Optimal. Leaf size=138 \[ -\frac{10 d+e}{9 x^9}-\frac{5 (9 d+2 e)}{8 x^8}-\frac{15 (8 d+3 e)}{7 x^7}-\frac{5 (7 d+4 e)}{x^6}-\frac{42 (6 d+5 e)}{5 x^5}-\frac{21 (5 d+6 e)}{2 x^4}-\frac{10 (4 d+7 e)}{x^3}-\frac{15 (3 d+8 e)}{2 x^2}-\frac{5 (2 d+9 e)}{x}+(d+10 e) \log (x)-\frac{d}{10 x^{10}}+e x \]
[Out]
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Rubi [A] time = 0.216087, antiderivative size = 138, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105 \[ -\frac{10 d+e}{9 x^9}-\frac{5 (9 d+2 e)}{8 x^8}-\frac{15 (8 d+3 e)}{7 x^7}-\frac{5 (7 d+4 e)}{x^6}-\frac{42 (6 d+5 e)}{5 x^5}-\frac{21 (5 d+6 e)}{2 x^4}-\frac{10 (4 d+7 e)}{x^3}-\frac{15 (3 d+8 e)}{2 x^2}-\frac{5 (2 d+9 e)}{x}+(d+10 e) \log (x)-\frac{d}{10 x^{10}}+e x \]
Antiderivative was successfully verified.
[In] Int[((d + e*x)*(1 + 2*x + x^2)^5)/x^11,x]
[Out]
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Rubi in Sympy [A] time = 27.7034, size = 121, normalized size = 0.88 \[ - \frac{d}{10 x^{10}} + e x + \left (d + 10 e\right ) \log{\left (x \right )} - \frac{10 d + 45 e}{x} - \frac{\frac{45 d}{2} + 60 e}{x^{2}} - \frac{40 d + 70 e}{x^{3}} - \frac{\frac{105 d}{2} + 63 e}{x^{4}} - \frac{\frac{252 d}{5} + 42 e}{x^{5}} - \frac{35 d + 20 e}{x^{6}} - \frac{\frac{120 d}{7} + \frac{45 e}{7}}{x^{7}} - \frac{\frac{45 d}{8} + \frac{5 e}{4}}{x^{8}} - \frac{\frac{10 d}{9} + \frac{e}{9}}{x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x+d)*(x**2+2*x+1)**5/x**11,x)
[Out]
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Mathematica [A] time = 0.111072, size = 140, normalized size = 1.01 \[ \frac{-10 d-e}{9 x^9}-\frac{5 (9 d+2 e)}{8 x^8}-\frac{15 (8 d+3 e)}{7 x^7}-\frac{5 (7 d+4 e)}{x^6}-\frac{42 (6 d+5 e)}{5 x^5}-\frac{21 (5 d+6 e)}{2 x^4}-\frac{10 (4 d+7 e)}{x^3}-\frac{15 (3 d+8 e)}{2 x^2}-\frac{5 (2 d+9 e)}{x}+(d+10 e) \log (x)-\frac{d}{10 x^{10}}+e x \]
Antiderivative was successfully verified.
