Optimal. Leaf size=218 \[ -\frac{a^{10} A}{5 x^5}-\frac{a^9 (a B+10 A b)}{4 x^4}-\frac{5 a^8 b (2 a B+9 A b)}{3 x^3}-\frac{15 a^7 b^2 (3 a B+8 A b)}{2 x^2}-\frac{30 a^6 b^3 (4 a B+7 A b)}{x}+42 a^5 b^4 \log (x) (5 a B+6 A b)+42 a^4 b^5 x (6 a B+5 A b)+15 a^3 b^6 x^2 (7 a B+4 A b)+5 a^2 b^7 x^3 (8 a B+3 A b)+\frac{1}{5} b^9 x^5 (10 a B+A b)+\frac{5}{4} a b^8 x^4 (9 a B+2 A b)+\frac{1}{6} b^{10} B x^6 \]
[Out]
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Rubi [A] time = 0.475959, antiderivative size = 218, 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 \[ -\frac{a^{10} A}{5 x^5}-\frac{a^9 (a B+10 A b)}{4 x^4}-\frac{5 a^8 b (2 a B+9 A b)}{3 x^3}-\frac{15 a^7 b^2 (3 a B+8 A b)}{2 x^2}-\frac{30 a^6 b^3 (4 a B+7 A b)}{x}+42 a^5 b^4 \log (x) (5 a B+6 A b)+42 a^4 b^5 x (6 a B+5 A b)+15 a^3 b^6 x^2 (7 a B+4 A b)+5 a^2 b^7 x^3 (8 a B+3 A b)+\frac{1}{5} b^9 x^5 (10 a B+A b)+\frac{5}{4} a b^8 x^4 (9 a B+2 A b)+\frac{1}{6} b^{10} B x^6 \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)^10*(A + B*x))/x^6,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{A a^{10}}{5 x^{5}} + \frac{B b^{10} x^{6}}{6} - \frac{a^{9} \left (10 A b + B a\right )}{4 x^{4}} - \frac{5 a^{8} b \left (9 A b + 2 B a\right )}{3 x^{3}} - \frac{15 a^{7} b^{2} \left (8 A b + 3 B a\right )}{2 x^{2}} - \frac{30 a^{6} b^{3} \left (7 A b + 4 B a\right )}{x} + 42 a^{5} b^{4} \left (6 A b + 5 B a\right ) \log{\left (x \right )} + 210 a^{4} b^{5} x \left (A b + \frac{6 B a}{5}\right ) + 30 a^{3} b^{6} \left (4 A b + 7 B a\right ) \int x\, dx + 5 a^{2} b^{7} x^{3} \left (3 A b + 8 B a\right ) + \frac{5 a b^{8} x^{4} \left (2 A b + 9 B a\right )}{4} + \frac{b^{9} x^{5} \left (A b + 10 B a\right )}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**10*(B*x+A)/x**6,x)
[Out]
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Mathematica [A] time = 0.132747, size = 210, normalized size = 0.96 \[ -\frac{a^{10} (4 A+5 B x)}{20 x^5}-\frac{5 a^9 b (3 A+4 B x)}{6 x^4}-\frac{15 a^8 b^2 (2 A+3 B x)}{2 x^3}-\frac{60 a^7 b^3 (A+2 B x)}{x^2}-\frac{210 a^6 A b^4}{x}+42 a^5 b^4 \log (x) (5 a B+6 A b)+252 a^5 b^5 B x+105 a^4 b^6 x (2 A+B x)+20 a^3 b^7 x^2 (3 A+2 B x)+\frac{15}{4} a^2 b^8 x^3 (4 A+3 B x)+\frac{1}{2} a b^9 x^4 (5 A+4 B x)+\frac{1}{30} b^{10} x^5 (6 A+5 B x) \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)^10*(A + B*x))/x^6,x]
[Out]
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Maple [A] time = 0.013, size = 240, normalized size = 1.1 \[{\frac{{b}^{10}B{x}^{6}}{6}}+{\frac{A{x}^{5}{b}^{10}}{5}}+2\,B{x}^{5}a{b}^{9}+{\frac{5\,A{x}^{4}a{b}^{9}}{2}}+{\frac{45\,B{x}^{4}{a}^{2}{b}^{8}}{4}}+15\,A{x}^{3}{a}^{2}{b}^{8}+40\,B{x}^{3}{a}^{3}{b}^{7}+60\,A{x}^{2}{a}^{3}{b}^{7}+105\,B{x}^{2}{a}^{4}{b}^{6}+210\,Ax{a}^{4}{b}^{6}+252\,Bx{a}^{5}{b}^{5}+252\,A\ln \left ( x \right ){a}^{5}{b}^{5}+210\,B\ln \left ( x \right ){a}^{6}{b}^{4}-60\,{\frac{{a}^{7}{b}^{3}A}{{x}^{2}}}-{\frac{45\,{a}^{8}{b}^{2}B}{2\,{x}^{2}}}-{\frac{A{a}^{10}}{5\,{x}^{5}}}-210\,{\frac{{a}^{6}{b}^{4}A}{x}}-120\,{\frac{{a}^{7}{b}^{3}B}{x}}-15\,{\frac{{a}^{8}{b}^{2}A}{{x}^{3}}}-{\frac{10\,{a}^{9}bB}{3\,{x}^{3}}}-{\frac{5\,{a}^{9}bA}{2\,{x}^{4}}}-{\frac{{a}^{10}B}{4\,{x}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^10*(B*x+A)/x^6,x)
[Out]
