3.8.53 \(\int \frac {156621970562+2 e^{8+16 x}+e^{7+14 x} (-368-16 x)+53292920040 x+7984703253 x^2+687869280 x^3+37265659 x^4+1300140 x^5+28529 x^6+360 x^7+2 x^8+e^{6+12 x} (29624+2568 x+56 x^2)+e^{5+10 x} (-1362704-176640 x-7680 x^2-112 x^3)+e^{4+8 x} (39177740+6750040 x+438853 x^2+12752 x^3+140 x^4)+e^{3+6 x} (-720870416-154764240 x-13374316 x^2-580936 x^3-12696 x^4-112 x^5)+e^{2+4 x} (8290009784+2129030328 x+229267542 x^2+13236768 x^3+432290 x^4+7584 x^5+56 x^6)+e^{1+2 x} (-54477207152-16271075104 x-2096082092 x^2-150849272 x^3-6550112 x^4-171720 x^5-2520 x^6-16 x^7)}{313243941124+4 e^{8+16 x}+e^{7+14 x} (-736-32 x)+106585840080 x+15967727460 x^2+1375548120 x^3+74525153 x^4+2600280 x^5+57060 x^6+720 x^7+4 x^8+e^{6+12 x} (59248+5136 x+112 x^2)+e^{5+10 x} (-2725408-353280 x-15360 x^2-224 x^3)+e^{4+8 x} (78355480+13500080 x+877700 x^2+25520 x^3+280 x^4)+e^{3+6 x} (-1441740832-309528480 x-26748080 x^2-1162960 x^3-25440 x^4-224 x^5)+e^{2+4 x} (16580019568+4258060656 x+458516040 x^2+26497832 x^3+866760 x^4+15216 x^5+112 x^6)+e^{1+2 x} (-108954414304-32542150208 x-4191872176 x^2-301868192 x^3-13124704 x^4-344528 x^5-5056 x^6-32 x^7)} \, dx\)
Optimal. Leaf size=31 \[ \frac {x}{2-\frac {x^2}{\left (-\left (-23+e^{1+2 x}-x\right )^2+x\right )^2}} \]
________________________________________________________________________________________
Rubi [F] time = 49.71, antiderivative size = 0, normalized size of antiderivative = 0.00,
number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used =
{} \begin {gather*} \int \frac {156621970562+2 e^{8+16 x}+e^{7+14 x} (-368-16 x)+53292920040 x+7984703253 x^2+687869280 x^3+37265659 x^4+1300140 x^5+28529 x^6+360 x^7+2 x^8+e^{6+12 x} \left (29624+2568 x+56 x^2\right )+e^{5+10 x} \left (-1362704-176640 x-7680 x^2-112 x^3\right )+e^{4+8 x} \left (39177740+6750040 x+438853 x^2+12752 x^3+140 x^4\right )+e^{3+6 x} \left (-720870416-154764240 x-13374316 x^2-580936 x^3-12696 x^4-112 x^5\right )+e^{2+4 x} \left (8290009784+2129030328 x+229267542 x^2+13236768 x^3+432290 x^4+7584 x^5+56 x^6\right )+e^{1+2 x} \left (-54477207152-16271075104 x-2096082092 x^2-150849272 x^3-6550112 x^4-171720 x^5-2520 x^6-16 x^7\right )}{313243941124+4 e^{8+16 x}+e^{7+14 x} (-736-32 x)+106585840080 x+15967727460 x^2+1375548120 x^3+74525153 x^4+2600280 x^5+57060 x^6+720 x^7+4 x^8+e^{6+12 x} \left (59248+5136 x+112 x^2\right )+e^{5+10 x} \left (-2725408-353280 x-15360 x^2-224 x^3\right )+e^{4+8 x} \left (78355480+13500080 x+877700 x^2+25520 x^3+280 x^4\right )+e^{3+6 x} \left (-1441740832-309528480 x-26748080 x^2-1162960 x^3-25440 x^4-224 x^5\right )+e^{2+4 x} \left (16580019568+4258060656 x+458516040 x^2+26497832 x^3+866760 x^4+15216 x^5+112 x^6\right )+e^{1+2 x} \left (-108954414304-32542150208 x-4191872176 x^2-301868192 x^3-13124704 x^4-344528 x^5-5056 x^6-32 x^7\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Int[(156621970562 + 2*E^(8 + 16*x) + E^(7 + 14*x)*(-368 - 16*x) + 53292920040*x + 7984703253*x^2 + 687869280*x
^3 + 37265659*x^4 + 1300140*x^5 + 28529*x^6 + 360*x^7 + 2*x^8 + E^(6 + 12*x)*(29624 + 2568*x + 56*x^2) + E^(5
+ 10*x)*(-1362704 - 176640*x - 7680*x^2 - 112*x^3) + E^(4 + 8*x)*(39177740 + 6750040*x + 438853*x^2 + 12752*x^
3 + 140*x^4) + E^(3 + 6*x)*(-720870416 - 154764240*x - 13374316*x^2 - 580936*x^3 - 12696*x^4 - 112*x^5) + E^(2
+ 4*x)*(8290009784 + 2129030328*x + 229267542*x^2 + 13236768*x^3 + 432290*x^4 + 7584*x^5 + 56*x^6) + E^(1 + 2
*x)*(-54477207152 - 16271075104*x - 2096082092*x^2 - 150849272*x^3 - 6550112*x^4 - 171720*x^5 - 2520*x^6 - 16*
x^7))/(313243941124 + 4*E^(8 + 16*x) + E^(7 + 14*x)*(-736 - 32*x) + 106585840080*x + 15967727460*x^2 + 1375548
