Integrand size = 782, antiderivative size = 36 \[ \int \frac {-31500 x-11520 x^2-900 x^3+\left (10800 x+1800 x^2\right ) \log (3)-900 x \log ^2(3)+e^x \left (11250 x-1350 x^3-180 x^4+\left (-4500 x+900 x^2+360 x^3\right ) \log (3)+\left (450 x-180 x^2\right ) \log ^2(3)\right )+\left (11250 x+4500 x^2+450 x^3+\left (-4500 x-900 x^2\right ) \log (3)+450 x \log ^2(3)\right ) \log (5)+\left (12600 x+4464 x^2+360 x^3+\left (-4320 x-720 x^2\right ) \log (3)+360 x \log ^2(3)+e^x \left (-4500 x-900 x^2+180 x^3+36 x^4+\left (1800 x-72 x^3\right ) \log (3)+\left (-180 x+36 x^2\right ) \log ^2(3)\right )+\left (-4500 x-1800 x^2-180 x^3+\left (1800 x+360 x^2\right ) \log (3)-180 x \log ^2(3)\right ) \log (5)\right ) \log \left (\frac {196+56 x+4 x^2+(-56-8 x) \log (3)+4 \log ^2(3)+e^{2 x} \left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right )+\left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)\right ) \log (5)+\left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right ) \log ^2(5)+e^x \left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)+\left (50+20 x+2 x^2+(-20-4 x) \log (3)+2 \log ^2(3)\right ) \log (5)\right )}{25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)}\right )+\left (-1260 x-432 x^2-36 x^3+\left (432 x+72 x^2\right ) \log (3)-36 x \log ^2(3)+e^x \left (450 x+180 x^2+18 x^3+\left (-180 x-36 x^2\right ) \log (3)+18 x \log ^2(3)\right )+\left (450 x+180 x^2+18 x^3+\left (-180 x-36 x^2\right ) \log (3)+18 x \log ^2(3)\right ) \log (5)\right ) \log ^2\left (\frac {196+56 x+4 x^2+(-56-8 x) \log (3)+4 \log ^2(3)+e^{2 x} \left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right )+\left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)\right ) \log (5)+\left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right ) \log ^2(5)+e^x \left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)+\left (50+20 x+2 x^2+(-20-4 x) \log (3)+2 \log ^2(3)\right ) \log (5)\right )}{25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)}\right )}{-70-24 x-2 x^2+(24+4 x) \log (3)-2 \log ^2(3)+e^x \left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right )+\left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right ) \log (5)} \, dx=9 x^2 \left (5-\log \left (\left (2-e^x-\frac {4}{-5-x+\log (3)}-\log (5)\right )^2\right )\right )^2 \] Output:
9*(5-ln((2-exp(x)-ln(5)-4/(ln(3)-5-x))^2))^2*x^2
Leaf count is larger than twice the leaf count of optimal. \(104\) vs. \(2(36)=72\).
Time = 0.29 (sec) , antiderivative size = 104, normalized size of antiderivative = 2.89 \[ \int \frac {-31500 x-11520 x^2-900 x^3+\left (10800 x+1800 x^2\right ) \log (3)-900 x \log ^2(3)+e^x \left (11250 x-1350 x^3-180 x^4+\left (-4500 x+900 x^2+360 x^3\right ) \log (3)+\left (450 x-180 x^2\right ) \log ^2(3)\right )+\left (11250 x+4500 x^2+450 x^3+\left (-4500 x-900 x^2\right ) \log (3)+450 x \log ^2(3)\right ) \log (5)+\left (12600 x+4464 x^2+360 x^3+\left (-4320 x-720 x^2\right ) \log (3)+360 x \log ^2(3)+e^x \left (-4500 x-900 x^2+180 x^3+36 x^4+\left (1800 x-72 x^3\right ) \log (3)+\left (-180 x+36 x^2\right ) \log ^2(3)\right )+\left (-4500 x-1800 x^2-180 x^3+\left (1800 x+360 x^2\right ) \log (3)-180 x \log ^2(3)\right ) \log (5)\right ) \log \left (\frac {196+56 x+4 x^2+(-56-8 x) \log (3)+4 \log ^2(3)+e^{2 x} \left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right )+\left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)\right ) \log (5)+\left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right ) \log ^2(5)+e^x \left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)+\left (50+20 x+2 x^2+(-20-4 x) \log (3)+2 \log ^2(3)\right ) \log (5)\right )}{25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)}\right )+\left (-1260 x-432 x^2-36 x^3+\left (432 x+72 x^2\right ) \log (3)-36 x \log ^2(3)+e^x \left (450 x+180 x^2+18 x^3+\left (-180 x-36 x^2\right ) \log (3)+18 x \log ^2(3)\right )+\left (450 x+180 x^2+18 x^3+\left (-180 x-36 x^2\right ) \log (3)+18 x \log ^2(3)\right ) \log (5)\right ) \log ^2\left (\frac {196+56 x+4 x^2+(-56-8 x) \log (3)+4 \log ^2(3)+e^{2 x} \left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right )+\left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)\right ) \log (5)+\left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right ) \log ^2(5)+e^x \left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)+\left (50+20 x+2 x^2+(-20-4 x) \log (3)+2 \log ^2(3)\right ) \log (5)\right )}{25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)}\right )}{-70-24 x-2 x^2+(24+4 x) \log (3)-2 \log ^2(3)+e^x \left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right )+\left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right ) \log (5)} \, dx=18 \left (\frac {25 x^2}{2}-5 x^2 \log \left (\frac {\left (-14+e^x (5+x-\log (3))+x (-2+\log (5))-\log (3) \log (5)+\log (28125)\right )^2}{(5+x-\log (3))^2}\right )+\frac {1}{2} x^2 \log ^2\left (\frac {\left (-14+e^x (5+x-\log (3))+x (-2+\log (5))-\log (3) \log (5)+\log (28125)\right )^2}{(5+x-\log (3))^2}\right )\right ) \] Input:
Integrate[(-31500*x - 11520*x^2 - 900*x^3 + (10800*x + 1800*x^2)*Log[3] - 900*x*Log[3]^2 + E^x*(11250*x - 1350*x^3 - 180*x^4 + (-4500*x + 900*x^2 + 360*x^3)*Log[3] + (450*x - 180*x^2)*Log[3]^2) + (11250*x + 4500*x^2 + 450* x^3 + (-4500*x - 900*x^2)*Log[3] + 450*x*Log[3]^2)*Log[5] + (12600*x + 446 4*x^2 + 360*x^3 + (-4320*x - 720*x^2)*Log[3] + 360*x*Log[3]^2 + E^x*(-4500 *x - 900*x^2 + 180*x^3 + 36*x^4 + (1800*x - 72*x^3)*Log[3] + (-180*x + 36* x^2)*Log[3]^2) + (-4500*x - 1800*x^2 - 180*x^3 + (1800*x + 360*x^2)*Log[3] - 180*x*Log[3]^2)*Log[5])*Log[(196 + 56*x + 4*x^2 + (-56 - 8*x)*Log[3] + 4*Log[3]^2 + E^(2*x)*(25 + 10*x + x^2 + (-10 - 2*x)*Log[3] + Log[3]^2) + ( -140 - 48*x - 4*x^2 + (48 + 8*x)*Log[3] - 4*Log[3]^2)*Log[5] + (25 + 10*x + x^2 + (-10 - 2*x)*Log[3] + Log[3]^2)*Log[5]^2 + E^x*(-140 - 48*x - 4*x^2 + (48 + 8*x)*Log[3] - 4*Log[3]^2 + (50 + 20*x + 2*x^2 + (-20 - 4*x)*Log[3 ] + 2*Log[3]^2)*Log[5]))/(25 + 10*x + x^2 + (-10 - 2*x)*Log[3] + Log[3]^2) ] + (-1260*x - 432*x^2 - 36*x^3 + (432*x + 72*x^2)*Log[3] - 36*x*Log[3]^2 + E^x*(450*x + 180*x^2 + 18*x^3 + (-180*x - 36*x^2)*Log[3] + 18*x*Log[3]^2 ) + (450*x + 180*x^2 + 18*x^3 + (-180*x - 36*x^2)*Log[3] + 18*x*Log[3]^2)* Log[5])*Log[(196 + 56*x + 4*x^2 + (-56 - 8*x)*Log[3] + 4*Log[3]^2 + E^(2*x )*(25 + 10*x + x^2 + (-10 - 2*x)*Log[3] + Log[3]^2) + (-140 - 48*x - 4*x^2 + (48 + 8*x)*Log[3] - 4*Log[3]^2)*Log[5] + (25 + 10*x + x^2 + (-10 - 2*x) *Log[3] + Log[3]^2)*Log[5]^2 + E^x*(-140 - 48*x - 4*x^2 + (48 + 8*x)*Log[3 ] - 4*Log[3]^2 + (50 + 20*x + 2*x^2 + (-20 - 4*x)*Log[3] + 2*Log[3]^2)*Log [5]))/(25 + 10*x + x^2 + (-10 - 2*x)*Log[3] + Log[3]^2)]^2)/(-70 - 24*x - 2*x^2 + (24 + 4*x)*Log[3] - 2*Log[3]^2 + E^x*(25 + 10*x + x^2 + (-10 - 2*x )*Log[3] + Log[3]^2) + (25 + 10*x + x^2 + (-10 - 2*x)*Log[3] + Log[3]^2)*L og[5]),x]
Output:
