∫ e2(−198x−558x2−18x3+288x4−72x5+e2x(−50x2−10x3+32x4−8x5)+ex(60x+336x2+36x3−192x4+48x5)) _____________________________________________________________________________________________________________________________________________ 9+90x+189x2−180x3+36x4+ex(−30x−138x2+120x3−24x4)+e2x(25x2−20x3+4x4) (−1188−756x−7452x2−7020x3+14904x4−6480x5+864x6+ex(360+612x+5040x2+9180x3−15336x4+6480x5−864x6)+e3x(500x3−600x4+240x5−32x6)+e2x(−900x2−3780x3+5256x4−2160x5+288x6)) ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________27+405x+1863x2 +1755x3 −3726x4 +1620x5 −216x6 +e2x (225x2 +945x3 −1314x4 +540x5 −72x6 )+e3x (−125x3 +150x4 −60x5 +8x6 )+ex (−135x−1296x2 −2295x3 +3834x4 −1620x5 +216x6 ) dx

3.94.27 \(\int \frac {e^{\frac {2 (-198 x-558 x^2-18 x^3+288 x^4-72 x^5+e^{2 x} (-50 x^2-10 x^3+32 x^4-8 x^5)+e^x (60 x+336 x^2+36 x^3-192 x^4+48 x^5))}{9+90 x+189 x^2-180 x^3+36 x^4+e^x (-30 x-138 x^2+120 x^3-24 x^4)+e^{2 x} (25 x^2-20 x^3+4 x^4)}} (-1188-756 x-7452 x^2-7020 x^3+14904 x^4-6480 x^5+864 x^6+e^x (360+612 x+5040 x^2+9180 x^3-15336 x^4+6480 x^5-864 x^6)+e^{3 x} (500 x^3-600 x^4+240 x^5-32 x^6)+e^{2 x} (-900 x^2-3780 x^3+5256 x^4-2160 x^5+288 x^6))}{27+405 x+1863 x^2+1755 x^3-3726 x^4+1620 x^5-216 x^6+e^{2 x} (225 x^2+945 x^3-1314 x^4+540 x^5-72 x^6)+e^{3 x} (-125 x^3+150 x^4-60 x^5+8 x^6)+e^x (-135 x-1296 x^2-2295 x^3+3834 x^4-1620 x^5+216 x^6)} \, dx\)

Optimal. Leaf size=30 \[ e^{-4+4 \left (-x+\frac {9}{\left (-3+\left (3-e^x\right ) x (-5+2 x)\right )^2}\right )} \]

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Rubi [F] time = 90.99, 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 {\exp \left (\frac {2 \left (-198 x-558 x^2-18 x^3+288 x^4-72 x^5+e^{2 x} \left (-50 x^2-10 x^3+32 x^4-8 x^5\right )+e^x \left (60 x+336 x^2+36 x^3-192 x^4+48 x^5\right )\right )}{9+90 x+189 x^2-180 x^3+36 x^4+e^x \left (-30 x-138 x^2+120 x^3-24 x^4\right )+e^{2 x} \left (25 x^2-20 x^3+4 x^4\right )}\right ) \left (-1188-756 x-7452 x^2-7020 x^3+14904 x^4-6480 x^5+864 x^6+e^x \left (360+612 x+5040 x^2+9180 x^3-15336 x^4+6480 x^5-864 x^6\right )+e^{3 x} \left (500 x^3-600 x^4+240 x^5-32 x^6\right )+e^{2 x} \left (-900 x^2-3780 x^3+5256 x^4-2160 x^5+288 x^6\right )\right )}{27+405 x+1863 x^2+1755 x^3-3726 x^4+1620 x^5-216 x^6+e^{2 x} \left (225 x^2+945 x^3-1314 x^4+540 x^5-72 x^6\right )+e^{3 x} \left (-125 x^3+150 x^4-60 x^5+8 x^6\right )+e^x \left (-135 x-1296 x^2-2295 x^3+3834 x^4-1620 x^5+216 x^6\right )} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[(E^((2*(-198*x - 558*x^2 - 18*x^3 + 288*x^4 - 72*x^5 + E^(2*x)*(-50*x^2 - 10*x^3 + 32*x^4 - 8*x^5) + E^x*(

60*x + 336*x^2 + 36*x^3 - 192*x^4 + 48*x^5)))/(9 + 90*x + 189*x^2 - 180*x^3 + 36*x^4 + E^x*(-30*x - 138*x^2 +

120*x^3 - 24*x^4) + E^(2*x)*(25*x^2 - 20*x^3 + 4*x^4)))*(-1188 - 756*x - 7452*x^2 - 7020*x^3 + 14904*x^4 - 648

