3.99.75 \(\int \frac {20-12 e^{10-8 x}-40 x-8 x^2+24 x^3-12 x^4+e^{5-4 x} (-76-8 x+24 x^2)}{25-10 x+31 x^2-36 x^3+15 x^4-18 x^5+9 x^6+e^{10-8 x} (e^6-6 e^3 x+9 x^2)+e^6 (x^2-2 x^3+x^4)+e^3 (-10 x+12 x^2-8 x^3+12 x^4-6 x^5)+e^{5-4 x} (30 x-6 x^2+18 x^3-18 x^4+e^6 (2 x-2 x^2)+e^3 (-10+2 x-12 x^2+12 x^3))} \, dx\)

Optimal. Leaf size=38 \[ \frac {4}{-e^3+3 x-\frac {5-x}{-e^{5-4 x}-x+x^2}} \]

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Rubi [F]  time = 20.62, 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 {20-12 e^{10-8 x}-40 x-8 x^2+24 x^3-12 x^4+e^{5-4 x} \left (-76-8 x+24 x^2\right )}{25-10 x+31 x^2-36 x^3+15 x^4-18 x^5+9 x^6+e^{10-8 x} \left (e^6-6 e^3 x+9 x^2\right )+e^6 \left (x^2-2 x^3+x^4\right )+e^3 \left (-10 x+12 x^2-8 x^3+12 x^4-6 x^5\right )+e^{5-4 x} \left (30 x-6 x^2+18 x^3-18 x^4+e^6 \left (2 x-2 x^2\right )+e^3 \left (-10+2 x-12 x^2+12 x^3\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(20 - 12*E^(10 - 8*x) - 40*x - 8*x^2 + 24*x^3 - 12*x^4 + E^(5 - 4*x)*(-76 - 8*x + 24*x^2))/(25 - 10*x + 31
*x^2 - 36*x^3 + 15*x^4 - 18*x^5 + 9*x^6 + E^(10 - 8*x)*(E^6 - 6*E^3*x + 9*x^2) + E^6*(x^2 - 2*x^3 + x^4) + E^3
*(-10*x + 12*x^2 - 8*x^3 + 12*x^4 - 6*x^5) + E^(5 - 4*x)*(30*x - 6*x^2 + 18*x^3 - 18*x^4 + E^6*(2*x - 2*x^2) +
E^3*(-10 + 2*x - 12*x^2 + 12*x^3))),x]

[Out]

