∫ −320−32x+e4294967296x4+2147483648x5+469762048x6+58720256x7+4587520x8+229376x9+7168x10+128x11+x12 (−400x−60x2−2x3−3435973836800x5−2834678415360x6−1027570925568x7−216426086400x8−29418848256x9−2702966784x10−170311680x11−7277568x12−202080x13−3296x14−24x15)_______ −4096+768e4294967296x4+2147483648x5+469762048x6+58720256x7+4587520x8+229376x9+7168x10+128x11+x12x2−48e8589934592x4+4294967296x5+939524096x6+117440512x7+9175040x8+458752x9+14336x10+256x11+2x12x4+e12884901888x4+6442450944x5+1409286144x6+176160768x7+13762560x8+688128x9+21504x10+384x11+3x12x6 dx

3.39.84 \(\int \frac {-320-32 x+e^{4294967296 x^4+2147483648 x^5+469762048 x^6+58720256 x^7+4587520 x^8+229376 x^9+7168 x^{10}+128 x^{11}+x^{12}} (-400 x-60 x^2-2 x^3-3435973836800 x^5-2834678415360 x^6-1027570925568 x^7-216426086400 x^8-29418848256 x^9-2702966784 x^{10}-170311680 x^{11}-7277568 x^{12}-202080 x^{13}-3296 x^{14}-24 x^{15})}{-4096+768 e^{4294967296 x^4+2147483648 x^5+469762048 x^6+58720256 x^7+4587520 x^8+229376 x^9+7168 x^{10}+128 x^{11}+x^{12}} x^2-48 e^{8589934592 x^4+4294967296 x^5+939524096 x^6+117440512 x^7+9175040 x^8+458752 x^9+14336 x^{10}+256 x^{11}+2 x^{12}} x^4+e^{12884901888 x^4+6442450944 x^5+1409286144 x^6+176160768 x^7+13762560 x^8+688128 x^9+21504 x^{10}+384 x^{11}+3 x^{12}} x^6} \, dx\)

Optimal. Leaf size=25 \[ \frac {(10+x)^2}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^2} \]

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Rubi [F] time = 8.25, 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 {-320-32 x+\exp \left (4294967296 x^4+2147483648 x^5+469762048 x^6+58720256 x^7+4587520 x^8+229376 x^9+7168 x^{10}+128 x^{11}+x^{12}\right ) \left (-400 x-60 x^2-2 x^3-3435973836800 x^5-2834678415360 x^6-1027570925568 x^7-216426086400 x^8-29418848256 x^9-2702966784 x^{10}-170311680 x^{11}-7277568 x^{12}-202080 x^{13}-3296 x^{14}-24 x^{15}\right )}{-4096+768 \exp \left (4294967296 x^4+2147483648 x^5+469762048 x^6+58720256 x^7+4587520 x^8+229376 x^9+7168 x^{10}+128 x^{11}+x^{12}\right ) x^2-48 \exp \left (8589934592 x^4+4294967296 x^5+939524096 x^6+117440512 x^7+9175040 x^8+458752 x^9+14336 x^{10}+256 x^{11}+2 x^{12}\right ) x^4+\exp \left (12884901888 x^4+6442450944 x^5+1409286144 x^6+176160768 x^7+13762560 x^8+688128 x^9+21504 x^{10}+384 x^{11}+3 x^{12}\right ) x^6} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[(-320 - 32*x + E^(4294967296*x^4 + 2147483648*x^5 + 469762048*x^6 + 58720256*x^7 + 4587520*x^8 + 229376*x^

9 + 7168*x^10 + 128*x^11 + x^12)*(-400*x - 60*x^2 - 2*x^3 - 3435973836800*x^5 - 2834678415360*x^6 - 1027570925

568*x^7 - 216426086400*x^8 - 29418848256*x^9 - 2702966784*x^10 - 170311680*x^11 - 7277568*x^12 - 202080*x^13 -

3296*x^14 - 24*x^15))/(-4096 + 768*E^(4294967296*x^4 + 2147483648*x^5 + 469762048*x^6 + 58720256*x^7 + 458752

0*x^8 + 229376*x^9 + 7168*x^10 + 128*x^11 + x^12)*x^2 - 48*E^(8589934592*x^4 + 4294967296*x^5 + 939524096*x^6

