Optimal. Leaf size=119 \[ \frac{1}{17} (x+1)^{17} (d-7 e)-\frac{3}{16} (x+1)^{16} (2 d-7 e)+\frac{1}{3} (x+1)^{15} (3 d-7 e)-\frac{5}{14} (x+1)^{14} (4 d-7 e)+\frac{3}{13} (x+1)^{13} (5 d-7 e)-\frac{1}{12} (x+1)^{12} (6 d-7 e)+\frac{1}{11} (x+1)^{11} (d-e)+\frac{1}{18} e (x+1)^{18} \]
[Out]
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Rubi [A] time = 0.246738, antiderivative size = 119, 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 \[ \frac{1}{17} (x+1)^{17} (d-7 e)-\frac{3}{16} (x+1)^{16} (2 d-7 e)+\frac{1}{3} (x+1)^{15} (3 d-7 e)-\frac{5}{14} (x+1)^{14} (4 d-7 e)+\frac{3}{13} (x+1)^{13} (5 d-7 e)-\frac{1}{12} (x+1)^{12} (6 d-7 e)+\frac{1}{11} (x+1)^{11} (d-e)+\frac{1}{18} e (x+1)^{18} \]
Antiderivative was successfully verified.
[In] Int[x^6*(d + e*x)*(1 + 2*x + x^2)^5,x]
[Out]
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Rubi in Sympy [A] time = 29.0288, size = 104, normalized size = 0.87 \[ \frac{e \left (x + 1\right )^{18}}{18} + \left (\frac{d}{17} - \frac{7 e}{17}\right ) \left (x + 1\right )^{17} + \left (\frac{d}{11} - \frac{e}{11}\right ) \left (x + 1\right )^{11} - \left (\frac{3 d}{8} - \frac{21 e}{16}\right ) \left (x + 1\right )^{16} - \left (\frac{d}{2} - \frac{7 e}{12}\right ) \left (x + 1\right )^{12} + \left (d - \frac{7 e}{3}\right ) \left (x + 1\right )^{15} + \left (\frac{15 d}{13} - \frac{21 e}{13}\right ) \left (x + 1\right )^{13} - \left (\frac{10 d}{7} - \frac{5 e}{2}\right ) \left (x + 1\right )^{14} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**6*(e*x+d)*(x**2+2*x+1)**5,x)
[Out]
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Mathematica [A] time = 0.0419952, size = 150, normalized size = 1.26 \[ \frac{1}{17} x^{17} (d+10 e)+\frac{5}{16} x^{16} (2 d+9 e)+x^{15} (3 d+8 e)+\frac{15}{7} x^{14} (4 d+7 e)+\frac{42}{13} x^{13} (5 d+6 e)+\frac{7}{2} x^{12} (6 d+5 e)+\frac{30}{11} x^{11} (7 d+4 e)+\frac{3}{2} x^{10} (8 d+3 e)+\frac{5}{9} x^9 (9 d+2 e)+\frac{1}{8} x^8 (10 d+e)+\frac{d x^7}{7}+\frac{e x^{18}}{18} \]
Antiderivative was successfully verified.
