Integrand size = 193, antiderivative size = 25 \[ \int \frac {3 x^2+8 x^3-1280 x^6-32 x^4 \log (5)+3 x^2 \log ^2(5)}{1+24 x+192 x^2+512 x^3+768 x^4+12288 x^5+49152 x^6+196608 x^8+1572864 x^9+16777216 x^{12}+\left (96 x^2+1536 x^3+6144 x^4+49152 x^6+393216 x^7+6291456 x^{10}\right ) \log (5)+\left (3+48 x+192 x^2+4608 x^4+36864 x^5+983040 x^8\right ) \log ^2(5)+\left (192 x^2+1536 x^3+81920 x^6\right ) \log ^3(5)+\left (3+24 x+3840 x^4\right ) \log ^4(5)+96 x^2 \log ^5(5)+\log ^6(5)} \, dx=\frac {x}{\left (4+\frac {1+4 x+\left (16 x^2+\log (5)\right )^2}{x}\right )^2} \] Output:
x/((1+4*x+(16*x^2+ln(5))^2)/x+4)^2
Time = 0.02 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {3 x^2+8 x^3-1280 x^6-32 x^4 \log (5)+3 x^2 \log ^2(5)}{1+24 x+192 x^2+512 x^3+768 x^4+12288 x^5+49152 x^6+196608 x^8+1572864 x^9+16777216 x^{12}+\left (96 x^2+1536 x^3+6144 x^4+49152 x^6+393216 x^7+6291456 x^{10}\right ) \log (5)+\left (3+48 x+192 x^2+4608 x^4+36864 x^5+983040 x^8\right ) \log ^2(5)+\left (192 x^2+1536 x^3+81920 x^6\right ) \log ^3(5)+\left (3+24 x+3840 x^4\right ) \log ^4(5)+96 x^2 \log ^5(5)+\log ^6(5)} \, dx=\frac {x^3}{\left (1+8 x+256 x^4+32 x^2 \log (5)+\log ^2(5)\right )^2} \] Input:
Integrate[(3*x^2 + 8*x^3 - 1280*x^6 - 32*x^4*Log[5] + 3*x^2*Log[5]^2)/(1 + 24*x + 192*x^2 + 512*x^3 + 768*x^4 + 12288*x^5 + 49152*x^6 + 196608*x^8 + 1572864*x^9 + 16777216*x^12 + (96*x^2 + 1536*x^3 + 6144*x^4 + 49152*x^6 + 393216*x^7 + 6291456*x^10)*Log[5] + (3 + 48*x + 192*x^2 + 4608*x^4 + 3686 4*x^5 + 983040*x^8)*Log[5]^2 + (192*x^2 + 1536*x^3 + 81920*x^6)*Log[5]^3 + (3 + 24*x + 3840*x^4)*Log[5]^4 + 96*x^2*Log[5]^5 + Log[5]^6),x]
Output:
x^3/(1 + 8*x + 256*x^4 + 32*x^2*Log[5] + Log[5]^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.
\(\displaystyle \int \frac {-1280 x^6-32 x^4 \log (5)+8 x^3+3 x^2+3 x^2 \log ^2(5)}{16777216 x^{12}+1572864 x^9+196608 x^8+49152 x^6+12288 x^5+768 x^4+\left (3840 x^4+24 x+3\right ) \log ^4(5)+512 x^3+192 x^2+96 x^2 \log ^5(5)+\left (81920 x^6+1536 x^3+192 x^2\right ) \log ^3(5)+\left (983040 x^8+36864 x^5+4608 x^4+192 x^2+48 x+3\right ) \log ^2(5)+\left (6291456 x^{10}+393216 x^7+49152 x^6+6144 x^4+1536 x^3+96 x^2\right ) \log (5)+24 x+1+\log ^6(5)} \, dx\) |
\(\Big \downarrow \) 6 |
