∫ 617025600−524471760x−623591460x2+611580105x3−211803255x4+37236375x5−3533625x6+172125x7−3375x8+e3x(125−75x−125x2+75x3−15x4+x5)+e2x(63900−47565x−63225x2+46065x3−11475x4+1215x5−45x6)+ex(10879920−8987112x−10753785x2+9244827x3−2756547x4+390825x5−26325x6+675x7)_____________________________________________________________________________________________________________________________________________________________________________________________________________________________ −729000000x2+619650000x3−212017500x4+37236375x5−3533625x6+172125x7−3375x8+e3x(−125x2+75x3−15x4+x5)+e2x(−67500x2+46125x3−11475x4+1215x5−45x6)+ex(−12150000x2+9315000x3−2757375x4+390825x5−26325x6+675x7) dx

3.89.56 $\int \frac{617025600 - 524471760 x - 623591460 x^{2} + 611580105 x^{3} - 211803255 x^{4} + 37236375 x^{5} - 3533625 x^{6} + 172125 x^{7} - 3375 x^{8} + e^{3 x} (125 - 75 x - 125 x^{2} + 75 x^{3} - 15 x^{4} + x^{5}) + e^{2 x} (63900 - 47565 x - 63225 x^{2} + 46065 x^{3} - 11475 x^{4} + 1215 x^{5} - 45 x^{6}) + e^{x} (10879920 - 8987112 x - 10753785 x^{2} + 9244827 x^{3} - 2756547 x^{4} + 390825 x^{5} - 26325 x^{6} + 675 x^{7})}{- 729000000 x^{2} + 619650000 x^{3} - 212017500 x^{4} + 37236375 x^{5} - 3533625 x^{6} + 172125 x^{7} - 3375 x^{8} + e^{3 x} (- 125 x^{2} + 75 x^{3} - 15 x^{4} + x^{5}) + e^{2 x} (- 67500 x^{2} + 46125 x^{3} - 11475 x^{4} + 1215 x^{5} - 45 x^{6}) + e^{x} (- 12150000 x^{2} + 9315000 x^{3} - 2757375 x^{4} + 390825 x^{5} - 26325 x^{6} + 675 x^{7})} d x$

Optimal. Leaf size=37 $\frac{\frac{{(5 + \frac{2}{- 5 + \frac{e^{x}}{3 (- 12 + x)}})}^{2}}{(- 5 + x)^{2}} + x + x^{2}}{x}$

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Rubi [F] time = 4.92, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, $\frac{number of rules}{integrand size}$ = 0.000, Rules used = {} $\begin{matrix} \int \frac{617025600 - 524471760 x - 623591460 x^{2} + 611580105 x^{3} - 211803255 x^{4} + 37236375 x^{5} - 3533625 x^{6} + 172125 x^{7} - 3375 x^{8} + e^{3 x} (125 - 75 x - 125 x^{2} + 75 x^{3} - 15 x^{4} + x^{5}) + e^{2 x} (63900 - 47565 x - 63225 x^{2} + 46065 x^{3} - 11475 x^{4} + 1215 x^{5} - 45 x^{6}) + e^{x} (10879920 - 8987112 x - 10753785 x^{2} + 9244827 x^{3} - 2756547 x^{4} + 390825 x^{5} - 26325 x^{6} + 675 x^{7})}{- 729000000 x^{2} + 619650000 x^{3} - 212017500 x^{4} + 37236375 x^{5} - 3533625 x^{6} + 172125 x^{7} - 3375 x^{8} + e^{3 x} (- 125 x^{2} + 75 x^{3} - 15 x^{4} + x^{5}) + e^{2 x} (- 67500 x^{2} + 46125 x^{3} - 11475 x^{4} + 1215 x^{5} - 45 x^{6}) + e^{x} (- 12150000 x^{2} + 9315000 x^{3} - 2757375 x^{4} + 390825 x^{5} - 26325 x^{6} + 675 x^{7})} d x \end{matrix}$

Veriﬁcation is not applicable to the result.

