Optimal. Leaf size=30 \[ e^{-3-x+x \left (1+25 e^x x \left (4+\left (-e^x+x\right )^2\right )^2\right )} \]
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Rubi [F] time = 28.72, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \exp \left (-3+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )\right ) \left (e^{5 x} \left (50 x+125 x^2\right )+e^{4 x} \left (-300 x^2-400 x^3\right )+e^{3 x} \left (400 x+600 x^2+600 x^3+450 x^4\right )+e^{2 x} \left (-1200 x^2-800 x^3-500 x^4-200 x^5\right )+e^x \left (800 x+400 x^2+800 x^3+200 x^4+150 x^5+25 x^6\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-100 \exp \left (-3+4 x+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )\right ) x^2 (3+4 x)+25 \exp \left (-3+5 x+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )\right ) x (2+5 x)-100 \exp \left (-3+2 x+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )\right ) x^2 \left (12+8 x+5 x^2+2 x^3\right )+50 \exp \left (-3+3 x+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )\right ) x \left (8+12 x+12 x^2+9 x^3\right )+25 \exp \left (-3+x+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )\right ) x \left (32+16 x+32 x^2+8 x^3+6 x^4+x^5\right )\right ) \, dx\\ &=25 \int \exp \left (-3+5 x+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )\right ) x (2+5 x) \, dx+25 \int \exp \left (-3+x+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )\right ) x \left (32+16 x+32 x^2+8 x^3+6 x^4+x^5\right ) \, dx+50 \int \exp \left (-3+3 x+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )\right ) x \left (8+12 x+12 x^2+9 x^3\right ) \, dx-100 \int \exp \left (-3+4 x+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )\right ) x^2 (3+4 x) \, dx-100 \int \exp \left (-3+2 x+25 e^{5 x} x^2-100 e^{4 x} x^3+e^{3 x} \left (200 x^2+150 x^4\right )+e^{2 x} \left (-400 x^3-100 x^5\right )+e^x \left (400 x^2+200 x^4+25 x^6\right )\right ) x^2 \left (12+8 x+5 x^2+2 x^3\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [B] time = 0.14, size = 71, normalized size = 2.37 \begin {gather*} e^{-3+25 e^{5 x} x^2-100 e^{4 x} x^3-100 e^{2 x} x^3 \left (4+x^2\right )+25 e^x x^2 \left (4+x^2\right )^2+50 e^{3 x} x^2 \left (4+3 x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.51, size = 71, normalized size = 2.37 \begin {gather*} e^{\left (-100 \, x^{3} e^{\left (4 \, x\right )} + 25 \, x^{2} e^{\left (5 \, x\right )} + 50 \, {\left (3 \, x^{4} + 4 \, x^{2}\right )} e^{\left (3 \, x\right )} - 100 \, {\left (x^{5} + 4 \, x^{3}\right )} e^{\left (2 \, x\right )} + 25 \, {\left (x^{6} + 8 \, x^{4} + 16 \, x^{2}\right )} e^{x} - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int 25 \, {\left ({\left (5 \, x^{2} + 2 \, x\right )} e^{\left (5 \, x\right )} - 4 \, {\left (4 \, x^{3} + 3 \, x^{2}\right )} e^{\left (4 \, x\right )} + 2 \, {\left (9 \, x^{4} + 12 \, x^{3} + 12 \, x^{2} + 8 \, x\right )} e^{\left (3 \, x\right )} - 4 \, {\left (2 \, x^{5} + 5 \, x^{4} + 8 \, x^{3} + 12 \, x^{2}\right )} e^{\left (2 \, x\right )} + {\left (x^{6} + 6 \, x^{5} + 8 \, x^{4} + 32 \, x^{3} + 16 \, x^{2} + 32 \, x\right )} e^{x}\right )} e^{\left (-100 \, x^{3} e^{\left (4 \, x\right )} + 25 \, x^{2} e^{\left (5 \, x\right )} + 50 \, {\left (3 \, x^{4} + 4 \, x^{2}\right )} e^{\left (3 \, x\right )} - 100 \, {\left (x^{5} + 4 \, x^{3}\right )} e^{\left (2 \, x\right )} + 25 \, {\left (x^{6} + 8 \, x^{4} + 16 \, x^{2}\right )} e^{x} - 3\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.14, size = 79, normalized size = 2.63
method | result | size |
risch | \({\mathrm e}^{25 x^{6} {\mathrm e}^{x}-100 x^{5} {\mathrm e}^{2 x}+200 \,{\mathrm e}^{x} x^{4}+150 \,{\mathrm e}^{3 x} x^{4}-400 \,{\mathrm e}^{2 x} x^{3}-100 x^{3} {\mathrm e}^{4 x}+400 \,{\mathrm e}^{x} x^{2}+25 x^{2} {\mathrm e}^{5 x}+200 x^{2} {\mathrm e}^{3 x}-3}\) | \(79\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.74, size = 78, normalized size = 2.60 \begin {gather*} e^{\left (25 \, x^{6} e^{x} - 100 \, x^{5} e^{\left (2 \, x\right )} + 150 \, x^{4} e^{\left (3 \, x\right )} + 200 \, x^{4} e^{x} - 100 \, x^{3} e^{\left (4 \, x\right )} - 400 \, x^{3} e^{\left (2 \, x\right )} + 25 \, x^{2} e^{\left (5 \, x\right )} + 200 \, x^{2} e^{\left (3 \, x\right )} + 400 \, x^{2} e^{x} - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 8.33, size = 87, normalized size = 2.90 \begin {gather*} {\mathrm {e}}^{-3}\,{\mathrm {e}}^{25\,x^6\,{\mathrm {e}}^x}\,{\mathrm {e}}^{200\,x^4\,{\mathrm {e}}^x}\,{\mathrm {e}}^{400\,x^2\,{\mathrm {e}}^x}\,{\mathrm {e}}^{25\,x^2\,{\mathrm {e}}^{5\,x}}\,{\mathrm {e}}^{-100\,x^3\,{\mathrm {e}}^{4\,x}}\,{\mathrm {e}}^{-100\,x^5\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{150\,x^4\,{\mathrm {e}}^{3\,x}}\,{\mathrm {e}}^{200\,x^2\,{\mathrm {e}}^{3\,x}}\,{\mathrm {e}}^{-400\,x^3\,{\mathrm {e}}^{2\,x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.60, size = 73, normalized size = 2.43 \begin {gather*} e^{- 100 x^{3} e^{4 x} + 25 x^{2} e^{5 x} + \left (150 x^{4} + 200 x^{2}\right ) e^{3 x} + \left (- 100 x^{5} - 400 x^{3}\right ) e^{2 x} + \left (25 x^{6} + 200 x^{4} + 400 x^{2}\right ) e^{x} - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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