Optimal. Leaf size=51 \[ \frac{8 \left (1-x^2\right )^{7/4}}{21 e (e x)^{7/2}}-\frac{2 \left (1-x^2\right )^{3/4}}{3 e (e x)^{7/2}} \]
[Out]
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Rubi [A] time = 0.0644011, antiderivative size = 51, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ \frac{8 \left (1-x^2\right )^{7/4}}{21 e (e x)^{7/2}}-\frac{2 \left (1-x^2\right )^{3/4}}{3 e (e x)^{7/2}} \]
Antiderivative was successfully verified.
[In] Int[1/((1 - x)^(1/4)*(e*x)^(9/2)*(1 + x)^(1/4)),x]
[Out]
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Rubi in Sympy [A] time = 7.4369, size = 39, normalized size = 0.76 \[ \frac{8 \left (- x^{2} + 1\right )^{\frac{7}{4}}}{21 e \left (e x\right )^{\frac{7}{2}}} - \frac{2 \left (- x^{2} + 1\right )^{\frac{3}{4}}}{3 e \left (e x\right )^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-x)**(1/4)/(e*x)**(9/2)/(1+x)**(1/4),x)
[Out]
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Mathematica [A] time = 0.0233888, size = 35, normalized size = 0.69 \[ -\frac{2 \left (1-x^2\right )^{3/4} \left (4 x^2+3\right ) \sqrt{e x}}{21 e^5 x^4} \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - x)^(1/4)*(e*x)^(9/2)*(1 + x)^(1/4)),x]
[Out]
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Maple [A] time = 0.007, size = 28, normalized size = 0.6 \[ -{\frac{2\,x \left ( 4\,{x}^{2}+3 \right ) }{21} \left ( 1+x \right ) ^{{\frac{3}{4}}} \left ( 1-x \right ) ^{{\frac{3}{4}}} \left ( ex \right ) ^{-{\frac{9}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-x)^(1/4)/(e*x)^(9/2)/(1+x)^(1/4),x)
[Out]
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Maxima [A] time = 1.42587, size = 46, normalized size = 0.9 \[ \frac{2 \,{\left (4 \, x^{5} - x^{3} - 3 \, x\right )}}{21 \, e^{\frac{9}{2}}{\left (x + 1\right )}^{\frac{1}{4}} x^{\frac{9}{2}}{\left (-x + 1\right )}^{\frac{1}{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((e*x)^(9/2)*(x + 1)^(1/4)*(-x + 1)^(1/4)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212544, size = 50, normalized size = 0.98 \[ \frac{2 \,{\left (4 \, x^{4} - x^{2} - 3\right )}}{21 \, \sqrt{e x} e^{4}{\left (x + 1\right )}^{\frac{1}{4}} x^{3}{\left (-x + 1\right )}^{\frac{1}{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((e*x)^(9/2)*(x + 1)^(1/4)*(-x + 1)^(1/4)),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(1/(1-x)**(1/4)/(e*x)**(9/2)/(1+x)**(1/4),x)
[Out]
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GIAC/XCAS [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((e*x)^(9/2)*(x + 1)^(1/4)*(-x + 1)^(1/4)),x, algorithm="giac")
[Out]