3.55.10 \(\int \frac {-5 x^6+e x^6+e^{-\frac {3 x}{-5+e}} (320-240 x+60 x^2-5 x^3+e (-64+48 x-12 x^2+x^3))+e^{-\frac {2 x}{-5+e}} (-240 x^2+120 x^3-15 x^4+e (48 x^2-24 x^3+3 x^4))+e^{-\frac {x}{-5+e}} (-320 x^3+132 x^4-23 x^5+e (64 x^3-20 x^4+3 x^5))}{-5 x^6+e x^6+e^{-\frac {3 x}{-5+e}} (320-240 x+60 x^2-5 x^3+e (-64+48 x-12 x^2+x^3))+e^{-\frac {2 x}{-5+e}} (-240 x^2+120 x^3-15 x^4+e (48 x^2-24 x^3+3 x^4))+e^{-\frac {x}{-5+e}} (60 x^4-15 x^5+e (-12 x^4+3 x^5))} \, dx\)

Optimal. Leaf size=29 \[ x-\frac {4 x^2}{\left (\frac {e^{\frac {x}{5-e}} (-4+x)}{x}+x\right )^2} \]

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Rubi [F]  time = 4.08, 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 {-5 x^6+e x^6+e^{-\frac {3 x}{-5+e}} \left (320-240 x+60 x^2-5 x^3+e \left (-64+48 x-12 x^2+x^3\right )\right )+e^{-\frac {2 x}{-5+e}} \left (-240 x^2+120 x^3-15 x^4+e \left (48 x^2-24 x^3+3 x^4\right )\right )+e^{-\frac {x}{-5+e}} \left (-320 x^3+132 x^4-23 x^5+e \left (64 x^3-20 x^4+3 x^5\right )\right )}{-5 x^6+e x^6+e^{-\frac {3 x}{-5+e}} \left (320-240 x+60 x^2-5 x^3+e \left (-64+48 x-12 x^2+x^3\right )\right )+e^{-\frac {2 x}{-5+e}} \left (-240 x^2+120 x^3-15 x^4+e \left (48 x^2-24 x^3+3 x^4\right )\right )+e^{-\frac {x}{-5+e}} \left (60 x^4-15 x^5+e \left (-12 x^4+3 x^5\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-5*x^6 + E*x^6 + (320 - 240*x + 60*x^2 - 5*x^3 + E*(-64 + 48*x - 12*x^2 + x^3))/E^((3*x)/(-5 + E)) + (-24
0*x^2 + 120*x^3 - 15*x^4 + E*(48*x^2 - 24*x^3 + 3*x^4))/E^((2*x)/(-5 + E)) + (-320*x^3 + 132*x^4 - 23*x^5 + E*
(64*x^3 - 20*x^4 + 3*x^5))/E^(x/(-5 + E)))/(-5*x^6 + E*x^6 + (320 - 240*x + 60*x^2 - 5*x^3 + E*(-64 + 48*x - 1
2*x^2 + x^3))/E^((3*x)/(-5 + E)) + (-240*x^2 + 120*x^3 - 15*x^4 + E*(48*x^2 - 24*x^3 + 3*x^4))/E^((2*x)/(-5 +
E)) + (60*x^4 - 15*x^5 + E*(-12*x^4 + 3*x^5))/E^(x/(-5 + E))),x]

[Out]

x - (128*(29 - 5*E)*Defer[Int][(-4 + x + E^(x/(-5 + E))*x^2)^(-3), x])/(5 - E) + 1024*Defer[Int][1/(x*(-4 + x
+ E^(x/(-5 + E))*x^2)^3), x] + (128*(8 - E)*Defer[Int][x/(-4 + x + E^(x/(-5 + E))*x^2)^3, x])/(5 - E) - (8*(17
- E)*Defer[Int][x^2/(-4 + x + E^(x/(-5 + E))*x^2)^3, x])/(5 - E) + (8*Defer[Int][x^3/(-4 + x + E^(x/(-5 + E))
*x^2)^3, x])/(5 - E) - (64*(19 - 3*E)*Defer[Int][(-4 + x + E^(x/(-5 + E))*x^2)^(-2), x])/(5 - E) + 512*Defer[I
nt][1/(x*(-4 + x + E^(x/(-5 + E))*x^2)^2), x] + (16*(13 - E)*Defer[Int][x/(-4 + x + E^(x/(-5 + E))*x^2)^2, x])
/(5 - E) - (16*Defer[Int][x^2/(-4 + x + E^(x/(-5 + E))*x^2)^2, x])/(5 - E) - (8*(9 - E)*Defer[Int][(-4 + x + E
^(x/(-5 + E))*x^2)^(-1), x])/(5 - E) + 64*Defer[Int][1/(x*(-4 + x + E^(x/(-5 + E))*x^2)), x] + (8*Defer[Int][x
/(-4 + x + E^(x/(-5 + E))*x^2), x])/(5 - E)