(4*x)/(5 - (1 + E^3)*x + (3 + E^3)*x^2 - 3*x^3) - (4*x^2)/(5 - (1 + E^3)*x + (3 + E^3)*x^2 - 3*x^3) - 20*E^10*
(42 + E^3 - E^6)*Defer[Int][1/((5 - (1 + E^3)*x + (3 + E^3)*x^2 - 3*x^3)^2*(E^8 - 3*E^5*x - E^(3 + 4*x)*(-1 +
x)*x + E^(4*x)*(-5 + x - 3*x^2 + 3*x^3))^2), x] + 4*E^10*(72 - 2*E^3 - 9*E^6)*Defer[Int][x/((5 - (1 + E^3)*x +
(3 + E^3)*x^2 - 3*x^3)^2*(E^8 - 3*E^5*x - E^(3 + 4*x)*(-1 + x)*x + E^(4*x)*(-5 + x - 3*x^2 + 3*x^3))^2), x] -
12*E^10*(14 - 9*E^3)*Defer[Int][x^2/((5 - (1 + E^3)*x + (3 + E^3)*x^2 - 3*x^3)^2*(E^8 - 3*E^5*x - E^(3 + 4*x)
*(-1 + x)*x + E^(4*x)*(-5 + x - 3*x^2 + 3*x^3))^2), x] + 36*E^10*(3 - 2*E^3)*Defer[Int][1/((5 - (1 + E^3)*x +
(3 + E^3)*x^2 - 3*x^3)*(E^8 - 3*E^5*x - E^(3 + 4*x)*(-1 + x)*x + E^(4*x)*(-5 + x - 3*x^2 + 3*x^3))^2), x] + 8*
E^10*(27 + 2*E^3)*Defer[Int][x/((5 - (1 + E^3)*x + (3 + E^3)*x^2 - 3*x^3)*(E^8 - 3*E^5*x - E^(3 + 4*x)*(-1 + x
)*x + E^(4*x)*(-5 + x - 3*x^2 + 3*x^3))^2), x] + 48*E^10*Defer[Int][x^2/((-5 + (1 + E^3)*x - (3 + E^3)*x^2 + 3
*x^3)*(E^8 - 3*E^5*x - E^(3 + 4*x)*(-1 + x)*x + E^(4*x)*(-5 + x - 3*x^2 + 3*x^3))^2), x] + 40*E^5*(2 - E^3)*De
fer[Int][1/((5 - (1 + E^3)*x + (3 + E^3)*x^2 - 3*x^3)^2*(E^8 - 3*E^5*x - E^(3 + 4*x)*(-1 + x)*x + E^(4*x)*(-5
+ x - 3*x^2 + 3*x^3))), x] + 32*E^5*(7 + 2*E^3)*Defer[Int][x/((5 - (1 + E^3)*x + (3 + E^3)*x^2 - 3*x^3)^2*(E^8
- 3*E^5*x - E^(3 + 4*x)*(-1 + x)*x + E^(4*x)*(-5 + x - 3*x^2 + 3*x^3))), x] - 8*E^5*(42 - E^3)*Defer[Int][x^2
/((5 - (1 + E^3)*x + (3 + E^3)*x^2 - 3*x^3)^2*(E^8 - 3*E^5*x - E^(3 + 4*x)*(-1 + x)*x + E^(4*x)*(-5 + x - 3*x^
2 + 3*x^3))), x] + 60*E^5*Defer[Int][1/((5 - (1 + E^3)*x + (3 + E^3)*x^2 - 3*x^3)*(E^8 - 3*E^5*x - E^(3 + 4*x)
*(-1 + x)*x + E^(4*x)*(-5 + x - 3*x^2 + 3*x^3))), x] + 16*E^5*Defer[Int][x/((-5 + (1 + E^3)*x - (3 + E^3)*x^2
+ 3*x^3)*(E^8 - 3*E^5*x - E^(3 + 4*x)*(-1 + x)*x + E^(4*x)*(-5 + x - 3*x^2 + 3*x^3))), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 \left (-3 e^{10}-e^{5+4 x} \left (19+2 x-6 x^2\right )-e^{8 x} \left (-5+10 x+2 x^2-6 x^3+3 x^4\right )\right )}{\left (e^8-3 e^5 x-e^{3+4 x} (-1+x) x+e^{4 x} \left (-5+x-3 x^2+3 x^3\right )\right )^2} \, dx\\ &=4 \int \frac {-3 e^{10}-e^{5+4 x} \left (19+2 x-6 x^2\right )-e^{8 x} \left (-5+10 x+2 x^2-6 x^3+3 x^4\right )}{\left (e^8-3 e^5 x-e^{3+4 x} (-1+x) x+e^{4 x} \left (-5+x-3 x^2+3 x^3\right )\right )^2} \, dx\\ &=4 \int \left (\frac {5-10 x-2 x^2+6 x^3-3 x^4}{\left (5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3\right )^2}+\frac {e^5 \left (5 \left (19-2 e^3\right )+\left (21+e^3\right ) x-7 \left (5-3 e^3\right ) x^2-\left (57+4 e^3\right ) x^3+12 x^4\right )}{\left (5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3\right )^2 \left (e^8-5 e^{4 x}-3 e^5 x+e^{4 x} \left (1+e^3\right ) x-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+3 e^{4 x} x^3\right )}+\frac {e^{10} \left (-75 \left (1-\frac {1}{15} e^3 \left (-19+e^3\right )\right )+315 \left (1+\frac {1}{35} e^3 \left (1+e^3\right )\right ) x-75 \left (1+\frac {2}{75} e^3 \left (29+11 e^3\right )\right ) x^2+93 \left (1+\frac {4}{93} e^3 \left (33+e^3\right )\right ) x^3-198 \left (1+\frac {4 e^3}{33}\right ) x^4+36 x^5\right )}{\left (5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3\right )^2 \left (e^8-5 e^{4 x}-3 e^5 x+e^{4 x} \left (1+e^3\right ) x-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+3 e^{4 x} x^3\right )^2}\right ) \, dx\\ &=4 \int \frac {5-10 x-2 x^2+6 x^3-3 x^4}{\left (5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3\right )^2} \, dx+\left (4 e^5\right ) \int \frac {5 \left (19-2 e^3\right )+\left (21+e^3\right ) x-7 \left (5-3 e^3\right ) x^2-\left (57+4 e^3\right ) x^3+12 x^4}{\left (5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3\right )^2 \left (e^8-5 e^{4 x}-3 e^5 x+e^{4 x} \left (1+e^3\right ) x-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+3 e^{4 x} x^3\right )} \, dx+\left (4 e^{10}\right ) \int \frac {-75 \left (1-\frac {1}{15} e^3 \left (-19+e^3\right )\right )+315 \left (1+\frac {1}{35} e^3 \left (1+e^3\right )\right ) x-75 \left (1+\frac {2}{75} e^3 \left (29+11 e^3\right )\right ) x^2+93 \left (1+\frac {4}{93} e^3 \left (33+e^3\right )\right ) x^3-198 \left (1+\frac {4 e^3}{33}\right ) x^4+36 x^5}{\left (5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3\right )^2 \left (e^8-5 e^{4 x}-3 e^5 x+e^{4 x} \left (1+e^3\right ) x-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+3 e^{4 x} x^3\right )^2} \, dx\\ &=-\frac {4 x^2}{5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3}+\frac {4}{3} \int \frac {15-3 \left (3+e^3\right ) x^2+18 x^3}{\left (5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3\right )^2} \, dx+\left (4 e^5\right ) \int \frac {5 \left (19-2 e^3\right )+\left (21+e^3\right ) x-7 \left (5-3 e^3\right ) x^2-\left (57+4 e^3\right ) x^3+12 x^4}{\left (5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3\right )^2 \left (e^8-3 e^5 x-e^{3+4 x} (-1+x) x+e^{4 x} \left (-5+x-3 x^2+3 