Optimal. Leaf size=38 \[ \frac{3 (b x-a)^{5/3}}{5 b^2}+\frac{3 a (b x-a)^{2/3}}{2 b^2} \]
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Rubi [A] time = 0.0273403, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{3 (b x-a)^{5/3}}{5 b^2}+\frac{3 a (b x-a)^{2/3}}{2 b^2} \]
Antiderivative was successfully verified.
[In] Int[x/(-a + b*x)^(1/3),x]
[Out]
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Rubi in Sympy [A] time = 5.19663, size = 31, normalized size = 0.82 \[ \frac{3 a \left (- a + b x\right )^{\frac{2}{3}}}{2 b^{2}} + \frac{3 \left (- a + b x\right )^{\frac{5}{3}}}{5 b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(b*x-a)**(1/3),x)
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Mathematica [A] time = 0.0133036, size = 26, normalized size = 0.68 \[ \frac{3 (b x-a)^{2/3} (3 a+2 b x)}{10 b^2} \]
Antiderivative was successfully verified.
[In] Integrate[x/(-a + b*x)^(1/3),x]
[Out]
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Maple [A] time = 0.004, size = 23, normalized size = 0.6 \[{\frac{6\,bx+9\,a}{10\,{b}^{2}} \left ( bx-a \right ) ^{{\frac{2}{3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(b*x-a)^(1/3),x)
[Out]
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Maxima [A] time = 1.33791, size = 41, normalized size = 1.08 \[ \frac{3 \,{\left (b x - a\right )}^{\frac{5}{3}}}{5 \, b^{2}} + \frac{3 \,{\left (b x - a\right )}^{\frac{2}{3}} a}{2 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x - a)^(1/3),x, algorithm="maxima")
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Fricas [A] time = 0.20897, size = 30, normalized size = 0.79 \[ \frac{3 \,{\left (2 \, b x + 3 \, a\right )}{\left (b x - a\right )}^{\frac{2}{3}}}{10 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x - a)^(1/3),x, algorithm="fricas")
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Sympy [A] time = 3.92547, size = 389, normalized size = 10.24 \[ \begin{cases} - \frac{9 a^{\frac{11}{3}} \left (-1 + \frac{b x}{a}\right )^{\frac{2}{3}}}{- 10 a^{2} b^{2} + 10 a b^{3} x} - \frac{9 a^{\frac{11}{3}} e^{\frac{5 i \pi }{3}}}{- 10 a^{2} b^{2} + 10 a b^{3} x} + \frac{3 a^{\frac{8}{3}} b x \left (-1 + \frac{b x}{a}\right )^{\frac{2}{3}}}{- 10 a^{2} b^{2} + 10 a b^{3} x} + \frac{9 a^{\frac{8}{3}} b x e^{\frac{5 i \pi }{3}}}{- 10 a^{2} b^{2} + 10 a b^{3} x} + \frac{6 a^{\frac{5}{3}} b^{2} x^{2} \left (-1 + \frac{b x}{a}\right )^{\frac{2}{3}}}{- 10 a^{2} b^{2} + 10 a b^{3} x} & \text{for}\: \left |{\frac{b x}{a}}\right | > 1 \\\frac{9 a^{\frac{11}{3}} \left (1 - \frac{b x}{a}\right )^{\frac{2}{3}} e^{\frac{5 i \pi }{3}}}{- 10 a^{2} b^{2} + 10 a b^{3} x} - \frac{9 a^{\frac{11}{3}} e^{\frac{5 i \pi }{3}}}{- 10 a^{2} b^{2} + 10 a b^{3} x} - \frac{3 a^{\frac{8}{3}} b x \left (1 - \frac{b x}{a}\right )^{\frac{2}{3}} e^{\frac{5 i \pi }{3}}}{- 10 a^{2} b^{2} + 10 a b^{3} x} + \frac{9 a^{\frac{8}{3}} b x e^{\frac{5 i \pi }{3}}}{- 10 a^{2} b^{2} + 10 a b^{3} x} - \frac{6 a^{\frac{5}{3}} b^{2} x^{2} \left (1 - \frac{b x}{a}\right )^{\frac{2}{3}} e^{\frac{5 i \pi }{3}}}{- 10 a^{2} b^{2} + 10 a b^{3} x} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x-a)**(1/3),x)
[Out]
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GIAC/XCAS [A] time = 0.204289, size = 39, normalized size = 1.03 \[ \frac{3 \,{\left (2 \,{\left (b x - a\right )}^{\frac{5}{3}} + 5 \,{\left (b x - a\right )}^{\frac{2}{3}} a\right )}}{10 \, b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x - a)^(1/3),x, algorithm="giac")
[Out]