∫ −1500e15−3xx5+e20−4x(−2500x5+2500x6)+ex(e20−4x(2500x3−2500x4)+e15−3x(−1500x3+1500x4))+(−2700e10−2xx5+e15−3x(−6000x5+4500x6)+ex(e15−3x(6000x3−4500x4)+e10−2x(−2700x3+2700x4))) log(−ex+x2 2x )+(−1620e5−xx5+e10−2x(−5400x5+2700x6)+ex(e10−2x(5400x3−2700x4)+e5−x(−1620x3+1620x4))) log2(−ex+x2 2x )+(−324x5+e5−x(−2160x5+540x6)+ex(−324x3+324x4+e5−x(2160x3−540x4))) log3(−ex+x2 2x )+(324exx3−324x5) log4(−ex+x2 2x ) ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

3.20.96 \(\int \frac {-1500 e^{15-3 x} x^5+e^{20-4 x} (-2500 x^5+2500 x^6)+e^x (e^{20-4 x} (2500 x^3-2500 x^4)+e^{15-3 x} (-1500 x^3+1500 x^4))+(-2700 e^{10-2 x} x^5+e^{15-3 x} (-6000 x^5+4500 x^6)+e^x (e^{15-3 x} (6000 x^3-4500 x^4)+e^{10-2 x} (-2700 x^3+2700 x^4))) \log (\frac {-e^x+x^2}{2 x})+(-1620 e^{5-x} x^5+e^{10-2 x} (-5400 x^5+2700 x^6)+e^x (e^{10-2 x} (5400 x^3-2700 x^4)+e^{5-x} (-1620 x^3+1620 x^4))) \log ^2(\frac {-e^x+x^2}{2 x})+(-324 x^5+e^{5-x} (-2160 x^5+540 x^6)+e^x (-324 x^3+324 x^4+e^{5-x} (2160 x^3-540 x^4))) \log ^3(\frac {-e^x+x^2}{2 x})+(324 e^x x^3-324 x^5) \log ^4(\frac {-e^x+x^2}{2 x})}{81 e^x-81 x^2} \, dx\) [1996]

Optimal. Leaf size=32 \[ \left (\frac {5}{3} e^{5-x} x+x \log \left (\frac {1}{2} \left (-\frac {e^x}{x}+x\right )\right )\right )^4 \]

[Out]

(x*ln(1/2*x-1/2*exp(x)/x)+5/3*x*exp(5-x))^4

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Rubi [F]
time = 112.03, 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 {-1500 e^{15-3 x} x^5+e^{20-4 x} \left (-2500 x^5+2500 x^6\right )+e^x \left (e^{20-4 x} \left (2500 x^3-2500 x^4\right )+e^{15-3 x} \left (-1500 x^3+1500 x^4\right )\right )+\left (-2700 e^{10-2 x} x^5+e^{15-3 x} \left (-6000 x^5+4500 x^6\right )+e^x \left (e^{15-3 x} \left (6000 x^3-4500 x^4\right )+e^{10-2 x} \left (-2700 x^3+2700 x^4\right )\right )\right ) \log \left (\frac {-e^x+x^2}{2 x}\right )+\left (-1620 e^{5-x} x^5+e^{10-2 x} \left (-5400 x^5+2700 x^6\right )+e^x \left (e^{10-2 x} \left (5400 x^3-2700 x^4\right )+e^{5-x} \left (-1620 x^3+1620 x^4\right )\right )\right ) \log ^2\left (\frac {-e^x+x^2}{2 x}\right )+\left (-324 x^5+e^{5-x} \left (-2160 x^5+540 x^6\right )+e^x \left (-324 x^3+324 x^4+e^{5-x} \left (2160 x^3-540 x^4\right )\right )\right ) \log ^3\left (\frac {-e^x+x^2}{2 x}\right )+\left (324 e^x x^3-324 x^5\right ) \log ^4\left (\frac {-e^x+x^2}{2 x}\right )}{81 e^x-81 x^2} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[(-1500*E^(15 - 3*x)*x^5 + E^(20 - 4*x)*(-2500*x^5 + 2500*x^6) + E^x*(E^(20 - 4*x)*(2500*x^3 - 2500*x^4) +