+ 117440512*x^7 + 9175040*x^8 + 458752*x^9 + 14336*x^10 + 256*x^11 + 2*x^12)*x^4 + E^(12884901888*x^4 + 644245

0944*x^5 + 1409286144*x^6 + 176160768*x^7 + 13762560*x^8 + 688128*x^9 + 21504*x^10 + 384*x^11 + 3*x^12)*x^6),x

]

[Out]

-1280*Defer[Int][(-16 + E^(x^4*(16 + x)^8)*x^2)^(-3), x] - 6400*Defer[Int][1/(x*(-16 + E^(x^4*(16 + x)^8)*x^2)

^3), x] - 64*Defer[Int][x/(-16 + E^(x^4*(16 + x)^8)*x^2)^3, x] - 54975581388800*Defer[Int][x^3/(-16 + E^(x^4*(

16 + x)^8)*x^2)^3, x] - 45354854645760*Defer[Int][x^4/(-16 + E^(x^4*(16 + x)^8)*x^2)^3, x] - 16441134809088*De

fer[Int][x^5/(-16 + E^(x^4*(16 + x)^8)*x^2)^3, x] - 3462817382400*Defer[Int][x^6/(-16 + E^(x^4*(16 + x)^8)*x^2

)^3, x] - 470701572096*Defer[Int][x^7/(-16 + E^(x^4*(16 + x)^8)*x^2)^3, x] - 43247468544*Defer[Int][x^8/(-16 +

E^(x^4*(16 + x)^8)*x^2)^3, x] - 2724986880*Defer[Int][x^9/(-16 + E^(x^4*(16 + x)^8)*x^2)^3, x] - 116441088*De

fer[Int][x^10/(-16 + E^(x^4*(16 + x)^8)*x^2)^3, x] - 3233280*Defer[Int][x^11/(-16 + E^(x^4*(16 + x)^8)*x^2)^3,

x] - 52736*Defer[Int][x^12/(-16 + E^(x^4*(16 + x)^8)*x^2)^3, x] - 384*Defer[Int][x^13/(-16 + E^(x^4*(16 + x)^

8)*x^2)^3, x] - 60*Defer[Int][(-16 + E^(x^4*(16 + x)^8)*x^2)^(-2), x] - 400*Defer[Int][1/(x*(-16 + E^(x^4*(16

+ x)^8)*x^2)^2), x] - 2*Defer[Int][x/(-16 + E^(x^4*(16 + x)^8)*x^2)^2, x] - 3435973836800*Defer[Int][x^3/(-16

+ E^(x^4*(16 + x)^8)*x^2)^2, x] - 2834678415360*Defer[Int][x^4/(-16 + E^(x^4*(16 + x)^8)*x^2)^2, x] - 10275709

25568*Defer[Int][x^5/(-16 + E^(x^4*(16 + x)^8)*x^2)^2, x] - 216426086400*Defer[Int][x^6/(-16 + E^(x^4*(16 + x)

^8)*x^2)^2, x] - 29418848256*Defer[Int][x^7/(-16 + E^(x^4*(16 + x)^8)*x^2)^2, x] - 2702966784*Defer[Int][x^8/(

-16 + E^(x^4*(16 + x)^8)*x^2)^2, x] - 170311680*Defer[Int][x^9/(-16 + E^(x^4*(16 + x)^8)*x^2)^2, x] - 7277568*

Defer[Int][x^10/(-16 + E^(x^4*(16 + x)^8)*x^2)^2, x] - 202080*Defer[Int][x^11/(-16 + E^(x^4*(16 + x)^8)*x^2)^2

, x] - 3296*Defer[Int][x^12/(-16 + E^(x^4*(16 + x)^8)*x^2)^2, x] - 24*Defer[Int][x^13/(-16 + E^(x^4*(16 + x)^8

