Optimal. Leaf size=76 \[ -\frac{b \left (a+b x^2\right )^6 (A b-4 a B)}{336 a^3 x^{12}}+\frac{\left (a+b x^2\right )^6 (A b-4 a B)}{56 a^2 x^{14}}-\frac{A \left (a+b x^2\right )^6}{16 a x^{16}} \]
[Out]
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Rubi [A] time = 0.171961, antiderivative size = 76, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ -\frac{b \left (a+b x^2\right )^6 (A b-4 a B)}{336 a^3 x^{12}}+\frac{\left (a+b x^2\right )^6 (A b-4 a B)}{56 a^2 x^{14}}-\frac{A \left (a+b x^2\right )^6}{16 a x^{16}} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^2)^5*(A + B*x^2))/x^17,x]
[Out]
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Rubi in Sympy [A] time = 14.1668, size = 68, normalized size = 0.89 \[ - \frac{A \left (a + b x^{2}\right )^{6}}{16 a x^{16}} + \frac{\left (a + b x^{2}\right )^{6} \left (A b - 4 B a\right )}{56 a^{2} x^{14}} - \frac{b \left (a + b x^{2}\right )^{6} \left (A b - 4 B a\right )}{336 a^{3} x^{12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**5*(B*x**2+A)/x**17,x)
[Out]
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Mathematica [A] time = 0.0567621, size = 121, normalized size = 1.59 \[ -\frac{3 a^5 \left (7 A+8 B x^2\right )+20 a^4 b x^2 \left (6 A+7 B x^2\right )+56 a^3 b^2 x^4 \left (5 A+6 B x^2\right )+84 a^2 b^3 x^6 \left (4 A+5 B x^2\right )+70 a b^4 x^8 \left (3 A+4 B x^2\right )+28 b^5 x^{10} \left (2 A+3 B x^2\right )}{336 x^{16}} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^2)^5*(A + B*x^2))/x^17,x]
[Out]
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Maple [A] time = 0.009, size = 104, normalized size = 1.4 \[ -{\frac{5\,{a}^{3}b \left ( 2\,Ab+Ba \right ) }{12\,{x}^{12}}}-{\frac{A{a}^{5}}{16\,{x}^{16}}}-{\frac{{b}^{4} \left ( Ab+5\,Ba \right ) }{6\,{x}^{6}}}-{\frac{B{b}^{5}}{4\,{x}^{4}}}-{\frac{{a}^{2}{b}^{2} \left ( Ab+Ba \right ) }{{x}^{10}}}-{\frac{5\,a{b}^{3} \left ( Ab+2\,Ba \right ) }{8\,{x}^{8}}}-{\frac{{a}^{4} \left ( 5\,Ab+Ba \right ) }{14\,{x}^{14}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^5*(B*x^2+A)/x^17,x)
[Out]
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Maxima [A] time = 1.33512, size = 163, normalized size = 2.14 \[ -\frac{84 \, B b^{5} x^{12} + 56 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{10} + 210 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{8} + 336 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{6} + 21 \, A a^{5} + 140 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{4} + 24 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{2}}{336 \, x^{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^5/x^17,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.221645, size = 163, normalized size = 2.14 \[ -\frac{84 \, B b^{5} x^{12} + 56 \,{\left (5 \, B a b^{4} + A b^{5}\right )} x^{10} + 210 \,{\left (2 \, B a^{2} b^{3} + A a b^{4}\right )} x^{8} + 336 \,{\left (B a^{3} b^{2} + A a^{2} b^{3}\right )} x^{6} + 21 \, A a^{5} + 140 \,{\left (B a^{4} b + 2 \, A a^{3} b^{2}\right )} x^{4} + 24 \,{\left (B a^{5} + 5 \, A a^{4} b\right )} x^{2}}{336 \, x^{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^5/x^17,x, algorithm="fricas")
[Out]
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Sympy [A] time = 152.951, size = 128, normalized size = 1.68 \[ - \frac{21 A a^{5} + 84 B b^{5} x^{12} + x^{10} \left (56 A b^{5} + 280 B a b^{4}\right ) + x^{8} \left (210 A a b^{4} + 420 B a^{2} b^{3}\right ) + x^{6} \left (336 A a^{2} b^{3} + 336 B a^{3} b^{2}\right ) + x^{4} \left (280 A a^{3} b^{2} + 140 B a^{4} b\right ) + x^{2} \left (120 A a^{4} b + 24 B a^{5}\right )}{336 x^{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**5*(B*x**2+A)/x**17,x)
[Out]
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GIAC/XCAS [A] time = 0.230495, size = 171, normalized size = 2.25 \[ -\frac{84 \, B b^{5} x^{12} + 280 \, B a b^{4} x^{10} + 56 \, A b^{5} x^{10} + 420 \, B a^{2} b^{3} x^{8} + 210 \, A a b^{4} x^{8} + 336 \, B a^{3} b^{2} x^{6} + 336 \, A a^{2} b^{3} x^{6} + 140 \, B a^{4} b x^{4} + 280 \, A a^{3} b^{2} x^{4} + 24 \, B a^{5} x^{2} + 120 \, A a^{4} b x^{2} + 21 \, A a^{5}}{336 \, x^{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^5/x^17,x, algorithm="giac")
[Out]