3.93.23 \(\int \frac {2-4 x}{x^3} \, dx\)

Optimal. Leaf size=20 \[ 2+3 e^{e^e}+\frac {4-\frac {1}{x}}{x} \]

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Rubi [A]  time = 0.00, antiderivative size = 12, normalized size of antiderivative = 0.60, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {37} \begin {gather*} -\frac {(1-2 x)^2}{x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(2 - 4*x)/x^3,x]

[Out]

-((1 - 2*x)^2/x^2)

Rule 37

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[((a + b*x)^(m + 1)*(c + d*x)^(n +
1))/((b*c - a*d)*(m + 1)), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[b*c - a*d, 0] && EqQ[m + n + 2, 0] && NeQ
[m, -1]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\frac {(1-2 x)^2}{x^2}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.55 \begin {gather*} -\frac {1}{x^2}+\frac {4}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(2 - 4*x)/x^3,x]

[Out]

-x^(-2) + 4/x

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fricas [A]  time = 0.78, size = 9, normalized size = 0.45 \begin {gather*} \frac {4 \, x - 1}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x+2)/x^3,x, algorithm="fricas")

[Out]

(4*x - 1)/x^2

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giac [A]  time = 0.23, size = 9, normalized size = 0.45 \begin {gather*} \frac {4 \, x - 1}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x+2)/x^3,x, algorithm="giac")

[Out]

(4*x - 1)/x^2

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maple [A]  time = 0.01, size = 10, normalized size = 0.50

method	result	size
gosper	\(\frac {4 x -1}{x^{2}}\)	\(10\)
norman	\(\frac {4 x -1}{x^{2}}\)	\(10\)
risch	\(\frac {4 x -1}{x^{2}}\)	\(10\)
default	\(-\frac {1}{x^{2}}+\frac {4}{x}\)	\(12\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-4*x+2)/x^3,x,method=_RETURNVERBOSE)

[Out]

(4*x-1)/x^2

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maxima [A]  time = 0.36, size = 9, normalized size = 0.45 \begin {gather*} \frac {4 \, x - 1}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x+2)/x^3,x, algorithm="maxima")

[Out]

(4*x - 1)/x^2

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mupad [B]  time = 0.04, size = 9, normalized size = 0.45 \begin {gather*} \frac {4\,x-1}{x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(4*x - 2)/x^3,x)

[Out]

(4*x - 1)/x^2

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sympy [A]  time = 0.07, size = 8, normalized size = 0.40 \begin {gather*} - \frac {1 - 4 x}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x+2)/x**3,x)

[Out]

-(1 - 4*x)/x**2

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