Optimal. Leaf size=38 \[ \frac{2 a \sqrt{a+\frac{b}{x^3}}}{3 b^2}-\frac{2 \left (a+\frac{b}{x^3}\right )^{3/2}}{9 b^2} \]
[Out]
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Rubi [A] time = 0.0662499, antiderivative size = 38, 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 \[ \frac{2 a \sqrt{a+\frac{b}{x^3}}}{3 b^2}-\frac{2 \left (a+\frac{b}{x^3}\right )^{3/2}}{9 b^2} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[a + b/x^3]*x^7),x]
[Out]
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Rubi in Sympy [A] time = 6.99005, size = 34, normalized size = 0.89 \[ \frac{2 a \sqrt{a + \frac{b}{x^{3}}}}{3 b^{2}} - \frac{2 \left (a + \frac{b}{x^{3}}\right )^{\frac{3}{2}}}{9 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**7/(a+b/x**3)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0382642, size = 31, normalized size = 0.82 \[ \frac{2 \sqrt{a+\frac{b}{x^3}} \left (2 a x^3-b\right )}{9 b^2 x^3} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[a + b/x^3]*x^7),x]
[Out]
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Maple [A] time = 0.009, size = 39, normalized size = 1. \[{\frac{ \left ( 2\,a{x}^{3}+2\,b \right ) \left ( 2\,a{x}^{3}-b \right ) }{9\,{b}^{2}{x}^{6}}{\frac{1}{\sqrt{{\frac{a{x}^{3}+b}{{x}^{3}}}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^7/(a+b/x^3)^(1/2),x)
[Out]
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Maxima [A] time = 1.41509, size = 41, normalized size = 1.08 \[ -\frac{2 \,{\left (a + \frac{b}{x^{3}}\right )}^{\frac{3}{2}}}{9 \, b^{2}} + \frac{2 \, \sqrt{a + \frac{b}{x^{3}}} a}{3 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(a + b/x^3)*x^7),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.241734, size = 42, normalized size = 1.11 \[ \frac{2 \,{\left (2 \, a x^{3} - b\right )} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{9 \, b^{2} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(a + b/x^3)*x^7),x, algorithm="fricas")
[Out]
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Sympy [A] time = 9.11585, size = 255, normalized size = 6.71 \[ \frac{4 a^{\frac{7}{2}} b^{\frac{3}{2}} x^{6} \sqrt{\frac{a x^{3}}{b} + 1}}{9 a^{\frac{5}{2}} b^{3} x^{\frac{15}{2}} + 9 a^{\frac{3}{2}} b^{4} x^{\frac{9}{2}}} + \frac{2 a^{\frac{5}{2}} b^{\frac{5}{2}} x^{3} \sqrt{\frac{a x^{3}}{b} + 1}}{9 a^{\frac{5}{2}} b^{3} x^{\frac{15}{2}} + 9 a^{\frac{3}{2}} b^{4} x^{\frac{9}{2}}} - \frac{2 a^{\frac{3}{2}} b^{\frac{7}{2}} \sqrt{\frac{a x^{3}}{b} + 1}}{9 a^{\frac{5}{2}} b^{3} x^{\frac{15}{2}} + 9 a^{\frac{3}{2}} b^{4} x^{\frac{9}{2}}} - \frac{4 a^{4} b x^{\frac{15}{2}}}{9 a^{\frac{5}{2}} b^{3} x^{\frac{15}{2}} + 9 a^{\frac{3}{2}} b^{4} x^{\frac{9}{2}}} - \frac{4 a^{3} b^{2} x^{\frac{9}{2}}}{9 a^{\frac{5}{2}} b^{3} x^{\frac{15}{2}} + 9 a^{\frac{3}{2}} b^{4} x^{\frac{9}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**7/(a+b/x**3)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{a + \frac{b}{x^{3}}} x^{7}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(a + b/x^3)*x^7),x, algorithm="giac")
[Out]