Optimal. Leaf size=128 \[ \frac{(x+1)^{11} (6 d-17 e)}{272 x^{16}}-\frac{(x+1)^{11} (6 d-17 e)}{816 x^{15}}+\frac{(x+1)^{11} (6 d-17 e)}{2856 x^{14}}-\frac{(x+1)^{11} (6 d-17 e)}{12376 x^{13}}+\frac{(x+1)^{11} (6 d-17 e)}{74256 x^{12}}-\frac{(x+1)^{11} (6 d-17 e)}{816816 x^{11}}-\frac{d (x+1)^{11}}{17 x^{17}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.114732, antiderivative size = 128, normalized size of antiderivative = 1., number of steps used = 8, number of rules used = 4, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.21 \[ \frac{(x+1)^{11} (6 d-17 e)}{272 x^{16}}-\frac{(x+1)^{11} (6 d-17 e)}{816 x^{15}}+\frac{(x+1)^{11} (6 d-17 e)}{2856 x^{14}}-\frac{(x+1)^{11} (6 d-17 e)}{12376 x^{13}}+\frac{(x+1)^{11} (6 d-17 e)}{74256 x^{12}}-\frac{(x+1)^{11} (6 d-17 e)}{816816 x^{11}}-\frac{d (x+1)^{11}}{17 x^{17}} \]
Antiderivative was successfully verified.
[In] Int[((d + e*x)*(1 + 2*x + x^2)^5)/x^18,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 15.9727, size = 105, normalized size = 0.82 \[ - \frac{d \left (x + 1\right )^{11}}{17 x^{17}} - \frac{\left (\frac{d}{136136} - \frac{e}{48048}\right ) \left (x + 1\right )^{11}}{x^{11}} + \frac{\left (\frac{d}{12376} - \frac{e}{4368}\right ) \left (x + 1\right )^{11}}{x^{12}} - \frac{\left (\frac{3 d}{6188} - \frac{e}{728}\right ) \left (x + 1\right )^{11}}{x^{13}} + \frac{\left (\frac{d}{476} - \frac{e}{168}\right ) \left (x + 1\right )^{11}}{x^{14}} - \frac{\left (\frac{d}{136} - \frac{e}{48}\right ) \left (x + 1\right )^{11}}{x^{15}} + \frac{\left (\frac{3 d}{136} - \frac{e}{16}\right ) \left (x + 1\right )^{11}}{x^{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x+d)*(x**2+2*x+1)**5/x**18,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.106386, size = 151, normalized size = 1.18 \[ -\frac{10 d+e}{16 x^{16}}-\frac{9 d+2 e}{3 x^{15}}-\frac{15 (8 d+3 e)}{14 x^{14}}-\frac{30 (7 d+4 e)}{13 x^{13}}-\frac{7 (6 d+5 e)}{2 x^{12}}-\frac{42 (5 d+6 e)}{11 x^{11}}-\frac{3 (4 d+7 e)}{x^{10}}-\frac{5 (3 d+8 e)}{3 x^9}-\frac{5 (2 d+9 e)}{8 x^8}-\frac{d+10 e}{7 x^7}-\frac{d}{17 x^{17}}-\frac{e}{6 x^6} \]
Antiderivative was successfully verified.