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {(-5+e) x^6+e^{-\frac {3 x}{-5+e}} \left (320-240 x+60 x^2-5 x^3+e \left (-64+48 x-12 x^2+x^3\right )\right )+e^{-\frac {2 x}{-5+e}} \left (-240 x^2+120 x^3-15 x^4+e \left (48 x^2-24 x^3+3 x^4\right )\right )+e^{-\frac {x}{-5+e}} \left (-320 x^3+132 x^4-23 x^5+e \left (64 x^3-20 x^4+3 x^5\right )\right )}{-5 x^6+e x^6+e^{-\frac {3 x}{-5+e}} \left (320-240 x+60 x^2-5 x^3+e \left (-64+48 x-12 x^2+x^3\right )\right )+e^{-\frac {2 x}{-5+e}} \left (-240 x^2+120 x^3-15 x^4+e \left (48 x^2-24 x^3+3 x^4\right )\right )+e^{-\frac {x}{-5+e}} \left (60 x^4-15 x^5+e \left (-12 x^4+3 x^5\right )\right )} \, dx\\ &=\int \frac {(-5+e) x^6+e^{-\frac {3 x}{-5+e}} \left (320-240 x+60 x^2-5 x^3+e \left (-64+48 x-12 x^2+x^3\right )\right )+e^{-\frac {2 x}{-5+e}} \left (-240 x^2+120 x^3-15 x^4+e \left (48 x^2-24 x^3+3 x^4\right )\right )+e^{-\frac {x}{-5+e}} \left (-320 x^3+132 x^4-23 x^5+e \left (64 x^3-20 x^4+3 x^5\right )\right )}{(-5+e) x^6+e^{-\frac {3 x}{-5+e}} \left (320-240 x+60 x^2-5 x^3+e \left (-64+48 x-12 x^2+x^3\right )\right )+e^{-\frac {2 x}{-5+e}} \left (-240 x^2+120 x^3-15 x^4+e \left (48 x^2-24 x^3+3 x^4\right )\right )+e^{-\frac {x}{-5+e}} \left (60 x^4-15 x^5+e \left (-12 x^4+3 x^5\right )\right )} \, dx\\ &=\int \frac {-5 \left (1-\frac {e}{5}\right ) (-4+x)^3-15 \left (1-\frac {e}{5}\right ) e^{\frac {x}{-5+e}} (-4+x)^2 x^2-5 \left (1-\frac {e}{5}\right ) e^{\frac {3 x}{-5+e}} x^6+e^{1+\frac {2 x}{-5+e}} x^3 \left (64-20 x+3 x^2\right )-e^{\frac {2 x}{-5+e}} x^3 \left (320-132 x+23 x^2\right )}{(5-e) \left (4-x-e^{\frac {x}{-5+e}} x^2\right )^3} \, dx\\ &=\frac {\int \frac {-5 \left (1-\frac {e}{5}\right ) (-4+x)^3-15 \left (1-\frac {e}{5}\right ) e^{\frac {x}{-5+e}} (-4+x)^2 x^2-5 \left (1-\frac {e}{5}\right ) e^{\frac {3 x}{-5+e}} x^6+e^{1+\frac {2 x}{-5+e}} x^3 \left (64-20 x+3 x^2\right )-e^{\frac {2 x}{-5+e}} x^3 \left (320-132 x+23 x^2\right )}{\left (4-x-e^{\frac {x}{-5+e}} x^2\right )^3} \, dx}{5-e}\\ &=\frac {\int \left (5 \left (1-\frac {e}{5}\right )+\frac {8 (4-x)^2 \left (-8 (5-e)+(9-e) x-x^2\right )}{x \left (4-x-e^{\frac {x}{-5+e}} x^2\right )^3}+\frac {16 (4-x) \left (8 (5-e)-(9-e) x+x^2\right )}{x \left (4-x-e^{\frac {x}{-5+e}} x^2\right )^2}+\frac {8 \left (-8 (5-e)+(9-e) x-x^2\right )}{x \left (4-x-e^{\frac {x}{-5+e}} x^2\right )}\right ) \, dx}{5-e}\\ &=x+\frac {8 \int \frac {(4-x)^2 \left (-8 (5-e)+(9-e) x-x^2\right )}{x \left (4-x-e^{\frac {x}{-5+e}} x^2\right )^3} \, dx}{5-e}+\frac {8 \int \frac {-8 (5-e)+(9-e) x-x^2}{x \left (4-x-e^{\frac {x}{-5+e}} x^2\right )} \, dx}{5-e}+\frac {16 \int \frac {(4-x) \left (8 (5-e)-(9-e) x+x^2\right )}{x \left (4-x-e^{\frac {x}{-5+e}} x^2\right )^2} \, dx}{5-e}\\ &=x+\frac {8 \int \left (\frac {16 (-29+5 e)}{\left (-4+x+e^{\frac {x}{-5+e}} x^2\right )^3}-\frac {128 (-5+e)}{x \left (-4+x+e^{\frac {x}{-5+e}} x^2\right )^3}-\frac {16 (-8+e) x}{\left (-4+x+e^{\frac {x}{-5+e}} x^2\right )^3}+\frac {(-17+e) x^2}{\left (-4+x+e^{\frac {x}{-5+e}} x^2\right )^3}+\frac {x^3}{\left (-4+x+e^{\frac {x}{-5+e}} x^2\right )^3}\right ) \, dx}{5-e}+\frac {8 \int \left (-\frac {9 \left (1-\frac {e}{9}\right )}{-4+x+e^{\frac {x}{-5+e}} x^2}-\frac {8 (-5+e)}{x \left (-4+x+e^{\frac {x}{-5+e}} x^2\right )}+\frac {x}{-4+x+e^{\frac {x}{-5+e}} x^2}\right ) \, dx}{5-e}+\frac {16 \int \left (\frac {4 (-19+3 e)}{\left (-4+x+e^{\frac {x}{-5+e}} x^2\right )^2}-\frac {32 (-5+e)}{x \left (-4+x+e^{\frac {x}{-5+e}} x^2\right )^2}-\frac {(-13+e) x}{\left (-4+x+e^{\frac {x}{-5+e}} x^2\right )^2}-\frac {x^2}{\left (-4+x+e^{\frac {x}{-5+e}} x^2\right )^2}\right ) \, dx}{5-e}\\ &=x+64 \int \frac {1}{x \left (-4+x+e^{\frac {x}{-5+e}} x^2\right )} \, dx+512 \int \frac {1}{x \left (-4+x+e^{\frac {x}{-5+e}} x^2\right )^2} \, dx+1024 \int \frac {1}{x \left (-4+x+e^{\frac {x}{-5+e}} x^2\right )^3} \, dx+\frac {8 \int \frac {x^3}{\left (-4+x+e^{\frac {x}{-5+e}} x^2\right )^3} \, dx}{5-e}+\frac {8 \int \frac {x}{-4+x+e^{\frac {x}{-5+e}} x^2} \, dx}{5-e}-\frac {16 \int \frac {x^2}{\left (-4+x+e^{\frac {x}{-5+e}} x^2\right )^2} \, dx}{5-e}-\frac {(128 (29-5 e)) \int \frac {1}{\left (-4+x+e^{\frac {x}{-5+e}} x^2\right )^3} \, dx}{5-e}-\frac {(64 (19-3 e)) \int \frac {1}{\left (-4+x+e^{\frac {x}{-5+e}} x^2\right )^2} \, dx}{5-e}+\frac {(128 (8-e)) \int \frac {x}{\left (-4+x+e^{\frac {x}{-5+e}} x^2\right )^3} \, dx}{5-e}-\frac {(8 (9-e)) \int \frac {1}{-4+x+e^{\frac {x}{-5+e}} x^2} \, dx}{5-e}+\frac {(16 (13-e)) \int \frac {x}{\left (-4+x+e^{\frac {x}{-5+e}} x^2\right )^2} \, dx}{5-e}-\frac {(8 (17-e)) \int \frac {x^2}{\left (-4+x+e^{\frac {x}{-5+e}} x^2\right )^3} \, dx}{5-e}\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 2.15, size = 576, normalized size = 19.86 \begin {gather*} \frac {e^{-\frac {20}{-5+e}} (-4+x) x \left (2 e^{\frac {4 e}{-5+e}} (-8+x)^3 (-4+x)+4 e^{\frac {4 e+x}{-5+e}} (-8+x)^3 x^2+2 e^{\frac {2 (2 e+x)}{-5+e}} (-8+x)^3 x^3+4 e^{\frac {15+e+x}{-5+e}} x^2 \left (160-24 x+x^2\right ) \left (40-9 x+x^2\right )^2+2 e^{\frac {15+e+2 x}{-5+e}} x^3 \left (160-24 x+x^2\right ) \left (40-9 x+x^2\right )^2-10 e^{\frac {20}{-5+e}} (-4+x) \left (40-9 x+x^2\right )^3-20 e^{\frac {20+x}{-5+e}} x^2 \left (40-9 x+x^2\right )^3-10 e^{\frac {2 (10+x)}{-5+e}} x^3 \left (40-9 x+x^2\right )^3+4 e^{\frac {5+3 e+x}{-5+e}} (-8+x)^2 x^2 \left (160-32 x+3 x^2\right )+2 e^{\frac {5+3 e+2 x}{-5+e}} (-8+x)^2 x^3 \left (160-32 x+3 x^2\right )+2 e^{\frac {15+e}{-5+e}} \left (40-9 x+x^2\right )^2 \left (-640+256 x-28 x^2+x^3\right )-8 e^{\frac {5+3 e}{-5+e}} \left (4416-3104 x+864 x^2-111 x^3+5 x^4\right )+12 e^{\frac {10+2 e+x}{-5+e}} x^2 \left (-25600+13440 x-3248 x^2+430 x^3-31 x^4+x^5\right )+6 e^{\frac {2 (5+e+x)}{-5+e}} x^3 \left (-25600+13440 x-3248 x^2+430 x^3-31 x^4+x^5\right )+2 e^{3+\frac {20}{-5+e}} \left (-23296+16256 x-4608 x^2+740 x^3-72 x^4+3 x^5\right )+6 e^{\frac {2 (5+e)}{-5+e}} \left (102400-79360 x+26432 x^2-4968 x^3+554 x^4-35 x^5+x^6\right )\right )}{2 (-5+e) \left (40+e (-8+x)-9 x+x^2\right )^3 \left (-4+x+e^{\frac {x}{-5+e}} x^2\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-5*x^6 + E*x^6 + (320 - 240*x + 60*x^2 - 5*x^3 + E*(-64 + 48*x - 12*x^2 + x^3))/E^((3*x)/(-5 + E))
+ (-240*x^2 + 120*x^3 - 15*x^4 + E*(48*x^2 - 24*x^3 + 3*x^4))/E^((2*x)/(-5 + E)) + (-320*x^3 + 132*x^4 - 23*x^
5 + E*(64*x^3 - 20*x^4 + 3*x^5))/E^(x/(-5 + E)))/(-5*x^6 + E*x^6 + (320 - 240*x + 60*x^2 - 5*x^3 + E*(-64 + 48
*x - 12*x^2 + x^3))/E^((3*x)/(-5 + E)) + (-240*x^2 + 120*x^3 - 15*x^4 + E*(48*x^2 - 24*x^3 + 3*x^4))/E^((2*x)/
(-5 + E)) + (60*x^4 - 15*x^5 + E*(-12*x^4 + 3*x^5))/E^(x/(-5 + E))),x]

