3.308 \(\int \frac{\log (\log (x) \sin (x))}{x} \, dx\)

Optimal. Leaf size=12 \[ \text{CannotIntegrate}\left (\frac{\log (\log (x) \sin (x))}{x},x\right ) \]

[Out]

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

________________________________________________________________________________________

Rubi [A]  time = 0.0187267, 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 = {} \[ \int \frac{\log (\log (x) \sin (x))}{x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Defer[Int][Log[Log[x]*Sin[x]]/x, x]

Rubi steps

\begin{align*} \int \frac{\log (\log (x) \sin (x))}{x} \, dx &=\int \frac{\log (\log (x) \sin (x))}{x} \, dx\\ \end{align*}

Mathematica [A]  time = 2.25513, size = 0, normalized size = 0. \[ \int \frac{\log (\log (x) \sin (x))}{x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Integrate[Log[Log[x]*Sin[x]]/x, x]

________________________________________________________________________________________

Maple [A]  time = 0.417, size = 0, normalized size = 0. \begin{align*} \int{\frac{\ln \left ( \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(ln(x)*sin(x))/x,x)

[Out]

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

________________________________________________________________________________________

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 ) + \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(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)) + integrate(log(x)*sin(x)/(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1), x) - int
egrate(log(x)*sin(x)/(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1), x)

________________________________________________________________________________________

Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\log \left (\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(log(x)*sin(x))/x,x, algorithm="fricas")

[Out]

integral(log(log(x)*sin(x))/x, x)

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(log(log(x)*sin(x))/x, x)

________________________________________________________________________________________

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

[Out]

Exception raised: TypeError