Integrand size = 165, antiderivative size = 22 \[ \int \frac {-123904 x^2+5632 x^3-64 x^4+\left (4224 x+61856 x^2-4224 x^3+64 x^4\right ) \log (x)+\left (-32-1408 x+64 x^2\right ) \log ^2(x)+\left (123904 x^2-5632 x^3+64 x^4+\left (-2816 x-123840 x^2+8448 x^3-128 x^4\right ) \log (x)+\left (2816 x-128 x^2\right ) \log ^2(x)\right ) \log \left (\log ^2(x)\right )+\left (\left (-1408 x+61984 x^2-4224 x^3+64 x^4\right ) \log (x)+\left (32-1408 x+64 x^2\right ) \log ^2(x)\right ) \log ^2\left (\log ^2(x)\right )}{x \log (x)} \, dx=16 \left (-44 x+x^2+\log (x)\right )^2 \left (-1+\log \left (\log ^2(x)\right )\right )^2 \] Output:
16*(ln(ln(x)^2)-1)^2*(-44*x+ln(x)+x^2)^2
Time = 5.03 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.95 \[ \int \frac {-123904 x^2+5632 x^3-64 x^4+\left (4224 x+61856 x^2-4224 x^3+64 x^4\right ) \log (x)+\left (-32-1408 x+64 x^2\right ) \log ^2(x)+\left (123904 x^2-5632 x^3+64 x^4+\left (-2816 x-123840 x^2+8448 x^3-128 x^4\right ) \log (x)+\left (2816 x-128 x^2\right ) \log ^2(x)\right ) \log \left (\log ^2(x)\right )+\left (\left (-1408 x+61984 x^2-4224 x^3+64 x^4\right ) \log (x)+\left (32-1408 x+64 x^2\right ) \log ^2(x)\right ) \log ^2\left (\log ^2(x)\right )}{x \log (x)} \, dx=16 ((-44+x) x+\log (x))^2 \left (-1+\log \left (\log ^2(x)\right )\right )^2 \] Input:
Integrate[(-123904*x^2 + 5632*x^3 - 64*x^4 + (4224*x + 61856*x^2 - 4224*x^ 3 + 64*x^4)*Log[x] + (-32 - 1408*x + 64*x^2)*Log[x]^2 + (123904*x^2 - 5632 *x^3 + 64*x^4 + (-2816*x - 123840*x^2 + 8448*x^3 - 128*x^4)*Log[x] + (2816 *x - 128*x^2)*Log[x]^2)*Log[Log[x]^2] + ((-1408*x + 61984*x^2 - 4224*x^3 + 64*x^4)*Log[x] + (32 - 1408*x + 64*x^2)*Log[x]^2)*Log[Log[x]^2]^2)/(x*Log [x]),x]
Output:
16*((-44 + x)*x + Log[x])^2*(-1 + Log[Log[x]^2])^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.
| \(\displaystyle \int \frac {-64 x^4+5632 x^3-123904 x^2+\left (64 x^2-1408 x-32\right ) \log ^2(x)+\left (\left (64 x^2-1408 x+32\right ) \log ^2(x)+\left (64 x^4-4224 x^3+61984 x^2-1408 x\right ) \log (x)\right ) \log ^2\left (\log ^2(x)\right )+\left (64 x^4-5632 x^3+123904 x^2+\left (2816 x-128 x^2\right ) \log ^2(x)+\left (-128 x^4+8448 x^3-123840 x^2-2816 x\right ) \log (x)\right ) \log \left (\log ^2(x)\right )+\left (64 x^4-4224 x^3+61856 x^2+4224 x\right ) \log (x)}{x \log (x)} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {32 ((x-44) x+\log (x)) \left (1-\log \left (\log ^2(x)\right )\right ) \left (-\log (x) \left (-2 x^2+\left (2 x^2-44 x+1\right ) \log \left (\log ^2(x)\right )+44 x+1\right )-2 (x-44) x\right )}{x \log (x)}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 32 \int -\frac {((44-x) x-\log (x)) \left (1-\log \left (\log ^2(x)\right )\right ) \left (2 (44-x) x-\log (x) \left (-2 x^2+44 x+\left (2 x^2-44 x+1\right ) \log \left (\log ^2(x)\right )+1\right )\right )}{x \log (x)}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -32 \int \frac {((44-x) x-\log (x)) \left (1-\log \left (\log ^2(x)\right )\right ) \left (2 (44-x) x-\log (x) \left (-2 x^2+44 x+\left (2 x^2-44 x+1\right ) \log \left (\log ^2(x)\right )+1\right )\right )}{x \log (x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -32 \int \left (-\frac {\left (2 x^2-44 x+1\right ) \left (x^2-44 x+\log (x)\right ) \log ^2\left (\log ^2(x)\right )}{x}+\frac {2 \left (2 \log (x) x^3-x^3-132 \log (x) x^2+88 x^2+2 \log ^2(x) x+1935 \log (x) x-1936 x-44 \log ^2(x)+44 \log (x)\right ) \log \left (\log ^2(x)\right )}{\log (x)}+\frac {-2 \log (x) x^4+2 x^4+132 \log (x) x^3-176 x^3-2 \log ^2(x) x^2-1933 \log (x) x^2+3872 x^2+44 \log ^2(x) x-132 \log (x) x+\log ^2(x)}{x \log (x)}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -32 \left (-2 \int \frac {x^3 \log \left (\log ^2(x)\right )}{\log (x)}dx-2 \int x^3 \log ^2\left (\log ^2(x)\right )dx+176 \int \frac {x^2 \log \left (\log ^2(x)\right )}{\log (x)}dx+132 \int x^2 \log ^2\left (\log ^2(x)\right )dx-3872 \int \frac {x \log \left (\log ^2(x)\right )}{\log (x)}dx-88 \int \log (x) \log \left (\log ^2(x)\right )dx+4 \int x \log (x) \log \left (\log ^2(x)\right )dx+44 \int \log ^2\left (\log ^2(x)\right )dx-1937 \int x \log ^2\left (\log ^2(x)\right )dx+44 \int \log (x) \log ^2\left (\log ^2(x)\right )dx-2 \int x \log (x) \log ^2\left (\log ^2(x)\right )dx+2 \operatorname {ExpIntegralEi}(2 \log (x))-176 \operatorname {LogIntegral}(x)-\frac {x^4}{2}+x^4 \log \left (\log ^2(x)\right )+44 x^3-88 x^3 \log \left (\log ^2(x)\right )-966 x^2+1935 x^2 \log \left (\log ^2(x)\right )-x^2 \log (x)-176 x+88 x \log \left (\log ^2(x)\right )-\frac {\log ^2(x)}{2}-\frac {1}{2} \log ^2(x) \log ^2\left (\log ^2(x)\right )+\log ^2(x) \log \left (\log ^2(x)\right )+44 x \log (x)\right )\) |
Input:
Int[(-123904*x^2 + 5632*x^3 - 64*x^4 + (4224*x + 61856*x^2 - 4224*x^3 + 64 *x^4)*Log[x] + (-32 - 1408*x + 64*x^2)*Log[x]^2 + (123904*x^2 - 5632*x^3 + 64*x^4 + (-2816*x - 123840*x^2 + 8448*x^3 - 128*x^4)*Log[x] + (2816*x - 1 28*x^2)*Log[x]^2)*Log[Log[x]^2] + ((-1408*x + 61984*x^2 - 4224*x^3 + 64*x^ 4)*Log[x] + (32 - 1408*x + 64*x^2)*Log[x]^2)*Log[Log[x]^2]^2)/(x*Log[x]),x ]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(172\) vs. \(2(22)=44\).
