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

Optimal. Leaf size=15 $\text{CannotIntegrate}\left (\frac{\log \left (e^x \log (x) \sin (x)\right )}{x},x\right )$

[Out]

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

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Rubi [A]  time = 0.0219818, 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 = {} $\int \frac{\log \left (e^x \log (x) \sin (x)\right )}{x} \, dx$

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*}

Mathematica [A]  time = 0.790202, size = 0, normalized size = 0. $\int \frac{\log \left (e^x \log (x) \sin (x)\right )}{x} \, dx$

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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Maple [A]  time = 0.605, size = 0, normalized size = 0. \begin{align*} \int{\frac{\ln \left ({{\rm e}^{x}}\ln \left ( x \right ) \sin \left ( x \right ) \right ) }{x}}\, dx \end{align*}

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., size = 0, normalized size = 0. \begin{align*} -{\left (\log \left (2\right ) + 1\right )} \log \left (x\right ) + \frac{1}{2} \, \log \left (\cos \left (x\right )^{2} + \sin \left (x\right )^{2} + 2 \, \cos \left (x\right ) + 1\right ) \log \left (x\right ) + \frac{1}{2} \, \log \left (\cos \left (x\right )^{2} + \sin \left (x\right )^{2} - 2 \, \cos \left (x\right ) + 1\right ) \log \left (x\right ) + \log \left (x\right ) \log \left (\log \left (x\right )\right ) + x + \int \frac{\log \left (x\right ) \sin \left (x\right )}{\cos \left (x\right )^{2} + \sin \left (x\right )^{2} + 2 \, \cos \left (x\right ) + 1}\,{d x} - \int \frac{\log \left (x\right ) \sin \left (x\right )}{\cos \left (x\right )^{2} + \sin \left (x\right )^{2} - 2 \, \cos \left (x\right ) + 1}\,{d x} \end{align*}

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., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\log \left (e^{x} \log \left (x\right ) \sin \left (x\right )\right )}{x}, x\right ) \end{align*}

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 [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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Giac [F(-2)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: TypeError} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Exception raised: TypeError