3.117 \(\int \frac {\log (a+b e^x)}{x} \, dx\)

Optimal. Leaf size=15 \[ \text {Int}\left (\frac {\log \left (a+b e^x\right )}{x},x\right ) \]

[Out]

CannotIntegrate(ln(a+b*exp(x))/x,x)

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Rubi [A]  time = 0.03, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\log \left (a+b e^x\right )}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Log[a + b*E^x]/x,x]

[Out]

Defer[Int][Log[a + b*E^x]/x, x]

Rubi steps

\begin {align*} \int \frac {\log \left (a+b e^x\right )}{x} \, dx &=\int \frac {\log \left (a+b e^x\right )}{x} \, dx\\ \end {align*}

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Mathematica [A]  time = 0.05, size = 0, normalized size = 0.00 \[ \int \frac {\log \left (a+b e^x\right )}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Log[a + b*E^x]/x,x]

[Out]

Integrate[Log[a + b*E^x]/x, x]

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fricas [A]  time = 0.70, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\log \left (b e^{x} + a\right )}{x}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(log(b*e^x + a)/x, x)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\log \left (b e^{x} + a\right )}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(log(b*e^x + a)/x, x)

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maple [A]  time = 0.10, size = 0, normalized size = 0.00 \[ \int \frac {\ln \left (b \,{\mathrm e}^{x}+a \right )}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(ln(b*exp(x)+a)/x,x)

[Out]

int(ln(b*exp(x)+a)/x,x)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\log \left (b e^{x} + a\right )}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(log(b*e^x + a)/x, x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.07 \[ \int \frac {\ln \left (a+b\,{\mathrm {e}}^x\right )}{x} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(a + b*exp(x))/x,x)

[Out]

int(log(a + b*exp(x))/x, x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\log {\left (a + b e^{x} \right )}}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(ln(a+b*exp(x))/x,x)

[Out]

Integral(log(a + b*exp(x))/x, x)

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