\(\displaystyle \int \frac {-1280 x^6-32 x^4 \log (5)+8 x^3+x^2 \left (3+3 \log ^2(5)\right )}{16777216 x^{12}+1572864 x^9+196608 x^8+49152 x^6+12288 x^5+768 x^4+\left (3840 x^4+24 x+3\right ) \log ^4(5)+512 x^3+192 x^2+96 x^2 \log ^5(5)+\left (81920 x^6+1536 x^3+192 x^2\right ) \log ^3(5)+\left (983040 x^8+36864 x^5+4608 x^4+192 x^2+48 x+3\right ) \log ^2(5)+\left (6291456 x^{10}+393216 x^7+49152 x^6+6144 x^4+1536 x^3+96 x^2\right ) \log (5)+24 x+1+\log ^6(5)}dx\) |
\(\Big \downarrow \) 6 |
\(\displaystyle \int \frac {-1280 x^6-32 x^4 \log (5)+8 x^3+x^2 \left (3+3 \log ^2(5)\right )}{16777216 x^{12}+1572864 x^9+196608 x^8+49152 x^6+12288 x^5+768 x^4+\left (3840 x^4+24 x+3\right ) \log ^4(5)+512 x^3+x^2 \left (192+96 \log ^5(5)\right )+\left (81920 x^6+1536 x^3+192 x^2\right ) \log ^3(5)+\left (983040 x^8+36864 x^5+4608 x^4+192 x^2+48 x+3\right ) \log ^2(5)+\left (6291456 x^{10}+393216 x^7+49152 x^6+6144 x^4+1536 x^3+96 x^2\right ) \log (5)+24 x+1+\log ^6(5)}dx\) |
\(\Big \downarrow \) 2029 |
\(\displaystyle \int \frac {x^2 \left (-1280 x^4-32 x^2 \log (5)+8 x+3+3 \log ^2(5)\right )}{16777216 x^{12}+1572864 x^9+196608 x^8+49152 x^6+12288 x^5+768 x^4+\left (3840 x^4+24 x+3\right ) \log ^4(5)+512 x^3+x^2 \left (192+96 \log ^5(5)\right )+\left (81920 x^6+1536 x^3+192 x^2\right ) \log ^3(5)+\left (983040 x^8+36864 x^5+4608 x^4+192 x^2+48 x+3\right ) \log ^2(5)+\left (6291456 x^{10}+393216 x^7+49152 x^6+6144 x^4+1536 x^3+96 x^2\right ) \log (5)+24 x+1+\log ^6(5)}dx\) |
\(\Big \downarrow \) 2462 |
\(\displaystyle \int \left (\frac {\log (5)-10 x^2}{2 \left (256 x^4+32 x^2 \log (5)+8 x+1+\log ^2(5)\right )^2}+\frac {96 x^3+16 x^2 \left (1-\log ^2(5)\right )-8 x \log (5)-\log (5) \left (1+\log ^2(5)\right )}{2 \left (256 x^4+32 x^2 \log (5)+8 x+1+\log ^2(5)\right )^3}\right )dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle -7 \log (5) \int \frac {x}{\left (256 x^4+32 \log (5) x^2+8 x+\log ^2(5)+1\right )^3}dx+8 \left (1-\log ^2(5)\right ) \int \frac {x^2}{\left (256 x^4+32 \log (5) x^2+8 x+\log ^2(5)+1\right )^3}dx+\frac {1}{2} \log (5) \int \frac {1}{\left (256 x^4+32 \log (5) x^2+8 x+\log ^2(5)+1\right )^2}dx-5 \int \frac {x^2}{\left (256 x^4+32 \log (5) x^2+8 x+\log ^2(5)+1\right )^2}dx-\frac {1}{8} \left (3+4 \log ^3(5)+\log (625)\right ) \int \frac {1}{\left (256 x^4+32 \log (5) x^2+8 x+\log ^2(5)+1\right )^3}dx-\frac {3}{128 \left (256 x^4+32 x^2 \log (5)+8 x+1+\log ^2(5)\right )^2}\) |
Input:
Int[(3*x^2 + 8*x^3 - 1280*x^6 - 32*x^4*Log[5] + 3*x^2*Log[5]^2)/(1 + 24*x + 192*x^2 + 512*x^3 + 768*x^4 + 12288*x^5 + 49152*x^6 + 196608*x^8 + 15728 64*x^9 + 16777216*x^12 + (96*x^2 + 1536*x^3 + 6144*x^4 + 49152*x^6 + 39321 6*x^7 + 6291456*x^10)*Log[5] + (3 + 48*x + 192*x^2 + 4608*x^4 + 36864*x^5 + 983040*x^8)*Log[5]^2 + (192*x^2 + 1536*x^3 + 81920*x^6)*Log[5]^3 + (3 + 24*x + 3840*x^4)*Log[5]^4 + 96*x^2*Log[5]^5 + Log[5]^6),x]
Output:
$Aborted
Time = 0.36 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.12
method | result | size |
default | \(\frac {x^{3}}{\left (256 x^{4}+32 x^{2} \ln \left (5\right )+\ln \left (5\right )^{2}+8 x +1\right )^{2}}\) | \(28\) |
norman | \(\frac {x^{3}}{\left (256 x^{4}+32 x^{2} \ln \left (5\right )+\ln \left (5\right )^{2}+8 x +1\right )^{2}}\) | \(28\) |
gosper | \(\frac {x^{3}}{65536 x^{8}+16384 x^{6} \ln \left (5\right )+1536 x^{4} \ln \left (5\right )^{2}+64 \ln \left (5\right )^{3} x^{2}+4096 x^{5}+\ln \left (5\right )^{4}+512 x^{3} \ln \left (5\right )+512 x^{4}+16 x \ln \left (5\right )^{2}+64 x^{2} \ln \left (5\right )+2 \ln \left (5\right )^{2}+64 x^{2}+16 x +1}\) | \(88\) |
risch | \(\frac {x^{3}}{65536 x^{8}+16384 x^{6} \ln \left (5\right )+1536 x^{4} \ln \left (5\right )^{2}+64 \ln \left (5\right )^{3} x^{2}+4096 x^{5}+\ln \left (5\right )^{4}+512 x^{3} \ln \left (5\right )+512 x^{4}+16 x \ln \left (5\right )^{2}+64 x^{2} \ln \left (5\right )+2 \ln \left (5\right )^{2}+64 x^{2}+16 x +1}\) | \(88\) |
parallelrisch | \(\frac {x^{3}}{65536 x^{8}+16384 x^{6} \ln \left (5\right )+1536 x^{4} \ln \left (5\right )^{2}+64 \ln \left (5\right )^{3} x^{2}+4096 x^{5}+\ln \left (5\right )^{4}+512 x^{3} \ln \left (5\right )+512 x^{4}+16 x \ln \left (5\right )^{2}+64 x^{2} \ln \left (5\right )+2 \ln \left (5\right )^{2}+64 x^{2}+16 x +1}\) | \(88\) |
Input:
int((3*x^2*ln(5)^2-32*x^4*ln(5)-1280*x^6+8*x^3+3*x^2)/(ln(5)^6+96*x^2*ln(5 )^5+(3840*x^4+24*x+3)*ln(5)^4+(81920*x^6+1536*x^3+192*x^2)*ln(5)^3+(983040 *x^8+36864*x^5+4608*x^4+192*x^2+48*x+3)*ln(5)^2+(6291456*x^10+393216*x^7+4 9152*x^6+6144*x^4+1536*x^3+96*x^2)*ln(5)+16777216*x^12+1572864*x^9+196608* x^8+49152*x^6+12288*x^5+768*x^4+512*x^3+192*x^2+24*x+1),x,method=_RETURNVE RBOSE)
Output:
x^3/(256*x^4+32*x^2*ln(5)+ln(5)^2+8*x+1)^2
Leaf count of result is larger than twice the leaf count of optimal. 78 vs. \(2 (25) = 50\).
