Optimal. Leaf size=109 \[ \frac{a^{3/2} x \sqrt [4]{1-\frac{a}{b x^4}} E\left (\left .\frac{1}{2} \csc ^{-1}\left (\frac{\sqrt{b} x^2}{\sqrt{a}}\right )\right |2\right )}{4 b^{3/2} \sqrt [4]{a-b x^4}}-\frac{a \left (a-b x^4\right )^{3/4}}{4 b^2 x}-\frac{x^3 \left (a-b x^4\right )^{3/4}}{6 b} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.153926, antiderivative size = 109, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 6, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.375 \[ \frac{a^{3/2} x \sqrt [4]{1-\frac{a}{b x^4}} E\left (\left .\frac{1}{2} \csc ^{-1}\left (\frac{\sqrt{b} x^2}{\sqrt{a}}\right )\right |2\right )}{4 b^{3/2} \sqrt [4]{a-b x^4}}-\frac{a \left (a-b x^4\right )^{3/4}}{4 b^2 x}-\frac{x^3 \left (a-b x^4\right )^{3/4}}{6 b} \]
Antiderivative was successfully verified.
[In] Int[x^6/(a - b*x^4)^(1/4),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 19.6817, size = 88, normalized size = 0.81 \[ \frac{a^{\frac{3}{2}} x \sqrt [4]{- \frac{a}{b x^{4}} + 1} E\left (\frac{\operatorname{asin}{\left (\frac{\sqrt{a}}{\sqrt{b} x^{2}} \right )}}{2}\middle | 2\right )}{4 b^{\frac{3}{2}} \sqrt [4]{a - b x^{4}}} - \frac{a \left (a - b x^{4}\right )^{\frac{3}{4}}}{4 b^{2} x} - \frac{x^{3} \left (a - b x^{4}\right )^{\frac{3}{4}}}{6 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**6/(-b*x**4+a)**(1/4),x)
[Out]
_______________________________________________________________________________________
Mathematica [C] time = 0.0527921, size = 66, normalized size = 0.61 \[ \frac{x^3 \left (a \sqrt [4]{1-\frac{b x^4}{a}} \, _2F_1\left (\frac{1}{4},\frac{3}{4};\frac{7}{4};\frac{b x^4}{a}\right )-a+b x^4\right )}{6 b \sqrt [4]{a-b x^4}} \]
Antiderivative was successfully verified.
[In] Integrate[x^6/(a - b*x^4)^(1/4),x]
[Out]
_______________________________________________________________________________________
Maple [F] time = 0.043, size = 0, normalized size = 0. \[ \int{{x}^{6}{\frac{1}{\sqrt [4]{-b{x}^{4}+a}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^6/(-b*x^4+a)^(1/4),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{6}}{{\left (-b x^{4} + a\right )}^{\frac{1}{4}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^6/(-b*x^4 + a)^(1/4),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{x^{6}}{{\left (-b x^{4} + a\right )}^{\frac{1}{4}}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^6/(-b*x^4 + a)^(1/4),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 3.05551, size = 39, normalized size = 0.36 \[ \frac{x^{7} \Gamma \left (\frac{7}{4}\right ){{}_{2}F_{1}\left (\begin{matrix} \frac{1}{4}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle |{\frac{b x^{4} e^{2 i \pi }}{a}} \right )}}{4 \sqrt [4]{a} \Gamma \left (\frac{11}{4}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**6/(-b*x**4+a)**(1/4),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{6}}{{\left (-b x^{4} + a\right )}^{\frac{1}{4}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^6/(-b*x^4 + a)^(1/4),x, algorithm="giac")
[Out]