Optimal. Leaf size=25 \[ \frac{1}{11} (x+1)^{11} (d-e)+\frac{1}{12} e (x+1)^{12} \]
[Out]
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Rubi [A] time = 0.0298387, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ \frac{1}{11} (x+1)^{11} (d-e)+\frac{1}{12} e (x+1)^{12} \]
Antiderivative was successfully verified.
[In] Int[(d + e*x)*(1 + 2*x + x^2)^5,x]
[Out]
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Rubi in Sympy [A] time = 13.6105, size = 19, normalized size = 0.76 \[ \frac{e \left (x + 1\right )^{12}}{12} + \left (\frac{d}{11} - \frac{e}{11}\right ) \left (x + 1\right )^{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x+d)*(x**2+2*x+1)**5,x)
[Out]
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Mathematica [B] time = 0.0427318, size = 113, normalized size = 4.52 \[ d \left (\frac{x^{11}}{11}+x^{10}+5 x^9+15 x^8+30 x^7+42 x^6+42 x^5+30 x^4+15 x^3+5 x^2+x\right )+\frac{1}{132} e \left (11 x^{10}+120 x^9+594 x^8+1760 x^7+3465 x^6+4752 x^5+4620 x^4+3168 x^3+1485 x^2+440 x+66\right ) x^2 \]
Antiderivative was successfully verified.
[In] Integrate[(d + e*x)*(1 + 2*x + x^2)^5,x]
[Out]
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Maple [B] time = 0.002, size = 127, normalized size = 5.1 \[{\frac{e{x}^{12}}{12}}+{\frac{ \left ( d+10\,e \right ){x}^{11}}{11}}+{\frac{ \left ( 10\,d+45\,e \right ){x}^{10}}{10}}+{\frac{ \left ( 45\,d+120\,e \right ){x}^{9}}{9}}+{\frac{ \left ( 120\,d+210\,e \right ){x}^{8}}{8}}+{\frac{ \left ( 210\,d+252\,e \right ){x}^{7}}{7}}+{\frac{ \left ( 252\,d+210\,e \right ){x}^{6}}{6}}+{\frac{ \left ( 210\,d+120\,e \right ){x}^{5}}{5}}+{\frac{ \left ( 120\,d+45\,e \right ){x}^{4}}{4}}+{\frac{ \left ( 45\,d+10\,e \right ){x}^{3}}{3}}+{\frac{ \left ( 10\,d+e \right ){x}^{2}}{2}}+dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+d)*(x^2+2*x+1)^5,x)
[Out]
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Maxima [A] time = 0.678574, size = 170, normalized size = 6.8 \[ \frac{1}{12} \, e x^{12} + \frac{1}{11} \,{\left (d + 10 \, e\right )} x^{11} + \frac{1}{2} \,{\left (2 \, d + 9 \, e\right )} x^{10} + \frac{5}{3} \,{\left (3 \, d + 8 \, e\right )} x^{9} + \frac{15}{4} \,{\left (4 \, d + 7 \, e\right )} x^{8} + 6 \,{\left (5 \, d + 6 \, e\right )} x^{7} + 7 \,{\left (6 \, d + 5 \, e\right )} x^{6} + 6 \,{\left (7 \, d + 4 \, e\right )} x^{5} + \frac{15}{4} \,{\left (8 \, d + 3 \, e\right )} x^{4} + \frac{5}{3} \,{\left (9 \, d + 2 \, e\right )} x^{3} + \frac{1}{2} \,{\left (10 \, d + e\right )} x^{2} + d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 + 2*x + 1)^5,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.249421, size = 1, normalized size = 0.04 \[ \frac{1}{12} x^{12} e + \frac{10}{11} x^{11} e + \frac{1}{11} x^{11} d + \frac{9}{2} x^{10} e + x^{10} d + \frac{40}{3} x^{9} e + 5 x^{9} d + \frac{105}{4} x^{8} e + 15 x^{8} d + 36 x^{7} e + 30 x^{7} d + 35 x^{6} e + 42 x^{6} d + 24 x^{5} e + 42 x^{5} d + \frac{45}{4} x^{4} e + 30 x^{4} d + \frac{10}{3} x^{3} e + 15 x^{3} d + \frac{1}{2} x^{2} e + 5 x^{2} d + x d \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 + 2*x + 1)^5,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.189618, size = 119, normalized size = 4.76 \[ d x + \frac{e x^{12}}{12} + x^{11} \left (\frac{d}{11} + \frac{10 e}{11}\right ) + x^{10} \left (d + \frac{9 e}{2}\right ) + x^{9} \left (5 d + \frac{40 e}{3}\right ) + x^{8} \left (15 d + \frac{105 e}{4}\right ) + x^{7} \left (30 d + 36 e\right ) + x^{6} \left (42 d + 35 e\right ) + x^{5} \left (42 d + 24 e\right ) + x^{4} \left (30 d + \frac{45 e}{4}\right ) + x^{3} \left (15 d + \frac{10 e}{3}\right ) + x^{2} \left (5 d + \frac{e}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x+d)*(x**2+2*x+1)**5,x)
[Out]
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GIAC/XCAS [A] time = 0.266624, size = 189, normalized size = 7.56 \[ \frac{1}{12} \, x^{12} e + \frac{1}{11} \, d x^{11} + \frac{10}{11} \, x^{11} e + d x^{10} + \frac{9}{2} \, x^{10} e + 5 \, d x^{9} + \frac{40}{3} \, x^{9} e + 15 \, d x^{8} + \frac{105}{4} \, x^{8} e + 30 \, d x^{7} + 36 \, x^{7} e + 42 \, d x^{6} + 35 \, x^{6} e + 42 \, d x^{5} + 24 \, x^{5} e + 30 \, d x^{4} + \frac{45}{4} \, x^{4} e + 15 \, d x^{3} + \frac{10}{3} \, x^{3} e + 5 \, d x^{2} + \frac{1}{2} \, x^{2} e + d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 + 2*x + 1)^5,x, algorithm="giac")
[Out]