0*x^5 + 864*x^6 + E^x*(360 + 612*x + 5040*x^2 + 9180*x^3 - 15336*x^4 + 6480*x^5 - 864*x^6) + E^(3*x)*(500*x^3

- 600*x^4 + 240*x^5 - 32*x^6) + E^(2*x)*(-900*x^2 - 3780*x^3 + 5256*x^4 - 2160*x^5 + 288*x^6)))/(27 + 405*x +

1863*x^2 + 1755*x^3 - 3726*x^4 + 1620*x^5 - 216*x^6 + E^(2*x)*(225*x^2 + 945*x^3 - 1314*x^4 + 540*x^5 - 72*x^6

) + E^(3*x)*(-125*x^3 + 150*x^4 - 60*x^5 + 8*x^6) + E^x*(-135*x - 1296*x^2 - 2295*x^3 + 3834*x^4 - 1620*x^5 +

216*x^6)),x]

[Out]

-4*Defer[Int][E^((-4*x*(E^(2*x)*(5 - 2*x)^2*x*(1 + x) + 9*(11 + 31*x + x^2 - 16*x^3 + 4*x^4) - 6*E^x*(5 + 28*x

+ 3*x^2 - 16*x^3 + 4*x^4)))/(3 - 5*(-3 + E^x)*x + 2*(-3 + E^x)*x^2)^2), x] + 216*Defer[Int][1/(E^((4*x*(E^(2*

x)*(5 - 2*x)^2*x*(1 + x) + 9*(11 + 31*x + x^2 - 16*x^3 + 4*x^4) - 6*E^x*(5 + 28*x + 3*x^2 - 16*x^3 + 4*x^4)))/

(3 - 5*(-3 + E^x)*x + 2*(-3 + E^x)*x^2)^2)*(3 + 15*x - 5*E^x*x - 6*x^2 + 2*E^x*x^2)^3), x] + 216*Defer[Int][1/

(E^((4*x*(E^(2*x)*(5 - 2*x)^2*x*(1 + x) + 9*(11 + 31*x + x^2 - 16*x^3 + 4*x^4) - 6*E^x*(5 + 28*x + 3*x^2 - 16*

x^3 + 4*x^4)))/(3 - 5*(-3 + E^x)*x + 2*(-3 + E^x)*x^2)^2)*x*(3 + 15*x - 5*E^x*x - 6*x^2 + 2*E^x*x^2)^3), x] +

1080*Defer[Int][x/(E^((4*x*(E^(2*x)*(5 - 2*x)^2*x*(1 + x) + 9*(11 + 31*x + x^2 - 16*x^3 + 4*x^4) - 6*E^x*(5 +

28*x + 3*x^2 - 16*x^3 + 4*x^4)))/(3 - 5*(-3 + E^x)*x + 2*(-3 + E^x)*x^2)^2)*(3 + 15*x - 5*E^x*x - 6*x^2 + 2*E^

x*x^2)^3), x] - 432*Defer[Int][x^2/(E^((4*x*(E^(2*x)*(5 - 2*x)^2*x*(1 + x) + 9*(11 + 31*x + x^2 - 16*x^3 + 4*x

^4) - 6*E^x*(5 + 28*x + 3*x^2 - 16*x^3 + 4*x^4)))/(3 - 5*(-3 + E^x)*x + 2*(-3 + E^x)*x^2)^2)*(3 + 15*x - 5*E^x

*x - 6*x^2 + 2*E^x*x^2)^3), x] + 432*Defer[Int][1/(E^((4*x*(E^(2*x)*(5 - 2*x)^2*x*(1 + x) + 9*(11 + 31*x + x^2

- 16*x^3 + 4*x^4) - 6*E^x*(5 + 28*x + 3*x^2 - 16*x^3 + 4*x^4)))/(3 - 5*(-3 + E^x)*x + 2*(-3 + E^x)*x^2)^2)*(-

5 + 2*x)*(3 + 15*x - 5*E^x*x - 6*x^2 + 2*E^x*x^2)^3), x] - 72*Defer[Int][1/(E^((4*x*(E^(2*x)*(5 - 2*x)^2*x*(1

+ x) + 9*(11 + 31*x + x^2 - 16*x^3 + 4*x^4) - 6*E^x*(5 + 28*x + 3*x^2 - 16*x^3 + 4*x^4)))/(3 - 5*(-3 + E^x)*x

+ 2*(-3 + E^x)*x^2)^2)*(3 + 15*x - 5*E^x*x - 6*x^2 + 2*E^x*x^2)^2), x] - 72*Defer[Int][1/(E^((4*x*(E^(2*x)*(5

