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

Optimal. Leaf size=14 $\text{CannotIntegrate}\left (\frac{\log \left (a+b e^x\right )}{x},x\right )$

[Out]

CannotIntegrate[Log[a + b*E^x]/x, x]

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Rubi [A]  time = 0.0320759, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, $$\frac{\text{number of rules}}{\text{integrand size}}$$ = 0., 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*}

Mathematica [A]  time = 0.0514136, size = 0, normalized size = 0. $\int \frac{\log \left (a+b e^x\right )}{x} \, dx$

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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Maple [A]  time = 0.026, size = 0, normalized size = 0. \begin{align*} \int{\frac{\ln \left ( a+b{{\rm e}^{x}} \right ) }{x}}\, dx \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\log \left (b e^{x} + a\right )}{x}\,{d x} \end{align*}

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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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\log \left (b e^{x} + a\right )}{x}, x\right ) \end{align*}

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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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\log{\left (a + b e^{x} \right )}}{x}\, dx \end{align*}

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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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\log \left (b e^{x} + a\right )}{x}\,{d x} \end{align*}

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)