\(\int \frac {32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x (-128 x+8 x^2+64 x^3-8 x^5)}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} (65536 x-12288 x^2-97536 x^3+12272 x^4+61056 x^5-4608 x^6-20432 x^7+768 x^8+3840 x^9-48 x^{10}-384 x^{11}+16 x^{13}+e^{2 x} (17+15 x-8 x^2-4 x^3+x^4)+e^x (-1024-960 x+128 x^2+1052 x^3+320 x^4-396 x^5-120 x^6+64 x^7+12 x^8-4 x^9))}{65536+20480 x-103680 x^2-36496 x^3+67192 x^4+25920 x^5-22736 x^6-9448 x^7+4224 x^8+1872 x^9-408 x^{10}-192 x^{11}+16 x^{12}+8 x^{13}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x (-128 x+8 x^2+64 x^3-8 x^5)}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} (32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12})} \, dx\) [1871]

Optimal result

Integrand size = 530, antiderivative size = 34 \[ \int \frac {32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x \left (-128 x+8 x^2+64 x^3-8 x^5\right )}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} \left (65536 x-12288 x^2-97536 x^3+12272 x^4+61056 x^5-4608 x^6-20432 x^7+768 x^8+3840 x^9-48 x^{10}-384 x^{11}+16 x^{13}+e^{2 x} \left (17+15 x-8 x^2-4 x^3+x^4\right )+e^x \left (-1024-960 x+128 x^2+1052 x^3+320 x^4-396 x^5-120 x^6+64 x^7+12 x^8-4 x^9\right )\right )}{65536+20480 x-103680 x^2-36496 x^3+67192 x^4+25920 x^5-22736 x^6-9448 x^7+4224 x^8+1872 x^9-408 x^{10}-192 x^{11}+16 x^{12}+8 x^{13}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x \left (-128 x+8 x^2+64 x^3-8 x^5\right )}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} \left (32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}\right )} \, dx=\log \left (2+e^{\left (-x+\frac {e^x}{4 \left (-x+\left (4-x^2\right )^2\right )}\right )^2}+x\right ) \] Output:

ln(x+2+exp((exp(x)/(4*(-x^2+4)^2-4*x)-x)^2))
 

Mathematica [A] (verified)

Time = 1.79 (sec) , antiderivative size = 57, normalized size of antiderivative = 1.68 \[ \int \frac {32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x \left (-128 x+8 x^2+64 x^3-8 x^5\right )}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} \left (65536 x-12288 x^2-97536 x^3+12272 x^4+61056 x^5-4608 x^6-20432 x^7+768 x^8+3840 x^9-48 x^{10}-384 x^{11}+16 x^{13}+e^{2 x} \left (17+15 x-8 x^2-4 x^3+x^4\right )+e^x \left (-1024-960 x+128 x^2+1052 x^3+320 x^4-396 x^5-120 x^6+64 x^7+12 x^8-4 x^9\right )\right )}{65536+20480 x-103680 x^2-36496 x^3+67192 x^4+25920 x^5-22736 x^6-9448 x^7+4224 x^8+1872 x^9-408 x^{10}-192 x^{11}+16 x^{12}+8 x^{13}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x \left (-128 x+8 x^2+64 x^3-8 x^5\right )}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} \left (32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}\right )} \, dx=\log \left (2+e^{x^2+\frac {e^{2 x}}{16 \left (16-x-8 x^2+x^4\right )^2}-\frac {e^x x}{2 \left (16-x-8 x^2+x^4\right )}}+x\right ) \] Input:

Integrate[(32768 - 6144*x - 48768*x^2 + 6136*x^3 + 30528*x^4 - 2304*x^5 - 
10216*x^6 + 384*x^7 + 1920*x^8 - 24*x^9 - 192*x^10 + 8*x^12 + E^((E^(2*x) 
+ 4096*x^2 - 512*x^3 - 4080*x^4 + 256*x^5 + 1536*x^6 - 32*x^7 - 256*x^8 + 
16*x^10 + E^x*(-128*x + 8*x^2 + 64*x^3 - 8*x^5))/(4096 - 512*x - 4080*x^2 
+ 256*x^3 + 1536*x^4 - 32*x^5 - 256*x^6 + 16*x^8))*(65536*x - 12288*x^2 - 
97536*x^3 + 12272*x^4 + 61056*x^5 - 4608*x^6 - 20432*x^7 + 768*x^8 + 3840* 
x^9 - 48*x^10 - 384*x^11 + 16*x^13 + E^(2*x)*(17 + 15*x - 8*x^2 - 4*x^3 + 
x^4) + E^x*(-1024 - 960*x + 128*x^2 + 1052*x^3 + 320*x^4 - 396*x^5 - 120*x 
^6 + 64*x^7 + 12*x^8 - 4*x^9)))/(65536 + 20480*x - 103680*x^2 - 36496*x^3 
+ 67192*x^4 + 25920*x^5 - 22736*x^6 - 9448*x^7 + 4224*x^8 + 1872*x^9 - 408 
*x^10 - 192*x^11 + 16*x^12 + 8*x^13 + E^((E^(2*x) + 4096*x^2 - 512*x^3 - 4 
080*x^4 + 256*x^5 + 1536*x^6 - 32*x^7 - 256*x^8 + 16*x^10 + E^x*(-128*x + 
8*x^2 + 64*x^3 - 8*x^5))/(4096 - 512*x - 4080*x^2 + 256*x^3 + 1536*x^4 - 3 
2*x^5 - 256*x^6 + 16*x^8))*(32768 - 6144*x - 48768*x^2 + 6136*x^3 + 30528* 
x^4 - 2304*x^5 - 10216*x^6 + 384*x^7 + 1920*x^8 - 24*x^9 - 192*x^10 + 8*x^ 
12)),x]
 

Output:

Log[2 + E^(x^2 + E^(2*x)/(16*(16 - x - 8*x^2 + x^4)^2) - (E^x*x)/(2*(16 - 
x - 8*x^2 + x^4))) + x]
 

Rubi [F]

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.

