Optimal. Leaf size=114 \[ -\frac{a^5 A}{6 x^6}-\frac{a^4 (a B+5 A b)}{4 x^4}-\frac{5 a^3 b (a B+2 A b)}{2 x^2}+10 a^2 b^2 \log (x) (a B+A b)+\frac{1}{4} b^4 x^4 (5 a B+A b)+\frac{5}{2} a b^3 x^2 (2 a B+A b)+\frac{1}{6} b^5 B x^6 \]
[Out]
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Rubi [A] time = 0.27327, antiderivative size = 114, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ -\frac{a^5 A}{6 x^6}-\frac{a^4 (a B+5 A b)}{4 x^4}-\frac{5 a^3 b (a B+2 A b)}{2 x^2}+10 a^2 b^2 \log (x) (a B+A b)+\frac{1}{4} b^4 x^4 (5 a B+A b)+\frac{5}{2} a b^3 x^2 (2 a B+A b)+\frac{1}{6} b^5 B x^6 \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^2)^5*(A + B*x^2))/x^7,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{A a^{5}}{6 x^{6}} + \frac{B b^{5} x^{6}}{6} - \frac{a^{4} \left (5 A b + B a\right )}{4 x^{4}} - \frac{5 a^{3} b \left (2 A b + B a\right )}{2 x^{2}} + 5 a^{2} b^{2} \left (A b + B a\right ) \log{\left (x^{2} \right )} + \frac{5 a b^{3} x^{2} \left (A b + 2 B a\right )}{2} + \frac{b^{4} \left (A b + 5 B a\right ) \int ^{x^{2}} x\, dx}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**5*(B*x**2+A)/x**7,x)
[Out]
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Mathematica [A] time = 0.0683826, size = 116, normalized size = 1.02 \[ \frac{1}{12} \left (-\frac{a^5 \left (2 A+3 B x^2\right )}{x^6}-\frac{15 a^4 b \left (A+2 B x^2\right )}{x^4}-\frac{60 a^3 A b^2}{x^2}+120 a^2 b^2 \log (x) (a B+A b)+60 a^2 b^3 B x^2+15 a b^4 x^2 \left (2 A+B x^2\right )+b^5 x^4 \left (3 A+2 B x^2\right )\right ) \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^2)^5*(A + B*x^2))/x^7,x]
[Out]
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Maple [A] time = 0.01, size = 124, normalized size = 1.1 \[{\frac{{b}^{5}B{x}^{6}}{6}}+{\frac{A{x}^{4}{b}^{5}}{4}}+{\frac{5\,B{x}^{4}a{b}^{4}}{4}}+{\frac{5\,A{x}^{2}a{b}^{4}}{2}}+5\,B{x}^{2}{a}^{2}{b}^{3}+10\,A\ln \left ( x \right ){a}^{2}{b}^{3}+10\,B\ln \left ( x \right ){a}^{3}{b}^{2}-{\frac{A{a}^{5}}{6\,{x}^{6}}}-{\frac{5\,{a}^{4}bA}{4\,{x}^{4}}}-{\frac{{a}^{5}B}{4\,{x}^{4}}}-5\,{\frac{{a}^{3}{b}^{2}A}{{x}^{2}}}-{\frac{5\,{a}^{4}bB}{2\,{x}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^5*(B*x^2+A)/x^7,x)
[Out]
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Maxima [A] time = 1.33862, size = 166, normalized size = 1.46 \[ \frac{1}{6} \, B b^{5} x^{6} + \frac{1}{4} \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{4} + \frac{5}{2} \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{2} + 5 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} \log \left (x^{2}\right ) - \frac{2 \, A a^{5} + 30 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{4} + 3 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{2}}{12 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^5/x^7,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.223637, size = 166, normalized size = 1.46 \[ \frac{2 \, B b^{5} x^{12} + 3 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{10} + 30 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{8} + 120 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{6} \log \left (x\right ) - 2 \, A a^{5} - 30 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{4} - 3 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{2}}{12 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^5/x^7,x, algorithm="fricas")
[Out]
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Sympy [A] time = 6.2285, size = 124, normalized size = 1.09 \[ \frac{B b^{5} x^{6}}{6} + 10 a^{2} b^{2} \left (A b + B a\right ) \log{\left (x \right )} + x^{4} \left (\frac{A b^{5}}{4} + \frac{5 B a b^{4}}{4}\right ) + x^{2} \left (\frac{5 A a b^{4}}{2} + 5 B a^{2} b^{3}\right ) - \frac{2 A a^{5} + x^{4} \left (60 A a^{3} b^{2} + 30 B a^{4} b\right ) + x^{2} \left (15 A a^{4} b + 3 B a^{5}\right )}{12 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**5*(B*x**2+A)/x**7,x)
[Out]
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GIAC/XCAS [A] time = 0.240123, size = 204, normalized size = 1.79 \[ \frac{1}{6} \, B b^{5} x^{6} + \frac{5}{4} \, B a b^{4} x^{4} + \frac{1}{4} \, A b^{5} x^{4} + 5 \, B a^{2} b^{3} x^{2} + \frac{5}{2} \, A a b^{4} x^{2} + 5 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )}{\rm ln}\left (x^{2}\right ) - \frac{110 \, B a^{3} b^{2} x^{6} + 110 \, A a^{2} b^{3} x^{6} + 30 \, B a^{4} b x^{4} + 60 \, A a^{3} b^{2} x^{4} + 3 \, B a^{5} x^{2} + 15 \, A a^{4} b x^{2} + 2 \, A a^{5}}{12 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^5/x^7,x, algorithm="giac")
[Out]