3.54.81 \(\int \frac {-256 x^2-128 x^4-128 x^5+e^{\frac {20-x}{2}} (-128 x^2-128 x^3)+e^{\frac {20-x}{4}} (-64 x^2+240 x^3+256 x^4)+e^x (8 x+8 x^2+8 x^3+e^{\frac {20-x}{2}} (8+8 x)+e^{\frac {20-x}{4}} (4-15 x-16 x^2))+(64 x^2-256 x^3-256 x^4+e^x (-4+e^{\frac {20-x}{4}} (-16-16 x)+16 x+16 x^2)+e^{\frac {20-x}{4}} (256 x^2+256 x^3)) \log (e^{2 x}-32 e^x x^2+256 x^4)+(-128 x^2-128 x^3+e^x (8+8 x)) \log ^2(e^{2 x}-32 e^x x^2+256 x^4)}{-64 e^{\frac {20-x}{2}} x^2+128 e^{\frac {20-x}{4}} x^3-64 x^4+e^x (4 e^{\frac {20-x}{2}}-8 e^{\frac {20-x}{4}} x+4 x^2)+(128 e^{\frac {20-x}{4}} x^2-128 x^3+e^x (-8 e^{\frac {20-x}{4}}+8 x)) \log (e^{2 x}-32 e^x x^2+256 x^4)+(4 e^x-64 x^2) \log ^2(e^{2 x}-32 e^x x^2+256 x^4)} \, dx\)

Optimal. Leaf size=34 \[ x \left (2+x-\frac {1}{-e^{5-\frac {x}{4}}+x+\log \left (\left (e^x-16 x^2\right )^2\right )}\right ) \]

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Rubi [F]  time = 180.00, 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*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-256*x^2 - 128*x^4 - 128*x^5 + E^((20 - x)/2)*(-128*x^2 - 128*x^3) + E^((20 - x)/4)*(-64*x^2 + 240*x^3 +
256*x^4) + E^x*(8*x + 8*x^2 + 8*x^3 + E^((20 - x)/2)*(8 + 8*x) + E^((20 - x)/4)*(4 - 15*x - 16*x^2)) + (64*x^2
- 256*x^3 - 256*x^4 + E^x*(-4 + E^((20 - x)/4)*(-16 - 16*x) + 16*x + 16*x^2) + E^((20 - x)/4)*(256*x^2 + 256*
x^3))*Log[E^(2*x) - 32*E^x*x^2 + 256*x^4] + (-128*x^2 - 128*x^3 + E^x*(8 + 8*x))*Log[E^(2*x) - 32*E^x*x^2 + 25
6*x^4]^2)/(-64*E^((20 - x)/2)*x^2 + 128*E^((20 - x)/4)*x^3 - 64*x^4 + E^x*(4*E^((20 - x)/2) - 8*E^((20 - x)/4)
*x + 4*x^2) + (128*E^((20 - x)/4)*x^2 - 128*x^3 + E^x*(-8*E^((20 - x)/4) + 8*x))*Log[E^(2*x) - 32*E^x*x^2 + 25
6*x^4] + (4*E^x - 64*x^2)*Log[E^(2*x) - 32*E^x*x^2 + 256*x^4]^2),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.36, size = 51, normalized size = 1.50 \begin {gather*} x \left (2+x-\frac {e^{x/4}}{-e^5+e^{x/4} x+e^{x/4} \log \left (\left (e^x-16 x^2\right )^2\right )}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-256*x^2 - 128*x^4 - 128*x^5 + E^((20 - x)/2)*(-128*x^2 - 128*x^3) + E^((20 - x)/4)*(-64*x^2 + 240*
x^3 + 256*x^4) + E^x*(8*x + 8*x^2 + 8*x^3 + E^((20 - x)/2)*(8 + 8*x) + E^((20 - x)/4)*(4 - 15*x - 16*x^2)) + (
64*x^2 - 256*x^3 - 256*x^4 + E^x*(-4 + E^((20 - x)/4)*(-16 - 16*x) + 16*x + 16*x^2) + E^((20 - x)/4)*(256*x^2
+ 256*x^3))*Log[E^(2*x) - 32*E^x*x^2 + 256*x^4] + (-128*x^2 - 128*x^3 + E^x*(8 + 8*x))*Log[E^(2*x) - 32*E^x*x^
2 + 256*x^4]^2)/(-64*E^((20 - x)/2)*x^2 + 128*E^((20 - x)/4)*x^3 - 64*x^4 + E^x*(4*E^((20 - x)/2) - 8*E^((20 -
x)/4)*x + 4*x^2) + (128*E^((20 - x)/4)*x^2 - 128*x^3 + E^x*(-8*E^((20 - x)/4) + 8*x))*Log[E^(2*x) - 32*E^x*x^
2 + 256*x^4] + (4*E^x - 64*x^2)*Log[E^(2*x) - 32*E^x*x^2 + 256*x^4]^2),x]

