3.110 \(\int \left (b x^2\right )^{2/3} \, dx\)

Optimal. Leaf size=14 \[ \frac{3}{7} x \left (b x^2\right )^{2/3} \]

[Out]

(3*x*(b*x^2)^(2/3))/7

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Rubi [A]  time = 0.00718682, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ \frac{3}{7} x \left (b x^2\right )^{2/3} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^2)^(2/3),x]

[Out]

(3*x*(b*x^2)^(2/3))/7

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Rubi in Sympy [A]  time = 1.26672, size = 12, normalized size = 0.86 \[ \frac{3 x \left (b x^{2}\right )^{\frac{2}{3}}}{7} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**2)**(2/3),x)

[Out]

3*x*(b*x**2)**(2/3)/7

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Mathematica [A]  time = 0.00208693, size = 14, normalized size = 1. \[ \frac{3}{7} x \left (b x^2\right )^{2/3} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^2)^(2/3),x]

[Out]

(3*x*(b*x^2)^(2/3))/7

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Maple [A]  time = 0.002, size = 11, normalized size = 0.8 \[{\frac{3\,x}{7} \left ( b{x}^{2} \right ) ^{{\frac{2}{3}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^2)^(2/3),x)

[Out]

3/7*x*(b*x^2)^(2/3)

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Maxima [A]  time = 1.43286, size = 14, normalized size = 1. \[ \frac{3}{7} \, \left (b x^{2}\right )^{\frac{2}{3}} x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3/7*(b*x^2)^(2/3)*x

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Fricas [A]  time = 0.218329, size = 18, normalized size = 1.29 \[ \frac{3 \, b x^{3}}{7 \, \left (b x^{2}\right )^{\frac{1}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3/7*b*x^3/(b*x^2)^(1/3)

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Sympy [A]  time = 0.85381, size = 15, normalized size = 1.07 \[ \frac{3 b^{\frac{2}{3}} x \left (x^{2}\right )^{\frac{2}{3}}}{7} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**2)**(2/3),x)

[Out]

3*b**(2/3)*x*(x**2)**(2/3)/7

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GIAC/XCAS [F]  time = 0., size = 0, normalized size = 0. \[ \int \left (b x^{2}\right )^{\frac{2}{3}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

integrate((b*x^2)^(2/3), x)