[In] Integrate[((d + e*x)*(1 + 2*x + x^2)^5)/x^18,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.008, size = 130, normalized size = 1. \[ -{\frac{252\,d+210\,e}{12\,{x}^{12}}}-{\frac{45\,d+10\,e}{15\,{x}^{15}}}-{\frac{10\,d+e}{16\,{x}^{16}}}-{\frac{210\,d+120\,e}{13\,{x}^{13}}}-{\frac{e}{6\,{x}^{6}}}-{\frac{120\,d+210\,e}{10\,{x}^{10}}}-{\frac{d}{17\,{x}^{17}}}-{\frac{10\,d+45\,e}{8\,{x}^{8}}}-{\frac{210\,d+252\,e}{11\,{x}^{11}}}-{\frac{120\,d+45\,e}{14\,{x}^{14}}}-{\frac{45\,d+120\,e}{9\,{x}^{9}}}-{\frac{d+10\,e}{7\,{x}^{7}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+d)*(x^2+2*x+1)^5/x^18,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.687783, size = 174, normalized size = 1.36 \[ -\frac{136136 \, e x^{11} + 116688 \,{\left (d + 10 \, e\right )} x^{10} + 510510 \,{\left (2 \, d + 9 \, e\right )} x^{9} + 1361360 \,{\left (3 \, d + 8 \, e\right )} x^{8} + 2450448 \,{\left (4 \, d + 7 \, e\right )} x^{7} + 3118752 \,{\left (5 \, d + 6 \, e\right )} x^{6} + 2858856 \,{\left (6 \, d + 5 \, e\right )} x^{5} + 1884960 \,{\left (7 \, d + 4 \, e\right )} x^{4} + 875160 \,{\left (8 \, d + 3 \, e\right )} x^{3} + 272272 \,{\left (9 \, d + 2 \, e\right )} x^{2} + 51051 \,{\left (10 \, d + e\right )} x + 48048 \, d}{816816 \, x^{17}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 + 2*x + 1)^5/x^18,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.275178, size = 174, normalized size = 1.36 \[ -\frac{136136 \, e x^{11} + 116688 \,{\left (d + 10 \, e\right )} x^{10} + 510510 \,{\left (2 \, d + 9 \, e\right )} x^{9} + 1361360 \,{\left (3 \, d + 8 \, e\right )} x^{8} + 2450448 \,{\left (4 \, d + 7 \, e\right )} x^{7} + 3118752 \,{\left (5 \, d + 6 \, e\right )} x^{6} + 2858856 \,{\left (6 \, d + 5 \, e\right )} x^{5} + 1884960 \,{\left (7 \, d + 4 \, e\right )} x^{4} + 875160 \,{\left (8 \, d + 3 \, e\right )} x^{3} + 272272 \,{\left (9 \, d + 2 \, e\right )} x^{2} + 51051 \,{\left (10 \, d + e\right )} x + 48048 \, d}{816816 \, x^{17}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 + 2*x + 1)^5/x^18,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 63.7925, size = 116, normalized size = 0.91 \[ - \frac{48048 d + 136136 e x^{11} + x^{10} \left (116688 d + 1166880 e\right ) + x^{9} \left (1021020 d + 4594590 e\right ) + x^{8} \left (4084080 d + 10890880 e\right ) + x^{7} \left (9801792 d + 17153136 e\right ) + x^{6} \left (15593760 d + 18712512 e\right ) + x^{5} \left (17153136 d + 14294280 e\right ) + x^{4} \left (13194720 d + 7539840 e\right ) + x^{3} \left (7001280 d + 2625480 e\right ) + x^{2} \left (2450448 d + 544544 e\right ) + x \left (510510 d + 51051 e\right )}{816816 x^{17}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x+d)*(x**2+2*x+1)**5/x**18,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.270306, size = 192, normalized size = 1.5 \[ -\frac{136136 \, x^{11} e + 116688 \, d x^{10} + 1166880 \, x^{10} e + 1021020 \, d x^{9} + 4594590 \, x^{9} e + 4084080 \, d x^{8} + 10890880 \, x^{8} e + 9801792 \, d x^{7} + 17153136 \, x^{7} e + 15593760 \, d x^{6} + 18712512 \, x^{6} e + 17153136 \, d x^{5} + 14294280 \, x^{5} e + 13194720 \, d x^{4} + 7539840 \, x^{4} e + 7001280 \, d x^{3} + 2625480 \, x^{3} e + 2450448 \, d x^{2} + 544544 \, x^{2} e + 510510 \, d x + 51051 \, x e + 48048 \, d}{816816 \, x^{17}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 + 2*x + 1)^5/x^18,x, algorithm="giac")
[Out]