Optimal. Leaf size=18 \[ \frac{3 (b x-a)^{2/3}}{2 b} \]
[Out]
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Rubi [A] time = 0.00718682, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{3 (b x-a)^{2/3}}{2 b} \]
Antiderivative was successfully verified.
[In] Int[(-a + b*x)^(-1/3),x]
[Out]
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Rubi in Sympy [A] time = 1.22866, size = 12, normalized size = 0.67 \[ \frac{3 \left (- a + b x\right )^{\frac{2}{3}}}{2 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x-a)**(1/3),x)
[Out]
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Mathematica [A] time = 0.00288401, size = 18, normalized size = 1. \[ \frac{3 (b x-a)^{2/3}}{2 b} \]
Antiderivative was successfully verified.
[In] Integrate[(-a + b*x)^(-1/3),x]
[Out]
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Maple [A] time = 0.004, size = 15, normalized size = 0.8 \[{\frac{3}{2\,b} \left ( bx-a \right ) ^{{\frac{2}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*x-a)^(1/3),x)
[Out]
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Maxima [A] time = 1.34011, size = 19, normalized size = 1.06 \[ \frac{3 \,{\left (b x - a\right )}^{\frac{2}{3}}}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x - a)^(-1/3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.207001, size = 19, normalized size = 1.06 \[ \frac{3 \,{\left (b x - a\right )}^{\frac{2}{3}}}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x - a)^(-1/3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.075599, size = 12, normalized size = 0.67 \[ \frac{3 \left (- a + b x\right )^{\frac{2}{3}}}{2 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x-a)**(1/3),x)
[Out]
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GIAC/XCAS [A] time = 0.206458, size = 19, normalized size = 1.06 \[ \frac{3 \,{\left (b x - a\right )}^{\frac{2}{3}}}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x - a)^(-1/3),x, algorithm="giac")
[Out]