)*x^2)^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 (10+x) \left (16+e^{x^4 (16+x)^8} x \left (20+x+171798691840 x^4+124554051584 x^5+38923141120 x^6+6928990208 x^7+778043392 x^8+57344000 x^9+2781184 x^{10}+85760 x^{11}+1528 x^{12}+12 x^{13}\right )\right )}{\left (16-e^{x^4 (16+x)^8} x^2\right )^3} \, dx\\ &=2 \int \frac {(10+x) \left (16+e^{x^4 (16+x)^8} x \left (20+x+171798691840 x^4+124554051584 x^5+38923141120 x^6+6928990208 x^7+778043392 x^8+57344000 x^9+2781184 x^{10}+85760 x^{11}+1528 x^{12}+12 x^{13}\right )\right )}{\left (16-e^{x^4 (16+x)^8} x^2\right )^3} \, dx\\ &=2 \int \left (-\frac {32 (10+x)^2 \left (1+8589934592 x^4+5368709120 x^5+1409286144 x^6+205520896 x^7+18350080 x^8+1032192 x^9+35840 x^{10}+704 x^{11}+6 x^{12}\right )}{x \left (-16+e^{x^4 (16+x)^8} x^2\right )^3}-\frac {200+30 x+x^2+1717986918400 x^4+1417339207680 x^5+513785462784 x^6+108213043200 x^7+14709424128 x^8+1351483392 x^9+85155840 x^{10}+3638784 x^{11}+101040 x^{12}+1648 x^{13}+12 x^{14}}{x \left (-16+e^{x^4 (16+x)^8} x^2\right )^2}\right ) \, dx\\ &=-\left (2 \int \frac {200+30 x+x^2+1717986918400 x^4+1417339207680 x^5+513785462784 x^6+108213043200 x^7+14709424128 x^8+1351483392 x^9+85155840 x^{10}+3638784 x^{11}+101040 x^{12}+1648 x^{13}+12 x^{14}}{x \left (-16+e^{x^4 (16+x)^8} x^2\right )^2} \, dx\right )-64 \int \frac {(10+x)^2 \left (1+8589934592 x^4+5368709120 x^5+1409286144 x^6+205520896 x^7+18350080 x^8+1032192 x^9+35840 x^{10}+704 x^{11}+6 x^{12}\right )}{x \left (-16+e^{x^4 (16+x)^8} x^2\right )^3} \, dx\\ &=-\left (2 \int \left (\frac {30}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^2}+\frac {200}{x \left (-16+e^{x^4 (16+x)^8} x^2\right )^2}+\frac {x}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^2}+\frac {1717986918400 x^3}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^2}+\frac {1417339207680 x^4}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^2}+\frac {513785462784 x^5}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^2}+\frac {108213043200 x^6}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^2}+\frac {14709424128 x^7}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^2}+\frac {1351483392 x^8}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^2}+\frac {85155840 x^9}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^2}+\frac {3638784 x^{10}}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^2}+\frac {101040 x^{11}}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^2}+\frac {1648 x^{12}}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^2}+\frac {12 x^{13}}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^2}\right ) \, dx\right )-64 \int \left (\frac {20}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^3}+\frac {100}{x \left (-16+e^{x^4 (16+x)^8} x^2\right )^3}+\frac {x}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^3}+\frac {858993459200 x^3}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^3}+\frac {708669603840 x^4}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^3}+\frac {256892731392 x^5}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^3}+\frac {54106521600 x^6}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^3}+\frac {7354712064 x^7}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^3}+\frac {675741696 x^8}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^3}+\frac {42577920 x^9}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^3}+\frac {1819392 x^{10}}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^3}+\frac {50520 x^{11}}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^3}+\frac {824 x^{12}}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^3}+\frac {6 x^{13}}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^3}\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A] time = 0.24, size = 25, normalized size = 1.00 \begin {gather*} \frac {(10+x)^2}{\left (-16+e^{x^4 (16+x)^8} x^2\right )^2} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(-320 - 32*x + E^(4294967296*x^4 + 2147483648*x^5 + 469762048*x^6 + 58720256*x^7 + 4587520*x^8 + 229

376*x^9 + 7168*x^10 + 128*x^11 + x^12)*(-400*x - 60*x^2 - 2*x^3 - 3435973836800*x^5 - 2834678415360*x^6 - 1027

570925568*x^7 - 216426086400*x^8 - 29418848256*x^9 - 2702966784*x^10 - 170311680*x^11 - 7277568*x^12 - 202080*

x^13 - 3296*x^14 - 24*x^15))/(-4096 + 768*E^(4294967296*x^4 + 2147483648*x^5 + 469762048*x^6 + 58720256*x^7 +

4587520*x^8 + 229376*x^9 + 7168*x^10 + 128*x^11 + x^12)*x^2 - 48*E^(8589934592*x^4 + 4294967296*x^5 + 93952409

