Optimal. Leaf size=33 \[ -\frac{\left (d^2-e^2 x^2\right )^{9/2}}{9 d e (d+e x)^9} \]
[Out]
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Rubi [A] time = 0.0366368, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042 \[ -\frac{\left (d^2-e^2 x^2\right )^{9/2}}{9 d e (d+e x)^9} \]
Antiderivative was successfully verified.
[In] Int[(d^2 - e^2*x^2)^(7/2)/(d + e*x)^9,x]
[Out]
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Rubi in Sympy [A] time = 4.88217, size = 26, normalized size = 0.79 \[ - \frac{\left (d^{2} - e^{2} x^{2}\right )^{\frac{9}{2}}}{9 d e \left (d + e x\right )^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-e**2*x**2+d**2)**(7/2)/(e*x+d)**9,x)
[Out]
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Mathematica [A] time = 0.0742725, size = 41, normalized size = 1.24 \[ -\frac{(d-e x)^4 \sqrt{d^2-e^2 x^2}}{9 d e (d+e x)^5} \]
Antiderivative was successfully verified.
[In] Integrate[(d^2 - e^2*x^2)^(7/2)/(d + e*x)^9,x]
[Out]
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Maple [A] time = 0.01, size = 36, normalized size = 1.1 \[ -{\frac{-ex+d}{9\, \left ( ex+d \right ) ^{8}de} \left ( -{e}^{2}{x}^{2}+{d}^{2} \right ) ^{{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-e^2*x^2+d^2)^(7/2)/(e*x+d)^9,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-e^2*x^2 + d^2)^(7/2)/(e*x + d)^9,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.236118, size = 386, normalized size = 11.7 \[ -\frac{2 \,{\left (e^{8} x^{9} + 18 \, d^{2} e^{6} x^{7} - 99 \, d^{4} e^{4} x^{5} + 24 \, d^{6} e^{2} x^{3} + 72 \, d^{8} x + 12 \,{\left (5 \, d^{3} e^{4} x^{5} - 5 \, d^{5} e^{2} x^{3} - 6 \, d^{7} x\right )} \sqrt{-e^{2} x^{2} + d^{2}}\right )}}{9 \,{\left (d e^{9} x^{9} + 9 \, d^{2} e^{8} x^{8} + 18 \, d^{3} e^{7} x^{7} - 18 \, d^{4} e^{6} x^{6} - 99 \, d^{5} e^{5} x^{5} - 99 \, d^{6} e^{4} x^{4} + 24 \, d^{7} e^{3} x^{3} + 108 \, d^{8} e^{2} x^{2} + 72 \, d^{9} e x + 16 \, d^{10} -{\left (d e^{8} x^{8} - 22 \, d^{3} e^{6} x^{6} - 60 \, d^{4} e^{5} x^{5} - 39 \, d^{5} e^{4} x^{4} + 60 \, d^{6} e^{3} x^{3} + 116 \, d^{7} e^{2} x^{2} + 72 \, d^{8} e x + 16 \, d^{9}\right )} \sqrt{-e^{2} x^{2} + d^{2}}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-e^2*x^2 + d^2)^(7/2)/(e*x + d)^9,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((-e**2*x**2+d**2)**(7/2)/(e*x+d)**9,x)
[Out]
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GIAC/XCAS [A] time = 0.606707, size = 1, normalized size = 0.03 \[ \mathit{Done} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-e^2*x^2 + d^2)^(7/2)/(e*x + d)^9,x, algorithm="giac")
[Out]