\(\displaystyle \int \frac {\left (16 x^{13}-384 x^{11}-48 x^{10}+3840 x^9+768 x^8-20432 x^7-4608 x^6+61056 x^5+12272 x^4-97536 x^3-12288 x^2+e^{2 x} \left (x^4-4 x^3-8 x^2+15 x+17\right )+e^x \left (-4 x^9+12 x^8+64 x^7-120 x^6-396 x^5+320 x^4+1052 x^3+128 x^2-960 x-1024\right )+65536 x\right ) \exp \left (\frac {16 x^{10}-256 x^8-32 x^7+1536 x^6+256 x^5-4080 x^4-512 x^3+4096 x^2+e^x \left (-8 x^5+64 x^3+8 x^2-128 x\right )+e^{2 x}}{16 x^8-256 x^6-32 x^5+1536 x^4+256 x^3-4080 x^2-512 x+4096}\right )+8 x^{12}-192 x^{10}-24 x^9+1920 x^8+384 x^7-10216 x^6-2304 x^5+30528 x^4+6136 x^3-48768 x^2-6144 x+32768}{\left (8 x^{12}-192 x^{10}-24 x^9+1920 x^8+384 x^7-10216 x^6-2304 x^5+30528 x^4+6136 x^3-48768 x^2-6144 x+32768\right ) \exp \left (\frac {16 x^{10}-256 x^8-32 x^7+1536 x^6+256 x^5-4080 x^4-512 x^3+4096 x^2+e^x \left (-8 x^5+64 x^3+8 x^2-128 x\right )+e^{2 x}}{16 x^8-256 x^6-32 x^5+1536 x^4+256 x^3-4080 x^2-512 x+4096}\right )+8 x^{13}+16 x^{12}-192 x^{11}-408 x^{10}+1872 x^9+4224 x^8-9448 x^7-22736 x^6+25920 x^5+67192 x^4-36496 x^3-103680 x^2+20480 x+65536} \, dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {\left (16 x \left (x^4-8 x^2-x+16\right )^3+e^{2 x} \left (x^4-4 x^3-8 x^2+15 x+17\right )-4 e^x \left (x^9-3 x^8-16 x^7+30 x^6+99 x^5-80 x^4-263 x^3-32 x^2+240 x+256\right )\right ) \exp \left (\frac {\left (4 x \left (-x^4+8 x^2+x-16\right )+e^x\right )^2}{16 \left (x^4-8 x^2-x+16\right )^2}\right )+8 x^{12}-192 x^{10}-24 x^9+1920 x^8+384 x^7-10216 x^6-2304 x^5+30528 x^4+6136 x^3-48768 x^2-6144 x+32768}{8 \left (x^4-8 x^2-x+16\right )^3 \left (\exp \left (\frac {\left (4 x \left (-x^4+8 x^2+x-16\right )+e^x\right )^2}{16 \left (x^4-8 x^2-x+16\right )^2}\right )+x+2\right )}dx\)

\(\Big \downarrow \) 27

\(\displaystyle \frac {1}{8} \int \frac {8 x^{12}-192 x^{10}-24 x^9+1920 x^8+384 x^7-10216 x^6-2304 x^5+30528 x^4+6136 x^3-48768 x^2-6144 x+\exp \left (\frac {\left (e^x-4 x \left (x^4-8 x^2-x+16\right )\right )^2}{16 \left (x^4-8 x^2-x+16\right )^2}\right ) \left (16 x \left (x^4-8 x^2-x+16\right )^3+e^{2 x} \left (x^4-4 x^3-8 x^2+15 x+17\right )-4 e^x \left (x^9-3 x^8-16 x^7+30 x^6+99 x^5-80 x^4-263 x^3-32 x^2+240 x+256\right )\right )+32768}{\left (x+\exp \left (\frac {\left (e^x-4 x \left (x^4-8 x^2-x+16\right )\right )^2}{16 \left (x^4-8 x^2-x+16\right )^2}\right )+2\right ) \left (x^4-8 x^2-x+16\right )^3}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \frac {1}{8} \int \left (\frac {16 x^{13}-384 x^{11}-48 x^{10}-4 e^x x^9+3840 x^9+12 e^x x^8+768 x^8+64 e^x x^7-20432 x^7-120 e^x x^6-4608 x^6-396 e^x x^5+61056 x^5+320 e^x x^4+e^{2 x} x^4+12272 x^4+1052 e^x x^3-4 e^{2 x} x^3-97536 x^3+128 e^x x^2-8 e^{2 x} x^2-12288 x^2-960 e^x x+15 e^{2 x} x+65536 x-1024 e^x+17 e^{2 x}}{\left (x^4-8 x^2-x+16\right )^3}-\frac {16 x^{14}+32 x^{13}-392 x^{12}-816 x^{11}-4 e^x x^{10}+3936 x^{10}+4 e^x x^9+8472 x^9+88 e^x x^8-20816 x^8+8 e^x x^7-45856 x^7-636 e^x x^6+62056 x^6-472 e^x x^5+e^{2 x} x^5+136688 x^5+1692 e^x x^4-2 e^{2 x} x^4-103520 x^4+2232 e^x x^3-16 e^{2 x} x^3-213496 x^3-704 e^x x^2-e^{2 x} x^2+89728 x^2-2944 e^x x+47 e^{2 x} x+137216 x-2048 e^x+34 e^{2 x}-32768}{\left (x+\exp \left (\frac {\left (4 x \left (-x^4+8 x^2+x-16\right )+e^x\right )^2}{16 \left (x^4-8 x^2-x+16\right )^2}\right )+2\right ) \left (x^4-8 x^2-x+16\right )^3}\right )dx\)

