3.67.39 \(\int \frac {e^{e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} (1568 x+3276 x^2-1462 x^3-54 x^4+42 x^5+4 x^6)}{784-280 x-31 x^2+10 x^3+x^4} \, dx\)

Optimal. Leaf size=36 \[ e^{e^{x \left (5+\frac {x}{-x+\frac {5 (5-x)}{-\frac {3}{x}+x}}\right )} x^2} \]

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Rubi [F]  time = 24.11, 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^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) \left (1568 x+3276 x^2-1462 x^3-54 x^4+42 x^5+4 x^6\right )}{784-280 x-31 x^2+10 x^3+x^4} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(E^((-137*x + 25*x^2 + 4*x^3)/(-28 + 5*x + x^2))*x^2 + (-137*x + 25*x^2 + 4*x^3)/(-28 + 5*x + x^2))*(15
68*x + 3276*x^2 - 1462*x^3 - 54*x^4 + 42*x^5 + 4*x^6))/(784 - 280*x - 31*x^2 + 10*x^3 + x^4),x]

[Out]

50*Defer[Int][E^(E^((-137*x + 25*x^2 + 4*x^3)/(-28 + 5*x + x^2))*x^2 + (-137*x + 25*x^2 + 4*x^3)/(-28 + 5*x +
x^2)), x] + (532000*Defer[Int][E^(E^((-137*x + 25*x^2 + 4*x^3)/(-28 + 5*x + x^2))*x^2 + (-137*x + 25*x^2 + 4*x
^3)/(-28 + 5*x + x^2))/(-5 + Sqrt[137] - 2*x)^2, x])/137 + (77180*(5 - Sqrt[137])*Defer[Int][E^(E^((-137*x + 2
5*x^2 + 4*x^3)/(-28 + 5*x + x^2))*x^2 + (-137*x + 25*x^2 + 4*x^3)/(-28 + 5*x + x^2))/(-5 + Sqrt[137] - 2*x)^2,
x])/137 + (6700*Defer[Int][E^(E^((-137*x + 25*x^2 + 4*x^3)/(-28 + 5*x + x^2))*x^2 + (-137*x + 25*x^2 + 4*x^3)
/(-28 + 5*x + x^2))/(-5 + Sqrt[137] - 2*x), x])/Sqrt[137] + 2*Defer[Int][E^(E^((-137*x + 25*x^2 + 4*x^3)/(-28
+ 5*x + x^2))*x^2 + (-137*x + 25*x^2 + 4*x^3)/(-28 + 5*x + x^2))*x, x] + 4*Defer[Int][E^(E^((-137*x + 25*x^2 +
4*x^3)/(-28 + 5*x + x^2))*x^2 + (-137*x + 25*x^2 + 4*x^3)/(-28 + 5*x + x^2))*x^2, x] - (60*(1781 - 270*Sqrt[1
37])*Defer[Int][E^(E^((-137*x + 25*x^2 + 4*x^3)/(-28 + 5*x + x^2))*x^2 + (-137*x + 25*x^2 + 4*x^3)/(-28 + 5*x
+ x^2))/(5 - Sqrt[137] + 2*x), x])/137 + (532000*Defer[Int][E^(E^((-137*x + 25*x^2 + 4*x^3)/(-28 + 5*x + x^2))
*x^2 + (-137*x + 25*x^2 + 4*x^3)/(-28 + 5*x + x^2))/(5 + Sqrt[137] + 2*x)^2, x])/137 + (77180*(5 + Sqrt[137])*
Defer[Int][E^(E^((-137*x + 25*x^2 + 4*x^3)/(-28 + 5*x + x^2))*x^2 + (-137*x + 25*x^2 + 4*x^3)/(-28 + 5*x + x^2
))/(5 + Sqrt[137] + 2*x)^2, x])/137 + (6700*Defer[Int][E^(E^((-137*x + 25*x^2 + 4*x^3)/(-28 + 5*x + x^2))*x^2
+ (-137*x + 25*x^2 + 4*x^3)/(-28 + 5*x + x^2))/(5 + Sqrt[137] + 2*x), x])/Sqrt[137] - (60*(1781 + 270*Sqrt[137
])*Defer[Int][E^(E^((-137*x + 25*x^2 + 4*x^3)/(-28 + 5*x + x^2))*x^2 + (-137*x + 25*x^2 + 4*x^3)/(-28 + 5*x +
x^2))/(5 + Sqrt[137] + 2*x), x])/137