E^(15 - 3*x)*(-1500*x^3 + 1500*x^4)) + (-2700*E^(10 - 2*x)*x^5 + E^(15 - 3*x)*(-6000*x^5 + 4500*x^6) + E^x*(E^

(15 - 3*x)*(6000*x^3 - 4500*x^4) + E^(10 - 2*x)*(-2700*x^3 + 2700*x^4)))*Log[(-E^x + x^2)/(2*x)] + (-1620*E^(5

- x)*x^5 + E^(10 - 2*x)*(-5400*x^5 + 2700*x^6) + E^x*(E^(10 - 2*x)*(5400*x^3 - 2700*x^4) + E^(5 - x)*(-1620*x

^3 + 1620*x^4)))*Log[(-E^x + x^2)/(2*x)]^2 + (-324*x^5 + E^(5 - x)*(-2160*x^5 + 540*x^6) + E^x*(-324*x^3 + 324

*x^4 + E^(5 - x)*(2160*x^3 - 540*x^4)))*Log[(-E^x + x^2)/(2*x)]^3 + (324*E^x*x^3 - 324*x^5)*Log[(-E^x + x^2)/(

2*x)]^4)/(81*E^x - 81*x^2),x]

[Out]

(-2625*E^(10 - 4*x))/4096 + (625*E^(15 - 4*x))/2304 - (4000*E^(10 - 3*x))/2187 - (25*E^(10 - 2*x))/3 - (2625*E

^(10 - 4*x)*x)/1024 + (625*E^(15 - 4*x)*x)/576 - (4000*E^(10 - 3*x)*x)/729 - (175*E^(10 - 2*x)*x)/6 - (2625*E^

(10 - 4*x)*x^2)/512 + (625*E^(15 - 4*x)*x^2)/288 - (2000*E^(10 - 3*x)*x^2)/243 - (175*E^(10 - 2*x)*x^2)/6 - (8

75*E^(10 - 4*x)*x^3)/128 + (625*E^(15 - 4*x)*x^3)/216 - (2000*E^(10 - 3*x)*x^3)/243 - (50*E^(10 - 2*x)*x^3)/3

- (875*E^(10 - 4*x)*x^4)/128 + (625*E^(15 - 4*x)*x^4)/216 + (625*E^(20 - 4*x)*x^4)/81 - (500*E^(10 - 3*x)*x^4)

/81 - (25*E^(10 - 2*x)*x^4)/3 - (175*E^(10 - 4*x)*x^5)/32 + (125*E^(15 - 4*x)*x^5)/54 - (100*E^(10 - 3*x)*x^5)

/27 - (175*E^(10 - 4*x)*x^6)/48 - (125*E^(15 - 4*x)*x^6)/27 - (100*E^(10 - 3*x)*x^6)/27 - (25*E^(10 - 4*x)*x^7

)/12 - (25*E^(10 - 4*x)*x^8)/12 - (25*E^10*ExpIntegralEi[-2*x])/2 - (25*E^(10 - 2*x)*Log[-1/2*(E^x - x^2)/x])/

2 - 25*E^(10 - 2*x)*x*Log[-1/2*(E^x - x^2)/x] - 25*E^(10 - 2*x)*x^2*Log[-1/2*(E^x - x^2)/x] - (50*E^(10 - 2*x)

*x^3*Log[-1/2*(E^x - x^2)/x])/3 + (500*E^(15 - 3*x)*x^4*Log[-1/2*(E^x - x^2)/x])/27 - (50*E^(10 - 2*x)*x^4*Log

[-1/2*(E^x - x^2)/x])/3 - (100*E^(10 - 3*x)*x^6*Log[-1/2*(E^x - x^2)/x])/9 - (25*E^(10 - 4*x)*x^8*Log[-1/2*(E^

x - x^2)/x])/3 + 25*Defer[Int][(E^(10 - 2*x)*x)/(-E^x + x^2), x] + (75*Defer[Int][(E^(10 - 2*x)*x^2)/(-E^x + x

^2), x])/2 + 25*Defer[Int][(E^(10 - 2*x)*x^3)/(-E^x + x^2), x] + (25*Defer[Int][(E^(10 - 2*x)*x^4)/(-E^x + x^2

), x])/3 - (1000*Defer[Int][(E^(15 - 3*x)*x^5)/(-E^x + x^2), x])/27 + (50*Defer[Int][(E^(10 - 2*x)*x^5)/(-E^x

