Optimal. Leaf size=96 \[ a^6 A \log (x)+6 a^5 A b x+\frac{15}{2} a^4 A b^2 x^2+\frac{20}{3} a^3 A b^3 x^3+\frac{15}{4} a^2 A b^4 x^4+\frac{6}{5} a A b^5 x^5+\frac{B (a+b x)^7}{7 b}+\frac{1}{6} A b^6 x^6 \]
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Rubi [A] time = 0.0875051, antiderivative size = 96, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 27, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ a^6 A \log (x)+6 a^5 A b x+\frac{15}{2} a^4 A b^2 x^2+\frac{20}{3} a^3 A b^3 x^3+\frac{15}{4} a^2 A b^4 x^4+\frac{6}{5} a A b^5 x^5+\frac{B (a+b x)^7}{7 b}+\frac{1}{6} A b^6 x^6 \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ A a^{6} \log{\left (x \right )} + 6 A a^{5} b x + 15 A a^{4} b^{2} \int x\, dx + \frac{20 A a^{3} b^{3} x^{3}}{3} + \frac{15 A a^{2} b^{4} x^{4}}{4} + \frac{6 A a b^{5} x^{5}}{5} + \frac{A b^{6} x^{6}}{6} + \frac{B \left (a + b x\right )^{7}}{7 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3/x,x)
[Out]
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Mathematica [A] time = 0.0608454, size = 128, normalized size = 1.33 \[ a^6 A \log (x)+a^6 B x+3 a^5 b x (2 A+B x)+\frac{5}{2} a^4 b^2 x^2 (3 A+2 B x)+\frac{5}{3} a^3 b^3 x^3 (4 A+3 B x)+\frac{3}{4} a^2 b^4 x^4 (5 A+4 B x)+\frac{1}{5} a b^5 x^5 (6 A+5 B x)+\frac{1}{42} b^6 x^6 (7 A+6 B x) \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x,x]
[Out]
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Maple [A] time = 0.004, size = 142, normalized size = 1.5 \[{\frac{B{b}^{6}{x}^{7}}{7}}+{\frac{A{b}^{6}{x}^{6}}{6}}+B{x}^{6}a{b}^{5}+{\frac{6\,aA{b}^{5}{x}^{5}}{5}}+3\,B{x}^{5}{a}^{2}{b}^{4}+{\frac{15\,{a}^{2}A{b}^{4}{x}^{4}}{4}}+5\,B{x}^{4}{a}^{3}{b}^{3}+{\frac{20\,{a}^{3}A{b}^{3}{x}^{3}}{3}}+5\,B{x}^{3}{a}^{4}{b}^{2}+{\frac{15\,{a}^{4}A{b}^{2}{x}^{2}}{2}}+3\,B{x}^{2}{a}^{5}b+6\,{a}^{5}Abx+B{a}^{6}x+{a}^{6}A\ln \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^3/x,x)
[Out]
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Maxima [A] time = 0.67682, size = 192, normalized size = 2. \[ \frac{1}{7} \, B b^{6} x^{7} + A a^{6} \log \left (x\right ) + \frac{1}{6} \,{\left (6 \, B a b^{5} + A b^{6}\right )} x^{6} + \frac{3}{5} \,{\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} x^{5} + \frac{5}{4} \,{\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} x^{4} + \frac{5}{3} \,{\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} x^{3} + \frac{3}{2} \,{\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} x^{2} +{\left (B a^{6} + 6 \, A a^{5} b\right )} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)^3*(B*x + A)/x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.267714, size = 192, normalized size = 2. \[ \frac{1}{7} \, B b^{6} x^{7} + A a^{6} \log \left (x\right ) + \frac{1}{6} \,{\left (6 \, B a b^{5} + A b^{6}\right )} x^{6} + \frac{3}{5} \,{\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} x^{5} + \frac{5}{4} \,{\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} x^{4} + \frac{5}{3} \,{\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} x^{3} + \frac{3}{2} \,{\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} x^{2} +{\left (B a^{6} + 6 \, A a^{5} b\right )} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)^3*(B*x + A)/x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.71429, size = 148, normalized size = 1.54 \[ A a^{6} \log{\left (x \right )} + \frac{B b^{6} x^{7}}{7} + x^{6} \left (\frac{A b^{6}}{6} + B a b^{5}\right ) + x^{5} \left (\frac{6 A a b^{5}}{5} + 3 B a^{2} b^{4}\right ) + x^{4} \left (\frac{15 A a^{2} b^{4}}{4} + 5 B a^{3} b^{3}\right ) + x^{3} \left (\frac{20 A a^{3} b^{3}}{3} + 5 B a^{4} b^{2}\right ) + x^{2} \left (\frac{15 A a^{4} b^{2}}{2} + 3 B a^{5} b\right ) + x \left (6 A a^{5} b + B a^{6}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**3/x,x)
[Out]
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GIAC/XCAS [A] time = 0.268594, size = 192, normalized size = 2. \[ \frac{1}{7} \, B b^{6} x^{7} + B a b^{5} x^{6} + \frac{1}{6} \, A b^{6} x^{6} + 3 \, B a^{2} b^{4} x^{5} + \frac{6}{5} \, A a b^{5} x^{5} + 5 \, B a^{3} b^{3} x^{4} + \frac{15}{4} \, A a^{2} b^{4} x^{4} + 5 \, B a^{4} b^{2} x^{3} + \frac{20}{3} \, A a^{3} b^{3} x^{3} + 3 \, B a^{5} b x^{2} + \frac{15}{2} \, A a^{4} b^{2} x^{2} + B a^{6} x + 6 \, A a^{5} b x + A a^{6}{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)^3*(B*x + A)/x,x, algorithm="giac")
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