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) x \left (784+1638 x-731 x^2-27 x^3+21 x^4+2 x^5\right )}{784-280 x-31 x^2+10 x^3+x^4} \, dx\\ &=2 \int \frac {\exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) x \left (784+1638 x-731 x^2-27 x^3+21 x^4+2 x^5\right )}{784-280 x-31 x^2+10 x^3+x^4} \, dx\\ &=2 \int \left (25 \exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right )+\exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) x+2 \exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) x^2-\frac {5 \exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) \left (3920-1400 x-225 x^2+78 x^3\right )}{784-280 x-31 x^2+10 x^3+x^4}\right ) \, dx\\ &=2 \int \exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) x \, dx+4 \int \exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) x^2 \, dx-10 \int \frac {\exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) \left (3920-1400 x-225 x^2+78 x^3\right )}{784-280 x-31 x^2+10 x^3+x^4} \, dx+50 \int \exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) \, dx\\ &=2 \int \exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) x \, dx+4 \int \exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) x^2 \, dx-10 \int \left (\frac {\exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) (-13300+3859 x)}{\left (-28+5 x+x^2\right )^2}+\frac {3 \exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) (-205+26 x)}{-28+5 x+x^2}\right ) \, dx+50 \int \exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) \, dx\\ &=2 \int \exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) x \, dx+4 \int \exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) x^2 \, dx-10 \int \frac {\exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) (-13300+3859 x)}{\left (-28+5 x+x^2\right )^2} \, dx-30 \int \frac {\exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) (-205+26 x)}{-28+5 x+x^2} \, dx+50 \int \exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) \, dx\\ &=2 \int \exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) x \, dx+4 \int \exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) x^2 \, dx-10 \int \left (-\frac {13300 \exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right )}{\left (-28+5 x+x^2\right )^2}+\frac {3859 \exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) x}{\left (-28+5 x+x^2\right )^2}\right ) \, dx-30 \int \left (\frac {\left (26-\frac {540}{\sqrt {137}}\right ) \exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right )}{5-\sqrt {137}+2 x}+\frac {\left (26+\frac {540}{\sqrt {137}}\right ) \exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right )}{5+\sqrt {137}+2 x}\right ) \, dx+50 \int \exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) \, dx\\ &=2 \int \exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) x \, dx+4 \int \exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) x^2 \, dx+50 \int \exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) \, dx-38590 \int \frac {\exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right ) x}{\left (-28+5 x+x^2\right )^2} \, dx+133000 \int \frac {\exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right )}{\left (-28+5 x+x^2\right )^2} \, dx-\frac {1}{137} \left (60 \left (1781-270 \sqrt {137}\right )\right ) \int \frac {\exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right )}{5-\sqrt {137}+2 x} \, dx-\frac {1}{137} \left (60 \left (1781+270 \sqrt {137}\right )\right ) \int \frac {\exp \left (e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}\right )}{5+\sqrt {137}+2 x} \, dx\\ &=2 \int e^{e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x \, dx+4 \int e^{e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2 \, dx+50 \int e^{e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} \, dx-38590 \int \left (\frac {2 \left (-5+\sqrt {137}\right ) e^{e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}}}{137 \left (-5+\sqrt {137}-2 x\right )^2}-\frac {10 e^{e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}}}{137 \sqrt {137} \left (-5+\sqrt {137}-2 x\right )}+\frac {2 \left (-5-\sqrt {137}\right ) e^{e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}}}{137 \left (5+\sqrt {137}+2 x\right )^2}-\frac {10 e^{e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}}}{137 \sqrt {137} \left (5+\sqrt {137}+2 x\right )}\right ) \, dx+133000 \int \left (\frac {4 e^{e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}}}{137 \left (-5+\sqrt {137}-2 x\right )^2}+\frac {4 e^{e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}}}{137 \sqrt {137} \left (-5+\sqrt {137}-2 x\right )}+\frac {4 e^{e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}}}{137 \left (5+\sqrt {137}+2 x\right )^2}+\frac {4 e^{e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}}}{137 \sqrt {137} \left (5+\sqrt {137}+2 x\right )}\right ) \, dx-\frac {1}{137} \left (60 \left (1781-270 \sqrt {137}\right )\right ) \int \frac {e^{e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}}}{5-\sqrt {137}+2 x} \, dx-\frac {1}{137} \left (60 \left (1781+270 \sqrt {137}\right )\right ) \int \frac {e^{e^{\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}} x^2+\frac {-137 x+25 x^2+4 x^3}{-28+5 x+x^2}}}{5+\sqrt {137}+2 x} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.17, size = 30, normalized size = 0.83 \begin {gather*} e^{e^{5+4 x-\frac {10 (-14+5 x)}{-28+5 x+x^2}} x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(E^((-137*x + 25*x^2 + 4*x^3)/(-28 + 5*x + x^2))*x^2 + (-137*x + 25*x^2 + 4*x^3)/(-28 + 5*x + x^2
))*(1568*x + 3276*x^2 - 1462*x^3 - 54*x^4 + 42*x^5 + 4*x^6))/(784 - 280*x - 31*x^2 + 10*x^3 + x^4),x]

