Optimal. Leaf size=44 \[ \frac{b \sqrt{a+b x^4}}{3 a^2 x^2}-\frac{\sqrt{a+b x^4}}{6 a x^6} \]
[Out]
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Rubi [A] time = 0.0406231, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{b \sqrt{a+b x^4}}{3 a^2 x^2}-\frac{\sqrt{a+b x^4}}{6 a x^6} \]
Antiderivative was successfully verified.
[In] Int[1/(x^7*Sqrt[a + b*x^4]),x]
[Out]
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Rubi in Sympy [A] time = 4.34652, size = 36, normalized size = 0.82 \[ - \frac{\sqrt{a + b x^{4}}}{6 a x^{6}} + \frac{b \sqrt{a + b x^{4}}}{3 a^{2} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**7/(b*x**4+a)**(1/2),x)
[Out]
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Mathematica [A] time = 0.023233, size = 29, normalized size = 0.66 \[ -\frac{\left (a-2 b x^4\right ) \sqrt{a+b x^4}}{6 a^2 x^6} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^7*Sqrt[a + b*x^4]),x]
[Out]
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Maple [A] time = 0.007, size = 26, normalized size = 0.6 \[ -{\frac{-2\,b{x}^{4}+a}{6\,{a}^{2}{x}^{6}}\sqrt{b{x}^{4}+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^7/(b*x^4+a)^(1/2),x)
[Out]
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Maxima [A] time = 1.43673, size = 47, normalized size = 1.07 \[ \frac{\frac{3 \, \sqrt{b x^{4} + a} b}{x^{2}} - \frac{{\left (b x^{4} + a\right )}^{\frac{3}{2}}}{x^{6}}}{6 \, a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^4 + a)*x^7),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.233565, size = 36, normalized size = 0.82 \[ \frac{{\left (2 \, b x^{4} - a\right )} \sqrt{b x^{4} + a}}{6 \, a^{2} x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^4 + a)*x^7),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.59953, size = 44, normalized size = 1. \[ - \frac{\sqrt{b} \sqrt{\frac{a}{b x^{4}} + 1}}{6 a x^{4}} + \frac{b^{\frac{3}{2}} \sqrt{\frac{a}{b x^{4}} + 1}}{3 a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**7/(b*x**4+a)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.220643, size = 36, normalized size = 0.82 \[ -\frac{{\left (b + \frac{a}{x^{4}}\right )}^{\frac{3}{2}} - 3 \, \sqrt{b + \frac{a}{x^{4}}} b}{6 \, a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x^4 + a)*x^7),x, algorithm="giac")
[Out]