Optimal. Leaf size=56 \[ \frac{a^2 \sqrt [4]{a+b x^4}}{b^3}+\frac{\left (a+b x^4\right )^{9/4}}{9 b^3}-\frac{2 a \left (a+b x^4\right )^{5/4}}{5 b^3} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0852534, antiderivative size = 56, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{a^2 \sqrt [4]{a+b x^4}}{b^3}+\frac{\left (a+b x^4\right )^{9/4}}{9 b^3}-\frac{2 a \left (a+b x^4\right )^{5/4}}{5 b^3} \]
Antiderivative was successfully verified.
[In] Int[x^11/(a + b*x^4)^(3/4),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 10.5072, size = 49, normalized size = 0.88 \[ \frac{a^{2} \sqrt [4]{a + b x^{4}}}{b^{3}} - \frac{2 a \left (a + b x^{4}\right )^{\frac{5}{4}}}{5 b^{3}} + \frac{\left (a + b x^{4}\right )^{\frac{9}{4}}}{9 b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**11/(b*x**4+a)**(3/4),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0268645, size = 39, normalized size = 0.7 \[ \frac{\sqrt [4]{a+b x^4} \left (32 a^2-8 a b x^4+5 b^2 x^8\right )}{45 b^3} \]
Antiderivative was successfully verified.
[In] Integrate[x^11/(a + b*x^4)^(3/4),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.008, size = 36, normalized size = 0.6 \[{\frac{5\,{b}^{2}{x}^{8}-8\,ab{x}^{4}+32\,{a}^{2}}{45\,{b}^{3}}\sqrt [4]{b{x}^{4}+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^11/(b*x^4+a)^(3/4),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.41126, size = 62, normalized size = 1.11 \[ \frac{{\left (b x^{4} + a\right )}^{\frac{9}{4}}}{9 \, b^{3}} - \frac{2 \,{\left (b x^{4} + a\right )}^{\frac{5}{4}} a}{5 \, b^{3}} + \frac{{\left (b x^{4} + a\right )}^{\frac{1}{4}} a^{2}}{b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(b*x^4 + a)^(3/4),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.228284, size = 47, normalized size = 0.84 \[ \frac{{\left (5 \, b^{2} x^{8} - 8 \, a b x^{4} + 32 \, a^{2}\right )}{\left (b x^{4} + a\right )}^{\frac{1}{4}}}{45 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(b*x^4 + a)^(3/4),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 9.98532, size = 68, normalized size = 1.21 \[ \begin{cases} \frac{32 a^{2} \sqrt [4]{a + b x^{4}}}{45 b^{3}} - \frac{8 a x^{4} \sqrt [4]{a + b x^{4}}}{45 b^{2}} + \frac{x^{8} \sqrt [4]{a + b x^{4}}}{9 b} & \text{for}\: b \neq 0 \\\frac{x^{12}}{12 a^{\frac{3}{4}}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**11/(b*x**4+a)**(3/4),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.214636, size = 58, normalized size = 1.04 \[ \frac{5 \,{\left (b x^{4} + a\right )}^{\frac{9}{4}} - 18 \,{\left (b x^{4} + a\right )}^{\frac{5}{4}} a + 45 \,{\left (b x^{4} + a\right )}^{\frac{1}{4}} a^{2}}{45 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(b*x^4 + a)^(3/4),x, algorithm="giac")
[Out]