+ x^2), x])/3 + (500*Defer[Int][(E^(15 - 3*x)*x^6)/(-E^x + x^2), x])/27 - (50*Defer[Int][(E^(10 - 2*x)*x^6)/(-

E^x + x^2), x])/3 + (1000*Defer[Int][(E^(15 - 4*x)*x^7)/(-E^x + x^2), x])/27 + (200*Defer[Int][(E^(10 - 3*x)*x

^7)/(-E^x + x^2), x])/9 - (500*Defer[Int][(E^(15 - 4*x)*x^8)/(-E^x + x^2), x])/27 - (100*Defer[Int][(E^(10 - 3

*x)*x^8)/(-E^x + x^2), x])/9 + (50*Defer[Int][(E^(10 - 4*x)*x^9)/(-E^x + x^2), x])/3 + (200*Log[-1/2*(E^x - x^

2)/x]*Defer[Int][(E^(10 - 4*x)*x^9)/(-E^x + x^2), x])/3 - (25*Defer[Int][(E^(10 - 4*x)*x^10)/(-E^x + x^2), x])

/3 - (100*Log[-1/2*(E^x - x^2)/x]*Defer[Int][(E^(10 - 4*x)*x^10)/(-E^x + x^2), x])/3 + (200*Defer[Int][E^(10 -

2*x)*x^3*Log[(-E^x + x^2)/(2*x)]^2, x])/3 - 20*Defer[Int][E^(5 - x)*x^3*Log[(-E^x + x^2)/(2*x)]^2, x] - (100*

Defer[Int][E^(10 - 2*x)*x^4*Log[(-E^x + x^2)/(2*x)]^2, x])/3 + 20*Defer[Int][E^(5 - x)*x^4*Log[(-E^x + x^2)/(2

*x)]^2, x] - 40*Defer[Int][E^(5 - 2*x)*x^5*Log[(-E^x + x^2)/(2*x)]^2, x] + 20*Defer[Int][E^(5 - 2*x)*x^6*Log[(

-E^x + x^2)/(2*x)]^2, x] - 40*Defer[Int][E^(5 - 3*x)*x^7*Log[(-E^x + x^2)/(2*x)]^2, x] + 20*Defer[Int][E^(5 -

3*x)*x^8*Log[(-E^x + x^2)/(2*x)]^2, x] - 40*Defer[Int][E^(5 - 4*x)*x^9*Log[(-E^x + x^2)/(2*x)]^2, x] + 20*Defe

r[Int][E^(5 - 4*x)*x^10*Log[(-E^x + x^2)/(2*x)]^2, x] + 40*Defer[Int][(E^(5 - 4*x)*x^11*Log[(-E^x + x^2)/(2*x)

]^2)/(-E^x + x^2), x] - 20*Defer[Int][(E^(5 - 4*x)*x^12*Log[(-E^x + x^2)/(2*x)]^2)/(-E^x + x^2), x] - 4*Defer[

Int][x^3*Log[(-E^x + x^2)/(2*x)]^3, x] + (80*Defer[Int][E^(5 - x)*x^3*Log[(-E^x + x^2)/(2*x)]^3, x])/3 + 4*Def

er[Int][x^4*Log[(-E^x + x^2)/(2*x)]^3, x] - (20*Defer[Int][E^(5 - x)*x^4*Log[(-E^x + x^2)/(2*x)]^3, x])/3 - 8*

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

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

x] - 8*Defer[Int][(x^9*Log[(-E^x + x^2)/(2*x)]^3)/E^(3*x), x] + 4*Defer[Int][(x^10*Log[(-E^x + x^2)/(2*x)]^3)

/E^(3*x), x] - 8*Defer[Int][(x^11*Log[(-E^x + x^2)/(2*x)]^3)/E^(4*x), x] + 4*Defer[Int][(x^12*Log[(-E^x + x^2)

/(2*x)]^3)/E^(4*x), x] + 8*Defer[Int][(x^13*Log[(-E^x + x^2)/(2*x)]^3)/(E^(4*x)*(-E^x + x^2)), x] - 4*Defer[In

t][(x^14*Log[(-E^x + x^2)/(2*x)]^3)/(E^(4*x)*(-E^x + x^2)), x] + 4*Defer[Int][x^3*Log[(-E^x + x^2)/(2*x)]^4, x