[Out]

x*(2 + x - E^(x/4)/(-E^5 + E^(x/4)*x + E^(x/4)*Log[(E^x - 16*x^2)^2]))

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fricas [B]  time = 0.89, size = 114, normalized size = 3.35 \begin {gather*} \frac {x^{3} + 2 \, x^{2} - {\left (x^{2} + 2 \, x\right )} e^{\left (-\frac {1}{4} \, x + 5\right )} + {\left (x^{2} + 2 \, x\right )} \log \left ({\left (256 \, x^{4} e^{\left (-2 \, x + 40\right )} - 32 \, x^{2} e^{\left (-x + 40\right )} + e^{40}\right )} e^{\left (2 \, x - 40\right )}\right ) - x}{x - e^{\left (-\frac {1}{4} \, x + 5\right )} + \log \left ({\left (256 \, x^{4} e^{\left (-2 \, x + 40\right )} - 32 \, x^{2} e^{\left (-x + 40\right )} + e^{40}\right )} e^{\left (2 \, x - 40\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x+8)*exp(x)-128*x^3-128*x^2)*log(exp(x)^2-32*exp(x)*x^2+256*x^4)^2+(((-16*x-16)*exp(-1/4*x+5)+1
6*x^2+16*x-4)*exp(x)+(256*x^3+256*x^2)*exp(-1/4*x+5)-256*x^4-256*x^3+64*x^2)*log(exp(x)^2-32*exp(x)*x^2+256*x^
4)+((8*x+8)*exp(-1/4*x+5)^2+(-16*x^2-15*x+4)*exp(-1/4*x+5)+8*x^3+8*x^2+8*x)*exp(x)+(-128*x^3-128*x^2)*exp(-1/4
*x+5)^2+(256*x^4+240*x^3-64*x^2)*exp(-1/4*x+5)-128*x^5-128*x^4-256*x^2)/((4*exp(x)-64*x^2)*log(exp(x)^2-32*exp
(x)*x^2+256*x^4)^2+((-8*exp(-1/4*x+5)+8*x)*exp(x)+128*x^2*exp(-1/4*x+5)-128*x^3)*log(exp(x)^2-32*exp(x)*x^2+25
6*x^4)+(4*exp(-1/4*x+5)^2-8*x*exp(-1/4*x+5)+4*x^2)*exp(x)-64*x^2*exp(-1/4*x+5)^2+128*x^3*exp(-1/4*x+5)-64*x^4)
,x, algorithm="fricas")

[Out]

(x^3 + 2*x^2 - (x^2 + 2*x)*e^(-1/4*x + 5) + (x^2 + 2*x)*log((256*x^4*e^(-2*x + 40) - 32*x^2*e^(-x + 40) + e^40
)*e^(2*x - 40)) - x)/(x - e^(-1/4*x + 5) + log((256*x^4*e^(-2*x + 40) - 32*x^2*e^(-x + 40) + e^40)*e^(2*x - 40
)))

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giac [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x+8)*exp(x)-128*x^3-128*x^2)*log(exp(x)^2-32*exp(x)*x^2+256*x^4)^2+(((-16*x-16)*exp(-1/4*x+5)+1
6*x^2+16*x-4)*exp(x)+(256*x^3+256*x^2)*exp(-1/4*x+5)-256*x^4-256*x^3+64*x^2)*log(exp(x)^2-32*exp(x)*x^2+256*x^
4)+((8*x+8)*exp(-1/4*x+5)^2+(-16*x^2-15*x+4)*exp(-1/4*x+5)+8*x^3+8*x^2+8*x)*exp(x)+(-128*x^3-128*x^2)*exp(-1/4
*x+5)^2+(256*x^4+240*x^3-64*x^2)*exp(-1/4*x+5)-128*x^5-128*x^4-256*x^2)/((4*exp(x)-64*x^2)*log(exp(x)^2-32*exp
(x)*x^2+256*x^4)^2+((-8*exp(-1/4*x+5)+8*x)*exp(x)+128*x^2*exp(-1/4*x+5)-128*x^3)*log(exp(x)^2-32*exp(x)*x^2+25
6*x^4)+(4*exp(-1/4*x+5)^2-8*x*exp(-1/4*x+5)+4*x^2)*exp(x)-64*x^2*exp(-1/4*x+5)^2+128*x^3*exp(-1/4*x+5)-64*x^4)
,x, algorithm="giac")