Time = 0.09 (sec) , antiderivative size = 78, normalized size of antiderivative = 3.12 \[ \int \frac {3 x^2+8 x^3-1280 x^6-32 x^4 \log (5)+3 x^2 \log ^2(5)}{1+24 x+192 x^2+512 x^3+768 x^4+12288 x^5+49152 x^6+196608 x^8+1572864 x^9+16777216 x^{12}+\left (96 x^2+1536 x^3+6144 x^4+49152 x^6+393216 x^7+6291456 x^{10}\right ) \log (5)+\left (3+48 x+192 x^2+4608 x^4+36864 x^5+983040 x^8\right ) \log ^2(5)+\left (192 x^2+1536 x^3+81920 x^6\right ) \log ^3(5)+\left (3+24 x+3840 x^4\right ) \log ^4(5)+96 x^2 \log ^5(5)+\log ^6(5)} \, dx=\frac {x^{3}}{65536 \, x^{8} + 4096 \, x^{5} + 64 \, x^{2} \log \left (5\right )^{3} + 512 \, x^{4} + \log \left (5\right )^{4} + 2 \, {\left (768 \, x^{4} + 8 \, x + 1\right )} \log \left (5\right )^{2} + 64 \, x^{2} + 64 \, {\left (256 \, x^{6} + 8 \, x^{3} + x^{2}\right )} \log \left (5\right ) + 16 \, x + 1} \] Input:
integrate((3*x^2*log(5)^2-32*x^4*log(5)-1280*x^6+8*x^3+3*x^2)/(log(5)^6+96 *x^2*log(5)^5+(3840*x^4+24*x+3)*log(5)^4+(81920*x^6+1536*x^3+192*x^2)*log( 5)^3+(983040*x^8+36864*x^5+4608*x^4+192*x^2+48*x+3)*log(5)^2+(6291456*x^10 +393216*x^7+49152*x^6+6144*x^4+1536*x^3+96*x^2)*log(5)+16777216*x^12+15728 64*x^9+196608*x^8+49152*x^6+12288*x^5+768*x^4+512*x^3+192*x^2+24*x+1),x, a lgorithm="fricas")
Output:
x^3/(65536*x^8 + 4096*x^5 + 64*x^2*log(5)^3 + 512*x^4 + log(5)^4 + 2*(768* x^4 + 8*x + 1)*log(5)^2 + 64*x^2 + 64*(256*x^6 + 8*x^3 + x^2)*log(5) + 16* x + 1)
Leaf count of result is larger than twice the leaf count of optimal. 82 vs. \(2 (20) = 40\).
Time = 4.64 (sec) , antiderivative size = 82, normalized size of antiderivative = 3.28 \[ \int \frac {3 x^2+8 x^3-1280 x^6-32 x^4 \log (5)+3 x^2 \log ^2(5)}{1+24 x+192 x^2+512 x^3+768 x^4+12288 x^5+49152 x^6+196608 x^8+1572864 x^9+16777216 x^{12}+\left (96 x^2+1536 x^3+6144 x^4+49152 x^6+393216 x^7+6291456 x^{10}\right ) \log (5)+\left (3+48 x+192 x^2+4608 x^4+36864 x^5+983040 x^8\right ) \log ^2(5)+\left (192 x^2+1536 x^3+81920 x^6\right ) \log ^3(5)+\left (3+24 x+3840 x^4\right ) \log ^4(5)+96 x^2 \log ^5(5)+\log ^6(5)} \, dx=\frac {x^{3}}{65536 x^{8} + 16384 x^{6} \log {\left (5 \right )} + 4096 x^{5} + x^{4} \cdot \left (512 + 1536 \log {\left (5 \right )}^{2}\right ) + 512 x^{3} \log {\left (5 \right )} + x^{2} \cdot \left (64 + 64 \log {\left (5 \right )} + 64 \log {\left (5 \right )}^{3}\right ) + x \left (16 + 16 \log {\left (5 \right )}^{2}\right ) + 1 + 2 \log {\left (5 \right )}^{2} + \log {\left (5 \right )}^{4}} \] Input:
integrate((3*x**2*ln(5)**2-32*x**4*ln(5)-1280*x**6+8*x**3+3*x**2)/(ln(5)** 6+96*x**2*ln(5)**5+(3840*x**4+24*x+3)*ln(5)**4+(81920*x**6+1536*x**3+192*x **2)*ln(5)**3+(983040*x**8+36864*x**5+4608*x**4+192*x**2+48*x+3)*ln(5)**2+ (6291456*x**10+393216*x**7+49152*x**6+6144*x**4+1536*x**3+96*x**2)*ln(5)+1 6777216*x**12+1572864*x**9+196608*x**8+49152*x**6+12288*x**5+768*x**4+512* x**3+192*x**2+24*x+1),x)
Output:
x**3/(65536*x**8 + 16384*x**6*log(5) + 4096*x**5 + x**4*(512 + 1536*log(5) **2) + 512*x**3*log(5) + x**2*(64 + 64*log(5) + 64*log(5)**3) + x*(16 + 16 *log(5)**2) + 1 + 2*log(5)**2 + log(5)**4)
Leaf count of result is larger than twice the leaf count of optimal. 77 vs. \(2 (25) = 50\).
