Optimal. Leaf size=18 \[ -\frac{1}{7 b \left (a+b x^2\right )^{7/2}} \]
[Out]
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Rubi [A] time = 0.0109965, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{1}{7 b \left (a+b x^2\right )^{7/2}} \]
Antiderivative was successfully verified.
[In] Int[x/(a + b*x^2)^(9/2),x]
[Out]
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Rubi in Sympy [A] time = 2.16294, size = 15, normalized size = 0.83 \[ - \frac{1}{7 b \left (a + b x^{2}\right )^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(b*x**2+a)**(9/2),x)
[Out]
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Mathematica [A] time = 0.00838707, size = 18, normalized size = 1. \[ -\frac{1}{7 b \left (a+b x^2\right )^{7/2}} \]
Antiderivative was successfully verified.
[In] Integrate[x/(a + b*x^2)^(9/2),x]
[Out]
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Maple [A] time = 0.005, size = 15, normalized size = 0.8 \[ -{\frac{1}{7\,b} \left ( b{x}^{2}+a \right ) ^{-{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(b*x^2+a)^(9/2),x)
[Out]
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Maxima [A] time = 1.34539, size = 19, normalized size = 1.06 \[ -\frac{1}{7 \,{\left (b x^{2} + a\right )}^{\frac{7}{2}} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x^2 + a)^(9/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.252929, size = 77, normalized size = 4.28 \[ -\frac{\sqrt{b x^{2} + a}}{7 \,{\left (b^{5} x^{8} + 4 \, a b^{4} x^{6} + 6 \, a^{2} b^{3} x^{4} + 4 \, a^{3} b^{2} x^{2} + a^{4} b\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x^2 + a)^(9/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 18.901, size = 90, normalized size = 5. \[ \begin{cases} - \frac{1}{7 a^{3} b \sqrt{a + b x^{2}} + 21 a^{2} b^{2} x^{2} \sqrt{a + b x^{2}} + 21 a b^{3} x^{4} \sqrt{a + b x^{2}} + 7 b^{4} x^{6} \sqrt{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 a^{\frac{9}{2}}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x**2+a)**(9/2),x)
[Out]
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GIAC/XCAS [A] time = 0.211185, size = 19, normalized size = 1.06 \[ -\frac{1}{7 \,{\left (b x^{2} + a\right )}^{\frac{7}{2}} b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x^2 + a)^(9/2),x, algorithm="giac")
[Out]