Time = 1.98 (sec) , antiderivative size = 173, normalized size of antiderivative = 7.86
| method | result | size |
| parallelrisch | \(16 \ln \left (\ln \left (x \right )^{2}\right )^{2} x^{4}-32 \ln \left (\ln \left (x \right )^{2}\right ) x^{4}-1408 x^{3} \ln \left (\ln \left (x \right )^{2}\right )^{2}+32 \ln \left (x \right ) \ln \left (\ln \left (x \right )^{2}\right )^{2} x^{2}+16 x^{4}+2816 \ln \left (\ln \left (x \right )^{2}\right ) x^{3}-64 \ln \left (x \right ) \ln \left (\ln \left (x \right )^{2}\right ) x^{2}+30976 x^{2} \ln \left (\ln \left (x \right )^{2}\right )^{2}-1408 \ln \left (x \right ) \ln \left (\ln \left (x \right )^{2}\right )^{2} x +16 \ln \left (x \right )^{2} \ln \left (\ln \left (x \right )^{2}\right )^{2}-1408 x^{3}+32 x^{2} \ln \left (x \right )-61952 x^{2} \ln \left (\ln \left (x \right )^{2}\right )+2816 x \ln \left (x \right ) \ln \left (\ln \left (x \right )^{2}\right )-32 \ln \left (x \right )^{2} \ln \left (\ln \left (x \right )^{2}\right )+30976 x^{2}-1408 x \ln \left (x \right )+16 \ln \left (x \right )^{2}\) | \(173\) |
| risch | \(\text {Expression too large to display}\) | \(1608\) |
Input:
int((((64*x^2-1408*x+32)*ln(x)^2+(64*x^4-4224*x^3+61984*x^2-1408*x)*ln(x)) *ln(ln(x)^2)^2+((-128*x^2+2816*x)*ln(x)^2+(-128*x^4+8448*x^3-123840*x^2-28 16*x)*ln(x)+64*x^4-5632*x^3+123904*x^2)*ln(ln(x)^2)+(64*x^2-1408*x-32)*ln( x)^2+(64*x^4-4224*x^3+61856*x^2+4224*x)*ln(x)-64*x^4+5632*x^3-123904*x^2)/ x/ln(x),x,method=_RETURNVERBOSE)
Output:
16*ln(ln(x)^2)^2*x^4-32*ln(ln(x)^2)*x^4-1408*x^3*ln(ln(x)^2)^2+32*ln(x)*ln (ln(x)^2)^2*x^2+16*x^4+2816*ln(ln(x)^2)*x^3-64*ln(x)*ln(ln(x)^2)*x^2+30976 *x^2*ln(ln(x)^2)^2-1408*ln(x)*ln(ln(x)^2)^2*x+16*ln(x)^2*ln(ln(x)^2)^2-140 8*x^3+32*x^2*ln(x)-61952*x^2*ln(ln(x)^2)+2816*x*ln(x)*ln(ln(x)^2)-32*ln(x) ^2*ln(ln(x)^2)+30976*x^2-1408*x*ln(x)+16*ln(x)^2
Leaf count of result is larger than twice the leaf count of optimal. 107 vs. \(2 (22) = 44\).
Time = 0.07 (sec) , antiderivative size = 107, normalized size of antiderivative = 4.86 \[ \int \frac {-123904 x^2+5632 x^3-64 x^4+\left (4224 x+61856 x^2-4224 x^3+64 x^4\right ) \log (x)+\left (-32-1408 x+64 x^2\right ) \log ^2(x)+\left (123904 x^2-5632 x^3+64 x^4+\left (-2816 x-123840 x^2+8448 x^3-128 x^4\right ) \log (x)+\left (2816 x-128 x^2\right ) \log ^2(x)\right ) \log \left (\log ^2(x)\right )+\left (\left (-1408 x+61984 x^2-4224 x^3+64 x^4\right ) \log (x)+\left (32-1408 x+64 x^2\right ) \log ^2(x)\right ) \log ^2\left (\log ^2(x)\right )}{x \log (x)} \, dx=16 \, x^{4} - 1408 \, x^{3} + 16 \, {\left (x^{4} - 88 \, x^{3} + 1936 \, x^{2} + 2 \, {\left (x^{2} - 44 \, x\right )} \log \left (x\right ) + \log \left (x\right )^{2}\right )} \log \left (\log \left (x\right )^{2}\right )^{2} + 30976 \, x^{2} - 32 \, {\left (x^{4} - 88 \, x^{3} + 1936 \, x^{2} + 2 \, {\left (x^{2} - 44 \, x\right )} \log \left (x\right ) + \log \left (x\right )^{2}\right )} \log \left (\log \left (x\right )^{2}\right ) + 32 \, {\left (x^{2} - 44 \, x\right )} \log \left (x\right ) + 16 \, \log \left (x\right )^{2} \] Input:
integrate((((64*x^2-1408*x+32)*log(x)^2+(64*x^4-4224*x^3+61984*x^2-1408*x) *log(x))*log(log(x)^2)^2+((-128*x^2+2816*x)*log(x)^2+(-128*x^4+8448*x^3-12 3840*x^2-2816*x)*log(x)+64*x^4-5632*x^3+123904*x^2)*log(log(x)^2)+(64*x^2- 1408*x-32)*log(x)^2+(64*x^4-4224*x^3+61856*x^2+4224*x)*log(x)-64*x^4+5632* x^3-123904*x^2)/x/log(x),x, algorithm="fricas")
Output:
16*x^4 - 1408*x^3 + 16*(x^4 - 88*x^3 + 1936*x^2 + 2*(x^2 - 44*x)*log(x) + log(x)^2)*log(log(x)^2)^2 + 30976*x^2 - 32*(x^4 - 88*x^3 + 1936*x^2 + 2*(x ^2 - 44*x)*log(x) + log(x)^2)*log(log(x)^2) + 32*(x^2 - 44*x)*log(x) + 16* log(x)^2
Leaf count of result is larger than twice the leaf count of optimal. 122 vs. \(2 (22) = 44\).
