Optimal. Leaf size=51 \[ -\frac{a^2 A}{6 x^6}-\frac{a (a B+2 A b)}{4 x^4}-\frac{b (2 a B+A b)}{2 x^2}+b^2 B \log (x) \]
[Out]
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Rubi [A] time = 0.0988146, antiderivative size = 51, 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 \[ -\frac{a^2 A}{6 x^6}-\frac{a (a B+2 A b)}{4 x^4}-\frac{b (2 a B+A b)}{2 x^2}+b^2 B \log (x) \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^2)^2*(A + B*x^2))/x^7,x]
[Out]
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Rubi in Sympy [A] time = 15.6329, size = 51, normalized size = 1. \[ - \frac{A a^{2}}{6 x^{6}} + \frac{B b^{2} \log{\left (x^{2} \right )}}{2} - \frac{a \left (2 A b + B a\right )}{4 x^{4}} - \frac{b \left (A b + 2 B a\right )}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**2*(B*x**2+A)/x**7,x)
[Out]
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Mathematica [A] time = 0.0482106, size = 54, normalized size = 1.06 \[ b^2 B \log (x)-\frac{a^2 \left (2 A+3 B x^2\right )+6 a b x^2 \left (A+2 B x^2\right )+6 A b^2 x^4}{12 x^6} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^2)^2*(A + B*x^2))/x^7,x]
[Out]
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Maple [A] time = 0.009, size = 52, normalized size = 1. \[{b}^{2}B\ln \left ( x \right ) -{\frac{A{a}^{2}}{6\,{x}^{6}}}-{\frac{abA}{2\,{x}^{4}}}-{\frac{{a}^{2}B}{4\,{x}^{4}}}-{\frac{{b}^{2}A}{2\,{x}^{2}}}-{\frac{abB}{{x}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^2*(B*x^2+A)/x^7,x)
[Out]
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Maxima [A] time = 1.34602, size = 74, normalized size = 1.45 \[ \frac{1}{2} \, B b^{2} \log \left (x^{2}\right ) - \frac{6 \,{\left (2 \, B a b + A b^{2}\right )} x^{4} + 2 \, A a^{2} + 3 \,{\left (B a^{2} + 2 \, A a b\right )} x^{2}}{12 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^2/x^7,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.238589, size = 74, normalized size = 1.45 \[ \frac{12 \, B b^{2} x^{6} \log \left (x\right ) - 6 \,{\left (2 \, B a b + A b^{2}\right )} x^{4} - 2 \, A a^{2} - 3 \,{\left (B a^{2} + 2 \, A a b\right )} x^{2}}{12 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^2/x^7,x, algorithm="fricas")
[Out]
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Sympy [A] time = 4.57595, size = 53, normalized size = 1.04 \[ B b^{2} \log{\left (x \right )} - \frac{2 A a^{2} + x^{4} \left (6 A b^{2} + 12 B a b\right ) + x^{2} \left (6 A a b + 3 B a^{2}\right )}{12 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**2*(B*x**2+A)/x**7,x)
[Out]
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GIAC/XCAS [A] time = 0.229301, size = 89, normalized size = 1.75 \[ \frac{1}{2} \, B b^{2}{\rm ln}\left (x^{2}\right ) - \frac{11 \, B b^{2} x^{6} + 12 \, B a b x^{4} + 6 \, A b^{2} x^{4} + 3 \, B a^{2} x^{2} + 6 \, A a b x^{2} + 2 \, A a^{2}}{12 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^2/x^7,x, algorithm="giac")
[Out]