[Out]

((-4 + x)*x*(2*E^((4*E)/(-5 + E))*(-8 + x)^3*(-4 + x) + 4*E^((4*E + x)/(-5 + E))*(-8 + x)^3*x^2 + 2*E^((2*(2*E
+ x))/(-5 + E))*(-8 + x)^3*x^3 + 4*E^((15 + E + x)/(-5 + E))*x^2*(160 - 24*x + x^2)*(40 - 9*x + x^2)^2 + 2*E^
((15 + E + 2*x)/(-5 + E))*x^3*(160 - 24*x + x^2)*(40 - 9*x + x^2)^2 - 10*E^(20/(-5 + E))*(-4 + x)*(40 - 9*x +
x^2)^3 - 20*E^((20 + x)/(-5 + E))*x^2*(40 - 9*x + x^2)^3 - 10*E^((2*(10 + x))/(-5 + E))*x^3*(40 - 9*x + x^2)^3
+ 4*E^((5 + 3*E + x)/(-5 + E))*(-8 + x)^2*x^2*(160 - 32*x + 3*x^2) + 2*E^((5 + 3*E + 2*x)/(-5 + E))*(-8 + x)^
2*x^3*(160 - 32*x + 3*x^2) + 2*E^((15 + E)/(-5 + E))*(40 - 9*x + x^2)^2*(-640 + 256*x - 28*x^2 + x^3) - 8*E^((
5 + 3*E)/(-5 + E))*(4416 - 3104*x + 864*x^2 - 111*x^3 + 5*x^4) + 12*E^((10 + 2*E + x)/(-5 + E))*x^2*(-25600 +
13440*x - 3248*x^2 + 430*x^3 - 31*x^4 + x^5) + 6*E^((2*(5 + E + x))/(-5 + E))*x^3*(-25600 + 13440*x - 3248*x^2
+ 430*x^3 - 31*x^4 + x^5) + 2*E^(3 + 20/(-5 + E))*(-23296 + 16256*x - 4608*x^2 + 740*x^3 - 72*x^4 + 3*x^5) +
6*E^((2*(5 + E))/(-5 + E))*(102400 - 79360*x + 26432*x^2 - 4968*x^3 + 554*x^4 - 35*x^5 + x^6)))/(2*(-5 + E)*E^
(20/(-5 + E))*(40 + E*(-8 + x) - 9*x + x^2)^3*(-4 + x + E^(x/(-5 + E))*x^2)^2)

