Optimal. Leaf size=210 \[ \frac{a^4 x^2}{2}+\frac{32 a^3 x^3}{3}+\frac{1}{5} \left (3 a^2-1536 a+20480\right ) x^{10}-\frac{16}{3} \left (a^2-128 a+896\right ) x^9-\frac{32}{7} \left (15 a^2-288 a+512\right ) x^7+\frac{16}{5} a \left (a^2-48 a+128\right ) x^5+8 (12-a) a^2 x^4+\frac{2}{3} \left (-a^3+192 a^2-1536 a+1024\right ) x^6+\frac{2}{7} (640-a) x^{14}-\frac{16}{13} (464-3 a) x^{13}+\frac{8}{3} (524-9 a) x^{12}-\frac{32}{11} (928-35 a) x^{11}+8 (128-3 a) (4-a) x^8+\frac{x^{18}}{18}-\frac{16 x^{17}}{17}+8 x^{16}-\frac{224 x^{15}}{5} \]
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Rubi [A] time = 0.483287, antiderivative size = 210, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042 \[ \frac{a^4 x^2}{2}+\frac{32 a^3 x^3}{3}+\frac{1}{5} \left (3 a^2-1536 a+20480\right ) x^{10}-\frac{16}{3} \left (a^2-128 a+896\right ) x^9-\frac{32}{7} \left (15 a^2-288 a+512\right ) x^7+\frac{16}{5} a \left (a^2-48 a+128\right ) x^5+8 (12-a) a^2 x^4+\frac{2}{3} \left (-a^3+192 a^2-1536 a+1024\right ) x^6+\frac{2}{7} (640-a) x^{14}-\frac{16}{13} (464-3 a) x^{13}+\frac{8}{3} (524-9 a) x^{12}-\frac{32}{11} (928-35 a) x^{11}+8 (128-3 a) (4-a) x^8+\frac{x^{18}}{18}-\frac{16 x^{17}}{17}+8 x^{16}-\frac{224 x^{15}}{5} \]
Antiderivative was successfully verified.
[In] Int[x*(a + 8*x - 8*x^2 + 4*x^3 - x^4)^4,x]
[Out]
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Rubi in Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*(-x**4+4*x**3-8*x**2+a+8*x)**4,x)
[Out]
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Mathematica [A] time = 0.048177, size = 204, normalized size = 0.97 \[ \frac{a^4 x^2}{2}+\frac{32 a^3 x^3}{3}+\frac{1}{5} \left (3 a^2-1536 a+20480\right ) x^{10}-\frac{16}{3} \left (a^2-128 a+896\right ) x^9+8 \left (3 a^2-140 a+512\right ) x^8-\frac{32}{7} \left (15 a^2-288 a+512\right ) x^7+\frac{16}{5} a \left (a^2-48 a+128\right ) x^5-8 (a-12) a^2 x^4-\frac{2}{3} \left (a^3-192 a^2+1536 a-1024\right ) x^6-\frac{2}{7} (a-640) x^{14}+\frac{16}{13} (3 a-464) x^{13}-\frac{8}{3} (9 a-524) x^{12}+\frac{32}{11} (35 a-928) x^{11}+\frac{x^{18}}{18}-\frac{16 x^{17}}{17}+8 x^{16}-\frac{224 x^{15}}{5} \]
Antiderivative was successfully verified.
