Optimal. Leaf size=44 \[ \frac{2 b x^7}{35 a^2 \left (a+b x^2\right )^{7/2}}+\frac{x^5}{5 a \left (a+b x^2\right )^{7/2}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0493929, 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 \[ \frac{2 b x^7}{35 a^2 \left (a+b x^2\right )^{7/2}}+\frac{x^5}{5 a \left (a+b x^2\right )^{7/2}} \]
Antiderivative was successfully verified.
[In] Int[x^4/(a + b*x^2)^(9/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.53708, size = 37, normalized size = 0.84 \[ \frac{x^{5}}{5 a \left (a + b x^{2}\right )^{\frac{7}{2}}} + \frac{2 b x^{7}}{35 a^{2} \left (a + b x^{2}\right )^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4/(b*x**2+a)**(9/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0332654, size = 31, normalized size = 0.7 \[ \frac{x^5 \left (7 a+2 b x^2\right )}{35 a^2 \left (a+b x^2\right )^{7/2}} \]
Antiderivative was successfully verified.
[In] Integrate[x^4/(a + b*x^2)^(9/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.008, size = 28, normalized size = 0.6 \[{\frac{{x}^{5} \left ( 2\,b{x}^{2}+7\,a \right ) }{35\,{a}^{2}} \left ( b{x}^{2}+a \right ) ^{-{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4/(b*x^2+a)^(9/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34811, size = 115, normalized size = 2.61 \[ -\frac{x^{3}}{4 \,{\left (b x^{2} + a\right )}^{\frac{7}{2}} b} + \frac{3 \, x}{140 \,{\left (b x^{2} + a\right )}^{\frac{5}{2}} b^{2}} + \frac{2 \, x}{35 \, \sqrt{b x^{2} + a} a^{2} b^{2}} + \frac{x}{35 \,{\left (b x^{2} + a\right )}^{\frac{3}{2}} a b^{2}} - \frac{3 \, a x}{28 \,{\left (b x^{2} + a\right )}^{\frac{7}{2}} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(b*x^2 + a)^(9/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.252244, size = 96, normalized size = 2.18 \[ \frac{{\left (2 \, b x^{7} + 7 \, a x^{5}\right )} \sqrt{b x^{2} + a}}{35 \,{\left (a^{2} b^{4} x^{8} + 4 \, a^{3} b^{3} x^{6} + 6 \, a^{4} b^{2} x^{4} + 4 \, a^{5} b x^{2} + a^{6}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(b*x^2 + a)^(9/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 10.0758, size = 199, normalized size = 4.52 \[ \frac{7 a x^{5}}{35 a^{\frac{11}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{9}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{7}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{5}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{2 b x^{7}}{35 a^{\frac{11}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{9}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}} + 105 a^{\frac{7}{2}} b^{2} x^{4} \sqrt{1 + \frac{b x^{2}}{a}} + 35 a^{\frac{5}{2}} b^{3} x^{6} \sqrt{1 + \frac{b x^{2}}{a}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4/(b*x**2+a)**(9/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.221414, size = 39, normalized size = 0.89 \[ \frac{x^{5}{\left (\frac{2 \, b x^{2}}{a^{2}} + \frac{7}{a}\right )}}{35 \,{\left (b x^{2} + a\right )}^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(b*x^2 + a)^(9/2),x, algorithm="giac")
[Out]