\(\Big \downarrow \) 7299

\(\displaystyle \frac {1}{8} \int \left (\frac {16 x^{13}-384 x^{11}-48 x^{10}-4 e^x x^9+3840 x^9+12 e^x x^8+768 x^8+64 e^x x^7-20432 x^7-120 e^x x^6-4608 x^6-396 e^x x^5+61056 x^5+320 e^x x^4+e^{2 x} x^4+12272 x^4+1052 e^x x^3-4 e^{2 x} x^3-97536 x^3+128 e^x x^2-8 e^{2 x} x^2-12288 x^2-960 e^x x+15 e^{2 x} x+65536 x-1024 e^x+17 e^{2 x}}{\left (x^4-8 x^2-x+16\right )^3}-\frac {16 x^{14}+32 x^{13}-392 x^{12}-816 x^{11}-4 e^x x^{10}+3936 x^{10}+4 e^x x^9+8472 x^9+88 e^x x^8-20816 x^8+8 e^x x^7-45856 x^7-636 e^x x^6+62056 x^6-472 e^x x^5+e^{2 x} x^5+136688 x^5+1692 e^x x^4-2 e^{2 x} x^4-103520 x^4+2232 e^x x^3-16 e^{2 x} x^3-213496 x^3-704 e^x x^2-e^{2 x} x^2+89728 x^2-2944 e^x x+47 e^{2 x} x+137216 x-2048 e^x+34 e^{2 x}-32768}{\left (x+\exp \left (\frac {\left (4 x \left (-x^4+8 x^2+x-16\right )+e^x\right )^2}{16 \left (x^4-8 x^2-x+16\right )^2}\right )+2\right ) \left (x^4-8 x^2-x+16\right )^3}\right )dx\)

Input:

Int[(32768 - 6144*x - 48768*x^2 + 6136*x^3 + 30528*x^4 - 2304*x^5 - 10216* 
x^6 + 384*x^7 + 1920*x^8 - 24*x^9 - 192*x^10 + 8*x^12 + E^((E^(2*x) + 4096 
*x^2 - 512*x^3 - 4080*x^4 + 256*x^5 + 1536*x^6 - 32*x^7 - 256*x^8 + 16*x^1 
0 + E^x*(-128*x + 8*x^2 + 64*x^3 - 8*x^5))/(4096 - 512*x - 4080*x^2 + 256* 
x^3 + 1536*x^4 - 32*x^5 - 256*x^6 + 16*x^8))*(65536*x - 12288*x^2 - 97536* 
x^3 + 12272*x^4 + 61056*x^5 - 4608*x^6 - 20432*x^7 + 768*x^8 + 3840*x^9 - 
48*x^10 - 384*x^11 + 16*x^13 + E^(2*x)*(17 + 15*x - 8*x^2 - 4*x^3 + x^4) + 
 E^x*(-1024 - 960*x + 128*x^2 + 1052*x^3 + 320*x^4 - 396*x^5 - 120*x^6 + 6 
4*x^7 + 12*x^8 - 4*x^9)))/(65536 + 20480*x - 103680*x^2 - 36496*x^3 + 6719 
2*x^4 + 25920*x^5 - 22736*x^6 - 9448*x^7 + 4224*x^8 + 1872*x^9 - 408*x^10 
- 192*x^11 + 16*x^12 + 8*x^13 + E^((E^(2*x) + 4096*x^2 - 512*x^3 - 4080*x^ 
4 + 256*x^5 + 1536*x^6 - 32*x^7 - 256*x^8 + 16*x^10 + E^x*(-128*x + 8*x^2 
+ 64*x^3 - 8*x^5))/(4096 - 512*x - 4080*x^2 + 256*x^3 + 1536*x^4 - 32*x^5 
- 256*x^6 + 16*x^8))*(32768 - 6144*x - 48768*x^2 + 6136*x^3 + 30528*x^4 - 
2304*x^5 - 10216*x^6 + 384*x^7 + 1920*x^8 - 24*x^9 - 192*x^10 + 8*x^12)),x 
]
 

Output:

$Aborted
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(95\) vs. \(2(31)=62\).

Time = 0.97 (sec) , antiderivative size = 96, normalized size of antiderivative = 2.82

\[\ln \left (2+x +{\mathrm e}^{-\frac {-16 x^{10}+256 x^{8}+32 x^{7}+8 x^{5} {\mathrm e}^{x}-1536 x^{6}-256 x^{5}-64 \,{\mathrm e}^{x} x^{3}+4080 x^{4}-8 \,{\mathrm e}^{x} x^{2}+512 x^{3}+128 \,{\mathrm e}^{x} x -4096 x^{2}-{\mathrm e}^{2 x}}{16 \left (x^{4}-8 x^{2}-x +16\right )^{2}}}\right )\]

Input:

int((((x^4-4*x^3-8*x^2+15*x+17)*exp(x)^2+(-4*x^9+12*x^8+64*x^7-120*x^6-396 
*x^5+320*x^4+1052*x^3+128*x^2-960*x-1024)*exp(x)+16*x^13-384*x^11-48*x^10+ 
3840*x^9+768*x^8-20432*x^7-4608*x^6+61056*x^5+12272*x^4-97536*x^3-12288*x^ 
2+65536*x)*exp((exp(x)^2+(-8*x^5+64*x^3+8*x^2-128*x)*exp(x)+16*x^10-256*x^ 
8-32*x^7+1536*x^6+256*x^5-4080*x^4-512*x^3+4096*x^2)/(16*x^8-256*x^6-32*x^ 
5+1536*x^4+256*x^3-4080*x^2-512*x+4096))+8*x^12-192*x^10-24*x^9+1920*x^8+3 
84*x^7-10216*x^6-2304*x^5+30528*x^4+6136*x^3-48768*x^2-6144*x+32768)/((8*x 
^12-192*x^10-24*x^9+1920*x^8+384*x^7-10216*x^6-2304*x^5+30528*x^4+6136*x^3 
-48768*x^2-6144*x+32768)*exp((exp(x)^2+(-8*x^5+64*x^3+8*x^2-128*x)*exp(x)+ 
16*x^10-256*x^8-32*x^7+1536*x^6+256*x^5-4080*x^4-512*x^3+4096*x^2)/(16*x^8 
-256*x^6-32*x^5+1536*x^4+256*x^3-4080*x^2-512*x+4096))+8*x^13+16*x^12-192* 
x^11-408*x^10+1872*x^9+4224*x^8-9448*x^7-22736*x^6+25920*x^5+67192*x^4-364 
96*x^3-103680*x^2+20480*x+65536),x)
 

Output:

ln(2+x+exp(-1/16*(-16*x^10+256*x^8+32*x^7+8*x^5*exp(x)-1536*x^6-256*x^5-64 
*exp(x)*x^3+4080*x^4-8*exp(x)*x^2+512*x^3+128*exp(x)*x-4096*x^2-exp(2*x))/ 
(x^4-8*x^2-x+16)^2))
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 108 vs. \(2 (30) = 60\).