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fricas [B]  time = 0.53, size = 100, normalized size = 3.45 \begin {gather*} \frac {x^{5} - 4 \, x^{4} + 2 \, {\left (x^{4} - 4 \, x^{3}\right )} e^{\left (-\frac {x}{e - 5}\right )} + {\left (x^{3} - 8 \, x^{2} + 16 \, x\right )} e^{\left (-\frac {2 \, x}{e - 5}\right )}}{x^{4} + 2 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{\left (-\frac {x}{e - 5}\right )} + {\left (x^{2} - 8 \, x + 16\right )} e^{\left (-\frac {2 \, x}{e - 5}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^3-12*x^2+48*x-64)*exp(1)-5*x^3+60*x^2-240*x+320)*exp(-x/(exp(1)-5))^3+((3*x^4-24*x^3+48*x^2)*ex
p(1)-15*x^4+120*x^3-240*x^2)*exp(-x/(exp(1)-5))^2+((3*x^5-20*x^4+64*x^3)*exp(1)-23*x^5+132*x^4-320*x^3)*exp(-x
/(exp(1)-5))+x^6*exp(1)-5*x^6)/(((x^3-12*x^2+48*x-64)*exp(1)-5*x^3+60*x^2-240*x+320)*exp(-x/(exp(1)-5))^3+((3*
x^4-24*x^3+48*x^2)*exp(1)-15*x^4+120*x^3-240*x^2)*exp(-x/(exp(1)-5))^2+((3*x^5-12*x^4)*exp(1)-15*x^5+60*x^4)*e
xp(-x/(exp(1)-5))+x^6*exp(1)-5*x^6),x, algorithm="fricas")

[Out]

(x^5 - 4*x^4 + 2*(x^4 - 4*x^3)*e^(-x/(e - 5)) + (x^3 - 8*x^2 + 16*x)*e^(-2*x/(e - 5)))/(x^4 + 2*(x^3 - 4*x^2)*
e^(-x/(e - 5)) + (x^2 - 8*x + 16)*e^(-2*x/(e - 5)))

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giac [B]  time = 5.01, size = 108, normalized size = 3.72 \begin {gather*} \frac {x^{5} e^{\left (\frac {2 \, x}{e - 5}\right )} + 2 \, x^{4} e^{\left (\frac {x}{e - 5}\right )} + x^{3} - 32 \, x^{2} e^{\left (\frac {x}{e - 5}\right )} - 4 \, x^{2} - 16 \, x + 64}{x^{4} e^{\left (\frac {2 \, x}{e - 5}\right )} + 2 \, x^{3} e^{\left (\frac {x}{e - 5}\right )} - 8 \, x^{2} e^{\left (\frac {x}{e - 5}\right )} + x^{2} - 8 \, x + 16} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^3-12*x^2+48*x-64)*exp(1)-5*x^3+60*x^2-240*x+320)*exp(-x/(exp(1)-5))^3+((3*x^4-24*x^3+48*x^2)*ex
p(1)-15*x^4+120*x^3-240*x^2)*exp(-x/(exp(1)-5))^2+((3*x^5-20*x^4+64*x^3)*exp(1)-23*x^5+132*x^4-320*x^3)*exp(-x
/(exp(1)-5))+x^6*exp(1)-5*x^6)/(((x^3-12*x^2+48*x-64)*exp(1)-5*x^3+60*x^2-240*x+320)*exp(-x/(exp(1)-5))^3+((3*
x^4-24*x^3+48*x^2)*exp(1)-15*x^4+120*x^3-240*x^2)*exp(-x/(exp(1)-5))^2+((3*x^5-12*x^4)*exp(1)-15*x^5+60*x^4)*e
xp(-x/(exp(1)-5))+x^6*exp(1)-5*x^6),x, algorithm="giac")