6*x^6 + 117440512*x^7 + 9175040*x^8 + 458752*x^9 + 14336*x^10 + 256*x^11 + 2*x^12)*x^4 + E^(12884901888*x^4 +

6442450944*x^5 + 1409286144*x^6 + 176160768*x^7 + 13762560*x^8 + 688128*x^9 + 21504*x^10 + 384*x^11 + 3*x^12)*

x^6),x]

[Out]

(10 + x)^2/(-16 + E^(x^4*(16 + x)^8)*x^2)^2

________________________________________________________________________________________

fricas [B] time = 0.84, size = 114, normalized size = 4.56 \begin {gather*} \frac {x^{2} + 20 \, x + 100}{x^{4} e^{\left (2 \, x^{12} + 256 \, x^{11} + 14336 \, x^{10} + 458752 \, x^{9} + 9175040 \, x^{8} + 117440512 \, x^{7} + 939524096 \, x^{6} + 4294967296 \, x^{5} + 8589934592 \, x^{4}\right )} - 32 \, x^{2} e^{\left (x^{12} + 128 \, x^{11} + 7168 \, x^{10} + 229376 \, x^{9} + 4587520 \, x^{8} + 58720256 \, x^{7} + 469762048 \, x^{6} + 2147483648 \, x^{5} + 4294967296 \, x^{4}\right )} + 256} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-24*x^15-3296*x^14-202080*x^13-7277568*x^12-170311680*x^11-2702966784*x^10-29418848256*x^9-2164260

86400*x^8-1027570925568*x^7-2834678415360*x^6-3435973836800*x^5-2*x^3-60*x^2-400*x)*exp(x^12+128*x^11+7168*x^1

0+229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)-32*x-320)/(x^6*exp(x^12+128

*x^11+7168*x^10+229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)^3-48*x^4*exp(

x^12+128*x^11+7168*x^10+229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)^2+768

*x^2*exp(x^12+128*x^11+7168*x^10+229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x

^4)-4096),x, algorithm="fricas")

[Out]

(x^2 + 20*x + 100)/(x^4*e^(2*x^12 + 256*x^11 + 14336*x^10 + 458752*x^9 + 9175040*x^8 + 117440512*x^7 + 9395240

96*x^6 + 4294967296*x^5 + 8589934592*x^4) - 32*x^2*e^(x^12 + 128*x^11 + 7168*x^10 + 229376*x^9 + 4587520*x^8 +

58720256*x^7 + 469762048*x^6 + 2147483648*x^5 + 4294967296*x^4) + 256)

________________________________________________________________________________________

giac [B] time = 1.08, size = 114, normalized size = 4.56 \begin {gather*} \frac {x^{2} + 20 \, x + 100}{x^{4} e^{\left (2 \, x^{12} + 256 \, x^{11} + 14336 \, x^{10} + 458752 \, x^{9} + 9175040 \, x^{8} + 117440512 \, x^{7} + 939524096 \, x^{6} + 4294967296 \, x^{5} + 8589934592 \, x^{4}\right )} - 32 \, x^{2} e^{\left (x^{12} + 128 \, x^{11} + 7168 \, x^{10} + 229376 \, x^{9} + 4587520 \, x^{8} + 58720256 \, x^{7} + 469762048 \, x^{6} + 2147483648 \, x^{5} + 4294967296 \, x^{4}\right )} + 256} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-24*x^15-3296*x^14-202080*x^13-7277568*x^12-170311680*x^11-2702966784*x^10-29418848256*x^9-2164260

86400*x^8-1027570925568*x^7-2834678415360*x^6-3435973836800*x^5-2*x^3-60*x^2-400*x)*exp(x^12+128*x^11+7168*x^1

0+229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)-32*x-320)/(x^6*exp(x^12+128

*x^11+7168*x^10+229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)^3-48*x^4*exp(

x^12+128*x^11+7168*x^10+229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)^2+768

*x^2*exp(x^12+128*x^11+7168*x^10+229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x

^4)-4096),x, algorithm="giac")

[Out]

(x^2 + 20*x + 100)/(x^4*e^(2*x^12 + 256*x^11 + 14336*x^10 + 458752*x^9 + 9175040*x^8 + 117440512*x^7 + 9395240

