\(\int \frac {1}{(-3+x)^4} \, dx\) [254]

Optimal result

Integrand size = 5, antiderivative size = 11 \[ \int \frac {1}{(-3+x)^4} \, dx=\frac {1}{3 (3-x)^3} \]

[Out]

1/3/(3-x)^3

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {32} \[ \int \frac {1}{(-3+x)^4} \, dx=\frac {1}{3 (3-x)^3} \]

[In]

Int[(-3 + x)^(-4),x]

[Out]

1/(3*(3 - x)^3)

Rule 32

Int[((a_.) + (b_.)*(x_))^(m_), x_Symbol] :> Simp[(a + b*x)^(m + 1)/(b*(m + 1)), x] /; FreeQ[{a, b, m}, x] && N
eQ[m, -1]

Rubi steps \begin{align*} \text {integral}& = \frac {1}{3 (3-x)^3} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82 \[ \int \frac {1}{(-3+x)^4} \, dx=-\frac {1}{3 (-3+x)^3} \]

[In]

Integrate[(-3 + x)^(-4),x]

[Out]

-1/3*1/(-3 + x)^3

Maple [A] (verified)

Time = 0.09 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73

method	result	size
gosper	\(-\frac {1}{3 \left (-3+x \right )^{3}}\)	\(8\)
default	\(-\frac {1}{3 \left (-3+x \right )^{3}}\)	\(8\)
norman	\(-\frac {1}{3 \left (-3+x \right )^{3}}\)	\(8\)
risch	\(-\frac {1}{3 \left (-3+x \right )^{3}}\)	\(8\)
parallelrisch	\(-\frac {1}{3 \left (-3+x \right )^{3}}\)	\(8\)
meijerg	\(\frac {x \left (\frac {1}{9} x^{2}-x +3\right )}{243 \left (1-\frac {x}{3}\right )^{3}}\)	\(21\)

[In]

int(1/(-3+x)^4,x,method=_RETURNVERBOSE)

[Out]

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

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 17 vs. \(2 (7) = 14\).

Time = 0.23 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.55 \[ \int \frac {1}{(-3+x)^4} \, dx=-\frac {1}{3 \, {\left (x^{3} - 9 \, x^{2} + 27 \, x - 27\right )}} \]

[In]

integrate(1/(-3+x)^4,x, algorithm="fricas")

[Out]

-1/3/(x^3 - 9*x^2 + 27*x - 27)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 17 vs. \(2 (7) = 14\).

Time = 0.04 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.55 \[ \int \frac {1}{(-3+x)^4} \, dx=- \frac {1}{3 x^{3} - 27 x^{2} + 81 x - 81} \]

[In]

integrate(1/(-3+x)**4,x)

[Out]

-1/(3*x**3 - 27*x**2 + 81*x - 81)

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64 \[ \int \frac {1}{(-3+x)^4} \, dx=-\frac {1}{3 \, {\left (x - 3\right )}^{3}} \]

[In]

integrate(1/(-3+x)^4,x, algorithm="maxima")

[Out]

-1/3/(x - 3)^3

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64 \[ \int \frac {1}{(-3+x)^4} \, dx=-\frac {1}{3 \, {\left (x - 3\right )}^{3}} \]

[In]

integrate(1/(-3+x)^4,x, algorithm="giac")

[Out]

-1/3/(x - 3)^3

Mupad [B] (verification not implemented)

Time = 0.06 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64 \[ \int \frac {1}{(-3+x)^4} \, dx=-\frac {1}{3\,{\left (x-3\right )}^3} \]

[In]

int(1/(x - 3)^4,x)

[Out]

-1/(3*(x - 3)^3)