Integrand size = 243, antiderivative size = 28 \[ \int \frac {64+\left (-240 x+48 x^2\right ) \log ^2(10)+\left (300 x^2-120 x^3+12 x^4\right ) \log ^4(10)+\left (-125 x^3+75 x^4-15 x^5+x^6\right ) \log ^6(10)+e^{\frac {-336+\left (640 x-128 x^2\right ) \log ^2(10)+\left (-300 x^2+120 x^3-12 x^4\right ) \log ^4(10)}{16+\left (-40 x+8 x^2\right ) \log ^2(10)+\left (25 x^2-10 x^3+x^4\right ) \log ^4(10)}} \left (\left (-800 x+320 x^2\right ) \log ^2(10)+\left (800 x^2-480 x^3+64 x^4\right ) \log ^4(10)\right )}{64 x+\left (-240 x^2+48 x^3\right ) \log ^2(10)+\left (300 x^3-120 x^4+12 x^5\right ) \log ^4(10)+\left (-125 x^4+75 x^5-15 x^6+x^7\right ) \log ^6(10)} \, dx=e^{4-\left (4+\frac {4}{4+(-5+x) x \log ^2(10)}\right )^2}+\log (x) \] Output:
exp(4-(4/(4+ln(10)^2*x*(-5+x))+4)^2)+ln(x)
Time = 0.24 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.75 \[ \int \frac {64+\left (-240 x+48 x^2\right ) \log ^2(10)+\left (300 x^2-120 x^3+12 x^4\right ) \log ^4(10)+\left (-125 x^3+75 x^4-15 x^5+x^6\right ) \log ^6(10)+e^{\frac {-336+\left (640 x-128 x^2\right ) \log ^2(10)+\left (-300 x^2+120 x^3-12 x^4\right ) \log ^4(10)}{16+\left (-40 x+8 x^2\right ) \log ^2(10)+\left (25 x^2-10 x^3+x^4\right ) \log ^4(10)}} \left (\left (-800 x+320 x^2\right ) \log ^2(10)+\left (800 x^2-480 x^3+64 x^4\right ) \log ^4(10)\right )}{64 x+\left (-240 x^2+48 x^3\right ) \log ^2(10)+\left (300 x^3-120 x^4+12 x^5\right ) \log ^4(10)+\left (-125 x^4+75 x^5-15 x^6+x^7\right ) \log ^6(10)} \, dx=e^{-12-\frac {16}{\left (4-5 x \log ^2(10)+x^2 \log ^2(10)\right )^2}-\frac {32}{4-5 x \log ^2(10)+x^2 \log ^2(10)}}+\log (x) \] Input:
Integrate[(64 + (-240*x + 48*x^2)*Log[10]^2 + (300*x^2 - 120*x^3 + 12*x^4) *Log[10]^4 + (-125*x^3 + 75*x^4 - 15*x^5 + x^6)*Log[10]^6 + E^((-336 + (64 0*x - 128*x^2)*Log[10]^2 + (-300*x^2 + 120*x^3 - 12*x^4)*Log[10]^4)/(16 + (-40*x + 8*x^2)*Log[10]^2 + (25*x^2 - 10*x^3 + x^4)*Log[10]^4))*((-800*x + 320*x^2)*Log[10]^2 + (800*x^2 - 480*x^3 + 64*x^4)*Log[10]^4))/(64*x + (-2 40*x^2 + 48*x^3)*Log[10]^2 + (300*x^3 - 120*x^4 + 12*x^5)*Log[10]^4 + (-12 5*x^4 + 75*x^5 - 15*x^6 + x^7)*Log[10]^6),x]
Output:
E^(-12 - 16/(4 - 5*x*Log[10]^2 + x^2*Log[10]^2)^2 - 32/(4 - 5*x*Log[10]^2 + x^2*Log[10]^2)) + Log[x]
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.
| \(\displaystyle \int \frac {\left (\left (320 x^2-800 x\right ) \log ^2(10)+\left (64 x^4-480 x^3+800 x^2\right ) \log ^4(10)\right ) \exp \left (\frac {\left (640 x-128 x^2\right ) \log ^2(10)+\left (-12 x^4+120 x^3-300 x^2\right ) \log ^4(10)-336}{\left (8 x^2-40 x\right ) \log ^2(10)+\left (x^4-10 x^3+25 x^2\right ) \log ^4(10)+16}\right )+\left (48 x^2-240 x\right ) \log ^2(10)+\left (12 x^4-120 x^3+300 x^2\right ) \log ^4(10)+\left (x^6-15 x^5+75 x^4-125 x^3\right ) \log ^6(10)+64}{\left (48 x^3-240 x^2\right ) \log ^2(10)+\left (12 x^5-120 x^4+300 x^3\right ) \log ^4(10)+\left (x^7-15 x^6+75 x^5-125 x^4\right ) \log ^6(10)+64 x} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {\left (\left (320 x^2-800 x\right ) \log ^2(10)+\left (64 x^4-480 x^3+800 x^2\right ) \log ^4(10)\right ) \exp \left (\frac {\left (640 x-128 x^2\right ) \log ^2(10)+\left (-12 x^4+120 x^3-300 x^2\right ) \log ^4(10)-336}{\left (8 x^2-40 x\right ) \log ^2(10)+\left (x^4-10 x^3+25 x^2\right ) \log ^4(10)+16}\right )+\left (48 x^2-240 x\right ) \log ^2(10)+\left (12 x^4-120 x^3+300 x^2\right ) \log ^4(10)+\left (x^6-15 x^5+75 x^4-125 x^3\right ) \log ^6(10)+64}{x \left (x^6 \log ^6(10)-15 x^5 \log ^6(10)+3 x^4 \log ^4(10) \left (4+25 \log ^2(10)\right )-5 x^3 \log ^4(10) \left (24+25 \log ^2(10)\right )+12 x^2 \log ^2(10) \left (4+25 \log ^2(10)\right )-240 x \log ^2(10)+64\right )}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \left (-\frac {12 \log (10) \left (\log ^2(10) \left (48 x^2-240 x\right )+e^{\frac {\log ^2(10) \left (640 x-128 x^2\right )+\left (-12 x^4+120 x^3-300 x^2\right ) \log ^4(10)-336}{\log ^2(10) \left (8 x^2-40 x\right )+\left (x^4-10 x^3+25 x^2\right ) \log ^4(10)+16}} \left (\log ^2(10) \left (320 x^2-800 x\right )+\left (64 x^4-480 x^3+800 x^2\right ) \log ^4(10)\right )+\left (x^6-15 x^5+75 x^4-125 x^3\right ) \log ^6(10)+\left (12 x^4-120 x^3+300 x^2\right ) \log ^4(10)+64\right )}{x \left (-16+25 \log ^2(10)\right )^{5/2} \left (-2 \log ^2(10) x+\log (10) \sqrt {-16+25 \log ^2(10)}+5 \log ^2(10)\right )}-\frac {12 \log (10) \left (\log ^2(10) \left (48 x^2-240 x\right )+e^{\frac {\log ^2(10) \left (640 x-128 x^2\right )+\left (-12 x^4+120 x^3-300 x^2\right ) \log ^4(10)-336}{\log ^2(10) \left (8 x^2-40 x\right )+\left (x^4-10 x^3+25 x^2\right ) \log ^4(10)+16}} \left (\log ^2(10) \left (320 x^2-800 x\right )+\left (64 x^4-480 x^3+800 x^2\right ) \log ^4(10)\right )+\left (x^6-15 x^5+75 x^4-125 x^3\right ) \log ^6(10)+\left (12 x^4-120 x^3+300 x^2\right ) \log ^4(10)+64\right )}{x \left (-16+25 \log ^2(10)\right )^{5/2} \left (2 \log ^2(10) x+\log (10) \sqrt {-16+25 \log ^2(10)}-5 \log ^2(10)\right )}-\frac {12 \log ^2(10) \left (\log ^2(10) \left (48 x^2-240 x\right )+e^{\frac {\log ^2(10) \left (640 x-128 x^2\right )+\left (-12 x^4+120 x^3-300 x^2\right ) \log ^4(10)-336}{\log ^2(10) \left (8 x^2-40 x\right )+\left (x^4-10 x^3+25 x^2\right ) \log ^4(10)+16}} \left (\log ^2(10) \left (320 x^2-800 x\right )+\left (64 x^4-480 x^3+800 x^2\right ) \log ^4(10)\right )+\left (x^6-15 x^5+75 x^4-125 x^3\right ) \log ^6(10)+\left (12 x^4-120 x^3+300 x^2\right ) \log ^4(10)+64\right )}{x \left (-16+25 \log ^2(10)\right )^2 \left (-2 \log ^2(10) x+\log (10) \sqrt {-16+25 \log ^2(10)}+5 \log ^2(10)\right )^2}-\frac {12 \log ^2(10) \left (\log ^2(10) \left (48 x^2-240 x\right )+e^{\frac {\log ^2(10) \left (640 x-128 x^2\right )+\left (-12 x^4+120 x^3-300 x^2\right ) \log ^4(10)-336}{\log ^2(10) \left (8 x^2-40 x\right )+\left (x^4-10 x^3+25 x^2\right ) \log ^4(10)+16}} \left (\log ^2(10) \left (320 x^2-800 x\right )+\left (64 x^4-480 x^3+800 x^2\right ) \log ^4(10)\right )+\left (x^6-15 x^5+75 x^4-125 x^3\right ) \log ^6(10)+\left (12 x^4-120 x^3+300 x^2\right ) \log ^4(10)+64\right )}{x \left (-16+25 \log ^2(10)\right )^2 \left (2 \log ^2(10) x+\log (10) \sqrt {-16+25 \log ^2(10)}-5 \log ^2(10)\right )^2}-\frac {8 \log ^3(10) \left (\log ^2(10) \left (48 x^2-240 x\right )+e^{\frac {\log ^2(10) \left (640 x-128 x^2\right )+\left (-12 x^4+120 x^3-300 x^2\right ) \log ^4(10)-336}{\log ^2(10) \left (8 x^2-40 x\right )+\left (x^4-10 x^3+25 x^2\right ) \log ^4(10)+16}} \left (\log ^2(10) \left (320 x^2-800 x\right )+\left (64 x^4-480 x^3+800 x^2\right ) \log ^4(10)\right )+\left (x^6-15 x^5+75 x^4-125 x^3\right ) \log ^6(10)+\left (12 x^4-120 x^3+300 x^2\right ) \log ^4(10)+64\right )}{x \left (-16+25 \log ^2(10)\right )^{3/2} \left (-2 \log ^2(10) x+\log (10) \sqrt {-16+25 \log ^2(10)}+5 \log ^2(10)\right )^3}-\frac {8 \log ^3(10) \left (\log ^2(10) \left (48 x^2-240 x\right )+e^{\frac {\log ^2(10) \left (640 x-128 x^2\right )+\left (-12 x^4+120 x^3-300 x^2\right ) \log ^4(10)-336}{\log ^2(10) \left (8 x^2-40 x\right )+\left (x^4-10 x^3+25 x^2\right ) \log ^4(10)+16}} \left (\log ^2(10) \left (320 x^2-800 x\right )+\left (64 x^4-480 x^3+800 x^2\right ) \log ^4(10)\right )+\left (x^6-15 x^5+75 x^4-125 x^3\right ) \log ^6(10)+\left (12 x^4-120 x^3+300 x^2\right ) \log ^4(10)+64\right )}{x \left (-16+25 \log ^2(10)\right )^{3/2} \left (2 \log ^2(10) x+\log (10) \sqrt {-16+25 \log ^2(10)}-5 \log ^2(10)\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \left (\frac {32 (2 x-5) \log ^2(10) \left (x^2 \log ^2(10)-5 x \log ^2(10)+5\right ) \exp \left (-\frac {4 \left (3 x^4 \log ^4(10)-30 x^3 \log ^4(10)+x^2 \log ^2(10) \left (32+75 \log ^2(10)\right )-160 x \log ^2(10)+84\right )}{\left (x^2 \log ^2(10)-5 x \log ^2(10)+4\right )^2}\right )}{\left (x^2 \log ^2(10)-5 x \log ^2(10)+4\right )^3}+\frac {1}{x}\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {32 (5-2 x) \log ^2(10) \left (x^2 \left (-\log ^2(10)\right )+5 x \log ^2(10)-5\right ) \exp \left (-\frac {4 \left (3 x^4 \log ^4(10)-30 x^3 \log ^4(10)+x^2 \log ^2(10) \left (32+75 \log ^2(10)\right )-160 x \log ^2(10)+84\right )}{\left (x^2 \log ^2(10)-5 x \log ^2(10)+4\right )^2}\right )}{\left (x^2 \log ^2(10)-5 x \log ^2(10)+4\right )^3}+\frac {1}{x}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \int \left (\frac {32 (5-2 x) \log ^2(10) \left (x^2 \left (-\log ^2(10)\right )+5 x \log ^2(10)-5\right ) \exp \left (-\frac {4 \left (3 x^4 \log ^4(10)-30 x^3 \log ^4(10)+x^2 \log ^2(10) \left (32+75 \log ^2(10)\right )-160 x \log ^2(10)+84\right )}{\left (x^2 \log ^2(10)-5 x \log ^2(10)+4\right )^2}\right )}{\left (x^2 \log ^2(10)-5 x \log ^2(10)+4\right )^3}+\frac {1}{x}\right )dx\) |
Input:
Int[(64 + (-240*x + 48*x^2)*Log[10]^2 + (300*x^2 - 120*x^3 + 12*x^4)*Log[1 0]^4 + (-125*x^3 + 75*x^4 - 15*x^5 + x^6)*Log[10]^6 + E^((-336 + (640*x - 128*x^2)*Log[10]^2 + (-300*x^2 + 120*x^3 - 12*x^4)*Log[10]^4)/(16 + (-40*x + 8*x^2)*Log[10]^2 + (25*x^2 - 10*x^3 + x^4)*Log[10]^4))*((-800*x + 320*x ^2)*Log[10]^2 + (800*x^2 - 480*x^3 + 64*x^4)*Log[10]^4))/(64*x + (-240*x^2 + 48*x^3)*Log[10]^2 + (300*x^3 - 120*x^4 + 12*x^5)*Log[10]^4 + (-125*x^4 + 75*x^5 - 15*x^6 + x^7)*Log[10]^6),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(447\) vs. \(2(27)=54\).
Time = 1.93 (sec) , antiderivative size = 448, normalized size of antiderivative = 16.00
\[\frac {\left (25 \ln \left (10\right )^{4}+8 \ln \left (10\right )^{2}\right ) x^{2} {\mathrm e}^{\frac {\left (-12 x^{4}+120 x^{3}-300 x^{2}\right ) \ln \left (10\right )^{4}+\left (-128 x^{2}+640 x \right ) \ln \left (10\right )^{2}-336}{\left (x^{4}-10 x^{3}+25 x^{2}\right ) \ln \left (10\right )^{4}+\left (8 x^{2}-40 x \right ) \ln \left (10\right )^{2}+16}}+\ln \left (10\right )^{4} x^{4} {\mathrm e}^{\frac {\left (-12 x^{4}+120 x^{3}-300 x^{2}\right ) \ln \left (10\right )^{4}+\left (-128 x^{2}+640 x \right ) \ln \left (10\right )^{2}-336}{\left (x^{4}-10 x^{3}+25 x^{2}\right ) \ln \left (10\right )^{4}+\left (8 x^{2}-40 x \right ) \ln \left (10\right )^{2}+16}}-40 \ln \left (10\right )^{2} x \,{\mathrm e}^{\frac {\left (-12 x^{4}+120 x^{3}-300 x^{2}\right ) \ln \left (10\right )^{4}+\left (-128 x^{2}+640 x \right ) \ln \left (10\right )^{2}-336}{\left (x^{4}-10 x^{3}+25 x^{2}\right ) \ln \left (10\right )^{4}+\left (8 x^{2}-40 x \right ) \ln \left (10\right )^{2}+16}}-10 \ln \left (10\right )^{4} x^{3} {\mathrm e}^{\frac {\left (-12 x^{4}+120 x^{3}-300 x^{2}\right ) \ln \left (10\right )^{4}+\left (-128 x^{2}+640 x \right ) \ln \left (10\right )^{2}-336}{\left (x^{4}-10 x^{3}+25 x^{2}\right ) \ln \left (10\right )^{4}+\left (8 x^{2}-40 x \right ) \ln \left (10\right )^{2}+16}}+16 \,{\mathrm e}^{\frac {\left (-12 x^{4}+120 x^{3}-300 x^{2}\right ) \ln \left (10\right )^{4}+\left (-128 x^{2}+640 x \right ) \ln \left (10\right )^{2}-336}{\left (x^{4}-10 x^{3}+25 x^{2}\right ) \ln \left (10\right )^{4}+\left (8 x^{2}-40 x \right ) \ln \left (10\right )^{2}+16}}}{\left (\ln \left (10\right )^{2} x^{2}-5 \ln \left (10\right )^{2} x +4\right )^{2}}+\ln \left (x \right )\]
