3.58.68 \(\int \frac {-2+2 x}{25 e^{24} x^3} \, dx\)

Optimal. Leaf size=19 \[ \frac {\left (x-x^2\right )^2}{25 e^{24} x^4} \]

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Rubi [A]  time = 0.00, antiderivative size = 17, normalized size of antiderivative = 0.89, number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {12, 37} \begin {gather*} \frac {(1-x)^2}{25 e^{24} x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-2 + 2*x)/(25*E^24*x^3),x]

[Out]

(1 - x)^2/(25*E^24*x^2)

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

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 {\int \frac {-2+2 x}{x^3} \, dx}{25 e^{24}}\\ &=\frac {(1-x)^2}{25 e^{24} x^2}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 20, normalized size = 1.05 \begin {gather*} \frac {2 \left (\frac {1}{2 x^2}-\frac {1}{x}\right )}{25 e^{24}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-2 + 2*x)/(25*E^24*x^3),x]

[Out]

(2*(1/(2*x^2) - x^(-1)))/(25*E^24)

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fricas [A]  time = 0.56, size = 12, normalized size = 0.63 \begin {gather*} -\frac {{\left (2 \, x - 1\right )} e^{\left (-24\right )}}{25 \, x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*(2*x-2)/x^3/exp(12)^2,x, algorithm="fricas")

[Out]

-1/25*(2*x - 1)*e^(-24)/x^2

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giac [A]  time = 0.22, size = 12, normalized size = 0.63 \begin {gather*} -\frac {{\left (2 \, x - 1\right )} e^{\left (-24\right )}}{25 \, x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*(2*x-2)/x^3/exp(12)^2,x, algorithm="giac")

[Out]

-1/25*(2*x - 1)*e^(-24)/x^2

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maple [A]  time = 0.05, size = 13, normalized size = 0.68

method	result	size
risch	\(\frac {{\mathrm e}^{-24} \left (1-2 x \right )}{25 x^{2}}\)	\(13\)
gosper	\(-\frac {\left (2 x -1\right ) {\mathrm e}^{-24}}{25 x^{2}}\)	\(15\)
default	\(\frac {2 \,{\mathrm e}^{-24} \left (-\frac {1}{x}+\frac {1}{2 x^{2}}\right )}{25}\)	\(18\)
norman	\(\frac {\left (\frac {{\mathrm e}^{-12}}{25}-\frac {2 \,{\mathrm e}^{-12} x}{25}\right ) {\mathrm e}^{-12}}{x^{2}}\)	\(23\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/25*(2*x-2)/x^3/exp(12)^2,x,method=_RETURNVERBOSE)

[Out]

1/25*exp(-24)/x^2*(1-2*x)

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maxima [A]  time = 0.37, size = 12, normalized size = 0.63 \begin {gather*} -\frac {{\left (2 \, x - 1\right )} e^{\left (-24\right )}}{25 \, x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*(2*x-2)/x^3/exp(12)^2,x, algorithm="maxima")

[Out]

-1/25*(2*x - 1)*e^(-24)/x^2

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mupad [B]  time = 0.04, size = 12, normalized size = 0.63 \begin {gather*} -\frac {{\mathrm {e}}^{-24}\,\left (2\,x-1\right )}{25\,x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-24)*((2*x)/25 - 2/25))/x^3,x)

[Out]

-(exp(-24)*(2*x - 1))/(25*x^2)

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sympy [A]  time = 0.07, size = 12, normalized size = 0.63 \begin {gather*} \frac {1 - 2 x}{25 x^{2} e^{24}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*(2*x-2)/x**3/exp(12)**2,x)

[Out]

(1 - 2*x)*exp(-24)/(25*x**2)

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