Optimal. Leaf size=92 \[ \frac{81 b^3 \sqrt [3]{a+b x^3}}{140 a^4 x}-\frac{27 b^2 \sqrt [3]{a+b x^3}}{140 a^3 x^4}+\frac{9 b \sqrt [3]{a+b x^3}}{70 a^2 x^7}-\frac{\sqrt [3]{a+b x^3}}{10 a x^{10}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0941144, antiderivative size = 92, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{81 b^3 \sqrt [3]{a+b x^3}}{140 a^4 x}-\frac{27 b^2 \sqrt [3]{a+b x^3}}{140 a^3 x^4}+\frac{9 b \sqrt [3]{a+b x^3}}{70 a^2 x^7}-\frac{\sqrt [3]{a+b x^3}}{10 a x^{10}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^11*(a + b*x^3)^(2/3)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 9.74862, size = 83, normalized size = 0.9 \[ - \frac{\sqrt [3]{a + b x^{3}}}{10 a x^{10}} + \frac{9 b \sqrt [3]{a + b x^{3}}}{70 a^{2} x^{7}} - \frac{27 b^{2} \sqrt [3]{a + b x^{3}}}{140 a^{3} x^{4}} + \frac{81 b^{3} \sqrt [3]{a + b x^{3}}}{140 a^{4} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**11/(b*x**3+a)**(2/3),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0372198, size = 53, normalized size = 0.58 \[ \frac{\sqrt [3]{a+b x^3} \left (-14 a^3+18 a^2 b x^3-27 a b^2 x^6+81 b^3 x^9\right )}{140 a^4 x^{10}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^11*(a + b*x^3)^(2/3)),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.008, size = 50, normalized size = 0.5 \[ -{\frac{-81\,{b}^{3}{x}^{9}+27\,a{b}^{2}{x}^{6}-18\,{a}^{2}b{x}^{3}+14\,{a}^{3}}{140\,{x}^{10}{a}^{4}}\sqrt [3]{b{x}^{3}+a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^11/(b*x^3+a)^(2/3),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43711, size = 93, normalized size = 1.01 \[ \frac{\frac{140 \,{\left (b x^{3} + a\right )}^{\frac{1}{3}} b^{3}}{x} - \frac{105 \,{\left (b x^{3} + a\right )}^{\frac{4}{3}} b^{2}}{x^{4}} + \frac{60 \,{\left (b x^{3} + a\right )}^{\frac{7}{3}} b}{x^{7}} - \frac{14 \,{\left (b x^{3} + a\right )}^{\frac{10}{3}}}{x^{10}}}{140 \, a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^3 + a)^(2/3)*x^11),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.237884, size = 66, normalized size = 0.72 \[ \frac{{\left (81 \, b^{3} x^{9} - 27 \, a b^{2} x^{6} + 18 \, a^{2} b x^{3} - 14 \, a^{3}\right )}{\left (b x^{3} + a\right )}^{\frac{1}{3}}}{140 \, a^{4} x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^3 + a)^(2/3)*x^11),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 11.5598, size = 692, normalized size = 7.52 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**11/(b*x**3+a)**(2/3),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x^{3} + a\right )}^{\frac{2}{3}} x^{11}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^3 + a)^(2/3)*x^11),x, algorithm="giac")
[Out]