[In]

Int[(617025600 - 524471760*x - 623591460*x^2 + 611580105*x^3 - 211803255*x^4 + 37236375*x^5 - 3533625*x^6 + 17

2125*x^7 - 3375*x^8 + E^(3*x)*(125 - 75*x - 125*x^2 + 75*x^3 - 15*x^4 + x^5) + E^(2*x)*(63900 - 47565*x - 6322

5*x^2 + 46065*x^3 - 11475*x^4 + 1215*x^5 - 45*x^6) + E^x*(10879920 - 8987112*x - 10753785*x^2 + 9244827*x^3 -

2756547*x^4 + 390825*x^5 - 26325*x^6 + 675*x^7))/(-729000000*x^2 + 619650000*x^3 - 212017500*x^4 + 37236375*x^

5 - 3533625*x^6 + 172125*x^7 - 3375*x^8 + E^(3*x)*(-125*x^2 + 75*x^3 - 15*x^4 + x^5) + E^(2*x)*(-67500*x^2 + 4

6125*x^3 - 11475*x^4 + 1215*x^5 - 45*x^6) + E^x*(-12150000*x^2 + 9315000*x^3 - 2757375*x^4 + 390825*x^5 - 2632

5*x^6 + 675*x^7)),x]

[Out]

5/(5 - x)^2 + (5 - x)^(-1) + x^(-1) + x - 1080*Defer[Int][(180 + E^x - 15*x)^(-3), x] - (3528*Defer[Int][1/((1

80 + E^x - 15*x)^2*(-5 + x)^3), x])/5 + 168*Defer[Int][1/((180 + E^x - 15*x)*(-5 + x)^3), x] + 84672*Defer[Int

][1/((180 + E^x - 15*x)^3*(-5 + x)^2), x] - (265356*Defer[Int][1/((180 + E^x - 15*x)^2*(-5 + x)^2), x])/25 + (

276*Defer[Int][1/((180 + E^x - 15*x)*(-5 + x)^2), x])/5 - (258552*Defer[Int][1/((180 + E^x - 15*x)^3*(-5 + x))

, x])/5 + (126468*Defer[Int][1/((180 + E^x - 15*x)^2*(-5 + x)), x])/25 - (144*Defer[Int][1/((180 + E^x - 15*x)

*(-5 + x)), x])/5 - (5184*Defer[Int][1/((180 + E^x - 15*x)^2*x^2), x])/25 + (144*Defer[Int][1/((180 + E^x - 15

*x)*x^2), x])/5 + (404352*Defer[Int][1/((180 + E^x - 15*x)^3*x), x])/5 - (150768*Defer[Int][1/((180 + E^x - 15

