Optimal. Leaf size=104 \[ \frac{4 a^{5/2} \left (\frac{b x^4}{a}+1\right )^{3/4} F\left (\left .\frac{1}{2} \tan ^{-1}\left (\frac{\sqrt{b} x^2}{\sqrt{a}}\right )\right |2\right )}{7 b^{5/2} \left (a+b x^4\right )^{3/4}}-\frac{2 a x^2 \sqrt [4]{a+b x^4}}{7 b^2}+\frac{x^6 \sqrt [4]{a+b x^4}}{7 b} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.151385, antiderivative size = 104, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 4, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.267 \[ \frac{4 a^{5/2} \left (\frac{b x^4}{a}+1\right )^{3/4} F\left (\left .\frac{1}{2} \tan ^{-1}\left (\frac{\sqrt{b} x^2}{\sqrt{a}}\right )\right |2\right )}{7 b^{5/2} \left (a+b x^4\right )^{3/4}}-\frac{2 a x^2 \sqrt [4]{a+b x^4}}{7 b^2}+\frac{x^6 \sqrt [4]{a+b x^4}}{7 b} \]
Antiderivative was successfully verified.
[In] Int[x^9/(a + b*x^4)^(3/4),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 14.8906, size = 92, normalized size = 0.88 \[ \frac{4 a^{\frac{5}{2}} \left (1 + \frac{b x^{4}}{a}\right )^{\frac{3}{4}} F\left (\frac{\operatorname{atan}{\left (\frac{\sqrt{b} x^{2}}{\sqrt{a}} \right )}}{2}\middle | 2\right )}{7 b^{\frac{5}{2}} \left (a + b x^{4}\right )^{\frac{3}{4}}} - \frac{2 a x^{2} \sqrt [4]{a + b x^{4}}}{7 b^{2}} + \frac{x^{6} \sqrt [4]{a + b x^{4}}}{7 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**9/(b*x**4+a)**(3/4),x)
[Out]
_______________________________________________________________________________________
Mathematica [C] time = 0.0585937, size = 79, normalized size = 0.76 \[ \frac{x^2 \left (2 a^2 \left (\frac{b x^4}{a}+1\right )^{3/4} \, _2F_1\left (\frac{1}{2},\frac{3}{4};\frac{3}{2};-\frac{b x^4}{a}\right )-2 a^2-a b x^4+b^2 x^8\right )}{7 b^2 \left (a+b x^4\right )^{3/4}} \]
Antiderivative was successfully verified.
[In] Integrate[x^9/(a + b*x^4)^(3/4),x]
[Out]
_______________________________________________________________________________________
Maple [F] time = 0.037, size = 0, normalized size = 0. \[ \int{{x}^{9} \left ( b{x}^{4}+a \right ) ^{-{\frac{3}{4}}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^9/(b*x^4+a)^(3/4),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{9}}{{\left (b x^{4} + a\right )}^{\frac{3}{4}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(b*x^4 + a)^(3/4),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{x^{9}}{{\left (b x^{4} + a\right )}^{\frac{3}{4}}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(b*x^4 + a)^(3/4),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 4.27567, size = 27, normalized size = 0.26 \[ \frac{x^{10}{{}_{2}F_{1}\left (\begin{matrix} \frac{3}{4}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle |{\frac{b x^{4} e^{i \pi }}{a}} \right )}}{10 a^{\frac{3}{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**9/(b*x**4+a)**(3/4),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{9}}{{\left (b x^{4} + a\right )}^{\frac{3}{4}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^9/(b*x^4 + a)^(3/4),x, algorithm="giac")
[Out]