x^3\right )\right )} \, dx+\left (4 e^{10}\right ) \int \frac {-75+315 x-75 x^2+93 x^3-198 x^4+36 x^5+e^6 \left (5+9 x-22 x^2+4 x^3\right )+e^3 \left (-95+9 x-58 x^2+132 x^3-24 x^4\right )}{\left (5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3\right )^2 \left (e^8-3 e^5 x-e^{3+4 x} (-1+x) x+e^{4 x} \left (-5+x-3 x^2+3 x^3\right )\right )^2} \, dx\\ &=\frac {4 x}{5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3}-\frac {4 x^2}{5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3}+\left (4 e^5\right ) \int \left (\frac {2 \left (5 \left (2-e^3\right )+4 \left (7+2 e^3\right ) x-\left (42-e^3\right ) x^2\right )}{\left (5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3\right )^2 \left (e^8-5 e^{4 x}-3 e^5 x+e^{4 x} \left (1+e^3\right ) x-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+3 e^{4 x} x^3\right )}+\frac {15-4 x}{\left (5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3\right ) \left (e^8-5 e^{4 x}-3 e^5 x+e^{4 x} \left (1+e^3\right ) x-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+3 e^{4 x} x^3\right )}\right ) \, dx+\left (4 e^{10}\right ) \int \left (\frac {-5 \left (42+e^3-e^6\right )+\left (72-2 e^3-9 e^6\right ) x-3 \left (14-9 e^3\right ) x^2}{\left (5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3\right )^2 \left (e^8-5 e^{4 x}-3 e^5 x+e^{4 x} \left (1+e^3\right ) x-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+3 e^{4 x} x^3\right )^2}+\frac {9 \left (3-2 e^3\right )+2 \left (27+2 e^3\right ) x-12 x^2}{\left (5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3\right ) \left (e^8-5 e^{4 x}-3 e^5 x+e^{4 x} \left (1+e^3\right ) x-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+3 e^{4 x} x^3\right )^2}\right ) \, dx\\ &=\frac {4 x}{5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3}-\frac {4 x^2}{5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3}+\left (4 e^5\right ) \int \frac {15-4 x}{\left (5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3\right ) \left (e^8-5 e^{4 x}-3 e^5 x+e^{4 x} \left (1+e^3\right ) x-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+3 e^{4 x} x^3\right )} \, dx+\left (8 e^5\right ) \int \frac {5 \left (2-e^3\right )+4 \left (7+2 e^3\right ) x-\left (42-e^3\right ) x^2}{\left (5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3\right )^2 \left (e^8-5 e^{4 x}-3 e^5 x+e^{4 x} \left (1+e^3\right ) x-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+3 e^{4 x} x^3\right )} \, dx+\left (4 e^{10}\right ) \int \frac {-5 \left (42+e^3-e^6\right )+\left (72-2 e^3-9 e^6\right ) x-3 \left (14-9 e^3\right ) x^2}{\left (5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3\right )^2 \left (e^8-5 e^{4 x}-3 e^5 x+e^{4 x} \left (1+e^3\right ) x-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+3 e^{4 x} x^3\right )^2} \, dx+\left (4 e^{10}\right ) \int \frac {9 \left (3-2 e^3\right )+2 \left (27+2 e^3\right ) x-12 x^2}{\left (5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3\right ) \left (e^8-5 e^{4 x}-3 e^5 x+e^{4 x} \left (1+e^3\right ) x-3 e^{4 x} \left (1+\frac {e^3}{3}\right ) x^2+3 e^{4 x} x^3\right )^2} \, dx\\ &=\frac {4 x}{5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3}-\frac {4 x^2}{5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3}+\left (4 e^5\right ) \int \frac {15-4 x}{\left (5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3\right ) \left (e^8-3 e^5 x-e^{3+4 x} (-1+x) x+e^{4 x} \left (-5+x-3 x^2+3 x^3\right )\right )} \, dx+\left (8 e^5\right ) \int \frac {5 \left (2-e^3\right )+4 \left (7+2 e^3\right ) x-\left (42-e^3\right ) x^2}{\left (5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3\right )^2 \left (e^8-3 e^5 x-e^{3+4 x} (-1+x) x+e^{4 x} \left (-5+x-3 x^2+3 x^3\right )\right )} \, dx+\left (4 e^{10}\right ) \int \frac {-5 \left (42+e^3-e^6\right )+\left (72-2 e^3-9 e^6\right ) x-3 \left (14-9 e^3\right ) x^2}{\left (5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3\right )^2 \left (e^8-3 e^5 x-e^{3+4 x} (-1+x) x+e^{4 x} \left (-5+x-3 x^2+3 x^3\right )\right )^2} \, dx+\left (4 e^{10}\right ) \int \frac {9 \left (3-2 e^3\right )+2 \left (27+2 e^3\right ) x-12 x^2}{\left (5-\left (1+e^3\right ) x+\left (3+e^3\right ) x^2-3 x^3\right ) \left (e^8-3 e^5 x-e^{3+4 x} (-1+x) x+e^{4 x} \left (-5+x-3 x^2+3 x^3\right )\right )^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.12, size = 61, normalized size = 1.61 \begin {gather*} -\frac {4 \left (e^5-e^{4 x} (-1+x) x\right )}{e^8-3 e^5 x-e^{3+4 x} (-1+x) x+e^{4 x} \left (-5+x-3 x^2+3 x^3\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(20 - 12*E^(10 - 8*x) - 40*x - 8*x^2 + 24*x^3 - 12*x^4 + E^(5 - 4*x)*(-76 - 8*x + 24*x^2))/(25 - 10*
x + 31*x^2 - 36*x^3 + 15*x^4 - 18*x^5 + 9*x^6 + E^(10 - 8*x)*(E^6 - 6*E^3*x + 9*x^2) + E^6*(x^2 - 2*x^3 + x^4)
+ E^3*(-10*x + 12*x^2 - 8*x^3 + 12*x^4 - 6*x^5) + E^(5 - 4*x)*(30*x - 6*x^2 + 18*x^3 - 18*x^4 + E^6*(2*x - 2*
x^2) + E^3*(-10 + 2*x - 12*x^2 + 12*x^3))),x]