120*x^3 + 74525153*x^4 + 2600280*x^5 + 57060*x^6 + 720*x^7 + 4*x^8 + E^(6 + 12*x)*(59248 + 5136*x + 112*x^2) +
E^(5 + 10*x)*(-2725408 - 353280*x - 15360*x^2 - 224*x^3) + E^(4 + 8*x)*(78355480 + 13500080*x + 877700*x^2 +
25520*x^3 + 280*x^4) + E^(3 + 6*x)*(-1441740832 - 309528480*x - 26748080*x^2 - 1162960*x^3 - 25440*x^4 - 224*x
^5) + E^(2 + 4*x)*(16580019568 + 4258060656*x + 458516040*x^2 + 26497832*x^3 + 866760*x^4 + 15216*x^5 + 112*x^
6) + E^(1 + 2*x)*(-108954414304 - 32542150208*x - 4191872176*x^2 - 301868192*x^3 - 13124704*x^4 - 344528*x^5 -
5056*x^6 - 32*x^7)),x]
[Out]
x/2 + 2191118*Defer[Int][x^3/(559682 + 2*E^(4 + 8*x) + 95220*x + 6165*x^2 + 180*x^3 + 2*x^4 - 8*E^(3 + 6*x)*(2
3 + x) + 4*E^(2 + 4*x)*(1587 + 137*x + 3*x^2) - 8*E^(1 + 2*x)*(12167 + 1564*x + 68*x^2 + x^3))^2, x] - 285752*
Defer[Int][(E^(1 + 2*x)*x^3)/(559682 + 2*E^(4 + 8*x) + 95220*x + 6165*x^2 + 180*x^3 + 2*x^4 - 8*E^(3 + 6*x)*(2
3 + x) + 4*E^(2 + 4*x)*(1587 + 137*x + 3*x^2) - 8*E^(1 + 2*x)*(12167 + 1564*x + 68*x^2 + x^3))^2, x] + 12422*D
efer[Int][(E^(2 + 4*x)*x^3)/(559682 + 2*E^(4 + 8*x) + 95220*x + 6165*x^2 + 180*x^3 + 2*x^4 - 8*E^(3 + 6*x)*(23
+ x) + 4*E^(2 + 4*x)*(1587 + 137*x + 3*x^2) - 8*E^(1 + 2*x)*(12167 + 1564*x + 68*x^2 + x^3))^2, x] - 180*Defe
r[Int][(E^(3 + 6*x)*x^3)/(559682 + 2*E^(4 + 8*x) + 95220*x + 6165*x^2 + 180*x^3 + 2*x^4 - 8*E^(3 + 6*x)*(23 +
x) + 4*E^(2 + 4*x)*(1587 + 137*x + 3*x^2) - 8*E^(1 + 2*x)*(12167 + 1564*x + 68*x^2 + x^3))^2, x] + 374715*Defe
r[Int][x^4/(559682 + 2*E^(4 + 8*x) + 95220*x + 6165*x^2 + 180*x^3 + 2*x^4 - 8*E^(3 + 6*x)*(23 + x) + 4*E^(2 +
4*x)*(1587 + 137*x + 3*x^2) - 8*E^(1 + 2*x)*(12167 + 1564*x + 68*x^2 + x^3))^2, x] - 36992*Defer[Int][(E^(1 +
2*x)*x^4)/(559682 + 2*E^(4 + 8*x) + 95220*x + 6165*x^2 + 180*x^3 + 2*x^4 - 8*E^(3 + 6*x)*(23 + x) + 4*E^(2 + 4
*x)*(1587 + 137*x + 3*x^2) - 8*E^(1 + 2*x)*(12167 + 1564*x + 68*x^2 + x^3))^2, x] + 1084*Defer[Int][(E^(2 + 4*
x)*x^4)/(559682 + 2*E^(4 + 8*x) + 95220*x + 6165*x^2 + 180*x^3 + 2*x^4 - 8*E^(3 + 6*x)*(23 + x) + 4*E^(2 + 4*x
)*(1587 + 137*x + 3*x^2) - 8*E^(1 + 2*x)*(12167 + 1564*x + 68*x^2 + x^3))^2, x] - 8*Defer[Int][(E^(3 + 6*x)*x^
4)/(559682 + 2*E^(4 + 8*x) + 95220*x + 6165*x^2 + 180*x^3 + 2*x^4 - 8*E^(3 + 6*x)*(23 + x) + 4*E^(2 + 4*x)*(15
87 + 137*x + 3*x^2) - 8*E^(1 + 2*x)*(12167 + 1564*x + 68*x^2 + x^3))^2, x] + 24390*Defer[Int][x^5/(559682 + 2*
E^(4 + 8*x) + 95220*x + 6165*x^2 + 180*x^3 + 2*x^4 - 8*E^(3 + 6*x)*(23 + x) + 4*E^(2 + 4*x)*(1587 + 137*x + 3*
x^2) - 8*E^(1 + 2*x)*(12167 + 1564*x + 68*x^2 + x^3))^2, x] - 1620*Defer[Int][(E^(1 + 2*x)*x^5)/(559682 + 2*E^
(4 + 8*x) + 95220*x + 6165*x^2 + 180*x^3 + 2*x^4 - 8*E^(3 + 6*x)*(23 + x) + 4*E^(2 + 4*x)*(1587 + 137*x + 3*x^
2) - 8*E^(1 + 2*x)*(12167 + 1564*x + 68*x^2 + x^3))^2, x] + 24*Defer[Int][(E^(2 + 4*x)*x^5)/(559682 + 2*E^(4 +
8*x) + 95220*x + 6165*x^2 + 180*x^3 + 2*x^4 - 8*E^(3 + 6*x)*(23 + x) + 4*E^(2 + 4*x)*(1587 + 137*x + 3*x^2) -
8*E^(1 + 2*x)*(12167 + 1564*x + 68*x^2 + x^3))^2, x] + 716*Defer[Int][x^6/(559682 + 2*E^(4 + 8*x) + 95220*x +
6165*x^2 + 180*x^3 + 2*x^4 - 8*E^(3 + 6*x)*(23 + x) + 4*E^(2 + 4*x)*(1587 + 137*x + 3*x^2) - 8*E^(1 + 2*x)*(1
2167 + 1564*x + 68*x^2 + x^3))^2, x] - 24*Defer[Int][(E^(1 + 2*x)*x^6)/(559682 + 2*E^(4 + 8*x) + 95220*x + 616
5*x^2 + 180*x^3 + 2*x^4 - 8*E^(3 + 6*x)*(23 + x) + 4*E^(2 + 4*x)*(1587 + 137*x + 3*x^2) - 8*E^(1 + 2*x)*(12167
+ 1564*x + 68*x^2 + x^3))^2, x] + 8*Defer[Int][x^7/(559682 + 2*E^(4 + 8*x) + 95220*x + 6165*x^2 + 180*x^3 + 2
*x^4 - 8*E^(3 + 6*x)*(23 + x) + 4*E^(2 + 4*x)*(1587 + 137*x + 3*x^2) - 8*E^(1 + 2*x)*(12167 + 1564*x + 68*x^2
