Optimal. Leaf size=38 \[ \frac{2 a \left (a+\frac{b}{x^3}\right )^{3/2}}{9 b^2}-\frac{2 \left (a+\frac{b}{x^3}\right )^{5/2}}{15 b^2} \]
[Out]
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Rubi [A] time = 0.067862, 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 \[ \frac{2 a \left (a+\frac{b}{x^3}\right )^{3/2}}{9 b^2}-\frac{2 \left (a+\frac{b}{x^3}\right )^{5/2}}{15 b^2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[a + b/x^3]/x^7,x]
[Out]
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Rubi in Sympy [A] time = 6.96968, size = 34, normalized size = 0.89 \[ \frac{2 a \left (a + \frac{b}{x^{3}}\right )^{\frac{3}{2}}}{9 b^{2}} - \frac{2 \left (a + \frac{b}{x^{3}}\right )^{\frac{5}{2}}}{15 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a+b/x**3)**(1/2)/x**7,x)
[Out]
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Mathematica [A] time = 0.0300582, size = 42, normalized size = 1.11 \[ \frac{2 \sqrt{a+\frac{b}{x^3}} \left (2 a^2 x^6-a b x^3-3 b^2\right )}{45 b^2 x^6} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[a + b/x^3]/x^7,x]
[Out]
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Maple [A] time = 0.009, size = 39, normalized size = 1. \[{\frac{ \left ( 2\,a{x}^{3}+2\,b \right ) \left ( 2\,a{x}^{3}-3\,b \right ) }{45\,{b}^{2}{x}^{6}}\sqrt{{\frac{a{x}^{3}+b}{{x}^{3}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a+b/x^3)^(1/2)/x^7,x)
[Out]
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Maxima [A] time = 1.44038, size = 41, normalized size = 1.08 \[ -\frac{2 \,{\left (a + \frac{b}{x^{3}}\right )}^{\frac{5}{2}}}{15 \, b^{2}} + \frac{2 \,{\left (a + \frac{b}{x^{3}}\right )}^{\frac{3}{2}} a}{9 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a + b/x^3)/x^7,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.236311, size = 57, normalized size = 1.5 \[ \frac{2 \,{\left (2 \, a^{2} x^{6} - a b x^{3} - 3 \, b^{2}\right )} \sqrt{\frac{a x^{3} + b}{x^{3}}}}{45 \, b^{2} x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a + b/x^3)/x^7,x, algorithm="fricas")
[Out]
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Sympy [A] time = 7.91368, size = 313, normalized size = 8.24 \[ \frac{4 a^{\frac{11}{2}} b^{\frac{3}{2}} x^{9} \sqrt{\frac{a x^{3}}{b} + 1}}{45 a^{\frac{7}{2}} b^{3} x^{\frac{21}{2}} + 45 a^{\frac{5}{2}} b^{4} x^{\frac{15}{2}}} + \frac{2 a^{\frac{9}{2}} b^{\frac{5}{2}} x^{6} \sqrt{\frac{a x^{3}}{b} + 1}}{45 a^{\frac{7}{2}} b^{3} x^{\frac{21}{2}} + 45 a^{\frac{5}{2}} b^{4} x^{\frac{15}{2}}} - \frac{8 a^{\frac{7}{2}} b^{\frac{7}{2}} x^{3} \sqrt{\frac{a x^{3}}{b} + 1}}{45 a^{\frac{7}{2}} b^{3} x^{\frac{21}{2}} + 45 a^{\frac{5}{2}} b^{4} x^{\frac{15}{2}}} - \frac{6 a^{\frac{5}{2}} b^{\frac{9}{2}} \sqrt{\frac{a x^{3}}{b} + 1}}{45 a^{\frac{7}{2}} b^{3} x^{\frac{21}{2}} + 45 a^{\frac{5}{2}} b^{4} x^{\frac{15}{2}}} - \frac{4 a^{6} b x^{\frac{21}{2}}}{45 a^{\frac{7}{2}} b^{3} x^{\frac{21}{2}} + 45 a^{\frac{5}{2}} b^{4} x^{\frac{15}{2}}} - \frac{4 a^{5} b^{2} x^{\frac{15}{2}}}{45 a^{\frac{7}{2}} b^{3} x^{\frac{21}{2}} + 45 a^{\frac{5}{2}} b^{4} x^{\frac{15}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a+b/x**3)**(1/2)/x**7,x)
[Out]
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GIAC/XCAS [A] time = 0.236696, size = 39, normalized size = 1.03 \[ -\frac{2 \,{\left (3 \,{\left (a + \frac{b}{x^{3}}\right )}^{\frac{5}{2}} - 5 \,{\left (a + \frac{b}{x^{3}}\right )}^{\frac{3}{2}} a\right )}}{45 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(a + b/x^3)/x^7,x, algorithm="giac")
[Out]