\(\int \frac {32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x (-128 x+8 x^2+64 x^3-8 x^5)}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} (65536 x-12288 x^2-97536 x^3+12272 x^4+61056 x^5-4608 x^6-20432 x^7+768 x^8+3840 x^9-48 x^{10}-384 x^{11}+16 x^{13}+e^{2 x} (17+15 x-8 x^2-4 x^3+x^4)+e^x (-1024-960 x+128 x^2+1052 x^3+320 x^4-396 x^5-120 x^6+64 x^7+12 x^8-4 x^9))}{65536+20480 x-103680 x^2-36496 x^3+67192 x^4+25920 x^5-22736 x^6-9448 x^7+4224 x^8+1872 x^9-408 x^{10}-192 x^{11}+16 x^{12}+8 x^{13}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x (-128 x+8 x^2+64 x^3-8 x^5)}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} (32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12})} \, dx\) [7871]

Optimal result

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

[Out]

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

Rubi [F(-1)]

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

[In]

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
^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 - 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]

[Out]

$Aborted

Rubi steps Aborted

Mathematica [A] (verified)

Time = 2.92 (sec) , antiderivative size = 57, normalized size of antiderivative = 1.68 \[ \int \frac {32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x \left (-128 x+8 x^2+64 x^3-8 x^5\right )}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} \left (65536 x-12288 x^2-97536 x^3+12272 x^4+61056 x^5-4608 x^6-20432 x^7+768 x^8+3840 x^9-48 x^{10}-384 x^{11}+16 x^{13}+e^{2 x} \left (17+15 x-8 x^2-4 x^3+x^4\right )+e^x \left (-1024-960 x+128 x^2+1052 x^3+320 x^4-396 x^5-120 x^6+64 x^7+12 x^8-4 x^9\right )\right )}{65536+20480 x-103680 x^2-36496 x^3+67192 x^4+25920 x^5-22736 x^6-9448 x^7+4224 x^8+1872 x^9-408 x^{10}-192 x^{11}+16 x^{12}+8 x^{13}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x \left (-128 x+8 x^2+64 x^3-8 x^5\right )}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} \left (32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}\right )} \, dx=\log \left (2+e^{x^2+\frac {e^{2 x}}{16 \left (16-x-8 x^2+x^4\right )^2}-\frac {e^x x}{2 \left (16-x-8 x^2+x^4\right )}}+x\right ) \]

[In]

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 - 25
6*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 + 3
840*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 - 3649
6*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 - 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]

[Out]

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]

Maple [B] (verified)

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

Time = 0.90 (sec) , antiderivative size = 96, normalized size of antiderivative = 2.82

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

[In]

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+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)*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^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),x)

[Out]

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+51
2*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 = 0.28 (sec) , antiderivative size = 108, normalized size of antiderivative = 3.18 \[ \int \frac {32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x \left (-128 x+8 x^2+64 x^3-8 x^5\right )}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} \left (65536 x-12288 x^2-97536 x^3+12272 x^4+61056 x^5-4608 x^6-20432 x^7+768 x^8+3840 x^9-48 x^{10}-384 x^{11}+16 x^{13}+e^{2 x} \left (17+15 x-8 x^2-4 x^3+x^4\right )+e^x \left (-1024-960 x+128 x^2+1052 x^3+320 x^4-396 x^5-120 x^6+64 x^7+12 x^8-4 x^9\right )\right )}{65536+20480 x-103680 x^2-36496 x^3+67192 x^4+25920 x^5-22736 x^6-9448 x^7+4224 x^8+1872 x^9-408 x^{10}-192 x^{11}+16 x^{12}+8 x^{13}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x \left (-128 x+8 x^2+64 x^3-8 x^5\right )}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} \left (32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}\right )} \, dx=\log \left (x + e^{\left (\frac {16 \, x^{10} - 256 \, x^{8} - 32 \, x^{7} + 1536 \, x^{6} + 256 \, x^{5} - 4080 \, x^{4} - 512 \, x^{3} + 4096 \, x^{2} - 8 \, {\left (x^{5} - 8 \, x^{3} - x^{2} + 16 \, x\right )} e^{x} + e^{\left (2 \, x\right )}}{16 \, {\left (x^{8} - 16 \, x^{6} - 2 \, x^{5} + 96 \, x^{4} + 16 \, x^{3} - 255 \, x^{2} - 32 \, x + 256\right )}}\right )} + 2\right ) \]

[In]

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-
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^5-40
80*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^2-12
8*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^4-36496*x^3-103680*x^2+20480*x+65536),x, algorithm="fricas")

[Out]

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 = 4.83 (sec) , antiderivative size = 109, normalized size of antiderivative = 3.21 \[ \int \frac {32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x \left (-128 x+8 x^2+64 x^3-8 x^5\right )}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} \left (65536 x-12288 x^2-97536 x^3+12272 x^4+61056 x^5-4608 x^6-20432 x^7+768 x^8+3840 x^9-48 x^{10}-384 x^{11}+16 x^{13}+e^{2 x} \left (17+15 x-8 x^2-4 x^3+x^4\right )+e^x \left (-1024-960 x+128 x^2+1052 x^3+320 x^4-396 x^5-120 x^6+64 x^7+12 x^8-4 x^9\right )\right )}{65536+20480 x-103680 x^2-36496 x^3+67192 x^4+25920 x^5-22736 x^6-9448 x^7+4224 x^8+1872 x^9-408 x^{10}-192 x^{11}+16 x^{12}+8 x^{13}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x \left (-128 x+8 x^2+64 x^3-8 x^5\right )}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} \left (32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}\right )} \, dx=\log {\left (x + e^{\frac {16 x^{10} - 256 x^{8} - 32 x^{7} + 1536 x^{6} + 256 x^{5} - 4080 x^{4} - 512 x^{3} + 4096 x^{2} + \left (- 8 x^{5} + 64 x^{3} + 8 x^{2} - 128 x\right ) e^{x} + e^{2 x}}{16 x^{8} - 256 x^{6} - 32 x^{5} + 1536 x^{4} + 256 x^{3} - 4080 x^{2} - 512 x + 4096}} + 2 \right )} \]

