Optimal. Leaf size=138 \[ -\frac{10 d+e}{7 x^7}-\frac{5 (9 d+2 e)}{6 x^6}-\frac{3 (8 d+3 e)}{x^5}-\frac{15 (7 d+4 e)}{2 x^4}-\frac{14 (6 d+5 e)}{x^3}+\frac{1}{2} x^2 (d+10 e)-\frac{21 (5 d+6 e)}{x^2}+5 x (2 d+9 e)-\frac{30 (4 d+7 e)}{x}+15 (3 d+8 e) \log (x)-\frac{d}{8 x^8}+\frac{e x^3}{3} \]
[Out]
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Rubi [A] time = 0.222617, 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 \[ -\frac{10 d+e}{7 x^7}-\frac{5 (9 d+2 e)}{6 x^6}-\frac{3 (8 d+3 e)}{x^5}-\frac{15 (7 d+4 e)}{2 x^4}-\frac{14 (6 d+5 e)}{x^3}+\frac{1}{2} x^2 (d+10 e)-\frac{21 (5 d+6 e)}{x^2}+5 x (2 d+9 e)-\frac{30 (4 d+7 e)}{x}+15 (3 d+8 e) \log (x)-\frac{d}{8 x^8}+\frac{e x^3}{3} \]
Antiderivative was successfully verified.
[In] Int[((d + e*x)*(1 + 2*x + x^2)^5)/x^9,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{d}{8 x^{8}} + \frac{e x^{3}}{3} + x \left (10 d + 45 e\right ) + \left (d + 10 e\right ) \int x\, dx + \left (45 d + 120 e\right ) \log{\left (x \right )} - \frac{120 d + 210 e}{x} - \frac{105 d + 126 e}{x^{2}} - \frac{84 d + 70 e}{x^{3}} - \frac{\frac{105 d}{2} + 30 e}{x^{4}} - \frac{24 d + 9 e}{x^{5}} - \frac{\frac{15 d}{2} + \frac{5 e}{3}}{x^{6}} - \frac{\frac{10 d}{7} + \frac{e}{7}}{x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x+d)*(x**2+2*x+1)**5/x**9,x)
[Out]
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Mathematica [A] time = 0.090719, size = 140, normalized size = 1.01 \[ \frac{-10 d-e}{7 x^7}-\frac{5 (9 d+2 e)}{6 x^6}-\frac{3 (8 d+3 e)}{x^5}-\frac{15 (7 d+4 e)}{2 x^4}-\frac{14 (6 d+5 e)}{x^3}+\frac{1}{2} x^2 (d+10 e)-\frac{21 (5 d+6 e)}{x^2}+5 x (2 d+9 e)-\frac{30 (4 d+7 e)}{x}+15 (3 d+8 e) \log (x)-\frac{d}{8 x^8}+\frac{e x^3}{3} \]
Antiderivative was successfully verified.