- 2*x)^2*x*(1 + x) + 9*(11 + 31*x + x^2 - 16*x^3 + 4*x^4) - 6*E^x*(5 + 28*x + 3*x^2 - 16*x^3 + 4*x^4)))/(3 - 5

*(-3 + E^x)*x + 2*(-3 + E^x)*x^2)^2)*x*(3 + 15*x - 5*E^x*x - 6*x^2 + 2*E^x*x^2)^2), x] - 144*Defer[Int][1/(E^(

(4*x*(E^(2*x)*(5 - 2*x)^2*x*(1 + x) + 9*(11 + 31*x + x^2 - 16*x^3 + 4*x^4) - 6*E^x*(5 + 28*x + 3*x^2 - 16*x^3

+ 4*x^4)))/(3 - 5*(-3 + E^x)*x + 2*(-3 + E^x)*x^2)^2)*(-5 + 2*x)*(3 + 15*x - 5*E^x*x - 6*x^2 + 2*E^x*x^2)^2),

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 \exp \left (-\frac {4 x \left (e^{2 x} (5-2 x)^2 x (1+x)+9 \left (11+31 x+x^2-16 x^3+4 x^4\right )-6 e^x \left (5+28 x+3 x^2-16 x^3+4 x^4\right )\right )}{\left (3-5 \left (-3+e^x\right ) x+2 \left (-3+e^x\right ) x^2\right )^2}\right ) \left (-e^{3 x} x^3 (-5+2 x)^3+9 e^{2 x} (5-2 x)^2 x^2 \left (-1-5 x+2 x^2\right )+27 \left (-11-7 x-69 x^2-65 x^3+138 x^4-60 x^5+8 x^6\right )-9 e^x \left (-10-17 x-140 x^2-255 x^3+426 x^4-180 x^5+24 x^6\right )\right )}{\left (3-5 \left (-3+e^x\right ) x+2 \left (-3+e^x\right ) x^2\right )^3} \, dx\\ &=4 \int \frac {\exp \left (-\frac {4 x \left (e^{2 x} (5-2 x)^2 x (1+x)+9 \left (11+31 x+x^2-16 x^3+4 x^4\right )-6 e^x \left (5+28 x+3 x^2-16 x^3+4 x^4\right )\right )}{\left (3-5 \left (-3+e^x\right ) x+2 \left (-3+e^x\right ) x^2\right )^2}\right ) \left (-e^{3 x} x^3 (-5+2 x)^3+9 e^{2 x} (5-2 x)^2 x^2 \left (-1-5 x+2 x^2\right )+27 \left (-11-7 x-69 x^2-65 x^3+138 x^4-60 x^5+8 x^6\right )-9 e^x \left (-10-17 x-140 x^2-255 x^3+426 x^4-180 x^5+24 x^6\right )\right )}{\left (3-5 \left (-3+e^x\right ) x+2 \left (-3+e^x\right ) x^2\right )^3} \, dx\\ &=4 \int \left (-\exp \left (-\frac {4 x \left (e^{2 x} (5-2 x)^2 x (1+x)+9 \left (11+31 x+x^2-16 x^3+4 x^4\right )-6 e^x \left (5+28 x+3 x^2-16 x^3+4 x^4\right )\right )}{\left (3-5 \left (-3+e^x\right ) x+2 \left (-3+e^x\right ) x^2\right )^2}\right )-\frac {18 \exp \left (-\frac {4 x \left (e^{2 x} (5-2 x)^2 x (1+x)+9 \left (11+31 x+x^2-16 x^3+4 x^4\right )-6 e^x \left (5+28 x+3 x^2-16 x^3+4 x^4\right )\right )}{\left (3-5 \left (-3+e^x\right ) x+2 \left (-3+e^x\right ) x^2\right )^2}\right ) \left (-5-x+2 x^2\right )}{x (-5+2 x) \left (3+15 x-5 e^x x-6 x^2+2 e^x x^2\right )^2}-\frac {54 \exp \left (-\frac {4 x \left (e^{2 x} (5-2 x)^2 x (1+x)+9 \left (11+31 x+x^2-16 x^3+4 x^4\right )-6 e^x \left (5+28 x+3 x^2-16 x^3+4 x^4\right )\right )}{\left (3-5 \left (-3+e^x\right ) x+2 \left (-3+e^x\right ) x^2\right )^2}\right ) \left (5+x+23 x^2-20 x^3+4 x^4\right )}{x (-5+2 x) \left (3+15 x-5 e^x x-6 x^2+2 e^x x^2\right )^3}\right ) \, dx\\ &=-\left (4 \int \exp \left (-\frac {4 x \left (e^{2 x} (5-2 x)^2 x (1+x)+9 \left (11+31 x+x^2-16 x^3+4 x^4\right )-6 e^x \left (5+28 x+3 x^2-16 x^3+4 x^4\right )\right )}{\left (3-5 \left (-3+e^x\right ) x+2 \left (-3+e^x\right ) x^2\right )^2}\right ) \, dx\right )-72 \int \frac {\exp \left (-\frac {4 x \left (e^{2 x} (5-2 x)^2 x (1+x)+9 \left (11+31 x+x^2-16 x^3+4 x^4\right )-6 e^x \left (5+28 x+3 x^2-16 x^3+4 x^4\right )\right )}{\left (3-5 \left (-3+e^x\right ) x+2 \left (-3+e^x\right ) x^2\right )^2}\right ) \left (-5-x+2 x^2\right )}{x (-5+2 x) \left (3+15 x-5 e^x x-6 x^2+2 e^x x^2\right )^2} \, dx-216 \int \frac {\exp \left (-\frac {4 x \left (e^{2 x} (5-2 x)^2 x (1+x)+9 \left (11+31 x+x^2-16 x^3+4 x^4\right )-6 e^x \left (5+28 x+3 x^2-16 x^3+4 x^4\right )\right )}{\left (3-5 \left (-3+e^x\right ) x+2 \left (-3+e^x\right ) x^2\right )^2}\right ) \left (5+x+23 x^2-20 x^3+4 x^4\right )}{x (-5+2 x) \left (3+15 x-5 e^x x-6 x^2+2 e^x x^2\right )^3} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A] time = 0.44, size = 31, normalized size = 1.03 \begin {gather*} e^{-4-4 x+\frac {36}{\left (3-5 \left (-3+e^x\right ) x+2 \left (-3+e^x\right ) x^2\right )^2}} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(E^((2*(-198*x - 558*x^2 - 18*x^3 + 288*x^4 - 72*x^5 + E^(2*x)*(-50*x^2 - 10*x^3 + 32*x^4 - 8*x^5) +