[Out]

Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,sageVARx):;OUTP
UT:exp(t_nostep)^2=exp(2*t_nostep)exp(t_nostep)^2=exp(2*t_nostep)exp(t_nostep)^2=exp(2*t_nostep)exp(t_nostep)^
2=exp(2*t_n

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maple [C]  time = 0.30, size = 150, normalized size = 4.41

method	result	size
risch	\(x^{2}+2 x -\frac {2 x \,{\mathrm e}^{\frac {x}{4}}}{-i \pi \mathrm {csgn}\left (i \left (\frac {{\mathrm e}^{x}}{16}-x^{2}\right )\right )^{2} \mathrm {csgn}\left (i \left (\frac {{\mathrm e}^{x}}{16}-x^{2}\right )^{2}\right ) {\mathrm e}^{\frac {x}{4}}-2 i \pi \,\mathrm {csgn}\left (i \left (\frac {{\mathrm e}^{x}}{16}-x^{2}\right )\right ) \mathrm {csgn}\left (i \left (\frac {{\mathrm e}^{x}}{16}-x^{2}\right )^{2}\right )^{2} {\mathrm e}^{\frac {x}{4}}-i \pi \mathrm {csgn}\left (i \left (\frac {{\mathrm e}^{x}}{16}-x^{2}\right )^{2}\right )^{3} {\mathrm e}^{\frac {x}{4}}+2 x \,{\mathrm e}^{\frac {x}{4}}+4 \,{\mathrm e}^{\frac {x}{4}} \ln \left (-\frac {{\mathrm e}^{x}}{16}+x^{2}\right )-2 \,{\mathrm e}^{5}}\)	\(150\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((8*x+8)*exp(x)-128*x^3-128*x^2)*ln(exp(x)^2-32*exp(x)*x^2+256*x^4)^2+(((-16*x-16)*exp(-1/4*x+5)+16*x^2+1
6*x-4)*exp(x)+(256*x^3+256*x^2)*exp(-1/4*x+5)-256*x^4-256*x^3+64*x^2)*ln(exp(x)^2-32*exp(x)*x^2+256*x^4)+((8*x
+8)*exp(-1/4*x+5)^2+(-16*x^2-15*x+4)*exp(-1/4*x+5)+8*x^3+8*x^2+8*x)*exp(x)+(-128*x^3-128*x^2)*exp(-1/4*x+5)^2+
(256*x^4+240*x^3-64*x^2)*exp(-1/4*x+5)-128*x^5-128*x^4-256*x^2)/((4*exp(x)-64*x^2)*ln(exp(x)^2-32*exp(x)*x^2+2
56*x^4)^2+((-8*exp(-1/4*x+5)+8*x)*exp(x)+128*x^2*exp(-1/4*x+5)-128*x^3)*ln(exp(x)^2-32*exp(x)*x^2+256*x^4)+(4*
exp(-1/4*x+5)^2-8*x*exp(-1/4*x+5)+4*x^2)*exp(x)-64*x^2*exp(-1/4*x+5)^2+128*x^3*exp(-1/4*x+5)-64*x^4),x,method=
_RETURNVERBOSE)

[Out]

x^2+2*x-2*x*exp(1/4*x)/(-I*Pi*csgn(I*(1/16*exp(x)-x^2))^2*csgn(I*(1/16*exp(x)-x^2)^2)*exp(1/4*x)-2*I*Pi*csgn(I
*(1/16*exp(x)-x^2))*csgn(I*(1/16*exp(x)-x^2)^2)^2*exp(1/4*x)-I*Pi*csgn(I*(1/16*exp(x)-x^2)^2)^3*exp(1/4*x)+2*x
*exp(1/4*x)+4*exp(1/4*x)*ln(-1/16*exp(x)+x^2)-2*exp(5))

