\(\int \frac {\log (e^x \log (x) \sin (x))}{x} \, dx\) [313]

Optimal result

Integrand size = 13, antiderivative size = 13 \[ \int \frac {\log \left (e^x \log (x) \sin (x)\right )}{x} \, dx=\text {Int}\left (\frac {\log \left (e^x \log (x) \sin (x)\right )}{x},x\right ) \]

[Out]

CannotIntegrate(ln(exp(x)*ln(x)*sin(x))/x,x)

Rubi [N/A]

Not integrable

Time = 0.02 (sec) , antiderivative size = 13, 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 = {} \[ \int \frac {\log \left (e^x \log (x) \sin (x)\right )}{x} \, dx=\int \frac {\log \left (e^x \log (x) \sin (x)\right )}{x} \, dx \]

[In]

Int[Log[E^x*Log[x]*Sin[x]]/x,x]

[Out]

Defer[Int][Log[E^x*Log[x]*Sin[x]]/x, x]

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

Mathematica [N/A]

Not integrable

Time = 0.71 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.15 \[ \int \frac {\log \left (e^x \log (x) \sin (x)\right )}{x} \, dx=\int \frac {\log \left (e^x \log (x) \sin (x)\right )}{x} \, dx \]

[In]

Integrate[Log[E^x*Log[x]*Sin[x]]/x,x]

[Out]

Integrate[Log[E^x*Log[x]*Sin[x]]/x, x]

Maple [N/A]

Not integrable

Time = 0.52 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.92

\[\int \frac {\ln \left ({\mathrm e}^{x} \ln \left (x \right ) \sin \left (x \right )\right )}{x}d x\]

[In]

int(ln(exp(x)*ln(x)*sin(x))/x,x)

[Out]

int(ln(exp(x)*ln(x)*sin(x))/x,x)

Fricas [N/A]

Not integrable

Time = 0.30 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.08 \[ \int \frac {\log \left (e^x \log (x) \sin (x)\right )}{x} \, dx=\int { \frac {\log \left (e^{x} \log \left (x\right ) \sin \left (x\right )\right )}{x} \,d x } \]

[In]

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

[Out]

integral(log(e^x*log(x)*sin(x))/x, x)

Sympy [N/A]

Not integrable

Time = 13.28 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.08 \[ \int \frac {\log \left (e^x \log (x) \sin (x)\right )}{x} \, dx=\int \frac {\log {\left (e^{x} \log {\left (x \right )} \sin {\left (x \right )} \right )}}{x}\, dx \]

[In]

integrate(ln(exp(x)*ln(x)*sin(x))/x,x)

[Out]

Integral(log(exp(x)*log(x)*sin(x))/x, x)

Maxima [N/A]

Not integrable

Time = 0.57 (sec) , antiderivative size = 102, normalized size of antiderivative = 7.85 \[ \int \frac {\log \left (e^x \log (x) \sin (x)\right )}{x} \, dx=\int { \frac {\log \left (e^{x} \log \left (x\right ) \sin \left (x\right )\right )}{x} \,d x } \]

[In]

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

[Out]

-(log(2) + 1)*log(x) + 1/2*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1)*log(x) + 1/2*log(cos(x)^2 + sin(x)^2 - 2*co
s(x) + 1)*log(x) + log(x)*log(log(x)) + x + integrate(log(x)*sin(x)/(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1), x) -
integrate(log(x)*sin(x)/(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1), x)

Giac [N/A]

Not integrable

Time = 0.37 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.08 \[ \int \frac {\log \left (e^x \log (x) \sin (x)\right )}{x} \, dx=\int { \frac {\log \left (e^{x} \log \left (x\right ) \sin \left (x\right )\right )}{x} \,d x } \]

[In]

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

[Out]

integrate(log(e^x*log(x)*sin(x))/x, x)

Mupad [N/A]

Not integrable

Time = 1.64 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.08 \[ \int \frac {\log \left (e^x \log (x) \sin (x)\right )}{x} \, dx=\int \frac {\ln \left ({\mathrm {e}}^x\,\ln \left (x\right )\,\sin \left (x\right )\right )}{x} \,d x \]

[In]

int(log(exp(x)*log(x)*sin(x))/x,x)

[Out]

int(log(exp(x)*log(x)*sin(x))/x, x)