Input:
int((((64*x^4-480*x^3+800*x^2)*ln(10)^4+(320*x^2-800*x)*ln(10)^2)*exp(((-1 2*x^4+120*x^3-300*x^2)*ln(10)^4+(-128*x^2+640*x)*ln(10)^2-336)/((x^4-10*x^ 3+25*x^2)*ln(10)^4+(8*x^2-40*x)*ln(10)^2+16))+(x^6-15*x^5+75*x^4-125*x^3)* ln(10)^6+(12*x^4-120*x^3+300*x^2)*ln(10)^4+(48*x^2-240*x)*ln(10)^2+64)/((x ^7-15*x^6+75*x^5-125*x^4)*ln(10)^6+(12*x^5-120*x^4+300*x^3)*ln(10)^4+(48*x ^3-240*x^2)*ln(10)^2+64*x),x)
Output:
((25*ln(10)^4+8*ln(10)^2)*x^2*exp(((-12*x^4+120*x^3-300*x^2)*ln(10)^4+(-12 8*x^2+640*x)*ln(10)^2-336)/((x^4-10*x^3+25*x^2)*ln(10)^4+(8*x^2-40*x)*ln(1 0)^2+16))+ln(10)^4*x^4*exp(((-12*x^4+120*x^3-300*x^2)*ln(10)^4+(-128*x^2+6 40*x)*ln(10)^2-336)/((x^4-10*x^3+25*x^2)*ln(10)^4+(8*x^2-40*x)*ln(10)^2+16 ))-40*ln(10)^2*x*exp(((-12*x^4+120*x^3-300*x^2)*ln(10)^4+(-128*x^2+640*x)* ln(10)^2-336)/((x^4-10*x^3+25*x^2)*ln(10)^4+(8*x^2-40*x)*ln(10)^2+16))-10* ln(10)^4*x^3*exp(((-12*x^4+120*x^3-300*x^2)*ln(10)^4+(-128*x^2+640*x)*ln(1 0)^2-336)/((x^4-10*x^3+25*x^2)*ln(10)^4+(8*x^2-40*x)*ln(10)^2+16))+16*exp( ((-12*x^4+120*x^3-300*x^2)*ln(10)^4+(-128*x^2+640*x)*ln(10)^2-336)/((x^4-1 0*x^3+25*x^2)*ln(10)^4+(8*x^2-40*x)*ln(10)^2+16)))/(ln(10)^2*x^2-5*ln(10)^ 2*x+4)^2+ln(x)
Leaf count of result is larger than twice the leaf count of optimal. 77 vs. \(2 (25) = 50\).
Time = 0.09 (sec) , antiderivative size = 77, normalized size of antiderivative = 2.75 \[ \int \frac {64+\left (-240 x+48 x^2\right ) \log ^2(10)+\left (300 x^2-120 x^3+12 x^4\right ) \log ^4(10)+\left (-125 x^3+75 x^4-15 x^5+x^6\right ) \log ^6(10)+e^{\frac {-336+\left (640 x-128 x^2\right ) \log ^2(10)+\left (-300 x^2+120 x^3-12 x^4\right ) \log ^4(10)}{16+\left (-40 x+8 x^2\right ) \log ^2(10)+\left (25 x^2-10 x^3+x^4\right ) \log ^4(10)}} \left (\left (-800 x+320 x^2\right ) \log ^2(10)+\left (800 x^2-480 x^3+64 x^4\right ) \log ^4(10)\right )}{64 x+\left (-240 x^2+48 x^3\right ) \log ^2(10)+\left (300 x^3-120 x^4+12 x^5\right ) \log ^4(10)+\left (-125 x^4+75 x^5-15 x^6+x^7\right ) \log ^6(10)} \, dx=e^{\left (-\frac {4 \, {\left (3 \, {\left (x^{4} - 10 \, x^{3} + 25 \, x^{2}\right )} \log \left (10\right )^{4} + 32 \, {\left (x^{2} - 5 \, x\right )} \log \left (10\right )^{2} + 84\right )}}{{\left (x^{4} - 10 \, x^{3} + 25 \, x^{2}\right )} \log \left (10\right )^{4} + 8 \, {\left (x^{2} - 5 \, x\right )} \log \left (10\right )^{2} + 16}\right )} + \log \left (x\right ) \] Input:
integrate((((64*x^4-480*x^3+800*x^2)*log(10)^4+(320*x^2-800*x)*log(10)^2)* exp(((-12*x^4+120*x^3-300*x^2)*log(10)^4+(-128*x^2+640*x)*log(10)^2-336)/( (x^4-10*x^3+25*x^2)*log(10)^4+(8*x^2-40*x)*log(10)^2+16))+(x^6-15*x^5+75*x ^4-125*x^3)*log(10)^6+(12*x^4-120*x^3+300*x^2)*log(10)^4+(48*x^2-240*x)*lo g(10)^2+64)/((x^7-15*x^6+75*x^5-125*x^4)*log(10)^6+(12*x^5-120*x^4+300*x^3 )*log(10)^4+(48*x^3-240*x^2)*log(10)^2+64*x),x, algorithm="fricas")
Output:
e^(-4*(3*(x^4 - 10*x^3 + 25*x^2)*log(10)^4 + 32*(x^2 - 5*x)*log(10)^2 + 84 )/((x^4 - 10*x^3 + 25*x^2)*log(10)^4 + 8*(x^2 - 5*x)*log(10)^2 + 16)) + lo g(x)
Leaf count of result is larger than twice the leaf count of optimal. 73 vs. \(2 (22) = 44\).
