Optimal. Leaf size=131 \[ -\frac{a^6 A}{2 x^2}-\frac{a^5 (a B+6 A b)}{x}+3 a^4 b \log (x) (2 a B+5 A b)+5 a^3 b^2 x (3 a B+4 A b)+\frac{5}{2} a^2 b^3 x^2 (4 a B+3 A b)+\frac{1}{4} b^5 x^4 (6 a B+A b)+a b^4 x^3 (5 a B+2 A b)+\frac{1}{5} b^6 B x^5 \]
[Out]
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Rubi [A] time = 0.218007, 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 \[ -\frac{a^6 A}{2 x^2}-\frac{a^5 (a B+6 A b)}{x}+3 a^4 b \log (x) (2 a B+5 A b)+5 a^3 b^2 x (3 a B+4 A b)+\frac{5}{2} a^2 b^3 x^2 (4 a B+3 A b)+\frac{1}{4} b^5 x^4 (6 a B+A b)+a b^4 x^3 (5 a B+2 A b)+\frac{1}{5} b^6 B x^5 \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^3,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{A a^{6}}{2 x^{2}} + \frac{B b^{6} x^{5}}{5} - \frac{a^{5} \left (6 A b + B a\right )}{x} + 3 a^{4} b \left (5 A b + 2 B a\right ) \log{\left (x \right )} + 15 a^{3} b^{2} x \left (\frac{4 A b}{3} + B a\right ) + 5 a^{2} b^{3} \left (3 A b + 4 B a\right ) \int x\, dx + a b^{4} x^{3} \left (2 A b + 5 B a\right ) + \frac{b^{5} x^{4} \left (A b + 6 B a\right )}{4} \]
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**3,x)
[Out]
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Mathematica [A] time = 0.126125, size = 128, normalized size = 0.98 \[ -\frac{a^6 (A+2 B x)}{2 x^2}-\frac{6 a^5 A b}{x}+3 a^4 b \log (x) (2 a B+5 A b)+15 a^4 b^2 B x+10 a^3 b^3 x (2 A+B x)+\frac{5}{2} a^2 b^4 x^2 (3 A+2 B x)+\frac{1}{2} a b^5 x^3 (4 A+3 B x)+\frac{1}{20} b^6 x^4 (5 A+4 B x) \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^3,x]
[Out]
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Maple [A] time = 0.01, size = 144, normalized size = 1.1 \[{\frac{{b}^{6}B{x}^{5}}{5}}+{\frac{A{x}^{4}{b}^{6}}{4}}+{\frac{3\,B{x}^{4}a{b}^{5}}{2}}+2\,A{x}^{3}a{b}^{5}+5\,B{x}^{3}{a}^{2}{b}^{4}+{\frac{15\,A{x}^{2}{a}^{2}{b}^{4}}{2}}+10\,B{x}^{2}{a}^{3}{b}^{3}+20\,Ax{a}^{3}{b}^{3}+15\,Bx{a}^{4}{b}^{2}+15\,A\ln \left ( x \right ){a}^{4}{b}^{2}+6\,B\ln \left ( x \right ){a}^{5}b-{\frac{A{a}^{6}}{2\,{x}^{2}}}-6\,{\frac{A{a}^{5}b}{x}}-{\frac{B{a}^{6}}{x}} \]
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^3,x)
[Out]
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Maxima [A] time = 0.676979, size = 193, normalized size = 1.47 \[ \frac{1}{5} \, B b^{6} x^{5} + \frac{1}{4} \,{\left (6 \, B a b^{5} + A b^{6}\right )} x^{4} +{\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} x^{3} + \frac{5}{2} \,{\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} x^{2} + 5 \,{\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} x + 3 \,{\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} \log \left (x\right ) - \frac{A a^{6} + 2 \,{\left (B a^{6} + 6 \, A a^{5} b\right )} x}{2 \, x^{2}} \]
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^3,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.282104, size = 201, normalized size = 1.53 \[ \frac{4 \, B b^{6} x^{7} - 10 \, A a^{6} + 5 \,{\left (6 \, B a b^{5} + A b^{6}\right )} x^{6} + 20 \,{\left (5 \, B a^{2} b^{4} + 2 \, A a b^{5}\right )} x^{5} + 50 \,{\left (4 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4}\right )} x^{4} + 100 \,{\left (3 \, B a^{4} b^{2} + 4 \, A a^{3} b^{3}\right )} x^{3} + 60 \,{\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )} x^{2} \log \left (x\right ) - 20 \,{\left (B a^{6} + 6 \, A a^{5} b\right )} x}{20 \, x^{2}} \]
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^3,x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.59396, size = 146, normalized size = 1.11 \[ \frac{B b^{6} x^{5}}{5} + 3 a^{4} b \left (5 A b + 2 B a\right ) \log{\left (x \right )} + x^{4} \left (\frac{A b^{6}}{4} + \frac{3 B a b^{5}}{2}\right ) + x^{3} \left (2 A a b^{5} + 5 B a^{2} b^{4}\right ) + x^{2} \left (\frac{15 A a^{2} b^{4}}{2} + 10 B a^{3} b^{3}\right ) + x \left (20 A a^{3} b^{3} + 15 B a^{4} b^{2}\right ) - \frac{A a^{6} + x \left (12 A a^{5} b + 2 B a^{6}\right )}{2 x^{2}} \]
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**3,x)
[Out]
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GIAC/XCAS [A] time = 0.269825, size = 194, normalized size = 1.48 \[ \frac{1}{5} \, B b^{6} x^{5} + \frac{3}{2} \, B a b^{5} x^{4} + \frac{1}{4} \, A b^{6} x^{4} + 5 \, B a^{2} b^{4} x^{3} + 2 \, A a b^{5} x^{3} + 10 \, B a^{3} b^{3} x^{2} + \frac{15}{2} \, A a^{2} b^{4} x^{2} + 15 \, B a^{4} b^{2} x + 20 \, A a^{3} b^{3} x + 3 \,{\left (2 \, B a^{5} b + 5 \, A a^{4} b^{2}\right )}{\rm ln}\left ({\left | x \right |}\right ) - \frac{A a^{6} + 2 \,{\left (B a^{6} + 6 \, A a^{5} b\right )} x}{2 \, x^{2}} \]
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^3,x, algorithm="giac")
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