] - (200*Defer[Int][Defer[Int][(E^(10 - 4*x)*x^9)/(-E^x + x^2), x], x])/3 + (200*Defer[Int][Defer[Int][(E^(10

- 4*x)*x^9)/(-E^x + x^2), x]/x, x])/3 - (400*Defer[Int][(x*Defer[Int][(E^(10 - 4*x)*x^9)/(-E^x + x^2), x])/(-E

^x + x^2), x])/3 + (200*Defer[Int][(x^2*Defer[Int][(E^(10 - 4*x)*x^9)/(-E^x + x^2), x])/(-E^x + x^2), x])/3 +

(100*Defer[Int][Defer[Int][(E^(10 - 4*x)*x^10)/(-E^x + x^2), x], x])/3 - (100*Defer[Int][Defer[Int][(E^(10 - 4

*x)*x^10)/(-E^x + x^2), x]/x, x])/3 + (200*Defer[Int][(x*Defer[Int][(E^(10 - 4*x)*x^10)/(-E^x + x^2), x])/(-E^

x + x^2), x])/3 - (100*Defer[Int][(x^2*Defer[Int][(E^(10 - 4*x)*x^10)/(-E^x + x^2), x])/(-E^x + x^2), x])/3

Rubi steps

Aborted

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Mathematica [A]
time = 0.28, size = 42, normalized size = 1.31 \begin {gather*} \frac {1}{81} e^{-4 x} x^4 \left (5 e^5+3 e^x \log \left (\frac {-e^x+x^2}{2 x}\right )\right )^4 \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(-1500*E^(15 - 3*x)*x^5 + E^(20 - 4*x)*(-2500*x^5 + 2500*x^6) + E^x*(E^(20 - 4*x)*(2500*x^3 - 2500*x

^4) + E^(15 - 3*x)*(-1500*x^3 + 1500*x^4)) + (-2700*E^(10 - 2*x)*x^5 + E^(15 - 3*x)*(-6000*x^5 + 4500*x^6) + E

^x*(E^(15 - 3*x)*(6000*x^3 - 4500*x^4) + E^(10 - 2*x)*(-2700*x^3 + 2700*x^4)))*Log[(-E^x + x^2)/(2*x)] + (-162

0*E^(5 - x)*x^5 + E^(10 - 2*x)*(-5400*x^5 + 2700*x^6) + E^x*(E^(10 - 2*x)*(5400*x^3 - 2700*x^4) + E^(5 - x)*(-

1620*x^3 + 1620*x^4)))*Log[(-E^x + x^2)/(2*x)]^2 + (-324*x^5 + E^(5 - x)*(-2160*x^5 + 540*x^6) + E^x*(-324*x^3

+ 324*x^4 + E^(5 - x)*(2160*x^3 - 540*x^4)))*Log[(-E^x + x^2)/(2*x)]^3 + (324*E^x*x^3 - 324*x^5)*Log[(-E^x +

x^2)/(2*x)]^4)/(81*E^x - 81*x^2),x]

[Out]

(x^4*(5*E^5 + 3*E^x*Log[(-E^x + x^2)/(2*x)])^4)/(81*E^(4*x))

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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order 3.
time = 3.62, size = 11218, normalized size = 350.56


method	result	size

risch	\(\text {Expression too large to display}\)	\(11218\)

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((324*exp(x)*x^3-324*x^5)*ln(1/2*(-exp(x)+x^2)/x)^4+(((-540*x^4+2160*x^3)*exp(5-x)+324*x^4-324*x^3)*exp(x)

+(540*x^6-2160*x^5)*exp(5-x)-324*x^5)*ln(1/2*(-exp(x)+x^2)/x)^3+(((-2700*x^4+5400*x^3)*exp(5-x)^2+(1620*x^4-16

