\(\int \frac {\log (\log (x) \sin (x))}{x} \, dx\) [308]

Optimal result

Integrand size = 10, antiderivative size = 10 \[ \int \frac {\log (\log (x) \sin (x))}{x} \, dx=\text {Int}\left (\frac {\log (\log (x) \sin (x))}{x},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 10, 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 = {} \[ \int \frac {\log (\log (x) \sin (x))}{x} \, dx=\int \frac {\log (\log (x) \sin (x))}{x} \, dx \]

[In]

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

[Out]

Defer[Int][Log[Log[x]*Sin[x]]/x, x]

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

Mathematica [N/A]

Not integrable

Time = 1.94 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\log (\log (x) \sin (x))}{x} \, dx=\int \frac {\log (\log (x) \sin (x))}{x} \, dx \]

[In]

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

[Out]

Integrate[Log[Log[x]*Sin[x]]/x, x]

Maple [N/A]

Not integrable

Time = 0.57 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00

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

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.29 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\log (\log (x) \sin (x))}{x} \, dx=\int { \frac {\log \left (\log \left (x\right ) \sin \left (x\right )\right )}{x} \,d x } \]

[In]

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

[Out]

integral(log(log(x)*sin(x))/x, x)

Sympy [N/A]

Not integrable

Time = 3.83 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int \frac {\log (\log (x) \sin (x))}{x} \, dx=\int \frac {\log {\left (\log {\left (x \right )} \sin {\left (x \right )} \right )}}{x}\, dx \]

[In]

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

[Out]

Integral(log(log(x)*sin(x))/x, x)

Maxima [N/A]

Not integrable

Time = 0.58 (sec) , antiderivative size = 101, normalized size of antiderivative = 10.10 \[ \int \frac {\log (\log (x) \sin (x))}{x} \, dx=\int { \frac {\log \left (\log \left (x\right ) \sin \left (x\right )\right )}{x} \,d x } \]

[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)

Giac [N/A]

Not integrable

Time = 0.35 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\log (\log (x) \sin (x))}{x} \, dx=\int { \frac {\log \left (\log \left (x\right ) \sin \left (x\right )\right )}{x} \,d x } \]

[In]

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

[Out]

integrate(log(log(x)*sin(x))/x, x)

Mupad [N/A]

Not integrable

Time = 1.64 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {\log (\log (x) \sin (x))}{x} \, dx=\int \frac {\ln \left (\ln \left (x\right )\,\sin \left (x\right )\right )}{x} \,d x \]

[In]

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

[Out]

int(log(log(x)*sin(x))/x, x)