Time = 0.04 (sec) , antiderivative size = 77, normalized size of antiderivative = 3.08 \[ \int \frac {3 x^2+8 x^3-1280 x^6-32 x^4 \log (5)+3 x^2 \log ^2(5)}{1+24 x+192 x^2+512 x^3+768 x^4+12288 x^5+49152 x^6+196608 x^8+1572864 x^9+16777216 x^{12}+\left (96 x^2+1536 x^3+6144 x^4+49152 x^6+393216 x^7+6291456 x^{10}\right ) \log (5)+\left (3+48 x+192 x^2+4608 x^4+36864 x^5+983040 x^8\right ) \log ^2(5)+\left (192 x^2+1536 x^3+81920 x^6\right ) \log ^3(5)+\left (3+24 x+3840 x^4\right ) \log ^4(5)+96 x^2 \log ^5(5)+\log ^6(5)} \, dx=\frac {x^{3}}{65536 \, x^{8} + 16384 \, x^{6} \log \left (5\right ) + 512 \, {\left (3 \, \log \left (5\right )^{2} + 1\right )} x^{4} + 4096 \, x^{5} + 512 \, x^{3} \log \left (5\right ) + \log \left (5\right )^{4} + 64 \, {\left (\log \left (5\right )^{3} + \log \left (5\right ) + 1\right )} x^{2} + 16 \, {\left (\log \left (5\right )^{2} + 1\right )} x + 2 \, \log \left (5\right )^{2} + 1} \] Input:
integrate((3*x^2*log(5)^2-32*x^4*log(5)-1280*x^6+8*x^3+3*x^2)/(log(5)^6+96 *x^2*log(5)^5+(3840*x^4+24*x+3)*log(5)^4+(81920*x^6+1536*x^3+192*x^2)*log( 5)^3+(983040*x^8+36864*x^5+4608*x^4+192*x^2+48*x+3)*log(5)^2+(6291456*x^10 +393216*x^7+49152*x^6+6144*x^4+1536*x^3+96*x^2)*log(5)+16777216*x^12+15728 64*x^9+196608*x^8+49152*x^6+12288*x^5+768*x^4+512*x^3+192*x^2+24*x+1),x, a lgorithm="maxima")
Output:
x^3/(65536*x^8 + 16384*x^6*log(5) + 512*(3*log(5)^2 + 1)*x^4 + 4096*x^5 + 512*x^3*log(5) + log(5)^4 + 64*(log(5)^3 + log(5) + 1)*x^2 + 16*(log(5)^2 + 1)*x + 2*log(5)^2 + 1)
Time = 0.14 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {3 x^2+8 x^3-1280 x^6-32 x^4 \log (5)+3 x^2 \log ^2(5)}{1+24 x+192 x^2+512 x^3+768 x^4+12288 x^5+49152 x^6+196608 x^8+1572864 x^9+16777216 x^{12}+\left (96 x^2+1536 x^3+6144 x^4+49152 x^6+393216 x^7+6291456 x^{10}\right ) \log (5)+\left (3+48 x+192 x^2+4608 x^4+36864 x^5+983040 x^8\right ) \log ^2(5)+\left (192 x^2+1536 x^3+81920 x^6\right ) \log ^3(5)+\left (3+24 x+3840 x^4\right ) \log ^4(5)+96 x^2 \log ^5(5)+\log ^6(5)} \, dx=\frac {x^{3}}{{\left (256 \, x^{4} + 32 \, x^{2} \log \left (5\right ) + \log \left (5\right )^{2} + 8 \, x + 1\right )}^{2}} \] Input:
integrate((3*x^2*log(5)^2-32*x^4*log(5)-1280*x^6+8*x^3+3*x^2)/(log(5)^6+96 *x^2*log(5)^5+(3840*x^4+24*x+3)*log(5)^4+(81920*x^6+1536*x^3+192*x^2)*log( 5)^3+(983040*x^8+36864*x^5+4608*x^4+192*x^2+48*x+3)*log(5)^2+(6291456*x^10 +393216*x^7+49152*x^6+6144*x^4+1536*x^3+96*x^2)*log(5)+16777216*x^12+15728 64*x^9+196608*x^8+49152*x^6+12288*x^5+768*x^4+512*x^3+192*x^2+24*x+1),x, a lgorithm="giac")
Output:
x^3/(256*x^4 + 32*x^2*log(5) + log(5)^2 + 8*x + 1)^2
