3.2.85 \(\int e^x (\frac {1}{x}+\log (x)) \, dx\) [185]

Optimal. Leaf size=6 \[ e^x \log (x) \]

[Out]

exp(x)*ln(x)

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Rubi [A]
time = 0.01, antiderivative size = 6, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {2326} \begin {gather*} e^x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^x*(x^(-1) + Log[x]),x]

[Out]

E^x*Log[x]

Rule 2326

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} &=e^x \log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.01, size = 6, normalized size = 1.00 \begin {gather*} e^x \log (x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^x*(x^(-1) + Log[x]),x]

[Out]

E^x*Log[x]

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Maple [A]
time = 0.04, size = 6, normalized size = 1.00

method	result	size
norman	\({\mathrm e}^{x} \ln \left (x \right )\)	\(6\)
risch	\({\mathrm e}^{x} \ln \left (x \right )\)	\(6\)
parallelrisch	\({\mathrm e}^{x} \ln \left (x \right )\)	\(6\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x)*(1/x+ln(x)),x,method=_RETURNVERBOSE)

[Out]

exp(x)*ln(x)

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Maxima [A]
time = 0.43, size = 5, normalized size = 0.83 \begin {gather*} e^{x} \log \left (x\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)*(1/x+log(x)),x, algorithm="maxima")

[Out]

e^x*log(x)

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Fricas [A]
time = 0.58, size = 5, normalized size = 0.83 \begin {gather*} e^{x} \log \left (x\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)*(1/x+log(x)),x, algorithm="fricas")

[Out]

e^x*log(x)

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Sympy [A]
time = 0.07, size = 5, normalized size = 0.83 \begin {gather*} e^{x} \log {\left (x \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)*(1/x+ln(x)),x)

[Out]

exp(x)*log(x)

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Giac [A]
time = 0.44, size = 5, normalized size = 0.83 \begin {gather*} e^{x} \log \left (x\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)*(1/x+log(x)),x, algorithm="giac")

[Out]

e^x*log(x)

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Mupad [B]
time = 0.12, size = 5, normalized size = 0.83 \begin {gather*} {\mathrm {e}}^x\,\ln \left (x\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x)*(log(x) + 1/x),x)

[Out]

exp(x)*log(x)

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Chatgpt [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {not solved} \end {gather*}

Antiderivative was successfully verified.

[In]

int(exp(x)*(1/x+ln(x)),x)

[Out]

not solved

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