Integrand size = 53, antiderivative size = 17 \[ \int \frac {29229056+446 \log (x)+(-14614529-223 \log (x)) \log \left (x^2\right )+\left (131072+2 \log (x)+(-65536-\log (x)) \log \left (x^2\right )\right ) \log (65536+\log (x))}{(65536+\log (x)) \log ^2\left (x^2\right )} \, dx=\frac {x (-223-\log (65536+\log (x)))}{\log \left (x^2\right )} \] Output:
x/ln(x^2)*(-223-ln(ln(x)+65536))
Time = 0.10 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.41 \[ \int \frac {29229056+446 \log (x)+(-14614529-223 \log (x)) \log \left (x^2\right )+\left (131072+2 \log (x)+(-65536-\log (x)) \log \left (x^2\right )\right ) \log (65536+\log (x))}{(65536+\log (x)) \log ^2\left (x^2\right )} \, dx=-\frac {223 x}{\log \left (x^2\right )}-\frac {x \log (65536+\log (x))}{\log \left (x^2\right )} \] Input:
Integrate[(29229056 + 446*Log[x] + (-14614529 - 223*Log[x])*Log[x^2] + (13 1072 + 2*Log[x] + (-65536 - Log[x])*Log[x^2])*Log[65536 + Log[x]])/((65536 + Log[x])*Log[x^2]^2),x]
Output:
(-223*x)/Log[x^2] - (x*Log[65536 + Log[x]])/Log[x^2]
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.
\(\displaystyle \int \frac {(-223 \log (x)-14614529) \log \left (x^2\right )+\left ((-\log (x)-65536) \log \left (x^2\right )+2 \log (x)+131072\right ) \log (\log (x)+65536)+446 \log (x)+29229056}{(\log (x)+65536) \log ^2\left (x^2\right )} \, dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (\frac {-223 \log \left (x^2\right ) \log (x)-14614529 \log \left (x^2\right )+446 \log (x)+29229056}{(\log (x)+65536) \log ^2\left (x^2\right )}-\frac {\left (\log \left (x^2\right )-2\right ) \log (\log (x)+65536)}{\log ^2\left (x^2\right )}\right )dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle 2 \int \frac {\log (\log (x)+65536)}{\log ^2\left (x^2\right )}dx-14614529 \int \frac {1}{(\log (x)+65536) \log \left (x^2\right )}dx-223 \int \frac {\log (x)}{(\log (x)+65536) \log \left (x^2\right )}dx-\int \frac {\log (\log (x)+65536)}{\log \left (x^2\right )}dx+\frac {223 x \operatorname {ExpIntegralEi}\left (\frac {\log \left (x^2\right )}{2}\right )}{2 \sqrt {x^2}}-\frac {223 x}{\log \left (x^2\right )}\) |
Input:
Int[(29229056 + 446*Log[x] + (-14614529 - 223*Log[x])*Log[x^2] + (131072 + 2*Log[x] + (-65536 - Log[x])*Log[x^2])*Log[65536 + Log[x]])/((65536 + Log [x])*Log[x^2]^2),x]
Output:
$Aborted
Time = 8.17 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.24
method | result | size |
parallelrisch | \(-\frac {131072 x \ln \left (\ln \left (x \right )+65536\right )+29229056 x}{131072 \ln \left (x^{2}\right )}\) | \(21\) |
risch | \(-\frac {2 i x \ln \left (\ln \left (x \right )+65536\right )}{4 i \ln \left (x \right )+\pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )-2 \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}+\pi \operatorname {csgn}\left (i x^{2}\right )^{3}}-\frac {446 i x}{4 i \ln \left (x \right )+\pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )-2 \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}+\pi \operatorname {csgn}\left (i x^{2}\right )^{3}}\) | \(119\) |
Input:
int((((-ln(x)-65536)*ln(x^2)+2*ln(x)+131072)*ln(ln(x)+65536)+(-223*ln(x)-1 4614529)*ln(x^2)+446*ln(x)+29229056)/(ln(x)+65536)/ln(x^2)^2,x,method=_RET URNVERBOSE)
Output:
-1/131072*(131072*x*ln(ln(x)+65536)+29229056*x)/ln(x^2)
Time = 0.09 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00 \[ \int \frac {29229056+446 \log (x)+(-14614529-223 \log (x)) \log \left (x^2\right )+\left (131072+2 \log (x)+(-65536-\log (x)) \log \left (x^2\right )\right ) \log (65536+\log (x))}{(65536+\log (x)) \log ^2\left (x^2\right )} \, dx=-\frac {x \log \left (\log \left (x\right ) + 65536\right ) + 223 \, x}{2 \, \log \left (x\right )} \] Input:
integrate((((-log(x)-65536)*log(x^2)+2*log(x)+131072)*log(log(x)+65536)+(- 223*log(x)-14614529)*log(x^2)+446*log(x)+29229056)/(log(x)+65536)/log(x^2) ^2,x, algorithm="fricas")
Output:
-1/2*(x*log(log(x) + 65536) + 223*x)/log(x)
Time = 0.14 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.29 \[ \int \frac {29229056+446 \log (x)+(-14614529-223 \log (x)) \log \left (x^2\right )+\left (131072+2 \log (x)+(-65536-\log (x)) \log \left (x^2\right )\right ) \log (65536+\log (x))}{(65536+\log (x)) \log ^2\left (x^2\right )} \, dx=- \frac {x \log {\left (\log {\left (x \right )} + 65536 \right )}}{2 \log {\left (x \right )}} - \frac {223 x}{2 \log {\left (x \right )}} \] Input:
integrate((((-ln(x)-65536)*ln(x**2)+2*ln(x)+131072)*ln(ln(x)+65536)+(-223* ln(x)-14614529)*ln(x**2)+446*ln(x)+29229056)/(ln(x)+65536)/ln(x**2)**2,x)
Output:
-x*log(log(x) + 65536)/(2*log(x)) - 223*x/(2*log(x))
Time = 0.06 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00 \[ \int \frac {29229056+446 \log (x)+(-14614529-223 \log (x)) \log \left (x^2\right )+\left (131072+2 \log (x)+(-65536-\log (x)) \log \left (x^2\right )\right ) \log (65536+\log (x))}{(65536+\log (x)) \log ^2\left (x^2\right )} \, dx=-\frac {x \log \left (\log \left (x\right ) + 65536\right ) + 223 \, x}{2 \, \log \left (x\right )} \] Input:
integrate((((-log(x)-65536)*log(x^2)+2*log(x)+131072)*log(log(x)+65536)+(- 223*log(x)-14614529)*log(x^2)+446*log(x)+29229056)/(log(x)+65536)/log(x^2) ^2,x, algorithm="maxima")
Output:
-1/2*(x*log(log(x) + 65536) + 223*x)/log(x)
Time = 0.13 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.18 \[ \int \frac {29229056+446 \log (x)+(-14614529-223 \log (x)) \log \left (x^2\right )+\left (131072+2 \log (x)+(-65536-\log (x)) \log \left (x^2\right )\right ) \log (65536+\log (x))}{(65536+\log (x)) \log ^2\left (x^2\right )} \, dx=-\frac {x \log \left (\log \left (x\right ) + 65536\right )}{2 \, \log \left (x\right )} - \frac {223 \, x}{2 \, \log \left (x\right )} \] Input:
integrate((((-log(x)-65536)*log(x^2)+2*log(x)+131072)*log(log(x)+65536)+(- 223*log(x)-14614529)*log(x^2)+446*log(x)+29229056)/(log(x)+65536)/log(x^2) ^2,x, algorithm="giac")
Output:
-1/2*x*log(log(x) + 65536)/log(x) - 223/2*x/log(x)
Time = 3.03 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.94 \[ \int \frac {29229056+446 \log (x)+(-14614529-223 \log (x)) \log \left (x^2\right )+\left (131072+2 \log (x)+(-65536-\log (x)) \log \left (x^2\right )\right ) \log (65536+\log (x))}{(65536+\log (x)) \log ^2\left (x^2\right )} \, dx=-\frac {x\,\left (\ln \left (\ln \left (x\right )+65536\right )+223\right )}{\ln \left (x^2\right )} \] Input:
int((446*log(x) - log(x^2)*(223*log(x) + 14614529) + log(log(x) + 65536)*( 2*log(x) - log(x^2)*(log(x) + 65536) + 131072) + 29229056)/(log(x^2)^2*(lo g(x) + 65536)),x)
Output:
-(x*(log(log(x) + 65536) + 223))/log(x^2)
Time = 0.19 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00 \[ \int \frac {29229056+446 \log (x)+(-14614529-223 \log (x)) \log \left (x^2\right )+\left (131072+2 \log (x)+(-65536-\log (x)) \log \left (x^2\right )\right ) \log (65536+\log (x))}{(65536+\log (x)) \log ^2\left (x^2\right )} \, dx=\frac {x \left (-\mathrm {log}\left (\mathrm {log}\left (x \right )+65536\right )-223\right )}{\mathrm {log}\left (x^{2}\right )} \] Input:
int((((-log(x)-65536)*log(x^2)+2*log(x)+131072)*log(log(x)+65536)+(-223*lo g(x)-14614529)*log(x^2)+446*log(x)+29229056)/(log(x)+65536)/log(x^2)^2,x)
Output:
(x*( - log(log(x) + 65536) - 223))/log(x**2)