Optimal. Leaf size=87 \[ \frac{a^2 (a+b x)^{11} (A b-a B)}{11 b^4}+\frac{(a+b x)^{13} (A b-3 a B)}{13 b^4}-\frac{a (a+b x)^{12} (2 A b-3 a B)}{12 b^4}+\frac{B (a+b x)^{14}}{14 b^4} \]
[Out]
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Rubi [A] time = 0.389367, antiderivative size = 87, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ \frac{a^2 (a+b x)^{11} (A b-a B)}{11 b^4}+\frac{(a+b x)^{13} (A b-3 a B)}{13 b^4}-\frac{a (a+b x)^{12} (2 A b-3 a B)}{12 b^4}+\frac{B (a+b x)^{14}}{14 b^4} \]
Antiderivative was successfully verified.
[In] Int[x^2*(a + b*x)^10*(A + B*x),x]
[Out]
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Rubi in Sympy [A] time = 50.2002, size = 78, normalized size = 0.9 \[ \frac{B \left (a + b x\right )^{14}}{14 b^{4}} + \frac{a^{2} \left (a + b x\right )^{11} \left (A b - B a\right )}{11 b^{4}} - \frac{a \left (a + b x\right )^{12} \left (2 A b - 3 B a\right )}{12 b^{4}} + \frac{\left (a + b x\right )^{13} \left (A b - 3 B a\right )}{13 b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*(b*x+a)**10*(B*x+A),x)
[Out]
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Mathematica [B] time = 0.0512075, size = 226, normalized size = 2.6 \[ \frac{1}{3} a^{10} A x^3+\frac{1}{4} a^9 x^4 (a B+10 A b)+a^8 b x^5 (2 a B+9 A b)+\frac{5}{2} a^7 b^2 x^6 (3 a B+8 A b)+\frac{30}{7} a^6 b^3 x^7 (4 a B+7 A b)+\frac{21}{4} a^5 b^4 x^8 (5 a B+6 A b)+\frac{14}{3} a^4 b^5 x^9 (6 a B+5 A b)+3 a^3 b^6 x^{10} (7 a B+4 A b)+\frac{15}{11} a^2 b^7 x^{11} (8 a B+3 A b)+\frac{1}{13} b^9 x^{13} (10 a B+A b)+\frac{5}{12} a b^8 x^{12} (9 a B+2 A b)+\frac{1}{14} b^{10} B x^{14} \]
Antiderivative was successfully verified.
[In] Integrate[x^2*(a + b*x)^10*(A + B*x),x]
[Out]
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Maple [B] time = 0.001, size = 244, normalized size = 2.8 \[{\frac{{b}^{10}B{x}^{14}}{14}}+{\frac{ \left ({b}^{10}A+10\,a{b}^{9}B \right ){x}^{13}}{13}}+{\frac{ \left ( 10\,a{b}^{9}A+45\,{a}^{2}{b}^{8}B \right ){x}^{12}}{12}}+{\frac{ \left ( 45\,{a}^{2}{b}^{8}A+120\,{a}^{3}{b}^{7}B \right ){x}^{11}}{11}}+{\frac{ \left ( 120\,{a}^{3}{b}^{7}A+210\,{a}^{4}{b}^{6}B \right ){x}^{10}}{10}}+{\frac{ \left ( 210\,{a}^{4}{b}^{6}A+252\,{a}^{5}{b}^{5}B \right ){x}^{9}}{9}}+{\frac{ \left ( 252\,{a}^{5}{b}^{5}A+210\,{a}^{6}{b}^{4}B \right ){x}^{8}}{8}}+{\frac{ \left ( 210\,{a}^{6}{b}^{4}A+120\,{a}^{7}{b}^{3}B \right ){x}^{7}}{7}}+{\frac{ \left ( 120\,{a}^{7}{b}^{3}A+45\,{a}^{8}{b}^{2}B \right ){x}^{6}}{6}}+{\frac{ \left ( 45\,{a}^{8}{b}^{2}A+10\,{a}^{9}bB \right ){x}^{5}}{5}}+{\frac{ \left ( 10\,{a}^{9}bA+{a}^{10}B \right ){x}^{4}}{4}}+{\frac{{a}^{10}A{x}^{3}}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*(b*x+a)^10*(B*x+A),x)
[Out]
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Maxima [A] time = 1.34323, size = 327, normalized size = 3.76 \[ \frac{1}{14} \, B b^{10} x^{14} + \frac{1}{3} \, A a^{10} x^{3} + \frac{1}{13} \,{\left (10 \, B a b^{9} + A b^{10}\right )} x^{13} + \frac{5}{12} \,{\left (9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right )} x^{12} + \frac{15}{11} \,{\left (8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right )} x^{11} + 3 \,{\left (7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right )} x^{10} + \frac{14}{3} \,{\left (6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right )} x^{9} + \frac{21}{4} \,{\left (5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right )} x^{8} + \frac{30}{7} \,{\left (4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right )} x^{7} + \frac{5}{2} \,{\left (3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right )} x^{6} +{\left (2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right )} x^{5} + \frac{1}{4} \,{\left (B a^{10} + 10 \, A a^{9} b\right )} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^10*x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.182812, size = 1, normalized size = 0.01 \[ \frac{1}{14} x^{14} b^{10} B + \frac{10}{13} x^{13} b^{9} a B + \frac{1}{13} x^{13} b^{10} A + \frac{15}{4} x^{12} b^{8} a^{2} B + \frac{5}{6} x^{12} b^{9} a A + \frac{120}{11} x^{11} b^{7} a^{3} B + \frac{45}{11} x^{11} b^{8} a^{2} A + 21 x^{10} b^{6} a^{4} B + 12 x^{10} b^{7} a^{3} A + 28 x^{9} b^{5} a^{5} B + \frac{70}{3} x^{9} b^{6} a^{4} A + \frac{105}{4} x^{8} b^{4} a^{6} B + \frac{63}{2} x^{8} b^{5} a^{5} A + \frac{120}{7} x^{7} b^{3} a^{7} B + 30 x^{7} b^{4} a^{6} A + \frac{15}{2} x^{6} b^{2} a^{8} B + 20 x^{6} b^{3} a^{7} A + 2 x^{5} b a^{9} B + 9 x^{5} b^{2} a^{8} A + \frac{1}{4} x^{4} a^{10} B + \frac{5}{2} x^{4} b a^{9} A + \frac{1}{3} x^{3} a^{10} A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^10*x^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.266173, size = 262, normalized size = 3.01 \[ \frac{A a^{10} x^{3}}{3} + \frac{B b^{10} x^{14}}{14} + x^{13} \left (\frac{A b^{10}}{13} + \frac{10 B a b^{9}}{13}\right ) + x^{12} \left (\frac{5 A a b^{9}}{6} + \frac{15 B a^{2} b^{8}}{4}\right ) + x^{11} \left (\frac{45 A a^{2} b^{8}}{11} + \frac{120 B a^{3} b^{7}}{11}\right ) + x^{10} \left (12 A a^{3} b^{7} + 21 B a^{4} b^{6}\right ) + x^{9} \left (\frac{70 A a^{4} b^{6}}{3} + 28 B a^{5} b^{5}\right ) + x^{8} \left (\frac{63 A a^{5} b^{5}}{2} + \frac{105 B a^{6} b^{4}}{4}\right ) + x^{7} \left (30 A a^{6} b^{4} + \frac{120 B a^{7} b^{3}}{7}\right ) + x^{6} \left (20 A a^{7} b^{3} + \frac{15 B a^{8} b^{2}}{2}\right ) + x^{5} \left (9 A a^{8} b^{2} + 2 B a^{9} b\right ) + x^{4} \left (\frac{5 A a^{9} b}{2} + \frac{B a^{10}}{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*(b*x+a)**10*(B*x+A),x)
[Out]
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GIAC/XCAS [A] time = 0.318629, size = 331, normalized size = 3.8 \[ \frac{1}{14} \, B b^{10} x^{14} + \frac{10}{13} \, B a b^{9} x^{13} + \frac{1}{13} \, A b^{10} x^{13} + \frac{15}{4} \, B a^{2} b^{8} x^{12} + \frac{5}{6} \, A a b^{9} x^{12} + \frac{120}{11} \, B a^{3} b^{7} x^{11} + \frac{45}{11} \, A a^{2} b^{8} x^{11} + 21 \, B a^{4} b^{6} x^{10} + 12 \, A a^{3} b^{7} x^{10} + 28 \, B a^{5} b^{5} x^{9} + \frac{70}{3} \, A a^{4} b^{6} x^{9} + \frac{105}{4} \, B a^{6} b^{4} x^{8} + \frac{63}{2} \, A a^{5} b^{5} x^{8} + \frac{120}{7} \, B a^{7} b^{3} x^{7} + 30 \, A a^{6} b^{4} x^{7} + \frac{15}{2} \, B a^{8} b^{2} x^{6} + 20 \, A a^{7} b^{3} x^{6} + 2 \, B a^{9} b x^{5} + 9 \, A a^{8} b^{2} x^{5} + \frac{1}{4} \, B a^{10} x^{4} + \frac{5}{2} \, A a^{9} b x^{4} + \frac{1}{3} \, A a^{10} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^10*x^2,x, algorithm="giac")
[Out]