Time = 0.88 (sec) , antiderivative size = 73, normalized size of antiderivative = 2.61 \[ \int \frac {64+\left (-240 x+48 x^2\right ) \log ^2(10)+\left (300 x^2-120 x^3+12 x^4\right ) \log ^4(10)+\left (-125 x^3+75 x^4-15 x^5+x^6\right ) \log ^6(10)+e^{\frac {-336+\left (640 x-128 x^2\right ) \log ^2(10)+\left (-300 x^2+120 x^3-12 x^4\right ) \log ^4(10)}{16+\left (-40 x+8 x^2\right ) \log ^2(10)+\left (25 x^2-10 x^3+x^4\right ) \log ^4(10)}} \left (\left (-800 x+320 x^2\right ) \log ^2(10)+\left (800 x^2-480 x^3+64 x^4\right ) \log ^4(10)\right )}{64 x+\left (-240 x^2+48 x^3\right ) \log ^2(10)+\left (300 x^3-120 x^4+12 x^5\right ) \log ^4(10)+\left (-125 x^4+75 x^5-15 x^6+x^7\right ) \log ^6(10)} \, dx=e^{\frac {\left (- 128 x^{2} + 640 x\right ) \log {\left (10 \right )}^{2} + \left (- 12 x^{4} + 120 x^{3} - 300 x^{2}\right ) \log {\left (10 \right )}^{4} - 336}{\left (8 x^{2} - 40 x\right ) \log {\left (10 \right )}^{2} + \left (x^{4} - 10 x^{3} + 25 x^{2}\right ) \log {\left (10 \right )}^{4} + 16}} + \log {\left (x \right )} \] Input:
integrate((((64*x**4-480*x**3+800*x**2)*ln(10)**4+(320*x**2-800*x)*ln(10)* *2)*exp(((-12*x**4+120*x**3-300*x**2)*ln(10)**4+(-128*x**2+640*x)*ln(10)** 2-336)/((x**4-10*x**3+25*x**2)*ln(10)**4+(8*x**2-40*x)*ln(10)**2+16))+(x** 6-15*x**5+75*x**4-125*x**3)*ln(10)**6+(12*x**4-120*x**3+300*x**2)*ln(10)** 4+(48*x**2-240*x)*ln(10)**2+64)/((x**7-15*x**6+75*x**5-125*x**4)*ln(10)**6 +(12*x**5-120*x**4+300*x**3)*ln(10)**4+(48*x**3-240*x**2)*ln(10)**2+64*x), x)
Output:
exp(((-128*x**2 + 640*x)*log(10)**2 + (-12*x**4 + 120*x**3 - 300*x**2)*log (10)**4 - 336)/((8*x**2 - 40*x)*log(10)**2 + (x**4 - 10*x**3 + 25*x**2)*lo g(10)**4 + 16)) + log(x)
Leaf count of result is larger than twice the leaf count of optimal. 3013 vs. \(2 (25) = 50\).
Time = 2.80 (sec) , antiderivative size = 3013, normalized size of antiderivative = 107.61 \[ \int \frac {64+\left (-240 x+48 x^2\right ) \log ^2(10)+\left (300 x^2-120 x^3+12 x^4\right ) \log ^4(10)+\left (-125 x^3+75 x^4-15 x^5+x^6\right ) \log ^6(10)+e^{\frac {-336+\left (640 x-128 x^2\right ) \log ^2(10)+\left (-300 x^2+120 x^3-12 x^4\right ) \log ^4(10)}{16+\left (-40 x+8 x^2\right ) \log ^2(10)+\left (25 x^2-10 x^3+x^4\right ) \log ^4(10)}} \left (\left (-800 x+320 x^2\right ) \log ^2(10)+\left (800 x^2-480 x^3+64 x^4\right ) \log ^4(10)\right )}{64 x+\left (-240 x^2+48 x^3\right ) \log ^2(10)+\left (300 x^3-120 x^4+12 x^5\right ) \log ^4(10)+\left (-125 x^4+75 x^5-15 x^6+x^7\right ) \log ^6(10)} \, dx=\text {Too large to display} \] Input:
integrate((((64*x^4-480*x^3+800*x^2)*log(10)^4+(320*x^2-800*x)*log(10)^2)* exp(((-12*x^4+120*x^3-300*x^2)*log(10)^4+(-128*x^2+640*x)*log(10)^2-336)/( (x^4-10*x^3+25*x^2)*log(10)^4+(8*x^2-40*x)*log(10)^2+16))+(x^6-15*x^5+75*x ^4-125*x^3)*log(10)^6+(12*x^4-120*x^3+300*x^2)*log(10)^4+(48*x^2-240*x)*lo g(10)^2+64)/((x^7-15*x^6+75*x^5-125*x^4)*log(10)^6+(12*x^5-120*x^4+300*x^3 )*log(10)^4+(48*x^3-240*x^2)*log(10)^2+64*x),x, algorithm="maxima")
Output:
75/2*((120*x^3*log(10)^4 - (625*log(10)^6 + 100*log(10)^4 + 256*log(10)^2) *x^2 + 200*(5*log(10)^4 + 4*log(10)^2)*x - 400*log(10)^2 - 512)/(10000*log (10)^8 - 12800*log(10)^6 + (625*log(10)^12 - 800*log(10)^10 + 256*log(10)^ 8)*x^4 - 10*(625*log(10)^12 - 800*log(10)^10 + 256*log(10)^8)*x^3 + 4096*l og(10)^4 + (15625*log(10)^12 - 15000*log(10)^10 + 2048*log(10)^6)*x^2 - 40 *(625*log(10)^10 - 800*log(10)^8 + 256*log(10)^6)*x) + 120*log((2*x*log(10 )^2 - 5*log(10)^2 - sqrt(25*log(10)^2 - 16)*log(10))/(2*x*log(10)^2 - 5*lo g(10)^2 + sqrt(25*log(10)^2 - 16)*log(10)))/((625*log(10)^6 - 800*log(10)^ 4 + 256*log(10)^2)*sqrt(25*log(10)^2 - 16)*log(10)))*log(10)^6 - 1/2*((500 *(25*log(10)^8 - 30*log(10)^6 + 8*log(10)^4)*x^3 - 30000*log(10)^4 - (4687 5*log(10)^8 - 47500*log(10)^6 + 4400*log(10)^4 + 2048*log(10)^2)*x^2 + 40* (1875*log(10)^6 - 2200*log(10)^4 + 496*log(10)^2)*x + 33600*log(10)^2 - 61 44)/(10000*log(10)^10 - 12800*log(10)^8 + 4096*log(10)^6 + (625*log(10)^14 - 800*log(10)^12 + 256*log(10)^10)*x^4 - 10*(625*log(10)^14 - 800*log(10) ^12 + 256*log(10)^10)*x^3 + (15625*log(10)^14 - 15000*log(10)^12 + 2048*lo g(10)^8)*x^2 - 40*(625*log(10)^12 - 800*log(10)^10 + 256*log(10)^8)*x) - 2 5*(125*log(10)^4 - 200*log(10)^2 + 96)*log((2*x*log(10)^2 - 5*log(10)^2 - sqrt(25*log(10)^2 - 16)*log(10))/(2*x*log(10)^2 - 5*log(10)^2 + sqrt(25*lo g(10)^2 - 16)*log(10)))/((625*log(10)^8 - 800*log(10)^6 + 256*log(10)^4)*s qrt(25*log(10)^2 - 16)*log(10)) - log(x^2*log(10)^2 - 5*x*log(10)^2 + 4...
Leaf count of result is larger than twice the leaf count of optimal. 326 vs. \(2 (25) = 50\).
Time = 1.49 (sec) , antiderivative size = 326, normalized size of antiderivative = 11.64 \[ \int \frac {64+\left (-240 x+48 x^2\right ) \log ^2(10)+\left (300 x^2-120 x^3+12 x^4\right ) \log ^4(10)+\left (-125 x^3+75 x^4-15 x^5+x^6\right ) \log ^6(10)+e^{\frac {-336+\left (640 x-128 x^2\right ) \log ^2(10)+\left (-300 x^2+120 x^3-12 x^4\right ) \log ^4(10)}{16+\left (-40 x+8 x^2\right ) \log ^2(10)+\left (25 x^2-10 x^3+x^4\right ) \log ^4(10)}} \left (\left (-800 x+320 x^2\right ) \log ^2(10)+\left (800 x^2-480 x^3+64 x^4\right ) \log ^4(10)\right )}{64 x+\left (-240 x^2+48 x^3\right ) \log ^2(10)+\left (300 x^3-120 x^4+12 x^5\right ) \log ^4(10)+\left (-125 x^4+75 x^5-15 x^6+x^7\right ) \log ^6(10)} \, dx=e^{\left (-\frac {12 \, x^{4} \log \left (10\right )^{4}}{x^{4} \log \left (10\right )^{4} - 10 \, x^{3} \log \left (10\right )^{4} + 25 \, x^{2} \log \left (10\right )^{4} + 8 \, x^{2} \log \left (10\right )^{2} - 40 \, x \log \left (10\right )^{2} + 16} + \frac {120 \, x^{3} \log \left (10\right )^{4}}{x^{4} \log \left (10\right )^{4} - 10 \, x^{3} \log \left (10\right )^{4} + 25 \, x^{2} \log \left (10\right )^{4} + 8 \, x^{2} \log \left (10\right )^{2} - 40 \, x \log \left (10\right )^{2} + 16} - \frac {300 \, x^{2} \log \left (10\right )^{4}}{x^{4} \log \left (10\right )^{4} - 10 \, x^{3} \log \left (10\right )^{4} + 25 \, x^{2} \log \left (10\right )^{4} + 8 \, x^{2} \log \left (10\right )^{2} - 40 \, x \log \left (10\right )^{2} + 16} - \frac {128 \, x^{2} \log \left (10\right )^{2}}{x^{4} \log \left (10\right )^{4} - 10 \, x^{3} \log \left (10\right )^{4} + 25 \, x^{2} \log \left (10\right )^{4} + 8 \, x^{2} \log \left (10\right )^{2} - 40 \, x \log \left (10\right )^{2} + 16} + \frac {640 \, x \log \left (10\right )^{2}}{x^{4} \log \left (10\right )^{4} - 10 \, x^{3} \log \left (10\right )^{4} + 25 \, x^{2} \log \left (10\right )^{4} + 8 \, x^{2} \log \left (10\right )^{2} - 40 \, x \log \left (10\right )^{2} + 16} - \frac {336}{x^{4} \log \left (10\right )^{4} - 10 \, x^{3} \log \left (10\right )^{4} + 25 \, x^{2} \log \left (10\right )^{4} + 8 \, x^{2} \log \left (10\right )^{2} - 40 \, x \log \left (10\right )^{2} + 16}\right )} + \log \left (x\right ) \] Input:
