∫ e(−29−2x) log(4)+(1−log(4)) log(x) _____________________________________________ log (4) (1+(−1−2x) log(4)) ___________________________________________________________________

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Rubi [A] time = 0.18, antiderivative size = 16, normalized size of antiderivative = 0.89, number of steps used = 3, number of rules used = 3, integrand size = 43, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.070, Rules used = {12, 2274, 2197} \begin {gather*} e^{-2 x-29} x^{\frac {1}{\log (4)}-1} \end {gather*}

Int[(E^(((-29 - 2*x)*Log[4] + (1 - Log[4])*Log[x])/Log[4])*(1 + (-1 - 2*x)*Log[4]))/(x*Log[4]),x]

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

Int[(F_)^((c_.)*(v_))*(u_)^(m_.)*(w_), x_Symbol] :> With[{b = Coefficient[v, x, 1], d = Coefficient[u, x, 0],

e = Coefficient[u, x, 1], f = Coefficient[w, x, 0], g = Coefficient[w, x, 1]}, Simp[(g*u^(m + 1)*F^(c*v))/(b*c

*e*Log[F]), x] /; EqQ[e*g*(m + 1) - b*c*(e*f - d*g)*Log[F], 0]] /; FreeQ[{F, c, m}, x] && LinearQ[{u, v, w}, x

Int[(u_.)*(F_)^((a_.)*(Log[z_]*(b_.) + (v_.))), x_Symbol] :> Int[u*F^(a*v)*z^(a*b*Log[F]), x] /; FreeQ[{F, a,

\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {\exp \left (\frac {(-29-2 x) \log (4)+(1-\log (4)) \log (x)}{\log (4)}\right ) (1+(-1-2 x) \log (4))}{x} \, dx}{\log (4)}\\ &=\frac {\int e^{-29-2 x} x^{-1+\frac {1-\log (4)}{\log (4)}} (1+(-1-2 x) \log (4)) \, dx}{\log (4)}\\ &=e^{-29-2 x} x^{-1+\frac {1}{\log (4)}}\\ \end {aligned} \end {gather*}

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Mathematica [A] time = 0.04, size = 25, normalized size = 1.39 \begin {gather*} \frac {e^{-29-2 x} x^{-1+\frac {1}{\log (4)}} \log (16)}{2 \log (4)} \end {gather*}

Integrate[(E^(((-29 - 2*x)*Log[4] + (1 - Log[4])*Log[x])/Log[4])*(1 + (-1 - 2*x)*Log[4]))/(x*Log[4]),x]

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fricas [A] time = 0.57, size = 26, normalized size = 1.44 \begin {gather*} e^{\left (-\frac {2 \, {\left (2 \, x + 29\right )} \log \relax (2) + {\left (2 \, \log \relax (2) - 1\right )} \log \relax (x)}{2 \, \log \relax (2)}\right )} \end {gather*}

integrate(1/2*(2*(-2*x-1)*log(2)+1)*exp(1/2*((1-2*log(2))*log(x)+2*(-2*x-29)*log(2))/log(2))/x/log(2),x, algor

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giac [A] time = 0.27, size = 18, normalized size = 1.00 \begin {gather*} e^{\left (-2 \, x + \frac {\log \relax (x)}{2 \, \log \relax (2)} - \log \relax (x) - 29\right )} \end {gather*}

integrate(1/2*(2*(-2*x-1)*log(2)+1)*exp(1/2*((1-2*log(2))*log(x)+2*(-2*x-29)*log(2))/log(2))/x/log(2),x, algor

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method	result	size

risch	\(\frac {x^{\frac {1}{2 \ln \relax (2)}} {\mathrm e}^{-2 x -29}}{x}\)	\(19\)
norman	\({\mathrm e}^{\frac {\left (1-2 \ln \relax (2)\right ) \ln \relax (x )+2 \left (-2 x -29\right ) \ln \relax (2)}{2 \ln \relax (2)}}\)	\(27\)
gosper	\({\mathrm e}^{-\frac {2 \ln \relax (2) \ln \relax (x )+4 x \ln \relax (2)-\ln \relax (x )+58 \ln \relax (2)}{2 \ln \relax (2)}}\)	\(28\)

int(1/2*(2*(-2*x-1)*ln(2)+1)*exp(1/2*((1-2*ln(2))*ln(x)+2*(-2*x-29)*ln(2))/ln(2))/x/ln(2),x,method=_RETURNVERB

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maxima [A] time = 0.62, size = 18, normalized size = 1.00 \begin {gather*} \frac {e^{\left (-2 \, x + \frac {\log \relax (x)}{2 \, \log \relax (2)} - 29\right )}}{x} \end {gather*}

integrate(1/2*(2*(-2*x-1)*log(2)+1)*exp(1/2*((1-2*log(2))*log(x)+2*(-2*x-29)*log(2))/log(2))/x/log(2),x, algor

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mupad [B] time = 1.54, size = 17, normalized size = 0.94 \begin {gather*} x^{\frac {1}{2\,\ln \relax (2)}-1}\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{-29} \end {gather*}

int(-(exp(-(log(2)*(2*x + 29) + (log(x)*(2*log(2) - 1))/2)/log(2))*(2*log(2)*(2*x + 1) - 1))/(2*x*log(2)),x)

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sympy [B] time = 14.70, size = 117, normalized size = 6.50 \begin {gather*} \frac {- \frac {\left (2 x\right )^{2 - \frac {1}{2 \log {\relax (2 )}}} \Gamma \left (-1 + \frac {1}{2 \log {\relax (2 )}}, 2 x\right )}{2 x^{2 - \frac {1}{2 \log {\relax (2 )}}}} + \frac {\left (2 x\right )^{2 - \frac {1}{2 \log {\relax (2 )}}} \log {\relax (2 )} \Gamma \left (-1 + \frac {1}{2 \log {\relax (2 )}}, 2 x\right )}{x^{2 - \frac {1}{2 \log {\relax (2 )}}}} + \frac {2 \left (2 x\right )^{1 - \frac {1}{2 \log {\relax (2 )}}} \log {\relax (2 )} \Gamma \left (\frac {1}{2 \log {\relax (2 )}}, 2 x\right )}{x^{1 - \frac {1}{2 \log {\relax (2 )}}}}}{2 e^{29} \log {\relax (2 )}} \end {gather*}

integrate(1/2*(2*(-2*x-1)*ln(2)+1)*exp(1/2*((1-2*ln(2))*ln(x)+2*(-2*x-29)*ln(2))/ln(2))/x/ln(2),x)

(-x**(-2 + 1/(2*log(2)))*(2*x)**(2 - 1/(2*log(2)))*uppergamma(-1 + 1/(2*log(2)), 2*x)/2 + x**(-2 + 1/(2*log(2)

))*(2*x)**(2 - 1/(2*log(2)))*log(2)*uppergamma(-1 + 1/(2*log(2)), 2*x) + 2*x**(-1 + 1/(2*log(2)))*(2*x)**(1 -

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3.27.48 \(\int \frac {e^{\frac {(-29-2 x) \log (4)+(1-\log (4)) \log (x)}{\log (4)}} (1+(-1-2 x) \log (4))}{x \log (4)} \, dx\)