Optimal. Leaf size=68 \[ -\frac{4 b^2 \sqrt{a+b x^4}}{15 a^3 x^2}+\frac{2 b \sqrt{a+b x^4}}{15 a^2 x^6}-\frac{\sqrt{a+b x^4}}{10 a x^{10}} \]
[Out]
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Rubi [A] time = 0.0658592, antiderivative size = 68, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{4 b^2 \sqrt{a+b x^4}}{15 a^3 x^2}+\frac{2 b \sqrt{a+b x^4}}{15 a^2 x^6}-\frac{\sqrt{a+b x^4}}{10 a x^{10}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^11*Sqrt[a + b*x^4]),x]
[Out]
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Rubi in Sympy [A] time = 6.8055, size = 61, normalized size = 0.9 \[ - \frac{\sqrt{a + b x^{4}}}{10 a x^{10}} + \frac{2 b \sqrt{a + b x^{4}}}{15 a^{2} x^{6}} - \frac{4 b^{2} \sqrt{a + b x^{4}}}{15 a^{3} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**11/(b*x**4+a)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0340686, size = 42, normalized size = 0.62 \[ -\frac{\sqrt{a+b x^4} \left (3 a^2-4 a b x^4+8 b^2 x^8\right )}{30 a^3 x^{10}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^11*Sqrt[a + b*x^4]),x]
[Out]
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Maple [A] time = 0.007, size = 39, normalized size = 0.6 \[ -{\frac{8\,{b}^{2}{x}^{8}-4\,ab{x}^{4}+3\,{a}^{2}}{30\,{x}^{10}{a}^{3}}\sqrt{b{x}^{4}+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^11/(b*x^4+a)^(1/2),x)
[Out]
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Maxima [A] time = 1.43589, size = 70, normalized size = 1.03 \[ -\frac{\frac{15 \, \sqrt{b x^{4} + a} b^{2}}{x^{2}} - \frac{10 \,{\left (b x^{4} + a\right )}^{\frac{3}{2}} b}{x^{6}} + \frac{3 \,{\left (b x^{4} + a\right )}^{\frac{5}{2}}}{x^{10}}}{30 \, a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^4 + a)*x^11),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.267401, size = 51, normalized size = 0.75 \[ -\frac{{\left (8 \, b^{2} x^{8} - 4 \, a b x^{4} + 3 \, a^{2}\right )} \sqrt{b x^{4} + a}}{30 \, a^{3} x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^4 + a)*x^11),x, algorithm="fricas")
[Out]
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Sympy [A] time = 8.00128, size = 298, normalized size = 4.38 \[ - \frac{3 a^{4} b^{\frac{9}{2}} \sqrt{\frac{a}{b x^{4}} + 1}}{30 a^{5} b^{4} x^{8} + 60 a^{4} b^{5} x^{12} + 30 a^{3} b^{6} x^{16}} - \frac{2 a^{3} b^{\frac{11}{2}} x^{4} \sqrt{\frac{a}{b x^{4}} + 1}}{30 a^{5} b^{4} x^{8} + 60 a^{4} b^{5} x^{12} + 30 a^{3} b^{6} x^{16}} - \frac{3 a^{2} b^{\frac{13}{2}} x^{8} \sqrt{\frac{a}{b x^{4}} + 1}}{30 a^{5} b^{4} x^{8} + 60 a^{4} b^{5} x^{12} + 30 a^{3} b^{6} x^{16}} - \frac{12 a b^{\frac{15}{2}} x^{12} \sqrt{\frac{a}{b x^{4}} + 1}}{30 a^{5} b^{4} x^{8} + 60 a^{4} b^{5} x^{12} + 30 a^{3} b^{6} x^{16}} - \frac{8 b^{\frac{17}{2}} x^{16} \sqrt{\frac{a}{b x^{4}} + 1}}{30 a^{5} b^{4} x^{8} + 60 a^{4} b^{5} x^{12} + 30 a^{3} b^{6} x^{16}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**11/(b*x**4+a)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.217594, size = 58, normalized size = 0.85 \[ -\frac{3 \,{\left (b + \frac{a}{x^{4}}\right )}^{\frac{5}{2}} - 10 \,{\left (b + \frac{a}{x^{4}}\right )}^{\frac{3}{2}} b + 15 \, \sqrt{b + \frac{a}{x^{4}}} b^{2}}{30 \, a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^4 + a)*x^11),x, algorithm="giac")
[Out]