Optimal. Leaf size=51 \[ \frac{2 x^{15/2}}{35 a^2 \left (a x+b x^3\right )^{5/2}}+\frac{x^{17/2}}{7 a \left (a x+b x^3\right )^{7/2}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.120685, 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 \[ \frac{2 x^{15/2}}{35 a^2 \left (a x+b x^3\right )^{5/2}}+\frac{x^{17/2}}{7 a \left (a x+b x^3\right )^{7/2}} \]
Antiderivative was successfully verified.
[In] Int[x^(17/2)/(a*x + b*x^3)^(9/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 12.2469, size = 42, normalized size = 0.82 \[ \frac{x^{\frac{17}{2}}}{7 a \left (a x + b x^{3}\right )^{\frac{7}{2}}} + \frac{2 x^{\frac{15}{2}}}{35 a^{2} \left (a x + b x^{3}\right )^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(17/2)/(b*x**3+a*x)**(9/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0456865, size = 44, normalized size = 0.86 \[ \frac{x^{9/2} \sqrt{x \left (a+b x^2\right )} \left (7 a+2 b x^2\right )}{35 a^2 \left (a+b x^2\right )^4} \]
Antiderivative was successfully verified.
[In] Integrate[x^(17/2)/(a*x + b*x^3)^(9/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.008, size = 37, normalized size = 0.7 \[{\frac{ \left ( b{x}^{2}+a \right ) \left ( 2\,b{x}^{2}+7\,a \right ) }{35\,{a}^{2}}{x}^{{\frac{19}{2}}} \left ( b{x}^{3}+ax \right ) ^{-{\frac{9}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(17/2)/(b*x^3+a*x)^(9/2),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{\frac{17}{2}}}{{\left (b x^{3} + a x\right )}^{\frac{9}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(17/2)/(b*x^3 + a*x)^(9/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.210888, size = 103, normalized size = 2.02 \[ \frac{{\left (2 \, b x^{6} + 7 \, a x^{4}\right )} \sqrt{b x^{3} + a x} \sqrt{x}}{35 \,{\left (a^{2} b^{4} x^{8} + 4 \, a^{3} b^{3} x^{6} + 6 \, a^{4} b^{2} x^{4} + 4 \, a^{5} b x^{2} + a^{6}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(17/2)/(b*x^3 + a*x)^(9/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
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**(17/2)/(b*x**3+a*x)**(9/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.234793, size = 39, normalized size = 0.76 \[ \frac{x^{5}{\left (\frac{2 \, b x^{2}}{a^{2}} + \frac{7}{a}\right )}}{35 \,{\left (b x^{2} + a\right )}^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^(17/2)/(b*x^3 + a*x)^(9/2),x, algorithm="giac")
[Out]