18*((25*x^2)/2 - 5*x^2*Log[(-14 + E^x*(5 + x - Log[3]) + x*(-2 + Log[5]) - Log[3]*Log[5] + Log[28125])^2/(5 + x - Log[3])^2] + (x^2*Log[(-14 + E^x*( 5 + x - Log[3]) + x*(-2 + Log[5]) - Log[3]*Log[5] + Log[28125])^2/(5 + x - Log[3])^2]^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 {-900 x^3-11520 x^2+\left (1800 x^2+10800 x\right ) \log (3)+\left (-36 x^3-432 x^2+\left (72 x^2+432 x\right ) \log (3)+e^x \left (18 x^3+180 x^2+\left (-36 x^2-180 x\right ) \log (3)+450 x+18 x \log ^2(3)\right )+\log (5) \left (18 x^3+180 x^2+\left (-36 x^2-180 x\right ) \log (3)+450 x+18 x \log ^2(3)\right )-1260 x-36 x \log ^2(3)\right ) \log ^2\left (\frac {4 x^2+e^{2 x} \left (x^2+10 x+(-2 x-10) \log (3)+25+\log ^2(3)\right )+e^x \left (-4 x^2+\log (5) \left (2 x^2+20 x+(-4 x-20) \log (3)+50+2 \log ^2(3)\right )-48 x+(8 x+48) \log (3)-140-4 \log ^2(3)\right )+\log ^2(5) \left (x^2+10 x+(-2 x-10) \log (3)+25+\log ^2(3)\right )+\log (5) \left (-4 x^2-48 x+(8 x+48) \log (3)-140-4 \log ^2(3)\right )+56 x+(-8 x-56) \log (3)+196+4 \log ^2(3)}{x^2+10 x+(-2 x-10) \log (3)+25+\log ^2(3)}\right )+\log (5) \left (450 x^3+4500 x^2+\left (-900 x^2-4500 x\right ) \log (3)+11250 x+450 x \log ^2(3)\right )+e^x \left (-180 x^4-1350 x^3+\left (450 x-180 x^2\right ) \log ^2(3)+\left (360 x^3+900 x^2-4500 x\right ) \log (3)+11250 x\right )+\left (360 x^3+4464 x^2+\left (-720 x^2-4320 x\right ) \log (3)+\log (5) \left (-180 x^3-1800 x^2+\left (360 x^2+1800 x\right ) \log (3)-4500 x-180 x \log ^2(3)\right )+e^x \left (36 x^4+180 x^3+\left (1800 x-72 x^3\right ) \log (3)-900 x^2+\left (36 x^2-180 x\right ) \log ^2(3)-4500 x\right )+12600 x+360 x \log ^2(3)\right ) \log \left (\frac {4 x^2+e^{2 x} \left (x^2+10 x+(-2 x-10) \log (3)+25+\log ^2(3)\right )+e^x \left (-4 x^2+\log (5) \left (2 x^2+20 x+(-4 x-20) \log (3)+50+2 \log ^2(3)\right )-48 x+(8 x+48) \log (3)-140-4 \log ^2(3)\right )+\log ^2(5) \left (x^2+10 x+(-2 x-10) \log (3)+25+\log ^2(3)\right )+\log (5) \left (-4 x^2-48 x+(8 x+48) \log (3)-140-4 \log ^2(3)\right )+56 x+(-8 x-56) \log (3)+196+4 \log ^2(3)}{x^2+10 x+(-2 x-10) \log (3)+25+\log ^2(3)}\right )-31500 x-900 x \log ^2(3)}{-2 x^2+e^x \left (x^2+10 x+(-2 x-10) \log (3)+25+\log ^2(3)\right )+\log (5) \left (x^2+10 x+(-2 x-10) \log (3)+25+\log ^2(3)\right )-24 x+(4 x+24) \log (3)-70-2 \log ^2(3)} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {-900 x^3-11520 x^2+\left (1800 x^2+10800 x\right ) \log (3)+\left (-36 x^3-432 x^2+\left (72 x^2+432 x\right ) \log (3)+e^x \left (18 x^3+180 x^2+\left (-36 x^2-180 x\right ) \log (3)+450 x+18 x \log ^2(3)\right )+\log (5) \left (18 x^3+180 x^2+\left (-36 x^2-180 x\right ) \log (3)+450 x+18 x \log ^2(3)\right )-1260 x-36 x \log ^2(3)\right ) \log ^2\left (\frac {4 x^2+e^{2 x} \left (x^2+10 x+(-2 x-10) \log (3)+25+\log ^2(3)\right )+e^x \left (-4 x^2+\log (5) \left (2 x^2+20 x+(-4 x-20) \log (3)+50+2 \log ^2(3)\right )-48 x+(8 x+48) \log (3)-140-4 \log ^2(3)\right )+\log ^2(5) \left (x^2+10 x+(-2 x-10) \log (3)+25+\log ^2(3)\right )+\log (5) \left (-4 x^2-48 x+(8 x+48) \log (3)-140-4 \log ^2(3)\right )+56 x+(-8 x-56) \log (3)+196+4 \log ^2(3)}{x^2+10 x+(-2 x-10) \log (3)+25+\log ^2(3)}\right )+\log (5) \left (450 x^3+4500 x^2+\left (-900 x^2-4500 x\right ) \log (3)+11250 x+450 x \log ^2(3)\right )+e^x \left (-180 x^4-1350 x^3+\left (450 x-180 x^2\right ) \log ^2(3)+\left (360 x^3+900 x^2-4500 x\right ) \log (3)+11250 x\right )+\left (360 x^3+4464 x^2+\left (-720 x^2-4320 x\right ) \log (3)+\log (5) \left (-180 x^3-1800 x^2+\left (360 x^2+1800 x\right ) \log (3)-4500 x-180 x \log ^2(3)\right )+e^x \left (36 x^4+180 x^3+\left (1800 x-72 x^3\right ) \log (3)-900 x^2+\left (36 x^2-180 x\right ) \log ^2(3)-4500 x\right )+12600 x+360 x \log ^2(3)\right ) \log \left (\frac {4 x^2+e^{2 x} \left (x^2+10 x+(-2 x-10) \log (3)+25+\log ^2(3)\right )+e^x \left (-4 x^2+\log (5) \left (2 x^2+20 x+(-4 x-20) \log (3)+50+2 \log ^2(3)\right )-48 x+(8 x+48) \log (3)-140-4 \log ^2(3)\right )+\log ^2(5) \left (x^2+10 x+(-2 x-10) \log (3)+25+\log ^2(3)\right )+\log (5) \left (-4 x^2-48 x+(8 x+48) \log (3)-140-4 \log ^2(3)\right )+56 x+(-8 x-56) \log (3)+196+4 \log ^2(3)}{x^2+10 x+(-2 x-10) \log (3)+25+\log ^2(3)}\right )+x \left (-31500-900 \log ^2(3)\right )}{-2 x^2+e^x \left (x^2+10 x+(-2 x-10) \log (3)+25+\log ^2(3)\right )+\log (5) \left (x^2+10 x+(-2 x-10) \log (3)+25+\log ^2(3)\right )-24 x+(4 x+24) \log (3)-70-2 \log ^2(3)}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {18 x \left (-50 x^2+2 \left (-5 x^2 (\log (5)-2)+2 x (62+5 \log (3) (\log (5)-2)-25 \log (5))+e^x (x-5) (x+5-\log (3))^2-5 (\log (3)-5) (14+\log (3) \log (5)-\log (28125))\right ) \log \left (\frac {\left (x (\log (5)-2)+e^x (x+5-\log (3))-14+\log (28125)-\log (3) \log (5)\right )^2}{(x+5-\log (3))^2}\right )-640 x+(x+5-\log (3)) \left (x (\log (5)-2)+e^x (x+5-\log (3))-14+\log (28125)-\log (3) \log (5)\right ) \log ^2\left (\frac {\left (x (\log (5)-2)+e^x (x+5-\log (3))-14+\log (28125)-\log (3) \log (5)\right )^2}{(x+5-\log (3))^2}\right )-5 e^x (2 x-5) (x+5-\log (3))^2+25 \log (5) (x+5-\log (3))^2+100 (x+6) \log (3)-50 \left (35+\log ^2(3)\right )\right )}{(x+5-\log (3)) \left (x (\log (5)-2)+e^x (x+5-\log (3))-14 \left (1+\frac {1}{14} (\log (3) \log (5)-\log (28125))\right )\right )}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 18 \int \frac {x \left (50 x^2+640 x-5 e^x (5-2 x) (x-\log (3)+5)^2+(x-\log (3)+5) \left ((2-\log (5)) x-e^x (x-\log (3)+5)-\log (28125)+\log (3) \log (5)+14\right ) \log ^2\left (\frac {\left ((2-\log (5)) x-e^x (x-\log (3)+5)-\log (28125)+\log (3) \log (5)+14\right )^2}{(x-\log (3)+5)^2}\right )+2 \left (-5 (2-\log (5)) x^2-2 (62-5 \log (3) (2-\log (5))-25 \log (5)) x+e^x (5-x) (x-\log (3)+5)^2-5 (5-\log (3)) (14+\log (3) \log (5)-\log (28125))\right ) \log \left (\frac {\left ((2-\log (5)) x-e^x (x-\log (3)+5)-\log (28125)+\log (3) \log (5)+14\right )^2}{(x-\log (3)+5)^2}\right )-25 (x-\log (3)+5)^2 \log (5)+50 \left (35+\log ^2(3)\right )-100 (x+6) \log (3)\right )}{(x-\log (3)+5) \left ((2-\log (5)) x-e^x (x-\log (3)+5)-\log (28125)+\log (3) \log (5)+14\right )}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle 18 \int \frac {x \left (-50 x^2-640 x+5 e^x (5-2 x) (x-\log (3)+5)^2-(x-\log (3)+5) \left ((2-\log (5)) x-e^x (x-\log (3)+5)-\log (28125)+\log (3) \log (5)+14\right ) \log ^2\left (\frac {\left ((2-\log (5)) x-e^x (x-\log (3)+5)-\log (28125)+\log (3) \log (5)+14\right )^2}{(x-\log (3)+5)^2}\right )-2 \left (-5 (2-\log (5)) x^2-2 (62-5 \log (3) (2-\log (5))-25 \log (5)) x+e^x (5-x) (x-\log (3)+5)^2-5 (5-\log (3)) (14+\log (3) \log (5)-\log (28125))\right ) \log \left (\frac {\left ((2-\log (5)) x-e^x (x-\log (3)+5)-\log (28125)+\log (3) \log (5)+14\right )^2}{(x-\log (3)+5)^2}\right )+25 (x-\log (3)+5)^2 \log (5)-50 \left (35+\log ^2(3)\right )+100 (x+6) \log (3)\right )}{(x-\log (3)+5) \left (-((2-\log (5)) x)+e^x (x-\log (3)+5)-14 \left (1+\frac {1}{14} (\log (3) \log (5)-\log (28125))\right )\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 18 \int \left (\frac {\left (4 \left (1-\frac {\log (5)}{2}\right ) \log \left (\frac {\left ((-2+\log (5)) x+e^x (x-\log (3)+5)+\log (28125)-\log (3) \log (5)-14\right )^2}{(x-\log (3)+5)^2}\right ) x^2-20 \left (1-\frac {\log (5)}{2}\right ) x^2+48 \left (1+\frac {1}{24} (\log (5) \log (9)-\log (791015625))\right ) \log \left (\frac {\left ((-2+\log (5)) x+e^x (x-\log (3)+5)+\log (28125)-\log (3) \log (5)-14\right )^2}{(x-\log (3)+5)^2}\right ) x-240 \left (1+\frac {1}{24} (\log (5) \log (9)-\log (791015625))\right ) x+148 \left (1+\frac {1}{74} \left (-25 \log (5)-\log ^2(3) \log (5)+\log (3) (-24+\log (87890625))\right )\right ) \log \left (\frac {\left ((-2+\log (5)) x+e^x (x-\log (3)+5)+\log (28125)-\log (3) \log (5)-14\right )^2}{(x-\log (3)+5)^2}\right )-740 \left (1+\frac {1}{148} \left (-38 \log (3)-\log ^2(3) \log (25)+(-5+\log (9)) \log (87890625)\right )\right )\right ) x^2}{(x-\log (3)+5) \left (e^x x-2 \left (1-\frac {\log (5)}{2}\right ) x-14 \left (1+\frac {1}{14} (\log (3) \log (5)-\log (28125))\right )+5 e^x \left (1-\frac {\log (3)}{5}\right )\right )}+\left (\log \left (\frac {\left ((-2+\log (5)) x+e^x (x-\log (3)+5)+\log (28125)-\log (3) \log (5)-14\right )^2}{(x-\log (3)+5)^2}\right )-5\right ) \left (2 x+\log \left (\frac {\left ((-2+\log (5)) x+e^x (x-\log (3)+5)+\log (28125)-\log (3) \log (5)-14\right )^2}{(x-\log (3)+5)^2}\right )-5\right ) x\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle 18 \int \left (\frac {\left (4 \left (1-\frac {\log (5)}{2}\right ) \log \left (\frac {\left ((-2+\log (5)) x+e^x (x-\log (3)+5)+\log (28125)-\log (3) \log (5)-14\right )^2}{(x-\log (3)+5)^2}\right ) x^2-20 \left (1-\frac {\log (5)}{2}\right ) x^2+48 \left (1+\frac {1}{24} (\log (5) \log (9)-\log (791015625))\right ) \log \left (\frac {\left ((-2+\log (5)) x+e^x (x-\log (3)+5)+\log (28125)-\log (3) \log (5)-14\right )^2}{(x-\log (3)+5)^2}\right ) x-240 \left (1+\frac {1}{24} (\log (5) \log (9)-\log (791015625))\right ) x+148 \left (1+\frac {1}{74} \left (-25 \log (5)-\log ^2(3) \log (5)+\log (3) (-24+\log (87890625))\right )\right ) \log \left (\frac {\left ((-2+\log (5)) x+e^x (x-\log (3)+5)+\log (28125)-\log (3) \log (5)-14\right )^2}{(x-\log (3)+5)^2}\right )-740 \left (1+\frac {1}{148} \left (-38 \log (3)-\log ^2(3) \log (25)+(-5+\log (9)) \log (87890625)\right )\right )\right ) x^2}{(x-\log (3)+5) \left (e^x x-2 \left (1-\frac {\log (5)}{2}\right ) x-14 \left (1+\frac {1}{14} (\log (3) \log (5)-\log (28125))\right )+5 e^x \left (1-\frac {\log (3)}{5}\right )\right )}+\left (\log \left (\frac {\left ((-2+\log (5)) x+e^x (x-\log (3)+5)+\log (28125)-\log (3) \log (5)-14\right )^2}{(x-\log (3)+5)^2}\right )-5\right ) \left (2 x+\log \left (\frac {\left ((-2+\log (5)) x+e^x (x-\log (3)+5)+\log (28125)-\log (3) \log (5)-14\right )^2}{(x-\log (3)+5)^2}\right )-5\right ) x\right )dx\) |
Input:
Int[(-31500*x - 11520*x^2 - 900*x^3 + (10800*x + 1800*x^2)*Log[3] - 900*x* Log[3]^2 + E^x*(11250*x - 1350*x^3 - 180*x^4 + (-4500*x + 900*x^2 + 360*x^ 3)*Log[3] + (450*x - 180*x^2)*Log[3]^2) + (11250*x + 4500*x^2 + 450*x^3 + (-4500*x - 900*x^2)*Log[3] + 450*x*Log[3]^2)*Log[5] + (12600*x + 4464*x^2 + 360*x^3 + (-4320*x - 720*x^2)*Log[3] + 360*x*Log[3]^2 + E^x*(-4500*x - 9 00*x^2 + 180*x^3 + 36*x^4 + (1800*x - 72*x^3)*Log[3] + (-180*x + 36*x^2)*L og[3]^2) + (-4500*x - 1800*x^2 - 180*x^3 + (1800*x + 360*x^2)*Log[3] - 180 *x*Log[3]^2)*Log[5])*Log[(196 + 56*x + 4*x^2 + (-56 - 8*x)*Log[3] + 4*Log[ 3]^2 + E^(2*x)*(25 + 10*x + x^2 + (-10 - 2*x)*Log[3] + Log[3]^2) + (-140 - 48*x - 4*x^2 + (48 + 8*x)*Log[3] - 4*Log[3]^2)*Log[5] + (25 + 10*x + x^2 + (-10 - 2*x)*Log[3] + Log[3]^2)*Log[5]^2 + E^x*(-140 - 48*x - 4*x^2 + (48 + 8*x)*Log[3] - 4*Log[3]^2 + (50 + 20*x + 2*x^2 + (-20 - 4*x)*Log[3] + 2* Log[3]^2)*Log[5]))/(25 + 10*x + x^2 + (-10 - 2*x)*Log[3] + Log[3]^2)] + (- 1260*x - 432*x^2 - 36*x^3 + (432*x + 72*x^2)*Log[3] - 36*x*Log[3]^2 + E^x* (450*x + 180*x^2 + 18*x^3 + (-180*x - 36*x^2)*Log[3] + 18*x*Log[3]^2) + (4 50*x + 180*x^2 + 18*x^3 + (-180*x - 36*x^2)*Log[3] + 18*x*Log[3]^2)*Log[5] )*Log[(196 + 56*x + 4*x^2 + (-56 - 8*x)*Log[3] + 4*Log[3]^2 + E^(2*x)*(25 + 10*x + x^2 + (-10 - 2*x)*Log[3] + Log[3]^2) + (-140 - 48*x - 4*x^2 + (48 + 8*x)*Log[3] - 4*Log[3]^2)*Log[5] + (25 + 10*x + x^2 + (-10 - 2*x)*Log[3 ] + Log[3]^2)*Log[5]^2 + E^x*(-140 - 48*x - 4*x^2 + (48 + 8*x)*Log[3] - 4* Log[3]^2 + (50 + 20*x + 2*x^2 + (-20 - 4*x)*Log[3] + 2*Log[3]^2)*Log[5]))/ (25 + 10*x + x^2 + (-10 - 2*x)*Log[3] + Log[3]^2)]^2)/(-70 - 24*x - 2*x^2 + (24 + 4*x)*Log[3] - 2*Log[3]^2 + E^x*(25 + 10*x + x^2 + (-10 - 2*x)*Log[ 3] + Log[3]^2) + (25 + 10*x + x^2 + (-10 - 2*x)*Log[3] + Log[3]^2)*Log[5]) ,x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(1103\) vs. \(2(35)=70\).
Time = 6.67 (sec) , antiderivative size = 1104, normalized size of antiderivative = 30.67
| method | result | size |
| parallelrisch | \(\text {Expression too large to display}\) | \(1104\) |
| risch | \(\text {Expression too large to display}\) | \(6974\) |
Input:
int((((18*x*ln(3)^2+(-36*x^2-180*x)*ln(3)+18*x^3+180*x^2+450*x)*exp(x)+(18 *x*ln(3)^2+(-36*x^2-180*x)*ln(3)+18*x^3+180*x^2+450*x)*ln(5)-36*x*ln(3)^2+ (72*x^2+432*x)*ln(3)-36*x^3-432*x^2-1260*x)*ln(((ln(3)^2+(-2*x-10)*ln(3)+x ^2+10*x+25)*exp(x)^2+((2*ln(3)^2+(-4*x-20)*ln(3)+2*x^2+20*x+50)*ln(5)-4*ln (3)^2+(8*x+48)*ln(3)-4*x^2-48*x-140)*exp(x)+(ln(3)^2+(-2*x-10)*ln(3)+x^2+1 0*x+25)*ln(5)^2+(-4*ln(3)^2+(8*x+48)*ln(3)-4*x^2-48*x-140)*ln(5)+4*ln(3)^2 +(-8*x-56)*ln(3)+4*x^2+56*x+196)/(ln(3)^2+(-2*x-10)*ln(3)+x^2+10*x+25))^2+ (((36*x^2-180*x)*ln(3)^2+(-72*x^3+1800*x)*ln(3)+36*x^4+180*x^3-900*x^2-450 0*x)*exp(x)+(-180*x*ln(3)^2+(360*x^2+1800*x)*ln(3)-180*x^3-1800*x^2-4500*x )*ln(5)+360*x*ln(3)^2+(-720*x^2-4320*x)*ln(3)+360*x^3+4464*x^2+12600*x)*ln (((ln(3)^2+(-2*x-10)*ln(3)+x^2+10*x+25)*exp(x)^2+((2*ln(3)^2+(-4*x-20)*ln( 3)+2*x^2+20*x+50)*ln(5)-4*ln(3)^2+(8*x+48)*ln(3)-4*x^2-48*x-140)*exp(x)+(l n(3)^2+(-2*x-10)*ln(3)+x^2+10*x+25)*ln(5)^2+(-4*ln(3)^2+(8*x+48)*ln(3)-4*x ^2-48*x-140)*ln(5)+4*ln(3)^2+(-8*x-56)*ln(3)+4*x^2+56*x+196)/(ln(3)^2+(-2* x-10)*ln(3)+x^2+10*x+25))+((-180*x^2+450*x)*ln(3)^2+(360*x^3+900*x^2-4500* x)*ln(3)-180*x^4-1350*x^3+11250*x)*exp(x)+(450*x*ln(3)^2+(-900*x^2-4500*x) *ln(3)+450*x^3+4500*x^2+11250*x)*ln(5)-900*x*ln(3)^2+(1800*x^2+10800*x)*ln (3)-900*x^3-11520*x^2-31500*x)/((ln(3)^2+(-2*x-10)*ln(3)+x^2+10*x+25)*exp( x)+(ln(3)^2+(-2*x-10)*ln(3)+x^2+10*x+25)*ln(5)-2*ln(3)^2+(4*x+24)*ln(3)-2* x^2-24*x-70),x,method=_RETURNVERBOSE)
Output:
9*ln(((ln(3)^2+(-2*x-10)*ln(3)+x^2+10*x+25)*exp(x)^2+((2*ln(3)^2+(-4*x-20) *ln(3)+2*x^2+20*x+50)*ln(5)-4*ln(3)^2+(8*x+48)*ln(3)-4*x^2-48*x-140)*exp(x )+(ln(3)^2+(-2*x-10)*ln(3)+x^2+10*x+25)*ln(5)^2+(-4*ln(3)^2+(8*x+48)*ln(3) -4*x^2-48*x-140)*ln(5)+4*ln(3)^2+(-8*x-56)*ln(3)+4*x^2+56*x+196)/(ln(3)^2- 2*x*ln(3)+x^2-10*ln(3)+10*x+25))^2*x^2+1080*ln(3)^2*ln(-ln(3)+5+x)-1080*ln (3)^2*ln(-ln(5)*ln(3)+x*ln(5)-exp(x)*ln(3)+exp(x)*x+5*ln(5)+2*ln(3)+5*exp( x)-2*x-14)+540*ln(((ln(3)^2+(-2*x-10)*ln(3)+x^2+10*x+25)*exp(x)^2+((2*ln(3 )^2+(-4*x-20)*ln(3)+2*x^2+20*x+50)*ln(5)-4*ln(3)^2+(8*x+48)*ln(3)-4*x^2-48 *x-140)*exp(x)+(ln(3)^2+(-2*x-10)*ln(3)+x^2+10*x+25)*ln(5)^2+(-4*ln(3)^2+( 8*x+48)*ln(3)-4*x^2-48*x-140)*ln(5)+4*ln(3)^2+(-8*x-56)*ln(3)+4*x^2+56*x+1 96)/(ln(3)^2-2*x*ln(3)+x^2-10*ln(3)+10*x+25))*ln(3)^2-90*ln(((ln(3)^2+(-2* x-10)*ln(3)+x^2+10*x+25)*exp(x)^2+((2*ln(3)^2+(-4*x-20)*ln(3)+2*x^2+20*x+5 0)*ln(5)-4*ln(3)^2+(8*x+48)*ln(3)-4*x^2-48*x-140)*exp(x)+(ln(3)^2+(-2*x-10 )*ln(3)+x^2+10*x+25)*ln(5)^2+(-4*ln(3)^2+(8*x+48)*ln(3)-4*x^2-48*x-140)*ln (5)+4*ln(3)^2+(-8*x-56)*ln(3)+4*x^2+56*x+196)/(ln(3)^2-2*x*ln(3)+x^2-10*ln (3)+10*x+25))*x^2-1350*ln(3)^2-10800*ln(3)*ln(-ln(3)+5+x)+10800*ln(3)*ln(- ln(5)*ln(3)+x*ln(5)-exp(x)*ln(3)+exp(x)*x+5*ln(5)+2*ln(3)+5*exp(x)-2*x-14) -5400*ln(((ln(3)^2+(-2*x-10)*ln(3)+x^2+10*x+25)*exp(x)^2+((2*ln(3)^2+(-4*x -20)*ln(3)+2*x^2+20*x+50)*ln(5)-4*ln(3)^2+(8*x+48)*ln(3)-4*x^2-48*x-140)*e xp(x)+(ln(3)^2+(-2*x-10)*ln(3)+x^2+10*x+25)*ln(5)^2+(-4*ln(3)^2+(8*x+48...