[In] Integrate[((d + e*x)*(1 + 2*x + x^2)^5)/x^11,x]
[Out]
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Maple [A] time = 0.012, size = 128, normalized size = 0.9 \[ ex+d\ln \left ( x \right ) +10\,e\ln \left ( x \right ) -35\,{\frac{d}{{x}^{6}}}-20\,{\frac{e}{{x}^{6}}}-{\frac{105\,d}{2\,{x}^{4}}}-63\,{\frac{e}{{x}^{4}}}-{\frac{d}{10\,{x}^{10}}}-{\frac{45\,d}{8\,{x}^{8}}}-{\frac{5\,e}{4\,{x}^{8}}}-{\frac{10\,d}{9\,{x}^{9}}}-{\frac{e}{9\,{x}^{9}}}-40\,{\frac{d}{{x}^{3}}}-70\,{\frac{e}{{x}^{3}}}-{\frac{45\,d}{2\,{x}^{2}}}-60\,{\frac{e}{{x}^{2}}}-{\frac{252\,d}{5\,{x}^{5}}}-42\,{\frac{e}{{x}^{5}}}-10\,{\frac{d}{x}}-45\,{\frac{e}{x}}-{\frac{120\,d}{7\,{x}^{7}}}-{\frac{45\,e}{7\,{x}^{7}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+d)*(x^2+2*x+1)^5/x^11,x)
[Out]
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Maxima [A] time = 0.708637, size = 169, normalized size = 1.22 \[ e x +{\left (d + 10 \, e\right )} \log \left (x\right ) - \frac{12600 \,{\left (2 \, d + 9 \, e\right )} x^{9} + 18900 \,{\left (3 \, d + 8 \, e\right )} x^{8} + 25200 \,{\left (4 \, d + 7 \, e\right )} x^{7} + 26460 \,{\left (5 \, d + 6 \, e\right )} x^{6} + 21168 \,{\left (6 \, d + 5 \, e\right )} x^{5} + 12600 \,{\left (7 \, d + 4 \, e\right )} x^{4} + 5400 \,{\left (8 \, d + 3 \, e\right )} x^{3} + 1575 \,{\left (9 \, d + 2 \, e\right )} x^{2} + 280 \,{\left (10 \, d + e\right )} x + 252 \, d}{2520 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 + 2*x + 1)^5/x^11,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.28454, size = 177, normalized size = 1.28 \[ \frac{2520 \, e x^{11} + 2520 \,{\left (d + 10 \, e\right )} x^{10} \log \left (x\right ) - 12600 \,{\left (2 \, d + 9 \, e\right )} x^{9} - 18900 \,{\left (3 \, d + 8 \, e\right )} x^{8} - 25200 \,{\left (4 \, d + 7 \, e\right )} x^{7} - 26460 \,{\left (5 \, d + 6 \, e\right )} x^{6} - 21168 \,{\left (6 \, d + 5 \, e\right )} x^{5} - 12600 \,{\left (7 \, d + 4 \, e\right )} x^{4} - 5400 \,{\left (8 \, d + 3 \, e\right )} x^{3} - 1575 \,{\left (9 \, d + 2 \, e\right )} x^{2} - 280 \,{\left (10 \, d + e\right )} x - 252 \, d}{2520 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 + 2*x + 1)^5/x^11,x, algorithm="fricas")
[Out]
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Sympy [A] time = 23.6216, size = 109, normalized size = 0.79 \[ e x + \left (d + 10 e\right ) \log{\left (x \right )} - \frac{252 d + x^{9} \left (25200 d + 113400 e\right ) + x^{8} \left (56700 d + 151200 e\right ) + x^{7} \left (100800 d + 176400 e\right ) + x^{6} \left (132300 d + 158760 e\right ) + x^{5} \left (127008 d + 105840 e\right ) + x^{4} \left (88200 d + 50400 e\right ) + x^{3} \left (43200 d + 16200 e\right ) + x^{2} \left (14175 d + 3150 e\right ) + x \left (2800 d + 280 e\right )}{2520 x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x+d)*(x**2+2*x+1)**5/x**11,x)
[Out]
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GIAC/XCAS [A] time = 0.269365, size = 185, normalized size = 1.34 \[ x e +{\left (d + 10 \, e\right )}{\rm ln}\left ({\left | x \right |}\right ) - \frac{12600 \,{\left (2 \, d + 9 \, e\right )} x^{9} + 18900 \,{\left (3 \, d + 8 \, e\right )} x^{8} + 25200 \,{\left (4 \, d + 7 \, e\right )} x^{7} + 26460 \,{\left (5 \, d + 6 \, e\right )} x^{6} + 21168 \,{\left (6 \, d + 5 \, e\right )} x^{5} + 12600 \,{\left (7 \, d + 4 \, e\right )} x^{4} + 5400 \,{\left (8 \, d + 3 \, e\right )} x^{3} + 1575 \,{\left (9 \, d + 2 \, e\right )} x^{2} + 280 \,{\left (10 \, d + e\right )} x + 252 \, d}{2520 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 + 2*x + 1)^5/x^11,x, algorithm="giac")
[Out]