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x+8)*exp(x)-128*x^3-128*x^2)*log(exp(x)^2-32*exp(x)*x^2+256*x^4)^2+(((-16*x-16)*exp(-1/4*x+5)+1
6*x^2+16*x-4)*exp(x)+(256*x^3+256*x^2)*exp(-1/4*x+5)-256*x^4-256*x^3+64*x^2)*log(exp(x)^2-32*exp(x)*x^2+256*x^
4)+((8*x+8)*exp(-1/4*x+5)^2+(-16*x^2-15*x+4)*exp(-1/4*x+5)+8*x^3+8*x^2+8*x)*exp(x)+(-128*x^3-128*x^2)*exp(-1/4
*x+5)^2+(256*x^4+240*x^3-64*x^2)*exp(-1/4*x+5)-128*x^5-128*x^4-256*x^2)/((4*exp(x)-64*x^2)*log(exp(x)^2-32*exp
(x)*x^2+256*x^4)^2+((-8*exp(-1/4*x+5)+8*x)*exp(x)+128*x^2*exp(-1/4*x+5)-128*x^3)*log(exp(x)^2-32*exp(x)*x^2+25
6*x^4)+(4*exp(-1/4*x+5)^2-8*x*exp(-1/4*x+5)+4*x^2)*exp(x)-64*x^2*exp(-1/4*x+5)^2+128*x^3*exp(-1/4*x+5)-64*x^4)
,x, algorithm="maxima")

[Out]

