3.96.87 \(\int \frac {e^{\frac {3-3 x-3 x^2+4 x^3+e^x (-1+x^2)}{-1+x^2}} (-3+9 x^2-4 x^4+e^x (-1+2 x^2-x^4))}{1-2 x^2+x^4} \, dx\)

Optimal. Leaf size=27 \[ 9-e^{-3+e^x+4 x+\frac {x^2}{-x+x^3}} \]

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Rubi [F]  time = 12.47, 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 (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right ) \left (-3+9 x^2-4 x^4+e^x \left (-1+2 x^2-x^4\right )\right )}{1-2 x^2+x^4} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^((3 - 3*x - 3*x^2 + 4*x^3 + E^x*(-1 + x^2))/(-1 + x^2))*(-3 + 9*x^2 - 4*x^4 + E^x*(-1 + 2*x^2 - x^4)))/
(1 - 2*x^2 + x^4),x]

[Out]

-Defer[Int][E^((3 - E^x - 4*x - 3*x^2 + E^x*x^2 + 5*x^3)/(-1 + x^2)), x] - 4*Defer[Int][E^((3 - 3*x - 3*x^2 +
4*x^3 + E^x*(-1 + x^2))/(-1 + x^2)), x] + (3*Defer[Int][E^((3 - 3*x - 3*x^2 + 4*x^3 + E^x*(-1 + x^2))/(-1 + x^
2))/(1 - x)^2, x])/2 - Defer[Int][E^((3 - 3*x - 3*x^2 + 4*x^3 + E^x*(-1 + x^2))/(-1 + x^2))/(-1 + x)^2, x] + D
efer[Int][E^((3 - 3*x - 3*x^2 + 4*x^3 + E^x*(-1 + x^2))/(-1 + x^2))/(1 + x)^2, x]/2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right ) \left (-3+9 x^2-4 x^4+e^x \left (-1+2 x^2-x^4\right )\right )}{\left (-1+x^2\right )^2} \, dx\\ &=\int \left (-\exp \left (x+\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )-\frac {3 \exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{\left (-1+x^2\right )^2}+\frac {9 \exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right ) x^2}{\left (-1+x^2\right )^2}-\frac {4 \exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right ) x^4}{\left (-1+x^2\right )^2}\right ) \, dx\\ &=-\left (3 \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{\left (-1+x^2\right )^2} \, dx\right )-4 \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right ) x^4}{\left (-1+x^2\right )^2} \, dx+9 \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right ) x^2}{\left (-1+x^2\right )^2} \, dx-\int \exp \left (x+\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right ) \, dx\\ &=-\left (3 \int \left (\frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{4 (1-x)^2}+\frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{4 (1+x)^2}+\frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{2 \left (1-x^2\right )}\right ) \, dx\right )-4 \int \left (\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )+\frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{4 (-1+x)^2}+\frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{4 (1+x)^2}+\frac {3 \exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{2 \left (-1+x^2\right )}\right ) \, dx+9 \int \left (\frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{\left (-1+x^2\right )^2}+\frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{-1+x^2}\right ) \, dx-\int e^{\frac {3-e^x-4 x-3 x^2+e^x x^2+5 x^3}{-1+x^2}} \, dx\\ &=-\left (\frac {3}{4} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{(1-x)^2} \, dx\right )-\frac {3}{4} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{(1+x)^2} \, dx-\frac {3}{2} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{1-x^2} \, dx-4 \int \exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right ) \, dx-6 \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{-1+x^2} \, dx+9 \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{\left (-1+x^2\right )^2} \, dx+9 \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{-1+x^2} \, dx-\int e^{\frac {3-e^x-4 x-3 x^2+e^x x^2+5 x^3}{-1+x^2}} \, dx-\int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{(-1+x)^2} \, dx-\int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{(1+x)^2} \, dx\\ &=-\left (\frac {3}{4} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{(1-x)^2} \, dx\right )-\frac {3}{4} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{(1+x)^2} \, dx-\frac {3}{2} \int \left (\frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{2 (1-x)}+\frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{2 (1+x)}\right ) \, dx-4 \int \exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right ) \, dx-6 \int \left (-\frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{2 (1-x)}-\frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{2 (1+x)}\right ) \, dx+9 \int \left (-\frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{2 (1-x)}-\frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{2 (1+x)}\right ) \, dx+9 \int \left (\frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{4 (1-x)^2}+\frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{4 (1+x)^2}+\frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{2 \left (1-x^2\right )}\right ) \, dx-\int e^{\frac {3-e^x-4 x-3 x^2+e^x x^2+5 x^3}{-1+x^2}} \, dx-\int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{(-1+x)^2} \, dx-\int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{(1+x)^2} \, dx\\ &=-\left (\frac {3}{4} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{(1-x)^2} \, dx\right )-\frac {3}{4} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{1-x} \, dx-\frac {3}{4} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{(1+x)^2} \, dx-\frac {3}{4} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{1+x} \, dx+\frac {9}{4} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{(1-x)^2} \, dx+\frac {9}{4} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{(1+x)^2} \, dx+3 \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{1-x} \, dx+3 \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{1+x} \, dx-4 \int \exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right ) \, dx-\frac {9}{2} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{1-x} \, dx-\frac {9}{2} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{1+x} \, dx+\frac {9}{2} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{1-x^2} \, dx-\int e^{\frac {3-e^x-4 x-3 x^2+e^x x^2+5 x^3}{-1+x^2}} \, dx-\int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{(-1+x)^2} \, dx-\int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{(1+x)^2} \, dx\\ &=-\left (\frac {3}{4} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{(1-x)^2} \, dx\right )-\frac {3}{4} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{1-x} \, dx-\frac {3}{4} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{(1+x)^2} \, dx-\frac {3}{4} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{1+x} \, dx+\frac {9}{4} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{(1-x)^2} \, dx+\frac {9}{4} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{(1+x)^2} \, dx+3 \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{1-x} \, dx+3 \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{1+x} \, dx-4 \int \exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right ) \, dx-\frac {9}{2} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{1-x} \, dx-\frac {9}{2} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{1+x} \, dx+\frac {9}{2} \int \left (\frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{2 (1-x)}+\frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{2 (1+x)}\right ) \, dx-\int e^{\frac {3-e^x-4 x-3 x^2+e^x x^2+5 x^3}{-1+x^2}} \, dx-\int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{(-1+x)^2} \, dx-\int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{(1+x)^2} \, dx\\ &=-\left (\frac {3}{4} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{(1-x)^2} \, dx\right )-\frac {3}{4} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{1-x} \, dx-\frac {3}{4} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{(1+x)^2} \, dx-\frac {3}{4} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{1+x} \, dx+\frac {9}{4} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{(1-x)^2} \, dx+\frac {9}{4} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{1-x} \, dx+\frac {9}{4} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{(1+x)^2} \, dx+\frac {9}{4} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{1+x} \, dx+3 \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{1-x} \, dx+3 \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{1+x} \, dx-4 \int \exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right ) \, dx-\frac {9}{2} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{1-x} \, dx-\frac {9}{2} \int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{1+x} \, dx-\int e^{\frac {3-e^x-4 x-3 x^2+e^x x^2+5 x^3}{-1+x^2}} \, dx-\int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{(-1+x)^2} \, dx-\int \frac {\exp \left (\frac {3-3 x-3 x^2+4 x^3+e^x \left (-1+x^2\right )}{-1+x^2}\right )}{(1+x)^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 1.19, size = 21, normalized size = 0.78 \begin {gather*} -e^{-3+e^x+4 x+\frac {x}{-1+x^2}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((3 - 3*x - 3*x^2 + 4*x^3 + E^x*(-1 + x^2))/(-1 + x^2))*(-3 + 9*x^2 - 4*x^4 + E^x*(-1 + 2*x^2 - x
^4)))/(1 - 2*x^2 + x^4),x]

[Out]

-E^(-3 + E^x + 4*x + x/(-1 + x^2))

