3.82.14 \(\int \frac {e^{-29+e^x} (-1+e^x x \log (3 x))}{x \log ^2(3 x)} \, dx\)

Optimal. Leaf size=14 \[ \frac {e^{-29+e^x}}{\log (3 x)} \]

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Rubi [A]  time = 0.13, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {2288} \begin {gather*} \frac {e^{e^x-29}}{\log (3 x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^(-29 + E^x)*(-1 + E^x*x*Log[3*x]))/(x*Log[3*x]^2),x]

[Out]

E^(-29 + E^x)/Log[3*x]

Rule 2288

Int[(y_.)*(F_)^(u_)*((v_) + (w_)), x_Symbol] :> With[{z = (v*y)/(Log[F]*D[u, x])}, Simp[F^u*z, x] /; EqQ[D[z,
x], w*y]] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {e^{-29+e^x}}{\log (3 x)}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.02, size = 14, normalized size = 1.00 \begin {gather*} \frac {e^{-29+e^x}}{\log (3 x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(-29 + E^x)*(-1 + E^x*x*Log[3*x]))/(x*Log[3*x]^2),x]

[Out]

E^(-29 + E^x)/Log[3*x]

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fricas [A]  time = 1.21, size = 12, normalized size = 0.86 \begin {gather*} \frac {e^{\left (e^{x} - 29\right )}}{\log \left (3 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x*exp(x)*log(3*x)-1)*exp(exp(x))/x/exp(29)/log(3*x)^2,x, algorithm="fricas")

[Out]

e^(e^x - 29)/log(3*x)

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giac [A]  time = 0.22, size = 12, normalized size = 0.86 \begin {gather*} \frac {e^{\left (e^{x} - 29\right )}}{\log \left (3 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x*exp(x)*log(3*x)-1)*exp(exp(x))/x/exp(29)/log(3*x)^2,x, algorithm="giac")

[Out]

e^(e^x - 29)/log(3*x)

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maple [A]  time = 0.05, size = 13, normalized size = 0.93

method	result	size
risch	\(\frac {{\mathrm e}^{{\mathrm e}^{x}-29}}{\ln \left (3 x \right )}\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x*exp(x)*ln(3*x)-1)*exp(exp(x))/x/exp(29)/ln(3*x)^2,x,method=_RETURNVERBOSE)

[Out]

1/ln(3*x)*exp(exp(x)-29)

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maxima [A]  time = 0.51, size = 17, normalized size = 1.21 \begin {gather*} \frac {e^{\left (e^{x}\right )}}{e^{29} \log \relax (3) + e^{29} \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x*exp(x)*log(3*x)-1)*exp(exp(x))/x/exp(29)/log(3*x)^2,x, algorithm="maxima")

[Out]

e^(e^x)/(e^29*log(3) + e^29*log(x))

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mupad [B]  time = 5.92, size = 12, normalized size = 0.86 \begin {gather*} \frac {{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^{-29}}{\ln \left (3\,x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(exp(x))*exp(-29)*(x*log(3*x)*exp(x) - 1))/(x*log(3*x)^2),x)

[Out]

(exp(exp(x))*exp(-29))/log(3*x)

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sympy [A]  time = 0.29, size = 12, normalized size = 0.86 \begin {gather*} \frac {e^{e^{x}}}{e^{29} \log {\left (3 x \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x*exp(x)*ln(3*x)-1)*exp(exp(x))/x/exp(29)/ln(3*x)**2,x)

[Out]

exp(-29)*exp(exp(x))/log(3*x)

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