Leaf count of result is larger than twice the leaf count of optimal. 352 vs. \(2 (33) = 66\).
Time = 0.17 (sec) , antiderivative size = 352, normalized size of antiderivative = 9.78 \[ \int \frac {-31500 x-11520 x^2-900 x^3+\left (10800 x+1800 x^2\right ) \log (3)-900 x \log ^2(3)+e^x \left (11250 x-1350 x^3-180 x^4+\left (-4500 x+900 x^2+360 x^3\right ) \log (3)+\left (450 x-180 x^2\right ) \log ^2(3)\right )+\left (11250 x+4500 x^2+450 x^3+\left (-4500 x-900 x^2\right ) \log (3)+450 x \log ^2(3)\right ) \log (5)+\left (12600 x+4464 x^2+360 x^3+\left (-4320 x-720 x^2\right ) \log (3)+360 x \log ^2(3)+e^x \left (-4500 x-900 x^2+180 x^3+36 x^4+\left (1800 x-72 x^3\right ) \log (3)+\left (-180 x+36 x^2\right ) \log ^2(3)\right )+\left (-4500 x-1800 x^2-180 x^3+\left (1800 x+360 x^2\right ) \log (3)-180 x \log ^2(3)\right ) \log (5)\right ) \log \left (\frac {196+56 x+4 x^2+(-56-8 x) \log (3)+4 \log ^2(3)+e^{2 x} \left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right )+\left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)\right ) \log (5)+\left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right ) \log ^2(5)+e^x \left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)+\left (50+20 x+2 x^2+(-20-4 x) \log (3)+2 \log ^2(3)\right ) \log (5)\right )}{25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)}\right )+\left (-1260 x-432 x^2-36 x^3+\left (432 x+72 x^2\right ) \log (3)-36 x \log ^2(3)+e^x \left (450 x+180 x^2+18 x^3+\left (-180 x-36 x^2\right ) \log (3)+18 x \log ^2(3)\right )+\left (450 x+180 x^2+18 x^3+\left (-180 x-36 x^2\right ) \log (3)+18 x \log ^2(3)\right ) \log (5)\right ) \log ^2\left (\frac {196+56 x+4 x^2+(-56-8 x) \log (3)+4 \log ^2(3)+e^{2 x} \left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right )+\left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)\right ) \log (5)+\left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right ) \log ^2(5)+e^x \left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)+\left (50+20 x+2 x^2+(-20-4 x) \log (3)+2 \log ^2(3)\right ) \log (5)\right )}{25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)}\right )}{-70-24 x-2 x^2+(24+4 x) \log (3)-2 \log ^2(3)+e^x \left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right )+\left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right ) \log (5)} \, dx=9 \, x^{2} \log \left (\frac {{\left (x^{2} - 2 \, {\left (x + 5\right )} \log \left (3\right ) + \log \left (3\right )^{2} + 10 \, x + 25\right )} \log \left (5\right )^{2} + 4 \, x^{2} + {\left (x^{2} - 2 \, {\left (x + 5\right )} \log \left (3\right ) + \log \left (3\right )^{2} + 10 \, x + 25\right )} e^{\left (2 \, x\right )} - 2 \, {\left (2 \, x^{2} - {\left (x^{2} - 2 \, {\left (x + 5\right )} \log \left (3\right ) + \log \left (3\right )^{2} + 10 \, x + 25\right )} \log \left (5\right ) - 4 \, {\left (x + 6\right )} \log \left (3\right ) + 2 \, \log \left (3\right )^{2} + 24 \, x + 70\right )} e^{x} - 4 \, {\left (x^{2} - 2 \, {\left (x + 6\right )} \log \left (3\right ) + \log \left (3\right )^{2} + 12 \, x + 35\right )} \log \left (5\right ) - 8 \, {\left (x + 7\right )} \log \left (3\right ) + 4 \, \log \left (3\right )^{2} + 56 \, x + 196}{x^{2} - 2 \, {\left (x + 5\right )} \log \left (3\right ) + \log \left (3\right )^{2} + 10 \, x + 25}\right )^{2} - 90 \, x^{2} \log \left (\frac {{\left (x^{2} - 2 \, {\left (x + 5\right )} \log \left (3\right ) + \log \left (3\right )^{2} + 10 \, x + 25\right )} \log \left (5\right )^{2} + 4 \, x^{2} + {\left (x^{2} - 2 \, {\left (x + 5\right )} \log \left (3\right ) + \log \left (3\right )^{2} + 10 \, x + 25\right )} e^{\left (2 \, x\right )} - 2 \, {\left (2 \, x^{2} - {\left (x^{2} - 2 \, {\left (x + 5\right )} \log \left (3\right ) + \log \left (3\right )^{2} + 10 \, x + 25\right )} \log \left (5\right ) - 4 \, {\left (x + 6\right )} \log \left (3\right ) + 2 \, \log \left (3\right )^{2} + 24 \, x + 70\right )} e^{x} - 4 \, {\left (x^{2} - 2 \, {\left (x + 6\right )} \log \left (3\right ) + \log \left (3\right )^{2} + 12 \, x + 35\right )} \log \left (5\right ) - 8 \, {\left (x + 7\right )} \log \left (3\right ) + 4 \, \log \left (3\right )^{2} + 56 \, x + 196}{x^{2} - 2 \, {\left (x + 5\right )} \log \left (3\right ) + \log \left (3\right )^{2} + 10 \, x + 25}\right ) + 225 \, x^{2} \] Input:
integrate((((18*x*log(3)^2+(-36*x^2-180*x)*log(3)+18*x^3+180*x^2+450*x)*ex p(x)+(18*x*log(3)^2+(-36*x^2-180*x)*log(3)+18*x^3+180*x^2+450*x)*log(5)-36 *x*log(3)^2+(72*x^2+432*x)*log(3)-36*x^3-432*x^2-1260*x)*log(((log(3)^2+(- 2*x-10)*log(3)+x^2+10*x+25)*exp(x)^2+((2*log(3)^2+(-4*x-20)*log(3)+2*x^2+2 0*x+50)*log(5)-4*log(3)^2+(8*x+48)*log(3)-4*x^2-48*x-140)*exp(x)+(log(3)^2 +(-2*x-10)*log(3)+x^2+10*x+25)*log(5)^2+(-4*log(3)^2+(8*x+48)*log(3)-4*x^2 -48*x-140)*log(5)+4*log(3)^2+(-8*x-56)*log(3)+4*x^2+56*x+196)/(log(3)^2+(- 2*x-10)*log(3)+x^2+10*x+25))^2+(((36*x^2-180*x)*log(3)^2+(-72*x^3+1800*x)* log(3)+36*x^4+180*x^3-900*x^2-4500*x)*exp(x)+(-180*x*log(3)^2+(360*x^2+180 0*x)*log(3)-180*x^3-1800*x^2-4500*x)*log(5)+360*x*log(3)^2+(-720*x^2-4320* x)*log(3)+360*x^3+4464*x^2+12600*x)*log(((log(3)^2+(-2*x-10)*log(3)+x^2+10 *x+25)*exp(x)^2+((2*log(3)^2+(-4*x-20)*log(3)+2*x^2+20*x+50)*log(5)-4*log( 3)^2+(8*x+48)*log(3)-4*x^2-48*x-140)*exp(x)+(log(3)^2+(-2*x-10)*log(3)+x^2 +10*x+25)*log(5)^2+(-4*log(3)^2+(8*x+48)*log(3)-4*x^2-48*x-140)*log(5)+4*l og(3)^2+(-8*x-56)*log(3)+4*x^2+56*x+196)/(log(3)^2+(-2*x-10)*log(3)+x^2+10 *x+25))+((-180*x^2+450*x)*log(3)^2+(360*x^3+900*x^2-4500*x)*log(3)-180*x^4 -1350*x^3+11250*x)*exp(x)+(450*x*log(3)^2+(-900*x^2-4500*x)*log(3)+450*x^3 +4500*x^2+11250*x)*log(5)-900*x*log(3)^2+(1800*x^2+10800*x)*log(3)-900*x^3 -11520*x^2-31500*x)/((log(3)^2+(-2*x-10)*log(3)+x^2+10*x+25)*exp(x)+(log(3 )^2+(-2*x-10)*log(3)+x^2+10*x+25)*log(5)-2*log(3)^2+(4*x+24)*log(3)-2*x^2- 24*x-70),x, algorithm="fricas")
Output:
9*x^2*log(((x^2 - 2*(x + 5)*log(3) + log(3)^2 + 10*x + 25)*log(5)^2 + 4*x^ 2 + (x^2 - 2*(x + 5)*log(3) + log(3)^2 + 10*x + 25)*e^(2*x) - 2*(2*x^2 - ( x^2 - 2*(x + 5)*log(3) + log(3)^2 + 10*x + 25)*log(5) - 4*(x + 6)*log(3) + 2*log(3)^2 + 24*x + 70)*e^x - 4*(x^2 - 2*(x + 6)*log(3) + log(3)^2 + 12*x + 35)*log(5) - 8*(x + 7)*log(3) + 4*log(3)^2 + 56*x + 196)/(x^2 - 2*(x + 5)*log(3) + log(3)^2 + 10*x + 25))^2 - 90*x^2*log(((x^2 - 2*(x + 5)*log(3) + log(3)^2 + 10*x + 25)*log(5)^2 + 4*x^2 + (x^2 - 2*(x + 5)*log(3) + log( 3)^2 + 10*x + 25)*e^(2*x) - 2*(2*x^2 - (x^2 - 2*(x + 5)*log(3) + log(3)^2 + 10*x + 25)*log(5) - 4*(x + 6)*log(3) + 2*log(3)^2 + 24*x + 70)*e^x - 4*( x^2 - 2*(x + 6)*log(3) + log(3)^2 + 12*x + 35)*log(5) - 8*(x + 7)*log(3) + 4*log(3)^2 + 56*x + 196)/(x^2 - 2*(x + 5)*log(3) + log(3)^2 + 10*x + 25)) + 225*x^2
Leaf count of result is larger than twice the leaf count of optimal. 413 vs. \(2 (27) = 54\).
