Optimal. Leaf size=51 \[ -\frac{2 x^{5/2}}{35 b^2 \left (a x+b x^3\right )^{5/2}}-\frac{x^{11/2}}{7 b \left (a x+b x^3\right )^{7/2}} \]
[Out]
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Rubi [A] time = 0.121487, antiderivative size = 51, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105 \[ -\frac{2 x^{5/2}}{35 b^2 \left (a x+b x^3\right )^{5/2}}-\frac{x^{11/2}}{7 b \left (a x+b x^3\right )^{7/2}} \]
Antiderivative was successfully verified.
[In] Int[x^(15/2)/(a*x + b*x^3)^(9/2),x]
[Out]
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Rubi in Sympy [A] time = 12.4103, size = 44, normalized size = 0.86 \[ - \frac{x^{\frac{11}{2}}}{7 b \left (a x + b x^{3}\right )^{\frac{7}{2}}} - \frac{2 x^{\frac{5}{2}}}{35 b^{2} \left (a x + b x^{3}\right )^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(15/2)/(b*x**3+a*x)**(9/2),x)
[Out]
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Mathematica [A] time = 0.0338084, size = 44, normalized size = 0.86 \[ -\frac{\sqrt{x} \left (2 a+7 b x^2\right )}{35 b^2 \left (a+b x^2\right )^3 \sqrt{x \left (a+b x^2\right )}} \]
Antiderivative was successfully verified.
[In] Integrate[x^(15/2)/(a*x + b*x^3)^(9/2),x]
[Out]
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Maple [A] time = 0.007, size = 37, normalized size = 0.7 \[ -{\frac{ \left ( b{x}^{2}+a \right ) \left ( 7\,b{x}^{2}+2\,a \right ) }{35\,{b}^{2}}{x}^{{\frac{9}{2}}} \left ( b{x}^{3}+ax \right ) ^{-{\frac{9}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(15/2)/(b*x^3+a*x)^(9/2),x)
[Out]
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Maxima [A] time = 1.50049, size = 32, normalized size = 0.63 \[ -\frac{7 \, b x^{2} + 2 \, a}{35 \,{\left (b x^{2} + a\right )}^{\frac{7}{2}} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(15/2)/(b*x^3 + a*x)^(9/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.21041, size = 86, normalized size = 1.69 \[ -\frac{7 \, b x^{3} + 2 \, a x}{35 \,{\left (b^{5} x^{6} + 3 \, a b^{4} x^{4} + 3 \, a^{2} b^{3} x^{2} + a^{3} b^{2}\right )} \sqrt{b x^{3} + a x} \sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(15/2)/(b*x^3 + a*x)^(9/2),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(15/2)/(b*x**3+a*x)**(9/2),x)
[Out]
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GIAC/XCAS [A] time = 0.229927, size = 45, normalized size = 0.88 \[ -\frac{7 \, b x^{2} + 2 \, a}{35 \,{\left (b x^{2} + a\right )}^{\frac{7}{2}} b^{2}} + \frac{2}{35 \, a^{\frac{5}{2}} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(15/2)/(b*x^3 + a*x)^(9/2),x, algorithm="giac")
[Out]