Time = 0.10 (sec) , antiderivative size = 108, normalized size of antiderivative = 3.18 \[ \int \frac {32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x \left (-128 x+8 x^2+64 x^3-8 x^5\right )}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} \left (65536 x-12288 x^2-97536 x^3+12272 x^4+61056 x^5-4608 x^6-20432 x^7+768 x^8+3840 x^9-48 x^{10}-384 x^{11}+16 x^{13}+e^{2 x} \left (17+15 x-8 x^2-4 x^3+x^4\right )+e^x \left (-1024-960 x+128 x^2+1052 x^3+320 x^4-396 x^5-120 x^6+64 x^7+12 x^8-4 x^9\right )\right )}{65536+20480 x-103680 x^2-36496 x^3+67192 x^4+25920 x^5-22736 x^6-9448 x^7+4224 x^8+1872 x^9-408 x^{10}-192 x^{11}+16 x^{12}+8 x^{13}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x \left (-128 x+8 x^2+64 x^3-8 x^5\right )}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} \left (32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}\right )} \, dx=\log \left (x + e^{\left (\frac {16 \, x^{10} - 256 \, x^{8} - 32 \, x^{7} + 1536 \, x^{6} + 256 \, x^{5} - 4080 \, x^{4} - 512 \, x^{3} + 4096 \, x^{2} - 8 \, {\left (x^{5} - 8 \, x^{3} - x^{2} + 16 \, x\right )} e^{x} + e^{\left (2 \, x\right )}}{16 \, {\left (x^{8} - 16 \, x^{6} - 2 \, x^{5} + 96 \, x^{4} + 16 \, x^{3} - 255 \, x^{2} - 32 \, x + 256\right )}}\right )} + 2\right ) \] Input:

integrate((((x^4-4*x^3-8*x^2+15*x+17)*exp(x)^2+(-4*x^9+12*x^8+64*x^7-120*x 
^6-396*x^5+320*x^4+1052*x^3+128*x^2-960*x-1024)*exp(x)+16*x^13-384*x^11-48 
*x^10+3840*x^9+768*x^8-20432*x^7-4608*x^6+61056*x^5+12272*x^4-97536*x^3-12 
288*x^2+65536*x)*exp((exp(x)^2+(-8*x^5+64*x^3+8*x^2-128*x)*exp(x)+16*x^10- 
256*x^8-32*x^7+1536*x^6+256*x^5-4080*x^4-512*x^3+4096*x^2)/(16*x^8-256*x^6 
-32*x^5+1536*x^4+256*x^3-4080*x^2-512*x+4096))+8*x^12-192*x^10-24*x^9+1920 
*x^8+384*x^7-10216*x^6-2304*x^5+30528*x^4+6136*x^3-48768*x^2-6144*x+32768) 
/((8*x^12-192*x^10-24*x^9+1920*x^8+384*x^7-10216*x^6-2304*x^5+30528*x^4+61 
36*x^3-48768*x^2-6144*x+32768)*exp((exp(x)^2+(-8*x^5+64*x^3+8*x^2-128*x)*e 
xp(x)+16*x^10-256*x^8-32*x^7+1536*x^6+256*x^5-4080*x^4-512*x^3+4096*x^2)/( 
16*x^8-256*x^6-32*x^5+1536*x^4+256*x^3-4080*x^2-512*x+4096))+8*x^13+16*x^1 
2-192*x^11-408*x^10+1872*x^9+4224*x^8-9448*x^7-22736*x^6+25920*x^5+67192*x 
^4-36496*x^3-103680*x^2+20480*x+65536),x, algorithm="fricas")
 

Output:

log(x + e^(1/16*(16*x^10 - 256*x^8 - 32*x^7 + 1536*x^6 + 256*x^5 - 4080*x^ 
4 - 512*x^3 + 4096*x^2 - 8*(x^5 - 8*x^3 - x^2 + 16*x)*e^x + e^(2*x))/(x^8 
- 16*x^6 - 2*x^5 + 96*x^4 + 16*x^3 - 255*x^2 - 32*x + 256)) + 2)
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 109 vs. \(2 (24) = 48\).

Time = 5.18 (sec) , antiderivative size = 109, normalized size of antiderivative = 3.21 \[ \int \frac {32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x \left (-128 x+8 x^2+64 x^3-8 x^5\right )}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} \left (65536 x-12288 x^2-97536 x^3+12272 x^4+61056 x^5-4608 x^6-20432 x^7+768 x^8+3840 x^9-48 x^{10}-384 x^{11}+16 x^{13}+e^{2 x} \left (17+15 x-8 x^2-4 x^3+x^4\right )+e^x \left (-1024-960 x+128 x^2+1052 x^3+320 x^4-396 x^5-120 x^6+64 x^7+12 x^8-4 x^9\right )\right )}{65536+20480 x-103680 x^2-36496 x^3+67192 x^4+25920 x^5-22736 x^6-9448 x^7+4224 x^8+1872 x^9-408 x^{10}-192 x^{11}+16 x^{12}+8 x^{13}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x \left (-128 x+8 x^2+64 x^3-8 x^5\right )}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} \left (32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}\right )} \, dx=\log {\left (x + e^{\frac {16 x^{10} - 256 x^{8} - 32 x^{7} + 1536 x^{6} + 256 x^{5} - 4080 x^{4} - 512 x^{3} + 4096 x^{2} + \left (- 8 x^{5} + 64 x^{3} + 8 x^{2} - 128 x\right ) e^{x} + e^{2 x}}{16 x^{8} - 256 x^{6} - 32 x^{5} + 1536 x^{4} + 256 x^{3} - 4080 x^{2} - 512 x + 4096}} + 2 \right )} \] Input:

integrate((((x**4-4*x**3-8*x**2+15*x+17)*exp(x)**2+(-4*x**9+12*x**8+64*x** 
7-120*x**6-396*x**5+320*x**4+1052*x**3+128*x**2-960*x-1024)*exp(x)+16*x**1 
3-384*x**11-48*x**10+3840*x**9+768*x**8-20432*x**7-4608*x**6+61056*x**5+12 
272*x**4-97536*x**3-12288*x**2+65536*x)*exp((exp(x)**2+(-8*x**5+64*x**3+8* 
x**2-128*x)*exp(x)+16*x**10-256*x**8-32*x**7+1536*x**6+256*x**5-4080*x**4- 
512*x**3+4096*x**2)/(16*x**8-256*x**6-32*x**5+1536*x**4+256*x**3-4080*x**2 
-512*x+4096))+8*x**12-192*x**10-24*x**9+1920*x**8+384*x**7-10216*x**6-2304 
*x**5+30528*x**4+6136*x**3-48768*x**2-6144*x+32768)/((8*x**12-192*x**10-24 
*x**9+1920*x**8+384*x**7-10216*x**6-2304*x**5+30528*x**4+6136*x**3-48768*x 
**2-6144*x+32768)*exp((exp(x)**2+(-8*x**5+64*x**3+8*x**2-128*x)*exp(x)+16* 
x**10-256*x**8-32*x**7+1536*x**6+256*x**5-4080*x**4-512*x**3+4096*x**2)/(1 
6*x**8-256*x**6-32*x**5+1536*x**4+256*x**3-4080*x**2-512*x+4096))+8*x**13+ 
16*x**12-192*x**11-408*x**10+1872*x**9+4224*x**8-9448*x**7-22736*x**6+2592 
0*x**5+67192*x**4-36496*x**3-103680*x**2+20480*x+65536),x)
 

Output:

log(x + exp((16*x**10 - 256*x**8 - 32*x**7 + 1536*x**6 + 256*x**5 - 4080*x 
**4 - 512*x**3 + 4096*x**2 + (-8*x**5 + 64*x**3 + 8*x**2 - 128*x)*exp(x) + 
 exp(2*x))/(16*x**8 - 256*x**6 - 32*x**5 + 1536*x**4 + 256*x**3 - 4080*x** 
2 - 512*x + 4096)) + 2)
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 124 vs. \(2 (30) = 60\).

Time = 4.00 (sec) , antiderivative size = 124, normalized size of antiderivative = 3.65 \[ \int \frac {32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x \left (-128 x+8 x^2+64 x^3-8 x^5\right )}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} \left (65536 x-12288 x^2-97536 x^3+12272 x^4+61056 x^5-4608 x^6-20432 x^7+768 x^8+3840 x^9-48 x^{10}-384 x^{11}+16 x^{13}+e^{2 x} \left (17+15 x-8 x^2-4 x^3+x^4\right )+e^x \left (-1024-960 x+128 x^2+1052 x^3+320 x^4-396 x^5-120 x^6+64 x^7+12 x^8-4 x^9\right )\right )}{65536+20480 x-103680 x^2-36496 x^3+67192 x^4+25920 x^5-22736 x^6-9448 x^7+4224 x^8+1872 x^9-408 x^{10}-192 x^{11}+16 x^{12}+8 x^{13}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x \left (-128 x+8 x^2+64 x^3-8 x^5\right )}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} \left (32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}\right )} \, dx=\frac {2 \, x^{6} - 16 \, x^{4} - 2 \, x^{3} + 32 \, x^{2} - x e^{x}}{2 \, {\left (x^{4} - 8 \, x^{2} - x + 16\right )}} + \log \left ({\left ({\left (x + 2\right )} e^{\left (\frac {x e^{x}}{2 \, {\left (x^{4} - 8 \, x^{2} - x + 16\right )}}\right )} + e^{\left (x^{2} + \frac {e^{\left (2 \, x\right )}}{16 \, {\left (x^{8} - 16 \, x^{6} - 2 \, x^{5} + 96 \, x^{4} + 16 \, x^{3} - 255 \, x^{2} - 32 \, x + 256\right )}}\right )}\right )} e^{\left (-x^{2}\right )}\right ) \] Input:

integrate((((x^4-4*x^3-8*x^2+15*x+17)*exp(x)^2+(-4*x^9+12*x^8+64*x^7-120*x 
^6-396*x^5+320*x^4+1052*x^3+128*x^2-960*x-1024)*exp(x)+16*x^13-384*x^11-48 
*x^10+3840*x^9+768*x^8-20432*x^7-4608*x^6+61056*x^5+12272*x^4-97536*x^3-12 
288*x^2+65536*x)*exp((exp(x)^2+(-8*x^5+64*x^3+8*x^2-128*x)*exp(x)+16*x^10- 
256*x^8-32*x^7+1536*x^6+256*x^5-4080*x^4-512*x^3+4096*x^2)/(16*x^8-256*x^6 
-32*x^5+1536*x^4+256*x^3-4080*x^2-512*x+4096))+8*x^12-192*x^10-24*x^9+1920 
*x^8+384*x^7-10216*x^6-2304*x^5+30528*x^4+6136*x^3-48768*x^2-6144*x+32768) 
/((8*x^12-192*x^10-24*x^9+1920*x^8+384*x^7-10216*x^6-2304*x^5+30528*x^4+61 
36*x^3-48768*x^2-6144*x+32768)*exp((exp(x)^2+(-8*x^5+64*x^3+8*x^2-128*x)*e 
xp(x)+16*x^10-256*x^8-32*x^7+1536*x^6+256*x^5-4080*x^4-512*x^3+4096*x^2)/( 
16*x^8-256*x^6-32*x^5+1536*x^4+256*x^3-4080*x^2-512*x+4096))+8*x^13+16*x^1 
2-192*x^11-408*x^10+1872*x^9+4224*x^8-9448*x^7-22736*x^6+25920*x^5+67192*x 
^4-36496*x^3-103680*x^2+20480*x+65536),x, algorithm="maxima")
 

Output:

1/2*(2*x^6 - 16*x^4 - 2*x^3 + 32*x^2 - x*e^x)/(x^4 - 8*x^2 - x + 16) + log 
(((x + 2)*e^(1/2*x*e^x/(x^4 - 8*x^2 - x + 16)) + e^(x^2 + 1/16*e^(2*x)/(x^ 
8 - 16*x^6 - 2*x^5 + 96*x^4 + 16*x^3 - 255*x^2 - 32*x + 256)))*e^(-x^2))
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 113 vs. \(2 (30) = 60\).

