\(\int \frac {x^3+(-24+3 x) \log (\log (2))}{x^3} \, dx\) [2269]

Optimal result

Integrand size = 17, antiderivative size = 15 \[ \int \frac {x^3+(-24+3 x) \log (\log (2))}{x^3} \, dx=-7+e+x-\frac {3 (-4+x) \log (\log (2))}{x^2} \] Output:

x-3*(-4+x)*ln(ln(2))/x^2-7+exp(1)
 

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.20 \[ \int \frac {x^3+(-24+3 x) \log (\log (2))}{x^3} \, dx=x+\frac {12 \log (\log (2))}{x^2}-\frac {3 \log (\log (2))}{x} \] Input:

Integrate[(x^3 + (-24 + 3*x)*Log[Log[2]])/x^3,x]
 

Output:

x + (12*Log[Log[2]])/x^2 - (3*Log[Log[2]])/x
 

Rubi [F]

Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.

Failed to integrate

Input:

Int[(x^3 + (-24 + 3*x)*Log[Log[2]])/x^3,x]
 

Output:

$Aborted
                                                                                    
                                                                                    
 

Maple [A] (verified)

Time = 0.07 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.27

method	result	size
default	\(x -\frac {3 \ln \left (\ln \left (2\right )\right )}{x}+\frac {12 \ln \left (\ln \left (2\right )\right )}{x^{2}}\)	\(19\)
risch	\(x +\frac {-3 x \ln \left (\ln \left (2\right )\right )+12 \ln \left (\ln \left (2\right )\right )}{x^{2}}\)	\(19\)
norman	\(\frac {x^{3}-3 x \ln \left (\ln \left (2\right )\right )+12 \ln \left (\ln \left (2\right )\right )}{x^{2}}\)	\(20\)
gosper	\(-\frac {-x^{3}+3 x \ln \left (\ln \left (2\right )\right )-12 \ln \left (\ln \left (2\right )\right )}{x^{2}}\)	\(23\)
parallelrisch	\(-\frac {-x^{3}+3 x \ln \left (\ln \left (2\right )\right )-12 \ln \left (\ln \left (2\right )\right )}{x^{2}}\)	\(23\)

Input:

int(((3*x-24)*ln(ln(2))+x^3)/x^3,x,method=_RETURNVERBOSE)
 

Output:

x-3*ln(ln(2))/x+12*ln(ln(2))/x^2
 

Fricas [A] (verification not implemented)

Time = 0.07 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.07 \[ \int \frac {x^3+(-24+3 x) \log (\log (2))}{x^3} \, dx=\frac {x^{3} - 3 \, {\left (x - 4\right )} \log \left (\log \left (2\right )\right )}{x^{2}} \] Input:

integrate(((3*x-24)*log(log(2))+x^3)/x^3,x, algorithm="fricas")
 

Output:

(x^3 - 3*(x - 4)*log(log(2)))/x^2
 

Sympy [A] (verification not implemented)

Time = 0.06 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.27 \[ \int \frac {x^3+(-24+3 x) \log (\log (2))}{x^3} \, dx=x + \frac {- 3 x \log {\left (\log {\left (2 \right )} \right )} + 12 \log {\left (\log {\left (2 \right )} \right )}}{x^{2}} \] Input:

integrate(((3*x-24)*ln(ln(2))+x**3)/x**3,x)
 

Output:

x + (-3*x*log(log(2)) + 12*log(log(2)))/x**2
 

Maxima [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.20 \[ \int \frac {x^3+(-24+3 x) \log (\log (2))}{x^3} \, dx=x - \frac {3 \, {\left (x \log \left (\log \left (2\right )\right ) - 4 \, \log \left (\log \left (2\right )\right )\right )}}{x^{2}} \] Input:

integrate(((3*x-24)*log(log(2))+x^3)/x^3,x, algorithm="maxima")
                                                                                    
                                                                                    
 

Output:

x - 3*(x*log(log(2)) - 4*log(log(2)))/x^2
 

Giac [A] (verification not implemented)

Time = 0.11 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.20 \[ \int \frac {x^3+(-24+3 x) \log (\log (2))}{x^3} \, dx=x - \frac {3 \, {\left (x \log \left (\log \left (2\right )\right ) - 4 \, \log \left (\log \left (2\right )\right )\right )}}{x^{2}} \] Input:

integrate(((3*x-24)*log(log(2))+x^3)/x^3,x, algorithm="giac")
 

Output:

x - 3*(x*log(log(2)) - 4*log(log(2)))/x^2
 

Mupad [B] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.20 \[ \int \frac {x^3+(-24+3 x) \log (\log (2))}{x^3} \, dx=x+\frac {12\,\ln \left (\ln \left (2\right )\right )-3\,x\,\ln \left (\ln \left (2\right )\right )}{x^2} \] Input:

int((log(log(2))*(3*x - 24) + x^3)/x^3,x)
 

Output:

x + (12*log(log(2)) - 3*x*log(log(2)))/x^2
 

Reduce [B] (verification not implemented)

Time = 0.19 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.27 \[ \int \frac {x^3+(-24+3 x) \log (\log (2))}{x^3} \, dx=\frac {-3 \,\mathrm {log}\left (\mathrm {log}\left (2\right )\right ) x +12 \,\mathrm {log}\left (\mathrm {log}\left (2\right )\right )+x^{3}}{x^{2}} \] Input:

int(((3*x-24)*log(log(2))+x^3)/x^3,x)
 

Output:

( - 3*log(log(2))*x + 12*log(log(2)) + x**3)/x**2