Optimal. Leaf size=71 \[ \frac{(x+1)^{11} (3 d-14 e)}{182 x^{13}}-\frac{(x+1)^{11} (3 d-14 e)}{1092 x^{12}}+\frac{(x+1)^{11} (3 d-14 e)}{12012 x^{11}}-\frac{d (x+1)^{11}}{14 x^{14}} \]
[Out]
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Rubi [A] time = 0.068653, antiderivative size = 71, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 4, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.21 \[ \frac{(x+1)^{11} (3 d-14 e)}{182 x^{13}}-\frac{(x+1)^{11} (3 d-14 e)}{1092 x^{12}}+\frac{(x+1)^{11} (3 d-14 e)}{12012 x^{11}}-\frac{d (x+1)^{11}}{14 x^{14}} \]
Antiderivative was successfully verified.
[In] Int[((d + e*x)*(1 + 2*x + x^2)^5)/x^15,x]
[Out]
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Rubi in Sympy [A] time = 10.0362, size = 58, normalized size = 0.82 \[ - \frac{d \left (x + 1\right )^{11}}{14 x^{14}} + \frac{\left (\frac{d}{4004} - \frac{e}{858}\right ) \left (x + 1\right )^{11}}{x^{11}} - \frac{\left (\frac{d}{364} - \frac{e}{78}\right ) \left (x + 1\right )^{11}}{x^{12}} + \frac{\left (\frac{3 d}{182} - \frac{e}{13}\right ) \left (x + 1\right )^{11}}{x^{13}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x+d)*(x**2+2*x+1)**5/x**15,x)
[Out]
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Mathematica [B] time = 0.0916089, size = 149, normalized size = 2.1 \[ -\frac{10 d+e}{13 x^{13}}-\frac{5 (9 d+2 e)}{12 x^{12}}-\frac{15 (8 d+3 e)}{11 x^{11}}-\frac{3 (7 d+4 e)}{x^{10}}-\frac{14 (6 d+5 e)}{3 x^9}-\frac{21 (5 d+6 e)}{4 x^8}-\frac{30 (4 d+7 e)}{7 x^7}-\frac{5 (3 d+8 e)}{2 x^6}-\frac{2 d+9 e}{x^5}-\frac{d+10 e}{4 x^4}-\frac{d}{14 x^{14}}-\frac{e}{3 x^3} \]
Antiderivative was successfully verified.
[In] Integrate[((d + e*x)*(1 + 2*x + x^2)^5)/x^15,x]
[Out]
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Maple [B] time = 0.01, size = 130, normalized size = 1.8 \[ -{\frac{45\,d+10\,e}{12\,{x}^{12}}}-{\frac{10\,d+e}{13\,{x}^{13}}}-{\frac{45\,d+120\,e}{6\,{x}^{6}}}-{\frac{d+10\,e}{4\,{x}^{4}}}-{\frac{210\,d+120\,e}{10\,{x}^{10}}}-{\frac{210\,d+252\,e}{8\,{x}^{8}}}-{\frac{120\,d+45\,e}{11\,{x}^{11}}}-{\frac{d}{14\,{x}^{14}}}-{\frac{252\,d+210\,e}{9\,{x}^{9}}}-{\frac{e}{3\,{x}^{3}}}-{\frac{10\,d+45\,e}{5\,{x}^{5}}}-{\frac{120\,d+210\,e}{7\,{x}^{7}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+d)*(x^2+2*x+1)^5/x^15,x)
[Out]
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Maxima [A] time = 0.687303, size = 174, normalized size = 2.45 \[ -\frac{4004 \, e x^{11} + 3003 \,{\left (d + 10 \, e\right )} x^{10} + 12012 \,{\left (2 \, d + 9 \, e\right )} x^{9} + 30030 \,{\left (3 \, d + 8 \, e\right )} x^{8} + 51480 \,{\left (4 \, d + 7 \, e\right )} x^{7} + 63063 \,{\left (5 \, d + 6 \, e\right )} x^{6} + 56056 \,{\left (6 \, d + 5 \, e\right )} x^{5} + 36036 \,{\left (7 \, d + 4 \, e\right )} x^{4} + 16380 \,{\left (8 \, d + 3 \, e\right )} x^{3} + 5005 \,{\left (9 \, d + 2 \, e\right )} x^{2} + 924 \,{\left (10 \, d + e\right )} x + 858 \, d}{12012 \, x^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 + 2*x + 1)^5/x^15,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.30122, size = 174, normalized size = 2.45 \[ -\frac{4004 \, e x^{11} + 3003 \,{\left (d + 10 \, e\right )} x^{10} + 12012 \,{\left (2 \, d + 9 \, e\right )} x^{9} + 30030 \,{\left (3 \, d + 8 \, e\right )} x^{8} + 51480 \,{\left (4 \, d + 7 \, e\right )} x^{7} + 63063 \,{\left (5 \, d + 6 \, e\right )} x^{6} + 56056 \,{\left (6 \, d + 5 \, e\right )} x^{5} + 36036 \,{\left (7 \, d + 4 \, e\right )} x^{4} + 16380 \,{\left (8 \, d + 3 \, e\right )} x^{3} + 5005 \,{\left (9 \, d + 2 \, e\right )} x^{2} + 924 \,{\left (10 \, d + e\right )} x + 858 \, d}{12012 \, x^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 + 2*x + 1)^5/x^15,x, algorithm="fricas")
[Out]
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Sympy [A] time = 43.0383, size = 116, normalized size = 1.63 \[ - \frac{858 d + 4004 e x^{11} + x^{10} \left (3003 d + 30030 e\right ) + x^{9} \left (24024 d + 108108 e\right ) + x^{8} \left (90090 d + 240240 e\right ) + x^{7} \left (205920 d + 360360 e\right ) + x^{6} \left (315315 d + 378378 e\right ) + x^{5} \left (336336 d + 280280 e\right ) + x^{4} \left (252252 d + 144144 e\right ) + x^{3} \left (131040 d + 49140 e\right ) + x^{2} \left (45045 d + 10010 e\right ) + x \left (9240 d + 924 e\right )}{12012 x^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x+d)*(x**2+2*x+1)**5/x**15,x)
[Out]
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GIAC/XCAS [A] time = 0.272168, size = 192, normalized size = 2.7 \[ -\frac{4004 \, x^{11} e + 3003 \, d x^{10} + 30030 \, x^{10} e + 24024 \, d x^{9} + 108108 \, x^{9} e + 90090 \, d x^{8} + 240240 \, x^{8} e + 205920 \, d x^{7} + 360360 \, x^{7} e + 315315 \, d x^{6} + 378378 \, x^{6} e + 336336 \, d x^{5} + 280280 \, x^{5} e + 252252 \, d x^{4} + 144144 \, x^{4} e + 131040 \, d x^{3} + 49140 \, x^{3} e + 45045 \, d x^{2} + 10010 \, x^{2} e + 9240 \, d x + 924 \, x e + 858 \, d}{12012 \, x^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 + 2*x + 1)^5/x^15,x, algorithm="giac")
[Out]