+ x^3))^2, x] + (3*Defer[Int][x^2/(559682 + 2*E^(4 + 8*x) + 95220*x + 6165*x^2 + 180*x^3 + 2*x^4 - 8*E^(3 + 6*
x)*(23 + x) + 4*E^(2 + 4*x)*(1587 + 137*x + 3*x^2) - 8*E^(1 + 2*x)*(12167 + 1564*x + 68*x^2 + x^3)), x])/2 - 4
*Defer[Int][x^3/(559682 + 2*E^(4 + 8*x) + 95220*x + 6165*x^2 + 180*x^3 + 2*x^4 - 8*E^(3 + 6*x)*(23 + x) + 4*E^
(2 + 4*x)*(1587 + 137*x + 3*x^2) - 8*E^(1 + 2*x)*(12167 + 1564*x + 68*x^2 + x^3)), x]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {156621970562+2 e^{8+16 x}+53292920040 x+7984703253 x^2+687869280 x^3+37265659 x^4+1300140 x^5+28529 x^6+360 x^7+2 x^8-16 e^{7+14 x} (23+x)+8 e^{6+12 x} \left (3703+321 x+7 x^2\right )-16 e^{5+10 x} \left (85169+11040 x+480 x^2+7 x^3\right )+e^{4+8 x} \left (39177740+6750040 x+438853 x^2+12752 x^3+140 x^4\right )-4 e^{3+6 x} \left (180217604+38691060 x+3343579 x^2+145234 x^3+3174 x^4+28 x^5\right )+2 e^{2+4 x} \left (4145004892+1064515164 x+114633771 x^2+6618384 x^3+216145 x^4+3792 x^5+28 x^6\right )-4 e^{1+2 x} \left (13619301788+4067768776 x+524020523 x^2+37712318 x^3+1637528 x^4+42930 x^5+630 x^6+4 x^7\right )}{\left (559682+2 e^{4+8 x}+95220 x+6165 x^2+180 x^3+2 x^4-8 e^{3+6 x} (23+x)+4 e^{2+4 x} \left (1587+137 x+3 x^2\right )-8 e^{1+2 x} \left (12167+1564 x+68 x^2+x^3\right )\right )^2} \, dx\\ &=\int \left (\frac {1}{2}-\frac {x^2 (-3+8 x)}{2 \left (559682-97336 e^{1+2 x}+6348 e^{2+4 x}-184 e^{3+6 x}+2 e^{4+8 x}+95220 x-12512 e^{1+2 x} x+548 e^{2+4 x} x-8 e^{3+6 x} x+6165 x^2-544 e^{1+2 x} x^2+12 e^{2+4 x} x^2+180 x^3-8 e^{1+2 x} x^3+2 x^4\right )}+\frac {x^3 \left (2191118-285752 e^{1+2 x}+12422 e^{2+4 x}-180 e^{3+6 x}+374715 x-36992 e^{1+2 x} x+1084 e^{2+4 x} x-8 e^{3+6 x} x+24390 x^2-1620 e^{1+2 x} x^2+24 e^{2+4 x} x^2+716 x^3-24 e^{1+2 x} x^3+8 x^4\right )}{\left (559682-97336 e^{1+2 x}+6348 e^{2+4 x}-184 e^{3+6 x}+2 e^{4+8 x}+95220 x-12512 e^{1+2 x} x+548 e^{2+4 x} x-8 e^{3+6 x} x+6165 x^2-544 e^{1+2 x} x^2+12 e^{2+4 x} x^2+180 x^3-8 e^{1+2 x} x^3+2 x^4\right )^2}\right ) \, dx\\ &=\frac {x}{2}-\frac {1}{2} \int \frac {x^2 (-3+8 x)}{559682-97336 e^{1+2 x}+6348 e^{2+4 x}-184 e^{3+6 x}+2 e^{4+8 x}+95220 x-12512 e^{1+2 x} x+548 e^{2+4 x} x-8 e^{3+6 x} x+6165 x^2-544 e^{1+2 x} x^2+12 e^{2+4 x} x^2+180 x^3-8 e^{1+2 x} x^3+2 x^4} \, dx+\int \frac {x^3 \left (2191118-285752 e^{1+2 x}+12422 e^{2+4 x}-180 e^{3+6 x}+374715 x-36992 e^{1+2 x} x+1084 e^{2+4 x} x-8 e^{3+6 x} x+24390 x^2-1620 e^{1+2 x} x^2+24 e^{2+4 x} x^2+716 x^3-24 e^{1+2 x} x^3+8 x^4\right )}{\left (559682-97336 e^{1+2 x}+6348 e^{2+4 x}-184 e^{3+6 x}+2 e^{4+8 x}+95220 x-12512 e^{1+2 x} x+548 e^{2+4 x} x-8 e^{3+6 x} x+6165 x^2-544 e^{1+2 x} x^2+12 e^{2+4 x} x^2+180 x^3-8 e^{1+2 x} x^3+2 x^4\right )^2} \, dx\\ &=\frac {x}{2}-\frac {1}{2} \int \frac {x^2 (-3+8 x)}{559682+2 e^{4+8 x}+95220 x+6165 x^2+180 x^3+2 x^4-8 e^{3+6 x} (23+x)+4 e^{2+4 x} \left (1587+137 x+3 x^2\right )-8 e^{1+2 x} \left (12167+1564 x+68 x^2+x^3\right )} \, dx+\int \frac {x^3 \left (2191118+374715 x+24390 x^2+716 x^3+8 x^4-4 e^{3+6 x} (45+2 x)+2 e^{2+4 x} \left (6211+542 x+12 x^2\right )-4 e^{1+2 x} \left (71438+9248 x+405 x^2+6 x^3\right )\right )}{\left (559682+2 e^{4+8 x}+95220 x+6165 x^2+180 x^3+2 x^4-8 e^{3+6 x} (23+x)+4 e^{2+4 x} \left (1587+137 x+3 x^2\right )-8 e^{1+2 x} \left (12167+1564 x+68 x^2+x^3\right )\right )^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [B] time = 0.26, size = 115, normalized size = 3.71 \begin {gather*} \frac {x \left (529+e^{2+4 x}+45 x+x^2-2 e^{1+2 x} (23+x)\right )^2}{559682+2 e^{4+8 x}+95220 x+6165 x^2+180 x^3+2 x^4-8 e^{3+6 x} (23+x)+4 e^{2+4 x} \left (1587+137 x+3 x^2\right )-8 e^{1+2 x} \left (12167+1564 x+68 x^2+x^3\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(156621970562 + 2*E^(8 + 16*x) + E^(7 + 14*x)*(-368 - 16*x) + 53292920040*x + 7984703253*x^2 + 68786