96*x^6 + 4294967296*x^5 + 8589934592*x^4) - 32*x^2*e^(x^12 + 128*x^11 + 7168*x^10 + 229376*x^9 + 4587520*x^8 +

58720256*x^7 + 469762048*x^6 + 2147483648*x^5 + 4294967296*x^4) + 256)

________________________________________________________________________________________

maple [F(-1)] time = 180.00, size = 0, normalized size = 0.00 hanged

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((-24*x^15-3296*x^14-202080*x^13-7277568*x^12-170311680*x^11-2702966784*x^10-29418848256*x^9-216426086400*

x^8-1027570925568*x^7-2834678415360*x^6-3435973836800*x^5-2*x^3-60*x^2-400*x)*exp(x^12+128*x^11+7168*x^10+2293

76*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)-32*x-320)/(x^6*exp(x^12+128*x^11+

7168*x^10+229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)^3-48*x^4*exp(x^12+1

28*x^11+7168*x^10+229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)^2+768*x^2*e

xp(x^12+128*x^11+7168*x^10+229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)-40

96),x,method=_RETURNVERBOSE)

[Out]

int(((-24*x^15-3296*x^14-202080*x^13-7277568*x^12-170311680*x^11-2702966784*x^10-29418848256*x^9-216426086400*

x^8-1027570925568*x^7-2834678415360*x^6-3435973836800*x^5-2*x^3-60*x^2-400*x)*exp(x^12+128*x^11+7168*x^10+2293

76*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)-32*x-320)/(x^6*exp(x^12+128*x^11+

7168*x^10+229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)^3-48*x^4*exp(x^12+1

28*x^11+7168*x^10+229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)^2+768*x^2*e

xp(x^12+128*x^11+7168*x^10+229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)-40

96),x,method=_RETURNVERBOSE)

________________________________________________________________________________________

maxima [B] time = 0.49, size = 114, normalized size = 4.56 \begin {gather*} \frac {x^{2} + 20 \, x + 100}{x^{4} e^{\left (2 \, x^{12} + 256 \, x^{11} + 14336 \, x^{10} + 458752 \, x^{9} + 9175040 \, x^{8} + 117440512 \, x^{7} + 939524096 \, x^{6} + 4294967296 \, x^{5} + 8589934592 \, x^{4}\right )} - 32 \, x^{2} e^{\left (x^{12} + 128 \, x^{11} + 7168 \, x^{10} + 229376 \, x^{9} + 4587520 \, x^{8} + 58720256 \, x^{7} + 469762048 \, x^{6} + 2147483648 \, x^{5} + 4294967296 \, x^{4}\right )} + 256} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-24*x^15-3296*x^14-202080*x^13-7277568*x^12-170311680*x^11-2702966784*x^10-29418848256*x^9-2164260

86400*x^8-1027570925568*x^7-2834678415360*x^6-3435973836800*x^5-2*x^3-60*x^2-400*x)*exp(x^12+128*x^11+7168*x^1

0+229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)-32*x-320)/(x^6*exp(x^12+128

*x^11+7168*x^10+229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)^3-48*x^4*exp(

x^12+128*x^11+7168*x^10+229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x^4)^2+768

*x^2*exp(x^12+128*x^11+7168*x^10+229376*x^9+4587520*x^8+58720256*x^7+469762048*x^6+2147483648*x^5+4294967296*x

^4)-4096),x, algorithm="maxima")

[Out]

(x^2 + 20*x + 100)/(x^4*e^(2*x^12 + 256*x^11 + 14336*x^10 + 458752*x^9 + 9175040*x^8 + 117440512*x^7 + 9395240

96*x^6 + 4294967296*x^5 + 8589934592*x^4) - 32*x^2*e^(x^12 + 128*x^11 + 7168*x^10 + 229376*x^9 + 4587520*x^8 +

58720256*x^7 + 469762048*x^6 + 2147483648*x^5 + 4294967296*x^4) + 256)

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mupad [B] time = 2.87, size = 114, normalized size = 4.56 \begin {gather*} \frac {x^2+20\,x+100}{x^4\,{\mathrm {e}}^{2\,x^{12}+256\,x^{11}+14336\,x^{10}+458752\,x^9+9175040\,x^8+117440512\,x^7+939524096\,x^6+4294967296\,x^5+8589934592\,x^4}-32\,x^2\,{\mathrm {e}}^{x^{12}+128\,x^{11}+7168\,x^{10}+229376\,x^9+4587520\,x^8+58720256\,x^7+469762048\,x^6+2147483648\,x^5+4294967296\,x^4}+256} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((32*x + exp(4294967296*x^4 + 2147483648*x^5 + 469762048*x^6 + 58720256*x^7 + 4587520*x^8 + 229376*x^9 + 71