[Out]

(x^5*e^(2*x/(e - 5)) + 2*x^4*e^(x/(e - 5)) + x^3 - 32*x^2*e^(x/(e - 5)) - 4*x^2 - 16*x + 64)/(x^4*e^(2*x/(e -
5)) + 2*x^3*e^(x/(e - 5)) - 8*x^2*e^(x/(e - 5)) + x^2 - 8*x + 16)

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maple [A]  time = 5.74, size = 38, normalized size = 1.31

method	result	size
risch	\(x -\frac {4 x^{4}}{\left (x^{2}+x \,{\mathrm e}^{-\frac {x}{{\mathrm e}-5}}-4 \,{\mathrm e}^{-\frac {x}{{\mathrm e}-5}}\right )^{2}}\)	\(38\)
norman	\(\frac {x^{5}+64 \,{\mathrm e}^{-\frac {2 x}{{\mathrm e}-5}}+{\mathrm e}^{-\frac {2 x}{{\mathrm e}-5}} x^{3}-32 x^{2} {\mathrm e}^{-\frac {x}{{\mathrm e}-5}}-16 x \,{\mathrm e}^{-\frac {2 x}{{\mathrm e}-5}}-4 x^{2} {\mathrm e}^{-\frac {2 x}{{\mathrm e}-5}}+2 x^{4} {\mathrm e}^{-\frac {x}{{\mathrm e}-5}}}{\left (x^{2}+x \,{\mathrm e}^{-\frac {x}{{\mathrm e}-5}}-4 \,{\mathrm e}^{-\frac {x}{{\mathrm e}-5}}\right )^{2}}\)	\(128\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((x^3-12*x^2+48*x-64)*exp(1)-5*x^3+60*x^2-240*x+320)*exp(-x/(exp(1)-5))^3+((3*x^4-24*x^3+48*x^2)*exp(1)-1
5*x^4+120*x^3-240*x^2)*exp(-x/(exp(1)-5))^2+((3*x^5-20*x^4+64*x^3)*exp(1)-23*x^5+132*x^4-320*x^3)*exp(-x/(exp(
1)-5))+x^6*exp(1)-5*x^6)/(((x^3-12*x^2+48*x-64)*exp(1)-5*x^3+60*x^2-240*x+320)*exp(-x/(exp(1)-5))^3+((3*x^4-24
*x^3+48*x^2)*exp(1)-15*x^4+120*x^3-240*x^2)*exp(-x/(exp(1)-5))^2+((3*x^5-12*x^4)*exp(1)-15*x^5+60*x^4)*exp(-x/
(exp(1)-5))+x^6*exp(1)-5*x^6),x,method=_RETURNVERBOSE)

[Out]

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

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maxima [B]  time = 0.67, size = 92, normalized size = 3.17 \begin {gather*} \frac {x^{5} e^{\left (\frac {2 \, x}{e - 5}\right )} + x^{3} - 4 \, x^{2} + 2 \, {\left (x^{4} - 16 \, x^{2}\right )} e^{\left (\frac {x}{e - 5}\right )} - 16 \, x + 64}{x^{4} e^{\left (\frac {2 \, x}{e - 5}\right )} + x^{2} + 2 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{\left (\frac {x}{e - 5}\right )} - 8 \, x + 16} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^3-12*x^2+48*x-64)*exp(1)-5*x^3+60*x^2-240*x+320)*exp(-x/(exp(1)-5))^3+((3*x^4-24*x^3+48*x^2)*ex
p(1)-15*x^4+120*x^3-240*x^2)*exp(-x/(exp(1)-5))^2+((3*x^5-20*x^4+64*x^3)*exp(1)-23*x^5+132*x^4-320*x^3)*exp(-x
/(exp(1)-5))+x^6*exp(1)-5*x^6)/(((x^3-12*x^2+48*x-64)*exp(1)-5*x^3+60*x^2-240*x+320)*exp(-x/(exp(1)-5))^3+((3*
x^4-24*x^3+48*x^2)*exp(1)-15*x^4+120*x^3-240*x^2)*exp(-x/(exp(1)-5))^2+((3*x^5-12*x^4)*exp(1)-15*x^5+60*x^4)*e
xp(-x/(exp(1)-5))+x^6*exp(1)-5*x^6),x, algorithm="maxima")

