Optimal. Leaf size=330 \[ \frac {\pi ^2 (3-4 \text {mc}) \text {mc}^8 \text {Ei}\left (-\frac {x}{y}\right )}{384 y}+\frac {1}{16} \pi ^2 (1-2 \text {mc}) \text {mc}^6 \text {Ei}\left (-\frac {x}{y}\right )+\frac {1}{32} \pi ^2 \text {mc}^3 y \left (-12 \text {mc}^2+3 \text {mc}-8 y\right ) \text {Ei}\left (-\frac {x}{y}\right )+\frac {\pi ^2 (3-4 \text {mc}) \text {mc}^8 e^{-\frac {x}{y}}}{384 x}+\frac {3}{8} \pi ^2 \text {mc}^5 y e^{-\frac {x}{y}}+\frac {1}{4} \pi ^2 \text {mc}^3 y^2 e^{-\frac {x}{y}}+\frac {1}{48} \pi ^2 (3-22 \text {mc}) \text {mc}^2 y^2 e^{-\frac {x}{y}}+\frac {1}{48} \pi ^2 (3-22 \text {mc}) \text {mc}^2 x y e^{-\frac {x}{y}}+\frac {1}{4} \pi ^2 \text {mc}^3 y^2 e^{-\frac {x}{y}} \log \left (\frac {x}{\text {mc}^2}\right )-\frac {1}{32} \pi ^2 \text {mc}^3 y (3 (1-4 \text {mc}) \text {mc}-8 x) e^{-\frac {x}{y}} \log \left (\frac {x}{\text {mc}^2}\right )-\frac {1}{128} \pi ^2 (4 \text {mc}+1) x^2 y e^{-\frac {x}{y}}-\frac {1}{64} \pi ^2 (4 \text {mc}+1) y^3 e^{-\frac {x}{y}}-\frac {1}{64} \pi ^2 (4 \text {mc}+1) x y^2 e^{-\frac {x}{y}} \]
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Rubi [A] time = 0.87, antiderivative size = 330, normalized size of antiderivative = 1.00, number of steps used = 20, number of rules used = 8, integrand size = 107, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.075, Rules used = {12, 6742, 2199, 2194, 2177, 2178, 2176, 2554} \[ \frac {\pi ^2 (3-4 \text {mc}) \text {mc}^8 \text {ExpIntegralEi}\left (-\frac {x}{y}\right )}{384 y}+\frac {1}{16} \pi ^2 (1-2 \text {mc}) \text {mc}^6 \text {ExpIntegralEi}\left (-\frac {x}{y}\right )+\frac {1}{32} \pi ^2 \text {mc}^3 y \left (-12 \text {mc}^2+3 \text {mc}-8 y\right ) \text {ExpIntegralEi}\left (-\frac {x}{y}\right )+\frac {1}{4} \pi ^2 \text {mc}^3 y^2 e^{-\frac {x}{y}}+\frac {1}{48} \pi ^2 (3-22 \text {mc}) \text {mc}^2 y^2 e^{-\frac {x}{y}}+\frac {1}{4} \pi ^2 \text {mc}^3 y^2 e^{-\frac {x}{y}} \log \left (\frac {x}{\text {mc}^2}\right )+\frac {\pi ^2 (3-4 \text {mc}) \text {mc}^8 e^{-\frac {x}{y}}}{384 x}+\frac {3}{8} \pi ^2 \text {mc}^5 y e^{-\frac {x}{y}}+\frac {1}{48} \pi ^2 (3-22 \text {mc}) \text {mc}^2 x y e^{-\frac {x}{y}}-\frac {1}{32} \pi ^2 \text {mc}^3 y (3 (1-4 \text {mc}) \text {mc}-8 x) e^{-\frac {x}{y}} \log \left (\frac {x}{\text {mc}^2}\right )-\frac {1}{128} \pi ^2 (4 \text {mc}+1) x^2 y e^{-\frac {x}{y}}-\frac {1}{64} \pi ^2 (4 \text {mc}+1) y^3 e^{-\frac {x}{y}}-\frac {1}{64} \pi ^2 (4 \text {mc}+1) x y^2 e^{-\frac {x}{y}} \]
Antiderivative was successfully verified.