E^x*(60*x + 336*x^2 + 36*x^3 - 192*x^4 + 48*x^5)))/(9 + 90*x + 189*x^2 - 180*x^3 + 36*x^4 + E^x*(-30*x - 138*

x^2 + 120*x^3 - 24*x^4) + E^(2*x)*(25*x^2 - 20*x^3 + 4*x^4)))*(-1188 - 756*x - 7452*x^2 - 7020*x^3 + 14904*x^4

- 6480*x^5 + 864*x^6 + E^x*(360 + 612*x + 5040*x^2 + 9180*x^3 - 15336*x^4 + 6480*x^5 - 864*x^6) + E^(3*x)*(50

0*x^3 - 600*x^4 + 240*x^5 - 32*x^6) + E^(2*x)*(-900*x^2 - 3780*x^3 + 5256*x^4 - 2160*x^5 + 288*x^6)))/(27 + 40

5*x + 1863*x^2 + 1755*x^3 - 3726*x^4 + 1620*x^5 - 216*x^6 + E^(2*x)*(225*x^2 + 945*x^3 - 1314*x^4 + 540*x^5 -

72*x^6) + E^(3*x)*(-125*x^3 + 150*x^4 - 60*x^5 + 8*x^6) + E^x*(-135*x - 1296*x^2 - 2295*x^3 + 3834*x^4 - 1620*

x^5 + 216*x^6)),x]

[Out]

E^(-4 - 4*x + 36/(3 - 5*(-3 + E^x)*x + 2*(-3 + E^x)*x^2)^2)

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fricas [B] time = 0.83, size = 147, normalized size = 4.90 \begin {gather*} e^{\left (-\frac {4 \, {\left (36 \, x^{5} - 144 \, x^{4} + 9 \, x^{3} + 279 \, x^{2} + {\left (4 \, x^{5} - 16 \, x^{4} + 5 \, x^{3} + 25 \, x^{2}\right )} e^{\left (2 \, x\right )} - 6 \, {\left (4 \, x^{5} - 16 \, x^{4} + 3 \, x^{3} + 28 \, x^{2} + 5 \, x\right )} e^{x} + 99 \, x\right )}}{36 \, x^{4} - 180 \, x^{3} + 189 \, x^{2} + {\left (4 \, x^{4} - 20 \, x^{3} + 25 \, x^{2}\right )} e^{\left (2 \, x\right )} - 6 \, {\left (4 \, x^{4} - 20 \, x^{3} + 23 \, x^{2} + 5 \, x\right )} e^{x} + 90 \, x + 9}\right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-32*x^6+240*x^5-600*x^4+500*x^3)*exp(x)^3+(288*x^6-2160*x^5+5256*x^4-3780*x^3-900*x^2)*exp(x)^2+(-