Time = 9.85 (sec) , antiderivative size = 113, normalized size of antiderivative = 3.32 \[ \int \frac {32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x \left (-128 x+8 x^2+64 x^3-8 x^5\right )}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} \left (65536 x-12288 x^2-97536 x^3+12272 x^4+61056 x^5-4608 x^6-20432 x^7+768 x^8+3840 x^9-48 x^{10}-384 x^{11}+16 x^{13}+e^{2 x} \left (17+15 x-8 x^2-4 x^3+x^4\right )+e^x \left (-1024-960 x+128 x^2+1052 x^3+320 x^4-396 x^5-120 x^6+64 x^7+12 x^8-4 x^9\right )\right )}{65536+20480 x-103680 x^2-36496 x^3+67192 x^4+25920 x^5-22736 x^6-9448 x^7+4224 x^8+1872 x^9-408 x^{10}-192 x^{11}+16 x^{12}+8 x^{13}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x \left (-128 x+8 x^2+64 x^3-8 x^5\right )}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} \left (32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}\right )} \, dx=\log \left (x + e^{\left (\frac {16 \, x^{10} - 256 \, x^{8} - 32 \, x^{7} + 1536 \, x^{6} - 8 \, x^{5} e^{x} + 256 \, x^{5} - 4080 \, x^{4} + 64 \, x^{3} e^{x} - 512 \, x^{3} + 8 \, x^{2} e^{x} + 4096 \, x^{2} - 128 \, x e^{x} + e^{\left (2 \, x\right )}}{16 \, {\left (x^{8} - 16 \, x^{6} - 2 \, x^{5} + 96 \, x^{4} + 16 \, x^{3} - 255 \, x^{2} - 32 \, x + 256\right )}}\right )} + 2\right ) \] Input:

integrate((((x^4-4*x^3-8*x^2+15*x+17)*exp(x)^2+(-4*x^9+12*x^8+64*x^7-120*x 
^6-396*x^5+320*x^4+1052*x^3+128*x^2-960*x-1024)*exp(x)+16*x^13-384*x^11-48 
*x^10+3840*x^9+768*x^8-20432*x^7-4608*x^6+61056*x^5+12272*x^4-97536*x^3-12 
288*x^2+65536*x)*exp((exp(x)^2+(-8*x^5+64*x^3+8*x^2-128*x)*exp(x)+16*x^10- 
256*x^8-32*x^7+1536*x^6+256*x^5-4080*x^4-512*x^3+4096*x^2)/(16*x^8-256*x^6 
-32*x^5+1536*x^4+256*x^3-4080*x^2-512*x+4096))+8*x^12-192*x^10-24*x^9+1920 
*x^8+384*x^7-10216*x^6-2304*x^5+30528*x^4+6136*x^3-48768*x^2-6144*x+32768) 
/((8*x^12-192*x^10-24*x^9+1920*x^8+384*x^7-10216*x^6-2304*x^5+30528*x^4+61 
36*x^3-48768*x^2-6144*x+32768)*exp((exp(x)^2+(-8*x^5+64*x^3+8*x^2-128*x)*e 
xp(x)+16*x^10-256*x^8-32*x^7+1536*x^6+256*x^5-4080*x^4-512*x^3+4096*x^2)/( 
16*x^8-256*x^6-32*x^5+1536*x^4+256*x^3-4080*x^2-512*x+4096))+8*x^13+16*x^1 
2-192*x^11-408*x^10+1872*x^9+4224*x^8-9448*x^7-22736*x^6+25920*x^5+67192*x 
^4-36496*x^3-103680*x^2+20480*x+65536),x, algorithm="giac")
 

Output:

log(x + e^(1/16*(16*x^10 - 256*x^8 - 32*x^7 + 1536*x^6 - 8*x^5*e^x + 256*x 
^5 - 4080*x^4 + 64*x^3*e^x - 512*x^3 + 8*x^2*e^x + 4096*x^2 - 128*x*e^x + 
e^(2*x))/(x^8 - 16*x^6 - 2*x^5 + 96*x^4 + 16*x^3 - 255*x^2 - 32*x + 256)) 
+ 2)
 

Mupad [B] (verification not implemented)