9280*x^3 + 37265659*x^4 + 1300140*x^5 + 28529*x^6 + 360*x^7 + 2*x^8 + E^(6 + 12*x)*(29624 + 2568*x + 56*x^2) +
E^(5 + 10*x)*(-1362704 - 176640*x - 7680*x^2 - 112*x^3) + E^(4 + 8*x)*(39177740 + 6750040*x + 438853*x^2 + 12
752*x^3 + 140*x^4) + E^(3 + 6*x)*(-720870416 - 154764240*x - 13374316*x^2 - 580936*x^3 - 12696*x^4 - 112*x^5)
+ E^(2 + 4*x)*(8290009784 + 2129030328*x + 229267542*x^2 + 13236768*x^3 + 432290*x^4 + 7584*x^5 + 56*x^6) + E^
(1 + 2*x)*(-54477207152 - 16271075104*x - 2096082092*x^2 - 150849272*x^3 - 6550112*x^4 - 171720*x^5 - 2520*x^6
- 16*x^7))/(313243941124 + 4*E^(8 + 16*x) + E^(7 + 14*x)*(-736 - 32*x) + 106585840080*x + 15967727460*x^2 + 1
375548120*x^3 + 74525153*x^4 + 2600280*x^5 + 57060*x^6 + 720*x^7 + 4*x^8 + E^(6 + 12*x)*(59248 + 5136*x + 112*
x^2) + E^(5 + 10*x)*(-2725408 - 353280*x - 15360*x^2 - 224*x^3) + E^(4 + 8*x)*(78355480 + 13500080*x + 877700*
x^2 + 25520*x^3 + 280*x^4) + E^(3 + 6*x)*(-1441740832 - 309528480*x - 26748080*x^2 - 1162960*x^3 - 25440*x^4 -
224*x^5) + E^(2 + 4*x)*(16580019568 + 4258060656*x + 458516040*x^2 + 26497832*x^3 + 866760*x^4 + 15216*x^5 +
112*x^6) + E^(1 + 2*x)*(-108954414304 - 32542150208*x - 4191872176*x^2 - 301868192*x^3 - 13124704*x^4 - 344528
*x^5 - 5056*x^6 - 32*x^7)),x]
[Out]
(x*(529 + E^(2 + 4*x) + 45*x + x^2 - 2*E^(1 + 2*x)*(23 + x))^2)/(559682 + 2*E^(4 + 8*x) + 95220*x + 6165*x^2 +
180*x^3 + 2*x^4 - 8*E^(3 + 6*x)*(23 + x) + 4*E^(2 + 4*x)*(1587 + 137*x + 3*x^2) - 8*E^(1 + 2*x)*(12167 + 1564
*x + 68*x^2 + x^3))
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fricas [B] time = 0.74, size = 173, normalized size = 5.58 \begin {gather*} \frac {x^{5} + 90 \, x^{4} + 3083 \, x^{3} + 47610 \, x^{2} + x e^{\left (8 \, x + 4\right )} - 4 \, {\left (x^{2} + 23 \, x\right )} e^{\left (6 \, x + 3\right )} + 2 \, {\left (3 \, x^{3} + 137 \, x^{2} + 1587 \, x\right )} e^{\left (4 \, x + 2\right )} - 4 \, {\left (x^{4} + 68 \, x^{3} + 1564 \, x^{2} + 12167 \, x\right )} e^{\left (2 \, x + 1\right )} + 279841 \, x}{2 \, x^{4} + 180 \, x^{3} + 6165 \, x^{2} - 8 \, {\left (x + 23\right )} e^{\left (6 \, x + 3\right )} + 4 \, {\left (3 \, x^{2} + 137 \, x + 1587\right )} e^{\left (4 \, x + 2\right )} - 8 \, {\left (x^{3} + 68 \, x^{2} + 1564 \, x + 12167\right )} e^{\left (2 \, x + 1\right )} + 95220 \, x + 2 \, e^{\left (8 \, x + 4\right )} + 559682} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((2*exp(2*x+1)^8+(-16*x-368)*exp(2*x+1)^7+(56*x^2+2568*x+29624)*exp(2*x+1)^6+(-112*x^3-7680*x^2-17664
0*x-1362704)*exp(2*x+1)^5+(140*x^4+12752*x^3+438853*x^2+6750040*x+39177740)*exp(2*x+1)^4+(-112*x^5-12696*x^4-5
80936*x^3-13374316*x^2-154764240*x-720870416)*exp(2*x+1)^3+(56*x^6+7584*x^5+432290*x^4+13236768*x^3+229267542*
x^2+2129030328*x+8290009784)*exp(2*x+1)^2+(-16*x^7-2520*x^6-171720*x^5-6550112*x^4-150849272*x^3-2096082092*x^
2-16271075104*x-54477207152)*exp(2*x+1)+2*x^8+360*x^7+28529*x^6+1300140*x^5+37265659*x^4+687869280*x^3+7984703
253*x^2+53292920040*x+156621970562)/(4*exp(2*x+1)^8+(-32*x-736)*exp(2*x+1)^7+(112*x^2+5136*x+59248)*exp(2*x+1)
^6+(-224*x^3-15360*x^2-353280*x-2725408)*exp(2*x+1)^5+(280*x^4+25520*x^3+877700*x^2+13500080*x+78355480)*exp(2
*x+1)^4+(-224*x^5-25440*x^4-1162960*x^3-26748080*x^2-309528480*x-1441740832)*exp(2*x+1)^3+(112*x^6+15216*x^5+8
66760*x^4+26497832*x^3+458516040*x^2+4258060656*x+16580019568)*exp(2*x+1)^2+(-32*x^7-5056*x^6-344528*x^5-13124
704*x^4-301868192*x^3-4191872176*x^2-32542150208*x-108954414304)*exp(2*x+1)+4*x^8+720*x^7+57060*x^6+2600280*x^
