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 = 0.0006913, 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, 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*}

Mathematica [A]  time = 0.0013664, 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)

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Maple [A]  time = 0., size = 8, normalized size = 0.7 \begin{align*} -{\frac{1}{3\, \left ( -3+x \right ) ^{3}}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]  time = 0.973595, size = 9, normalized size = 0.82 \begin{align*} -\frac{1}{3 \,{\left (x - 3\right )}^{3}} \end{align*}

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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Fricas [B]  time = 1.49917, size = 43, normalized size = 3.91 \begin{align*} -\frac{1}{3 \,{\left (x^{3} - 9 \, x^{2} + 27 \, x - 27\right )}} \end{align*}

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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Sympy [B]  time = 0.095338, size = 17, normalized size = 1.55 \begin{align*} - \frac{1}{3 x^{3} - 27 x^{2} + 81 x - 81} \end{align*}

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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Giac [A]  time = 1.07494, size = 9, normalized size = 0.82 \begin{align*} -\frac{1}{3 \,{\left (x - 3\right )}^{3}} \end{align*}

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