*x)^2*x), x])/25 + (144*Defer[Int][1/((180 + E^x - 15*x)*x), x])/5

Rubi steps

$\begin{matrix} \begin{aligned} integral & = \int \frac{- e^{3 x} (125 - 75 x - 125 x^{2} + 75 x^{3} - 15 x^{4} + x^{5}) + 135 (- 12 + x)^{3} (2645 - 1587 x - 3125 x^{2} + 1875 x^{3} - 375 x^{4} + 25 x^{5}) + 15 e^{2 x} (- 4260 + 3171 x + 4215 x^{2} - 3071 x^{3} + 765 x^{4} - 81 x^{5} + 3 x^{6}) - 9 e^{x} (1208880 - 998568 x - 1194865 x^{2} + 1027203 x^{3} - 306283 x^{4} + 43425 x^{5} - 2925 x^{6} + 75 x^{7})}{{(180 + e^{x} - 15 x)}^{3} (5 - x)^{3} x^{2}} d x \\ = \int (- \frac{1080 (- 13 + x) (- 12 + x)^{2}}{{(180 + e^{x} - 15 x)}^{3} (- 5 + x)^{2} x} - \frac{60 (60 + 24 x - 15 x^{2} + x^{3})}{(180 + e^{x} - 15 x) (- 5 + x)^{3} x^{2}} - \frac{36 (- 720 - 20508 x + 7510 x^{2} - 807 x^{3} + 27 x^{4})}{{(180 + e^{x} - 15 x)}^{2} (- 5 + x)^{3} x^{2}} + \frac{125 - 75 x - 125 x^{2} + 75 x^{3} - 15 x^{4} + x^{5}}{(- 5 + x)^{3} x^{2}}) d x \\ = - (36 \int \frac{- 720 - 20508 x + 7510 x^{2} - 807 x^{3} + 27 x^{4}}{{(180 + e^{x} - 15 x)}^{2} (- 5 + x)^{3} x^{2}} d x) - 60 \int \frac{60 + 24 x - 15 x^{2} + x^{3}}{(180 + e^{x} - 15 x) (- 5 + x)^{3} x^{2}} d x - 1080 \int \frac{(- 13 + x) (- 12 + x)^{2}}{{(180 + e^{x} - 15 x)}^{3} (- 5 + x)^{2} x} d x + \int \frac{125 - 75 x - 125 x^{2} + 75 x^{3} - 15 x^{4} + x^{5}}{(- 5 + x)^{3} x^{2}} d x \\ = - (36 \int (\frac{98}{5 {(180 + e^{x} - 15 x)}^{2} (- 5 + x)^{3}} + \frac{7371}{25 {(180 + e^{x} - 15 x)}^{2} (- 5 + x)^{2}} - \frac{3513}{25 {(180 + e^{x} - 15 x)}^{2} (- 5 + x)} + \frac{144}{25 {(180 + e^{x} - 15 x)}^{2} x^{2}} + \frac{4188}{25 {(180 + e^{x} - 15 x)}^{2} x}) d x) - 60 \int (- \frac{14}{5 (180 + e^{x} - 15 x) (- 5 + x)^{3}} - \frac{23}{25 (180 + e^{x} - 15 x) (- 5 + x)^{2}} + \frac{12}{25 (180 + e^{x} - 15 x) (- 5 + x)} - \frac{12}{25 (180 + e^{x} - 15 x) x^{2}} - \frac{12}{25 (180 + e^{x} - 15 x) x}) d x - 1080 \int (\frac{1}{{(180 + e^{x} - 15 x)}^{3}} - \frac{392}{5 {(180 + e^{x} - 15 x)}^{3} (- 5 + x)^{2}} + \frac{1197}{25 {(180 + e^{x} - 15 x)}^{3} (- 5 + x)} - \frac{1872}{25 {(180 + e^{x} - 15 x)}^{3} x}) d x + \int (1 - \frac{10}{(- 5 + x)^{3}} + \frac{1}{(- 5 + x)^{2}} - \frac{1}{x^{2}}) d x \\ = \frac{5}{(5 - x)^{2}} + \frac{1}{5 - x} + \frac{1}{x} + x - \frac{144}{5} \int \frac{1}{(180 + e^{x} - 15 x) (- 5 + x)} d x + \frac{144}{5} \int \frac{1}{(180 + e^{x} - 15 x) x^{2}} d x + \frac{144}{5} \int \frac{1}{(180 + e^{x} - 15 x) x} d x + \frac{276}{5} \int \frac{1}{(180 + e^{x} - 15 x) (- 5 + x)^{2}} d x + 168 \int \frac{1}{(180 + e^{x} - 15 x) (- 5 + x)^{3}} d x - \frac{5184}{25} \int \frac{1}{{(180 + e^{x} - 15 x)}^{2} x^{2}} d x - \frac{3528}{5} \int \frac{1}{{(180 + e^{x} - 15 x)}^{2} (- 5 + x)^{3}} d x - 1080 \int \frac{1}{{(180 + e^{x} - 15 x)}^{3}} d x + \frac{126468}{25} \int \frac{1}{{(180 + e^{x} - 15 x)}^{2} (- 5 + x)} d x - \frac{150768}{25} \int \frac{1}{{(180 + e^{x} - 15 x)}^{2} x} d x - \frac{265356}{25} \int \frac{1}{{(180 + e^{x} - 15 x)}^{2} (- 5 + x)^{2}} d x - \frac{258552}{5} \int \frac{1}{{(180 + e^{x} - 15 x)}^{3} (- 5 + x)} d x + \frac{404352}{5} \int \frac{1}{{(180 + e^{x} - 15 x)}^{3} x} d x + 84672 \int \frac{1}{{(180 + e^{x} - 15 x)}^{3} (- 5 + x)^{2}} d x \end{aligned} \end{matrix}$

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Mathematica [A] time = 0.17, size = 67, normalized size = 1.81 $\begin{matrix} \frac{1}{5 - x} + \frac{5}{(- 5 + x)^{2}} + \frac{1}{x} + \frac{60 (- 12 + x)}{(180 + e^{x} - 15 x) (- 5 + x)^{2} x} + \frac{36 (- 12 + x)^{2}}{{(180 + e^{x} - 15 x)}^{2} (- 5 + x)^{2} x} + x \end{matrix}$

Antiderivative was successfully veriﬁed.

