3.39.60 \(\int \frac {e^{84+2 x} (4 x^4-2 x^5)+e^{42+x} (4 x^6-2 x^7)+e^{x^2} (2 x^7-4 x^9+e^{126+3 x} (2 x-4 x^3)+e^{84+2 x} (6 x^3-12 x^5)+e^{42+x} (6 x^5-12 x^7))}{-x^9+e^{3 x^2} (e^{126+3 x}+3 e^{84+2 x} x^2+3 e^{42+x} x^4+x^6)+e^{2 x^2} (-3 e^{84+2 x} x^3-6 e^{42+x} x^5-3 x^7)+e^{x^2} (3 e^{42+x} x^6+3 x^8)} \, dx\)

Optimal. Leaf size=29 \[ \frac {x^2}{\left (-e^{x^2}+\frac {x^3}{e^{42+x}+x^2}\right )^2} \]

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Rubi [F]  time = 7.30, 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 {e^{84+2 x} \left (4 x^4-2 x^5\right )+e^{42+x} \left (4 x^6-2 x^7\right )+e^{x^2} \left (2 x^7-4 x^9+e^{126+3 x} \left (2 x-4 x^3\right )+e^{84+2 x} \left (6 x^3-12 x^5\right )+e^{42+x} \left (6 x^5-12 x^7\right )\right )}{-x^9+e^{3 x^2} \left (e^{126+3 x}+3 e^{84+2 x} x^2+3 e^{42+x} x^4+x^6\right )+e^{2 x^2} \left (-3 e^{84+2 x} x^3-6 e^{42+x} x^5-3 x^7\right )+e^{x^2} \left (3 e^{42+x} x^6+3 x^8\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(84 + 2*x)*(4*x^4 - 2*x^5) + E^(42 + x)*(4*x^6 - 2*x^7) + E^x^2*(2*x^7 - 4*x^9 + E^(126 + 3*x)*(2*x - 4
*x^3) + E^(84 + 2*x)*(6*x^3 - 12*x^5) + E^(42 + x)*(6*x^5 - 12*x^7)))/(-x^9 + E^(3*x^2)*(E^(126 + 3*x) + 3*E^(
84 + 2*x)*x^2 + 3*E^(42 + x)*x^4 + x^6) + E^(2*x^2)*(-3*E^(84 + 2*x)*x^3 - 6*E^(42 + x)*x^5 - 3*x^7) + E^x^2*(
3*E^(42 + x)*x^6 + 3*x^8)),x]

[Out]

