Optimal. Leaf size=21 \[ \frac{3}{2} a x^{2/3}+\frac{3}{5} b x^{5/3} \]
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Rubi [A] time = 0.0127264, 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 \[ \frac{3}{2} a x^{2/3}+\frac{3}{5} b x^{5/3} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)/x^(1/3),x]
[Out]
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Rubi in Sympy [A] time = 2.46658, size = 19, normalized size = 0.9 \[ \frac{3 a x^{\frac{2}{3}}}{2} + \frac{3 b x^{\frac{5}{3}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)/x**(1/3),x)
[Out]
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Mathematica [A] time = 0.00516613, size = 17, normalized size = 0.81 \[ \frac{3}{10} x^{2/3} (5 a+2 b x) \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)/x^(1/3),x]
[Out]
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Maple [A] time = 0.004, size = 14, normalized size = 0.7 \[{\frac{6\,bx+15\,a}{10}{x}^{{\frac{2}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)/x^(1/3),x)
[Out]
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Maxima [A] time = 1.34543, size = 18, normalized size = 0.86 \[ \frac{3}{5} \, b x^{\frac{5}{3}} + \frac{3}{2} \, a x^{\frac{2}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/x^(1/3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.204778, size = 18, normalized size = 0.86 \[ \frac{3}{10} \,{\left (2 \, b x + 5 \, a\right )} x^{\frac{2}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/x^(1/3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.60896, size = 19, normalized size = 0.9 \[ \frac{3 a x^{\frac{2}{3}}}{2} + \frac{3 b x^{\frac{5}{3}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)/x**(1/3),x)
[Out]
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GIAC/XCAS [A] time = 0.211454, size = 18, normalized size = 0.86 \[ \frac{3}{5} \, b x^{\frac{5}{3}} + \frac{3}{2} \, a x^{\frac{2}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/x^(1/3),x, algorithm="giac")
[Out]