[In] Integrate[x*(a + 8*x - 8*x^2 + 4*x^3 - x^4)^4,x]
[Out]
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Maple [A] time = 0.002, size = 267, normalized size = 1.3 \[{\frac{{x}^{18}}{18}}-{\frac{16\,{x}^{17}}{17}}+8\,{x}^{16}-{\frac{224\,{x}^{15}}{5}}+{\frac{ \left ( -4\,a+2560 \right ){x}^{14}}{14}}+{\frac{ \left ( 48\,a-7424 \right ){x}^{13}}{13}}+{\frac{ \left ( -288\,a+16768 \right ){x}^{12}}{12}}+{\frac{ \left ( 1120\,a-29696 \right ){x}^{11}}{11}}+{\frac{ \left ( 2\,{a}^{2}-2560\,a+24576+ \left ( -2\,a+128 \right ) ^{2} \right ){x}^{10}}{10}}+{\frac{ \left ( -16\,{a}^{2}+3584\,a-10240+2\, \left ( 8\,a-128 \right ) \left ( -2\,a+128 \right ) \right ){x}^{9}}{9}}+{\frac{ \left ( 64\,{a}^{2}-2560\,a+2\, \left ( -16\,a+64 \right ) \left ( -2\,a+128 \right ) + \left ( 8\,a-128 \right ) ^{2} \right ){x}^{8}}{8}}+{\frac{ \left ( -160\,{a}^{2}+32\,a \left ( -2\,a+128 \right ) +2\, \left ( -16\,a+64 \right ) \left ( 8\,a-128 \right ) \right ){x}^{7}}{7}}+{\frac{ \left ( 2\,{a}^{2} \left ( -2\,a+128 \right ) +32\,a \left ( 8\,a-128 \right ) + \left ( -16\,a+64 \right ) ^{2} \right ){x}^{6}}{6}}+{\frac{ \left ( 2\,{a}^{2} \left ( 8\,a-128 \right ) +32\,a \left ( -16\,a+64 \right ) \right ){x}^{5}}{5}}+{\frac{ \left ( 2\,{a}^{2} \left ( -16\,a+64 \right ) +256\,{a}^{2} \right ){x}^{4}}{4}}+{\frac{32\,{a}^{3}{x}^{3}}{3}}+{\frac{{a}^{4}{x}^{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*(-x^4+4*x^3-8*x^2+a+8*x)^4,x)
[Out]
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Maxima [A] time = 0.815219, size = 246, normalized size = 1.17 \[ \frac{1}{18} \, x^{18} - \frac{16}{17} \, x^{17} + 8 \, x^{16} - \frac{2}{7} \,{\left (a - 640\right )} x^{14} - \frac{224}{5} \, x^{15} + \frac{16}{13} \,{\left (3 \, a - 464\right )} x^{13} - \frac{8}{3} \,{\left (9 \, a - 524\right )} x^{12} + \frac{32}{11} \,{\left (35 \, a - 928\right )} x^{11} + \frac{1}{5} \,{\left (3 \, a^{2} - 1536 \, a + 20480\right )} x^{10} - \frac{16}{3} \,{\left (a^{2} - 128 \, a + 896\right )} x^{9} + 8 \,{\left (3 \, a^{2} - 140 \, a + 512\right )} x^{8} - \frac{32}{7} \,{\left (15 \, a^{2} - 288 \, a + 512\right )} x^{7} - \frac{2}{3} \,{\left (a^{3} - 192 \, a^{2} + 1536 \, a - 1024\right )} x^{6} + \frac{1}{2} \, a^{4} x^{2} + \frac{32}{3} \, a^{3} x^{3} + \frac{16}{5} \,{\left (a^{3} - 48 \, a^{2} + 128 \, a\right )} x^{5} - 8 \,{\left (a^{3} - 12 \, a^{2}\right )} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^4 - 4*x^3 + 8*x^2 - a - 8*x)^4*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.225836, size = 1, normalized size = 0. \[ \frac{1}{18} x^{18} - \frac{16}{17} x^{17} + 8 x^{16} - \frac{224}{5} x^{15} - \frac{2}{7} x^{14} a + \frac{1280}{7} x^{14} + \frac{48}{13} x^{13} a - \frac{7424}{13} x^{13} - 24 x^{12} a + \frac{4192}{3} x^{12} + \frac{1120}{11} x^{11} a + \frac{3}{5} x^{10} a^{2} - \frac{29696}{11} x^{11} - \frac{1536}{5} x^{10} a - \frac{16}{3} x^{9} a^{2} + 4096 x^{10} + \frac{2048}{3} x^{9} a + 24 x^{8} a^{2} - \frac{14336}{3} x^{9} - 1120 x^{8} a - \frac{480}{7} x^{7} a^{2} - \frac{2}{3} x^{6} a^{3} + 4096 x^{8} + \frac{9216}{7} x^{7} a + 128 x^{6} a^{2} + \frac{16}{5} x^{5} a^{3} - \frac{16384}{7} x^{7} - 1024 x^{6} a - \frac{768}{5} x^{5} a^{2} - 8 x^{4} a^{3} + \frac{2048}{3} x^{6} + \frac{2048}{5} x^{5} a + 96 x^{4} a^{2} + \frac{32}{3} x^{3} a^{3} + \frac{1}{2} x^{2} a^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^4 - 4*x^3 + 8*x^2 - a - 8*x)^4*x,x, algorithm="fricas")
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Sympy [A] time = 0.249164, size = 212, normalized size = 1.01 \[ \frac{a^{4} x^{2}}{2} + \frac{32 a^{3} x^{3}}{3} + \frac{x^{18}}{18} - \frac{16 x^{17}}{17} + 8 x^{16} - \frac{224 x^{15}}{5} + x^{14} \left (- \frac{2 a}{7} + \frac{1280}{7}\right ) + x^{13} \left (\frac{48 a}{13} - \frac{7424}{13}\right ) + x^{12} \left (- 24 a + \frac{4192}{3}\right ) + x^{11} \left (\frac{1120 a}{11} - \frac{29696}{11}\right ) + x^{10} \left (\frac{3 a^{2}}{5} - \frac{1536 a}{5} + 4096\right ) + x^{9} \left (- \frac{16 a^{2}}{3} + \frac{2048 a}{3} - \frac{14336}{3}\right ) + x^{8} \left (24 a^{2} - 1120 a + 4096\right ) + x^{7} \left (- \frac{480 a^{2}}{7} + \frac{9216 a}{7} - \frac{16384}{7}\right ) + x^{6} \left (- \frac{2 a^{3}}{3} + 128 a^{2} - 1024 a + \frac{2048}{3}\right ) + x^{5} \left (\frac{16 a^{3}}{5} - \frac{768 a^{2}}{5} + \frac{2048 a}{5}\right ) + x^{4} \left (- 8 a^{3} + 96 a^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*(-x**4+4*x**3-8*x**2+a+8*x)**4,x)
[Out]
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GIAC/XCAS [A] time = 0.259783, size = 300, normalized size = 1.43 \[ \frac{1}{18} \, x^{18} - \frac{16}{17} \, x^{17} + 8 \, x^{16} - \frac{2}{7} \, a x^{14} - \frac{224}{5} \, x^{15} + \frac{48}{13} \, a x^{13} + \frac{1280}{7} \, x^{14} - 24 \, a x^{12} - \frac{7424}{13} \, x^{13} + \frac{3}{5} \, a^{2} x^{10} + \frac{1120}{11} \, a x^{11} + \frac{4192}{3} \, x^{12} - \frac{16}{3} \, a^{2} x^{9} - \frac{1536}{5} \, a x^{10} - \frac{29696}{11} \, x^{11} + 24 \, a^{2} x^{8} + \frac{2048}{3} \, a x^{9} + 4096 \, x^{10} - \frac{2}{3} \, a^{3} x^{6} - \frac{480}{7} \, a^{2} x^{7} - 1120 \, a x^{8} - \frac{14336}{3} \, x^{9} + \frac{16}{5} \, a^{3} x^{5} + 128 \, a^{2} x^{6} + \frac{9216}{7} \, a x^{7} + 4096 \, x^{8} - 8 \, a^{3} x^{4} - \frac{768}{5} \, a^{2} x^{5} - 1024 \, a x^{6} - \frac{16384}{7} \, x^{7} + \frac{1}{2} \, a^{4} x^{2} + \frac{32}{3} \, a^{3} x^{3} + 96 \, a^{2} x^{4} + \frac{2048}{5} \, a x^{5} + \frac{2048}{3} \, x^{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x^4 - 4*x^3 + 8*x^2 - a - 8*x)^4*x,x, algorithm="giac")
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