6*Defer[Int][(E^(84 + 2*x)*x^4)/(E^(42 + x + x^2) + E^x^2*x^2 - x^3)^3, x] - 2*Defer[Int][(E^(84 + 2*x)*x^5)/(
E^(42 + x + x^2) + E^x^2*x^2 - x^3)^3, x] + 8*Defer[Int][(E^(42 + x)*x^6)/(E^(42 + x + x^2) + E^x^2*x^2 - x^3)
^3, x] - 4*Defer[Int][(E^(84 + 2*x)*x^6)/(E^(42 + x + x^2) + E^x^2*x^2 - x^3)^3, x] - 2*Defer[Int][(E^(42 + x)
*x^7)/(E^(42 + x + x^2) + E^x^2*x^2 - x^3)^3, x] - 8*Defer[Int][(E^(42 + x)*x^8)/(E^(42 + x + x^2) + E^x^2*x^2
- x^3)^3, x] + 2*Defer[Int][(E^(84 + 2*x)*x)/(E^(42 + x + x^2) + E^x^2*x^2 - x^3)^2, x] + 4*Defer[Int][(E^(42
+ x)*x^3)/(E^(42 + x + x^2) + E^x^2*x^2 - x^3)^2, x] - 4*Defer[Int][(E^(84 + 2*x)*x^3)/(E^(42 + x + x^2) + E^
x^2*x^2 - x^3)^2, x] - 8*Defer[Int][(E^(42 + x)*x^5)/(E^(42 + x + x^2) + E^x^2*x^2 - x^3)^2, x] - 2*Defer[Int]
[x^8/(-E^(42 + x + x^2) - E^x^2*x^2 + x^3)^3, x] + 4*Defer[Int][x^10/(-E^(42 + x + x^2) - E^x^2*x^2 + x^3)^3,
x] + 2*Defer[Int][x^5/(-E^(42 + x + x^2) - E^x^2*x^2 + x^3)^2, x] - 4*Defer[Int][x^7/(-E^(42 + x + x^2) - E^x^
2*x^2 + x^3)^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 x \left (e^{42+x}+x^2\right ) \left (-e^{42+x} (-2+x) x^3-e^{84+2 x+x^2} \left (-1+2 x^2\right )-2 e^{42+x+x^2} x^2 \left (-1+2 x^2\right )-e^{x^2} x^4 \left (-1+2 x^2\right )\right )}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^3} \, dx\\ &=2 \int \frac {x \left (e^{42+x}+x^2\right ) \left (-e^{42+x} (-2+x) x^3-e^{84+2 x+x^2} \left (-1+2 x^2\right )-2 e^{42+x+x^2} x^2 \left (-1+2 x^2\right )-e^{x^2} x^4 \left (-1+2 x^2\right )\right )}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^3} \, dx\\ &=2 \int \left (-\frac {x \left (e^{42+x}+x^2\right )^2 \left (-1+2 x^2\right )}{\left (-e^{42+x+x^2}-e^{x^2} x^2+x^3\right )^2}+\frac {x^4 \left (-3 e^{84+2 x}+e^{84+2 x} x-4 e^{42+x} x^2+2 e^{84+2 x} x^2+e^{42+x} x^3-x^4+4 e^{42+x} x^4+2 x^6\right )}{\left (-e^{42+x+x^2}-e^{x^2} x^2+x^3\right )^3}\right ) \, dx\\ &=-\left (2 \int \frac {x \left (e^{42+x}+x^2\right )^2 \left (-1+2 x^2\right )}{\left (-e^{42+x+x^2}-e^{x^2} x^2+x^3\right )^2} \, dx\right )+2 \int \frac {x^4 \left (-3 e^{84+2 x}+e^{84+2 x} x-4 e^{42+x} x^2+2 e^{84+2 x} x^2+e^{42+x} x^3-x^4+4 e^{42+x} x^4+2 x^6\right )}{\left (-e^{42+x+x^2}-e^{x^2} x^2+x^3\right )^3} \, dx\\ &=2 \int \left (\frac {3 e^{84+2 x} x^4}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^3}-\frac {e^{84+2 x} x^5}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^3}+\frac {4 e^{42+x} x^6}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^3}-\frac {2 e^{84+2 x} x^6}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^3}-\frac {e^{42+x} x^7}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^3}-\frac {4 e^{42+x} x^8}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^3}-\frac {x^8}{\left (-e^{42+x+x^2}-e^{x^2} x^2+x^3\right )^3}+\frac {2 x^{10}}{\left (-e^{42+x+x^2}-e^{x^2} x^2+x^3\right )^3}\right ) \, dx-2 \int \left (-\frac {x \left (e^{42+x}+x^2\right )^2}{\left (-e^{42+x+x^2}-e^{x^2} x^2+x^3\right )^2}+\frac {2 x^3 \left (e^{42+x}+x^2\right )^2}{\left (-e^{42+x+x^2}-e^{x^2} x^2+x^3\right )^2}\right ) \, dx\\ &=-\left (2 \int \frac {e^{84+2 x} x^5}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^3} \, dx\right )-2 \int \frac {e^{42+x} x^7}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^3} \, dx-2 \int \frac {x^8}{\left (-e^{42+x+x^2}-e^{x^2} x^2+x^3\right )^3} \, dx+2 \int \frac {x \left (e^{42+x}+x^2\right )^2}{\left (-e^{42+x+x^2}-e^{x^2} x^2+x^3\right )^2} \, dx-4 \int \frac {e^{84+2 