20*x^3)*exp(5-x))*exp(x)+(2700*x^6-5400*x^5)*exp(5-x)^2-1620*x^5*exp(5-x))*ln(1/2*(-exp(x)+x^2)/x)^2+(((-4500*

x^4+6000*x^3)*exp(5-x)^3+(2700*x^4-2700*x^3)*exp(5-x)^2)*exp(x)+(4500*x^6-6000*x^5)*exp(5-x)^3-2700*x^5*exp(5-

x)^2)*ln(1/2*(-exp(x)+x^2)/x)+((-2500*x^4+2500*x^3)*exp(5-x)^4+(1500*x^4-1500*x^3)*exp(5-x)^3)*exp(x)+(2500*x^

6-2500*x^5)*exp(5-x)^4-1500*x^5*exp(5-x)^3)/(81*exp(x)-81*x^2),x,method=_RETURNVERBOSE)

[Out]

result too large to display

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Maxima [F(-1)] Timed out
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(((324*exp(x)*x^3-324*x^5)*log(1/2*(-exp(x)+x^2)/x)^4+(((-540*x^4+2160*x^3)*exp(5-x)+324*x^4-324*x^3)

*exp(x)+(540*x^6-2160*x^5)*exp(5-x)-324*x^5)*log(1/2*(-exp(x)+x^2)/x)^3+(((-2700*x^4+5400*x^3)*exp(5-x)^2+(162

0*x^4-1620*x^3)*exp(5-x))*exp(x)+(2700*x^6-5400*x^5)*exp(5-x)^2-1620*x^5*exp(5-x))*log(1/2*(-exp(x)+x^2)/x)^2+

(((-4500*x^4+6000*x^3)*exp(5-x)^3+(2700*x^4-2700*x^3)*exp(5-x)^2)*exp(x)+(4500*x^6-6000*x^5)*exp(5-x)^3-2700*x

^5*exp(5-x)^2)*log(1/2*(-exp(x)+x^2)/x)+((-2500*x^4+2500*x^3)*exp(5-x)^4+(1500*x^4-1500*x^3)*exp(5-x)^3)*exp(x

)+(2500*x^6-2500*x^5)*exp(5-x)^4-1500*x^5*exp(5-x)^3)/(81*exp(x)-81*x^2),x, algorithm="maxima")

[Out]

Timed out

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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 116 vs. \(2 (29) = 58\).
time = 0.38, size = 116, normalized size = 3.62 \begin {gather*} \frac {1}{81} \, {\left (81 \, x^{4} e^{\left (4 \, x\right )} \log \left (\frac {x^{2} - e^{x}}{2 \, x}\right )^{4} + 540 \, x^{4} e^{\left (3 \, x + 5\right )} \log \left (\frac {x^{2} - e^{x}}{2 \, x}\right )^{3} + 1350 \, x^{4} e^{\left (2 \, x + 10\right )} \log \left (\frac {x^{2} - e^{x}}{2 \, x}\right )^{2} + 1500 \, x^{4} e^{\left (x + 15\right )} \log \left (\frac {x^{2} - e^{x}}{2 \, x}\right ) + 625 \, x^{4} e^{20}\right )} e^{\left (-4 \, x\right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((324*exp(x)*x^3-324*x^5)*log(1/2*(-exp(x)+x^2)/x)^4+(((-540*x^4+2160*x^3)*exp(5-x)+324*x^4-324*x^3)

*exp(x)+(540*x^6-2160*x^5)*exp(5-x)-324*x^5)*log(1/2*(-exp(x)+x^2)/x)^3+(((-2700*x^4+5400*x^3)*exp(5-x)^2+(162

0*x^4-1620*x^3)*exp(5-x))*exp(x)+(2700*x^6-5400*x^5)*exp(5-x)^2-1620*x^5*exp(5-x))*log(1/2*(-exp(x)+x^2)/x)^2+

(((-4500*x^4+6000*x^3)*exp(5-x)^3+(2700*x^4-2700*x^3)*exp(5-x)^2)*exp(x)+(4500*x^6-6000*x^5)*exp(5-x)^3-2700*x

^5*exp(5-x)^2)*log(1/2*(-exp(x)+x^2)/x)+((-2500*x^4+2500*x^3)*exp(5-x)^4+(1500*x^4-1500*x^3)*exp(5-x)^3)*exp(x

)+(2500*x^6-2500*x^5)*exp(5-x)^4-1500*x^5*exp(5-x)^3)/(81*exp(x)-81*x^2),x, algorithm="fricas")

[Out]

