\(\int \frac {\log (a+b e^x)}{x} \, dx\) [117]

Optimal result

Integrand size = 12, antiderivative size = 12 \[ \int \frac {\log \left (a+b e^x\right )}{x} \, dx=\text {Int}\left (\frac {\log \left (a+b e^x\right )}{x},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\log \left (a+b e^x\right )}{x} \, dx=\int \frac {\log \left (a+b e^x\right )}{x} \, dx \]

[In]

Int[Log[a + b*E^x]/x,x]

[Out]

Defer[Int][Log[a + b*E^x]/x, x]

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

Mathematica [N/A]

Not integrable

Time = 0.04 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\log \left (a+b e^x\right )}{x} \, dx=\int \frac {\log \left (a+b e^x\right )}{x} \, dx \]

[In]

Integrate[Log[a + b*E^x]/x,x]

[Out]

Integrate[Log[a + b*E^x]/x, x]

Maple [N/A]

Not integrable

Time = 0.06 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92

\[\int \frac {\ln \left (a +b \,{\mathrm e}^{x}\right )}{x}d x\]

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.30 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.08 \[ \int \frac {\log \left (a+b e^x\right )}{x} \, dx=\int { \frac {\log \left (b e^{x} + a\right )}{x} \,d x } \]

[In]

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

[Out]

integral(log(b*e^x + a)/x, x)

Sympy [N/A]

Not integrable

Time = 0.35 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {\log \left (a+b e^x\right )}{x} \, dx=\int \frac {\log {\left (a + b e^{x} \right )}}{x}\, dx \]

[In]

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

[Out]

Integral(log(a + b*exp(x))/x, x)

Maxima [N/A]

Not integrable

Time = 0.23 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.08 \[ \int \frac {\log \left (a+b e^x\right )}{x} \, dx=\int { \frac {\log \left (b e^{x} + a\right )}{x} \,d x } \]

[In]

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

[Out]

integrate(log(b*e^x + a)/x, x)

Giac [N/A]

Not integrable

Time = 0.32 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.08 \[ \int \frac {\log \left (a+b e^x\right )}{x} \, dx=\int { \frac {\log \left (b e^{x} + a\right )}{x} \,d x } \]

[In]

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

[Out]

integrate(log(b*e^x + a)/x, x)

Mupad [N/A]

Not integrable

Time = 1.42 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.08 \[ \int \frac {\log \left (a+b e^x\right )}{x} \, dx=\int \frac {\ln \left (a+b\,{\mathrm {e}}^x\right )}{x} \,d x \]

[In]

int(log(a + b*exp(x))/x,x)

[Out]

int(log(a + b*exp(x))/x, x)