Optimal. Leaf size=57 \[ -\frac{a^2}{2 b^3 \sqrt{a+b x^4}}-\frac{a \sqrt{a+b x^4}}{b^3}+\frac{\left (a+b x^4\right )^{3/2}}{6 b^3} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0846349, antiderivative size = 57, 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 \[ -\frac{a^2}{2 b^3 \sqrt{a+b x^4}}-\frac{a \sqrt{a+b x^4}}{b^3}+\frac{\left (a+b x^4\right )^{3/2}}{6 b^3} \]
Antiderivative was successfully verified.
[In] Int[x^11/(a + b*x^4)^(3/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 10.5486, size = 48, normalized size = 0.84 \[ - \frac{a^{2}}{2 b^{3} \sqrt{a + b x^{4}}} - \frac{a \sqrt{a + b x^{4}}}{b^{3}} + \frac{\left (a + b x^{4}\right )^{\frac{3}{2}}}{6 b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**11/(b*x**4+a)**(3/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0342107, size = 38, normalized size = 0.67 \[ \frac{-8 a^2-4 a b x^4+b^2 x^8}{6 b^3 \sqrt{a+b x^4}} \]
Antiderivative was successfully verified.
[In] Integrate[x^11/(a + b*x^4)^(3/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.008, size = 36, normalized size = 0.6 \[ -{\frac{-{b}^{2}{x}^{8}+4\,ab{x}^{4}+8\,{a}^{2}}{6\,{b}^{3}}{\frac{1}{\sqrt{b{x}^{4}+a}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^11/(b*x^4+a)^(3/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.4311, size = 63, normalized size = 1.11 \[ \frac{{\left (b x^{4} + a\right )}^{\frac{3}{2}}}{6 \, b^{3}} - \frac{\sqrt{b x^{4} + a} a}{b^{3}} - \frac{a^{2}}{2 \, \sqrt{b x^{4} + a} b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(b*x^4 + a)^(3/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.265801, size = 46, normalized size = 0.81 \[ \frac{b^{2} x^{8} - 4 \, a b x^{4} - 8 \, a^{2}}{6 \, \sqrt{b x^{4} + a} b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(b*x^4 + a)^(3/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 10.1977, size = 68, normalized size = 1.19 \[ \begin{cases} - \frac{4 a^{2}}{3 b^{3} \sqrt{a + b x^{4}}} - \frac{2 a x^{4}}{3 b^{2} \sqrt{a + b x^{4}}} + \frac{x^{8}}{6 b \sqrt{a + b x^{4}}} & \text{for}\: b \neq 0 \\\frac{x^{12}}{12 a^{\frac{3}{2}}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**11/(b*x**4+a)**(3/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.222902, size = 55, normalized size = 0.96 \[ \frac{{\left (b x^{4} + a\right )}^{\frac{3}{2}} - 6 \, \sqrt{b x^{4} + a} a - \frac{3 \, a^{2}}{\sqrt{b x^{4} + a}}}{6 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^11/(b*x^4 + a)^(3/2),x, algorithm="giac")
[Out]