Time = 0.35 (sec) , antiderivative size = 122, normalized size of antiderivative = 5.55 \[ \int \frac {-123904 x^2+5632 x^3-64 x^4+\left (4224 x+61856 x^2-4224 x^3+64 x^4\right ) \log (x)+\left (-32-1408 x+64 x^2\right ) \log ^2(x)+\left (123904 x^2-5632 x^3+64 x^4+\left (-2816 x-123840 x^2+8448 x^3-128 x^4\right ) \log (x)+\left (2816 x-128 x^2\right ) \log ^2(x)\right ) \log \left (\log ^2(x)\right )+\left (\left (-1408 x+61984 x^2-4224 x^3+64 x^4\right ) \log (x)+\left (32-1408 x+64 x^2\right ) \log ^2(x)\right ) \log ^2\left (\log ^2(x)\right )}{x \log (x)} \, dx=16 x^{4} - 1408 x^{3} + 30976 x^{2} + \left (32 x^{2} - 1408 x\right ) \log {\left (x \right )} + \left (- 32 x^{4} + 2816 x^{3} - 64 x^{2} \log {\left (x \right )} - 61952 x^{2} + 2816 x \log {\left (x \right )} - 32 \log {\left (x \right )}^{2}\right ) \log {\left (\log {\left (x \right )}^{2} \right )} + \left (16 x^{4} - 1408 x^{3} + 32 x^{2} \log {\left (x \right )} + 30976 x^{2} - 1408 x \log {\left (x \right )} + 16 \log {\left (x \right )}^{2}\right ) \log {\left (\log {\left (x \right )}^{2} \right )}^{2} + 16 \log {\left (x \right )}^{2} \] Input:
integrate((((64*x**2-1408*x+32)*ln(x)**2+(64*x**4-4224*x**3+61984*x**2-140 8*x)*ln(x))*ln(ln(x)**2)**2+((-128*x**2+2816*x)*ln(x)**2+(-128*x**4+8448*x **3-123840*x**2-2816*x)*ln(x)+64*x**4-5632*x**3+123904*x**2)*ln(ln(x)**2)+ (64*x**2-1408*x-32)*ln(x)**2+(64*x**4-4224*x**3+61856*x**2+4224*x)*ln(x)-6 4*x**4+5632*x**3-123904*x**2)/x/ln(x),x)
Output:
16*x**4 - 1408*x**3 + 30976*x**2 + (32*x**2 - 1408*x)*log(x) + (-32*x**4 + 2816*x**3 - 64*x**2*log(x) - 61952*x**2 + 2816*x*log(x) - 32*log(x)**2)*l og(log(x)**2) + (16*x**4 - 1408*x**3 + 32*x**2*log(x) + 30976*x**2 - 1408* x*log(x) + 16*log(x)**2)*log(log(x)**2)**2 + 16*log(x)**2