864*x^6+6480*x^5-15336*x^4+9180*x^3+5040*x^2+612*x+360)*exp(x)+864*x^6-6480*x^5+14904*x^4-7020*x^3-7452*x^2-75

6*x-1188)*exp(((-8*x^5+32*x^4-10*x^3-50*x^2)*exp(x)^2+(48*x^5-192*x^4+36*x^3+336*x^2+60*x)*exp(x)-72*x^5+288*x

^4-18*x^3-558*x^2-198*x)/((4*x^4-20*x^3+25*x^2)*exp(x)^2+(-24*x^4+120*x^3-138*x^2-30*x)*exp(x)+36*x^4-180*x^3+

189*x^2+90*x+9))^2/((8*x^6-60*x^5+150*x^4-125*x^3)*exp(x)^3+(-72*x^6+540*x^5-1314*x^4+945*x^3+225*x^2)*exp(x)^

2+(216*x^6-1620*x^5+3834*x^4-2295*x^3-1296*x^2-135*x)*exp(x)-216*x^6+1620*x^5-3726*x^4+1755*x^3+1863*x^2+405*x

+27),x, algorithm="fricas")

[Out]

e^(-4*(36*x^5 - 144*x^4 + 9*x^3 + 279*x^2 + (4*x^5 - 16*x^4 + 5*x^3 + 25*x^2)*e^(2*x) - 6*(4*x^5 - 16*x^4 + 3*

x^3 + 28*x^2 + 5*x)*e^x + 99*x)/(36*x^4 - 180*x^3 + 189*x^2 + (4*x^4 - 20*x^3 + 25*x^2)*e^(2*x) - 6*(4*x^4 - 2

0*x^3 + 23*x^2 + 5*x)*e^x + 90*x + 9))

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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-32*x^6+240*x^5-600*x^4+500*x^3)*exp(x)^3+(288*x^6-2160*x^5+5256*x^4-3780*x^3-900*x^2)*exp(x)^2+(-

864*x^6+6480*x^5-15336*x^4+9180*x^3+5040*x^2+612*x+360)*exp(x)+864*x^6-6480*x^5+14904*x^4-7020*x^3-7452*x^2-75

6*x-1188)*exp(((-8*x^5+32*x^4-10*x^3-50*x^2)*exp(x)^2+(48*x^5-192*x^4+36*x^3+336*x^2+60*x)*exp(x)-72*x^5+288*x

^4-18*x^3-558*x^2-198*x)/((4*x^4-20*x^3+25*x^2)*exp(x)^2+(-24*x^4+120*x^3-138*x^2-30*x)*exp(x)+36*x^4-180*x^3+

189*x^2+90*x+9))^2/((8*x^6-60*x^5+150*x^4-125*x^3)*exp(x)^3+(-72*x^6+540*x^5-1314*x^4+945*x^3+225*x^2)*exp(x)^

2+(216*x^6-1620*x^5+3834*x^4-2295*x^3-1296*x^2-135*x)*exp(x)-216*x^6+1620*x^5-3726*x^4+1755*x^3+1863*x^2+405*x

+27),x, algorithm="giac")

[Out]

Timed out

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maple [F] time = 4.74, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (-32 x^{6}+240 x^{5}-600 x^{4}+500 x^{3}\right ) {\mathrm e}^{3 x}+\left (288 x^{6}-2160 x^{5}+5256 x^{4}-3780 x^{3}-900 x^{2}\right ) {\mathrm e}^{2 x}+\left (-864 x^{6}+6480 x^{5}-15336 x^{4}+9180 x^{3}+5040 x^{2}+612 x +360\right ) {\mathrm e}^{x}+864 x^{6}-6480 x^{5}+14904 x^{4}-7020 x^{3}-7452 x^{2}-756 x -1188\right ) {\mathrm e}^{\frac {2 \left (-8 x^{5}+32 x^{4}-10 x^{3}-50 x^{2}\right ) {\mathrm e}^{2 x}+2 \left (48 x^{5}-192 x^{4}+36 x^{3}+336 x^{2}+60 x \right ) {\mathrm e}^{x}-144 x^{5}+576 x^{4}-36 x^{3}-1116 x^{2}-396 x}{\left (4 x^{4}-20 x^{3}+25 x^{2}\right ) {\mathrm e}^{2 x}+\left (-24 x^{4}+120 x^{3}-138 x^{2}-30 x \right ) {\mathrm e}^{x}+36 x^{4}-180 x^{3}+189 x^{2}+90 x +9}}}{\left (8 x^{6}-60 x^{5}+150 x^{4}-125 x^{3}\right ) {\mathrm e}^{3 x}+\left (-72 x^{6}+540 x^{5}-1314 x^{4}+945 x^{3}+225 x^{2}\right ) {\mathrm e}^{2 x}+\left (216 x^{6}-1620 x^{5}+3834 x^{4}-2295 x^{3}-1296 x^{2}-135 x \right ) {\mathrm e}^{x}-216 x^{6}+1620 x^{5}-3726 x^{4}+1755 x^{3}+1863 x^{2}+405 x +27}\, dx\]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((-32*x^6+240*x^5-600*x^4+500*x^3)*exp(x)^3+(288*x^6-2160*x^5+5256*x^4-3780*x^3-900*x^2)*exp(x)^2+(-864*x^

