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

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {32} \[ \frac {1}{3 (3-x)^3} \]

Antiderivative was successfully verified.

[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*} \int \frac {1}{(-3+x)^4} \, dx &=\frac {1}{3 (3-x)^3}\\ \end {align*}

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Mathematica [A]  time = 0.00, 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*1/(-3 + x)^3

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fricas [B]  time = 0.41, size = 17, normalized size = 1.55 \[ -\frac {1}{3 \, {\left (x^{3} - 9 \, x^{2} + 27 \, x - 27\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/3/(x^3 - 9*x^2 + 27*x - 27)

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giac [A]  time = 1.08, 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]

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

[Out]

-1/3/(x - 3)^3

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maple [A]  time = 0.00, size = 8, normalized size = 0.73 \[ -\frac {1}{3 \left (x -3\right )^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x-3)^4,x)

[Out]

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

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maxima [A]  time = 0.41, 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]

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

[Out]

-1/3/(x - 3)^3

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mupad [B]  time = 0.07, 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]

int(1/(x - 3)^4,x)

[Out]

-1/(3*(x - 3)^3)

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sympy [B]  time = 0.11, 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)

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