3.254 \(\int \frac{1}{(-3+x)^4} \, dx\)

Optimal. Leaf size=11 \[ \frac{1}{3 (3-x)^3} \]

[Out]

1/(3*(3 - x)^3)

_______________________________________________________________________________________

Rubi [A]  time = 0.00346382, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 5, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ \frac{1}{3 (3-x)^3} \]

Antiderivative was successfully verified.

[In]  Int[(-3 + x)^(-4),x]

[Out]

1/(3*(3 - x)^3)

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 0.53133, size = 7, normalized size = 0.64 \[ \frac{1}{3 \left (- x + 3\right )^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/(-3+x)**4,x)

[Out]

1/(3*(-x + 3)**3)

_______________________________________________________________________________________

Mathematica [A]  time = 0.0019471, size = 9, normalized size = 0.82 \[ -\frac{1}{3 (x-3)^3} \]

Antiderivative was successfully verified.

[In]  Integrate[(-3 + x)^(-4),x]

[Out]

-1/(3*(-3 + x)^3)

_______________________________________________________________________________________

Maple [A]  time = 0.001, size = 8, normalized size = 0.7 \[ -{\frac{1}{3\, \left ( -3+x \right ) ^{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(-3+x)^4,x)

[Out]

-1/3/(-3+x)^3

_______________________________________________________________________________________

Maxima [A]  time = 1.32975, size = 9, normalized size = 0.82 \[ -\frac{1}{3 \,{\left (x - 3\right )}^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x - 3)^(-4),x, algorithm="maxima")

[Out]

-1/3/(x - 3)^3

_______________________________________________________________________________________

Fricas [A]  time = 0.18834, size = 23, normalized size = 2.09 \[ -\frac{1}{3 \,{\left (x^{3} - 9 \, x^{2} + 27 \, x - 27\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x - 3)^(-4),x, algorithm="fricas")

[Out]

-1/3/(x^3 - 9*x^2 + 27*x - 27)

_______________________________________________________________________________________

Sympy [A]  time = 0.094065, size = 17, normalized size = 1.55 \[ - \frac{1}{3 x^{3} - 27 x^{2} + 81 x - 81} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(-3+x)**4,x)

[Out]

-1/(3*x**3 - 27*x**2 + 81*x - 81)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.198529, size = 9, normalized size = 0.82 \[ -\frac{1}{3 \,{\left (x - 3\right )}^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x - 3)^(-4),x, algorithm="giac")

[Out]

-1/3/(x - 3)^3