6+6480*x^5-15336*x^4+9180*x^3+5040*x^2+612*x+360)*exp(x)+864*x^6-6480*x^5+14904*x^4-7020*x^3-7452*x^2-756*x-11

88)*exp(((-8*x^5+32*x^4-10*x^3-50*x^2)*exp(x)^2+(48*x^5-192*x^4+36*x^3+336*x^2+60*x)*exp(x)-72*x^5+288*x^4-18*

x^3-558*x^2-198*x)/((4*x^4-20*x^3+25*x^2)*exp(x)^2+(-24*x^4+120*x^3-138*x^2-30*x)*exp(x)+36*x^4-180*x^3+189*x^

2+90*x+9))^2/((8*x^6-60*x^5+150*x^4-125*x^3)*exp(x)^3+(-72*x^6+540*x^5-1314*x^4+945*x^3+225*x^2)*exp(x)^2+(216

*x^6-1620*x^5+3834*x^4-2295*x^3-1296*x^2-135*x)*exp(x)-216*x^6+1620*x^5-3726*x^4+1755*x^3+1863*x^2+405*x+27),x

)

[Out]

int(((-32*x^6+240*x^5-600*x^4+500*x^3)*exp(x)^3+(288*x^6-2160*x^5+5256*x^4-3780*x^3-900*x^2)*exp(x)^2+(-864*x^

6+6480*x^5-15336*x^4+9180*x^3+5040*x^2+612*x+360)*exp(x)+864*x^6-6480*x^5+14904*x^4-7020*x^3-7452*x^2-756*x-11

88)*exp(((-8*x^5+32*x^4-10*x^3-50*x^2)*exp(x)^2+(48*x^5-192*x^4+36*x^3+336*x^2+60*x)*exp(x)-72*x^5+288*x^4-18*

x^3-558*x^2-198*x)/((4*x^4-20*x^3+25*x^2)*exp(x)^2+(-24*x^4+120*x^3-138*x^2-30*x)*exp(x)+36*x^4-180*x^3+189*x^

2+90*x+9))^2/((8*x^6-60*x^5+150*x^4-125*x^3)*exp(x)^3+(-72*x^6+540*x^5-1314*x^4+945*x^3+225*x^2)*exp(x)^2+(216

*x^6-1620*x^5+3834*x^4-2295*x^3-1296*x^2-135*x)*exp(x)-216*x^6+1620*x^5-3726*x^4+1755*x^3+1863*x^2+405*x+27),x

)

________________________________________________________________________________________

maxima [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-32*x^6+240*x^5-600*x^4+500*x^3)*exp(x)^3+(288*x^6-2160*x^5+5256*x^4-3780*x^3-900*x^2)*exp(x)^2+(-

864*x^6+6480*x^5-15336*x^4+9180*x^3+5040*x^2+612*x+360)*exp(x)+864*x^6-6480*x^5+14904*x^4-7020*x^3-7452*x^2-75

6*x-1188)*exp(((-8*x^5+32*x^4-10*x^3-50*x^2)*exp(x)^2+(48*x^5-192*x^4+36*x^3+336*x^2+60*x)*exp(x)-72*x^5+288*x

^4-18*x^3-558*x^2-198*x)/((4*x^4-20*x^3+25*x^2)*exp(x)^2+(-24*x^4+120*x^3-138*x^2-30*x)*exp(x)+36*x^4-180*x^3+

189*x^2+90*x+9))^2/((8*x^6-60*x^5+150*x^4-125*x^3)*exp(x)^3+(-72*x^6+540*x^5-1314*x^4+945*x^3+225*x^2)*exp(x)^

2+(216*x^6-1620*x^5+3834*x^4-2295*x^3-1296*x^2-135*x)*exp(x)-216*x^6+1620*x^5-3726*x^4+1755*x^3+1863*x^2+405*x

+27),x, algorithm="maxima")

[Out]

Timed out

________________________________________________________________________________________

mupad [B] time = 9.00, size = 1157, normalized size = 38.57 result too large to display