[In] Integrate[((d + e*x)*(1 + 2*x + x^2)^5)/x^9,x]
[Out]
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Maple [A] time = 0.012, size = 128, normalized size = 0.9 \[{\frac{e{x}^{3}}{3}}+{\frac{d{x}^{2}}{2}}+5\,e{x}^{2}+10\,dx+45\,ex+45\,d\ln \left ( x \right ) +120\,e\ln \left ( x \right ) -{\frac{15\,d}{2\,{x}^{6}}}-{\frac{5\,e}{3\,{x}^{6}}}-{\frac{105\,d}{2\,{x}^{4}}}-30\,{\frac{e}{{x}^{4}}}-{\frac{d}{8\,{x}^{8}}}-84\,{\frac{d}{{x}^{3}}}-70\,{\frac{e}{{x}^{3}}}-105\,{\frac{d}{{x}^{2}}}-126\,{\frac{e}{{x}^{2}}}-24\,{\frac{d}{{x}^{5}}}-9\,{\frac{e}{{x}^{5}}}-120\,{\frac{d}{x}}-210\,{\frac{e}{x}}-{\frac{10\,d}{7\,{x}^{7}}}-{\frac{e}{7\,{x}^{7}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+d)*(x^2+2*x+1)^5/x^9,x)
[Out]
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Maxima [A] time = 0.712985, size = 171, normalized size = 1.24 \[ \frac{1}{3} \, e x^{3} + \frac{1}{2} \,{\left (d + 10 \, e\right )} x^{2} + 5 \,{\left (2 \, d + 9 \, e\right )} x + 15 \,{\left (3 \, d + 8 \, e\right )} \log \left (x\right ) - \frac{5040 \,{\left (4 \, d + 7 \, e\right )} x^{7} + 3528 \,{\left (5 \, d + 6 \, e\right )} x^{6} + 2352 \,{\left (6 \, d + 5 \, e\right )} x^{5} + 1260 \,{\left (7 \, d + 4 \, e\right )} x^{4} + 504 \,{\left (8 \, d + 3 \, e\right )} x^{3} + 140 \,{\left (9 \, d + 2 \, e\right )} x^{2} + 24 \,{\left (10 \, d + e\right )} x + 21 \, d}{168 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 + 2*x + 1)^5/x^9,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.275426, size = 177, normalized size = 1.28 \[ \frac{56 \, e x^{11} + 84 \,{\left (d + 10 \, e\right )} x^{10} + 840 \,{\left (2 \, d + 9 \, e\right )} x^{9} + 2520 \,{\left (3 \, d + 8 \, e\right )} x^{8} \log \left (x\right ) - 5040 \,{\left (4 \, d + 7 \, e\right )} x^{7} - 3528 \,{\left (5 \, d + 6 \, e\right )} x^{6} - 2352 \,{\left (6 \, d + 5 \, e\right )} x^{5} - 1260 \,{\left (7 \, d + 4 \, e\right )} x^{4} - 504 \,{\left (8 \, d + 3 \, e\right )} x^{3} - 140 \,{\left (9 \, d + 2 \, e\right )} x^{2} - 24 \,{\left (10 \, d + e\right )} x - 21 \, d}{168 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 + 2*x + 1)^5/x^9,x, algorithm="fricas")
[Out]
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Sympy [A] time = 13.7994, size = 114, normalized size = 0.83 \[ \frac{e x^{3}}{3} + x^{2} \left (\frac{d}{2} + 5 e\right ) + x \left (10 d + 45 e\right ) + 15 \left (3 d + 8 e\right ) \log{\left (x \right )} - \frac{21 d + x^{7} \left (20160 d + 35280 e\right ) + x^{6} \left (17640 d + 21168 e\right ) + x^{5} \left (14112 d + 11760 e\right ) + x^{4} \left (8820 d + 5040 e\right ) + x^{3} \left (4032 d + 1512 e\right ) + x^{2} \left (1260 d + 280 e\right ) + x \left (240 d + 24 e\right )}{168 x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x+d)*(x**2+2*x+1)**5/x**9,x)
[Out]
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GIAC/XCAS [A] time = 0.271488, size = 188, normalized size = 1.36 \[ \frac{1}{3} \, x^{3} e + \frac{1}{2} \, d x^{2} + 5 \, x^{2} e + 10 \, d x + 45 \, x e + 15 \,{\left (3 \, d + 8 \, e\right )}{\rm ln}\left ({\left | x \right |}\right ) - \frac{5040 \,{\left (4 \, d + 7 \, e\right )} x^{7} + 3528 \,{\left (5 \, d + 6 \, e\right )} x^{6} + 2352 \,{\left (6 \, d + 5 \, e\right )} x^{5} + 1260 \,{\left (7 \, d + 4 \, e\right )} x^{4} + 504 \,{\left (8 \, d + 3 \, e\right )} x^{3} + 140 \,{\left (9 \, d + 2 \, e\right )} x^{2} + 24 \,{\left (10 \, d + e\right )} x + 21 \, d}{168 \, x^{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 + 2*x + 1)^5/x^9,x, algorithm="giac")
[Out]