3.14.97 \(\int \frac {e^{e^{-2 x} x^2 (9+\frac {e^x (-48-18 x)}{x}+\frac {e^{2 x} (61+48 x+9 x^2)}{x^2})} (18-18 x+\frac {e^x (-48+12 x+18 x^2)}{x}+\frac {e^{2 x} (48 x+18 x^2)}{x^2})}{-\frac {2 e^{2 x}}{x}+\frac {e^{2 x+e^{-2 x} x^2 (9+\frac {e^x (-48-18 x)}{x}+\frac {e^{2 x} (61+48 x+9 x^2)}{x^2})}}{x}} \, dx\)

Optimal. Leaf size=22 \[ \log \left (-2+e^{-3+\left (-8-3 x+3 e^{-x} x\right )^2}\right ) \]

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Rubi [F]  time = 71.94, 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 {\exp \left (e^{-2 x} x^2 \left (9+\frac {e^x (-48-18 x)}{x}+\frac {e^{2 x} \left (61+48 x+9 x^2\right )}{x^2}\right )\right ) \left (18-18 x+\frac {e^x \left (-48+12 x+18 x^2\right )}{x}+\frac {e^{2 x} \left (48 x+18 x^2\right )}{x^2}\right )}{-\frac {2 e^{2 x}}{x}+\frac {\exp \left (2 x+e^{-2 x} x^2 \left (9+\frac {e^x (-48-18 x)}{x}+\frac {e^{2 x} \left (61+48 x+9 x^2\right )}{x^2}\right )\right )}{x}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^((x^2*(9 + (E^x*(-48 - 18*x))/x + (E^(2*x)*(61 + 48*x + 9*x^2))/x^2))/E^(2*x))*(18 - 18*x + (E^x*(-48 +
12*x + 18*x^2))/x + (E^(2*x)*(48*x + 18*x^2))/x^2))/((-2*E^(2*x))/x + E^(2*x + (x^2*(9 + (E^x*(-48 - 18*x))/x
+ (E^(2*x)*(61 + 48*x + 9*x^2))/x^2))/E^(2*x))/x),x]

[Out]