68*x^10 + 128*x^11 + x^12)*(400*x + 60*x^2 + 2*x^3 + 3435973836800*x^5 + 2834678415360*x^6 + 1027570925568*x^7

+ 216426086400*x^8 + 29418848256*x^9 + 2702966784*x^10 + 170311680*x^11 + 7277568*x^12 + 202080*x^13 + 3296*x

^14 + 24*x^15) + 320)/(48*x^4*exp(8589934592*x^4 + 4294967296*x^5 + 939524096*x^6 + 117440512*x^7 + 9175040*x^

8 + 458752*x^9 + 14336*x^10 + 256*x^11 + 2*x^12) - 768*x^2*exp(4294967296*x^4 + 2147483648*x^5 + 469762048*x^6

+ 58720256*x^7 + 4587520*x^8 + 229376*x^9 + 7168*x^10 + 128*x^11 + x^12) - x^6*exp(12884901888*x^4 + 64424509

44*x^5 + 1409286144*x^6 + 176160768*x^7 + 13762560*x^8 + 688128*x^9 + 21504*x^10 + 384*x^11 + 3*x^12) + 4096),

[Out]

(20*x + x^2 + 100)/(x^4*exp(8589934592*x^4 + 4294967296*x^5 + 939524096*x^6 + 117440512*x^7 + 9175040*x^8 + 45

8752*x^9 + 14336*x^10 + 256*x^11 + 2*x^12) - 32*x^2*exp(4294967296*x^4 + 2147483648*x^5 + 469762048*x^6 + 5872

0256*x^7 + 4587520*x^8 + 229376*x^9 + 7168*x^10 + 128*x^11 + x^12) + 256)

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sympy [B] time = 0.60, size = 110, normalized size = 4.40 \begin {gather*} \frac {x^{2} + 20 x + 100}{x^{4} e^{2 x^{12} + 256 x^{11} + 14336 x^{10} + 458752 x^{9} + 9175040 x^{8} + 117440512 x^{7} + 939524096 x^{6} + 4294967296 x^{5} + 8589934592 x^{4}} - 32 x^{2} e^{x^{12} + 128 x^{11} + 7168 x^{10} + 229376 x^{9} + 4587520 x^{8} + 58720256 x^{7} + 469762048 x^{6} + 2147483648 x^{5} + 4294967296 x^{4}} + 256} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-24*x**15-3296*x**14-202080*x**13-7277568*x**12-170311680*x**11-2702966784*x**10-29418848256*x**9-

216426086400*x**8-1027570925568*x**7-2834678415360*x**6-3435973836800*x**5-2*x**3-60*x**2-400*x)*exp(x**12+128

*x**11+7168*x**10+229376*x**9+4587520*x**8+58720256*x**7+469762048*x**6+2147483648*x**5+4294967296*x**4)-32*x-

320)/(x**6*exp(x**12+128*x**11+7168*x**10+229376*x**9+4587520*x**8+58720256*x**7+469762048*x**6+2147483648*x**

5+4294967296*x**4)**3-48*x**4*exp(x**12+128*x**11+7168*x**10+229376*x**9+4587520*x**8+58720256*x**7+469762048*

x**6+2147483648*x**5+4294967296*x**4)**2+768*x**2*exp(x**12+128*x**11+7168*x**10+229376*x**9+4587520*x**8+5872

0256*x**7+469762048*x**6+2147483648*x**5+4294967296*x**4)-4096),x)

[Out]

(x**2 + 20*x + 100)/(x**4*exp(2*x**12 + 256*x**11 + 14336*x**10 + 458752*x**9 + 9175040*x**8 + 117440512*x**7

+ 939524096*x**6 + 4294967296*x**5 + 8589934592*x**4) - 32*x**2*exp(x**12 + 128*x**11 + 7168*x**10 + 229376*x*

*9 + 4587520*x**8 + 58720256*x**7 + 469762048*x**6 + 2147483648*x**5 + 4294967296*x**4) + 256)

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