Optimal. Leaf size=70 \[ -\frac{4 \sqrt [4]{1-\frac{1}{x^2}} \sqrt{e x} E\left (\left .\frac{1}{2} \csc ^{-1}(x)\right |2\right )}{5 e^4 \sqrt [4]{1-x^2}}-\frac{2 \left (1-x^2\right )^{3/4}}{5 e (e x)^{5/2}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0872142, antiderivative size = 70, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 5, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.208 \[ -\frac{4 \sqrt [4]{1-\frac{1}{x^2}} \sqrt{e x} E\left (\left .\frac{1}{2} \csc ^{-1}(x)\right |2\right )}{5 e^4 \sqrt [4]{1-x^2}}-\frac{2 \left (1-x^2\right )^{3/4}}{5 e (e x)^{5/2}} \]
Antiderivative was successfully verified.
[In] Int[1/((1 - x)^(1/4)*(e*x)^(7/2)*(1 + x)^(1/4)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 9.83284, size = 61, normalized size = 0.87 \[ - \frac{2 \left (- x^{2} + 1\right )^{\frac{3}{4}}}{5 e \left (e x\right )^{\frac{5}{2}}} - \frac{4 \sqrt{e x} \sqrt [4]{1 - \frac{1}{x^{2}}} E\left (\frac{\operatorname{asin}{\left (\frac{1}{x} \right )}}{2}\middle | 2\right )}{5 e^{4} \sqrt [4]{- x^{2} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-x)**(1/4)/(e*x)**(7/2)/(1+x)**(1/4),x)
[Out]
_______________________________________________________________________________________
Mathematica [C] time = 0.0507474, size = 51, normalized size = 0.73 \[ \frac{x \left (-8 x^4 \, _2F_1\left (\frac{1}{4},\frac{3}{4};\frac{7}{4};x^2\right )-6 \left (1-x^2\right )^{3/4} \left (2 x^2+1\right )\right )}{15 (e x)^{7/2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - x)^(1/4)*(e*x)^(7/2)*(1 + x)^(1/4)),x]
[Out]
_______________________________________________________________________________________
Maple [F] time = 0.069, size = 0, normalized size = 0. \[ \int{1{\frac{1}{\sqrt [4]{1-x}}} \left ( ex \right ) ^{-{\frac{7}{2}}}{\frac{1}{\sqrt [4]{1+x}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-x)^(1/4)/(e*x)^(7/2)/(1+x)^(1/4),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\left (e x\right )^{\frac{7}{2}}{\left (x + 1\right )}^{\frac{1}{4}}{\left (-x + 1\right )}^{\frac{1}{4}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((e*x)^(7/2)*(x + 1)^(1/4)*(-x + 1)^(1/4)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{\sqrt{e x} e^{3}{\left (x + 1\right )}^{\frac{1}{4}} x^{3}{\left (-x + 1\right )}^{\frac{1}{4}}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((e*x)^(7/2)*(x + 1)^(1/4)*(-x + 1)^(1/4)),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
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)**(7/2)/(1+x)**(1/4),x)
[Out]
_______________________________________________________________________________________
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)^(7/2)*(x + 1)^(1/4)*(-x + 1)^(1/4)),x, algorithm="giac")
[Out]