[In]

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**3-12288*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**3-4
8768*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**4-36496*x**3
-103680*x**2+20480*x+65536),x)

[Out]

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 = 4.33 (sec) , antiderivative size = 124, normalized size of antiderivative = 3.65 \[ \int \frac {32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x \left (-128 x+8 x^2+64 x^3-8 x^5\right )}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} \left (65536 x-12288 x^2-97536 x^3+12272 x^4+61056 x^5-4608 x^6-20432 x^7+768 x^8+3840 x^9-48 x^{10}-384 x^{11}+16 x^{13}+e^{2 x} \left (17+15 x-8 x^2-4 x^3+x^4\right )+e^x \left (-1024-960 x+128 x^2+1052 x^3+320 x^4-396 x^5-120 x^6+64 x^7+12 x^8-4 x^9\right )\right )}{65536+20480 x-103680 x^2-36496 x^3+67192 x^4+25920 x^5-22736 x^6-9448 x^7+4224 x^8+1872 x^9-408 x^{10}-192 x^{11}+16 x^{12}+8 x^{13}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x \left (-128 x+8 x^2+64 x^3-8 x^5\right )}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} \left (32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}\right )} \, dx=\frac {2 \, x^{6} - 16 \, x^{4} - 2 \, x^{3} + 32 \, x^{2} - x e^{x}}{2 \, {\left (x^{4} - 8 \, x^{2} - x + 16\right )}} + \log \left ({\left ({\left (x + 2\right )} e^{\left (\frac {x e^{x}}{2 \, {\left (x^{4} - 8 \, x^{2} - x + 16\right )}}\right )} + e^{\left (x^{2} + \frac {e^{\left (2 \, x\right )}}{16 \, {\left (x^{8} - 16 \, x^{6} - 2 \, x^{5} + 96 \, x^{4} + 16 \, x^{3} - 255 \, x^{2} - 32 \, x + 256\right )}}\right )}\right )} e^{\left (-x^{2}\right )}\right ) \]

[In]

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-
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^5-40
80*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^2-12
8*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^4-36496*x^3-103680*x^2+20480*x+65536),x, algorithm="maxima")

[Out]

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 = 11.17 (sec) , antiderivative size = 113, normalized size of antiderivative = 3.32 \[ \int \frac {32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x \left (-128 x+8 x^2+64 x^3-8 x^5\right )}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} \left (65536 x-12288 x^2-97536 x^3+12272 x^4+61056 x^5-4608 x^6-20432 x^7+768 x^8+3840 x^9-48 x^{10}-384 x^{11}+16 x^{13}+e^{2 x} \left (17+15 x-8 x^2-4 x^3+x^4\right )+e^x \left (-1024-960 x+128 x^2+1052 x^3+320 x^4-396 x^5-120 x^6+64 x^7+12 x^8-4 x^9\right )\right )}{65536+20480 x-103680 x^2-36496 x^3+67192 x^4+25920 x^5-22736 x^6-9448 x^7+4224 x^8+1872 x^9-408 x^{10}-192 x^{11}+16 x^{12}+8 x^{13}+e^{\frac {e^{2 x}+4096 x^2-512 x^3-4080 x^4+256 x^5+1536 x^6-32 x^7-256 x^8+16 x^{10}+e^x \left (-128 x+8 x^2+64 x^3-8 x^5\right )}{4096-512 x-4080 x^2+256 x^3+1536 x^4-32 x^5-256 x^6+16 x^8}} \left (32768-6144 x-48768 x^2+6136 x^3+30528 x^4-2304 x^5-10216 x^6+384 x^7+1920 x^8-24 x^9-192 x^{10}+8 x^{12}\right )} \, dx=\log \left (x + e^{\left (\frac {16 \, x^{10} - 256 \, x^{8} - 32 \, x^{7} + 1536 \, x^{6} - 8 \, x^{5} e^{x} + 256 \, x^{5} - 4080 \, x^{4} + 64 \, x^{3} e^{x} - 512 \, x^{3} + 8 \, x^{2} e^{x} + 4096 \, x^{2} - 128 \, x e^{x} + e^{\left (2 \, x\right )}}{16 \, {\left (x^{8} - 16 \, x^{6} - 2 \, x^{5} + 96 \, x^{4} + 16 \, x^{3} - 255 \, x^{2} - 32 \, x + 256\right )}}\right )} + 2\right ) \]

[In]

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-
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^5-40
80*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^2-12
8*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^4-36496*x^3-103680*x^2+20480*x+65536),x, algorithm="giac")

[Out]

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 = 13.34 (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 ) \]

[In]

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)/(512*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 - 204
32*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 + 1536*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 - 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) - 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)

[Out]

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)