(256*x^6*e^10 + 512*x^5*e^10 + 4*(16*x^5 + 96*x^4 + 80*x^3 - 3*(x^3 + 2*x^2 - x)*e^x)*e^(3/2*x) + (16*x^5*e^5
- 32*x^4*e^5 - 400*x^3*e^5 - 512*x^2*e^5 - (x^3*e^5 - 10*x^2*e^5 - 25*x*e^5)*e^x)*e^(5/4*x) - 64*(16*x^7 + 96*
x^6 + 112*x^5 - 64*x^4 - (3*x^5 + 6*x^4 - x^3 - 4*x^2)*e^x)*e^(1/2*x) - 16*(16*x^7*e^5 - 32*x^6*e^5 - 400*x^5*
e^5 - 512*x^4*e^5 - (x^5*e^5 - 10*x^4*e^5 - 25*x^3*e^5)*e^x)*e^(1/4*x) - (16*x^4*e^10 + 32*x^3*e^10 - (x^2*e^1
0 + 2*x*e^10)*e^x)*e^x - 16*(x^4*e^10 + 2*x^3*e^10)*e^x + 2*(4*(16*x^4 + 96*x^3 + 128*x^2 - 3*(x^2 + 2*x)*e^x)
*e^(3/2*x) + (16*x^4*e^5 + 32*x^3*e^5 - (x^2*e^5 + 2*x*e^5)*e^x)*e^(5/4*x) - 64*(16*x^6 + 96*x^5 + 128*x^4 - 3
*(x^4 + 2*x^3)*e^x)*e^(1/2*x) - 16*(16*x^6*e^5 + 32*x^5*e^5 - (x^4*e^5 + 2*x^3*e^5)*e^x)*e^(1/4*x))*log(-16*x^
2 + e^x))/(256*x^4*e^10 - 16*x^2*e^(x + 10) + 4*(16*x^3 + 64*x^2 - 3*x*e^x)*e^(3/2*x) + (16*x^3*e^5 - 64*x^2*e
^5 - 256*x*e^5 - (x*e^5 - 12*e^5)*e^x)*e^(5/4*x) - 64*(16*x^5 + 64*x^4 - 3*x^3*e^x)*e^(1/2*x) - 16*(16*x^5*e^5
- 64*x^4*e^5 - 256*x^3*e^5 - (x^3*e^5 - 12*x^2*e^5)*e^x)*e^(1/4*x) - (16*x^2*e^10 - e^(x + 10))*e^x + 2*(4*(1
6*x^2 + 64*x - 3*e^x)*e^(3/2*x) + (16*x^2*e^5 - e^(x + 5))*e^(5/4*x) - 64*(16*x^4 + 64*x^3 - 3*x^2*e^x)*e^(1/2
*x) - 16*(16*x^4*e^5 - x^2*e^(x + 5))*e^(1/4*x))*log(-16*x^2 + e^x)) + 1/4*integrate(-128*(16*(16*x^4 + 128*x^
3 - 128*x^2 + 3*(x^3 - 5*x^2 + 4*x)*e^x)*e^(11/4*x) + (16*x^5*e^5 + 32*x^4*e^5 + (3*x^3*e^5 - 18*x^2*e^5 + 16*
x*e^5)*e^x)*e^(5/2*x) - 16*(256*x^7 + 256*x^6 - 1024*x^5 + 2048*x^4 + 3*(x^3 - 5*x^2 + 4*x)*e^(2*x) - 32*(x^4
- 4*x^3 + 4*x^2)*e^x)*e^(7/4*x) - (1280*x^7*e^5 - 3584*x^6*e^5 + 4096*x^5*e^5 + (3*x^3*e^5 - 18*x^2*e^5 + 16*x
*e^5)*e^(2*x))*e^(3/2*x) - 256*(3*x^4*e^(2*x) - 16*(x^7 + x^6 - 4*x^5 + 8*x^4)*e^x)*e^(3/4*x) - 16*((x^5*e^5 +
2*x^4*e^5)*e^(2*x) - 16*(5*x^7*e^5 - 14*x^6*e^5 + 16*x^5*e^5)*e^x)*e^(1/2*x))/(65536*x^8*e^15 - 8192*x^6*e^(x
+ 15) + 256*x^4*e^(2*x + 15) - 16*(256*x^5 + 2048*x^4 + 4096*x^3 + 9*x*e^(2*x) - 96*(x^3 + 4*x^2)*e^x)*e^(11/
4*x) - 8*(256*x^5*e^5 + 512*x^4*e^5 - 4096*x^3*e^5 - 8192*x^2*e^5 + 3*(x*e^5 - 6*e^5)*e^(2*x) - 64*(x^3*e^5 -
2*x^2*e^5 - 12*x*e^5)*e^x)*e^(5/2*x) - (256*x^5*e^10 - 2048*x^4*e^10 - 8192*x^3*e^10 + (x*e^10 - 24*e^10)*e^(2
*x) - 32*(x^3*e^10 - 16*x^2*e^10 - 16*x*e^10)*e^x)*e^(9/4*x) + (256*x^4*e^15 - 32*x^2*e^(x + 15) + e^(2*x + 15
))*e^(2*x) + 512*(256*x^7 + 2048*x^6 + 4096*x^5 + 9*x^3*e^(2*x) - 96*(x^5 + 4*x^4)*e^x)*e^(7/4*x) + 256*(256*x
^7*e^5 + 512*x^6*e^5 - 4096*x^5*e^5 - 8192*x^4*e^5 + 3*(x^3*e^5 - 6*x^2*e^5)*e^(2*x) - 64*(x^5*e^5 - 2*x^4*e^5
- 12*x^3*e^5)*e^x)*e^(3/2*x) + 32*(256*x^7*e^10 - 2048*x^6*e^10 - 8192*x^5*e^10 + (x^3*e^10 - 24*x^2*e^10)*e^
(2*x) - 32*(x^5*e^10 - 16*x^4*e^10 - 16*x^3*e^10)*e^x)*e^(5/4*x) - 4096*(256*x^9 + 2048*x^8 + 4096*x^7 + 9*x^5
*e^(2*x) - 96*(x^7 + 4*x^6)*e^x)*e^(3/4*x) - 2048*(256*x^9*e^5 + 512*x^8*e^5 - 4096*x^7*e^5 - 8192*x^6*e^5 + 3
*(x^5*e^5 - 6*x^4*e^5)*e^(2*x) - 64*(x^7*e^5 - 2*x^6*e^5 - 12*x^5*e^5)*e^x)*e^(1/2*x) - 256*(256*x^9*e^10 - 20