\[ \int \frac {-123904 x^2+5632 x^3-64 x^4+\left (4224 x+61856 x^2-4224 x^3+64 x^4\right ) \log (x)+\left (-32-1408 x+64 x^2\right ) \log ^2(x)+\left (123904 x^2-5632 x^3+64 x^4+\left (-2816 x-123840 x^2+8448 x^3-128 x^4\right ) \log (x)+\left (2816 x-128 x^2\right ) \log ^2(x)\right ) \log \left (\log ^2(x)\right )+\left (\left (-1408 x+61984 x^2-4224 x^3+64 x^4\right ) \log (x)+\left (32-1408 x+64 x^2\right ) \log ^2(x)\right ) \log ^2\left (\log ^2(x)\right )}{x \log (x)} \, dx=\int { -\frac {32 \, {\left (2 \, x^{4} - 176 \, x^{3} - {\left ({\left (2 \, x^{2} - 44 \, x + 1\right )} \log \left (x\right )^{2} + {\left (2 \, x^{4} - 132 \, x^{3} + 1937 \, x^{2} - 44 \, x\right )} \log \left (x\right )\right )} \log \left (\log \left (x\right )^{2}\right )^{2} - {\left (2 \, x^{2} - 44 \, x - 1\right )} \log \left (x\right )^{2} + 3872 \, x^{2} - 2 \, {\left (x^{4} - 88 \, x^{3} - 2 \, {\left (x^{2} - 22 \, x\right )} \log \left (x\right )^{2} + 1936 \, x^{2} - {\left (2 \, x^{4} - 132 \, x^{3} + 1935 \, x^{2} + 44 \, x\right )} \log \left (x\right )\right )} \log \left (\log \left (x\right )^{2}\right ) - {\left (2 \, x^{4} - 132 \, x^{3} + 1933 \, x^{2} + 132 \, x\right )} \log \left (x\right )\right )}}{x \log \left (x\right )} \,d x } \] Input:
integrate((((64*x^2-1408*x+32)*log(x)^2+(64*x^4-4224*x^3+61984*x^2-1408*x) *log(x))*log(log(x)^2)^2+((-128*x^2+2816*x)*log(x)^2+(-128*x^4+8448*x^3-12 3840*x^2-2816*x)*log(x)+64*x^4-5632*x^3+123904*x^2)*log(log(x)^2)+(64*x^2- 1408*x-32)*log(x)^2+(64*x^4-4224*x^3+61856*x^2+4224*x)*log(x)-64*x^4+5632* x^3-123904*x^2)/x/log(x),x, algorithm="maxima")
Output:
-32*x^4*log(log(x)^2) + 16*x^4 + 2816*x^3*log(log(x)^2) - 1408*x^3 - 61920 *x^2*log(log(x)^2) + 32*x^2*log(x) + 64*(x^4 - 88*x^3 + 1936*x^2 + 2*(x^2 - 44*x)*log(x) + log(x)^2)*log(log(x))^2 + 30976*x^2 - 2816*x*log(log(x)^2 ) - 1408*x*log(x) + 16*log(x)^2 - 64*(x^2 + 2*(x^2 - 44*x)*log(x) + log(x) ^2 - 88*x)*log(log(x)) - 64*Ei(2*log(x)) + 5632*Ei(log(x)) + 32*integrate( 2*(x - 88)/log(x), x)
Leaf count of result is larger than twice the leaf count of optimal. 107 vs. \(2 (22) = 44\).