[Out]

E^(E^(5 + 4*x - (10*(-14 + 5*x))/(-28 + 5*x + x^2))*x^2)

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fricas [B]  time = 0.58, size = 94, normalized size = 2.61 \begin {gather*} e^{\left (\frac {4 \, x^{3} + 25 \, x^{2} + {\left (x^{4} + 5 \, x^{3} - 28 \, x^{2}\right )} e^{\left (\frac {4 \, x^{3} + 25 \, x^{2} - 137 \, x}{x^{2} + 5 \, x - 28}\right )} - 137 \, x}{x^{2} + 5 \, x - 28} - \frac {4 \, x^{3} + 25 \, x^{2} - 137 \, x}{x^{2} + 5 \, x - 28}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x^6+42*x^5-54*x^4-1462*x^3+3276*x^2+1568*x)*exp((4*x^3+25*x^2-137*x)/(x^2+5*x-28))*exp(x^2*exp((4
*x^3+25*x^2-137*x)/(x^2+5*x-28)))/(x^4+10*x^3-31*x^2-280*x+784),x, algorithm="fricas")

[Out]

e^((4*x^3 + 25*x^2 + (x^4 + 5*x^3 - 28*x^2)*e^((4*x^3 + 25*x^2 - 137*x)/(x^2 + 5*x - 28)) - 137*x)/(x^2 + 5*x
- 28) - (4*x^3 + 25*x^2 - 137*x)/(x^2 + 5*x - 28))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 \, {\left (2 \, x^{6} + 21 \, x^{5} - 27 \, x^{4} - 731 \, x^{3} + 1638 \, x^{2} + 784 \, x\right )} e^{\left (x^{2} e^{\left (\frac {4 \, x^{3} + 25 \, x^{2} - 137 \, x}{x^{2} + 5 \, x - 28}\right )} + \frac {4 \, x^{3} + 25 \, x^{2} - 137 \, x}{x^{2} + 5 \, x - 28}\right )}}{x^{4} + 10 \, x^{3} - 31 \, x^{2} - 280 \, x + 784}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x^6+42*x^5-54*x^4-1462*x^3+3276*x^2+1568*x)*exp((4*x^3+25*x^2-137*x)/(x^2+5*x-28))*exp(x^2*exp((4
*x^3+25*x^2-137*x)/(x^2+5*x-28)))/(x^4+10*x^3-31*x^2-280*x+784),x, algorithm="giac")