[In]

Integrate[(617025600 - 524471760*x - 623591460*x^2 + 611580105*x^3 - 211803255*x^4 + 37236375*x^5 - 3533625*x^

6 + 172125*x^7 - 3375*x^8 + E^(3*x)*(125 - 75*x - 125*x^2 + 75*x^3 - 15*x^4 + x^5) + E^(2*x)*(63900 - 47565*x

- 63225*x^2 + 46065*x^3 - 11475*x^4 + 1215*x^5 - 45*x^6) + E^x*(10879920 - 8987112*x - 10753785*x^2 + 9244827*

x^3 - 2756547*x^4 + 390825*x^5 - 26325*x^6 + 675*x^7))/(-729000000*x^2 + 619650000*x^3 - 212017500*x^4 + 37236

375*x^5 - 3533625*x^6 + 172125*x^7 - 3375*x^8 + E^(3*x)*(-125*x^2 + 75*x^3 - 15*x^4 + x^5) + E^(2*x)*(-67500*x

^2 + 46125*x^3 - 11475*x^4 + 1215*x^5 - 45*x^6) + E^x*(-12150000*x^2 + 9315000*x^3 - 2757375*x^4 + 390825*x^5

- 26325*x^6 + 675*x^7)),x]

[Out]

(5 - x)^(-1) + 5/(-5 + x)^2 + x^(-1) + (60*(-12 + x))/((180 + E^x - 15*x)*(-5 + x)^2*x) + (36*(-12 + x)^2)/((1

80 + E^x - 15*x)^2*(-5 + x)^2*x) + x

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fricas [B] time = 0.65, size = 142, normalized size = 3.84 $\begin{matrix} \frac{225 x^{6} - 7650 x^{5} + 92025 x^{4} - 459000 x^{3} + 814761 x^{2} + (x^{4} - 10 x^{3} + 25 x^{2} + 25) e^{(2 x)} - 30 (x^{5} - 22 x^{4} + 145 x^{3} - 300 x^{2} + 23 x - 276) e^{x} - 114264 x + 685584}{225 x^{5} - 7650 x^{4} + 92025 x^{3} - 459000 x^{2} + (x^{3} - 10 x^{2} + 25 x) e^{(2 x)} - 30 (x^{4} - 22 x^{3} + 145 x^{2} - 300 x) e^{x} + 810000 x} \end{matrix}$

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^5-15*x^4+75*x^3-125*x^2-75*x+125)*exp(x)^3+(-45*x^6+1215*x^5-11475*x^4+46065*x^3-63225*x^2-47565

*x+63900)*exp(x)^2+(675*x^7-26325*x^6+390825*x^5-2756547*x^4+9244827*x^3-10753785*x^2-8987112*x+10879920)*exp(

x)-3375*x^8+172125*x^7-3533625*x^6+37236375*x^5-211803255*x^4+611580105*x^3-623591460*x^2-524471760*x+61702560

0)/((x^5-15*x^4+75*x^3-125*x^2)*exp(x)^3+(-45*x^6+1215*x^5-11475*x^4+46125*x^3-67500*x^2)*exp(x)^2+(675*x^7-26

325*x^6+390825*x^5-2757375*x^4+9315000*x^3-12150000*x^2)*exp(x)-3375*x^8+172125*x^7-3533625*x^6+37236375*x^5-2

12017500*x^4+619650000*x^3-729000000*x^2),x, algorithm="fricas")

[Out]

(225*x^6 - 7650*x^5 + 92025*x^4 - 459000*x^3 + 814761*x^2 + (x^4 - 10*x^3 + 25*x^2 + 25)*e^(2*x) - 30*(x^5 - 2

2*x^4 + 145*x^3 - 300*x^2 + 23*x - 276)*e^x - 114264*x + 685584)/(225*x^5 - 7650*x^4 + 92025*x^3 - 459000*x^2

+ (x^3 - 10*x^2 + 25*x)*e^(2*x) - 30*(x^4 - 22*x^3 + 145*x^2 - 300*x)*e^x + 810000*x)

