3.104 \(\int \sqrt [3]{b x} \, dx\)

Optimal. Leaf size=14 \[ \frac{3 (b x)^{4/3}}{4 b} \]

[Out]

(3*(b*x)^(4/3))/(4*b)

_______________________________________________________________________________________

Rubi [A]  time = 0.00702459, 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 \[ \frac{3 (b x)^{4/3}}{4 b} \]

Antiderivative was successfully verified.

[In]  Int[(b*x)^(1/3),x]

[Out]

(3*(b*x)^(4/3))/(4*b)

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 1.33672, size = 10, normalized size = 0.71 \[ \frac{3 \left (b x\right )^{\frac{4}{3}}}{4 b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x)**(1/3),x)

[Out]

3*(b*x)**(4/3)/(4*b)

_______________________________________________________________________________________

Mathematica [A]  time = 0.00168791, size = 12, normalized size = 0.86 \[ \frac{3}{4} x \sqrt [3]{b x} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x)^(1/3),x]

[Out]

(3*x*(b*x)^(1/3))/4

_______________________________________________________________________________________

Maple [A]  time = 0.003, size = 9, normalized size = 0.6 \[{\frac{3\,x}{4}\sqrt [3]{bx}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x)^(1/3),x)

[Out]

3/4*x*(b*x)^(1/3)

_______________________________________________________________________________________

Maxima [A]  time = 1.43427, size = 14, normalized size = 1. \[ \frac{3 \, \left (b x\right )^{\frac{4}{3}}}{4 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x)^(1/3),x, algorithm="maxima")

[Out]

3/4*(b*x)^(4/3)/b

_______________________________________________________________________________________

Fricas [A]  time = 0.216398, size = 11, normalized size = 0.79 \[ \frac{3}{4} \, \left (b x\right )^{\frac{1}{3}} x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x)^(1/3),x, algorithm="fricas")

[Out]

3/4*(b*x)^(1/3)*x

_______________________________________________________________________________________

Sympy [A]  time = 0.063848, size = 10, normalized size = 0.71 \[ \frac{3 \left (b x\right )^{\frac{4}{3}}}{4 b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x)**(1/3),x)

[Out]

3*(b*x)**(4/3)/(4*b)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.249309, size = 11, normalized size = 0.79 \[ \frac{3}{4} \, \left (b x\right )^{\frac{1}{3}} x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x)^(1/3),x, algorithm="giac")

[Out]

3/4*(b*x)^(1/3)*x