Time = 1.37 (sec) , antiderivative size = 413, normalized size of antiderivative = 11.47 \[ \int \frac {-31500 x-11520 x^2-900 x^3+\left (10800 x+1800 x^2\right ) \log (3)-900 x \log ^2(3)+e^x \left (11250 x-1350 x^3-180 x^4+\left (-4500 x+900 x^2+360 x^3\right ) \log (3)+\left (450 x-180 x^2\right ) \log ^2(3)\right )+\left (11250 x+4500 x^2+450 x^3+\left (-4500 x-900 x^2\right ) \log (3)+450 x \log ^2(3)\right ) \log (5)+\left (12600 x+4464 x^2+360 x^3+\left (-4320 x-720 x^2\right ) \log (3)+360 x \log ^2(3)+e^x \left (-4500 x-900 x^2+180 x^3+36 x^4+\left (1800 x-72 x^3\right ) \log (3)+\left (-180 x+36 x^2\right ) \log ^2(3)\right )+\left (-4500 x-1800 x^2-180 x^3+\left (1800 x+360 x^2\right ) \log (3)-180 x \log ^2(3)\right ) \log (5)\right ) \log \left (\frac {196+56 x+4 x^2+(-56-8 x) \log (3)+4 \log ^2(3)+e^{2 x} \left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right )+\left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)\right ) \log (5)+\left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right ) \log ^2(5)+e^x \left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)+\left (50+20 x+2 x^2+(-20-4 x) \log (3)+2 \log ^2(3)\right ) \log (5)\right )}{25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)}\right )+\left (-1260 x-432 x^2-36 x^3+\left (432 x+72 x^2\right ) \log (3)-36 x \log ^2(3)+e^x \left (450 x+180 x^2+18 x^3+\left (-180 x-36 x^2\right ) \log (3)+18 x \log ^2(3)\right )+\left (450 x+180 x^2+18 x^3+\left (-180 x-36 x^2\right ) \log (3)+18 x \log ^2(3)\right ) \log (5)\right ) \log ^2\left (\frac {196+56 x+4 x^2+(-56-8 x) \log (3)+4 \log ^2(3)+e^{2 x} \left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right )+\left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)\right ) \log (5)+\left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right ) \log ^2(5)+e^x \left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)+\left (50+20 x+2 x^2+(-20-4 x) \log (3)+2 \log ^2(3)\right ) \log (5)\right )}{25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)}\right )}{-70-24 x-2 x^2+(24+4 x) \log (3)-2 \log ^2(3)+e^x \left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right )+\left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right ) \log (5)} \, dx=9 x^{2} \log {\left (\frac {4 x^{2} + 56 x + \left (- 8 x - 56\right ) \log {\left (3 \right )} + \left (- 4 x^{2} - 48 x + \left (8 x + 48\right ) \log {\left (3 \right )} - 140 - 4 \log {\left (3 \right )}^{2}\right ) \log {\left (5 \right )} + \left (x^{2} + 10 x + \left (- 2 x - 10\right ) \log {\left (3 \right )} + \log {\left (3 \right )}^{2} + 25\right ) e^{2 x} + \left (x^{2} + 10 x + \left (- 2 x - 10\right ) \log {\left (3 \right )} + \log {\left (3 \right )}^{2} + 25\right ) \log {\left (5 \right )}^{2} + \left (- 4 x^{2} - 48 x + \left (8 x + 48\right ) \log {\left (3 \right )} + \left (2 x^{2} + 20 x + \left (- 4 x - 20\right ) \log {\left (3 \right )} + 2 \log {\left (3 \right )}^{2} + 50\right ) \log {\left (5 \right )} - 140 - 4 \log {\left (3 \right )}^{2}\right ) e^{x} + 4 \log {\left (3 \right )}^{2} + 196}{x^{2} + 10 x + \left (- 2 x - 10\right ) \log {\left (3 \right )} + \log {\left (3 \right )}^{2} + 25} \right )}^{2} - 90 x^{2} \log {\left (\frac {4 x^{2} + 56 x + \left (- 8 x - 56\right ) \log {\left (3 \right )} + \left (- 4 x^{2} - 48 x + \left (8 x + 48\right ) \log {\left (3 \right )} - 140 - 4 \log {\left (3 \right )}^{2}\right ) \log {\left (5 \right )} + \left (x^{2} + 10 x + \left (- 2 x - 10\right ) \log {\left (3 \right )} + \log {\left (3 \right )}^{2} + 25\right ) e^{2 x} + \left (x^{2} + 10 x + \left (- 2 x - 10\right ) \log {\left (3 \right )} + \log {\left (3 \right )}^{2} + 25\right ) \log {\left (5 \right )}^{2} + \left (- 4 x^{2} - 48 x + \left (8 x + 48\right ) \log {\left (3 \right )} + \left (2 x^{2} + 20 x + \left (- 4 x - 20\right ) \log {\left (3 \right )} + 2 \log {\left (3 \right )}^{2} + 50\right ) \log {\left (5 \right )} - 140 - 4 \log {\left (3 \right )}^{2}\right ) e^{x} + 4 \log {\left (3 \right )}^{2} + 196}{x^{2} + 10 x + \left (- 2 x - 10\right ) \log {\left (3 \right )} + \log {\left (3 \right )}^{2} + 25} \right )} + 225 x^{2} \] Input:
integrate((((18*x*ln(3)**2+(-36*x**2-180*x)*ln(3)+18*x**3+180*x**2+450*x)* exp(x)+(18*x*ln(3)**2+(-36*x**2-180*x)*ln(3)+18*x**3+180*x**2+450*x)*ln(5) -36*x*ln(3)**2+(72*x**2+432*x)*ln(3)-36*x**3-432*x**2-1260*x)*ln(((ln(3)** 2+(-2*x-10)*ln(3)+x**2+10*x+25)*exp(x)**2+((2*ln(3)**2+(-4*x-20)*ln(3)+2*x **2+20*x+50)*ln(5)-4*ln(3)**2+(8*x+48)*ln(3)-4*x**2-48*x-140)*exp(x)+(ln(3 )**2+(-2*x-10)*ln(3)+x**2+10*x+25)*ln(5)**2+(-4*ln(3)**2+(8*x+48)*ln(3)-4* x**2-48*x-140)*ln(5)+4*ln(3)**2+(-8*x-56)*ln(3)+4*x**2+56*x+196)/(ln(3)**2 +(-2*x-10)*ln(3)+x**2+10*x+25))**2+(((36*x**2-180*x)*ln(3)**2+(-72*x**3+18 00*x)*ln(3)+36*x**4+180*x**3-900*x**2-4500*x)*exp(x)+(-180*x*ln(3)**2+(360 *x**2+1800*x)*ln(3)-180*x**3-1800*x**2-4500*x)*ln(5)+360*x*ln(3)**2+(-720* x**2-4320*x)*ln(3)+360*x**3+4464*x**2+12600*x)*ln(((ln(3)**2+(-2*x-10)*ln( 3)+x**2+10*x+25)*exp(x)**2+((2*ln(3)**2+(-4*x-20)*ln(3)+2*x**2+20*x+50)*ln (5)-4*ln(3)**2+(8*x+48)*ln(3)-4*x**2-48*x-140)*exp(x)+(ln(3)**2+(-2*x-10)* ln(3)+x**2+10*x+25)*ln(5)**2+(-4*ln(3)**2+(8*x+48)*ln(3)-4*x**2-48*x-140)* ln(5)+4*ln(3)**2+(-8*x-56)*ln(3)+4*x**2+56*x+196)/(ln(3)**2+(-2*x-10)*ln(3 )+x**2+10*x+25))+((-180*x**2+450*x)*ln(3)**2+(360*x**3+900*x**2-4500*x)*ln (3)-180*x**4-1350*x**3+11250*x)*exp(x)+(450*x*ln(3)**2+(-900*x**2-4500*x)* ln(3)+450*x**3+4500*x**2+11250*x)*ln(5)-900*x*ln(3)**2+(1800*x**2+10800*x) *ln(3)-900*x**3-11520*x**2-31500*x)/((ln(3)**2+(-2*x-10)*ln(3)+x**2+10*x+2 5)*exp(x)+(ln(3)**2+(-2*x-10)*ln(3)+x**2+10*x+25)*ln(5)-2*ln(3)**2+(4*x+24 )*ln(3)-2*x**2-24*x-70),x)
Output:
9*x**2*log((4*x**2 + 56*x + (-8*x - 56)*log(3) + (-4*x**2 - 48*x + (8*x + 48)*log(3) - 140 - 4*log(3)**2)*log(5) + (x**2 + 10*x + (-2*x - 10)*log(3) + log(3)**2 + 25)*exp(2*x) + (x**2 + 10*x + (-2*x - 10)*log(3) + log(3)** 2 + 25)*log(5)**2 + (-4*x**2 - 48*x + (8*x + 48)*log(3) + (2*x**2 + 20*x + (-4*x - 20)*log(3) + 2*log(3)**2 + 50)*log(5) - 140 - 4*log(3)**2)*exp(x) + 4*log(3)**2 + 196)/(x**2 + 10*x + (-2*x - 10)*log(3) + log(3)**2 + 25)) **2 - 90*x**2*log((4*x**2 + 56*x + (-8*x - 56)*log(3) + (-4*x**2 - 48*x + (8*x + 48)*log(3) - 140 - 4*log(3)**2)*log(5) + (x**2 + 10*x + (-2*x - 10) *log(3) + log(3)**2 + 25)*exp(2*x) + (x**2 + 10*x + (-2*x - 10)*log(3) + l og(3)**2 + 25)*log(5)**2 + (-4*x**2 - 48*x + (8*x + 48)*log(3) + (2*x**2 + 20*x + (-4*x - 20)*log(3) + 2*log(3)**2 + 50)*log(5) - 140 - 4*log(3)**2) *exp(x) + 4*log(3)**2 + 196)/(x**2 + 10*x + (-2*x - 10)*log(3) + log(3)**2 + 25)) + 225*x**2
Leaf count of result is larger than twice the leaf count of optimal. 124 vs. \(2 (33) = 66\).