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fricas [A]  time = 0.60, size = 34, normalized size = 1.26 \begin {gather*} -e^{\left (\frac {4 \, x^{3} - 3 \, x^{2} + {\left (x^{2} - 1\right )} e^{x} - 3 \, x + 3}{x^{2} - 1}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x^4+2*x^2-1)*exp(x)-4*x^4+9*x^2-3)*exp(((x^2-1)*exp(x)+4*x^3-3*x^2-3*x+3)/(x^2-1))/(x^4-2*x^2+1),
x, algorithm="fricas")

[Out]

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

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giac [B]  time = 0.21, size = 71, normalized size = 2.63 \begin {gather*} -e^{\left (\frac {4 \, x^{3}}{x^{2} - 1} + \frac {x^{2} e^{x}}{x^{2} - 1} - \frac {3 \, x^{2}}{x^{2} - 1} - \frac {3 \, x}{x^{2} - 1} - \frac {e^{x}}{x^{2} - 1} + \frac {3}{x^{2} - 1}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x^4+2*x^2-1)*exp(x)-4*x^4+9*x^2-3)*exp(((x^2-1)*exp(x)+4*x^3-3*x^2-3*x+3)/(x^2-1))/(x^4-2*x^2+1),
x, algorithm="giac")

[Out]

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

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maple [A]  time = 0.14, size = 40, normalized size = 1.48

method	result	size
risch	\(-{\mathrm e}^{\frac {{\mathrm e}^{x} x^{2}+4 x^{3}-3 x^{2}-{\mathrm e}^{x}-3 x +3}{\left (x -1\right ) \left (x +1\right )}}\)	\(40\)
norman	\(\frac {-x^{2} {\mathrm e}^{\frac {\left (x^{2}-1\right ) {\mathrm e}^{x}+4 x^{3}-3 x^{2}-3 x +3}{x^{2}-1}}+{\mathrm e}^{\frac {\left (x^{2}-1\right ) {\mathrm e}^{x}+4 x^{3}-3 x^{2}-3 x +3}{x^{2}-1}}}{x^{2}-1}\)	\(79\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-x^4+2*x^2-1)*exp(x)-4*x^4+9*x^2-3)*exp(((x^2-1)*exp(x)+4*x^3-3*x^2-3*x+3)/(x^2-1))/(x^4-2*x^2+1),x,meth
od=_RETURNVERBOSE)

[Out]

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

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maxima [A]  time = 0.52, size = 24, normalized size = 0.89 \begin {gather*} -e^{\left (4 \, x + \frac {1}{2 \, {\left (x + 1\right )}} + \frac {1}{2 \, {\left (x - 1\right )}} + e^{x} - 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x^4+2*x^2-1)*exp(x)-4*x^4+9*x^2-3)*exp(((x^2-1)*exp(x)+4*x^3-3*x^2-3*x+3)/(x^2-1))/(x^4-2*x^2+1),
x, algorithm="maxima")

[Out]

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

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mupad [B]  time = 7.41, size = 75, normalized size = 2.78 \begin {gather*} -{\mathrm {e}}^{\frac {x^2\,{\mathrm {e}}^x}{x^2-1}}\,{\mathrm {e}}^{-\frac {3\,x^2}{x^2-1}}\,{\mathrm {e}}^{\frac {4\,x^3}{x^2-1}}\,{\mathrm {e}}^{-\frac {{\mathrm {e}}^x}{x^2-1}}\,{\mathrm {e}}^{\frac {3}{x^2-1}}\,{\mathrm {e}}^{-\frac {3\,x}{x^2-1}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp((exp(x)*(x^2 - 1) - 3*x - 3*x^2 + 4*x^3 + 3)/(x^2 - 1))*(exp(x)*(x^4 - 2*x^2 + 1) - 9*x^2 + 4*x^4 +
3))/(x^4 - 2*x^2 + 1),x)

[Out]

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

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sympy [A]  time = 0.34, size = 31, normalized size = 1.15 \begin {gather*} - e^{\frac {4 x^{3} - 3 x^{2} - 3 x + \left (x^{2} - 1\right ) e^{x} + 3}{x^{2} - 1}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x**4+2*x**2-1)*exp(x)-4*x**4+9*x**2-3)*exp(((x**2-1)*exp(x)+4*x**3-3*x**2-3*x+3)/(x**2-1))/(x**4-
2*x**2+1),x)

[Out]

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

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