48*x - (48*x)/E^x + 9*x^2 + (9*x^2)/E^(2*x) - (18*x^2)/E^x - 96*Defer[Int][E^(48*(-1 + E^(-x))*x)/(2*E^(48*(-1
+ E^(-x))*x) - E^(61 + (9*(-1 + E^x)^2*x^2)/E^(2*x))), x] + 96*Defer[Int][E^(-49*x + (48*x)/E^x)/(2*E^(48*(-1
+ E^(-x))*x) - E^(61 + (9*(-1 + E^x)^2*x^2)/E^(2*x))), x] - 36*Defer[Int][(E^(48*(-1 + E^(-x))*x)*x)/(2*E^(48
*(-1 + E^(-x))*x) - E^(61 + (9*(-1 + E^x)^2*x^2)/E^(2*x))), x] - 36*Defer[Int][x/(E^((2*(-24 + 25*E^x)*x)/E^x)
*(2*E^(48*(-1 + E^(-x))*x) - E^(61 + (9*(-1 + E^x)^2*x^2)/E^(2*x)))), x] - 24*Defer[Int][(E^(-49*x + (48*x)/E^
x)*x)/(2*E^(48*(-1 + E^(-x))*x) - E^(61 + (9*(-1 + E^x)^2*x^2)/E^(2*x))), x] + 36*Defer[Int][x^2/(E^((2*(-24 +
25*E^x)*x)/E^x)*(2*E^(48*(-1 + E^(-x))*x) - E^(61 + (9*(-1 + E^x)^2*x^2)/E^(2*x)))), x] - 36*Defer[Int][(E^(-
49*x + (48*x)/E^x)*x^2)/(2*E^(48*(-1 + E^(-x))*x) - E^(61 + (9*(-1 + E^x)^2*x^2)/E^(2*x))), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {6 e^{-2 x} \left (-3 (-1+x) x+e^{2 x} (8+3 x)+e^x \left (-8+2 x+3 x^2\right )\right )}{1-2 \exp \left (-61+48 \left (-1+e^{-x}\right ) x-9 e^{-2 x} \left (-1+e^x\right )^2 x^2\right )} \, dx\\ &=6 \int \frac {e^{-2 x} \left (-3 (-1+x) x+e^{2 x} (8+3 x)+e^x \left (-8+2 x+3 x^2\right )\right )}{1-2 \exp \left (-61+48 \left (-1+e^{-x}\right ) x-9 e^{-2 x} \left (-1+e^x\right )^2 x^2\right )} \, dx\\ &=6 \int \left (e^{-2 x} \left (-1+e^x+x\right ) \left (8 e^x-3 x+3 e^x x\right )-\frac {2 e^{-2 x+48 \left (-1+e^{-x}\right ) x} \left (-8 e^x+8 e^{2 x}+3 x+2 e^x x+3 e^{2 x} x-3 x^2+3 e^x x^2\right )}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}}\right ) \, dx\\ &=6 \int e^{-2 x} \left (-1+e^x+x\right ) \left (8 e^x-3 x+3 e^x x\right ) \, dx-12 \int \frac {e^{-2 x+48 \left (-1+e^{-x}\right ) x} \left (-8 e^x+8 e^{2 x}+3 x+2 e^x x+3 e^{2 x} x-3 x^2+3 e^x x^2\right )}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx\\ &=6 \int \left (8+3 x-3 e^{-2 x} (-1+x) x+e^{-x} \left (-8+2 x+3 x^2\right )\right ) \, dx-12 \int \frac {e^{-2 e^{-x} \left (-24+25 e^x\right ) x} \left (-8 e^x+8 e^{2 x}+3 x+2 e^x x+3 e^{2 x} x-3 x^2+3 e^x x^2\right )}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx\\ &=48 x+9 x^2+6 \int e^{-x} \left (-8+2 x+3 x^2\right ) \, dx-12 \int \left (-\frac {8 e^{x-2 e^{-x} \left (-24+25 e^x\right ) x}}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}}+\frac {8 e^{2 x-2 e^{-x} \left (-24+25 e^x\right ) x}}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}}+\frac {3 e^{-2 e^{-x} \left (-24+25 e^x\right ) x} x}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}}+\frac {2 e^{x-2 e^{-x} \left (-24+25 e^x\right ) x} x}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}}+\frac {3 e^{2 x-2 e^{-x} \left (-24+25 e^x\right ) x} x}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}}-\frac {3 e^{-2 e^{-x} \left (-24+25 e^x\right ) x} x^2}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}}+\frac {3 e^{x-2 e^{-x} \left (-24+25 e^x\right ) x} x^2}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}}\right ) \, dx-18 \int e^{-2 x} (-1+x) x \, dx\\ &=48 x+9 x^2+6 \int \left (-8 e^{-x}+2 e^{-x} x+3 e^{-x} x^2\right ) \, dx-18 \int \left (-e^{-2 x} x+e^{-2 x} x^2\right ) \, dx-24 \int \frac {e^{x-2 e^{-x} \left (-24+25 e^x\right ) x} x}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx-36 \int \frac {e^{-2 e^{-x} \left (-24+25 e^x\right ) x} x}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx-36 \int \frac {e^{2 x-2 e^{-x} \left (-24+25 e^x\right ) x} x}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx+36 \int \frac {e^{-2 e^{-x} \left (-24+25 e^x\right ) x} x^2}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx-36 \int \frac {e^{x-2 e^{-x} \left (-24+25 e^x\right ) x} x^2}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx+96 \int \frac {e^{x-2 e^{-x} \left (-24+25 e^x\right ) x}}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx-96 \int \frac {e^{2 x-2 e^{-x} \left (-24+25 e^x\right ) x}}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx\\ &=48 x+9 x^2+12 \int e^{-x} x \, dx+18 \int e^{-2 x} x \, dx-18 \int e^{-2 x} x^2 \, dx+18 \int e^{-x} x^2 \, dx-24 \int \frac {e^{-49 x+48 e^{-x} x} x}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx-36 \int \frac {e^{48 \left (-1+e^{-x}\right ) x} x}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx-36 \int \frac {e^{-2 e^{-x} \left (-24+25 e^x\right ) x} x}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx+36 \int \frac {e^{-2 e^{-x} \left (-24+25 e^x\right ) x} x^2}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx-36 \int \frac {e^{-49 x+48 e^{-x} x} x^2}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx-48 \int e^{-x} \, dx-96 \int \frac {e^{48 \left (-1+e^{-x}\right ) x}}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx+96 \int \frac {e^{-49 x+48 e^{-x} x}}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx\\ &=48 e^{-x}+48 x-9 e^{-2 x} x-12 e^{-x} x+9 x^2+9 e^{-2 x} x^2-18 e^{-x} x^2+9 \int e^{-2 x} \, dx+12 \int e^{-x} \, dx-18 \int e^{-2 x} x \, dx-24 \int \frac {e^{-49 x+48 e^{-x} x} x}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx+36 \int e^{-x} x \, dx-36 \int \frac {e^{48 \left (-1+e^{-x}\right ) x} x}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx-36 \int \frac {e^{-2 e^{-x} \left (-24+25 e^x\right ) x} x}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx+36 \int \frac {e^{-2 e^{-x} \left (-24+25 e^x\right ) x} x^2}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx-36 \int \frac {e^{-49 x+48 e^{-x} x} x^2}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx-96 \int \frac {e^{48 \left (-1+e^{-x}\right ) x}}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx+96 \int \frac {e^{-49 x+48 e^{-x} x}}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx\\ &=-\frac {9}{2} e^{-2 x}+36 e^{-x}+48 x-48 e^{-x} x+9 x^2+9 e^{-2 x} x^2-18 e^{-x} x^2-9 \int e^{-2 x} \, dx-24 \int \frac {e^{-49 x+48 e^{-x} x} x}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx+36 \int e^{-x} \, dx-36 \int \frac {e^{48 \left (-1+e^{-x}\right ) x} x}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx-36 \int \frac {e^{-2 e^{-x} \left (-24+25 e^x\right ) x} x}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx+36 \int \frac {e^{-2 e^{-x} \left (-24+25 e^x\right ) x} x^2}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx-36 \int \frac {e^{-49 x+48 e^{-x} x} x^2}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx-96 \int \frac {e^{48 \left (-1+e^{-x}\right ) x}}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx+96 \int \frac {e^{-49 x+48 e^{-x} x}}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx\\ &=48 x-48 e^{-x} x+9 x^2+9 e^{-2 x} x^2-18 e^{-x} x^2-24 \int \frac {e^{-49 x+48 e^{-x} x} x}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx-36 \int \frac {e^{48 \left (-1+e^{-x}\right ) x} x}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx-36 \int \frac {e^{-2 e^{-x} \left (-24+25 e^x\right ) x} x}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx+36 \int \frac {e^{-2 e^{-x} \left (-24+25 e^x\right ) x} x^2}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx-36 \int \frac {e^{-49 x+48 e^{-x} x} x^2}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx-96 \int \frac {e^{48 \left (-1+e^{-x}\right ) x}}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx+96 \int \frac {e^{-49 x+48 e^{-x} x}}{2 e^{48 \left (-1+e^{-x}\right ) x}-e^{61+9 e^{-2 x} \left (-1+e^x\right )^2 x^2}} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [F]  time = 180.00, size = 0, normalized size = 0.00 \begin {gather*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(E^((x^2*(9 + (E^x*(-48 - 18*x))/x + (E^(2*x)*(61 + 48*x + 9*x^2))/x^2))/E^(2*x))*(18 - 18*x + (E^x*
(-48 + 12*x + 18*x^2))/x + (E^(2*x)*(48*x + 18*x^2))/x^2))/((-2*E^(2*x))/x + E^(2*x + (x^2*(9 + (E^x*(-48 - 18
*x))/x + (E^(2*x)*(61 + 48*x + 9*x^2))/x^2))/E^(2*x))/x),x]

