Optimal. Leaf size=85 \[ -\frac{27 \left (a+b x^2\right )^{10/3}}{280 a^3 c (c x)^{20/3}}+\frac{9 \left (a+b x^2\right )^{7/3}}{28 a^2 c (c x)^{20/3}}-\frac{3 \left (a+b x^2\right )^{4/3}}{8 a c (c x)^{20/3}} \]
[Out]
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Rubi [A] time = 0.0897418, antiderivative size = 85, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105 \[ -\frac{27 \left (a+b x^2\right )^{10/3}}{280 a^3 c (c x)^{20/3}}+\frac{9 \left (a+b x^2\right )^{7/3}}{28 a^2 c (c x)^{20/3}}-\frac{3 \left (a+b x^2\right )^{4/3}}{8 a c (c x)^{20/3}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x^2)^(1/3)/(c*x)^(23/3),x]
[Out]
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Rubi in Sympy [A] time = 10.6772, size = 73, normalized size = 0.86 \[ - \frac{3 \left (a + b x^{2}\right )^{\frac{4}{3}}}{8 a c \left (c x\right )^{\frac{20}{3}}} + \frac{9 \left (a + b x^{2}\right )^{\frac{7}{3}}}{28 a^{2} c \left (c x\right )^{\frac{20}{3}}} - \frac{27 \left (a + b x^{2}\right )^{\frac{10}{3}}}{280 a^{3} c \left (c x\right )^{\frac{20}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**(1/3)/(c*x)**(23/3),x)
[Out]
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Mathematica [A] time = 0.0486502, size = 63, normalized size = 0.74 \[ -\frac{3 \sqrt [3]{c x} \sqrt [3]{a+b x^2} \left (14 a^3+2 a^2 b x^2-3 a b^2 x^4+9 b^3 x^6\right )}{280 a^3 c^8 x^7} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x^2)^(1/3)/(c*x)^(23/3),x]
[Out]
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Maple [A] time = 0.009, size = 42, normalized size = 0.5 \[ -{\frac{3\,x \left ( 9\,{b}^{2}{x}^{4}-12\,ab{x}^{2}+14\,{a}^{2} \right ) }{280\,{a}^{3}} \left ( b{x}^{2}+a \right ) ^{{\frac{4}{3}}} \left ( cx \right ) ^{-{\frac{23}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^(1/3)/(c*x)^(23/3),x)
[Out]
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Maxima [A] time = 1.40159, size = 74, normalized size = 0.87 \[ -\frac{3 \,{\left (\frac{35 \,{\left (b x^{2} + a\right )}^{\frac{4}{3}} b^{2}}{x^{\frac{8}{3}}} - \frac{40 \,{\left (b x^{2} + a\right )}^{\frac{7}{3}} b}{x^{\frac{14}{3}}} + \frac{14 \,{\left (b x^{2} + a\right )}^{\frac{10}{3}}}{x^{\frac{20}{3}}}\right )}}{280 \, a^{3} c^{\frac{23}{3}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^(1/3)/(c*x)^(23/3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.230776, size = 77, normalized size = 0.91 \[ -\frac{3 \,{\left (9 \, b^{3} x^{6} - 3 \, a b^{2} x^{4} + 2 \, a^{2} b x^{2} + 14 \, a^{3}\right )}{\left (b x^{2} + a\right )}^{\frac{1}{3}} \left (c x\right )^{\frac{1}{3}}}{280 \, a^{3} c^{8} x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^(1/3)/(c*x)^(23/3),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((b*x**2+a)**(1/3)/(c*x)**(23/3),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (b x^{2} + a\right )}^{\frac{1}{3}}}{\left (c x\right )^{\frac{23}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^2 + a)^(1/3)/(c*x)^(23/3),x, algorithm="giac")
[Out]