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Maxima [A] time = 1.3615, size = 325, normalized size = 1.49 \[ \frac{1}{6} \, B b^{10} x^{6} + \frac{1}{5} \,{\left (10 \, B a b^{9} + A b^{10}\right )} x^{5} + \frac{5}{4} \,{\left (9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right )} x^{4} + 5 \,{\left (8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right )} x^{3} + 15 \,{\left (7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right )} x^{2} + 42 \,{\left (6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right )} x + 42 \,{\left (5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right )} \log \left (x\right ) - \frac{12 \, A a^{10} + 1800 \,{\left (4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right )} x^{4} + 450 \,{\left (3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right )} x^{3} + 100 \,{\left (2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right )} x^{2} + 15 \,{\left (B a^{10} + 10 \, A a^{9} b\right )} x}{60 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^10/x^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.210444, size = 331, normalized size = 1.52 \[ \frac{10 \, B b^{10} x^{11} - 12 \, A a^{10} + 12 \,{\left (10 \, B a b^{9} + A b^{10}\right )} x^{10} + 75 \,{\left (9 \, B a^{2} b^{8} + 2 \, A a b^{9}\right )} x^{9} + 300 \,{\left (8 \, B a^{3} b^{7} + 3 \, A a^{2} b^{8}\right )} x^{8} + 900 \,{\left (7 \, B a^{4} b^{6} + 4 \, A a^{3} b^{7}\right )} x^{7} + 2520 \,{\left (6 \, B a^{5} b^{5} + 5 \, A a^{4} b^{6}\right )} x^{6} + 2520 \,{\left (5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right )} x^{5} \log \left (x\right ) - 1800 \,{\left (4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right )} x^{4} - 450 \,{\left (3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right )} x^{3} - 100 \,{\left (2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right )} x^{2} - 15 \,{\left (B a^{10} + 10 \, A a^{9} b\right )} x}{60 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^10/x^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 9.79956, size = 243, normalized size = 1.11 \[ \frac{B b^{10} x^{6}}{6} + 42 a^{5} b^{4} \left (6 A b + 5 B a\right ) \log{\left (x \right )} + x^{5} \left (\frac{A b^{10}}{5} + 2 B a b^{9}\right ) + x^{4} \left (\frac{5 A a b^{9}}{2} + \frac{45 B a^{2} b^{8}}{4}\right ) + x^{3} \left (15 A a^{2} b^{8} + 40 B a^{3} b^{7}\right ) + x^{2} \left (60 A a^{3} b^{7} + 105 B a^{4} b^{6}\right ) + x \left (210 A a^{4} b^{6} + 252 B a^{5} b^{5}\right ) - \frac{12 A a^{10} + x^{4} \left (12600 A a^{6} b^{4} + 7200 B a^{7} b^{3}\right ) + x^{3} \left (3600 A a^{7} b^{3} + 1350 B a^{8} b^{2}\right ) + x^{2} \left (900 A a^{8} b^{2} + 200 B a^{9} b\right ) + x \left (150 A a^{9} b + 15 B a^{10}\right )}{60 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**10*(B*x+A)/x**6,x)
[Out]
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GIAC/XCAS [A] time = 0.250315, size = 325, normalized size = 1.49 \[ \frac{1}{6} \, B b^{10} x^{6} + 2 \, B a b^{9} x^{5} + \frac{1}{5} \, A b^{10} x^{5} + \frac{45}{4} \, B a^{2} b^{8} x^{4} + \frac{5}{2} \, A a b^{9} x^{4} + 40 \, B a^{3} b^{7} x^{3} + 15 \, A a^{2} b^{8} x^{3} + 105 \, B a^{4} b^{6} x^{2} + 60 \, A a^{3} b^{7} x^{2} + 252 \, B a^{5} b^{5} x + 210 \, A a^{4} b^{6} x + 42 \,{\left (5 \, B a^{6} b^{4} + 6 \, A a^{5} b^{5}\right )}{\rm ln}\left ({\left | x \right |}\right ) - \frac{12 \, A a^{10} + 1800 \,{\left (4 \, B a^{7} b^{3} + 7 \, A a^{6} b^{4}\right )} x^{4} + 450 \,{\left (3 \, B a^{8} b^{2} + 8 \, A a^{7} b^{3}\right )} x^{3} + 100 \,{\left (2 \, B a^{9} b + 9 \, A a^{8} b^{2}\right )} x^{2} + 15 \,{\left (B a^{10} + 10 \, A a^{9} b\right )} x}{60 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^10/x^6,x, algorithm="giac")
[Out]