Time = 0.28 (sec) , antiderivative size = 107, normalized size of antiderivative = 4.86 \[ \int \frac {-123904 x^2+5632 x^3-64 x^4+\left (4224 x+61856 x^2-4224 x^3+64 x^4\right ) \log (x)+\left (-32-1408 x+64 x^2\right ) \log ^2(x)+\left (123904 x^2-5632 x^3+64 x^4+\left (-2816 x-123840 x^2+8448 x^3-128 x^4\right ) \log (x)+\left (2816 x-128 x^2\right ) \log ^2(x)\right ) \log \left (\log ^2(x)\right )+\left (\left (-1408 x+61984 x^2-4224 x^3+64 x^4\right ) \log (x)+\left (32-1408 x+64 x^2\right ) \log ^2(x)\right ) \log ^2\left (\log ^2(x)\right )}{x \log (x)} \, dx=16 \, x^{4} - 1408 \, x^{3} + 16 \, {\left (x^{4} - 88 \, x^{3} + 1936 \, x^{2} + 2 \, {\left (x^{2} - 44 \, x\right )} \log \left (x\right ) + \log \left (x\right )^{2}\right )} \log \left (\log \left (x\right )^{2}\right )^{2} + 30976 \, x^{2} - 32 \, {\left (x^{4} - 88 \, x^{3} + 1936 \, x^{2} + 2 \, {\left (x^{2} - 44 \, x\right )} \log \left (x\right ) + \log \left (x\right )^{2}\right )} \log \left (\log \left (x\right )^{2}\right ) + 32 \, {\left (x^{2} - 44 \, x\right )} \log \left (x\right ) + 16 \, \log \left (x\right )^{2} \] Input:
integrate((((64*x^2-1408*x+32)*log(x)^2+(64*x^4-4224*x^3+61984*x^2-1408*x) *log(x))*log(log(x)^2)^2+((-128*x^2+2816*x)*log(x)^2+(-128*x^4+8448*x^3-12 3840*x^2-2816*x)*log(x)+64*x^4-5632*x^3+123904*x^2)*log(log(x)^2)+(64*x^2- 1408*x-32)*log(x)^2+(64*x^4-4224*x^3+61856*x^2+4224*x)*log(x)-64*x^4+5632* x^3-123904*x^2)/x/log(x),x, algorithm="giac")
Output:
16*x^4 - 1408*x^3 + 16*(x^4 - 88*x^3 + 1936*x^2 + 2*(x^2 - 44*x)*log(x) + log(x)^2)*log(log(x)^2)^2 + 30976*x^2 - 32*(x^4 - 88*x^3 + 1936*x^2 + 2*(x ^2 - 44*x)*log(x) + log(x)^2)*log(log(x)^2) + 32*(x^2 - 44*x)*log(x) + 16* log(x)^2
Time = 2.17 (sec) , antiderivative size = 120, normalized size of antiderivative = 5.45 \[ \int \frac {-123904 x^2+5632 x^3-64 x^4+\left (4224 x+61856 x^2-4224 x^3+64 x^4\right ) \log (x)+\left (-32-1408 x+64 x^2\right ) \log ^2(x)+\left (123904 x^2-5632 x^3+64 x^4+\left (-2816 x-123840 x^2+8448 x^3-128 x^4\right ) \log (x)+\left (2816 x-128 x^2\right ) \log ^2(x)\right ) \log \left (\log ^2(x)\right )+\left (\left (-1408 x+61984 x^2-4224 x^3+64 x^4\right ) \log (x)+\left (32-1408 x+64 x^2\right ) \log ^2(x)\right ) \log ^2\left (\log ^2(x)\right )}{x \log (x)} \, dx=16\,{\ln \left (x\right )}^2-\ln \left ({\ln \left (x\right )}^2\right )\,\left (32\,{\ln \left (x\right )}^2-\ln \left (x\right )\,\left (2816\,x-64\,x^2\right )+61952\,x^2-2816\,x^3+32\,x^4\right )-\ln \left (x\right )\,\left (1408\,x-32\,x^2\right )+{\ln \left ({\ln \left (x\right )}^2\right )}^2\,\left (16\,{\ln \left (x\right )}^2-\ln \left (x\right )\,\left (1408\,x-32\,x^2\right )+30976\,x^2-1408\,x^3+16\,x^4\right )+30976\,x^2-1408\,x^3+16\,x^4 \] Input:
int((log(x)*(4224*x + 61856*x^2 - 4224*x^3 + 64*x^4) - log(x)^2*(1408*x - 64*x^2 + 32) + log(log(x)^2)*(log(x)^2*(2816*x - 128*x^2) - log(x)*(2816*x + 123840*x^2 - 8448*x^3 + 128*x^4) + 123904*x^2 - 5632*x^3 + 64*x^4) - 12 3904*x^2 + 5632*x^3 - 64*x^4 + log(log(x)^2)^2*(log(x)^2*(64*x^2 - 1408*x + 32) - log(x)*(1408*x - 61984*x^2 + 4224*x^3 - 64*x^4)))/(x*log(x)),x)