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Rule 12
Rule 2176
Rule 2177
Rule 2178
Rule 2194
Rule 2199
Rule 2554
Rule 6742
Rubi steps
\begin {align*} \int \frac {e^{-\frac {x}{y}} \left (\pi ^2 \left (-3 \text {mc}^8+4 \text {mc}^9+24 \text {mc}^6 x-48 \text {mc}^7 x-144 \text {mc}^5 x^2-24 \text {mc}^2 x^3+176 \text {mc}^3 x^3+3 x^4+12 \text {mc} x^4\right )+12 \text {mc}^3 \pi ^2 \left (3 \text {mc}-12 \text {mc}^2-8 x\right ) x^2 \log \left (\frac {x}{\text {mc}^2}\right )\right )}{384 x^2} \, dx &=\frac {1}{384} \int \frac {e^{-\frac {x}{y}} \left (\pi ^2 \left (-3 \text {mc}^8+4 \text {mc}^9+24 \text {mc}^6 x-48 \text {mc}^7 x-144 \text {mc}^5 x^2-24 \text {mc}^2 x^3+176 \text {mc}^3 x^3+3 x^4+12 \text {mc} x^4\right )+12 \text {mc}^3 \pi ^2 \left (3 \text {mc}-12 \text {mc}^2-8 x\right ) x^2 \log \left (\frac {x}{\text {mc}^2}\right )\right )}{x^2} \, dx\\ &=\frac {1}{384} \int \left (\frac {e^{-\frac {x}{y}} \pi ^2 \left (\text {mc}^2-x\right ) \left (-(3-4 \text {mc}) \text {mc}^6+(21-44 \text {mc}) \text {mc}^4 x+(21-188 \text {mc}) \text {mc}^2 x^2-3 (1+4 \text {mc}) x^3\right )}{x^2}-12 e^{-\frac {x}{y}} \text {mc}^3 \pi ^2 \left (-3 \text {mc}+12 \text {mc}^2+8 x\right ) \log \left (\frac {x}{\text {mc}^2}\right )\right ) \, dx\\ &=\frac {1}{384} \pi ^2 \int \frac {e^{-\frac {x}{y}} \left (\text {mc}^2-x\right ) \left (-(3-4 \text {mc}) \text {mc}^6+(21-44 \text {mc}) \text {mc}^4 x+(21-188 \text {mc}) \text {mc}^2 x^2-3 (1+4 \text {mc}) x^3\right )}{x^2} \, dx-\frac {1}{32} \left (\text {mc}^3 \pi ^2\right ) \int e^{-\frac {x}{y}} \left (-3 \text {mc}+12 \text {mc}^2+8 x\right ) \log \left (\frac {x}{\text {mc}^2}\right ) \, dx\\ &=-\frac {1}{32} e^{-\frac {x}{y}} \text {mc}^3 \pi ^2 (3 (1-4 \text {mc}) \text {mc}-8 x) y \log \left (\frac {x}{\text {mc}^2}\right )+\frac {1}{4} e^{-\frac {x}{y}} \text {mc}^3 \pi ^2 y^2 \log \left (\frac {x}{\text {mc}^2}\right )+\frac {1}{384} \pi ^2 \int \left (-144 e^{-\frac {x}{y}} \text {mc}^5+\frac {e^{-\frac {x}{y}} \text {mc}^8 (-3+4 \text {mc})}{x^2}-\frac {24 e^{-\frac {x}{y}} \text {mc}^6 (-1+2 \text {mc})}{x}+8 e^{-\frac {x}{y}} \text {mc}^2 (-3+22 \text {mc}) x+3 e^{-\frac {x}{y}} (1+4 \text {mc}) x^2\right ) \, dx+\frac {1}{32} \left (\text {mc}^3 \pi ^2\right ) \int \frac {e^{-\frac {x}{y}} \left (3 \text {mc}-12 \text {mc}^2-8 x-8 y\right ) y}{x} \, dx\\ &=-\frac {1}{32} e^{-\frac {x}{y}} \text {mc}^3 \pi ^2 (3 (1-4 \text {mc}) \text {mc}-8 x) y \log \left (\frac {x}{\text {mc}^2}\right )+\frac {1}{4} e^{-\frac {x}{y}} \text {mc}^3 \pi ^2 y^2 \log \left (\frac {x}{\text {mc}^2}\right )-\frac {1}{48} \left ((3-22 \text {mc}) \text {mc}^2 \pi ^2\right ) \int e^{-\frac {x}{y}} x \, dx-\frac {1}{8} \left (3 \text {mc}^5 \pi ^2\right ) \int e^{-\frac {x}{y}} \, dx+\frac {1}{16} \left ((1-2 \text {mc}) \text {mc}^6 \pi ^2\right ) \int \frac {e^{-\frac {x}{y}}}{x} \, dx-\frac {1}{384} \left ((3-4 \text {mc}) \text {mc}^8 \pi ^2\right ) \int \frac {e^{-\frac {x}{y}}}{x^2} \, dx+\frac {1}{128} \left ((1+4 \text {mc}) \pi ^2\right ) \int e^{-\frac {x}{y}} x^2 \, dx+\frac {1}{32} \left (\text {mc}^3 \pi ^2 y\right ) \int \frac {e^{-\frac {x}{y}} \left (3 \text {mc}-12 \text {mc}^2-8 x-8 y\right )}{x} \, dx\\ &=\frac {e^{-\frac {x}{y}} (3-4 \text {mc}) \text {mc}^8 \pi ^2}{384 x}+\frac {3}{8} e^{-\frac {x}{y}} \text {mc}^5 \pi ^2 y+\frac {1}{48} e^{-\frac {x}{y}} (3-22 \text {mc}) \text {mc}^2 \pi ^2 x y-\frac {1}{128} e^{-\frac {x}{y}} (1+4 \text {mc}) \pi ^2 x^2 y+\frac {1}{16} (1-2 \text {mc}) \text {mc}^6 \pi ^2 \text {Ei}\left (-\frac {x}{y}\right )-\frac {1}{32} e^{-\frac {x}{y}} \text {mc}^3 \pi ^2 (3 (1-4 \text {mc}) \text {mc}-8 x) y \log \left (\frac {x}{\text {mc}^2}\right )+\frac {1}{4} e^{-\frac {x}{y}} \text {mc}^3 \pi ^2 y^2 \log \left (\frac {x}{\text {mc}^2}\right )+\frac {\left ((3-4 \text {mc}) \text {mc}^8 \pi ^2\right ) \int \frac {e^{-\frac {x}{y}}}{x} \, dx}{384 y}-\frac {1}{48} \left ((3-22 \text {mc}) \text {mc}^2 \pi ^2 y\right ) \int e^{-\frac {x}{y}} \, dx+\frac {1}{32} \left (\text {mc}^3 \pi ^2 y\right ) \int \left (-8 e^{-\frac {x}{y}}+\frac {e^{-\frac {x}{y}} \left (3 \text {mc}-12 \text {mc}^2-8 y\right )}{x}\right ) \, dx+\frac {1}{64} \left ((1+4 \text {mc}) \pi ^2 y\right ) \int e^{-\frac {x}{y}} x \, dx\\ &=\frac {e^{-\frac {x}{y}} (3-4 \text {mc}) \text {mc}^8 \pi ^2}{384 x}+\frac {3}{8} e^{-\frac {x}{y}} \text {mc}^5 \pi ^2 y+\frac {1}{48} e^{-\frac {x}{y}} (3-22 \text {mc}) \text {mc}^2 \pi ^2 x y-\frac {1}{128} e^{-\frac {x}{y}} (1+4 \text {mc}) \pi ^2 x^2 y+\frac {1}{48} e^{-\frac {x}{y}} (3-22 \text {mc}) \text {mc}^2 \pi ^2 y^2-\frac {1}{64} e^{-\frac {x}{y}} (1+4 \text {mc}) \pi ^2 x y^2+\frac {1}{16} (1-2 \text {mc}) \text {mc}^6 \pi ^2 \text {Ei}\left (-\frac {x}{y}\right )+\frac {(3-4 \text {mc}) \text {mc}^8 \pi ^2 \text {Ei}\left (-\frac {x}{y}\right )}{384 y}-\frac {1}{32} e^{-\frac {x}{y}} \text {mc}^3 \pi ^2 (3 (1-4 \text {mc}) \text {mc}-8 x) y \log \left (\frac {x}{\text {mc}^2}\right )+\frac {1}{4} e^{-\frac {x}{y}} \text {mc}^3 \pi ^2 y^2 \log \left (\frac {x}{\text {mc}^2}\right )-\frac {1}{4} \left (\text {mc}^3 \pi ^2 y\right ) \int e^{-\frac {x}{y}} \, dx+\frac {1}{32} \left (\text {mc}^3 \pi ^2 \left (3 \text {mc}-12 \text {mc}^2-8 y\right ) y\right ) \int \frac {e^{-\frac {x}{y}}}{x} \, dx+\frac {1}{64} \left ((1+4 \text {mc}) \pi ^2 y^2\right ) \int e^{-\frac {x}{y}} \, dx\\ &=\frac {e^{-\frac {x}{y}} (3-4 \text {mc}) \text {mc}^8 \pi ^2}{384 x}+\frac {3}{8} e^{-\frac {x}{y}} \text {mc}^5 \pi ^2 y+\frac {1}{48} e^{-\frac {x}{y}} (3-22 \text {mc}) \text {mc}^2 \pi ^2 x y-\frac {1}{128} e^{-\frac {x}{y}} (1+4 \text {mc}) \pi ^2 x^2 y+\frac {1}{48} e^{-\frac {x}{y}} (3-22 \text {mc}) \text {mc}^2 \pi ^2 y^2+\frac {1}{4} e^{-\frac {x}{y}} \text {mc}^3 \pi ^2 y^2-\frac {1}{64} e^{-\frac {x}{y}} (1+4 \text {mc}) \pi ^2 x y^2-\frac {1}{64} e^{-\frac {x}{y}} (1+4 \text {mc}) \pi ^2 y^3+\frac {1}{16} (1-2 \text {mc}) \text {mc}^6 \pi ^2 \text {Ei}\left (-\frac {x}{y}\right )+\frac {(3-4 \text {mc}) \text {mc}^8 \pi ^2 \text {Ei}\left (-\frac {x}{y}\right )}{384 y}+\frac {1}{32} \text {mc}^3 \pi ^2 \left (3 \text {mc}-12 \text {mc}^2-8 y\right ) y \text {Ei}\left (-\frac {x}{y}\right )-\frac {1}{32} e^{-\frac {x}{y}} \text {mc}^3 \pi ^2 (3 (1-4 \text {mc}) \text {mc}-8 x) y \log \left (\frac {x}{\text {mc}^2}\right )+\frac {1}{4} e^{-\frac {x}{y}} \text {mc}^3 \pi ^2 y^2 \log \left (\frac {x}{\text {mc}^2}\right )\\ \end {align*}
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Mathematica [A] time = 0.15, size = 181, normalized size = 0.55 \[ \frac {1}{384} \pi ^2 \left (\frac {e^{-\frac {x}{y}} \left (-4 \text {mc}^9+3 \text {mc}^8+144 \text {mc}^5 x y-16 \text {mc}^3 x y (11 x+5 y)+24 \text {mc}^2 x y (x+y)+12 \text {mc}^3 x y \left (12 \text {mc}^2-3 \text {mc}+8 (x+y)\right ) \log \left (\frac {x}{\text {mc}^2}\right )-12 \text {mc} x y \left (x^2+2 x y+2 y^2\right )-3 x y \left (x^2+2 x y+2 y^2\right )\right )}{x}-\frac {\text {mc}^3 \left (4 \text {mc}^6-3 \text {mc}^5+48 \text {mc}^4 y-24 \text {mc}^3 y+144 \text {mc}^2 y^2-36 \text {mc} y^2+96 y^3\right ) \text {Ei}\left (-\frac {x}{y}\right )}{y}\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 269, normalized size = 0.82 \[ \frac {12 \, {\left (8 \, \pi ^{2} \mathit {mc}^{3} x y^{3} + {\left (8 \, \pi ^{2} \mathit {mc}^{3} x^{2} + 3 \, \pi ^{2} {\left (4 \, \mathit {mc}^{5} - \mathit {mc}^{4}\right )} x\right )} y^{2}\right )} e^{\left (-\frac {x}{y}\right )} \log \left (\frac {x}{\mathit {mc}^{2}}\right ) - {\left (96 \, \pi ^{2} \mathit {mc}^{3} x y^{3} + 36 \, \pi ^{2} {\left (4 \, \mathit {mc}^{5} - \mathit {mc}^{4}\right )} x y^{2} + 24 \, \pi ^{2} {\left (2 \, \mathit {mc}^{7} - \mathit {mc}^{6}\right )} x y + \pi ^{2} {\left (4 \, \mathit {mc}^{9} - 3 \, \mathit {mc}^{8}\right )} x\right )} {\rm Ei}\left (-\frac {x}{y}\right ) - {\left (6 \, \pi ^{2} {\left (4 \, \mathit {mc} + 1\right )} x y^{4} + \pi ^{2} {\left (4 \, \mathit {mc}^{9} - 3 \, \mathit {mc}^{8}\right )} y + 2 \, {\left (3 \, \pi ^{2} {\left (4 \, \mathit {mc} + 1\right )} x^{2} + 4 \, \pi ^{2} {\left (10 \, \mathit {mc}^{3} - 3 \, \mathit {mc}^{2}\right )} x\right )} y^{3} - {\left (144 \, \pi ^{2} \mathit {mc}^{5} x - 3 \, \pi ^{2} {\left (4 \, \mathit {mc} + 1\right )} x^{3} - 8 \, \pi ^{2} {\left (22 \, \mathit {mc}^{3} - 3 \, \mathit {mc}^{2}\right )} x^{2}\right )} y^{2}\right )} e^{\left (-\frac {x}{y}\right )}}{384 \, x y} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.10, size = 472, normalized size = 1.43 \[ -\frac {4 \, \pi ^{2} \mathit {mc}^{9} x {\rm Ei}\left (-\frac {x}{y}\right ) + 4 \, \pi ^{2} \mathit {mc}^{9} y e^{\left (-\frac {x}{y}\right )} - 3 \, \pi ^{2} \mathit {mc}^{8} x {\rm Ei}\left (-\frac {x}{y}\right ) + 48 \, \pi ^{2} \mathit {mc}^{7} x y {\rm Ei}\left (-\frac {x}{y}\right ) - 3 \, \pi ^{2} \mathit {mc}^{8} y e^{\left (-\frac {x}{y}\right )} - 144 \, \pi ^{2} \mathit {mc}^{5} x y^{2} e^{\left (-\frac {x}{y}\right )} \log \left (\frac {x}{\mathit {mc}^{2}}\right ) - 24 \, \pi ^{2} \mathit {mc}^{6} x y {\rm Ei}\left (-\frac {x}{y}\right ) + 144 \, \pi ^{2} \mathit {mc}^{5} x y^{2} {\rm Ei}\left (-\frac {x}{y}\right ) - 144 \, \pi ^{2} \mathit {mc}^{5} x y^{2} e^{\left (-\frac {x}{y}\right )} + 36 \, \pi ^{2} \mathit {mc}^{4} x y^{2} e^{\left (-\frac {x}{y}\right )} \log \left (\frac {x}{\mathit {mc}^{2}}\right ) - 96 \, \pi ^{2} \mathit {mc}^{3} x^{2} y^{2} e^{\left (-\frac {x}{y}\right )} \log \left (\frac {x}{\mathit {mc}^{2}}\right ) - 96 \, \pi ^{2} \mathit {mc}^{3} x y^{3} e^{\left (-\frac {x}{y}\right )} \log \left (\frac {x}{\mathit {mc}^{2}}\right ) - 36 \, \pi ^{2} \mathit {mc}^{4} x y^{2} {\rm Ei}\left (-\frac {x}{y}\right ) + 96 \, \pi ^{2} \mathit {mc}^{3} x y^{3} {\rm Ei}\left (-\frac {x}{y}\right ) + 176 \, \pi ^{2} \mathit {mc}^{3} x^{2} y^{2} e^{\left (-\frac {x}{y}\right )} + 80 \, \pi ^{2} \mathit {mc}^{3} x y^{3} e^{\left (-\frac {x}{y}\right )} - 24 \, \pi ^{2} \mathit {mc}^{2} x^{2} y^{2} e^{\left (-\frac {x}{y}\right )} + 12 \, \pi ^{2} \mathit {mc} x^{3} y^{2} e^{\left (-\frac {x}{y}\right )} - 24 \, \pi ^{2} \mathit {mc}^{2} x y^{3} e^{\left (-\frac {x}{y}\right )} + 24 \, \pi ^{2} \mathit {mc} x^{2} y^{3} e^{\left (-\frac {x}{y}\right )} + 24 \, \pi ^{2} \mathit {mc} x y^{4} e^{\left (-\frac {x}{y}\right )} + 3 \, \pi ^{2} x^{3} y^{2} e^{\left (-\frac {x}{y}\right )} + 6 \, \pi ^{2} x^{2} y^{3} e^{\left (-\frac {x}{y}\right )} + 6 \, \pi ^{2} x y^{4} e^{\left (-\frac {x}{y}\right )}}{384 \, x y} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.22, size = 1356, normalized size = 4.11 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ -\frac {\pi ^{2} \mathit {mc}^{9} \Gamma \left (-1, \frac {x}{y}\right )}{96 \, y} - \frac {1}{8} \, \pi ^{2} \mathit {mc}^{7} {\rm Ei}\left (-\frac {x}{y}\right ) + \frac {\pi ^{2} \mathit {mc}^{8} \Gamma \left (-1, \frac {x}{y}\right )}{128 \, y} + \frac {3}{8} \, \pi ^{2} \mathit {mc}^{5} y e^{\left (-\frac {x}{y}\right )} \log \left (\frac {x}{\mathit {mc}^{2}}\right ) + \frac {1}{16} \, \pi ^{2} \mathit {mc}^{6} {\rm Ei}\left (-\frac {x}{y}\right ) - \frac {3}{8} \, \pi ^{2} \mathit {mc}^{5} y {\rm Ei}\left (-\frac {x}{y}\right ) + \frac {3}{8} \, \pi ^{2} \mathit {mc}^{5} y e^{\left (-\frac {x}{y}\right )} - \frac {3}{32} \, \pi ^{2} \mathit {mc}^{4} y e^{\left (-\frac {x}{y}\right )} \log \left (\frac {x}{\mathit {mc}^{2}}\right ) + \frac {3}{32} \, \pi ^{2} \mathit {mc}^{4} y {\rm Ei}\left (-\frac {x}{y}\right ) - \frac {11}{24} \, \pi ^{2} {\left (x y + y^{2}\right )} \mathit {mc}^{3} e^{\left (-\frac {x}{y}\right )} + \frac {1}{4} \, \pi ^{2} {\left ({\left (x y + y^{2}\right )} e^{\left (-\frac {x}{y}\right )} \log \relax (x) + \int \frac {{\left (2 \, x^{2} \log \left (\mathit {mc}\right ) - x y - y^{2}\right )} e^{\left (-\frac {x}{y}\right )}}{x}\,{d x}\right )} \mathit {mc}^{3} + \frac {1}{16} \, \pi ^{2} {\left (x y + y^{2}\right )} \mathit {mc}^{2} e^{\left (-\frac {x}{y}\right )} - \frac {1}{32} \, \pi ^{2} {\left (x^{2} y + 2 \, x y^{2} + 2 \, y^{3}\right )} \mathit {mc} e^{\left (-\frac {x}{y}\right )} - \frac {1}{128} \, \pi ^{2} {\left (x^{2} y + 2 \, x y^{2} + 2 \, y^{3}\right )} e^{\left (-\frac {x}{y}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.77, size = 265, normalized size = 0.80 \[ \mathrm {ei}\left (-\frac {x}{y}\right )\,\left (\frac {\frac {\Pi ^2\,{\mathrm {mc}}^8}{128}-\frac {\Pi ^2\,{\mathrm {mc}}^9}{96}}{y}+\frac {\Pi ^2\,{\mathrm {mc}}^6}{16}-\frac {\Pi ^2\,{\mathrm {mc}}^7}{8}+y\,\left (\frac {3\,\Pi ^2\,{\mathrm {mc}}^4}{32}-\frac {3\,\Pi ^2\,{\mathrm {mc}}^5}{8}\right )-\frac {\Pi ^2\,{\mathrm {mc}}^3\,y^2}{4}\right )-\frac {2\,\Pi ^2\,x^2\,y\,{\mathrm {e}}^{-\frac {x}{y}}\,\left (-72\,{\mathrm {mc}}^5+40\,{\mathrm {mc}}^3\,y-12\,{\mathrm {mc}}^2\,y+12\,\mathrm {mc}\,y^2+3\,y^2\right )+2\,\Pi ^2\,x^3\,y\,{\mathrm {e}}^{-\frac {x}{y}}\,\left (88\,{\mathrm {mc}}^3-12\,{\mathrm {mc}}^2+12\,y\,\mathrm {mc}+3\,y\right )+\Pi ^2\,{\mathrm {mc}}^8\,x\,{\mathrm {e}}^{-\frac {x}{y}}\,\left (4\,\mathrm {mc}-3\right )+3\,\Pi ^2\,x^4\,y\,{\mathrm {e}}^{-\frac {x}{y}}\,\left (4\,\mathrm {mc}+1\right )-96\,\Pi ^2\,{\mathrm {mc}}^3\,x^3\,y\,\ln \left (\frac {x}{{\mathrm {mc}}^2}\right )\,{\mathrm {e}}^{-\frac {x}{y}}-12\,\Pi ^2\,{\mathrm {mc}}^3\,x^2\,y\,\ln \left (\frac {x}{{\mathrm {mc}}^2}\right )\,{\mathrm {e}}^{-\frac {x}{y}}\,\left (12\,{\mathrm {mc}}^2-3\,\mathrm {mc}+8\,y\right )}{384\,x^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 21.74, size = 330, normalized size = 1.00 \[ - \frac {\pi ^{2} mc^{9} \operatorname {E}_{2}\left (\frac {x}{y}\right )}{96 x} + \frac {\pi ^{2} mc^{8} \operatorname {E}_{2}\left (\frac {x}{y}\right )}{128 x} - \frac {\pi ^{2} mc^{7} \operatorname {Ei}{\left (- \frac {x}{y} \right )}}{8} + \frac {\pi ^{2} mc^{6} \operatorname {Ei}{\left (- \frac {x}{y} \right )}}{16} + \frac {3 \pi ^{2} mc^{5} y e^{- \frac {x}{y}}}{8} - \frac {3 \pi ^{2} mc^{5} \left (y \operatorname {Ei}{\left (- \frac {x}{y} \right )} - y e^{- \frac {x}{y}} \log {\left (\frac {x}{mc^{2}} \right )}\right )}{8} + \frac {3 \pi ^{2} mc^{4} \left (y \operatorname {Ei}{\left (- \frac {x}{y} \right )} - y e^{- \frac {x}{y}} \log {\left (\frac {x}{mc^{2}} \right )}\right )}{32} + \frac {11 \pi ^{2} mc^{3} \left (- x y e^{- \frac {x}{y}} - y^{2} e^{- \frac {x}{y}}\right )}{24} - \frac {\pi ^{2} mc^{3} \left (y^{2} \operatorname {Ei}{\left (- \frac {x}{y} \right )} - y^{2} e^{- \frac {x}{y}} + \left (- x y e^{- \frac {x}{y}} - y^{2} e^{- \frac {x}{y}}\right ) \log {\left (\frac {x}{mc^{2}} \right )}\right )}{4} - \frac {\pi ^{2} mc^{2} \left (- x y e^{- \frac {x}{y}} - y^{2} e^{- \frac {x}{y}}\right )}{16} + \frac {\pi ^{2} mc \left (- x^{2} y e^{- \frac {x}{y}} - 2 x y^{2} e^{- \frac {x}{y}} - 2 y^{3} e^{- \frac {x}{y}}\right )}{32} + \frac {\pi ^{2} \left (- x^{2} y e^{- \frac {x}{y}} - 2 x y^{2} e^{- \frac {x}{y}} - 2 y^{3} e^{- \frac {x}{y}}\right )}{128} \]
Verification of antiderivative is not currently implemented for this CAS.
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