Optimal. Leaf size=133 \[ \frac{3 b^{5/2} \left (1-\frac{b x^4}{a}\right )^{3/4} F\left (\left .\frac{1}{2} \sin ^{-1}\left (\frac{\sqrt{b} x^2}{\sqrt{a}}\right )\right |2\right )}{8 a^{5/2} \left (a-b x^4\right )^{3/4}}-\frac{3 b^2 \sqrt [4]{a-b x^4}}{8 a^3 x^2}-\frac{3 b \sqrt [4]{a-b x^4}}{20 a^2 x^6}-\frac{\sqrt [4]{a-b x^4}}{10 a x^{10}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.204491, antiderivative size = 133, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 4, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25 \[ \frac{3 b^{5/2} \left (1-\frac{b x^4}{a}\right )^{3/4} F\left (\left .\frac{1}{2} \sin ^{-1}\left (\frac{\sqrt{b} x^2}{\sqrt{a}}\right )\right |2\right )}{8 a^{5/2} \left (a-b x^4\right )^{3/4}}-\frac{3 b^2 \sqrt [4]{a-b x^4}}{8 a^3 x^2}-\frac{3 b \sqrt [4]{a-b x^4}}{20 a^2 x^6}-\frac{\sqrt [4]{a-b x^4}}{10 a x^{10}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^11*(a - b*x^4)^(3/4)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 23.0554, size = 116, normalized size = 0.87 \[ - \frac{\sqrt [4]{a - b x^{4}}}{10 a x^{10}} - \frac{3 b \sqrt [4]{a - b x^{4}}}{20 a^{2} x^{6}} - \frac{3 b^{2} \sqrt [4]{a - b x^{4}}}{8 a^{3} x^{2}} + \frac{3 b^{\frac{5}{2}} \left (1 - \frac{b x^{4}}{a}\right )^{\frac{3}{4}} F\left (\frac{\operatorname{asin}{\left (\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right )}}{2}\middle | 2\right )}{8 a^{\frac{5}{2}} \left (a - b x^{4}\right )^{\frac{3}{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**11/(-b*x**4+a)**(3/4),x)
[Out]
_______________________________________________________________________________________
Mathematica [C] time = 0.0695509, size = 95, normalized size = 0.71 \[ \frac{-8 a^3-4 a^2 b x^4+15 b^3 x^{12} \left (1-\frac{b x^4}{a}\right )^{3/4} \, _2F_1\left (\frac{1}{2},\frac{3}{4};\frac{3}{2};\frac{b x^4}{a}\right )-18 a b^2 x^8+30 b^3 x^{12}}{80 a^3 x^{10} \left (a-b x^4\right )^{3/4}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^11*(a - b*x^4)^(3/4)),x]
[Out]
_______________________________________________________________________________________
Maple [F] time = 0.039, size = 0, normalized size = 0. \[ \int{\frac{1}{{x}^{11}} \left ( -b{x}^{4}+a \right ) ^{-{\frac{3}{4}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^11/(-b*x^4+a)^(3/4),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (-b x^{4} + a\right )}^{\frac{3}{4}} x^{11}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((-b*x^4 + a)^(3/4)*x^11),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{{\left (-b x^{4} + a\right )}^{\frac{3}{4}} x^{11}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((-b*x^4 + a)^(3/4)*x^11),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 12.5245, size = 34, normalized size = 0.26 \[ - \frac{{{}_{2}F_{1}\left (\begin{matrix} - \frac{5}{2}, \frac{3}{4} \\ - \frac{3}{2} \end{matrix}\middle |{\frac{b x^{4} e^{2 i \pi }}{a}} \right )}}{10 a^{\frac{3}{4}} x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**11/(-b*x**4+a)**(3/4),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (-b x^{4} + a\right )}^{\frac{3}{4}} x^{11}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((-b*x^4 + a)^(3/4)*x^11),x, algorithm="giac")
[Out]