Output:
16*log(x)^2 - log(log(x)^2)*(32*log(x)^2 - log(x)*(2816*x - 64*x^2) + 6195 2*x^2 - 2816*x^3 + 32*x^4) - log(x)*(1408*x - 32*x^2) + log(log(x)^2)^2*(1 6*log(x)^2 - log(x)*(1408*x - 32*x^2) + 30976*x^2 - 1408*x^3 + 16*x^4) + 3 0976*x^2 - 1408*x^3 + 16*x^4
Time = 0.23 (sec) , antiderivative size = 172, normalized size of antiderivative = 7.82 \[ \int \frac {-123904 x^2+5632 x^3-64 x^4+\left (4224 x+61856 x^2-4224 x^3+64 x^4\right ) \log (x)+\left (-32-1408 x+64 x^2\right ) \log ^2(x)+\left (123904 x^2-5632 x^3+64 x^4+\left (-2816 x-123840 x^2+8448 x^3-128 x^4\right ) \log (x)+\left (2816 x-128 x^2\right ) \log ^2(x)\right ) \log \left (\log ^2(x)\right )+\left (\left (-1408 x+61984 x^2-4224 x^3+64 x^4\right ) \log (x)+\left (32-1408 x+64 x^2\right ) \log ^2(x)\right ) \log ^2\left (\log ^2(x)\right )}{x \log (x)} \, dx=16 \mathrm {log}\left (\mathrm {log}\left (x \right )^{2}\right )^{2} \mathrm {log}\left (x \right )^{2}+32 \mathrm {log}\left (\mathrm {log}\left (x \right )^{2}\right )^{2} \mathrm {log}\left (x \right ) x^{2}-1408 \mathrm {log}\left (\mathrm {log}\left (x \right )^{2}\right )^{2} \mathrm {log}\left (x \right ) x +16 \mathrm {log}\left (\mathrm {log}\left (x \right )^{2}\right )^{2} x^{4}-1408 \mathrm {log}\left (\mathrm {log}\left (x \right )^{2}\right )^{2} x^{3}+30976 \mathrm {log}\left (\mathrm {log}\left (x \right )^{2}\right )^{2} x^{2}-32 \,\mathrm {log}\left (\mathrm {log}\left (x \right )^{2}\right ) \mathrm {log}\left (x \right )^{2}-64 \,\mathrm {log}\left (\mathrm {log}\left (x \right )^{2}\right ) \mathrm {log}\left (x \right ) x^{2}+2816 \,\mathrm {log}\left (\mathrm {log}\left (x \right )^{2}\right ) \mathrm {log}\left (x \right ) x -32 \,\mathrm {log}\left (\mathrm {log}\left (x \right )^{2}\right ) x^{4}+2816 \,\mathrm {log}\left (\mathrm {log}\left (x \right )^{2}\right ) x^{3}-61952 \,\mathrm {log}\left (\mathrm {log}\left (x \right )^{2}\right ) x^{2}+16 \mathrm {log}\left (x \right )^{2}+32 \,\mathrm {log}\left (x \right ) x^{2}-1408 \,\mathrm {log}\left (x \right ) x +16 x^{4}-1408 x^{3}+30976 x^{2} \] Input:
int((((64*x^2-1408*x+32)*log(x)^2+(64*x^4-4224*x^3+61984*x^2-1408*x)*log(x ))*log(log(x)^2)^2+((-128*x^2+2816*x)*log(x)^2+(-128*x^4+8448*x^3-123840*x ^2-2816*x)*log(x)+64*x^4-5632*x^3+123904*x^2)*log(log(x)^2)+(64*x^2-1408*x -32)*log(x)^2+(64*x^4-4224*x^3+61856*x^2+4224*x)*log(x)-64*x^4+5632*x^3-12 3904*x^2)/x/log(x),x)
Output:
16*(log(log(x)**2)**2*log(x)**2 + 2*log(log(x)**2)**2*log(x)*x**2 - 88*log (log(x)**2)**2*log(x)*x + log(log(x)**2)**2*x**4 - 88*log(log(x)**2)**2*x* *3 + 1936*log(log(x)**2)**2*x**2 - 2*log(log(x)**2)*log(x)**2 - 4*log(log( x)**2)*log(x)*x**2 + 176*log(log(x)**2)*log(x)*x - 2*log(log(x)**2)*x**4 + 176*log(log(x)**2)*x**3 - 3872*log(log(x)**2)*x**2 + log(x)**2 + 2*log(x) *x**2 - 88*log(x)*x + x**4 - 88*x**3 + 1936*x**2)