1/81*(81*x^4*e^(4*x)*log(1/2*(x^2 - e^x)/x)^4 + 540*x^4*e^(3*x + 5)*log(1/2*(x^2 - e^x)/x)^3 + 1350*x^4*e^(2*x

+ 10)*log(1/2*(x^2 - e^x)/x)^2 + 1500*x^4*e^(x + 15)*log(1/2*(x^2 - e^x)/x) + 625*x^4*e^20)*e^(-4*x)

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Sympy [F(-1)] Timed out
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(((324*exp(x)*x**3-324*x**5)*ln(1/2*(-exp(x)+x**2)/x)**4+(((-540*x**4+2160*x**3)*exp(5-x)+324*x**4-32

4*x**3)*exp(x)+(540*x**6-2160*x**5)*exp(5-x)-324*x**5)*ln(1/2*(-exp(x)+x**2)/x)**3+(((-2700*x**4+5400*x**3)*ex

p(5-x)**2+(1620*x**4-1620*x**3)*exp(5-x))*exp(x)+(2700*x**6-5400*x**5)*exp(5-x)**2-1620*x**5*exp(5-x))*ln(1/2*

(-exp(x)+x**2)/x)**2+(((-4500*x**4+6000*x**3)*exp(5-x)**3+(2700*x**4-2700*x**3)*exp(5-x)**2)*exp(x)+(4500*x**6

-6000*x**5)*exp(5-x)**3-2700*x**5*exp(5-x)**2)*ln(1/2*(-exp(x)+x**2)/x)+((-2500*x**4+2500*x**3)*exp(5-x)**4+(1

500*x**4-1500*x**3)*exp(5-x)**3)*exp(x)+(2500*x**6-2500*x**5)*exp(5-x)**4-1500*x**5*exp(5-x)**3)/(81*exp(x)-81

*x**2),x)

[Out]

Timed out

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Giac [F(-1)] Timed out
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(((324*exp(x)*x^3-324*x^5)*log(1/2*(-exp(x)+x^2)/x)^4+(((-540*x^4+2160*x^3)*exp(5-x)+324*x^4-324*x^3)

*exp(x)+(540*x^6-2160*x^5)*exp(5-x)-324*x^5)*log(1/2*(-exp(x)+x^2)/x)^3+(((-2700*x^4+5400*x^3)*exp(5-x)^2+(162

0*x^4-1620*x^3)*exp(5-x))*exp(x)+(2700*x^6-5400*x^5)*exp(5-x)^2-1620*x^5*exp(5-x))*log(1/2*(-exp(x)+x^2)/x)^2+

(((-4500*x^4+6000*x^3)*exp(5-x)^3+(2700*x^4-2700*x^3)*exp(5-x)^2)*exp(x)+(4500*x^6-6000*x^5)*exp(5-x)^3-2700*x

^5*exp(5-x)^2)*log(1/2*(-exp(x)+x^2)/x)+((-2500*x^4+2500*x^3)*exp(5-x)^4+(1500*x^4-1500*x^3)*exp(5-x)^3)*exp(x

)+(2500*x^6-2500*x^5)*exp(5-x)^4-1500*x^5*exp(5-x)^3)/(81*exp(x)-81*x^2),x, algorithm="giac")

[Out]

