Optimal. Leaf size=55 \[ \frac{1}{13} (x+1)^{13} (d-3 e)-\frac{1}{12} (x+1)^{12} (2 d-3 e)+\frac{1}{11} (x+1)^{11} (d-e)+\frac{1}{14} e (x+1)^{14} \]
[Out]
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Rubi [A] time = 0.185047, antiderivative size = 55, 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 \[ \frac{1}{13} (x+1)^{13} (d-3 e)-\frac{1}{12} (x+1)^{12} (2 d-3 e)+\frac{1}{11} (x+1)^{11} (d-e)+\frac{1}{14} e (x+1)^{14} \]
Antiderivative was successfully verified.
[In] Int[x^2*(d + e*x)*(1 + 2*x + x^2)^5,x]
[Out]
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Rubi in Sympy [A] time = 18.5101, size = 44, normalized size = 0.8 \[ \frac{e \left (x + 1\right )^{14}}{14} + \left (\frac{d}{13} - \frac{3 e}{13}\right ) \left (x + 1\right )^{13} + \left (\frac{d}{11} - \frac{e}{11}\right ) \left (x + 1\right )^{11} - \left (\frac{d}{6} - \frac{e}{4}\right ) \left (x + 1\right )^{12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*(e*x+d)*(x**2+2*x+1)**5,x)
[Out]
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Mathematica [B] time = 0.0374591, size = 148, normalized size = 2.69 \[ \frac{1}{13} x^{13} (d+10 e)+\frac{5}{12} x^{12} (2 d+9 e)+\frac{15}{11} x^{11} (3 d+8 e)+3 x^{10} (4 d+7 e)+\frac{14}{3} x^9 (5 d+6 e)+\frac{21}{4} x^8 (6 d+5 e)+\frac{30}{7} x^7 (7 d+4 e)+\frac{5}{2} x^6 (8 d+3 e)+x^5 (9 d+2 e)+\frac{1}{4} x^4 (10 d+e)+\frac{d x^3}{3}+\frac{e x^{14}}{14} \]
Antiderivative was successfully verified.
[In] Integrate[x^2*(d + e*x)*(1 + 2*x + x^2)^5,x]
[Out]
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Maple [B] time = 0.001, size = 130, normalized size = 2.4 \[{\frac{e{x}^{14}}{14}}+{\frac{ \left ( d+10\,e \right ){x}^{13}}{13}}+{\frac{ \left ( 10\,d+45\,e \right ){x}^{12}}{12}}+{\frac{ \left ( 45\,d+120\,e \right ){x}^{11}}{11}}+{\frac{ \left ( 120\,d+210\,e \right ){x}^{10}}{10}}+{\frac{ \left ( 210\,d+252\,e \right ){x}^{9}}{9}}+{\frac{ \left ( 252\,d+210\,e \right ){x}^{8}}{8}}+{\frac{ \left ( 210\,d+120\,e \right ){x}^{7}}{7}}+{\frac{ \left ( 120\,d+45\,e \right ){x}^{6}}{6}}+{\frac{ \left ( 45\,d+10\,e \right ){x}^{5}}{5}}+{\frac{ \left ( 10\,d+e \right ){x}^{4}}{4}}+{\frac{d{x}^{3}}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(e*x+d)*(x^2+2*x+1)^5,x)
[Out]
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Maxima [A] time = 0.674861, size = 173, normalized size = 3.15 \[ \frac{1}{14} \, e x^{14} + \frac{1}{13} \,{\left (d + 10 \, e\right )} x^{13} + \frac{5}{12} \,{\left (2 \, d + 9 \, e\right )} x^{12} + \frac{15}{11} \,{\left (3 \, d + 8 \, e\right )} x^{11} + 3 \,{\left (4 \, d + 7 \, e\right )} x^{10} + \frac{14}{3} \,{\left (5 \, d + 6 \, e\right )} x^{9} + \frac{21}{4} \,{\left (6 \, d + 5 \, e\right )} x^{8} + \frac{30}{7} \,{\left (7 \, d + 4 \, e\right )} x^{7} + \frac{5}{2} \,{\left (8 \, d + 3 \, e\right )} x^{6} +{\left (9 \, d + 2 \, e\right )} x^{5} + \frac{1}{4} \,{\left (10 \, d + e\right )} x^{4} + \frac{1}{3} \, d x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 + 2*x + 1)^5*x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.256624, size = 1, normalized size = 0.02 \[ \frac{1}{14} x^{14} e + \frac{10}{13} x^{13} e + \frac{1}{13} x^{13} d + \frac{15}{4} x^{12} e + \frac{5}{6} x^{12} d + \frac{120}{11} x^{11} e + \frac{45}{11} x^{11} d + 21 x^{10} e + 12 x^{10} d + 28 x^{9} e + \frac{70}{3} x^{9} d + \frac{105}{4} x^{8} e + \frac{63}{2} x^{8} d + \frac{120}{7} x^{7} e + 30 x^{7} d + \frac{15}{2} x^{6} e + 20 x^{6} d + 2 x^{5} e + 9 x^{5} d + \frac{1}{4} x^{4} e + \frac{5}{2} x^{4} d + \frac{1}{3} x^{3} d \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 + 2*x + 1)^5*x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.182618, size = 133, normalized size = 2.42 \[ \frac{d x^{3}}{3} + \frac{e x^{14}}{14} + x^{13} \left (\frac{d}{13} + \frac{10 e}{13}\right ) + x^{12} \left (\frac{5 d}{6} + \frac{15 e}{4}\right ) + x^{11} \left (\frac{45 d}{11} + \frac{120 e}{11}\right ) + x^{10} \left (12 d + 21 e\right ) + x^{9} \left (\frac{70 d}{3} + 28 e\right ) + x^{8} \left (\frac{63 d}{2} + \frac{105 e}{4}\right ) + x^{7} \left (30 d + \frac{120 e}{7}\right ) + x^{6} \left (20 d + \frac{15 e}{2}\right ) + x^{5} \left (9 d + 2 e\right ) + x^{4} \left (\frac{5 d}{2} + \frac{e}{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*(e*x+d)*(x**2+2*x+1)**5,x)
[Out]
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GIAC/XCAS [A] time = 0.266724, size = 194, normalized size = 3.53 \[ \frac{1}{14} \, x^{14} e + \frac{1}{13} \, d x^{13} + \frac{10}{13} \, x^{13} e + \frac{5}{6} \, d x^{12} + \frac{15}{4} \, x^{12} e + \frac{45}{11} \, d x^{11} + \frac{120}{11} \, x^{11} e + 12 \, d x^{10} + 21 \, x^{10} e + \frac{70}{3} \, d x^{9} + 28 \, x^{9} e + \frac{63}{2} \, d x^{8} + \frac{105}{4} \, x^{8} e + 30 \, d x^{7} + \frac{120}{7} \, x^{7} e + 20 \, d x^{6} + \frac{15}{2} \, x^{6} e + 9 \, d x^{5} + 2 \, x^{5} e + \frac{5}{2} \, d x^{4} + \frac{1}{4} \, x^{4} e + \frac{1}{3} \, d x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 + 2*x + 1)^5*x^2,x, algorithm="giac")
[Out]