[Out]

$Aborted

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fricas [B]  time = 0.82, size = 50, normalized size = 2.27 \begin {gather*} \log \left (e^{\left ({\left ({\left (9 \, x^{2} + 48 \, x + 61\right )} e^{\left (2 \, x - 2 \, \log \relax (x)\right )} - 6 \, {\left (3 \, x + 8\right )} e^{\left (x - \log \relax (x)\right )} + 9\right )} e^{\left (-2 \, x + 2 \, \log \relax (x)\right )}\right )} - 2\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((18*x^2+48*x)*exp(x-log(x))^2+(18*x^2+12*x-48)*exp(x-log(x))-18*x+18)*exp(((9*x^2+48*x+61)*exp(x-lo
g(x))^2+(-18*x-48)*exp(x-log(x))+9)/exp(x-log(x))^2)/(x*exp(x-log(x))^2*exp(((9*x^2+48*x+61)*exp(x-log(x))^2+(
-18*x-48)*exp(x-log(x))+9)/exp(x-log(x))^2)-2*x*exp(x-log(x))^2),x, algorithm="fricas")

[Out]

log(e^(((9*x^2 + 48*x + 61)*e^(2*x - 2*log(x)) - 6*(3*x + 8)*e^(x - log(x)) + 9)*e^(-2*x + 2*log(x))) - 2)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {6 \, {\left ({\left (3 \, x^{2} + 8 \, x\right )} e^{\left (2 \, x - 2 \, \log \relax (x)\right )} + {\left (3 \, x^{2} + 2 \, x - 8\right )} e^{\left (x - \log \relax (x)\right )} - 3 \, x + 3\right )} e^{\left ({\left ({\left (9 \, x^{2} + 48 \, x + 61\right )} e^{\left (2 \, x - 2 \, \log \relax (x)\right )} - 6 \, {\left (3 \, x + 8\right )} e^{\left (x - \log \relax (x)\right )} + 9\right )} e^{\left (-2 \, x + 2 \, \log \relax (x)\right )}\right )}}{x e^{\left ({\left ({\left (9 \, x^{2} + 48 \, x + 61\right )} e^{\left (2 \, x - 2 \, \log \relax (x)\right )} - 6 \, {\left (3 \, x + 8\right )} e^{\left (x - \log \relax (x)\right )} + 9\right )} e^{\left (-2 \, x + 2 \, \log \relax (x)\right )} + 2 \, x - 2 \, \log \relax (x)\right )} - 2 \, x e^{\left (2 \, x - 2 \, \log \relax (x)\right )}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((18*x^2+48*x)*exp(x-log(x))^2+(18*x^2+12*x-48)*exp(x-log(x))-18*x+18)*exp(((9*x^2+48*x+61)*exp(x-lo
g(x))^2+(-18*x-48)*exp(x-log(x))+9)/exp(x-log(x))^2)/(x*exp(x-log(x))^2*exp(((9*x^2+48*x+61)*exp(x-log(x))^2+(
-18*x-48)*exp(x-log(x))+9)/exp(x-log(x))^2)-2*x*exp(x-log(x))^2),x, algorithm="giac")

[Out]

integrate(6*((3*x^2 + 8*x)*e^(2*x - 2*log(x)) + (3*x^2 + 2*x - 8)*e^(x - log(x)) - 3*x + 3)*e^(((9*x^2 + 48*x
+ 61)*e^(2*x - 2*log(x)) - 6*(3*x + 8)*e^(x - log(x)) + 9)*e^(-2*x + 2*log(x)))/(x*e^(((9*x^2 + 48*x + 61)*e^(
2*x - 2*log(x)) - 6*(3*x + 8)*e^(x - log(x)) + 9)*e^(-2*x + 2*log(x)) + 2*x - 2*log(x)) - 2*x*e^(2*x - 2*log(x
))), x)

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maple [B]  time = 0.10, size = 123, normalized size = 5.59

method	result	size
risch	\(9 x^{2}+48 x +\left (-18 x^{2}-48 x \right ) {\mathrm e}^{-x}+9 x^{2} {\mathrm e}^{-2 x}-\left (\frac {\left (9 x^{2}+48 x +61\right ) {\mathrm e}^{2 x}}{x^{2}}+\frac {\left (-18 x -48\right ) {\mathrm e}^{x}}{x}+9\right ) x^{2} {\mathrm e}^{-2 x}+\ln \left ({\mathrm e}^{-\left (-9 \,{\mathrm e}^{2 x} x^{2}+18 \,{\mathrm e}^{x} x^{2}-48 x \,{\mathrm e}^{2 x}+48 \,{\mathrm e}^{x} x -9 x^{2}-61 \,{\mathrm e}^{2 x}\right ) {\mathrm e}^{-2 x}}-2\right )\)	\(123\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((18*x^2+48*x)*exp(x-ln(x))^2+(18*x^2+12*x-48)*exp(x-ln(x))-18*x+18)*exp(((9*x^2+48*x+61)*exp(x-ln(x))^2+(
-18*x-48)*exp(x-ln(x))+9)/exp(x-ln(x))^2)/(x*exp(x-ln(x))^2*exp(((9*x^2+48*x+61)*exp(x-ln(x))^2+(-18*x-48)*exp
(x-ln(x))+9)/exp(x-ln(x))^2)-2*x*exp(x-ln(x))^2),x,method=_RETURNVERBOSE)

[Out]

