3.313 \(\int \frac {\log (e^x \log (x) \sin (x))}{x} \, dx\)

Optimal. Leaf size=16 \[ \text {Int}\left (\frac {\log \left (e^x \log (x) \sin (x)\right )}{x},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.02, 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 = {} \[ \int \frac {\log \left (e^x \log (x) \sin (x)\right )}{x} \, dx \]

Verification is Not applicable to the result.

[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*} \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\\ \end {align*}

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Mathematica [A]  time = 0.88, size = 0, normalized size = 0.00 \[ \int \frac {\log \left (e^x \log (x) \sin (x)\right )}{x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.46, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\log \left (e^{x} \log \relax (x) \sin \relax (x)\right )}{x}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(log(e^x*log(x)*sin(x))/x, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 4.24, size = 0, normalized size = 0.00 \[ \int \frac {\ln \left ({\mathrm e}^{x} \ln \relax (x ) \sin \relax (x )\right )}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ -{\left (\log \relax (2) + 1\right )} \log \relax (x) + \frac {1}{2} \, \log \left (\cos \relax (x)^{2} + \sin \relax (x)^{2} + 2 \, \cos \relax (x) + 1\right ) \log \relax (x) + \frac {1}{2} \, \log \left (\cos \relax (x)^{2} + \sin \relax (x)^{2} - 2 \, \cos \relax (x) + 1\right ) \log \relax (x) + \log \relax (x) \log \left (\log \relax (x)\right ) + x + \int \frac {\log \relax (x) \sin \relax (x)}{\cos \relax (x)^{2} + \sin \relax (x)^{2} + 2 \, \cos \relax (x) + 1}\,{d x} - \int \frac {\log \relax (x) \sin \relax (x)}{\cos \relax (x)^{2} + \sin \relax (x)^{2} - 2 \, \cos \relax (x) + 1}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[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)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.06 \[ \int \frac {\ln \left ({\mathrm {e}}^x\,\ln \relax (x)\,\sin \relax (x)\right )}{x} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int(log(exp(x)*log(x)*sin(x))/x, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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