Optimal. Leaf size=229 \[ \frac{1}{11} a^{10} A x^{11}+\frac{1}{12} a^9 x^{12} (a B+10 A b)+\frac{5}{13} a^8 b x^{13} (2 a B+9 A b)+\frac{15}{14} a^7 b^2 x^{14} (3 a B+8 A b)+2 a^6 b^3 x^{15} (4 a B+7 A b)+\frac{21}{8} a^5 b^4 x^{16} (5 a B+6 A b)+\frac{42}{17} a^4 b^5 x^{17} (6 a B+5 A b)+\frac{5}{3} a^3 b^6 x^{18} (7 a B+4 A b)+\frac{15}{19} a^2 b^7 x^{19} (8 a B+3 A b)+\frac{1}{21} b^9 x^{21} (10 a B+A b)+\frac{1}{4} a b^8 x^{20} (9 a B+2 A b)+\frac{1}{22} b^{10} B x^{22} \]
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Rubi [A] time = 0.599225, antiderivative size = 229, 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 \[ \frac{1}{11} a^{10} A x^{11}+\frac{1}{12} a^9 x^{12} (a B+10 A b)+\frac{5}{13} a^8 b x^{13} (2 a B+9 A b)+\frac{15}{14} a^7 b^2 x^{14} (3 a B+8 A b)+2 a^6 b^3 x^{15} (4 a B+7 A b)+\frac{21}{8} a^5 b^4 x^{16} (5 a B+6 A b)+\frac{42}{17} a^4 b^5 x^{17} (6 a B+5 A b)+\frac{5}{3} a^3 b^6 x^{18} (7 a B+4 A b)+\frac{15}{19} a^2 b^7 x^{19} (8 a B+3 A b)+\frac{1}{21} b^9 x^{21} (10 a B+A b)+\frac{1}{4} a b^8 x^{20} (9 a B+2 A b)+\frac{1}{22} b^{10} B x^{22} \]
Antiderivative was successfully verified.
[In] Int[x^10*(a + b*x)^10*(A + B*x),x]
[Out]
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Rubi in Sympy [A] time = 115.112, size = 236, normalized size = 1.03 \[ \frac{A a^{10} x^{11}}{11} + \frac{B b^{10} x^{22}}{22} + \frac{a^{9} x^{12} \left (10 A b + B a\right )}{12} + \frac{5 a^{8} b x^{13} \left (9 A b + 2 B a\right )}{13} + \frac{15 a^{7} b^{2} x^{14} \left (8 A b + 3 B a\right )}{14} + 2 a^{6} b^{3} x^{15} \left (7 A b + 4 B a\right ) + \frac{21 a^{5} b^{4} x^{16} \left (6 A b + 5 B a\right )}{8} + \frac{42 a^{4} b^{5} x^{17} \left (5 A b + 6 B a\right )}{17} + \frac{5 a^{3} b^{6} x^{18} \left (4 A b + 7 B a\right )}{3} + \frac{15 a^{2} b^{7} x^{19} \left (3 A b + 8 B a\right )}{19} + \frac{a b^{8} x^{20} \left (2 A b + 9 B a\right )}{4} + \frac{b^{9} x^{21} \left (A b + 10 B a\right )}{21} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**10*(b*x+a)**10*(B*x+A),x)
[Out]
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Mathematica [A] time = 0.0558076, size = 229, normalized size = 1. \[ \frac{1}{11} a^{10} A x^{11}+\frac{1}{12} a^9 x^{12} (a B+10 A b)+\frac{5}{13} a^8 b x^{13} (2 a B+9 A b)+\frac{15}{14} a^7 b^2 x^{14} (3 a B+8 A b)+2 a^6 b^3 x^{15} (4 a B+7 A b)+\frac{21}{8} a^5 b^4 x^{16} (5 a B+6 A b)+\frac{42}{17} a^4 b^5 x^{17} (6 a B+5 A b)+\frac{5}{3} a^3 b^6 x^{18} (7 a B+4 A b)+\frac{15}{19} a^2 b^7 x^{19} (8 a B+3 A b)+\frac{1}{21} b^9 x^{21} (10 a B+A b)+\frac{1}{4} a b^8 x^{20} (9 a B+2 A b)+\frac{1}{22} b^{10} B x^{22} \]
Antiderivative was successfully verified.
