3.402 \(\int \frac{1}{\sqrt [3]{-a+b x}} \, dx\)

Optimal. Leaf size=18 \[ \frac{3 (b x-a)^{2/3}}{2 b} \]

[Out]

(3*(-a + b*x)^(2/3))/(2*b)

_______________________________________________________________________________________

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]

(3*(-a + b*x)^(2/3))/(2*b)

_______________________________________________________________________________________

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]

3*(-a + b*x)**(2/3)/(2*b)

_______________________________________________________________________________________

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]

(3*(-a + b*x)^(2/3))/(2*b)

_______________________________________________________________________________________

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]

3/2*(b*x-a)^(2/3)/b

_______________________________________________________________________________________

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]

3/2*(b*x - a)^(2/3)/b

_______________________________________________________________________________________

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]

3/2*(b*x - a)^(2/3)/b

_______________________________________________________________________________________

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]

3*(-a + b*x)**(2/3)/(2*b)

_______________________________________________________________________________________

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]

3/2*(b*x - a)^(2/3)/b