Time = 0.27 (sec) , antiderivative size = 124, normalized size of antiderivative = 3.44 \[ \int \frac {-31500 x-11520 x^2-900 x^3+\left (10800 x+1800 x^2\right ) \log (3)-900 x \log ^2(3)+e^x \left (11250 x-1350 x^3-180 x^4+\left (-4500 x+900 x^2+360 x^3\right ) \log (3)+\left (450 x-180 x^2\right ) \log ^2(3)\right )+\left (11250 x+4500 x^2+450 x^3+\left (-4500 x-900 x^2\right ) \log (3)+450 x \log ^2(3)\right ) \log (5)+\left (12600 x+4464 x^2+360 x^3+\left (-4320 x-720 x^2\right ) \log (3)+360 x \log ^2(3)+e^x \left (-4500 x-900 x^2+180 x^3+36 x^4+\left (1800 x-72 x^3\right ) \log (3)+\left (-180 x+36 x^2\right ) \log ^2(3)\right )+\left (-4500 x-1800 x^2-180 x^3+\left (1800 x+360 x^2\right ) \log (3)-180 x \log ^2(3)\right ) \log (5)\right ) \log \left (\frac {196+56 x+4 x^2+(-56-8 x) \log (3)+4 \log ^2(3)+e^{2 x} \left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right )+\left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)\right ) \log (5)+\left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right ) \log ^2(5)+e^x \left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)+\left (50+20 x+2 x^2+(-20-4 x) \log (3)+2 \log ^2(3)\right ) \log (5)\right )}{25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)}\right )+\left (-1260 x-432 x^2-36 x^3+\left (432 x+72 x^2\right ) \log (3)-36 x \log ^2(3)+e^x \left (450 x+180 x^2+18 x^3+\left (-180 x-36 x^2\right ) \log (3)+18 x \log ^2(3)\right )+\left (450 x+180 x^2+18 x^3+\left (-180 x-36 x^2\right ) \log (3)+18 x \log ^2(3)\right ) \log (5)\right ) \log ^2\left (\frac {196+56 x+4 x^2+(-56-8 x) \log (3)+4 \log ^2(3)+e^{2 x} \left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right )+\left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)\right ) \log (5)+\left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right ) \log ^2(5)+e^x \left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)+\left (50+20 x+2 x^2+(-20-4 x) \log (3)+2 \log ^2(3)\right ) \log (5)\right )}{25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)}\right )}{-70-24 x-2 x^2+(24+4 x) \log (3)-2 \log ^2(3)+e^x \left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right )+\left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right ) \log (5)} \, dx=36 \, x^{2} \log \left (x {\left (\log \left (5\right ) - 2\right )} + {\left (x - \log \left (3\right ) + 5\right )} e^{x} - {\left (\log \left (3\right ) - 5\right )} \log \left (5\right ) + 2 \, \log \left (3\right ) - 14\right )^{2} + 36 \, x^{2} \log \left (x - \log \left (3\right ) + 5\right )^{2} + 180 \, x^{2} \log \left (x - \log \left (3\right ) + 5\right ) + 225 \, x^{2} - 36 \, {\left (2 \, x^{2} \log \left (x - \log \left (3\right ) + 5\right ) + 5 \, x^{2}\right )} \log \left (x {\left (\log \left (5\right ) - 2\right )} + {\left (x - \log \left (3\right ) + 5\right )} e^{x} - {\left (\log \left (3\right ) - 5\right )} \log \left (5\right ) + 2 \, \log \left (3\right ) - 14\right ) \] Input:
integrate((((18*x*log(3)^2+(-36*x^2-180*x)*log(3)+18*x^3+180*x^2+450*x)*ex p(x)+(18*x*log(3)^2+(-36*x^2-180*x)*log(3)+18*x^3+180*x^2+450*x)*log(5)-36 *x*log(3)^2+(72*x^2+432*x)*log(3)-36*x^3-432*x^2-1260*x)*log(((log(3)^2+(- 2*x-10)*log(3)+x^2+10*x+25)*exp(x)^2+((2*log(3)^2+(-4*x-20)*log(3)+2*x^2+2 0*x+50)*log(5)-4*log(3)^2+(8*x+48)*log(3)-4*x^2-48*x-140)*exp(x)+(log(3)^2 +(-2*x-10)*log(3)+x^2+10*x+25)*log(5)^2+(-4*log(3)^2+(8*x+48)*log(3)-4*x^2 -48*x-140)*log(5)+4*log(3)^2+(-8*x-56)*log(3)+4*x^2+56*x+196)/(log(3)^2+(- 2*x-10)*log(3)+x^2+10*x+25))^2+(((36*x^2-180*x)*log(3)^2+(-72*x^3+1800*x)* log(3)+36*x^4+180*x^3-900*x^2-4500*x)*exp(x)+(-180*x*log(3)^2+(360*x^2+180 0*x)*log(3)-180*x^3-1800*x^2-4500*x)*log(5)+360*x*log(3)^2+(-720*x^2-4320* x)*log(3)+360*x^3+4464*x^2+12600*x)*log(((log(3)^2+(-2*x-10)*log(3)+x^2+10 *x+25)*exp(x)^2+((2*log(3)^2+(-4*x-20)*log(3)+2*x^2+20*x+50)*log(5)-4*log( 3)^2+(8*x+48)*log(3)-4*x^2-48*x-140)*exp(x)+(log(3)^2+(-2*x-10)*log(3)+x^2 +10*x+25)*log(5)^2+(-4*log(3)^2+(8*x+48)*log(3)-4*x^2-48*x-140)*log(5)+4*l og(3)^2+(-8*x-56)*log(3)+4*x^2+56*x+196)/(log(3)^2+(-2*x-10)*log(3)+x^2+10 *x+25))+((-180*x^2+450*x)*log(3)^2+(360*x^3+900*x^2-4500*x)*log(3)-180*x^4 -1350*x^3+11250*x)*exp(x)+(450*x*log(3)^2+(-900*x^2-4500*x)*log(3)+450*x^3 +4500*x^2+11250*x)*log(5)-900*x*log(3)^2+(1800*x^2+10800*x)*log(3)-900*x^3 -11520*x^2-31500*x)/((log(3)^2+(-2*x-10)*log(3)+x^2+10*x+25)*exp(x)+(log(3 )^2+(-2*x-10)*log(3)+x^2+10*x+25)*log(5)-2*log(3)^2+(4*x+24)*log(3)-2*x^2- 24*x-70),x, algorithm="maxima")
Output:
36*x^2*log(x*(log(5) - 2) + (x - log(3) + 5)*e^x - (log(3) - 5)*log(5) + 2 *log(3) - 14)^2 + 36*x^2*log(x - log(3) + 5)^2 + 180*x^2*log(x - log(3) + 5) + 225*x^2 - 36*(2*x^2*log(x - log(3) + 5) + 5*x^2)*log(x*(log(5) - 2) + (x - log(3) + 5)*e^x - (log(3) - 5)*log(5) + 2*log(3) - 14)
Leaf count of result is larger than twice the leaf count of optimal. 830 vs. \(2 (33) = 66\).