48*x^8*e^10 - 8192*x^7*e^10 + (x^5*e^10 - 24*x^4*e^10)*e^(2*x) - 32*(x^7*e^10 - 16*x^6*e^10 - 16*x^5*e^10)*e^x
)*e^(1/4*x) - 32*(256*x^6*e^15 - 32*x^4*e^(x + 15) + x^2*e^(2*x + 15))*e^x - 2*(16*(256*x^4 + 2048*x^3 + 4096*
x^2 - 96*(x^2 + 4*x)*e^x + 9*e^(2*x))*e^(11/4*x) + 8*(256*x^4*e^5 + 1024*x^3*e^5 - 64*(x^2*e^5 + x*e^5)*e^x +
3*e^(2*x + 5))*e^(5/2*x) + (256*x^4*e^10 - 32*x^2*e^(x + 10) + e^(2*x + 10))*e^(9/4*x) - 512*(256*x^6 + 2048*x
^5 + 4096*x^4 + 9*x^2*e^(2*x) - 96*(x^4 + 4*x^3)*e^x)*e^(7/4*x) - 256*(256*x^6*e^5 + 1024*x^5*e^5 + 3*x^2*e^(2
*x + 5) - 64*(x^4*e^5 + x^3*e^5)*e^x)*e^(3/2*x) - 32*(256*x^6*e^10 - 32*x^4*e^(x + 10) + x^2*e^(2*x + 10))*e^(
5/4*x) + 4096*(256*x^8 + 2048*x^7 + 4096*x^6 + 9*x^4*e^(2*x) - 96*(x^6 + 4*x^5)*e^x)*e^(3/4*x) + 2048*(256*x^8
*e^5 + 1024*x^7*e^5 + 3*x^4*e^(2*x + 5) - 64*(x^6*e^5 + x^5*e^5)*e^x)*e^(1/2*x) + 256*(256*x^8*e^10 - 32*x^6*e
^(x + 10) + x^4*e^(2*x + 10))*e^(1/4*x))*log(-16*x^2 + e^x)), x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} -\int \frac {{\ln \left ({\mathrm {e}}^{2\,x}-32\,x^2\,{\mathrm {e}}^x+256\,x^4\right )}^2\,\left (128\,x^2-{\mathrm {e}}^x\,\left (8\,x+8\right )+128\,x^3\right )-\ln \left ({\mathrm {e}}^{2\,x}-32\,x^2\,{\mathrm {e}}^x+256\,x^4\right )\,\left ({\mathrm {e}}^{5-\frac {x}{4}}\,\left (256\,x^3+256\,x^2\right )+64\,x^2-256\,x^3-256\,x^4+{\mathrm {e}}^x\,\left (16\,x-{\mathrm {e}}^{5-\frac {x}{4}}\,\left (16\,x+16\right )+16\,x^2-4\right )\right )-{\mathrm {e}}^x\,\left (8\,x+{\mathrm {e}}^{10-\frac {x}{2}}\,\left (8\,x+8\right )-{\mathrm {e}}^{5-\frac {x}{4}}\,\left (16\,x^2+15\,x-4\right )+8\,x^2+8\,x^3\right )+{\mathrm {e}}^{10-\frac {x}{2}}\,\left (128\,x^3+128\,x^2\right )+256\,x^2+128\,x^4+128\,x^5-{\mathrm {e}}^{5-\frac {x}{4}}\,\left (256\,x^4+240\,x^3-64\,x^2\right )}{{\mathrm {e}}^x\,\left (4\,{\mathrm {e}}^{10-\frac {x}{2}}-8\,x\,{\mathrm {e}}^{5-\frac {x}{4}}+4\,x^2\right )+\ln \left ({\mathrm {e}}^{2\,x}-32\,x^2\,{\mathrm {e}}^x+256\,x^4\right )\,\left ({\mathrm {e}}^x\,\left (8\,x-8\,{\mathrm {e}}^{5-\frac {x}{4}}\right )+128\,x^2\,{\mathrm {e}}^{5-\frac {x}{4}}-128\,x^3\right )+128\,x^3\,{\mathrm {e}}^{5-\frac {x}{4}}-64\,x^2\,{\mathrm {e}}^{10-\frac {x}{2}}-64\,x^4+{\ln \left ({\mathrm {e}}^{2\,x}-32\,x^2\,{\mathrm {e}}^x+256\,x^4\right )}^2\,\left (4\,{\mathrm {e}}^x-64\,x^2\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(exp(2*x) - 32*x^2*exp(x) + 256*x^4)^2*(128*x^2 - exp(x)*(8*x + 8) + 128*x^3) - log(exp(2*x) - 32*x^2
*exp(x) + 256*x^4)*(exp(5 - x/4)*(256*x^2 + 256*x^3) + 64*x^2 - 256*x^3 - 256*x^4 + exp(x)*(16*x - exp(5 - x/4
)*(16*x + 16) + 16*x^2 - 4)) - exp(x)*(8*x + exp(10 - x/2)*(8*x + 8) - exp(5 - x/4)*(15*x + 16*x^2 - 4) + 8*x^
2 + 8*x^3) + exp(10 - x/2)*(128*x^2 + 128*x^3) + 256*x^2 + 128*x^4 + 128*x^5 - exp(5 - x/4)*(240*x^3 - 64*x^2
+ 256*x^4))/(exp(x)*(4*exp(10 - x/2) - 8*x*exp(5 - x/4) + 4*x^2) + log(exp(2*x) - 32*x^2*exp(x) + 256*x^4)*(ex
p(x)*(8*x - 8*exp(5 - x/4)) + 128*x^2*exp(5 - x/4) - 128*x^3) + 128*x^3*exp(5 - x/4) - 64*x^2*exp(10 - x/2) -
64*x^4 + log(exp(2*x) - 32*x^2*exp(x) + 256*x^4)^2*(4*exp(x) - 64*x^2)),x)

