3.36.79 \(\int -\frac {8 x}{-13+10 e^6} \, dx\)

Optimal. Leaf size=14 \[ \frac {4 x^2}{13-10 e^6} \]

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Rubi [A]  time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {12, 30} \begin {gather*} \frac {4 x^2}{13-10 e^6} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-8*x)/(-13 + 10*E^6),x]

[Out]

(4*x^2)/(13 - 10*E^6)

Rule 12

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

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {8 \int x \, dx}{13-10 e^6}\\ &=\frac {4 x^2}{13-10 e^6}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} -\frac {4 x^2}{-13+10 e^6} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-8*x)/(-13 + 10*E^6),x]

[Out]

(-4*x^2)/(-13 + 10*E^6)

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fricas [A]  time = 1.03, size = 13, normalized size = 0.93 \begin {gather*} -\frac {4 \, x^{2}}{10 \, e^{6} - 13} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8*x/(2*x*exp(log(5/x)+6)-13),x, algorithm="fricas")

[Out]

-4*x^2/(10*e^6 - 13)

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giac [A]  time = 0.12, size = 13, normalized size = 0.93 \begin {gather*} -\frac {4 \, x^{2}}{10 \, e^{6} - 13} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8*x/(2*x*exp(log(5/x)+6)-13),x, algorithm="giac")

[Out]

-4*x^2/(10*e^6 - 13)

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maple [A]  time = 0.03, size = 14, normalized size = 1.00

method	result	size
norman	\(-\frac {4 x^{2}}{10 \,{\mathrm e}^{6}-13}\)	\(14\)
risch	\(-\frac {4 x^{2}}{10 \,{\mathrm e}^{6}-13}\)	\(14\)
gosper	\(-\frac {4 x^{2}}{2 x \,{\mathrm e}^{\ln \left (\frac {5}{x}\right )+6}-13}\)	\(22\)
default	\(-\frac {4 x^{2}}{2 \,{\mathrm e}^{6+\ln \left (\frac {5}{x}\right )+\ln \relax (x )}-13}\)	\(23\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-8*x/(2*x*exp(ln(5/x)+6)-13),x,method=_RETURNVERBOSE)

[Out]

-4/(10*exp(6)-13)*x^2

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maxima [A]  time = 0.51, size = 13, normalized size = 0.93 \begin {gather*} -\frac {4 \, x^{2}}{10 \, e^{6} - 13} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8*x/(2*x*exp(log(5/x)+6)-13),x, algorithm="maxima")

[Out]

-4*x^2/(10*e^6 - 13)

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mupad [B]  time = 0.10, size = 13, normalized size = 0.93 \begin {gather*} -\frac {4\,x^2}{10\,{\mathrm {e}}^6-13} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(8*x)/(2*x*exp(log(5/x) + 6) - 13),x)

[Out]

-(4*x^2)/(10*exp(6) - 13)

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sympy [A]  time = 0.06, size = 12, normalized size = 0.86 \begin {gather*} - \frac {4 x^{2}}{-13 + 10 e^{6}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-8*x/(2*x*exp(ln(5/x)+6)-13),x)

[Out]

-4*x**2/(-13 + 10*exp(6))

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