Optimal. Leaf size=59 \[ \frac{\sqrt{a} \left (1-\frac{b x^4}{a}\right )^{3/4} F\left (\left .\frac{1}{2} \sin ^{-1}\left (\frac{\sqrt{b} x^2}{\sqrt{a}}\right )\right |2\right )}{\sqrt{b} \left (a-b x^4\right )^{3/4}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0715815, antiderivative size = 59, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.214 \[ \frac{\sqrt{a} \left (1-\frac{b x^4}{a}\right )^{3/4} F\left (\left .\frac{1}{2} \sin ^{-1}\left (\frac{\sqrt{b} x^2}{\sqrt{a}}\right )\right |2\right )}{\sqrt{b} \left (a-b x^4\right )^{3/4}} \]
Antiderivative was successfully verified.
[In] Int[x/(a - b*x^4)^(3/4),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 9.10553, size = 49, normalized size = 0.83 \[ \frac{\sqrt{a} \left (1 - \frac{b x^{4}}{a}\right )^{\frac{3}{4}} F\left (\frac{\operatorname{asin}{\left (\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right )}}{2}\middle | 2\right )}{\sqrt{b} \left (a - b x^{4}\right )^{\frac{3}{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(-b*x**4+a)**(3/4),x)
[Out]
_______________________________________________________________________________________
Mathematica [C] time = 0.0321628, size = 53, normalized size = 0.9 \[ \frac{x^2 \left (\frac{a-b x^4}{a}\right )^{3/4} \, _2F_1\left (\frac{1}{2},\frac{3}{4};\frac{3}{2};\frac{b x^4}{a}\right )}{2 \left (a-b x^4\right )^{3/4}} \]
Antiderivative was successfully verified.
[In] Integrate[x/(a - b*x^4)^(3/4),x]
[Out]
_______________________________________________________________________________________
Maple [F] time = 0.032, size = 0, normalized size = 0. \[ \int{x \left ( -b{x}^{4}+a \right ) ^{-{\frac{3}{4}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(-b*x^4+a)^(3/4),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x}{{\left (-b x^{4} + a\right )}^{\frac{3}{4}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(-b*x^4 + a)^(3/4),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{x}{{\left (-b x^{4} + a\right )}^{\frac{3}{4}}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(-b*x^4 + a)^(3/4),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 2.40522, size = 29, normalized size = 0.49 \[ \frac{x^{2}{{}_{2}F_{1}\left (\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{3}{2} \end{matrix}\middle |{\frac{b x^{4} e^{2 i \pi }}{a}} \right )}}{2 a^{\frac{3}{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(-b*x**4+a)**(3/4),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x}{{\left (-b x^{4} + a\right )}^{\frac{3}{4}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(-b*x^4 + a)^(3/4),x, algorithm="giac")
[Out]