[Out]

integrate(2*(2*x^6 + 21*x^5 - 27*x^4 - 731*x^3 + 1638*x^2 + 784*x)*e^(x^2*e^((4*x^3 + 25*x^2 - 137*x)/(x^2 + 5
*x - 28)) + (4*x^3 + 25*x^2 - 137*x)/(x^2 + 5*x - 28))/(x^4 + 10*x^3 - 31*x^2 - 280*x + 784), x)

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maple [A]  time = 0.13, size = 29, normalized size = 0.81

method	result	size
risch	\({\mathrm e}^{x^{2} {\mathrm e}^{\frac {x \left (4 x^{2}+25 x -137\right )}{x^{2}+5 x -28}}}\)	\(29\)
norman	\(\frac {x^{2} {\mathrm e}^{x^{2} {\mathrm e}^{\frac {4 x^{3}+25 x^{2}-137 x}{x^{2}+5 x -28}}}+5 x \,{\mathrm e}^{x^{2} {\mathrm e}^{\frac {4 x^{3}+25 x^{2}-137 x}{x^{2}+5 x -28}}}-28 \,{\mathrm e}^{x^{2} {\mathrm e}^{\frac {4 x^{3}+25 x^{2}-137 x}{x^{2}+5 x -28}}}}{x^{2}+5 x -28}\)	\(115\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4*x^6+42*x^5-54*x^4-1462*x^3+3276*x^2+1568*x)*exp((4*x^3+25*x^2-137*x)/(x^2+5*x-28))*exp(x^2*exp((4*x^3+2
5*x^2-137*x)/(x^2+5*x-28)))/(x^4+10*x^3-31*x^2-280*x+784),x,method=_RETURNVERBOSE)

[Out]

exp(x^2*exp(x*(4*x^2+25*x-137)/(x^2+5*x-28)))

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maxima [A]  time = 0.88, size = 36, normalized size = 1.00 \begin {gather*} e^{\left (x^{2} e^{\left (4 \, x - \frac {50 \, x}{x^{2} + 5 \, x - 28} + \frac {140}{x^{2} + 5 \, x - 28} + 5\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x^6+42*x^5-54*x^4-1462*x^3+3276*x^2+1568*x)*exp((4*x^3+25*x^2-137*x)/(x^2+5*x-28))*exp(x^2*exp((4
*x^3+25*x^2-137*x)/(x^2+5*x-28)))/(x^4+10*x^3-31*x^2-280*x+784),x, algorithm="maxima")

[Out]

e^(x^2*e^(4*x - 50*x/(x^2 + 5*x - 28) + 140/(x^2 + 5*x - 28) + 5))

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mupad [B]  time = 0.37, size = 31, normalized size = 0.86 \begin {gather*} {\mathrm {e}}^{x^2\,{\mathrm {e}}^{\frac {4\,x^3+25\,x^2-137\,x}{x^2+5\,x-28}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(x^2*exp((25*x^2 - 137*x + 4*x^3)/(5*x + x^2 - 28)))*exp((25*x^2 - 137*x + 4*x^3)/(5*x + x^2 - 28))*(1
568*x + 3276*x^2 - 1462*x^3 - 54*x^4 + 42*x^5 + 4*x^6))/(10*x^3 - 31*x^2 - 280*x + x^4 + 784),x)

[Out]

exp(x^2*exp((25*x^2 - 137*x + 4*x^3)/(5*x + x^2 - 28)))

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sympy [A]  time = 1.04, size = 27, normalized size = 0.75 \begin {gather*} e^{x^{2} e^{\frac {4 x^{3} + 25 x^{2} - 137 x}{x^{2} + 5 x - 28}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x**6+42*x**5-54*x**4-1462*x**3+3276*x**2+1568*x)*exp((4*x**3+25*x**2-137*x)/(x**2+5*x-28))*exp(x*
*2*exp((4*x**3+25*x**2-137*x)/(x**2+5*x-28)))/(x**4+10*x**3-31*x**2-280*x+784),x)

[Out]

exp(x**2*exp((4*x**3 + 25*x**2 - 137*x)/(x**2 + 5*x - 28)))

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