Optimal. Leaf size=23 \[ -2-x+\left (-1-\left (3+25 e^{-5 x}\right )^2+x\right )^2 \]
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Rubi [B] time = 0.26, antiderivative size = 59, normalized size of antiderivative = 2.57, number of steps used = 8, number of rules used = 3, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {6742, 2194, 2176} \begin {gather*} x^2-21 x+390625 e^{-20 x}+187500 e^{-15 x}-125 e^{-10 x}-60 e^{-5 x}+125 e^{-10 x} (281-10 x)+60 e^{-5 x} (51-5 x) \end {gather*}
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-21-7812500 e^{-20 x}-2812500 e^{-15 x}+2 x+300 e^{-5 x} (-51+5 x)+1250 e^{-10 x} (-281+10 x)\right ) \, dx\\ &=-21 x+x^2+300 \int e^{-5 x} (-51+5 x) \, dx+1250 \int e^{-10 x} (-281+10 x) \, dx-2812500 \int e^{-15 x} \, dx-7812500 \int e^{-20 x} \, dx\\ &=390625 e^{-20 x}+187500 e^{-15 x}+125 e^{-10 x} (281-10 x)+60 e^{-5 x} (51-5 x)-21 x+x^2+300 \int e^{-5 x} \, dx+1250 \int e^{-10 x} \, dx\\ &=390625 e^{-20 x}+187500 e^{-15 x}-125 e^{-10 x}-60 e^{-5 x}+125 e^{-10 x} (281-10 x)+60 e^{-5 x} (51-5 x)-21 x+x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 45, normalized size = 1.96 \begin {gather*} 390625 e^{-20 x}+187500 e^{-15 x}+300 e^{-5 x} (10-x)+1250 e^{-10 x} (28-x)-21 x+x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.77, size = 43, normalized size = 1.87 \begin {gather*} {\left ({\left (x^{2} - 21 \, x\right )} e^{\left (20 \, x\right )} - 300 \, {\left (x - 10\right )} e^{\left (15 \, x\right )} - 1250 \, {\left (x - 28\right )} e^{\left (10 \, x\right )} + 187500 \, e^{\left (5 \, x\right )} + 390625\right )} e^{\left (-20 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.13, size = 45, normalized size = 1.96 \begin {gather*} x^{2} - 300 \, x e^{\left (-5 \, x\right )} - 1250 \, x e^{\left (-10 \, x\right )} - 21 \, x + 3000 \, e^{\left (-5 \, x\right )} + 35000 \, e^{\left (-10 \, x\right )} + 187500 \, e^{\left (-15 \, x\right )} + 390625 \, e^{\left (-20 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 40, normalized size = 1.74
method | result | size |
risch | \(x^{2}-21 x +\left (3000-300 x \right ) {\mathrm e}^{-5 x}+\left (35000-1250 x \right ) {\mathrm e}^{-10 x}+187500 \,{\mathrm e}^{-15 x}+390625 \,{\mathrm e}^{-20 x}\) | \(40\) |
derivativedivides | \(-21 x +x^{2}+390625 \,{\mathrm e}^{-20 x}+187500 \,{\mathrm e}^{-15 x}+35000 \,{\mathrm e}^{-10 x}+3000 \,{\mathrm e}^{-5 x}-1250 \,{\mathrm e}^{-10 x} x -300 x \,{\mathrm e}^{-5 x}\) | \(58\) |
default | \(-21 x +x^{2}+390625 \,{\mathrm e}^{-20 x}+187500 \,{\mathrm e}^{-15 x}+35000 \,{\mathrm e}^{-10 x}+3000 \,{\mathrm e}^{-5 x}-1250 \,{\mathrm e}^{-10 x} x -300 x \,{\mathrm e}^{-5 x}\) | \(58\) |
norman | \(\left (390625+x^{2} {\mathrm e}^{20 x}+35000 \,{\mathrm e}^{10 x}+3000 \,{\mathrm e}^{15 x}-1250 \,{\mathrm e}^{10 x} x -300 \,{\mathrm e}^{15 x} x -21 x \,{\mathrm e}^{20 x}+187500 \,{\mathrm e}^{5 x}\right ) {\mathrm e}^{-20 x}\) | \(69\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.35, size = 53, normalized size = 2.30 \begin {gather*} x^{2} - 60 \, {\left (5 \, x + 1\right )} e^{\left (-5 \, x\right )} - 125 \, {\left (10 \, x + 1\right )} e^{\left (-10 \, x\right )} - 21 \, x + 3060 \, e^{\left (-5 \, x\right )} + 35125 \, e^{\left (-10 \, x\right )} + 187500 \, e^{\left (-15 \, x\right )} + 390625 \, e^{\left (-20 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.18, size = 41, normalized size = 1.78 \begin {gather*} 187500\,{\mathrm {e}}^{-15\,x}-21\,x+390625\,{\mathrm {e}}^{-20\,x}-{\mathrm {e}}^{-5\,x}\,\left (300\,x-3000\right )-{\mathrm {e}}^{-10\,x}\,\left (1250\,x-35000\right )+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.15, size = 39, normalized size = 1.70 \begin {gather*} x^{2} - 21 x + \left (3000 - 300 x\right ) e^{- 5 x} + \left (35000 - 1250 x\right ) e^{- 10 x} + 187500 e^{- 15 x} + 390625 e^{- 20 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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