3.67.35 \(\int \frac {e^{-35+x+\log ^2(x)} (x+2 \log (x))}{x} \, dx\)

Optimal. Leaf size=9 \[ e^{-35+x+\log ^2(x)} \]

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Rubi [A]  time = 0.14, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {6706} \begin {gather*} e^{x+\log ^2(x)-35} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^(-35 + x + Log[x]^2)*(x + 2*Log[x]))/x,x]

[Out]

E^(-35 + x + Log[x]^2)

Rule 6706

Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Simp[(q*F^v)/Log[F], x] /;  !FalseQ[q]
] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=e^{-35+x+\log ^2(x)}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.05, size = 9, normalized size = 1.00 \begin {gather*} e^{-35+x+\log ^2(x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(-35 + x + Log[x]^2)*(x + 2*Log[x]))/x,x]

[Out]

E^(-35 + x + Log[x]^2)

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fricas [A]  time = 0.52, size = 8, normalized size = 0.89 \begin {gather*} e^{\left (\log \relax (x)^{2} + x - 35\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*log(x)+x)*exp(log(x)^2+x-35)/x,x, algorithm="fricas")

[Out]

e^(log(x)^2 + x - 35)

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giac [A]  time = 0.12, size = 8, normalized size = 0.89 \begin {gather*} e^{\left (\log \relax (x)^{2} + x - 35\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*log(x)+x)*exp(log(x)^2+x-35)/x,x, algorithm="giac")

[Out]

e^(log(x)^2 + x - 35)

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maple [A]  time = 0.02, size = 9, normalized size = 1.00

method	result	size
norman	\({\mathrm e}^{\ln \relax (x )^{2}+x -35}\)	\(9\)
risch	\({\mathrm e}^{\ln \relax (x )^{2}+x -35}\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*ln(x)+x)*exp(ln(x)^2+x-35)/x,x,method=_RETURNVERBOSE)

[Out]

exp(ln(x)^2+x-35)

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maxima [A]  time = 0.51, size = 8, normalized size = 0.89 \begin {gather*} e^{\left (\log \relax (x)^{2} + x - 35\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*log(x)+x)*exp(log(x)^2+x-35)/x,x, algorithm="maxima")

[Out]

e^(log(x)^2 + x - 35)

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mupad [B]  time = 4.38, size = 10, normalized size = 1.11 \begin {gather*} {\mathrm {e}}^{-35}\,{\mathrm {e}}^{{\ln \relax (x)}^2}\,{\mathrm {e}}^x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(x + log(x)^2 - 35)*(x + 2*log(x)))/x,x)

[Out]

exp(-35)*exp(log(x)^2)*exp(x)

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sympy [A]  time = 0.25, size = 8, normalized size = 0.89 \begin {gather*} e^{x + \log {\relax (x )}^{2} - 35} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*ln(x)+x)*exp(ln(x)**2+x-35)/x,x)

[Out]

exp(x + log(x)**2 - 35)

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