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giac [B] time = 0.21, size = 176, normalized size = 4.76 $\begin{matrix} \frac{225 x^{6} - 30 x^{5} e^{x} - 7650 x^{5} + x^{4} e^{(2 x)} + 660 x^{4} e^{x} + 92025 x^{4} - 10 x^{3} e^{(2 x)} - 4350 x^{3} e^{x} - 459000 x^{3} + 25 x^{2} e^{(2 x)} + 9000 x^{2} e^{x} + 814761 x^{2} - 690 x e^{x} - 114264 x + 25 e^{(2 x)} + 8280 e^{x} + 685584}{225 x^{5} - 30 x^{4} e^{x} - 7650 x^{4} + x^{3} e^{(2 x)} + 660 x^{3} e^{x} + 92025 x^{3} - 10 x^{2} e^{(2 x)} - 4350 x^{2} e^{x} - 459000 x^{2} + 25 x e^{(2 x)} + 9000 x e^{x} + 810000 x} \end{matrix}$

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^5-15*x^4+75*x^3-125*x^2-75*x+125)*exp(x)^3+(-45*x^6+1215*x^5-11475*x^4+46065*x^3-63225*x^2-47565

*x+63900)*exp(x)^2+(675*x^7-26325*x^6+390825*x^5-2756547*x^4+9244827*x^3-10753785*x^2-8987112*x+10879920)*exp(

x)-3375*x^8+172125*x^7-3533625*x^6+37236375*x^5-211803255*x^4+611580105*x^3-623591460*x^2-524471760*x+61702560

0)/((x^5-15*x^4+75*x^3-125*x^2)*exp(x)^3+(-45*x^6+1215*x^5-11475*x^4+46125*x^3-67500*x^2)*exp(x)^2+(675*x^7-26

325*x^6+390825*x^5-2757375*x^4+9315000*x^3-12150000*x^2)*exp(x)-3375*x^8+172125*x^7-3533625*x^6+37236375*x^5-2

12017500*x^4+619650000*x^3-729000000*x^2),x, algorithm="giac")

[Out]

(225*x^6 - 30*x^5*e^x - 7650*x^5 + x^4*e^(2*x) + 660*x^4*e^x + 92025*x^4 - 10*x^3*e^(2*x) - 4350*x^3*e^x - 459

000*x^3 + 25*x^2*e^(2*x) + 9000*x^2*e^x + 814761*x^2 - 690*x*e^x - 114264*x + 25*e^(2*x) + 8280*e^x + 685584)/

(225*x^5 - 30*x^4*e^x - 7650*x^4 + x^3*e^(2*x) + 660*x^3*e^x + 92025*x^3 - 10*x^2*e^(2*x) - 4350*x^2*e^x - 459

000*x^2 + 25*x*e^(2*x) + 9000*x*e^x + 810000*x)

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maple [A] time = 0.08, size = 58, normalized size = 1.57


method	result	size

risch	$x + \frac{25}{x (x^{2} - 10 x + 25)} - \frac{12 (72 x^{2} - 5 e^{x} x - 1728 x + 60 e^{x} + 10368)}{x {(x - 5)}^{2} {(15 x - e^{x} - 180)}^{2}}$	$58$

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((x^5-15*x^4+75*x^3-125*x^2-75*x+125)*exp(x)^3+(-45*x^6+1215*x^5-11475*x^4+46065*x^3-63225*x^2-47565*x+639

00)*exp(x)^2+(675*x^7-26325*x^6+390825*x^5-2756547*x^4+9244827*x^3-10753785*x^2-8987112*x+10879920)*exp(x)-337

5*x^8+172125*x^7-3533625*x^6+37236375*x^5-211803255*x^4+611580105*x^3-623591460*x^2-524471760*x+617025600)/((x

^5-15*x^4+75*x^3-125*x^2)*exp(x)^3+(-45*x^6+1215*x^5-11475*x^4+46125*x^3-67500*x^2)*exp(x)^2+(675*x^7-26325*x^

6+390825*x^5-2757375*x^4+9315000*x^3-12150000*x^2)*exp(x)-3375*x^8+172125*x^7-3533625*x^6+37236375*x^5-2120175

00*x^4+619650000*x^3-729000000*x^2),x,method=_RETURNVERBOSE)

[Out]

x+25/x/(x^2-10*x+25)-12*(72*x^2-5*exp(x)*x-1728*x+60*exp(x)+10368)/x/(x-5)^2/(15*x-exp(x)-180)^2