5+74525153*x^4+1375548120*x^3+15967727460*x^2+106585840080*x+313243941124),x, algorithm="fricas")
[Out]
(x^5 + 90*x^4 + 3083*x^3 + 47610*x^2 + x*e^(8*x + 4) - 4*(x^2 + 23*x)*e^(6*x + 3) + 2*(3*x^3 + 137*x^2 + 1587*
x)*e^(4*x + 2) - 4*(x^4 + 68*x^3 + 1564*x^2 + 12167*x)*e^(2*x + 1) + 279841*x)/(2*x^4 + 180*x^3 + 6165*x^2 - 8
*(x + 23)*e^(6*x + 3) + 4*(3*x^2 + 137*x + 1587)*e^(4*x + 2) - 8*(x^3 + 68*x^2 + 1564*x + 12167)*e^(2*x + 1) +
95220*x + 2*e^(8*x + 4) + 559682)
________________________________________________________________________________________
giac [B] time = 11.41, size = 242, normalized size = 7.81 \begin {gather*} \frac {2 \, x^{5} - 8 \, x^{4} e^{\left (2 \, x + 1\right )} + 180 \, x^{4} + 12 \, x^{3} e^{\left (4 \, x + 2\right )} - 544 \, x^{3} e^{\left (2 \, x + 1\right )} + 6167 \, x^{3} - 8 \, x^{2} e^{\left (6 \, x + 3\right )} + 548 \, x^{2} e^{\left (4 \, x + 2\right )} - 12512 \, x^{2} e^{\left (2 \, x + 1\right )} + 95220 \, x^{2} + 2 \, x e^{\left (8 \, x + 4\right )} - 184 \, x e^{\left (6 \, x + 3\right )} + 6348 \, x e^{\left (4 \, x + 2\right )} - 97336 \, x e^{\left (2 \, x + 1\right )} + 559682 \, x}{2 \, {\left (2 \, x^{4} - 8 \, x^{3} e^{\left (2 \, x + 1\right )} + 180 \, x^{3} + 12 \, x^{2} e^{\left (4 \, x + 2\right )} - 544 \, x^{2} e^{\left (2 \, x + 1\right )} + 6165 \, x^{2} - 8 \, x e^{\left (6 \, x + 3\right )} + 548 \, x e^{\left (4 \, x + 2\right )} - 12512 \, x e^{\left (2 \, x + 1\right )} + 95220 \, x + 2 \, e^{\left (8 \, x + 4\right )} - 184 \, e^{\left (6 \, x + 3\right )} + 6348 \, e^{\left (4 \, x + 2\right )} - 97336 \, e^{\left (2 \, x + 1\right )} + 559682\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((2*exp(2*x+1)^8+(-16*x-368)*exp(2*x+1)^7+(56*x^2+2568*x+29624)*exp(2*x+1)^6+(-112*x^3-7680*x^2-17664
0*x-1362704)*exp(2*x+1)^5+(140*x^4+12752*x^3+438853*x^2+6750040*x+39177740)*exp(2*x+1)^4+(-112*x^5-12696*x^4-5
80936*x^3-13374316*x^2-154764240*x-720870416)*exp(2*x+1)^3+(56*x^6+7584*x^5+432290*x^4+13236768*x^3+229267542*
x^2+2129030328*x+8290009784)*exp(2*x+1)^2+(-16*x^7-2520*x^6-171720*x^5-6550112*x^4-150849272*x^3-2096082092*x^
2-16271075104*x-54477207152)*exp(2*x+1)+2*x^8+360*x^7+28529*x^6+1300140*x^5+37265659*x^4+687869280*x^3+7984703
253*x^2+53292920040*x+156621970562)/(4*exp(2*x+1)^8+(-32*x-736)*exp(2*x+1)^7+(112*x^2+5136*x+59248)*exp(2*x+1)
^6+(-224*x^3-15360*x^2-353280*x-2725408)*exp(2*x+1)^5+(280*x^4+25520*x^3+877700*x^2+13500080*x+78355480)*exp(2
*x+1)^4+(-224*x^5-25440*x^4-1162960*x^3-26748080*x^2-309528480*x-1441740832)*exp(2*x+1)^3+(112*x^6+15216*x^5+8
66760*x^4+26497832*x^3+458516040*x^2+4258060656*x+16580019568)*exp(2*x+1)^2+(-32*x^7-5056*x^6-344528*x^5-13124
704*x^4-301868192*x^3-4191872176*x^2-32542150208*x-108954414304)*exp(2*x+1)+4*x^8+720*x^7+57060*x^6+2600280*x^
5+74525153*x^4+1375548120*x^3+15967727460*x^2+106585840080*x+313243941124),x, algorithm="giac")
[Out]
1/2*(2*x^5 - 8*x^4*e^(2*x + 1) + 180*x^4 + 12*x^3*e^(4*x + 2) - 544*x^3*e^(2*x + 1) + 6167*x^3 - 8*x^2*e^(6*x
+ 3) + 548*x^2*e^(4*x + 2) - 12512*x^2*e^(2*x + 1) + 95220*x^2 + 2*x*e^(8*x + 4) - 184*x*e^(6*x + 3) + 6348*x*
e^(4*x + 2) - 97336*x*e^(2*x + 1) + 559682*x)/(2*x^4 - 8*x^3*e^(2*x + 1) + 180*x^3 + 12*x^2*e^(4*x + 2) - 544*
x^2*e^(2*x + 1) + 6165*x^2 - 8*x*e^(6*x + 3) + 548*x*e^(4*x + 2) - 12512*x*e^(2*x + 1) + 95220*x + 2*e^(8*x +
4) - 184*e^(6*x + 3) + 6348*e^(4*x + 2) - 97336*e^(2*x + 1) + 559682)
________________________________________________________________________________________
maple [B] time = 0.29, size = 124, normalized size = 4.00