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(-(2*(198*x - exp(x)*(60*x + 336*x^2 + 36*x^3 - 192*x^4 + 48*x^5) + exp(2*x)*(50*x^2 + 10*x^3 - 32*x^

4 + 8*x^5) + 558*x^2 + 18*x^3 - 288*x^4 + 72*x^5))/(90*x - exp(x)*(30*x + 138*x^2 - 120*x^3 + 24*x^4) + exp(2*

x)*(25*x^2 - 20*x^3 + 4*x^4) + 189*x^2 - 180*x^3 + 36*x^4 + 9))*(756*x + exp(2*x)*(900*x^2 + 3780*x^3 - 5256*x

^4 + 2160*x^5 - 288*x^6) - exp(x)*(612*x + 5040*x^2 + 9180*x^3 - 15336*x^4 + 6480*x^5 - 864*x^6 + 360) - exp(3

*x)*(500*x^3 - 600*x^4 + 240*x^5 - 32*x^6) + 7452*x^2 + 7020*x^3 - 14904*x^4 + 6480*x^5 - 864*x^6 + 1188))/(40

5*x + exp(2*x)*(225*x^2 + 945*x^3 - 1314*x^4 + 540*x^5 - 72*x^6) - exp(x)*(135*x + 1296*x^2 + 2295*x^3 - 3834*

x^4 + 1620*x^5 - 216*x^6) - exp(3*x)*(125*x^3 - 150*x^4 + 60*x^5 - 8*x^6) + 1863*x^2 + 1755*x^3 - 3726*x^4 + 1

620*x^5 - 216*x^6 + 27),x)

[Out]

exp((72*x^3*exp(x))/(90*x - 138*x^2*exp(x) + 120*x^3*exp(x) - 24*x^4*exp(x) + 25*x^2*exp(2*x) - 20*x^3*exp(2*x

) + 4*x^4*exp(2*x) - 30*x*exp(x) + 189*x^2 - 180*x^3 + 36*x^4 + 9))*exp((96*x^5*exp(x))/(90*x - 138*x^2*exp(x)

+ 120*x^3*exp(x) - 24*x^4*exp(x) + 25*x^2*exp(2*x) - 20*x^3*exp(2*x) + 4*x^4*exp(2*x) - 30*x*exp(x) + 189*x^2

- 180*x^3 + 36*x^4 + 9))*exp(-(384*x^4*exp(x))/(90*x - 138*x^2*exp(x) + 120*x^3*exp(x) - 24*x^4*exp(x) + 25*x

^2*exp(2*x) - 20*x^3*exp(2*x) + 4*x^4*exp(2*x) - 30*x*exp(x) + 189*x^2 - 180*x^3 + 36*x^4 + 9))*exp((672*x^2*e

xp(x))/(90*x - 138*x^2*exp(x) + 120*x^3*exp(x) - 24*x^4*exp(x) + 25*x^2*exp(2*x) - 20*x^3*exp(2*x) + 4*x^4*exp

(2*x) - 30*x*exp(x) + 189*x^2 - 180*x^3 + 36*x^4 + 9))*exp(-(36*x^3)/(90*x - 138*x^2*exp(x) + 120*x^3*exp(x) -

24*x^4*exp(x) + 25*x^2*exp(2*x) - 20*x^3*exp(2*x) + 4*x^4*exp(2*x) - 30*x*exp(x) + 189*x^2 - 180*x^3 + 36*x^4

+ 9))*exp(-(144*x^5)/(90*x - 138*x^2*exp(x) + 120*x^3*exp(x) - 24*x^4*exp(x) + 25*x^2*exp(2*x) - 20*x^3*exp(2

*x) + 4*x^4*exp(2*x) - 30*x*exp(x) + 189*x^2 - 180*x^3 + 36*x^4 + 9))*exp((576*x^4)/(90*x - 138*x^2*exp(x) + 1

20*x^3*exp(x) - 24*x^4*exp(x) + 25*x^2*exp(2*x) - 20*x^3*exp(2*x) + 4*x^4*exp(2*x) - 30*x*exp(x) + 189*x^2 - 1

80*x^3 + 36*x^4 + 9))*exp(-(1116*x^2)/(90*x - 138*x^2*exp(x) + 120*x^3*exp(x) - 24*x^4*exp(x) + 25*x^2*exp(2*x

) - 20*x^3*exp(2*x) + 4*x^4*exp(2*x) - 30*x*exp(x) + 189*x^2 - 180*x^3 + 36*x^4 + 9))*exp(-(16*x^5*exp(2*x))/(

90*x - 138*x^2*exp(x) + 120*x^3*exp(x) - 24*x^4*exp(x) + 25*x^2*exp(2*x) - 20*x^3*exp(2*x) + 4*x^4*exp(2*x) -

