Optimal. Leaf size=57 \[ \frac{9 \left (a+b x^2\right )^{4/3}}{8 a^2 c (c x)^{8/3}}-\frac{3 \sqrt [3]{a+b x^2}}{2 a c (c x)^{8/3}} \]
[Out]
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Rubi [A] time = 0.0575739, antiderivative size = 57, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105 \[ \frac{9 \left (a+b x^2\right )^{4/3}}{8 a^2 c (c x)^{8/3}}-\frac{3 \sqrt [3]{a+b x^2}}{2 a c (c x)^{8/3}} \]
Antiderivative was successfully verified.
[In] Int[1/((c*x)^(11/3)*(a + b*x^2)^(2/3)),x]
[Out]
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Rubi in Sympy [A] time = 6.6536, size = 48, normalized size = 0.84 \[ - \frac{3 \sqrt [3]{a + b x^{2}}}{2 a c \left (c x\right )^{\frac{8}{3}}} + \frac{9 \left (a + b x^{2}\right )^{\frac{4}{3}}}{8 a^{2} c \left (c x\right )^{\frac{8}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(c*x)**(11/3)/(b*x**2+a)**(2/3),x)
[Out]
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Mathematica [A] time = 0.0372911, size = 34, normalized size = 0.6 \[ -\frac{3 x \left (a-3 b x^2\right ) \sqrt [3]{a+b x^2}}{8 a^2 (c x)^{11/3}} \]
Antiderivative was successfully verified.
[In] Integrate[1/((c*x)^(11/3)*(a + b*x^2)^(2/3)),x]
[Out]
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Maple [A] time = 0.007, size = 29, normalized size = 0.5 \[ -{\frac{3\,x \left ( -3\,b{x}^{2}+a \right ) }{8\,{a}^{2}}\sqrt [3]{b{x}^{2}+a} \left ( cx \right ) ^{-{\frac{11}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(c*x)^(11/3)/(b*x^2+a)^(2/3),x)
[Out]
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Maxima [A] time = 1.39331, size = 51, normalized size = 0.89 \[ \frac{3 \,{\left (\frac{4 \,{\left (b x^{2} + a\right )}^{\frac{1}{3}} b}{x^{\frac{2}{3}}} - \frac{{\left (b x^{2} + a\right )}^{\frac{4}{3}}}{x^{\frac{8}{3}}}\right )}}{8 \, a^{2} c^{\frac{11}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^2 + a)^(2/3)*(c*x)^(11/3)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.229495, size = 47, normalized size = 0.82 \[ \frac{3 \,{\left (3 \, b x^{2} - a\right )}{\left (b x^{2} + a\right )}^{\frac{1}{3}} \left (c x\right )^{\frac{1}{3}}}{8 \, a^{2} c^{4} x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^2 + a)^(2/3)*(c*x)^(11/3)),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(c*x)**(11/3)/(b*x**2+a)**(2/3),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (b x^{2} + a\right )}^{\frac{2}{3}} \left (c x\right )^{\frac{11}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^2 + a)^(2/3)*(c*x)^(11/3)),x, algorithm="giac")
[Out]