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\(\frac {x}{2}+\frac {x^{3}}{4 \,{\mathrm e}^{8 x +4}-16 \,{\mathrm e}^{6 x +3} x +24 \,{\mathrm e}^{4 x +2} x^{2}-16 \,{\mathrm e}^{2 x +1} x^{3}+4 x^{4}-368 \,{\mathrm e}^{6 x +3}+1096 \,{\mathrm e}^{4 x +2} x -1088 \,{\mathrm e}^{2 x +1} x^{2}+360 x^{3}+12696 \,{\mathrm e}^{4 x +2}-25024 x \,{\mathrm e}^{2 x +1}+12330 x^{2}-194672 \,{\mathrm e}^{2 x +1}+190440 x +1119364}\) |
\(124\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int((2*exp(2*x+1)^8+(-16*x-368)*exp(2*x+1)^7+(56*x^2+2568*x+29624)*exp(2*x+1)^6+(-112*x^3-7680*x^2-176640*x-13
62704)*exp(2*x+1)^5+(140*x^4+12752*x^3+438853*x^2+6750040*x+39177740)*exp(2*x+1)^4+(-112*x^5-12696*x^4-580936*
x^3-13374316*x^2-154764240*x-720870416)*exp(2*x+1)^3+(56*x^6+7584*x^5+432290*x^4+13236768*x^3+229267542*x^2+21
29030328*x+8290009784)*exp(2*x+1)^2+(-16*x^7-2520*x^6-171720*x^5-6550112*x^4-150849272*x^3-2096082092*x^2-1627
1075104*x-54477207152)*exp(2*x+1)+2*x^8+360*x^7+28529*x^6+1300140*x^5+37265659*x^4+687869280*x^3+7984703253*x^
2+53292920040*x+156621970562)/(4*exp(2*x+1)^8+(-32*x-736)*exp(2*x+1)^7+(112*x^2+5136*x+59248)*exp(2*x+1)^6+(-2
24*x^3-15360*x^2-353280*x-2725408)*exp(2*x+1)^5+(280*x^4+25520*x^3+877700*x^2+13500080*x+78355480)*exp(2*x+1)^
4+(-224*x^5-25440*x^4-1162960*x^3-26748080*x^2-309528480*x-1441740832)*exp(2*x+1)^3+(112*x^6+15216*x^5+866760*
x^4+26497832*x^3+458516040*x^2+4258060656*x+16580019568)*exp(2*x+1)^2+(-32*x^7-5056*x^6-344528*x^5-13124704*x^
4-301868192*x^3-4191872176*x^2-32542150208*x-108954414304)*exp(2*x+1)+4*x^8+720*x^7+57060*x^6+2600280*x^5+7452
5153*x^4+1375548120*x^3+15967727460*x^2+106585840080*x+313243941124),x,method=_RETURNVERBOSE)
[Out]
1/2*x+1/2*x^3/(2*exp(8*x+4)-8*exp(6*x+3)*x+12*exp(4*x+2)*x^2-8*exp(2*x+1)*x^3+2*x^4-184*exp(6*x+3)+548*exp(4*x
+2)*x-544*exp(2*x+1)*x^2+180*x^3+6348*exp(4*x+2)-12512*x*exp(2*x+1)+6165*x^2-97336*exp(2*x+1)+95220*x+559682)
________________________________________________________________________________________
maxima [B] time = 1.71, size = 204, normalized size = 6.58 \begin {gather*} \frac {x^{5} + 90 \, x^{4} + 3083 \, x^{3} + 47610 \, x^{2} - 4 \, {\left (x^{2} e^{3} + 23 \, x e^{3}\right )} e^{\left (6 \, x\right )} + 2 \, {\left (3 \, x^{3} e^{2} + 137 \, x^{2} e^{2} + 1587 \, x e^{2}\right )} e^{\left (4 \, x\right )} - 4 \, {\left (x^{4} e + 68 \, x^{3} e + 1564 \, x^{2} e + 12167 \, x e\right )} e^{\left (2 \, x\right )} + x e^{\left (8 \, x + 4\right )} + 279841 \, x}{2 \, x^{4} + 180 \, x^{3} + 6165 \, x^{2} - 8 \, {\left (x e^{3} + 23 \, e^{3}\right )} e^{\left (6 \, x\right )} + 4 \, {\left (3 \, x^{2} e^{2} + 137 \, x e^{2} + 1587 \, e^{2}\right )} e^{\left (4 \, x\right )} - 8 \, {\left (x^{3} e + 68 \, x^{2} e + 1564 \, x e + 12167 \, e\right )} e^{\left (2 \, x\right )} + 95220 \, x + 2 \, e^{\left (8 \, x + 4\right )} + 559682} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((2*exp(2*x+1)^8+(-16*x-368)*exp(2*x+1)^7+(56*x^2+2568*x+29624)*exp(2*x+1)^6+(-112*x^3-7680*x^2-17664
0*x-1362704)*exp(2*x+1)^5+(140*x^4+12752*x^3+438853*x^2+6750040*x+39177740)*exp(2*x+1)^4+(-112*x^5-12696*x^4-5
80936*x^3-13374316*x^2-154764240*x-720870416)*exp(2*x+1)^3+(56*x^6+7584*x^5+432290*x^4+13236768*x^3+229267542*
x^2+2129030328*x+8290009784)*exp(2*x+1)^2+(-16*x^7-2520*x^6-171720*x^5-6550112*x^4-150849272*x^3-2096082092*x^
2-16271075104*x-54477207152)*exp(2*x+1)+2*x^8+360*x^7+28529*x^6+1300140*x^5+37265659*x^4+687869280*x^3+7984703
253*x^2+53292920040*x+156621970562)/(4*exp(2*x+1)^8+(-32*x-736)*exp(2*x+1)^7+(112*x^2+5136*x+59248)*exp(2*x+1)
^6+(-224*x^3-15360*x^2-353280*x-2725408)*exp(2*x+1)^5+(280*x^4+25520*x^3+877700*x^2+13500080*x+78355480)*exp(2