integrate((((64*x^4-480*x^3+800*x^2)*log(10)^4+(320*x^2-800*x)*log(10)^2)* exp(((-12*x^4+120*x^3-300*x^2)*log(10)^4+(-128*x^2+640*x)*log(10)^2-336)/( (x^4-10*x^3+25*x^2)*log(10)^4+(8*x^2-40*x)*log(10)^2+16))+(x^6-15*x^5+75*x ^4-125*x^3)*log(10)^6+(12*x^4-120*x^3+300*x^2)*log(10)^4+(48*x^2-240*x)*lo g(10)^2+64)/((x^7-15*x^6+75*x^5-125*x^4)*log(10)^6+(12*x^5-120*x^4+300*x^3 )*log(10)^4+(48*x^3-240*x^2)*log(10)^2+64*x),x, algorithm="giac")
Output:
e^(-12*x^4*log(10)^4/(x^4*log(10)^4 - 10*x^3*log(10)^4 + 25*x^2*log(10)^4 + 8*x^2*log(10)^2 - 40*x*log(10)^2 + 16) + 120*x^3*log(10)^4/(x^4*log(10)^ 4 - 10*x^3*log(10)^4 + 25*x^2*log(10)^4 + 8*x^2*log(10)^2 - 40*x*log(10)^2 + 16) - 300*x^2*log(10)^4/(x^4*log(10)^4 - 10*x^3*log(10)^4 + 25*x^2*log( 10)^4 + 8*x^2*log(10)^2 - 40*x*log(10)^2 + 16) - 128*x^2*log(10)^2/(x^4*lo g(10)^4 - 10*x^3*log(10)^4 + 25*x^2*log(10)^4 + 8*x^2*log(10)^2 - 40*x*log (10)^2 + 16) + 640*x*log(10)^2/(x^4*log(10)^4 - 10*x^3*log(10)^4 + 25*x^2* log(10)^4 + 8*x^2*log(10)^2 - 40*x*log(10)^2 + 16) - 336/(x^4*log(10)^4 - 10*x^3*log(10)^4 + 25*x^2*log(10)^4 + 8*x^2*log(10)^2 - 40*x*log(10)^2 + 1 6)) + log(x)
Time = 3.56 (sec) , antiderivative size = 331, normalized size of antiderivative = 11.82 \[ \int \frac {64+\left (-240 x+48 x^2\right ) \log ^2(10)+\left (300 x^2-120 x^3+12 x^4\right ) \log ^4(10)+\left (-125 x^3+75 x^4-15 x^5+x^6\right ) \log ^6(10)+e^{\frac {-336+\left (640 x-128 x^2\right ) \log ^2(10)+\left (-300 x^2+120 x^3-12 x^4\right ) \log ^4(10)}{16+\left (-40 x+8 x^2\right ) \log ^2(10)+\left (25 x^2-10 x^3+x^4\right ) \log ^4(10)}} \left (\left (-800 x+320 x^2\right ) \log ^2(10)+\left (800 x^2-480 x^3+64 x^4\right ) \log ^4(10)\right )}{64 x+\left (-240 x^2+48 x^3\right ) \log ^2(10)+\left (300 x^3-120 x^4+12 x^5\right ) \log ^4(10)+\left (-125 x^4+75 x^5-15 x^6+x^7\right ) \log ^6(10)} \, dx=\ln \left (x\right )+{\mathrm {e}}^{-\frac {336}{8\,x^2\,{\ln \left (10\right )}^2+25\,x^2\,{\ln \left (10\right )}^4-10\,x^3\,{\ln \left (10\right )}^4+x^4\,{\ln \left (10\right )}^4-40\,x\,{\ln \left (10\right )}^2+16}}\,{\mathrm {e}}^{\frac {640\,x\,{\ln \left (10\right )}^2}{8\,x^2\,{\ln \left (10\right )}^2+25\,x^2\,{\ln \left (10\right )}^4-10\,x^3\,{\ln \left (10\right )}^4+x^4\,{\ln \left (10\right )}^4-40\,x\,{\ln \left (10\right )}^2+16}}\,{\mathrm {e}}^{-\frac {12\,x^4\,{\ln \left (10\right )}^4}{8\,x^2\,{\ln \left (10\right )}^2+25\,x^2\,{\ln \left (10\right )}^4-10\,x^3\,{\ln \left (10\right )}^4+x^4\,{\ln \left (10\right )}^4-40\,x\,{\ln \left (10\right )}^2+16}}\,{\mathrm {e}}^{\frac {120\,x^3\,{\ln \left (10\right )}^4}{8\,x^2\,{\ln \left (10\right )}^2+25\,x^2\,{\ln \left (10\right )}^4-10\,x^3\,{\ln \left (10\right )}^4+x^4\,{\ln \left (10\right )}^4-40\,x\,{\ln \left (10\right )}^2+16}}\,{\mathrm {e}}^{-\frac {128\,x^2\,{\ln \left (10\right )}^2}{8\,x^2\,{\ln \left (10\right )}^2+25\,x^2\,{\ln \left (10\right )}^4-10\,x^3\,{\ln \left (10\right )}^4+x^4\,{\ln \left (10\right )}^4-40\,x\,{\ln \left (10\right )}^2+16}}\,{\mathrm {e}}^{-\frac {300\,x^2\,{\ln \left (10\right )}^4}{8\,x^2\,{\ln \left (10\right )}^2+25\,x^2\,{\ln \left (10\right )}^4-10\,x^3\,{\ln \left (10\right )}^4+x^4\,{\ln \left (10\right )}^4-40\,x\,{\ln \left (10\right )}^2+16}} \] Input:
int((log(10)^4*(300*x^2 - 120*x^3 + 12*x^4) - log(10)^6*(125*x^3 - 75*x^4 + 15*x^5 - x^6) - log(10)^2*(240*x - 48*x^2) + exp(-(log(10)^4*(300*x^2 - 120*x^3 + 12*x^4) - log(10)^2*(640*x - 128*x^2) + 336)/(log(10)^4*(25*x^2 - 10*x^3 + x^4) - log(10)^2*(40*x - 8*x^2) + 16))*(log(10)^4*(800*x^2 - 48 0*x^3 + 64*x^4) - log(10)^2*(800*x - 320*x^2)) + 64)/(64*x + log(10)^4*(30 0*x^3 - 120*x^4 + 12*x^5) - log(10)^6*(125*x^4 - 75*x^5 + 15*x^6 - x^7) - log(10)^2*(240*x^2 - 48*x^3)),x)
Output:
log(x) + exp(-336/(8*x^2*log(10)^2 + 25*x^2*log(10)^4 - 10*x^3*log(10)^4 + x^4*log(10)^4 - 40*x*log(10)^2 + 16))*exp((640*x*log(10)^2)/(8*x^2*log(10 )^2 + 25*x^2*log(10)^4 - 10*x^3*log(10)^4 + x^4*log(10)^4 - 40*x*log(10)^2 + 16))*exp(-(12*x^4*log(10)^4)/(8*x^2*log(10)^2 + 25*x^2*log(10)^4 - 10*x ^3*log(10)^4 + x^4*log(10)^4 - 40*x*log(10)^2 + 16))*exp((120*x^3*log(10)^ 4)/(8*x^2*log(10)^2 + 25*x^2*log(10)^4 - 10*x^3*log(10)^4 + x^4*log(10)^4 - 40*x*log(10)^2 + 16))*exp(-(128*x^2*log(10)^2)/(8*x^2*log(10)^2 + 25*x^2 *log(10)^4 - 10*x^3*log(10)^4 + x^4*log(10)^4 - 40*x*log(10)^2 + 16))*exp( -(300*x^2*log(10)^4)/(8*x^2*log(10)^2 + 25*x^2*log(10)^4 - 10*x^3*log(10)^ 4 + x^4*log(10)^4 - 40*x*log(10)^2 + 16))
Time = 0.17 (sec) , antiderivative size = 188, normalized size of antiderivative = 6.71 \[ \int \frac {64+\left (-240 x+48 x^2\right ) \log ^2(10)+\left (300 x^2-120 x^3+12 x^4\right ) \log ^4(10)+\left (-125 x^3+75 x^4-15 x^5+x^6\right ) \log ^6(10)+e^{\frac {-336+\left (640 x-128 x^2\right ) \log ^2(10)+\left (-300 x^2+120 x^3-12 x^4\right ) \log ^4(10)}{16+\left (-40 x+8 x^2\right ) \log ^2(10)+\left (25 x^2-10 x^3+x^4\right ) \log ^4(10)}} \left (\left (-800 x+320 x^2\right ) \log ^2(10)+\left (800 x^2-480 x^3+64 x^4\right ) \log ^4(10)\right )}{64 x+\left (-240 x^2+48 x^3\right ) \log ^2(10)+\left (300 x^3-120 x^4+12 x^5\right ) \log ^4(10)+\left (-125 x^4+75 x^5-15 x^6+x^7\right ) \log ^6(10)} \, dx=\frac {e^{\frac {32 \mathrm {log}\left (10\right )^{2} x^{2}+144}{\mathrm {log}\left (10\right )^{4} x^{4}-10 \mathrm {log}\left (10\right )^{4} x^{3}+25 \mathrm {log}\left (10\right )^{4} x^{2}+8 \mathrm {log}\left (10\right )^{2} x^{2}-40 \mathrm {log}\left (10\right )^{2} x +16}} \mathrm {log}\left (x \right ) e^{12}+e^{\frac {160 \mathrm {log}\left (10\right )^{2} x}{\mathrm {log}\left (10\right )^{4} x^{4}-10 \mathrm {log}\left (10\right )^{4} x^{3}+25 \mathrm {log}\left (10\right )^{4} x^{2}+8 \mathrm {log}\left (10\right )^{2} x^{2}-40 \mathrm {log}\left (10\right )^{2} x +16}}}{e^{\frac {32 \mathrm {log}\left (10\right )^{2} x^{2}+144}{\mathrm {log}\left (10\right )^{4} x^{4}-10 \mathrm {log}\left (10\right )^{4} x^{3}+25 \mathrm {log}\left (10\right )^{4} x^{2}+8 \mathrm {log}\left (10\right )^{2} x^{2}-40 \mathrm {log}\left (10\right )^{2} x +16}} e^{12}} \] Input:
int((((64*x^4-480*x^3+800*x^2)*log(10)^4+(320*x^2-800*x)*log(10)^2)*exp((( -12*x^4+120*x^3-300*x^2)*log(10)^4+(-128*x^2+640*x)*log(10)^2-336)/((x^4-1 0*x^3+25*x^2)*log(10)^4+(8*x^2-40*x)*log(10)^2+16))+(x^6-15*x^5+75*x^4-125 *x^3)*log(10)^6+(12*x^4-120*x^3+300*x^2)*log(10)^4+(48*x^2-240*x)*log(10)^ 2+64)/((x^7-15*x^6+75*x^5-125*x^4)*log(10)^6+(12*x^5-120*x^4+300*x^3)*log( 10)^4+(48*x^3-240*x^2)*log(10)^2+64*x),x)
Output:
(e**((32*log(10)**2*x**2 + 144)/(log(10)**4*x**4 - 10*log(10)**4*x**3 + 25 *log(10)**4*x**2 + 8*log(10)**2*x**2 - 40*log(10)**2*x + 16))*log(x)*e**12 + e**((160*log(10)**2*x)/(log(10)**4*x**4 - 10*log(10)**4*x**3 + 25*log(1 0)**4*x**2 + 8*log(10)**2*x**2 - 40*log(10)**2*x + 16)))/(e**((32*log(10)* *2*x**2 + 144)/(log(10)**4*x**4 - 10*log(10)**4*x**3 + 25*log(10)**4*x**2 + 8*log(10)**2*x**2 - 40*log(10)**2*x + 16))*e**12)