Time = 4.13 (sec) , antiderivative size = 284, normalized size of antiderivative = 8.35 \[ \int \frac {32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x \left (-128 x+8 x^2+64 x^3-8 x^5\right )}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} \left (65536 x-12288 x^2-97536 x^3+12272 x^4+61056 x^5-4608 x^6-20432 x^7+768 x^8+3840 x^9-48 x^{10}-384 x^{11}+16 x^{13}+e^{2 x} \left (17+15 x-8 x^2-4 x^3+x^4\right )+e^x \left (-1024-960 x+128 x^2+1052 x^3+320 x^4-396 x^5-120 x^6+64 x^7+12 x^8-4 x^9\right )\right )}{65536+20480 x-103680 x^2-36496 x^3+67192 x^4+25920 x^5-22736 x^6-9448 x^7+4224 x^8+1872 x^9-408 x^{10}-192 x^{11}+16 x^{12}+8 x^{13}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x \left (-128 x+8 x^2+64 x^3-8 x^5\right )}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} \left (32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}\right )} \, dx=\ln \left (x+{\mathrm {e}}^{\frac {x^2\,{\mathrm {e}}^x}{2\,{\left (-x^4+8\,x^2+x-16\right )}^2}}\,{\mathrm {e}}^{\frac {4\,x^3\,{\mathrm {e}}^x}{{\left (-x^4+8\,x^2+x-16\right )}^2}}\,{\mathrm {e}}^{-\frac {x^5\,{\mathrm {e}}^x}{2\,{\left (-x^4+8\,x^2+x-16\right )}^2}}\,{\mathrm {e}}^{-\frac {2\,x^7}{{\left (-x^4+8\,x^2+x-16\right )}^2}}\,{\mathrm {e}}^{\frac {x^{10}}{{\left (-x^4+8\,x^2+x-16\right )}^2}}\,{\mathrm {e}}^{\frac {16\,x^5}{{\left (-x^4+8\,x^2+x-16\right )}^2}}\,{\mathrm {e}}^{-\frac {16\,x^8}{{\left (-x^4+8\,x^2+x-16\right )}^2}}\,{\mathrm {e}}^{-\frac {32\,x^3}{{\left (-x^4+8\,x^2+x-16\right )}^2}}\,{\mathrm {e}}^{\frac {96\,x^6}{{\left (-x^4+8\,x^2+x-16\right )}^2}}\,{\mathrm {e}}^{\frac {256\,x^2}{{\left (-x^4+8\,x^2+x-16\right )}^2}}\,{\mathrm {e}}^{-\frac {255\,x^4}{{\left (-x^4+8\,x^2+x-16\right )}^2}}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{2\,x}}{16\,{\left (-x^4+8\,x^2+x-16\right )}^2}}\,{\mathrm {e}}^{-\frac {8\,x\,{\mathrm {e}}^x}{{\left (-x^4+8\,x^2+x-16\right )}^2}}+2\right ) \] Input:

int((exp(-(exp(2*x) - exp(x)*(128*x - 8*x^2 - 64*x^3 + 8*x^5) + 4096*x^2 - 
 512*x^3 - 4080*x^4 + 256*x^5 + 1536*x^6 - 32*x^7 - 256*x^8 + 16*x^10)/(51 
2*x + 4080*x^2 - 256*x^3 - 1536*x^4 + 32*x^5 + 256*x^6 - 16*x^8 - 4096))*( 
65536*x + exp(2*x)*(15*x - 8*x^2 - 4*x^3 + x^4 + 17) - exp(x)*(960*x - 128 
*x^2 - 1052*x^3 - 320*x^4 + 396*x^5 + 120*x^6 - 64*x^7 - 12*x^8 + 4*x^9 + 
1024) - 12288*x^2 - 97536*x^3 + 12272*x^4 + 61056*x^5 - 4608*x^6 - 20432*x 
^7 + 768*x^8 + 3840*x^9 - 48*x^10 - 384*x^11 + 16*x^13) - 6144*x - 48768*x 
^2 + 6136*x^3 + 30528*x^4 - 2304*x^5 - 10216*x^6 + 384*x^7 + 1920*x^8 - 24 
*x^9 - 192*x^10 + 8*x^12 + 32768)/(20480*x - exp(-(exp(2*x) - exp(x)*(128* 
x - 8*x^2 - 64*x^3 + 8*x^5) + 4096*x^2 - 512*x^3 - 4080*x^4 + 256*x^5 + 15 
36*x^6 - 32*x^7 - 256*x^8 + 16*x^10)/(512*x + 4080*x^2 - 256*x^3 - 1536*x^ 
4 + 32*x^5 + 256*x^6 - 16*x^8 - 4096))*(6144*x + 48768*x^2 - 6136*x^3 - 30 
528*x^4 + 2304*x^5 + 10216*x^6 - 384*x^7 - 1920*x^8 + 24*x^9 + 192*x^10 - 
8*x^12 - 32768) - 103680*x^2 - 36496*x^3 + 67192*x^4 + 25920*x^5 - 22736*x 
^6 - 9448*x^7 + 4224*x^8 + 1872*x^9 - 408*x^10 - 192*x^11 + 16*x^12 + 8*x^ 
13 + 65536),x)
 

Output:

log(x + exp((x^2*exp(x))/(2*(x + 8*x^2 - x^4 - 16)^2))*exp((4*x^3*exp(x))/ 
(x + 8*x^2 - x^4 - 16)^2)*exp(-(x^5*exp(x))/(2*(x + 8*x^2 - x^4 - 16)^2))* 
exp(-(2*x^7)/(x + 8*x^2 - x^4 - 16)^2)*exp(x^10/(x + 8*x^2 - x^4 - 16)^2)* 
exp((16*x^5)/(x + 8*x^2 - x^4 - 16)^2)*exp(-(16*x^8)/(x + 8*x^2 - x^4 - 16 
)^2)*exp(-(32*x^3)/(x + 8*x^2 - x^4 - 16)^2)*exp((96*x^6)/(x + 8*x^2 - x^4 
 - 16)^2)*exp((256*x^2)/(x + 8*x^2 - x^4 - 16)^2)*exp(-(255*x^4)/(x + 8*x^ 
2 - x^4 - 16)^2)*exp(exp(2*x)/(16*(x + 8*x^2 - x^4 - 16)^2))*exp(-(8*x*exp 
(x))/(x + 8*x^2 - x^4 - 16)^2) + 2)
 

Reduce [F]

