3}-2 \,{\mathrm e}^{2 x}+7 \,{\mathrm e}^{x} x -10 \,{\mathrm e}^{x} x^{3}\right ) {\mathrm e}^{-x}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.38, size = 61, normalized size = 2.44 \begin {gather*} -10 \, x^{3} - 10 \, {\left (x^{3} + 3 \, x^{2} + 6 \, x + 6\right )} e^{\left (-x\right )} + 30 \, {\left (x^{2} + 2 \, x + 2\right )} e^{\left (-x\right )} + 6 \, {\left (x + 1\right )} e^{\left (-x\right )} + 7 \, x - 6 \, e^{\left (-x\right )} - 2 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 29, normalized size = 1.16 \begin {gather*} 7\,x-2\,{\mathrm {e}}^x+6\,x\,{\mathrm {e}}^{-x}-10\,x^3\,{\mathrm {e}}^{-x}-10\,x^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 24, normalized size = 0.96 \begin {gather*} - 10 x^{3} + 7 x + \left (- 10 x^{3} + 6 x\right ) e^{- x} - 2 e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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