Optimal. Leaf size=21 \[ \frac{3}{5} a x^{5/3}+\frac{3}{8} b x^{8/3} \]
[Out]
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Rubi [A] time = 0.0133689, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{3}{5} a x^{5/3}+\frac{3}{8} b x^{8/3} \]
Antiderivative was successfully verified.
[In] Int[x^(2/3)*(a + b*x),x]
[Out]
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Rubi in Sympy [A] time = 2.42239, size = 19, normalized size = 0.9 \[ \frac{3 a x^{\frac{5}{3}}}{5} + \frac{3 b x^{\frac{8}{3}}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(2/3)*(b*x+a),x)
[Out]
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Mathematica [A] time = 0.00510021, size = 17, normalized size = 0.81 \[ \frac{3}{40} x^{5/3} (8 a+5 b x) \]
Antiderivative was successfully verified.
[In] Integrate[x^(2/3)*(a + b*x),x]
[Out]
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Maple [A] time = 0.005, size = 14, normalized size = 0.7 \[{\frac{15\,bx+24\,a}{40}{x}^{{\frac{5}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(2/3)*(b*x+a),x)
[Out]
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Maxima [A] time = 1.34303, size = 18, normalized size = 0.86 \[ \frac{3}{8} \, b x^{\frac{8}{3}} + \frac{3}{5} \, a x^{\frac{5}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*x^(2/3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.203833, size = 22, normalized size = 1.05 \[ \frac{3}{40} \,{\left (5 \, b x^{2} + 8 \, a x\right )} x^{\frac{2}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*x^(2/3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.82854, size = 19, normalized size = 0.9 \[ \frac{3 a x^{\frac{5}{3}}}{5} + \frac{3 b x^{\frac{8}{3}}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**(2/3)*(b*x+a),x)
[Out]
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GIAC/XCAS [A] time = 0.207311, size = 18, normalized size = 0.86 \[ \frac{3}{8} \, b x^{\frac{8}{3}} + \frac{3}{5} \, a x^{\frac{5}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)*x^(2/3),x, algorithm="giac")
[Out]