Time = 80.08 (sec) , antiderivative size = 830, normalized size of antiderivative = 23.06 \[ \int \frac {-31500 x-11520 x^2-900 x^3+\left (10800 x+1800 x^2\right ) \log (3)-900 x \log ^2(3)+e^x \left (11250 x-1350 x^3-180 x^4+\left (-4500 x+900 x^2+360 x^3\right ) \log (3)+\left (450 x-180 x^2\right ) \log ^2(3)\right )+\left (11250 x+4500 x^2+450 x^3+\left (-4500 x-900 x^2\right ) \log (3)+450 x \log ^2(3)\right ) \log (5)+\left (12600 x+4464 x^2+360 x^3+\left (-4320 x-720 x^2\right ) \log (3)+360 x \log ^2(3)+e^x \left (-4500 x-900 x^2+180 x^3+36 x^4+\left (1800 x-72 x^3\right ) \log (3)+\left (-180 x+36 x^2\right ) \log ^2(3)\right )+\left (-4500 x-1800 x^2-180 x^3+\left (1800 x+360 x^2\right ) \log (3)-180 x \log ^2(3)\right ) \log (5)\right ) \log \left (\frac {196+56 x+4 x^2+(-56-8 x) \log (3)+4 \log ^2(3)+e^{2 x} \left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right )+\left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)\right ) \log (5)+\left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right ) \log ^2(5)+e^x \left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)+\left (50+20 x+2 x^2+(-20-4 x) \log (3)+2 \log ^2(3)\right ) \log (5)\right )}{25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)}\right )+\left (-1260 x-432 x^2-36 x^3+\left (432 x+72 x^2\right ) \log (3)-36 x \log ^2(3)+e^x \left (450 x+180 x^2+18 x^3+\left (-180 x-36 x^2\right ) \log (3)+18 x \log ^2(3)\right )+\left (450 x+180 x^2+18 x^3+\left (-180 x-36 x^2\right ) \log (3)+18 x \log ^2(3)\right ) \log (5)\right ) \log ^2\left (\frac {196+56 x+4 x^2+(-56-8 x) \log (3)+4 \log ^2(3)+e^{2 x} \left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right )+\left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)\right ) \log (5)+\left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right ) \log ^2(5)+e^x \left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)+\left (50+20 x+2 x^2+(-20-4 x) \log (3)+2 \log ^2(3)\right ) \log (5)\right )}{25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)}\right )}{-70-24 x-2 x^2+(24+4 x) \log (3)-2 \log ^2(3)+e^x \left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right )+\left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right ) \log (5)} \, dx=\text {Too large to display} \] Input:
integrate((((18*x*log(3)^2+(-36*x^2-180*x)*log(3)+18*x^3+180*x^2+450*x)*ex p(x)+(18*x*log(3)^2+(-36*x^2-180*x)*log(3)+18*x^3+180*x^2+450*x)*log(5)-36 *x*log(3)^2+(72*x^2+432*x)*log(3)-36*x^3-432*x^2-1260*x)*log(((log(3)^2+(- 2*x-10)*log(3)+x^2+10*x+25)*exp(x)^2+((2*log(3)^2+(-4*x-20)*log(3)+2*x^2+2 0*x+50)*log(5)-4*log(3)^2+(8*x+48)*log(3)-4*x^2-48*x-140)*exp(x)+(log(3)^2 +(-2*x-10)*log(3)+x^2+10*x+25)*log(5)^2+(-4*log(3)^2+(8*x+48)*log(3)-4*x^2 -48*x-140)*log(5)+4*log(3)^2+(-8*x-56)*log(3)+4*x^2+56*x+196)/(log(3)^2+(- 2*x-10)*log(3)+x^2+10*x+25))^2+(((36*x^2-180*x)*log(3)^2+(-72*x^3+1800*x)* log(3)+36*x^4+180*x^3-900*x^2-4500*x)*exp(x)+(-180*x*log(3)^2+(360*x^2+180 0*x)*log(3)-180*x^3-1800*x^2-4500*x)*log(5)+360*x*log(3)^2+(-720*x^2-4320* x)*log(3)+360*x^3+4464*x^2+12600*x)*log(((log(3)^2+(-2*x-10)*log(3)+x^2+10 *x+25)*exp(x)^2+((2*log(3)^2+(-4*x-20)*log(3)+2*x^2+20*x+50)*log(5)-4*log( 3)^2+(8*x+48)*log(3)-4*x^2-48*x-140)*exp(x)+(log(3)^2+(-2*x-10)*log(3)+x^2 +10*x+25)*log(5)^2+(-4*log(3)^2+(8*x+48)*log(3)-4*x^2-48*x-140)*log(5)+4*l og(3)^2+(-8*x-56)*log(3)+4*x^2+56*x+196)/(log(3)^2+(-2*x-10)*log(3)+x^2+10 *x+25))+((-180*x^2+450*x)*log(3)^2+(360*x^3+900*x^2-4500*x)*log(3)-180*x^4 -1350*x^3+11250*x)*exp(x)+(450*x*log(3)^2+(-900*x^2-4500*x)*log(3)+450*x^3 +4500*x^2+11250*x)*log(5)-900*x*log(3)^2+(1800*x^2+10800*x)*log(3)-900*x^3 -11520*x^2-31500*x)/((log(3)^2+(-2*x-10)*log(3)+x^2+10*x+25)*exp(x)+(log(3 )^2+(-2*x-10)*log(3)+x^2+10*x+25)*log(5)-2*log(3)^2+(4*x+24)*log(3)-2*x^2- 24*x-70),x, algorithm="giac")
Output:
9*x^2*log(2*x^2*e^x*log(5) + x^2*log(5)^2 - 4*x*e^x*log(5)*log(3) - 2*x*lo g(5)^2*log(3) + 2*e^x*log(5)*log(3)^2 + log(5)^2*log(3)^2 + x^2*e^(2*x) - 4*x^2*e^x - 4*x^2*log(5) + 20*x*e^x*log(5) + 10*x*log(5)^2 - 2*x*e^(2*x)*l og(3) + 8*x*e^x*log(3) + 8*x*log(5)*log(3) - 20*e^x*log(5)*log(3) - 10*log (5)^2*log(3) + e^(2*x)*log(3)^2 - 4*e^x*log(3)^2 - 4*log(5)*log(3)^2 + 4*x ^2 + 10*x*e^(2*x) - 48*x*e^x - 48*x*log(5) + 50*e^x*log(5) + 25*log(5)^2 - 8*x*log(3) - 10*e^(2*x)*log(3) + 48*e^x*log(3) + 48*log(5)*log(3) + 4*log (3)^2 + 56*x + 25*e^(2*x) - 140*e^x - 140*log(5) - 56*log(3) + 196)^2 - 18 *x^2*log(2*x^2*e^x*log(5) + x^2*log(5)^2 - 4*x*e^x*log(5)*log(3) - 2*x*log (5)^2*log(3) + 2*e^x*log(5)*log(3)^2 + log(5)^2*log(3)^2 + x^2*e^(2*x) - 4 *x^2*e^x - 4*x^2*log(5) + 20*x*e^x*log(5) + 10*x*log(5)^2 - 2*x*e^(2*x)*lo g(3) + 8*x*e^x*log(3) + 8*x*log(5)*log(3) - 20*e^x*log(5)*log(3) - 10*log( 5)^2*log(3) + e^(2*x)*log(3)^2 - 4*e^x*log(3)^2 - 4*log(5)*log(3)^2 + 4*x^ 2 + 10*x*e^(2*x) - 48*x*e^x - 48*x*log(5) + 50*e^x*log(5) + 25*log(5)^2 - 8*x*log(3) - 10*e^(2*x)*log(3) + 48*e^x*log(3) + 48*log(5)*log(3) + 4*log( 3)^2 + 56*x + 25*e^(2*x) - 140*e^x - 140*log(5) - 56*log(3) + 196)*log(x^2 - 2*x*log(3) + log(3)^2 + 10*x - 10*log(3) + 25) + 9*x^2*log(x^2 - 2*x*lo g(3) + log(3)^2 + 10*x - 10*log(3) + 25)^2 - 90*x^2*log(2*x^2*e^x*log(5) + x^2*log(5)^2 - 4*x*e^x*log(5)*log(3) - 2*x*log(5)^2*log(3) + 2*e^x*log(5) *log(3)^2 + log(5)^2*log(3)^2 + x^2*e^(2*x) - 4*x^2*e^x - 4*x^2*log(5) ...
Timed out. \[ \int \frac {-31500 x-11520 x^2-900 x^3+\left (10800 x+1800 x^2\right ) \log (3)-900 x \log ^2(3)+e^x \left (11250 x-1350 x^3-180 x^4+\left (-4500 x+900 x^2+360 x^3\right ) \log (3)+\left (450 x-180 x^2\right ) \log ^2(3)\right )+\left (11250 x+4500 x^2+450 x^3+\left (-4500 x-900 x^2\right ) \log (3)+450 x \log ^2(3)\right ) \log (5)+\left (12600 x+4464 x^2+360 x^3+\left (-4320 x-720 x^2\right ) \log (3)+360 x \log ^2(3)+e^x \left (-4500 x-900 x^2+180 x^3+36 x^4+\left (1800 x-72 x^3\right ) \log (3)+\left (-180 x+36 x^2\right ) \log ^2(3)\right )+\left (-4500 x-1800 x^2-180 x^3+\left (1800 x+360 x^2\right ) \log (3)-180 x \log ^2(3)\right ) \log (5)\right ) \log \left (\frac {196+56 x+4 x^2+(-56-8 x) \log (3)+4 \log ^2(3)+e^{2 x} \left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right )+\left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)\right ) \log (5)+\left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right ) \log ^2(5)+e^x \left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)+\left (50+20 x+2 x^2+(-20-4 x) \log (3)+2 \log ^2(3)\right ) \log (5)\right )}{25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)}\right )+\left (-1260 x-432 x^2-36 x^3+\left (432 x+72 x^2\right ) \log (3)-36 x \log ^2(3)+e^x \left (450 x+180 x^2+18 x^3+\left (-180 x-36 x^2\right ) \log (3)+18 x \log ^2(3)\right )+\left (450 x+180 x^2+18 x^3+\left (-180 x-36 x^2\right ) \log (3)+18 x \log ^2(3)\right ) \log (5)\right ) \log ^2\left (\frac {196+56 x+4 x^2+(-56-8 x) \log (3)+4 \log ^2(3)+e^{2 x} \left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right )+\left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)\right ) \log (5)+\left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right ) \log ^2(5)+e^x \left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)+\left (50+20 x+2 x^2+(-20-4 x) \log (3)+2 \log ^2(3)\right ) \log (5)\right )}{25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)}\right )}{-70-24 x-2 x^2+(24+4 x) \log (3)-2 \log ^2(3)+e^x \left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right )+\left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right ) \log (5)} \, dx=\text {Too large to display} \] Input:
int((31500*x + log((56*x - log(3)*(8*x + 56) + log(5)^2*(10*x - log(3)*(2* x + 10) + log(3)^2 + x^2 + 25) - exp(x)*(48*x - log(3)*(8*x + 48) - log(5) *(20*x - log(3)*(4*x + 20) + 2*log(3)^2 + 2*x^2 + 50) + 4*log(3)^2 + 4*x^2 + 140) - log(5)*(48*x - log(3)*(8*x + 48) + 4*log(3)^2 + 4*x^2 + 140) + e xp(2*x)*(10*x - log(3)*(2*x + 10) + log(3)^2 + x^2 + 25) + 4*log(3)^2 + 4* x^2 + 196)/(10*x - log(3)*(2*x + 10) + log(3)^2 + x^2 + 25))^2*(1260*x - l og(3)*(432*x + 72*x^2) - log(5)*(450*x - log(3)*(180*x + 36*x^2) + 18*x*lo g(3)^2 + 180*x^2 + 18*x^3) + 36*x*log(3)^2 - exp(x)*(450*x - log(3)*(180*x + 36*x^2) + 18*x*log(3)^2 + 180*x^2 + 18*x^3) + 432*x^2 + 36*x^3) - log(3 )*(10800*x + 1800*x^2) - log(5)*(11250*x - log(3)*(4500*x + 900*x^2) + 450 *x*log(3)^2 + 4500*x^2 + 450*x^3) + 900*x*log(3)^2 + 11520*x^2 + 900*x^3 - log((56*x - log(3)*(8*x + 56) + log(5)^2*(10*x - log(3)*(2*x + 10) + log( 3)^2 + x^2 + 25) - exp(x)*(48*x - log(3)*(8*x + 48) - log(5)*(20*x - log(3 )*(4*x + 20) + 2*log(3)^2 + 2*x^2 + 50) + 4*log(3)^2 + 4*x^2 + 140) - log( 5)*(48*x - log(3)*(8*x + 48) + 4*log(3)^2 + 4*x^2 + 140) + exp(2*x)*(10*x - log(3)*(2*x + 10) + log(3)^2 + x^2 + 25) + 4*log(3)^2 + 4*x^2 + 196)/(10 *x - log(3)*(2*x + 10) + log(3)^2 + x^2 + 25))*(12600*x - log(3)*(4320*x + 720*x^2) - log(5)*(4500*x - log(3)*(1800*x + 360*x^2) + 180*x*log(3)^2 + 1800*x^2 + 180*x^3) + 360*x*log(3)^2 + 4464*x^2 + 360*x^3 - exp(x)*(4500*x - log(3)*(1800*x - 72*x^3) + log(3)^2*(180*x - 36*x^2) + 900*x^2 - 180*x^ 3 - 36*x^4)) - exp(x)*(11250*x + log(3)*(900*x^2 - 4500*x + 360*x^3) + log (3)^2*(450*x - 180*x^2) - 1350*x^3 - 180*x^4))/(24*x - log(3)*(4*x + 24) - exp(x)*(10*x - log(3)*(2*x + 10) + log(3)^2 + x^2 + 25) - log(5)*(10*x - log(3)*(2*x + 10) + log(3)^2 + x^2 + 25) + 2*log(3)^2 + 2*x^2 + 70),x)
Output:
int((31500*x + log((56*x - log(3)*(8*x + 56) + log(5)^2*(10*x - log(3)*(2* x + 10) + log(3)^2 + x^2 + 25) - exp(x)*(48*x - log(3)*(8*x + 48) - log(5) *(20*x - log(3)*(4*x + 20) + 2*log(3)^2 + 2*x^2 + 50) + 4*log(3)^2 + 4*x^2 + 140) - log(5)*(48*x - log(3)*(8*x + 48) + 4*log(3)^2 + 4*x^2 + 140) + e xp(2*x)*(10*x - log(3)*(2*x + 10) + log(3)^2 + x^2 + 25) + 4*log(3)^2 + 4* x^2 + 196)/(10*x - log(3)*(2*x + 10) + log(3)^2 + x^2 + 25))^2*(1260*x - l og(3)*(432*x + 72*x^2) - log(5)*(450*x - log(3)*(180*x + 36*x^2) + 18*x*lo g(3)^2 + 180*x^2 + 18*x^3) + 36*x*log(3)^2 - exp(x)*(450*x - log(3)*(180*x + 36*x^2) + 18*x*log(3)^2 + 180*x^2 + 18*x^3) + 432*x^2 + 36*x^3) - log(3 )*(10800*x + 1800*x^2) - log(5)*(11250*x - log(3)*(4500*x + 900*x^2) + 450 *x*log(3)^2 + 4500*x^2 + 450*x^3) + 900*x*log(3)^2 + 11520*x^2 + 900*x^3 - log((56*x - log(3)*(8*x + 56) + log(5)^2*(10*x - log(3)*(2*x + 10) + log( 3)^2 + x^2 + 25) - exp(x)*(48*x - log(3)*(8*x + 48) - log(5)*(20*x - log(3 )*(4*x + 20) + 2*log(3)^2 + 2*x^2 + 50) + 4*log(3)^2 + 4*x^2 + 140) - log( 5)*(48*x - log(3)*(8*x + 48) + 4*log(3)^2 + 4*x^2 + 140) + exp(2*x)*(10*x - log(3)*(2*x + 10) + log(3)^2 + x^2 + 25) + 4*log(3)^2 + 4*x^2 + 196)/(10 *x - log(3)*(2*x + 10) + log(3)^2 + x^2 + 25))*(12600*x - log(3)*(4320*x + 720*x^2) - log(5)*(4500*x - log(3)*(1800*x + 360*x^2) + 180*x*log(3)^2 + 1800*x^2 + 180*x^3) + 360*x*log(3)^2 + 4464*x^2 + 360*x^3 - exp(x)*(4500*x - log(3)*(1800*x - 72*x^3) + log(3)^2*(180*x - 36*x^2) + 900*x^2 - 180...