9*x^2+48*x+(-18*x^2-48*x)*exp(-x)+9*x^2*exp(-2*x)-((9*x^2+48*x+61)/x^2*exp(2*x)+(-18*x-48)*exp(x)/x+9)*x^2*exp
(-2*x)+ln(exp(-(-9*exp(2*x)*x^2+18*exp(x)*x^2-48*x*exp(2*x)+48*exp(x)*x-9*x^2-61*exp(2*x))*exp(-2*x))-2)

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maxima [B]  time = 0.84, size = 81, normalized size = 3.68 \begin {gather*} 9 \, x^{2} - 6 \, {\left (3 \, x^{2} + 8 \, x\right )} e^{\left (-x\right )} + 48 \, x + \log \left (-{\left (2 \, e^{\left (18 \, x^{2} e^{\left (-x\right )} + 48 \, x e^{\left (-x\right )}\right )} - e^{\left (9 \, x^{2} e^{\left (-2 \, x\right )} + 9 \, x^{2} + 48 \, x + 61\right )}\right )} e^{\left (-9 \, x^{2} - 48 \, x - 61\right )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((18*x^2+48*x)*exp(x-log(x))^2+(18*x^2+12*x-48)*exp(x-log(x))-18*x+18)*exp(((9*x^2+48*x+61)*exp(x-lo
g(x))^2+(-18*x-48)*exp(x-log(x))+9)/exp(x-log(x))^2)/(x*exp(x-log(x))^2*exp(((9*x^2+48*x+61)*exp(x-log(x))^2+(
-18*x-48)*exp(x-log(x))+9)/exp(x-log(x))^2)-2*x*exp(x-log(x))^2),x, algorithm="maxima")

[Out]

9*x^2 - 6*(3*x^2 + 8*x)*e^(-x) + 48*x + log(-(2*e^(18*x^2*e^(-x) + 48*x*e^(-x)) - e^(9*x^2*e^(-2*x) + 9*x^2 +
48*x + 61))*e^(-9*x^2 - 48*x - 61))

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mupad [B]  time = 1.28, size = 44, normalized size = 2.00 \begin {gather*} \ln \left ({\mathrm {e}}^{48\,x}\,{\mathrm {e}}^{61}\,{\mathrm {e}}^{-48\,x\,{\mathrm {e}}^{-x}}\,{\mathrm {e}}^{9\,x^2}\,{\mathrm {e}}^{9\,x^2\,{\mathrm {e}}^{-2\,x}}\,{\mathrm {e}}^{-18\,x^2\,{\mathrm {e}}^{-x}}-2\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(exp(2*log(x) - 2*x)*(exp(2*x - 2*log(x))*(48*x + 9*x^2 + 61) - exp(x - log(x))*(18*x + 48) + 9))*(ex
p(x - log(x))*(12*x + 18*x^2 - 48) - 18*x + exp(2*x - 2*log(x))*(48*x + 18*x^2) + 18))/(2*x*exp(2*x - 2*log(x)
) - x*exp(exp(2*log(x) - 2*x)*(exp(2*x - 2*log(x))*(48*x + 9*x^2 + 61) - exp(x - log(x))*(18*x + 48) + 9))*exp
(2*x - 2*log(x))),x)

[Out]

log(exp(48*x)*exp(61)*exp(-48*x*exp(-x))*exp(9*x^2)*exp(9*x^2*exp(-2*x))*exp(-18*x^2*exp(-x)) - 2)

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sympy [B]  time = 0.38, size = 44, normalized size = 2.00 \begin {gather*} \log {\left (e^{x^{2} \left (9 + \frac {\left (- 18 x - 48\right ) e^{x}}{x} + \frac {\left (9 x^{2} + 48 x + 61\right ) e^{2 x}}{x^{2}}\right ) e^{- 2 x}} - 2 \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((18*x**2+48*x)*exp(x-ln(x))**2+(18*x**2+12*x-48)*exp(x-ln(x))-18*x+18)*exp(((9*x**2+48*x+61)*exp(x-
ln(x))**2+(-18*x-48)*exp(x-ln(x))+9)/exp(x-ln(x))**2)/(x*exp(x-ln(x))**2*exp(((9*x**2+48*x+61)*exp(x-ln(x))**2
+(-18*x-48)*exp(x-ln(x))+9)/exp(x-ln(x))**2)-2*x*exp(x-ln(x))**2),x)

[Out]

log(exp(x**2*(9 + (-18*x - 48)*exp(x)/x + (9*x**2 + 48*x + 61)*exp(2*x)/x**2)*exp(-2*x)) - 2)

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