Time = 0.16 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int \frac {3 x^2+8 x^3-1280 x^6-32 x^4 \log (5)+3 x^2 \log ^2(5)}{1+24 x+192 x^2+512 x^3+768 x^4+12288 x^5+49152 x^6+196608 x^8+1572864 x^9+16777216 x^{12}+\left (96 x^2+1536 x^3+6144 x^4+49152 x^6+393216 x^7+6291456 x^{10}\right ) \log (5)+\left (3+48 x+192 x^2+4608 x^4+36864 x^5+983040 x^8\right ) \log ^2(5)+\left (192 x^2+1536 x^3+81920 x^6\right ) \log ^3(5)+\left (3+24 x+3840 x^4\right ) \log ^4(5)+96 x^2 \log ^5(5)+\log ^6(5)} \, dx=\frac {x^3}{{\left (256\,x^4+32\,\ln \left (5\right )\,x^2+8\,x+{\ln \left (5\right )}^2+1\right )}^2} \] Input:
int((3*x^2*log(5)^2 - 32*x^4*log(5) + 3*x^2 + 8*x^3 - 1280*x^6)/(24*x + 96 *x^2*log(5)^5 + log(5)^3*(192*x^2 + 1536*x^3 + 81920*x^6) + log(5)^2*(48*x + 192*x^2 + 4608*x^4 + 36864*x^5 + 983040*x^8 + 3) + log(5)*(96*x^2 + 153 6*x^3 + 6144*x^4 + 49152*x^6 + 393216*x^7 + 6291456*x^10) + log(5)^4*(24*x + 3840*x^4 + 3) + log(5)^6 + 192*x^2 + 512*x^3 + 768*x^4 + 12288*x^5 + 49 152*x^6 + 196608*x^8 + 1572864*x^9 + 16777216*x^12 + 1),x)
Output:
x^3/(8*x + 32*x^2*log(5) + log(5)^2 + 256*x^4 + 1)^2
Time = 0.17 (sec) , antiderivative size = 87, normalized size of antiderivative = 3.48 \[ \int \frac {3 x^2+8 x^3-1280 x^6-32 x^4 \log (5)+3 x^2 \log ^2(5)}{1+24 x+192 x^2+512 x^3+768 x^4+12288 x^5+49152 x^6+196608 x^8+1572864 x^9+16777216 x^{12}+\left (96 x^2+1536 x^3+6144 x^4+49152 x^6+393216 x^7+6291456 x^{10}\right ) \log (5)+\left (3+48 x+192 x^2+4608 x^4+36864 x^5+983040 x^8\right ) \log ^2(5)+\left (192 x^2+1536 x^3+81920 x^6\right ) \log ^3(5)+\left (3+24 x+3840 x^4\right ) \log ^4(5)+96 x^2 \log ^5(5)+\log ^6(5)} \, dx=\frac {x^{3}}{\mathrm {log}\left (5\right )^{4}+64 \mathrm {log}\left (5\right )^{3} x^{2}+1536 x^{4} \mathrm {log}\left (5\right )^{2}+16 x \mathrm {log}\left (5\right )^{2}+2 \mathrm {log}\left (5\right )^{2}+16384 x^{6} \mathrm {log}\left (5\right )+512 \,\mathrm {log}\left (5\right ) x^{3}+64 \,\mathrm {log}\left (5\right ) x^{2}+65536 x^{8}+4096 x^{5}+512 x^{4}+64 x^{2}+16 x +1} \] Input:
int((3*x^2*log(5)^2-32*x^4*log(5)-1280*x^6+8*x^3+3*x^2)/(log(5)^6+96*x^2*l og(5)^5+(3840*x^4+24*x+3)*log(5)^4+(81920*x^6+1536*x^3+192*x^2)*log(5)^3+( 983040*x^8+36864*x^5+4608*x^4+192*x^2+48*x+3)*log(5)^2+(6291456*x^10+39321 6*x^7+49152*x^6+6144*x^4+1536*x^3+96*x^2)*log(5)+16777216*x^12+1572864*x^9 +196608*x^8+49152*x^6+12288*x^5+768*x^4+512*x^3+192*x^2+24*x+1),x)
Output:
x**3/(log(5)**4 + 64*log(5)**3*x**2 + 1536*log(5)**2*x**4 + 16*log(5)**2*x + 2*log(5)**2 + 16384*log(5)*x**6 + 512*log(5)*x**3 + 64*log(5)*x**2 + 65 536*x**8 + 4096*x**5 + 512*x**4 + 64*x**2 + 16*x + 1)