30*x*exp(x) + 189*x^2 - 180*x^3 + 36*x^4 + 9))*exp(-(20*x^3*exp(2*x))/(90*x - 138*x^2*exp(x) + 120*x^3*exp(x)

- 24*x^4*exp(x) + 25*x^2*exp(2*x) - 20*x^3*exp(2*x) + 4*x^4*exp(2*x) - 30*x*exp(x) + 189*x^2 - 180*x^3 + 36*x^

4 + 9))*exp((64*x^4*exp(2*x))/(90*x - 138*x^2*exp(x) + 120*x^3*exp(x) - 24*x^4*exp(x) + 25*x^2*exp(2*x) - 20*x

^3*exp(2*x) + 4*x^4*exp(2*x) - 30*x*exp(x) + 189*x^2 - 180*x^3 + 36*x^4 + 9))*exp(-(100*x^2*exp(2*x))/(90*x -

138*x^2*exp(x) + 120*x^3*exp(x) - 24*x^4*exp(x) + 25*x^2*exp(2*x) - 20*x^3*exp(2*x) + 4*x^4*exp(2*x) - 30*x*ex

p(x) + 189*x^2 - 180*x^3 + 36*x^4 + 9))*exp((120*x*exp(x))/(90*x - 138*x^2*exp(x) + 120*x^3*exp(x) - 24*x^4*ex

p(x) + 25*x^2*exp(2*x) - 20*x^3*exp(2*x) + 4*x^4*exp(2*x) - 30*x*exp(x) + 189*x^2 - 180*x^3 + 36*x^4 + 9))*exp

(-(396*x)/(90*x - 138*x^2*exp(x) + 120*x^3*exp(x) - 24*x^4*exp(x) + 25*x^2*exp(2*x) - 20*x^3*exp(2*x) + 4*x^4*

exp(2*x) - 30*x*exp(x) + 189*x^2 - 180*x^3 + 36*x^4 + 9))

________________________________________________________________________________________

sympy [B] time = 7.96, size = 143, normalized size = 4.77 \begin {gather*} e^{\frac {2 \left (- 72 x^{5} + 288 x^{4} - 18 x^{3} - 558 x^{2} - 198 x + \left (- 8 x^{5} + 32 x^{4} - 10 x^{3} - 50 x^{2}\right ) e^{2 x} + \left (48 x^{5} - 192 x^{4} + 36 x^{3} + 336 x^{2} + 60 x\right ) e^{x}\right )}{36 x^{4} - 180 x^{3} + 189 x^{2} + 90 x + \left (4 x^{4} - 20 x^{3} + 25 x^{2}\right ) e^{2 x} + \left (- 24 x^{4} + 120 x^{3} - 138 x^{2} - 30 x\right ) e^{x} + 9}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-32*x**6+240*x**5-600*x**4+500*x**3)*exp(x)**3+(288*x**6-2160*x**5+5256*x**4-3780*x**3-900*x**2)*e

xp(x)**2+(-864*x**6+6480*x**5-15336*x**4+9180*x**3+5040*x**2+612*x+360)*exp(x)+864*x**6-6480*x**5+14904*x**4-7

020*x**3-7452*x**2-756*x-1188)*exp(((-8*x**5+32*x**4-10*x**3-50*x**2)*exp(x)**2+(48*x**5-192*x**4+36*x**3+336*

x**2+60*x)*exp(x)-72*x**5+288*x**4-18*x**3-558*x**2-198*x)/((4*x**4-20*x**3+25*x**2)*exp(x)**2+(-24*x**4+120*x

**3-138*x**2-30*x)*exp(x)+36*x**4-180*x**3+189*x**2+90*x+9))**2/((8*x**6-60*x**5+150*x**4-125*x**3)*exp(x)**3+

(-72*x**6+540*x**5-1314*x**4+945*x**3+225*x**2)*exp(x)**2+(216*x**6-1620*x**5+3834*x**4-2295*x**3-1296*x**2-13

5*x)*exp(x)-216*x**6+1620*x**5-3726*x**4+1755*x**3+1863*x**2+405*x+27),x)

[Out]

exp(2*(-72*x**5 + 288*x**4 - 18*x**3 - 558*x**2 - 198*x + (-8*x**5 + 32*x**4 - 10*x**3 - 50*x**2)*exp(2*x) + (

48*x**5 - 192*x**4 + 36*x**3 + 336*x**2 + 60*x)*exp(x))/(36*x**4 - 180*x**3 + 189*x**2 + 90*x + (4*x**4 - 20*x

**3 + 25*x**2)*exp(2*x) + (-24*x**4 + 120*x**3 - 138*x**2 - 30*x)*exp(x) + 9))

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