[Out]

-int((log(exp(2*x) - 32*x^2*exp(x) + 256*x^4)^2*(128*x^2 - exp(x)*(8*x + 8) + 128*x^3) - log(exp(2*x) - 32*x^2
*exp(x) + 256*x^4)*(exp(5 - x/4)*(256*x^2 + 256*x^3) + 64*x^2 - 256*x^3 - 256*x^4 + exp(x)*(16*x - exp(5 - x/4
)*(16*x + 16) + 16*x^2 - 4)) - exp(x)*(8*x + exp(10 - x/2)*(8*x + 8) - exp(5 - x/4)*(15*x + 16*x^2 - 4) + 8*x^
2 + 8*x^3) + exp(10 - x/2)*(128*x^2 + 128*x^3) + 256*x^2 + 128*x^4 + 128*x^5 - exp(5 - x/4)*(240*x^3 - 64*x^2
+ 256*x^4))/(exp(x)*(4*exp(10 - x/2) - 8*x*exp(5 - x/4) + 4*x^2) + log(exp(2*x) - 32*x^2*exp(x) + 256*x^4)*(ex
p(x)*(8*x - 8*exp(5 - x/4)) + 128*x^2*exp(5 - x/4) - 128*x^3) + 128*x^3*exp(5 - x/4) - 64*x^2*exp(10 - x/2) -
64*x^4 + log(exp(2*x) - 32*x^2*exp(x) + 256*x^4)^2*(4*exp(x) - 64*x^2)), x)

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sympy [A]  time = 0.60, size = 39, normalized size = 1.15 \begin {gather*} x^{2} + 2 x - \frac {x}{x + \log {\left (256 x^{4} - 32 x^{2} e^{x} + e^{2 x} \right )} - \frac {e^{5}}{\sqrt [4]{e^{x}}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x+8)*exp(x)-128*x**3-128*x**2)*ln(exp(x)**2-32*exp(x)*x**2+256*x**4)**2+(((-16*x-16)*exp(-1/4*x
+5)+16*x**2+16*x-4)*exp(x)+(256*x**3+256*x**2)*exp(-1/4*x+5)-256*x**4-256*x**3+64*x**2)*ln(exp(x)**2-32*exp(x)
*x**2+256*x**4)+((8*x+8)*exp(-1/4*x+5)**2+(-16*x**2-15*x+4)*exp(-1/4*x+5)+8*x**3+8*x**2+8*x)*exp(x)+(-128*x**3
-128*x**2)*exp(-1/4*x+5)**2+(256*x**4+240*x**3-64*x**2)*exp(-1/4*x+5)-128*x**5-128*x**4-256*x**2)/((4*exp(x)-6
4*x**2)*ln(exp(x)**2-32*exp(x)*x**2+256*x**4)**2+((-8*exp(-1/4*x+5)+8*x)*exp(x)+128*x**2*exp(-1/4*x+5)-128*x**
3)*ln(exp(x)**2-32*exp(x)*x**2+256*x**4)+(4*exp(-1/4*x+5)**2-8*x*exp(-1/4*x+5)+4*x**2)*exp(x)-64*x**2*exp(-1/4
*x+5)**2+128*x**3*exp(-1/4*x+5)-64*x**4),x)

[Out]

x**2 + 2*x - x/(x + log(256*x**4 - 32*x**2*exp(x) + exp(2*x)) - exp(5)/exp(x)**(1/4))

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