3.48.74 \(\int \frac {e^{-262144 (4-x)} (-16+(16+4194304 x) \log (x))}{\log ^2(x)} \, dx\)

Optimal. Leaf size=16 \[ \frac {16 e^{-262144 (4-x)} x}{\log (x)} \]

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Rubi [A]  time = 0.03, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {2201} \begin {gather*} \frac {16 e^{-262144 (4-x)} x}{\log (x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-16 + (16 + 4194304*x)*Log[x])/(E^(262144*(4 - x))*Log[x]^2),x]

[Out]

(16*x)/(E^(262144*(4 - x))*Log[x])

Rule 2201

Int[Log[(d_.)*(x_)]^(n_.)*(F_)^((c_.)*((a_.) + (b_.)*(x_)))*((e_) + Log[(d_.)*(x_)]*(h_.)*((f_.) + (g_.)*(x_))
), x_Symbol] :> Simp[(e*x*F^(c*(a + b*x))*Log[d*x]^(n + 1))/(n + 1), x] /; FreeQ[{F, a, b, c, d, e, f, g, h, n
}, x] && EqQ[e - f*h*(n + 1), 0] && EqQ[g*h*(n + 1) - b*c*e*Log[F], 0] && NeQ[n, -1]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {16 e^{-262144 (4-x)} x}{\log (x)}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 14, normalized size = 0.88 \begin {gather*} \frac {16 e^{262144 (-4+x)} x}{\log (x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-16 + (16 + 4194304*x)*Log[x])/(E^(262144*(4 - x))*Log[x]^2),x]

[Out]

(16*E^(262144*(-4 + x))*x)/Log[x]

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fricas [A]  time = 0.60, size = 13, normalized size = 0.81 \begin {gather*} \frac {16 \, x e^{\left (262144 \, x - 1048576\right )}}{\log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4194304*x+16)*log(x)-16)/log(x)^2/exp(-262144*x+1048576),x, algorithm="fricas")

[Out]

16*x*e^(262144*x - 1048576)/log(x)

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giac [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4194304*x+16)*log(x)-16)/log(x)^2/exp(-262144*x+1048576),x, algorithm="giac")

[Out]

Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,sageVARx):;OUTP
UT:Polynomial exponent overflow. Error: Bad Argument Value

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maple [A]  time = 0.02, size = 14, normalized size = 0.88

method	result	size
risch	\(\frac {16 x \,{\mathrm e}^{262144 x -1048576}}{\ln \relax (x )}\)	\(14\)
norman	\(\frac {16 x \,{\mathrm e}^{262144 x -1048576}}{\ln \relax (x )}\)	\(16\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((4194304*x+16)*ln(x)-16)/ln(x)^2/exp(-262144*x+1048576),x,method=_RETURNVERBOSE)

[Out]

16*x*exp(262144*x-1048576)/ln(x)

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maxima [A]  time = 0.42, size = 13, normalized size = 0.81 \begin {gather*} \frac {16 \, x e^{\left (262144 \, x - 1048576\right )}}{\log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4194304*x+16)*log(x)-16)/log(x)^2/exp(-262144*x+1048576),x, algorithm="maxima")

[Out]

16*x*e^(262144*x - 1048576)/log(x)

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mupad [B]  time = 3.41, size = 13, normalized size = 0.81 \begin {gather*} \frac {16\,x\,{\mathrm {e}}^{262144\,x}\,{\mathrm {e}}^{-1048576}}{\ln \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(262144*x - 1048576)*(log(x)*(4194304*x + 16) - 16))/log(x)^2,x)

[Out]

(16*x*exp(262144*x)*exp(-1048576))/log(x)

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sympy [A]  time = 0.24, size = 12, normalized size = 0.75 \begin {gather*} \frac {16 x e^{262144 x - 1048576}}{\log {\relax (x )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4194304*x+16)*ln(x)-16)/ln(x)**2/exp(-262144*x+1048576),x)

[Out]

16*x*exp(262144*x - 1048576)/log(x)

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