*x+1)^4+(-224*x^5-25440*x^4-1162960*x^3-26748080*x^2-309528480*x-1441740832)*exp(2*x+1)^3+(112*x^6+15216*x^5+8
66760*x^4+26497832*x^3+458516040*x^2+4258060656*x+16580019568)*exp(2*x+1)^2+(-32*x^7-5056*x^6-344528*x^5-13124
704*x^4-301868192*x^3-4191872176*x^2-32542150208*x-108954414304)*exp(2*x+1)+4*x^8+720*x^7+57060*x^6+2600280*x^
5+74525153*x^4+1375548120*x^3+15967727460*x^2+106585840080*x+313243941124),x, algorithm="maxima")
[Out]
(x^5 + 90*x^4 + 3083*x^3 + 47610*x^2 - 4*(x^2*e^3 + 23*x*e^3)*e^(6*x) + 2*(3*x^3*e^2 + 137*x^2*e^2 + 1587*x*e^
2)*e^(4*x) - 4*(x^4*e + 68*x^3*e + 1564*x^2*e + 12167*x*e)*e^(2*x) + x*e^(8*x + 4) + 279841*x)/(2*x^4 + 180*x^
3 + 6165*x^2 - 8*(x*e^3 + 23*e^3)*e^(6*x) + 4*(3*x^2*e^2 + 137*x*e^2 + 1587*e^2)*e^(4*x) - 8*(x^3*e + 68*x^2*e
+ 1564*x*e + 12167*e)*e^(2*x) + 95220*x + 2*e^(8*x + 4) + 559682)
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {53292920040\,x+2\,{\mathrm {e}}^{16\,x+8}-{\mathrm {e}}^{14\,x+7}\,\left (16\,x+368\right )-{\mathrm {e}}^{6\,x+3}\,\left (112\,x^5+12696\,x^4+580936\,x^3+13374316\,x^2+154764240\,x+720870416\right )+{\mathrm {e}}^{12\,x+6}\,\left (56\,x^2+2568\,x+29624\right )-{\mathrm {e}}^{2\,x+1}\,\left (16\,x^7+2520\,x^6+171720\,x^5+6550112\,x^4+150849272\,x^3+2096082092\,x^2+16271075104\,x+54477207152\right )-{\mathrm {e}}^{10\,x+5}\,\left (112\,x^3+7680\,x^2+176640\,x+1362704\right )+{\mathrm {e}}^{4\,x+2}\,\left (56\,x^6+7584\,x^5+432290\,x^4+13236768\,x^3+229267542\,x^2+2129030328\,x+8290009784\right )+7984703253\,x^2+687869280\,x^3+37265659\,x^4+1300140\,x^5+28529\,x^6+360\,x^7+2\,x^8+{\mathrm {e}}^{8\,x+4}\,\left (140\,x^4+12752\,x^3+438853\,x^2+6750040\,x+39177740\right )+156621970562}{106585840080\,x+4\,{\mathrm {e}}^{16\,x+8}-{\mathrm {e}}^{14\,x+7}\,\left (32\,x+736\right )+{\mathrm {e}}^{4\,x+2}\,\left (112\,x^6+15216\,x^5+866760\,x^4+26497832\,x^3+458516040\,x^2+4258060656\,x+16580019568\right )+{\mathrm {e}}^{12\,x+6}\,\left (112\,x^2+5136\,x+59248\right )-{\mathrm {e}}^{6\,x+3}\,\left (224\,x^5+25440\,x^4+1162960\,x^3+26748080\,x^2+309528480\,x+1441740832\right )-{\mathrm {e}}^{2\,x+1}\,\left (32\,x^7+5056\,x^6+344528\,x^5+13124704\,x^4+301868192\,x^3+4191872176\,x^2+32542150208\,x+108954414304\right )-{\mathrm {e}}^{10\,x+5}\,\left (224\,x^3+15360\,x^2+353280\,x+2725408\right )+15967727460\,x^2+1375548120\,x^3+74525153\,x^4+2600280\,x^5+57060\,x^6+720\,x^7+4\,x^8+{\mathrm {e}}^{8\,x+4}\,\left (280\,x^4+25520\,x^3+877700\,x^2+13500080\,x+78355480\right )+313243941124} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((53292920040*x + 2*exp(16*x + 8) - exp(14*x + 7)*(16*x + 368) - exp(6*x + 3)*(154764240*x + 13374316*x^2 +
580936*x^3 + 12696*x^4 + 112*x^5 + 720870416) + exp(12*x + 6)*(2568*x + 56*x^2 + 29624) - exp(2*x + 1)*(16271
075104*x + 2096082092*x^2 + 150849272*x^3 + 6550112*x^4 + 171720*x^5 + 2520*x^6 + 16*x^7 + 54477207152) - exp(
10*x + 5)*(176640*x + 7680*x^2 + 112*x^3 + 1362704) + exp(4*x + 2)*(2129030328*x + 229267542*x^2 + 13236768*x^
3 + 432290*x^4 + 7584*x^5 + 56*x^6 + 8290009784) + 7984703253*x^2 + 687869280*x^3 + 37265659*x^4 + 1300140*x^5
+ 28529*x^6 + 360*x^7 + 2*x^8 + exp(8*x + 4)*(6750040*x + 438853*x^2 + 12752*x^3 + 140*x^4 + 39177740) + 1566
21970562)/(106585840080*x + 4*exp(16*x + 8) - exp(14*x + 7)*(32*x + 736) + exp(4*x + 2)*(4258060656*x + 458516
040*x^2 + 26497832*x^3 + 866760*x^4 + 15216*x^5 + 112*x^6 + 16580019568) + exp(12*x + 6)*(5136*x + 112*x^2 + 5
9248) - exp(6*x + 3)*(309528480*x + 26748080*x^2 + 1162960*x^3 + 25440*x^4 + 224*x^5 + 1441740832) - exp(2*x +
1)*(32542150208*x + 4191872176*x^2 + 301868192*x^3 + 13124704*x^4 + 344528*x^5 + 5056*x^6 + 32*x^7 + 10895441