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maxima [B] time = 0.54, size = 142, normalized size = 3.84 $\begin{matrix} \frac{225 x^{6} - 7650 x^{5} + 92025 x^{4} - 459000 x^{3} + 814761 x^{2} + (x^{4} - 10 x^{3} + 25 x^{2} + 25) e^{(2 x)} - 30 (x^{5} - 22 x^{4} + 145 x^{3} - 300 x^{2} + 23 x - 276) e^{x} - 114264 x + 685584}{225 x^{5} - 7650 x^{4} + 92025 x^{3} - 459000 x^{2} + (x^{3} - 10 x^{2} + 25 x) e^{(2 x)} - 30 (x^{4} - 22 x^{3} + 145 x^{2} - 300 x) e^{x} + 810000 x} \end{matrix}$

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^5-15*x^4+75*x^3-125*x^2-75*x+125)*exp(x)^3+(-45*x^6+1215*x^5-11475*x^4+46065*x^3-63225*x^2-47565

*x+63900)*exp(x)^2+(675*x^7-26325*x^6+390825*x^5-2756547*x^4+9244827*x^3-10753785*x^2-8987112*x+10879920)*exp(

x)-3375*x^8+172125*x^7-3533625*x^6+37236375*x^5-211803255*x^4+611580105*x^3-623591460*x^2-524471760*x+61702560

0)/((x^5-15*x^4+75*x^3-125*x^2)*exp(x)^3+(-45*x^6+1215*x^5-11475*x^4+46125*x^3-67500*x^2)*exp(x)^2+(675*x^7-26

325*x^6+390825*x^5-2757375*x^4+9315000*x^3-12150000*x^2)*exp(x)-3375*x^8+172125*x^7-3533625*x^6+37236375*x^5-2

12017500*x^4+619650000*x^3-729000000*x^2),x, algorithm="maxima")

[Out]

(225*x^6 - 7650*x^5 + 92025*x^4 - 459000*x^3 + 814761*x^2 + (x^4 - 10*x^3 + 25*x^2 + 25)*e^(2*x) - 30*(x^5 - 2

2*x^4 + 145*x^3 - 300*x^2 + 23*x - 276)*e^x - 114264*x + 685584)/(225*x^5 - 7650*x^4 + 92025*x^3 - 459000*x^2

+ (x^3 - 10*x^2 + 25*x)*e^(2*x) - 30*(x^4 - 22*x^3 + 145*x^2 - 300*x)*e^x + 810000*x)

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mupad [F] time = 0.00, size = -1, normalized size = -0.03 $\begin{matrix} \int \frac{524471760 x + e^{3 x} (- x^{5} + 15 x^{4} - 75 x^{3} + 125 x^{2} + 75 x - 125) + e^{x} (- 675 x^{7} + 26325 x^{6} - 390825 x^{5} + 2756547 x^{4} - 9244827 x^{3} + 10753785 x^{2} + 8987112 x - 10879920) + 623591460 x^{2} - 611580105 x^{3} + 211803255 x^{4} - 37236375 x^{5} + 3533625 x^{6} - 172125 x^{7} + 3375 x^{8} + e^{2 x} (45 x^{6} - 1215 x^{5} + 11475 x^{4} - 46065 x^{3} + 63225 x^{2} + 47565 x - 63900) - 617025600}{e^{2 x} (45 x^{6} - 1215 x^{5} + 11475 x^{4} - 46125 x^{3} + 67500 x^{2}) + e^{3 x} (- x^{5} + 15 x^{4} - 75 x^{3} + 125 x^{2}) + 729000000 x^{2} - 619650000 x^{3} + 212017500 x^{4} - 37236375 x^{5} + 3533625 x^{6} - 172125 x^{7} + 3375 x^{8} + e^{x} (- 675 x^{7} + 26325 x^{6} - 390825 x^{5} + 2757375 x^{4} - 9315000 x^{3} + 12150000 x^{2})} d x \end{matrix}$

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((524471760*x + exp(3*x)*(75*x + 125*x^2 - 75*x^3 + 15*x^4 - x^5 - 125) + exp(x)*(8987112*x + 10753785*x^2