x} x^6}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^3} \, dx+4 \int \frac {x^{10}}{\left (-e^{42+x+x^2}-e^{x^2} x^2+x^3\right )^3} \, dx-4 \int \frac {x^3 \left (e^{42+x}+x^2\right )^2}{\left (-e^{42+x+x^2}-e^{x^2} x^2+x^3\right )^2} \, dx+6 \int \frac {e^{84+2 x} x^4}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^3} \, dx+8 \int \frac {e^{42+x} x^6}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^3} \, dx-8 \int \frac {e^{42+x} x^8}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^3} \, dx\\ &=-\left (2 \int \frac {e^{84+2 x} x^5}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^3} \, dx\right )-2 \int \frac {e^{42+x} x^7}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^3} \, dx-2 \int \frac {x^8}{\left (-e^{42+x+x^2}-e^{x^2} x^2+x^3\right )^3} \, dx+2 \int \left (\frac {e^{84+2 x} x}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^2}+\frac {2 e^{42+x} x^3}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^2}+\frac {x^5}{\left (-e^{42+x+x^2}-e^{x^2} x^2+x^3\right )^2}\right ) \, dx-4 \int \frac {e^{84+2 x} x^6}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^3} \, dx+4 \int \frac {x^{10}}{\left (-e^{42+x+x^2}-e^{x^2} x^2+x^3\right )^3} \, dx-4 \int \left (\frac {e^{84+2 x} x^3}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^2}+\frac {2 e^{42+x} x^5}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^2}+\frac {x^7}{\left (-e^{42+x+x^2}-e^{x^2} x^2+x^3\right )^2}\right ) \, dx+6 \int \frac {e^{84+2 x} x^4}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^3} \, dx+8 \int \frac {e^{42+x} x^6}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^3} \, dx-8 \int \frac {e^{42+x} x^8}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^3} \, dx\\ &=-\left (2 \int \frac {e^{84+2 x} x^5}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^3} \, dx\right )-2 \int \frac {e^{42+x} x^7}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^3} \, dx+2 \int \frac {e^{84+2 x} x}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^2} \, dx-2 \int \frac {x^8}{\left (-e^{42+x+x^2}-e^{x^2} x^2+x^3\right )^3} \, dx+2 \int \frac {x^5}{\left (-e^{42+x+x^2}-e^{x^2} x^2+x^3\right )^2} \, dx-4 \int \frac {e^{84+2 x} x^6}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^3} \, dx+4 \int \frac {e^{42+x} x^3}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^2} \, dx-4 \int \frac {e^{84+2 x} x^3}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^2} \, dx+4 \int \frac {x^{10}}{\left (-e^{42+x+x^2}-e^{x^2} x^2+x^3\right )^3} \, dx-4 \int \frac {x^7}{\left (-e^{42+x+x^2}-e^{x^2} x^2+x^3\right )^2} \, dx+6 \int \frac {e^{84+2 x} x^4}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^3} \, dx+8 \int \frac {e^{42+x} x^6}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^3} \, dx-8 \int \frac {e^{42+x} x^8}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^3} \, dx-8 \int \frac {e^{42+x} x^5}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.12, size = 40, normalized size = 1.38 \begin {gather*} \frac {x^2 \left (e^{42+x}+x^2\right )^2}{\left (e^{42+x+x^2}+e^{x^2} x^2-x^3\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(84 + 2*x)*(4*x^4 - 2*x^5) + E^(42 + x)*(4*x^6 - 2*x^7) + E^x^2*(2*x^7 - 4*x^9 + E^(126 + 3*x)*(2
*x - 4*x^3) + E^(84 + 2*x)*(6*x^3 - 12*x^5) + E^(42 + x)*(6*x^5 - 12*x^7)))/(-x^9 + E^(3*x^2)*(E^(126 + 3*x) +
3*E^(84 + 2*x)*x^2 + 3*E^(42 + x)*x^4 + x^6) + E^(2*x^2)*(-3*E^(84 + 2*x)*x^3 - 6*E^(42 + x)*x^5 - 3*x^7) + E
^x^2*(3*E^(42 + x)*x^6 + 3*x^8)),x]