[In] Integrate[x^10*(a + b*x)^10*(A + B*x),x]
[Out]
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Maple [A] time = 0.003, size = 244, normalized size = 1.1 \[{\frac{{b}^{10}B{x}^{22}}{22}}+{\frac{ \left ({b}^{10}A+10\,a{b}^{9}B \right ){x}^{21}}{21}}+{\frac{ \left ( 10\,a{b}^{9}A+45\,{a}^{2}{b}^{8}B \right ){x}^{20}}{20}}+{\frac{ \left ( 45\,{a}^{2}{b}^{8}A+120\,{a}^{3}{b}^{7}B \right ){x}^{19}}{19}}+{\frac{ \left ( 120\,{a}^{3}{b}^{7}A+210\,{a}^{4}{b}^{6}B \right ){x}^{18}}{18}}+{\frac{ \left ( 210\,{a}^{4}{b}^{6}A+252\,{a}^{5}{b}^{5}B \right ){x}^{17}}{17}}+{\frac{ \left ( 252\,{a}^{5}{b}^{5}A+210\,{a}^{6}{b}^{4}B \right ){x}^{16}}{16}}+{\frac{ \left ( 210\,{a}^{6}{b}^{4}A+120\,{a}^{7}{b}^{3}B \right ){x}^{15}}{15}}+{\frac{ \left ( 120\,{a}^{7}{b}^{3}A+45\,{a}^{8}{b}^{2}B \right ){x}^{14}}{14}}+{\frac{ \left ( 45\,{a}^{8}{b}^{2}A+10\,{a}^{9}bB \right ){x}^{13}}{13}}+{\frac{ \left ( 10\,{a}^{9}bA+{a}^{10}B \right ){x}^{12}}{12}}+{\frac{{a}^{10}A{x}^{11}}{11}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^10*(b*x+a)^10*(B*x+A),x)
[Out]
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Maxima [A] time = 1.33121, size = 328, normalized size = 1.43 \[ \frac{1}{22} \, B b^{10} x^{22} + \frac{1}{11} \, A a^{10} x^{11} + \frac{1}{21} \,{\left (10 \, B a b^{9} + A b^{10}\right )} x^{21} + \frac{1}{4} \,{\left (9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right )} x^{20} + \frac{15}{19} \,{\left (8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right )} x^{19} + \frac{5}{3} \,{\left (7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right )} x^{18} + \frac{42}{17} \,{\left (6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right )} x^{17} + \frac{21}{8} \,{\left (5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right )} x^{16} + 2 \,{\left (4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right )} x^{15} + \frac{15}{14} \,{\left (3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right )} x^{14} + \frac{5}{13} \,{\left (2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right )} x^{13} + \frac{1}{12} \,{\left (B a^{10} + 10 \, A a^{9} b\right )} x^{12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^10*x^10,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.183419, size = 1, normalized size = 0. \[ \frac{1}{22} x^{22} b^{10} B + \frac{10}{21} x^{21} b^{9} a B + \frac{1}{21} x^{21} b^{10} A + \frac{9}{4} x^{20} b^{8} a^{2} B + \frac{1}{2} x^{20} b^{9} a A + \frac{120}{19} x^{19} b^{7} a^{3} B + \frac{45}{19} x^{19} b^{8} a^{2} A + \frac{35}{3} x^{18} b^{6} a^{4} B + \frac{20}{3} x^{18} b^{7} a^{3} A + \frac{252}{17} x^{17} b^{5} a^{5} B + \frac{210}{17} x^{17} b^{6} a^{4} A + \frac{105}{8} x^{16} b^{4} a^{6} B + \frac{63}{4} x^{16} b^{5} a^{5} A + 8 x^{15} b^{3} a^{7} B + 14 x^{15} b^{4} a^{6} A + \frac{45}{14} x^{14} b^{2} a^{8} B + \frac{60}{7} x^{14} b^{3} a^{7} A + \frac{10}{13} x^{13} b a^{9} B + \frac{45}{13} x^{13} b^{2} a^{8} A + \frac{1}{12} x^{12} a^{10} B + \frac{5}{6} x^{12} b a^{9} A + \frac{1}{11} x^{11} a^{10} A \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^10*x^10,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.255935, size = 269, normalized size = 1.17 \[ \frac{A a^{10} x^{11}}{11} + \frac{B b^{10} x^{22}}{22} + x^{21} \left (\frac{A b^{10}}{21} + \frac{10 B a b^{9}}{21}\right ) + x^{20} \left (\frac{A a b^{9}}{2} + \frac{9 B a^{2} b^{8}}{4}\right ) + x^{19} \left (\frac{45 A a^{2} b^{8}}{19} + \frac{120 B a^{3} b^{7}}{19}\right ) + x^{18} \left (\frac{20 A a^{3} b^{7}}{3} + \frac{35 B a^{4} b^{6}}{3}\right ) + x^{17} \left (\frac{210 A a^{4} b^{6}}{17} + \frac{252 B a^{5} b^{5}}{17}\right ) + x^{16} \left (\frac{63 A a^{5} b^{5}}{4} + \frac{105 B a^{6} b^{4}}{8}\right ) + x^{15} \left (14 A a^{6} b^{4} + 8 B a^{7} b^{3}\right ) + x^{14} \left (\frac{60 A a^{7} b^{3}}{7} + \frac{45 B a^{8} b^{2}}{14}\right ) + x^{13} \left (\frac{45 A a^{8} b^{2}}{13} + \frac{10 B a^{9} b}{13}\right ) + x^{12} \left (\frac{5 A a^{9} b}{6} + \frac{B a^{10}}{12}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**10*(b*x+a)**10*(B*x+A),x)
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GIAC/XCAS [A] time = 0.441109, size = 331, normalized size = 1.45 \[ \frac{1}{22} \, B b^{10} x^{22} + \frac{10}{21} \, B a b^{9} x^{21} + \frac{1}{21} \, A b^{10} x^{21} + \frac{9}{4} \, B a^{2} b^{8} x^{20} + \frac{1}{2} \, A a b^{9} x^{20} + \frac{120}{19} \, B a^{3} b^{7} x^{19} + \frac{45}{19} \, A a^{2} b^{8} x^{19} + \frac{35}{3} \, B a^{4} b^{6} x^{18} + \frac{20}{3} \, A a^{3} b^{7} x^{18} + \frac{252}{17} \, B a^{5} b^{5} x^{17} + \frac{210}{17} \, A a^{4} b^{6} x^{17} + \frac{105}{8} \, B a^{6} b^{4} x^{16} + \frac{63}{4} \, A a^{5} b^{5} x^{16} + 8 \, B a^{7} b^{3} x^{15} + 14 \, A a^{6} b^{4} x^{15} + \frac{45}{14} \, B a^{8} b^{2} x^{14} + \frac{60}{7} \, A a^{7} b^{3} x^{14} + \frac{10}{13} \, B a^{9} b x^{13} + \frac{45}{13} \, A a^{8} b^{2} x^{13} + \frac{1}{12} \, B a^{10} x^{12} + \frac{5}{6} \, A a^{9} b x^{12} + \frac{1}{11} \, A a^{10} x^{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^10*x^10,x, algorithm="giac")
[Out]