[Out]

(-4*(E^5 - E^(4*x)*(-1 + x)*x))/(E^8 - 3*E^5*x - E^(3 + 4*x)*(-1 + x)*x + E^(4*x)*(-5 + x - 3*x^2 + 3*x^3))

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fricas [A]  time = 0.73, size = 59, normalized size = 1.55 \begin {gather*} \frac {4 \, {\left (x^{2} - x - e^{\left (-4 \, x + 5\right )}\right )}}{3 \, x^{3} - 3 \, x^{2} - {\left (x^{2} - x\right )} e^{3} - {\left (3 \, x - e^{3}\right )} e^{\left (-4 \, x + 5\right )} + x - 5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-12*exp(-4*x+5)^2+(24*x^2-8*x-76)*exp(-4*x+5)-12*x^4+24*x^3-8*x^2-40*x+20)/((exp(3)^2-6*x*exp(3)+9*
x^2)*exp(-4*x+5)^2+((-2*x^2+2*x)*exp(3)^2+(12*x^3-12*x^2+2*x-10)*exp(3)-18*x^4+18*x^3-6*x^2+30*x)*exp(-4*x+5)+
(x^4-2*x^3+x^2)*exp(3)^2+(-6*x^5+12*x^4-8*x^3+12*x^2-10*x)*exp(3)+9*x^6-18*x^5+15*x^4-36*x^3+31*x^2-10*x+25),x
, algorithm="fricas")