Time = 0.22 (sec) , antiderivative size = 581, normalized size of antiderivative = 16.14 \[ \int \frac {-31500 x-11520 x^2-900 x^3+\left (10800 x+1800 x^2\right ) \log (3)-900 x \log ^2(3)+e^x \left (11250 x-1350 x^3-180 x^4+\left (-4500 x+900 x^2+360 x^3\right ) \log (3)+\left (450 x-180 x^2\right ) \log ^2(3)\right )+\left (11250 x+4500 x^2+450 x^3+\left (-4500 x-900 x^2\right ) \log (3)+450 x \log ^2(3)\right ) \log (5)+\left (12600 x+4464 x^2+360 x^3+\left (-4320 x-720 x^2\right ) \log (3)+360 x \log ^2(3)+e^x \left (-4500 x-900 x^2+180 x^3+36 x^4+\left (1800 x-72 x^3\right ) \log (3)+\left (-180 x+36 x^2\right ) \log ^2(3)\right )+\left (-4500 x-1800 x^2-180 x^3+\left (1800 x+360 x^2\right ) \log (3)-180 x \log ^2(3)\right ) \log (5)\right ) \log \left (\frac {196+56 x+4 x^2+(-56-8 x) \log (3)+4 \log ^2(3)+e^{2 x} \left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right )+\left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)\right ) \log (5)+\left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right ) \log ^2(5)+e^x \left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)+\left (50+20 x+2 x^2+(-20-4 x) \log (3)+2 \log ^2(3)\right ) \log (5)\right )}{25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)}\right )+\left (-1260 x-432 x^2-36 x^3+\left (432 x+72 x^2\right ) \log (3)-36 x \log ^2(3)+e^x \left (450 x+180 x^2+18 x^3+\left (-180 x-36 x^2\right ) \log (3)+18 x \log ^2(3)\right )+\left (450 x+180 x^2+18 x^3+\left (-180 x-36 x^2\right ) \log (3)+18 x \log ^2(3)\right ) \log (5)\right ) \log ^2\left (\frac {196+56 x+4 x^2+(-56-8 x) \log (3)+4 \log ^2(3)+e^{2 x} \left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right )+\left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)\right ) \log (5)+\left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right ) \log ^2(5)+e^x \left (-140-48 x-4 x^2+(48+8 x) \log (3)-4 \log ^2(3)+\left (50+20 x+2 x^2+(-20-4 x) \log (3)+2 \log ^2(3)\right ) \log (5)\right )}{25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)}\right )}{-70-24 x-2 x^2+(24+4 x) \log (3)-2 \log ^2(3)+e^x \left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right )+\left (25+10 x+x^2+(-10-2 x) \log (3)+\log ^2(3)\right ) \log (5)} \, dx =\text {Too large to display} \] Input:
int((((18*x*log(3)^2+(-36*x^2-180*x)*log(3)+18*x^3+180*x^2+450*x)*exp(x)+( 18*x*log(3)^2+(-36*x^2-180*x)*log(3)+18*x^3+180*x^2+450*x)*log(5)-36*x*log (3)^2+(72*x^2+432*x)*log(3)-36*x^3-432*x^2-1260*x)*log(((log(3)^2+(-2*x-10 )*log(3)+x^2+10*x+25)*exp(x)^2+((2*log(3)^2+(-4*x-20)*log(3)+2*x^2+20*x+50 )*log(5)-4*log(3)^2+(8*x+48)*log(3)-4*x^2-48*x-140)*exp(x)+(log(3)^2+(-2*x -10)*log(3)+x^2+10*x+25)*log(5)^2+(-4*log(3)^2+(8*x+48)*log(3)-4*x^2-48*x- 140)*log(5)+4*log(3)^2+(-8*x-56)*log(3)+4*x^2+56*x+196)/(log(3)^2+(-2*x-10 )*log(3)+x^2+10*x+25))^2+(((36*x^2-180*x)*log(3)^2+(-72*x^3+1800*x)*log(3) +36*x^4+180*x^3-900*x^2-4500*x)*exp(x)+(-180*x*log(3)^2+(360*x^2+1800*x)*l og(3)-180*x^3-1800*x^2-4500*x)*log(5)+360*x*log(3)^2+(-720*x^2-4320*x)*log (3)+360*x^3+4464*x^2+12600*x)*log(((log(3)^2+(-2*x-10)*log(3)+x^2+10*x+25) *exp(x)^2+((2*log(3)^2+(-4*x-20)*log(3)+2*x^2+20*x+50)*log(5)-4*log(3)^2+( 8*x+48)*log(3)-4*x^2-48*x-140)*exp(x)+(log(3)^2+(-2*x-10)*log(3)+x^2+10*x+ 25)*log(5)^2+(-4*log(3)^2+(8*x+48)*log(3)-4*x^2-48*x-140)*log(5)+4*log(3)^ 2+(-8*x-56)*log(3)+4*x^2+56*x+196)/(log(3)^2+(-2*x-10)*log(3)+x^2+10*x+25) )+((-180*x^2+450*x)*log(3)^2+(360*x^3+900*x^2-4500*x)*log(3)-180*x^4-1350* x^3+11250*x)*exp(x)+(450*x*log(3)^2+(-900*x^2-4500*x)*log(3)+450*x^3+4500* x^2+11250*x)*log(5)-900*x*log(3)^2+(1800*x^2+10800*x)*log(3)-900*x^3-11520 *x^2-31500*x)/((log(3)^2+(-2*x-10)*log(3)+x^2+10*x+25)*exp(x)+(log(3)^2+(- 2*x-10)*log(3)+x^2+10*x+25)*log(5)-2*log(3)^2+(4*x+24)*log(3)-2*x^2-24*x-7 0),x)
Output:
9*x**2*(log((e**(2*x)*log(3)**2 - 2*e**(2*x)*log(3)*x - 10*e**(2*x)*log(3) + e**(2*x)*x**2 + 10*e**(2*x)*x + 25*e**(2*x) + 2*e**x*log(5)*log(3)**2 - 4*e**x*log(5)*log(3)*x - 20*e**x*log(5)*log(3) + 2*e**x*log(5)*x**2 + 20* e**x*log(5)*x + 50*e**x*log(5) - 4*e**x*log(3)**2 + 8*e**x*log(3)*x + 48*e **x*log(3) - 4*e**x*x**2 - 48*e**x*x - 140*e**x + log(5)**2*log(3)**2 - 2* log(5)**2*log(3)*x - 10*log(5)**2*log(3) + log(5)**2*x**2 + 10*log(5)**2*x + 25*log(5)**2 - 4*log(5)*log(3)**2 + 8*log(5)*log(3)*x + 48*log(5)*log(3 ) - 4*log(5)*x**2 - 48*log(5)*x - 140*log(5) + 4*log(3)**2 - 8*log(3)*x - 56*log(3) + 4*x**2 + 56*x + 196)/(log(3)**2 - 2*log(3)*x - 10*log(3) + x** 2 + 10*x + 25))**2 - 10*log((e**(2*x)*log(3)**2 - 2*e**(2*x)*log(3)*x - 10 *e**(2*x)*log(3) + e**(2*x)*x**2 + 10*e**(2*x)*x + 25*e**(2*x) + 2*e**x*lo g(5)*log(3)**2 - 4*e**x*log(5)*log(3)*x - 20*e**x*log(5)*log(3) + 2*e**x*l og(5)*x**2 + 20*e**x*log(5)*x + 50*e**x*log(5) - 4*e**x*log(3)**2 + 8*e**x *log(3)*x + 48*e**x*log(3) - 4*e**x*x**2 - 48*e**x*x - 140*e**x + log(5)** 2*log(3)**2 - 2*log(5)**2*log(3)*x - 10*log(5)**2*log(3) + log(5)**2*x**2 + 10*log(5)**2*x + 25*log(5)**2 - 4*log(5)*log(3)**2 + 8*log(5)*log(3)*x + 48*log(5)*log(3) - 4*log(5)*x**2 - 48*log(5)*x - 140*log(5) + 4*log(3)**2 - 8*log(3)*x - 56*log(3) + 4*x**2 + 56*x + 196)/(log(3)**2 - 2*log(3)*x - 10*log(3) + x**2 + 10*x + 25)) + 25)