[Out]

(x^2*(E^(42 + x) + x^2)^2)/(E^(42 + x + x^2) + E^x^2*x^2 - x^3)^2

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fricas [B]  time = 1.06, size = 74, normalized size = 2.55 \begin {gather*} \frac {x^{6} + 2 \, x^{4} e^{\left (x + 42\right )} + x^{2} e^{\left (2 \, x + 84\right )}}{x^{6} + {\left (x^{4} + 2 \, x^{2} e^{\left (x + 42\right )} + e^{\left (2 \, x + 84\right )}\right )} e^{\left (2 \, x^{2}\right )} - 2 \, {\left (x^{5} + x^{3} e^{\left (x + 42\right )}\right )} e^{\left (x^{2}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x^3+2*x)*exp(x+42)^3+(-12*x^5+6*x^3)*exp(x+42)^2+(-12*x^7+6*x^5)*exp(x+42)-4*x^9+2*x^7)*exp(x^
2)+(-2*x^5+4*x^4)*exp(x+42)^2+(-2*x^7+4*x^6)*exp(x+42))/((exp(x+42)^3+3*x^2*exp(x+42)^2+3*x^4*exp(x+42)+x^6)*e
xp(x^2)^3+(-3*x^3*exp(x+42)^2-6*x^5*exp(x+42)-3*x^7)*exp(x^2)^2+(3*x^6*exp(x+42)+3*x^8)*exp(x^2)-x^9),x, algor
ithm="fricas")

[Out]

(x^6 + 2*x^4*e^(x + 42) + x^2*e^(2*x + 84))/(x^6 + (x^4 + 2*x^2*e^(x + 42) + e^(2*x + 84))*e^(2*x^2) - 2*(x^5
+ x^3*e^(x + 42))*e^(x^2))

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giac [B]  time = 7.38, size = 114, normalized size = 3.93 \begin {gather*} \frac {x^{6} e^{\left (2 \, x^{2}\right )} + 2 \, x^{4} e^{\left (2 \, x^{2} + x + 42\right )} + x^{2} e^{\left (2 \, x^{2} + 2 \, x + 84\right )}}{x^{6} e^{\left (2 \, x^{2}\right )} - 2 \, x^{5} e^{\left (3 \, x^{2}\right )} + x^{4} e^{\left (4 \, x^{2}\right )} - 2 \, x^{3} e^{\left (3 \, x^{2} + x + 42\right )} + 2 \, x^{2} e^{\left (4 \, x^{2} + x + 42\right )} + e^{\left (4 \, x^{2} + 2 \, x + 84\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x^3+2*x)*exp(x+42)^3+(-12*x^5+6*x^3)*exp(x+42)^2+(-12*x^7+6*x^5)*exp(x+42)-4*x^9+2*x^7)*exp(x^
2)+(-2*x^5+4*x^4)*exp(x+42)^2+(-2*x^7+4*x^6)*exp(x+42))/((exp(x+42)^3+3*x^2*exp(x+42)^2+3*x^4*exp(x+42)+x^6)*e
xp(x^2)^3+(-3*x^3*exp(x+42)^2-6*x^5*exp(x+42)-3*x^7)*exp(x^2)^2+(3*x^6*exp(x+42)+3*x^8)*exp(x^2)-x^9),x, algor
ithm="giac")

[Out]

(x^6*e^(2*x^2) + 2*x^4*e^(2*x^2 + x + 42) + x^2*e^(2*x^2 + 2*x + 84))/(x^6*e^(2*x^2) - 2*x^5*e^(3*x^2) + x^4*e
^(4*x^2) - 2*x^3*e^(3*x^2 + x + 42) + 2*x^2*e^(4*x^2 + x + 42) + e^(4*x^2 + 2*x + 84))