[Out]

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

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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((-12*exp(-4*x+5)^2+(24*x^2-8*x-76)*exp(-4*x+5)-12*x^4+24*x^3-8*x^2-40*x+20)/((exp(3)^2-6*x*exp(3)+9*
x^2)*exp(-4*x+5)^2+((-2*x^2+2*x)*exp(3)^2+(12*x^3-12*x^2+2*x-10)*exp(3)-18*x^4+18*x^3-6*x^2+30*x)*exp(-4*x+5)+
(x^4-2*x^3+x^2)*exp(3)^2+(-6*x^5+12*x^4-8*x^3+12*x^2-10*x)*exp(3)+9*x^6-18*x^5+15*x^4-36*x^3+31*x^2-10*x+25),x
, algorithm="giac")

[Out]

Timed out

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maple [A]  time = 0.84, size = 66, normalized size = 1.74

method	result	size
norman	\(\frac {-4 x^{2}+4 x +4 \,{\mathrm e}^{-4 x +5}}{x^{2} {\mathrm e}^{3}-3 x^{3}-x \,{\mathrm e}^{3}-{\mathrm e}^{3} {\mathrm e}^{-4 x +5}+3 x^{2}+3 \,{\mathrm e}^{-4 x +5} x -x +5}\)	\(66\)
risch	\(-\frac {4}{{\mathrm e}^{3}-3 x}-\frac {4 \left (x -5\right )}{\left ({\mathrm e}^{3}-3 x \right ) \left (x^{2} {\mathrm e}^{3}-3 x^{3}-x \,{\mathrm e}^{3}-{\mathrm e}^{-4 x +8}+3 x^{2}+3 \,{\mathrm e}^{-4 x +5} x -x +5\right )}\)	\(70\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-12*exp(-4*x+5)^2+(24*x^2-8*x-76)*exp(-4*x+5)-12*x^4+24*x^3-8*x^2-40*x+20)/((exp(3)^2-6*x*exp(3)+9*x^2)*e
xp(-4*x+5)^2+((-2*x^2+2*x)*exp(3)^2+(12*x^3-12*x^2+2*x-10)*exp(3)-18*x^4+18*x^3-6*x^2+30*x)*exp(-4*x+5)+(x^4-2
*x^3+x^2)*exp(3)^2+(-6*x^5+12*x^4-8*x^3+12*x^2-10*x)*exp(3)+9*x^6-18*x^5+15*x^4-36*x^3+31*x^2-10*x+25),x,metho
d=_RETURNVERBOSE)

[Out]

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

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maxima [A]  time = 0.56, size = 59, normalized size = 1.55 \begin {gather*} -\frac {4 \, {\left ({\left (x^{2} - x\right )} e^{\left (4 \, x\right )} - e^{5}\right )}}{3 \, x e^{5} - {\left (3 \, x^{3} - x^{2} {\left (e^{3} + 3\right )} + x {\left (e^{3} + 1\right )} - 5\right )} e^{\left (4 \, x\right )} - e^{8}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-12*exp(-4*x+5)^2+(24*x^2-8*x-76)*exp(-4*x+5)-12*x^4+24*x^3-8*x^2-40*x+20)/((exp(3)^2-6*x*exp(3)+9*
x^2)*exp(-4*x+5)^2+((-2*x^2+2*x)*exp(3)^2+(12*x^3-12*x^2+2*x-10)*exp(3)-18*x^4+18*x^3-6*x^2+30*x)*exp(-4*x+5)+
(x^4-2*x^3+x^2)*exp(3)^2+(-6*x^5+12*x^4-8*x^3+12*x^2-10*x)*exp(3)+9*x^6-18*x^5+15*x^4-36*x^3+31*x^2-10*x+25),x
, algorithm="maxima")

[Out]

