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

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 = 0.01, 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 = {} \begin {gather*} \int \frac {\log \left (e^x \log (x) \sin (x)\right )}{x} \, dx \end {gather*}

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 = 0.59, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\log \left (e^x \log (x) \sin (x)\right )}{x} \, dx \end {gather*}

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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Maple [A]
time = 0.04, size = 0, normalized size = 0.00 \[\int \frac {\ln \left ({\mathrm e}^{x} \ln \left (x \right ) \sin \left (x \right )\right )}{x}\, dx\]

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 \begin {gather*} \text {Failed to integrate} \end {gather*}

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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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\log {\left (e^{x} \log {\left (x \right )} \sin {\left (x \right )} \right )}}{x}\, dx \end {gather*}

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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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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

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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