3.111 \(\int (b x)^{2/3} \, dx\)

Optimal. Leaf size=14 \[ \frac{3 (b x)^{5/3}}{5 b} \]

[Out]

(3*(b*x)^(5/3))/(5*b)

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Rubi [A]  time = 0.0067686, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ \frac{3 (b x)^{5/3}}{5 b} \]

Antiderivative was successfully verified.

[In]  Int[(b*x)^(2/3),x]

[Out]

(3*(b*x)^(5/3))/(5*b)

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Rubi in Sympy [A]  time = 1.3932, size = 10, normalized size = 0.71 \[ \frac{3 \left (b x\right )^{\frac{5}{3}}}{5 b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x)**(2/3),x)

[Out]

3*(b*x)**(5/3)/(5*b)

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Mathematica [A]  time = 0.00172695, size = 12, normalized size = 0.86 \[ \frac{3}{5} x (b x)^{2/3} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x)^(2/3),x]

[Out]

(3*x*(b*x)^(2/3))/5

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Maple [A]  time = 0.004, size = 9, normalized size = 0.6 \[{\frac{3\,x}{5} \left ( bx \right ) ^{{\frac{2}{3}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x)^(2/3),x)

[Out]

3/5*x*(b*x)^(2/3)

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Maxima [A]  time = 1.44325, size = 14, normalized size = 1. \[ \frac{3 \, \left (b x\right )^{\frac{5}{3}}}{5 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x)^(2/3),x, algorithm="maxima")

[Out]

3/5*(b*x)^(5/3)/b

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Fricas [A]  time = 0.216908, size = 11, normalized size = 0.79 \[ \frac{3}{5} \, \left (b x\right )^{\frac{2}{3}} x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x)^(2/3),x, algorithm="fricas")

[Out]

3/5*(b*x)^(2/3)*x

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Sympy [A]  time = 0.071018, size = 10, normalized size = 0.71 \[ \frac{3 \left (b x\right )^{\frac{5}{3}}}{5 b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x)**(2/3),x)

[Out]

3*(b*x)**(5/3)/(5*b)

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GIAC/XCAS [A]  time = 0.233713, size = 11, normalized size = 0.79 \[ \frac{3}{5} \, \left (b x\right )^{\frac{2}{3}} x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x)^(2/3),x, algorithm="giac")

[Out]

3/5*(b*x)^(2/3)*x