Optimal. Leaf size=76 \[ -\frac{64 \left (1-x^2\right )^{11/4}}{231 e (e x)^{11/2}}+\frac{16 \left (1-x^2\right )^{7/4}}{21 e (e x)^{11/2}}-\frac{2 \left (1-x^2\right )^{3/4}}{3 e (e x)^{11/2}} \]
[Out]
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Rubi [A] time = 0.0845373, antiderivative size = 76, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ -\frac{64 \left (1-x^2\right )^{11/4}}{231 e (e x)^{11/2}}+\frac{16 \left (1-x^2\right )^{7/4}}{21 e (e x)^{11/2}}-\frac{2 \left (1-x^2\right )^{3/4}}{3 e (e x)^{11/2}} \]
Antiderivative was successfully verified.
[In] Int[1/((1 - x)^(1/4)*(e*x)^(13/2)*(1 + x)^(1/4)),x]
[Out]
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Rubi in Sympy [A] time = 9.96972, size = 60, normalized size = 0.79 \[ - \frac{64 \left (- x^{2} + 1\right )^{\frac{11}{4}}}{231 e \left (e x\right )^{\frac{11}{2}}} + \frac{16 \left (- x^{2} + 1\right )^{\frac{7}{4}}}{21 e \left (e x\right )^{\frac{11}{2}}} - \frac{2 \left (- x^{2} + 1\right )^{\frac{3}{4}}}{3 e \left (e x\right )^{\frac{11}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-x)**(1/4)/(e*x)**(13/2)/(1+x)**(1/4),x)
[Out]
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Mathematica [A] time = 0.0258965, size = 40, normalized size = 0.53 \[ -\frac{2 \left (1-x^2\right )^{3/4} \left (32 x^4+24 x^2+21\right ) \sqrt{e x}}{231 e^7 x^6} \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - x)^(1/4)*(e*x)^(13/2)*(1 + x)^(1/4)),x]
[Out]
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Maple [A] time = 0.006, size = 33, normalized size = 0.4 \[ -{\frac{2\,x \left ( 32\,{x}^{4}+24\,{x}^{2}+21 \right ) }{231} \left ( 1+x \right ) ^{{\frac{3}{4}}} \left ( 1-x \right ) ^{{\frac{3}{4}}} \left ( ex \right ) ^{-{\frac{13}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-x)^(1/4)/(e*x)^(13/2)/(1+x)^(1/4),x)
[Out]
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Maxima [A] time = 1.42837, size = 53, normalized size = 0.7 \[ \frac{2 \,{\left (32 \, x^{7} - 8 \, x^{5} - 3 \, x^{3} - 21 \, x\right )}}{231 \, e^{\frac{13}{2}}{\left (x + 1\right )}^{\frac{1}{4}} x^{\frac{13}{2}}{\left (-x + 1\right )}^{\frac{1}{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((e*x)^(13/2)*(x + 1)^(1/4)*(-x + 1)^(1/4)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.221371, size = 57, normalized size = 0.75 \[ \frac{2 \,{\left (32 \, x^{6} - 8 \, x^{4} - 3 \, x^{2} - 21\right )}}{231 \, \sqrt{e x} e^{6}{\left (x + 1\right )}^{\frac{1}{4}} x^{5}{\left (-x + 1\right )}^{\frac{1}{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((e*x)^(13/2)*(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)**(13/2)/(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)^(13/2)*(x + 1)^(1/4)*(-x + 1)^(1/4)),x, algorithm="giac")
[Out]