Timed out

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Mupad [F]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {{\mathrm {e}}^x\,\left ({\mathrm {e}}^{15-3\,x}\,\left (1500\,x^3-1500\,x^4\right )-{\mathrm {e}}^{20-4\,x}\,\left (2500\,x^3-2500\,x^4\right )\right )+{\ln \left (-\frac {\frac {{\mathrm {e}}^x}{2}-\frac {x^2}{2}}{x}\right )}^2\,\left ({\mathrm {e}}^x\,\left ({\mathrm {e}}^{5-x}\,\left (1620\,x^3-1620\,x^4\right )-{\mathrm {e}}^{10-2\,x}\,\left (5400\,x^3-2700\,x^4\right )\right )+{\mathrm {e}}^{10-2\,x}\,\left (5400\,x^5-2700\,x^6\right )+1620\,x^5\,{\mathrm {e}}^{5-x}\right )+{\ln \left (-\frac {\frac {{\mathrm {e}}^x}{2}-\frac {x^2}{2}}{x}\right )}^3\,\left ({\mathrm {e}}^{5-x}\,\left (2160\,x^5-540\,x^6\right )-{\mathrm {e}}^x\,\left ({\mathrm {e}}^{5-x}\,\left (2160\,x^3-540\,x^4\right )-324\,x^3+324\,x^4\right )+324\,x^5\right )+{\mathrm {e}}^{20-4\,x}\,\left (2500\,x^5-2500\,x^6\right )+1500\,x^5\,{\mathrm {e}}^{15-3\,x}-{\ln \left (-\frac {\frac {{\mathrm {e}}^x}{2}-\frac {x^2}{2}}{x}\right )}^4\,\left (324\,x^3\,{\mathrm {e}}^x-324\,x^5\right )+\ln \left (-\frac {\frac {{\mathrm {e}}^x}{2}-\frac {x^2}{2}}{x}\right )\,\left ({\mathrm {e}}^x\,\left ({\mathrm {e}}^{10-2\,x}\,\left (2700\,x^3-2700\,x^4\right )-{\mathrm {e}}^{15-3\,x}\,\left (6000\,x^3-4500\,x^4\right )\right )+{\mathrm {e}}^{15-3\,x}\,\left (6000\,x^5-4500\,x^6\right )+2700\,x^5\,{\mathrm {e}}^{10-2\,x}\right )}{81\,{\mathrm {e}}^x-81\,x^2} \,d x \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(x)*(exp(15 - 3*x)*(1500*x^3 - 1500*x^4) - exp(20 - 4*x)*(2500*x^3 - 2500*x^4)) + log(-(exp(x)/2 - x^

2/2)/x)^2*(exp(x)*(exp(5 - x)*(1620*x^3 - 1620*x^4) - exp(10 - 2*x)*(5400*x^3 - 2700*x^4)) + exp(10 - 2*x)*(54

00*x^5 - 2700*x^6) + 1620*x^5*exp(5 - x)) + log(-(exp(x)/2 - x^2/2)/x)^3*(exp(5 - x)*(2160*x^5 - 540*x^6) - ex

p(x)*(exp(5 - x)*(2160*x^3 - 540*x^4) - 324*x^3 + 324*x^4) + 324*x^5) + exp(20 - 4*x)*(2500*x^5 - 2500*x^6) +

1500*x^5*exp(15 - 3*x) - log(-(exp(x)/2 - x^2/2)/x)^4*(324*x^3*exp(x) - 324*x^5) + log(-(exp(x)/2 - x^2/2)/x)*

(exp(x)*(exp(10 - 2*x)*(2700*x^3 - 2700*x^4) - exp(15 - 3*x)*(6000*x^3 - 4500*x^4)) + exp(15 - 3*x)*(6000*x^5

- 4500*x^6) + 2700*x^5*exp(10 - 2*x)))/(81*exp(x) - 81*x^2),x)

[Out]

int(-(exp(x)*(exp(15 - 3*x)*(1500*x^3 - 1500*x^4) - exp(20 - 4*x)*(2500*x^3 - 2500*x^4)) + log(-(exp(x)/2 - x^

2/2)/x)^2*(exp(x)*(exp(5 - x)*(1620*x^3 - 1620*x^4) - exp(10 - 2*x)*(5400*x^3 - 2700*x^4)) + exp(10 - 2*x)*(54

00*x^5 - 2700*x^6) + 1620*x^5*exp(5 - x)) + log(-(exp(x)/2 - x^2/2)/x)^3*(exp(5 - x)*(2160*x^5 - 540*x^6) - ex

p(x)*(exp(5 - x)*(2160*x^3 - 540*x^4) - 324*x^3 + 324*x^4) + 324*x^5) + exp(20 - 4*x)*(2500*x^5 - 2500*x^6) +

1500*x^5*exp(15 - 3*x) - log(-(exp(x)/2 - x^2/2)/x)^4*(324*x^3*exp(x) - 324*x^5) + log(-(exp(x)/2 - x^2/2)/x)*

(exp(x)*(exp(10 - 2*x)*(2700*x^3 - 2700*x^4) - exp(15 - 3*x)*(6000*x^3 - 4500*x^4)) + exp(15 - 3*x)*(6000*x^5

- 4500*x^6) + 2700*x^5*exp(10 - 2*x)))/(81*exp(x) - 81*x^2), x)

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