Optimal. Leaf size=86 \[ -\frac{2 b^{3/2} x \sqrt [4]{1-\frac{a}{b x^4}} E\left (\left .\frac{1}{2} \csc ^{-1}\left (\frac{\sqrt{b} x^2}{\sqrt{a}}\right )\right |2\right )}{5 a^{3/2} \sqrt [4]{a-b x^4}}-\frac{\left (a-b x^4\right )^{3/4}}{5 a x^5} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.121565, antiderivative size = 86, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 5, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.312 \[ -\frac{2 b^{3/2} x \sqrt [4]{1-\frac{a}{b x^4}} E\left (\left .\frac{1}{2} \csc ^{-1}\left (\frac{\sqrt{b} x^2}{\sqrt{a}}\right )\right |2\right )}{5 a^{3/2} \sqrt [4]{a-b x^4}}-\frac{\left (a-b x^4\right )^{3/4}}{5 a x^5} \]
Antiderivative was successfully verified.
[In] Int[1/(x^6*(a - b*x^4)^(1/4)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 16.1433, size = 73, normalized size = 0.85 \[ - \frac{\left (a - b x^{4}\right )^{\frac{3}{4}}}{5 a x^{5}} - \frac{2 b^{\frac{3}{2}} x \sqrt [4]{- \frac{a}{b x^{4}} + 1} E\left (\frac{\operatorname{asin}{\left (\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right )}}{2}\middle | 2\right )}{5 a^{\frac{3}{2}} \sqrt [4]{a - b x^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**6/(-b*x**4+a)**(1/4),x)
[Out]
_______________________________________________________________________________________
Mathematica [C] time = 0.0629119, size = 84, normalized size = 0.98 \[ \frac{-3 \left (a^2+a b x^4-2 b^2 x^8\right )-4 b^2 x^8 \sqrt [4]{1-\frac{b x^4}{a}} \, _2F_1\left (\frac{1}{4},\frac{3}{4};\frac{7}{4};\frac{b x^4}{a}\right )}{15 a^2 x^5 \sqrt [4]{a-b x^4}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^6*(a - b*x^4)^(1/4)),x]
[Out]
_______________________________________________________________________________________
Maple [F] time = 0.054, size = 0, normalized size = 0. \[ \int{\frac{1}{{x}^{6}}{\frac{1}{\sqrt [4]{-b{x}^{4}+a}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^6/(-b*x^4+a)^(1/4),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (-b x^{4} + a\right )}^{\frac{1}{4}} x^{6}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((-b*x^4 + a)^(1/4)*x^6),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{{\left (-b x^{4} + a\right )}^{\frac{1}{4}} x^{6}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((-b*x^4 + a)^(1/4)*x^6),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 4.04249, size = 34, normalized size = 0.4 \[ - \frac{i e^{\frac{5 i \pi }{4}}{{}_{2}F_{1}\left (\begin{matrix} \frac{1}{4}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle |{\frac{a}{b x^{4}}} \right )}}{6 \sqrt [4]{b} x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**6/(-b*x**4+a)**(1/4),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (-b x^{4} + a\right )}^{\frac{1}{4}} x^{6}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((-b*x^4 + a)^(1/4)*x^6),x, algorithm="giac")
[Out]