Optimal. Leaf size=131 \[ -\frac{a^6 A}{5 x^5}-\frac{a^5 (a B+6 A b)}{4 x^4}-\frac{a^4 b (2 a B+5 A b)}{x^3}-\frac{5 a^3 b^2 (3 a B+4 A b)}{2 x^2}-\frac{5 a^2 b^3 (4 a B+3 A b)}{x}+b^5 x (6 a B+A b)+3 a b^4 \log (x) (5 a B+2 A b)+\frac{1}{2} b^6 B x^2 \]
[Out]
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Rubi [A] time = 0.220051, antiderivative size = 131, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 27, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.074 \[ -\frac{a^6 A}{5 x^5}-\frac{a^5 (a B+6 A b)}{4 x^4}-\frac{a^4 b (2 a B+5 A b)}{x^3}-\frac{5 a^3 b^2 (3 a B+4 A b)}{2 x^2}-\frac{5 a^2 b^3 (4 a B+3 A b)}{x}+b^5 x (6 a B+A b)+3 a b^4 \log (x) (5 a B+2 A b)+\frac{1}{2} b^6 B x^2 \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^6,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{A a^{6}}{5 x^{5}} + B b^{6} \int x\, dx - \frac{a^{5} \left (6 A b + B a\right )}{4 x^{4}} - \frac{a^{4} b \left (5 A b + 2 B a\right )}{x^{3}} - \frac{5 a^{3} b^{2} \left (4 A b + 3 B a\right )}{2 x^{2}} - \frac{5 a^{2} b^{3} \left (3 A b + 4 B a\right )}{x} + 3 a b^{4} \left (2 A b + 5 B a\right ) \log{\left (x \right )} + b^{5} x \left (A b + 6 B a\right ) \]
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**6,x)
[Out]
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Mathematica [A] time = 0.10287, size = 128, normalized size = 0.98 \[ -\frac{a^6 (4 A+5 B x)}{20 x^5}-\frac{a^5 b (3 A+4 B x)}{2 x^4}-\frac{5 a^4 b^2 (2 A+3 B x)}{2 x^3}-\frac{10 a^3 b^3 (A+2 B x)}{x^2}-\frac{15 a^2 A b^4}{x}+3 a b^4 \log (x) (5 a B+2 A b)+6 a b^5 B x+\frac{1}{2} b^6 x (2 A+B x) \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^6,x]
[Out]
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Maple [A] time = 0.013, size = 143, normalized size = 1.1 \[{\frac{{b}^{6}B{x}^{2}}{2}}+Ax{b}^{6}+6\,Bxa{b}^{5}+6\,A\ln \left ( x \right ) a{b}^{5}+15\,B\ln \left ( x \right ){a}^{2}{b}^{4}-{\frac{3\,A{a}^{5}b}{2\,{x}^{4}}}-{\frac{B{a}^{6}}{4\,{x}^{4}}}-5\,{\frac{A{b}^{2}{a}^{4}}{{x}^{3}}}-2\,{\frac{B{a}^{5}b}{{x}^{3}}}-10\,{\frac{A{a}^{3}{b}^{3}}{{x}^{2}}}-{\frac{15\,B{b}^{2}{a}^{4}}{2\,{x}^{2}}}-{\frac{A{a}^{6}}{5\,{x}^{5}}}-15\,{\frac{A{a}^{2}{b}^{4}}{x}}-20\,{\frac{B{a}^{3}{b}^{3}}{x}} \]
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^6,x)
[Out]
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Maxima [A] time = 0.678308, size = 194, normalized size = 1.48 \[ \frac{1}{2} \, B b^{6} x^{2} +{\left (6 \, B a b^{5} + A b^{6}\right )} x + 3 \,{\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} \log \left (x\right ) - \frac{4 \, A a^{6} + 100 \,{\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} x^{4} + 50 \,{\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} x^{3} + 20 \,{\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} x^{2} + 5 \,{\left (B a^{6} + 6 \, A a^{5} b\right )} x}{20 \, x^{5}} \]
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^6,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.28123, size = 201, normalized size = 1.53 \[ \frac{10 \, B b^{6} x^{7} - 4 \, A a^{6} + 20 \,{\left (6 \, B a b^{5} + A b^{6}\right )} x^{6} + 60 \,{\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} x^{5} \log \left (x\right ) - 100 \,{\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} x^{4} - 50 \,{\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} x^{3} - 20 \,{\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} x^{2} - 5 \,{\left (B a^{6} + 6 \, A a^{5} b\right )} x}{20 \, x^{5}} \]
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^6,x, algorithm="fricas")
[Out]
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Sympy [A] time = 8.27902, size = 143, normalized size = 1.09 \[ \frac{B b^{6} x^{2}}{2} + 3 a b^{4} \left (2 A b + 5 B a\right ) \log{\left (x \right )} + x \left (A b^{6} + 6 B a b^{5}\right ) - \frac{4 A a^{6} + x^{4} \left (300 A a^{2} b^{4} + 400 B a^{3} b^{3}\right ) + x^{3} \left (200 A a^{3} b^{3} + 150 B a^{4} b^{2}\right ) + x^{2} \left (100 A a^{4} b^{2} + 40 B a^{5} b\right ) + x \left (30 A a^{5} b + 5 B a^{6}\right )}{20 x^{5}} \]
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**6,x)
[Out]
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GIAC/XCAS [A] time = 0.270058, size = 194, normalized size = 1.48 \[ \frac{1}{2} \, B b^{6} x^{2} + 6 \, B a b^{5} x + A b^{6} x + 3 \,{\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )}{\rm ln}\left ({\left | x \right |}\right ) - \frac{4 \, A a^{6} + 100 \,{\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} x^{4} + 50 \,{\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} x^{3} + 20 \,{\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} x^{2} + 5 \,{\left (B a^{6} + 6 \, A a^{5} b\right )} x}{20 \, x^{5}} \]
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^6,x, algorithm="giac")
[Out]