-4*((x^2 - x)*e^(4*x) - e^5)/(3*x*e^5 - (3*x^3 - x^2*(e^3 + 3) + x*(e^3 + 1) - 5)*e^(4*x) - e^8)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int -\frac {40\,x+12\,{\mathrm {e}}^{10-8\,x}+{\mathrm {e}}^{5-4\,x}\,\left (-24\,x^2+8\,x+76\right )+8\,x^2-24\,x^3+12\,x^4-20}{{\mathrm {e}}^6\,\left (x^4-2\,x^3+x^2\right )-10\,x+{\mathrm {e}}^{10-8\,x}\,\left (9\,x^2-6\,{\mathrm {e}}^3\,x+{\mathrm {e}}^6\right )+{\mathrm {e}}^{5-4\,x}\,\left (30\,x+{\mathrm {e}}^6\,\left (2\,x-2\,x^2\right )+{\mathrm {e}}^3\,\left (12\,x^3-12\,x^2+2\,x-10\right )-6\,x^2+18\,x^3-18\,x^4\right )-{\mathrm {e}}^3\,\left (6\,x^5-12\,x^4+8\,x^3-12\,x^2+10\,x\right )+31\,x^2-36\,x^3+15\,x^4-18\,x^5+9\,x^6+25} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(40*x + 12*exp(10 - 8*x) + exp(5 - 4*x)*(8*x - 24*x^2 + 76) + 8*x^2 - 24*x^3 + 12*x^4 - 20)/(exp(6)*(x^2
- 2*x^3 + x^4) - 10*x + exp(10 - 8*x)*(exp(6) - 6*x*exp(3) + 9*x^2) + exp(5 - 4*x)*(30*x + exp(6)*(2*x - 2*x^2
) + exp(3)*(2*x - 12*x^2 + 12*x^3 - 10) - 6*x^2 + 18*x^3 - 18*x^4) - exp(3)*(10*x - 12*x^2 + 8*x^3 - 12*x^4 +
6*x^5) + 31*x^2 - 36*x^3 + 15*x^4 - 18*x^5 + 9*x^6 + 25),x)

[Out]

int(-(40*x + 12*exp(10 - 8*x) + exp(5 - 4*x)*(8*x - 24*x^2 + 76) + 8*x^2 - 24*x^3 + 12*x^4 - 20)/(exp(6)*(x^2
- 2*x^3 + x^4) - 10*x + exp(10 - 8*x)*(exp(6) - 6*x*exp(3) + 9*x^2) + exp(5 - 4*x)*(30*x + exp(6)*(2*x - 2*x^2
) + exp(3)*(2*x - 12*x^2 + 12*x^3 - 10) - 6*x^2 + 18*x^3 - 18*x^4) - exp(3)*(10*x - 12*x^2 + 8*x^3 - 12*x^4 +
6*x^5) + 31*x^2 - 36*x^3 + 15*x^4 - 18*x^5 + 9*x^6 + 25), x)

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sympy [B]  time = 0.68, size = 94, normalized size = 2.47 \begin {gather*} \frac {4 x - 20}{- 9 x^{4} + 9 x^{3} + 6 x^{3} e^{3} - x^{2} e^{6} - 6 x^{2} e^{3} - 3 x^{2} + 15 x + x e^{3} + x e^{6} + \left (9 x^{2} - 6 x e^{3} + e^{6}\right ) e^{5 - 4 x} - 5 e^{3}} + \frac {12}{9 x - 3 e^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-12*exp(-4*x+5)**2+(24*x**2-8*x-76)*exp(-4*x+5)-12*x**4+24*x**3-8*x**2-40*x+20)/((exp(3)**2-6*x*exp
(3)+9*x**2)*exp(-4*x+5)**2+((-2*x**2+2*x)*exp(3)**2+(12*x**3-12*x**2+2*x-10)*exp(3)-18*x**4+18*x**3-6*x**2+30*
x)*exp(-4*x+5)+(x**4-2*x**3+x**2)*exp(3)**2+(-6*x**5+12*x**4-8*x**3+12*x**2-10*x)*exp(3)+9*x**6-18*x**5+15*x**
4-36*x**3+31*x**2-10*x+25),x)

[Out]

(4*x - 20)/(-9*x**4 + 9*x**3 + 6*x**3*exp(3) - x**2*exp(6) - 6*x**2*exp(3) - 3*x**2 + 15*x + x*exp(3) + x*exp(
6) + (9*x**2 - 6*x*exp(3) + exp(6))*exp(5 - 4*x) - 5*exp(3)) + 12/(9*x - 3*exp(3))

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