Optimal. Leaf size=25 \[ \frac{\left (a x^3+b x^6\right )^{5/3}}{5 b x^5} \]
[Out]
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Rubi [A] time = 0.0126025, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{\left (a x^3+b x^6\right )^{5/3}}{5 b x^5} \]
Antiderivative was successfully verified.
[In] Int[(a*x^3 + b*x^6)^(2/3),x]
[Out]
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Rubi in Sympy [A] time = 1.37952, size = 19, normalized size = 0.76 \[ \frac{\left (a x^{3} + b x^{6}\right )^{\frac{5}{3}}}{5 b x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**6+a*x**3)**(2/3),x)
[Out]
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Mathematica [A] time = 0.0160823, size = 25, normalized size = 1. \[ \frac{\left (x^3 \left (a+b x^3\right )\right )^{5/3}}{5 b x^5} \]
Antiderivative was successfully verified.
[In] Integrate[(a*x^3 + b*x^6)^(2/3),x]
[Out]
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Maple [A] time = 0.006, size = 29, normalized size = 1.2 \[{\frac{b{x}^{3}+a}{5\,b{x}^{2}} \left ( b{x}^{6}+a{x}^{3} \right ) ^{{\frac{2}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^6+a*x^3)^(2/3),x)
[Out]
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Maxima [A] time = 0.771503, size = 19, normalized size = 0.76 \[ \frac{{\left (b x^{3} + a\right )}^{\frac{5}{3}}}{5 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^6 + a*x^3)^(2/3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.263995, size = 38, normalized size = 1.52 \[ \frac{{\left (b x^{6} + a x^{3}\right )}^{\frac{2}{3}}{\left (b x^{3} + a\right )}}{5 \, b x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^6 + a*x^3)^(2/3),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \left (a x^{3} + b x^{6}\right )^{\frac{2}{3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**6+a*x**3)**(2/3),x)
[Out]
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GIAC/XCAS [A] time = 0.285731, size = 19, normalized size = 0.76 \[ \frac{{\left (b x^{3} + a\right )}^{\frac{5}{3}}}{5 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^6 + a*x^3)^(2/3),x, algorithm="giac")
[Out]