[In] Integrate[x^6*(d + e*x)*(1 + 2*x + x^2)^5,x]
[Out]
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Maple [A] time = 0.002, size = 130, normalized size = 1.1 \[{\frac{e{x}^{18}}{18}}+{\frac{ \left ( d+10\,e \right ){x}^{17}}{17}}+{\frac{ \left ( 10\,d+45\,e \right ){x}^{16}}{16}}+{\frac{ \left ( 45\,d+120\,e \right ){x}^{15}}{15}}+{\frac{ \left ( 120\,d+210\,e \right ){x}^{14}}{14}}+{\frac{ \left ( 210\,d+252\,e \right ){x}^{13}}{13}}+{\frac{ \left ( 252\,d+210\,e \right ){x}^{12}}{12}}+{\frac{ \left ( 210\,d+120\,e \right ){x}^{11}}{11}}+{\frac{ \left ( 120\,d+45\,e \right ){x}^{10}}{10}}+{\frac{ \left ( 45\,d+10\,e \right ){x}^{9}}{9}}+{\frac{ \left ( 10\,d+e \right ){x}^{8}}{8}}+{\frac{d{x}^{7}}{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^6*(e*x+d)*(x^2+2*x+1)^5,x)
[Out]
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Maxima [A] time = 0.683946, size = 173, normalized size = 1.45 \[ \frac{1}{18} \, e x^{18} + \frac{1}{17} \,{\left (d + 10 \, e\right )} x^{17} + \frac{5}{16} \,{\left (2 \, d + 9 \, e\right )} x^{16} +{\left (3 \, d + 8 \, e\right )} x^{15} + \frac{15}{7} \,{\left (4 \, d + 7 \, e\right )} x^{14} + \frac{42}{13} \,{\left (5 \, d + 6 \, e\right )} x^{13} + \frac{7}{2} \,{\left (6 \, d + 5 \, e\right )} x^{12} + \frac{30}{11} \,{\left (7 \, d + 4 \, e\right )} x^{11} + \frac{3}{2} \,{\left (8 \, d + 3 \, e\right )} x^{10} + \frac{5}{9} \,{\left (9 \, d + 2 \, e\right )} x^{9} + \frac{1}{8} \,{\left (10 \, d + e\right )} x^{8} + \frac{1}{7} \, d x^{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 + 2*x + 1)^5*x^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.272299, size = 1, normalized size = 0.01 \[ \frac{1}{18} x^{18} e + \frac{10}{17} x^{17} e + \frac{1}{17} x^{17} d + \frac{45}{16} x^{16} e + \frac{5}{8} x^{16} d + 8 x^{15} e + 3 x^{15} d + 15 x^{14} e + \frac{60}{7} x^{14} d + \frac{252}{13} x^{13} e + \frac{210}{13} x^{13} d + \frac{35}{2} x^{12} e + 21 x^{12} d + \frac{120}{11} x^{11} e + \frac{210}{11} x^{11} d + \frac{9}{2} x^{10} e + 12 x^{10} d + \frac{10}{9} x^{9} e + 5 x^{9} d + \frac{1}{8} x^{8} e + \frac{5}{4} x^{8} d + \frac{1}{7} x^{7} d \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 + 2*x + 1)^5*x^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.182281, size = 134, normalized size = 1.13 \[ \frac{d x^{7}}{7} + \frac{e x^{18}}{18} + x^{17} \left (\frac{d}{17} + \frac{10 e}{17}\right ) + x^{16} \left (\frac{5 d}{8} + \frac{45 e}{16}\right ) + x^{15} \left (3 d + 8 e\right ) + x^{14} \left (\frac{60 d}{7} + 15 e\right ) + x^{13} \left (\frac{210 d}{13} + \frac{252 e}{13}\right ) + x^{12} \left (21 d + \frac{35 e}{2}\right ) + x^{11} \left (\frac{210 d}{11} + \frac{120 e}{11}\right ) + x^{10} \left (12 d + \frac{9 e}{2}\right ) + x^{9} \left (5 d + \frac{10 e}{9}\right ) + x^{8} \left (\frac{5 d}{4} + \frac{e}{8}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**6*(e*x+d)*(x**2+2*x+1)**5,x)
[Out]
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GIAC/XCAS [A] time = 0.269124, size = 194, normalized size = 1.63 \[ \frac{1}{18} \, x^{18} e + \frac{1}{17} \, d x^{17} + \frac{10}{17} \, x^{17} e + \frac{5}{8} \, d x^{16} + \frac{45}{16} \, x^{16} e + 3 \, d x^{15} + 8 \, x^{15} e + \frac{60}{7} \, d x^{14} + 15 \, x^{14} e + \frac{210}{13} \, d x^{13} + \frac{252}{13} \, x^{13} e + 21 \, d x^{12} + \frac{35}{2} \, x^{12} e + \frac{210}{11} \, d x^{11} + \frac{120}{11} \, x^{11} e + 12 \, d x^{10} + \frac{9}{2} \, x^{10} e + 5 \, d x^{9} + \frac{10}{9} \, x^{9} e + \frac{5}{4} \, d x^{8} + \frac{1}{8} \, x^{8} e + \frac{1}{7} \, d x^{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 + 2*x + 1)^5*x^6,x, algorithm="giac")
[Out]