- 9244827*x^3 + 2756547*x^4 - 390825*x^5 + 26325*x^6 - 675*x^7 - 10879920) + 623591460*x^2 - 611580105*x^3 + 2

11803255*x^4 - 37236375*x^5 + 3533625*x^6 - 172125*x^7 + 3375*x^8 + exp(2*x)*(47565*x + 63225*x^2 - 46065*x^3

+ 11475*x^4 - 1215*x^5 + 45*x^6 - 63900) - 617025600)/(exp(2*x)*(67500*x^2 - 46125*x^3 + 11475*x^4 - 1215*x^5

+ 45*x^6) + exp(3*x)*(125*x^2 - 75*x^3 + 15*x^4 - x^5) + 729000000*x^2 - 619650000*x^3 + 212017500*x^4 - 37236

375*x^5 + 3533625*x^6 - 172125*x^7 + 3375*x^8 + exp(x)*(12150000*x^2 - 9315000*x^3 + 2757375*x^4 - 390825*x^5

+ 26325*x^6 - 675*x^7)),x)

[Out]

int((524471760*x + exp(3*x)*(75*x + 125*x^2 - 75*x^3 + 15*x^4 - x^5 - 125) + exp(x)*(8987112*x + 10753785*x^2

- 9244827*x^3 + 2756547*x^4 - 390825*x^5 + 26325*x^6 - 675*x^7 - 10879920) + 623591460*x^2 - 611580105*x^3 + 2

11803255*x^4 - 37236375*x^5 + 3533625*x^6 - 172125*x^7 + 3375*x^8 + exp(2*x)*(47565*x + 63225*x^2 - 46065*x^3

+ 11475*x^4 - 1215*x^5 + 45*x^6 - 63900) - 617025600)/(exp(2*x)*(67500*x^2 - 46125*x^3 + 11475*x^4 - 1215*x^5

+ 45*x^6) + exp(3*x)*(125*x^2 - 75*x^3 + 15*x^4 - x^5) + 729000000*x^2 - 619650000*x^3 + 212017500*x^4 - 37236

375*x^5 + 3533625*x^6 - 172125*x^7 + 3375*x^8 + exp(x)*(12150000*x^2 - 9315000*x^3 + 2757375*x^4 - 390825*x^5

+ 26325*x^6 - 675*x^7)), x)

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sympy [B] time = 0.42, size = 95, normalized size = 2.57 $\begin{matrix} x + \frac{- 864 x^{2} + 20736 x + (60 x - 720) e^{x} - 124416}{225 x^{5} - 7650 x^{4} + 92025 x^{3} - 459000 x^{2} + 810000 x + (x^{3} - 10 x^{2} + 25 x) e^{2 x} + (- 30 x^{4} + 660 x^{3} - 4350 x^{2} + 9000 x) e^{x}} + \frac{25}{x^{3} - 10 x^{2} + 25 x} \end{matrix}$

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x**5-15*x**4+75*x**3-125*x**2-75*x+125)*exp(x)**3+(-45*x**6+1215*x**5-11475*x**4+46065*x**3-63225*

x**2-47565*x+63900)*exp(x)**2+(675*x**7-26325*x**6+390825*x**5-2756547*x**4+9244827*x**3-10753785*x**2-8987112

*x+10879920)*exp(x)-3375*x**8+172125*x**7-3533625*x**6+37236375*x**5-211803255*x**4+611580105*x**3-623591460*x

**2-524471760*x+617025600)/((x**5-15*x**4+75*x**3-125*x**2)*exp(x)**3+(-45*x**6+1215*x**5-11475*x**4+46125*x**

3-67500*x**2)*exp(x)**2+(675*x**7-26325*x**6+390825*x**5-2757375*x**4+9315000*x**3-12150000*x**2)*exp(x)-3375*

x**8+172125*x**7-3533625*x**6+37236375*x**5-212017500*x**4+619650000*x**3-729000000*x**2),x)

[Out]

x + (-864*x**2 + 20736*x + (60*x - 720)*exp(x) - 124416)/(225*x**5 - 7650*x**4 + 92025*x**3 - 459000*x**2 + 81

0000*x + (x**3 - 10*x**2 + 25*x)*exp(2*x) + (-30*x**4 + 660*x**3 - 4350*x**2 + 9000*x)*exp(x)) + 25/(x**3 - 10

*x**2 + 25*x)

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