\[ \int \frac {32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x \left (-128 x+8 x^2+64 x^3-8 x^5\right )}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} \left (65536 x-12288 x^2-97536 x^3+12272 x^4+61056 x^5-4608 x^6-20432 x^7+768 x^8+3840 x^9-48 x^{10}-384 x^{11}+16 x^{13}+e^{2 x} \left (17+15 x-8 x^2-4 x^3+x^4\right )+e^x \left (-1024-960 x+128 x^2+1052 x^3+320 x^4-396 x^5-120 x^6+64 x^7+12 x^8-4 x^9\right )\right )}{65536+20480 x-103680 x^2-36496 x^3+67192 x^4+25920 x^5-22736 x^6-9448 x^7+4224 x^8+1872 x^9-408 x^{10}-192 x^{11}+16 x^{12}+8 x^{13}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x \left (-128 x+8 x^2+64 x^3-8 x^5\right )}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} \left (32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}\right )} \, dx=\int \frac {\left (\left (x^{4}-4 x^{3}-8 x^{2}+15 x +17\right ) \left ({\mathrm e}^{x}\right )^{2}+\left (-4 x^{9}+12 x^{8}+64 x^{7}-120 x^{6}-396 x^{5}+320 x^{4}+1052 x^{3}+128 x^{2}-960 x -1024\right ) {\mathrm e}^{x}+16 x^{13}-384 x^{11}-48 x^{10}+3840 x^{9}+768 x^{8}-20432 x^{7}-4608 x^{6}+61056 x^{5}+12272 x^{4}-97536 x^{3}-12288 x^{2}+65536 x \right ) {\mathrm e}^{\frac {\left ({\mathrm e}^{x}\right )^{2}+\left (-8 x^{5}+64 x^{3}+8 x^{2}-128 x \right ) {\mathrm e}^{x}+16 x^{10}-256 x^{8}-32 x^{7}+1536 x^{6}+256 x^{5}-4080 x^{4}-512 x^{3}+4096 x^{2}}{16 x^{8}-256 x^{6}-32 x^{5}+1536 x^{4}+256 x^{3}-4080 x^{2}-512 x +4096}}+8 x^{12}-192 x^{10}-24 x^{9}+1920 x^{8}+384 x^{7}-10216 x^{6}-2304 x^{5}+30528 x^{4}+6136 x^{3}-48768 x^{2}-6144 x +32768}{\left (8 x^{12}-192 x^{10}-24 x^{9}+1920 x^{8}+384 x^{7}-10216 x^{6}-2304 x^{5}+30528 x^{4}+6136 x^{3}-48768 x^{2}-6144 x +32768\right ) {\mathrm e}^{\frac {\left ({\mathrm e}^{x}\right )^{2}+\left (-8 x^{5}+64 x^{3}+8 x^{2}-128 x \right ) {\mathrm e}^{x}+16 x^{10}-256 x^{8}-32 x^{7}+1536 x^{6}+256 x^{5}-4080 x^{4}-512 x^{3}+4096 x^{2}}{16 x^{8}-256 x^{6}-32 x^{5}+1536 x^{4}+256 x^{3}-4080 x^{2}-512 x +4096}}+8 x^{13}+16 x^{12}-192 x^{11}-408 x^{10}+1872 x^{9}+4224 x^{8}-9448 x^{7}-22736 x^{6}+25920 x^{5}+67192 x^{4}-36496 x^{3}-103680 x^{2}+20480 x +65536}d x \] Input:

int((((x^4-4*x^3-8*x^2+15*x+17)*exp(x)^2+(-4*x^9+12*x^8+64*x^7-120*x^6-396 
*x^5+320*x^4+1052*x^3+128*x^2-960*x-1024)*exp(x)+16*x^13-384*x^11-48*x^10+ 
3840*x^9+768*x^8-20432*x^7-4608*x^6+61056*x^5+12272*x^4-97536*x^3-12288*x^ 
2+65536*x)*exp((exp(x)^2+(-8*x^5+64*x^3+8*x^2-128*x)*exp(x)+16*x^10-256*x^ 
8-32*x^7+1536*x^6+256*x^5-4080*x^4-512*x^3+4096*x^2)/(16*x^8-256*x^6-32*x^ 
5+1536*x^4+256*x^3-4080*x^2-512*x+4096))+8*x^12-192*x^10-24*x^9+1920*x^8+3 
84*x^7-10216*x^6-2304*x^5+30528*x^4+6136*x^3-48768*x^2-6144*x+32768)/((8*x 
^12-192*x^10-24*x^9+1920*x^8+384*x^7-10216*x^6-2304*x^5+30528*x^4+6136*x^3 
-48768*x^2-6144*x+32768)*exp((exp(x)^2+(-8*x^5+64*x^3+8*x^2-128*x)*exp(x)+ 
16*x^10-256*x^8-32*x^7+1536*x^6+256*x^5-4080*x^4-512*x^3+4096*x^2)/(16*x^8 
-256*x^6-32*x^5+1536*x^4+256*x^3-4080*x^2-512*x+4096))+8*x^13+16*x^12-192* 
x^11-408*x^10+1872*x^9+4224*x^8-9448*x^7-22736*x^6+25920*x^5+67192*x^4-364 
96*x^3-103680*x^2+20480*x+65536),x)
 

Output:

int((((x^4-4*x^3-8*x^2+15*x+17)*exp(x)^2+(-4*x^9+12*x^8+64*x^7-120*x^6-396 
*x^5+320*x^4+1052*x^3+128*x^2-960*x-1024)*exp(x)+16*x^13-384*x^11-48*x^10+ 
3840*x^9+768*x^8-20432*x^7-4608*x^6+61056*x^5+12272*x^4-97536*x^3-12288*x^ 
2+65536*x)*exp((exp(x)^2+(-8*x^5+64*x^3+8*x^2-128*x)*exp(x)+16*x^10-256*x^ 
8-32*x^7+1536*x^6+256*x^5-4080*x^4-512*x^3+4096*x^2)/(16*x^8-256*x^6-32*x^ 
5+1536*x^4+256*x^3-4080*x^2-512*x+4096))+8*x^12-192*x^10-24*x^9+1920*x^8+3 
84*x^7-10216*x^6-2304*x^5+30528*x^4+6136*x^3-48768*x^2-6144*x+32768)/((8*x 
^12-192*x^10-24*x^9+1920*x^8+384*x^7-10216*x^6-2304*x^5+30528*x^4+6136*x^3 
-48768*x^2-6144*x+32768)*exp((exp(x)^2+(-8*x^5+64*x^3+8*x^2-128*x)*exp(x)+ 
16*x^10-256*x^8-32*x^7+1536*x^6+256*x^5-4080*x^4-512*x^3+4096*x^2)/(16*x^8 
-256*x^6-32*x^5+1536*x^4+256*x^3-4080*x^2-512*x+4096))+8*x^13+16*x^12-192* 
x^11-408*x^10+1872*x^9+4224*x^8-9448*x^7-22736*x^6+25920*x^5+67192*x^4-364 
96*x^3-103680*x^2+20480*x+65536),x)