4304) - exp(10*x + 5)*(353280*x + 15360*x^2 + 224*x^3 + 2725408) + 15967727460*x^2 + 1375548120*x^3 + 74525153
*x^4 + 2600280*x^5 + 57060*x^6 + 720*x^7 + 4*x^8 + exp(8*x + 4)*(13500080*x + 877700*x^2 + 25520*x^3 + 280*x^4
+ 78355480) + 313243941124),x)
[Out]
int((53292920040*x + 2*exp(16*x + 8) - exp(14*x + 7)*(16*x + 368) - exp(6*x + 3)*(154764240*x + 13374316*x^2 +
580936*x^3 + 12696*x^4 + 112*x^5 + 720870416) + exp(12*x + 6)*(2568*x + 56*x^2 + 29624) - exp(2*x + 1)*(16271
075104*x + 2096082092*x^2 + 150849272*x^3 + 6550112*x^4 + 171720*x^5 + 2520*x^6 + 16*x^7 + 54477207152) - exp(
10*x + 5)*(176640*x + 7680*x^2 + 112*x^3 + 1362704) + exp(4*x + 2)*(2129030328*x + 229267542*x^2 + 13236768*x^
3 + 432290*x^4 + 7584*x^5 + 56*x^6 + 8290009784) + 7984703253*x^2 + 687869280*x^3 + 37265659*x^4 + 1300140*x^5
+ 28529*x^6 + 360*x^7 + 2*x^8 + exp(8*x + 4)*(6750040*x + 438853*x^2 + 12752*x^3 + 140*x^4 + 39177740) + 1566
21970562)/(106585840080*x + 4*exp(16*x + 8) - exp(14*x + 7)*(32*x + 736) + exp(4*x + 2)*(4258060656*x + 458516
040*x^2 + 26497832*x^3 + 866760*x^4 + 15216*x^5 + 112*x^6 + 16580019568) + exp(12*x + 6)*(5136*x + 112*x^2 + 5
9248) - exp(6*x + 3)*(309528480*x + 26748080*x^2 + 1162960*x^3 + 25440*x^4 + 224*x^5 + 1441740832) - exp(2*x +
1)*(32542150208*x + 4191872176*x^2 + 301868192*x^3 + 13124704*x^4 + 344528*x^5 + 5056*x^6 + 32*x^7 + 10895441
4304) - exp(10*x + 5)*(353280*x + 15360*x^2 + 224*x^3 + 2725408) + 15967727460*x^2 + 1375548120*x^3 + 74525153
*x^4 + 2600280*x^5 + 57060*x^6 + 720*x^7 + 4*x^8 + exp(8*x + 4)*(13500080*x + 877700*x^2 + 25520*x^3 + 280*x^4
+ 78355480) + 313243941124), x)
________________________________________________________________________________________
sympy [B] time = 1.24, size = 88, normalized size = 2.84 \begin {gather*} \frac {x^{3}}{4 x^{4} + 360 x^{3} + 12330 x^{2} + 190440 x + \left (- 16 x - 368\right ) e^{6 x + 3} + \left (24 x^{2} + 1096 x + 12696\right ) e^{4 x + 2} + \left (- 16 x^{3} - 1088 x^{2} - 25024 x - 194672\right ) e^{2 x + 1} + 4 e^{8 x + 4} + 1119364} + \frac {x}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((2*exp(2*x+1)**8+(-16*x-368)*exp(2*x+1)**7+(56*x**2+2568*x+29624)*exp(2*x+1)**6+(-112*x**3-7680*x**2
-176640*x-1362704)*exp(2*x+1)**5+(140*x**4+12752*x**3+438853*x**2+6750040*x+39177740)*exp(2*x+1)**4+(-112*x**5
-12696*x**4-580936*x**3-13374316*x**2-154764240*x-720870416)*exp(2*x+1)**3+(56*x**6+7584*x**5+432290*x**4+1323
6768*x**3+229267542*x**2+2129030328*x+8290009784)*exp(2*x+1)**2+(-16*x**7-2520*x**6-171720*x**5-6550112*x**4-1
50849272*x**3-2096082092*x**2-16271075104*x-54477207152)*exp(2*x+1)+2*x**8+360*x**7+28529*x**6+1300140*x**5+37
265659*x**4+687869280*x**3+7984703253*x**2+53292920040*x+156621970562)/(4*exp(2*x+1)**8+(-32*x-736)*exp(2*x+1)
**7+(112*x**2+5136*x+59248)*exp(2*x+1)**6+(-224*x**3-15360*x**2-353280*x-2725408)*exp(2*x+1)**5+(280*x**4+2552
0*x**3+877700*x**2+13500080*x+78355480)*exp(2*x+1)**4+(-224*x**5-25440*x**4-1162960*x**3-26748080*x**2-3095284
80*x-1441740832)*exp(2*x+1)**3+(112*x**6+15216*x**5+866760*x**4+26497832*x**3+458516040*x**2+4258060656*x+1658
0019568)*exp(2*x+1)**2+(-32*x**7-5056*x**6-344528*x**5-13124704*x**4-301868192*x**3-4191872176*x**2-3254215020
8*x-108954414304)*exp(2*x+1)+4*x**8+720*x**7+57060*x**6+2600280*x**5+74525153*x**4+1375548120*x**3+15967727460
*x**2+106585840080*x+313243941124),x)
[Out]
x**3/(4*x**4 + 360*x**3 + 12330*x**2 + 190440*x + (-16*x - 368)*exp(6*x + 3) + (24*x**2 + 1096*x + 12696)*exp(
4*x + 2) + (-16*x**3 - 1088*x**2 - 25024*x - 194672)*exp(2*x + 1) + 4*exp(8*x + 4) + 1119364) + x/2
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