[Out]

(x^5*e^(2*x/(e - 5)) + x^3 - 4*x^2 + 2*(x^4 - 16*x^2)*e^(x/(e - 5)) - 16*x + 64)/(x^4*e^(2*x/(e - 5)) + x^2 +
2*(x^3 - 4*x^2)*e^(x/(e - 5)) - 8*x + 16)

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mupad [B]  time = 3.93, size = 59, normalized size = 2.03 \begin {gather*} \frac {x\,\left (x-4\right )\,\left (x+x^3\,{\mathrm {e}}^{\frac {2\,x}{\mathrm {e}-5}}-4\right )+2\,x^3\,{\mathrm {e}}^{\frac {x}{\mathrm {e}-5}}\,\left (x-4\right )}{{\left (x+x^2\,{\mathrm {e}}^{\frac {x}{\mathrm {e}-5}}-4\right )}^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-(3*x)/(exp(1) - 5))*(exp(1)*(48*x - 12*x^2 + x^3 - 64) - 240*x + 60*x^2 - 5*x^3 + 320) + exp(-(2*x)/
(exp(1) - 5))*(exp(1)*(48*x^2 - 24*x^3 + 3*x^4) - 240*x^2 + 120*x^3 - 15*x^4) + exp(-x/(exp(1) - 5))*(exp(1)*(
64*x^3 - 20*x^4 + 3*x^5) - 320*x^3 + 132*x^4 - 23*x^5) + x^6*exp(1) - 5*x^6)/(exp(-(3*x)/(exp(1) - 5))*(exp(1)
*(48*x - 12*x^2 + x^3 - 64) - 240*x + 60*x^2 - 5*x^3 + 320) - exp(-x/(exp(1) - 5))*(exp(1)*(12*x^4 - 3*x^5) -
60*x^4 + 15*x^5) + exp(-(2*x)/(exp(1) - 5))*(exp(1)*(48*x^2 - 24*x^3 + 3*x^4) - 240*x^2 + 120*x^3 - 15*x^4) +
x^6*exp(1) - 5*x^6),x)

[Out]

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

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sympy [B]  time = 0.58, size = 46, normalized size = 1.59 \begin {gather*} - \frac {4 x^{4}}{x^{4} + \left (2 x^{3} - 8 x^{2}\right ) e^{- \frac {x}{-5 + e}} + \left (x^{2} - 8 x + 16\right ) e^{- \frac {2 x}{-5 + e}}} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x**3-12*x**2+48*x-64)*exp(1)-5*x**3+60*x**2-240*x+320)*exp(-x/(exp(1)-5))**3+((3*x**4-24*x**3+48*
x**2)*exp(1)-15*x**4+120*x**3-240*x**2)*exp(-x/(exp(1)-5))**2+((3*x**5-20*x**4+64*x**3)*exp(1)-23*x**5+132*x**
4-320*x**3)*exp(-x/(exp(1)-5))+x**6*exp(1)-5*x**6)/(((x**3-12*x**2+48*x-64)*exp(1)-5*x**3+60*x**2-240*x+320)*e
xp(-x/(exp(1)-5))**3+((3*x**4-24*x**3+48*x**2)*exp(1)-15*x**4+120*x**3-240*x**2)*exp(-x/(exp(1)-5))**2+((3*x**
5-12*x**4)*exp(1)-15*x**5+60*x**4)*exp(-x/(exp(1)-5))+x**6*exp(1)-5*x**6),x)

[Out]

-4*x**4/(x**4 + (2*x**3 - 8*x**2)*exp(-x/(-5 + E)) + (x**2 - 8*x + 16)*exp(-2*x/(-5 + E))) + x

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