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maple [B]  time = 0.07, size = 69, normalized size = 2.38

method	result	size
risch	\(x^{2} {\mathrm e}^{-2 x^{2}}-\frac {\left (x^{3}-2 x^{2} {\mathrm e}^{x^{2}}-2 \,{\mathrm e}^{x^{2}+x +42}\right ) x^{5} {\mathrm e}^{-2 x^{2}}}{\left (x^{3}-x^{2} {\mathrm e}^{x^{2}}-{\mathrm e}^{x^{2}+x +42}\right )^{2}}\)	\(69\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-4*x^3+2*x)*exp(x+42)^3+(-12*x^5+6*x^3)*exp(x+42)^2+(-12*x^7+6*x^5)*exp(x+42)-4*x^9+2*x^7)*exp(x^2)+(-2
*x^5+4*x^4)*exp(x+42)^2+(-2*x^7+4*x^6)*exp(x+42))/((exp(x+42)^3+3*x^2*exp(x+42)^2+3*x^4*exp(x+42)+x^6)*exp(x^2
)^3+(-3*x^3*exp(x+42)^2-6*x^5*exp(x+42)-3*x^7)*exp(x^2)^2+(3*x^6*exp(x+42)+3*x^8)*exp(x^2)-x^9),x,method=_RETU
RNVERBOSE)

[Out]

x^2*exp(-2*x^2)-(x^3-2*x^2*exp(x^2)-2*exp(x^2+x+42))*x^5/(x^3-x^2*exp(x^2)-exp(x^2+x+42))^2*exp(-2*x^2)

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maxima [B]  time = 2.10, size = 74, normalized size = 2.55 \begin {gather*} \frac {x^{6} + 2 \, x^{4} e^{\left (x + 42\right )} + x^{2} e^{\left (2 \, x + 84\right )}}{x^{6} + {\left (x^{4} + 2 \, x^{2} e^{\left (x + 42\right )} + e^{\left (2 \, x + 84\right )}\right )} e^{\left (2 \, x^{2}\right )} - 2 \, {\left (x^{5} + x^{3} e^{\left (x + 42\right )}\right )} e^{\left (x^{2}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x^3+2*x)*exp(x+42)^3+(-12*x^5+6*x^3)*exp(x+42)^2+(-12*x^7+6*x^5)*exp(x+42)-4*x^9+2*x^7)*exp(x^
2)+(-2*x^5+4*x^4)*exp(x+42)^2+(-2*x^7+4*x^6)*exp(x+42))/((exp(x+42)^3+3*x^2*exp(x+42)^2+3*x^4*exp(x+42)+x^6)*e
xp(x^2)^3+(-3*x^3*exp(x+42)^2-6*x^5*exp(x+42)-3*x^7)*exp(x^2)^2+(3*x^6*exp(x+42)+3*x^8)*exp(x^2)-x^9),x, algor
ithm="maxima")

[Out]

(x^6 + 2*x^4*e^(x + 42) + x^2*e^(2*x + 84))/(x^6 + (x^4 + 2*x^2*e^(x + 42) + e^(2*x + 84))*e^(2*x^2) - 2*(x^5
+ x^3*e^(x + 42))*e^(x^2))

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mupad [B]  time = 2.45, size = 175, normalized size = 6.03 \begin {gather*} \frac {{\mathrm {e}}^{x+42}\,\left (6\,x^{10}+x^9-5\,x^8\right )-7\,x^6\,{\mathrm {e}}^{2\,x+84}+2\,x^7\,{\mathrm {e}}^{2\,x+84}+6\,x^8\,{\mathrm {e}}^{2\,x+84}-3\,x^4\,{\mathrm {e}}^{3\,x+126}+x^5\,{\mathrm {e}}^{3\,x+126}+2\,x^6\,{\mathrm {e}}^{3\,x+126}-x^{10}+2\,x^{12}}{\left ({\mathrm {e}}^{2\,x^2}\,{\left ({\mathrm {e}}^{x+42}+x^2\right )}^2+x^6-2\,x^3\,{\mathrm {e}}^{x^2}\,\left ({\mathrm {e}}^{x+42}+x^2\right )\right )\,\left (x^3\,{\mathrm {e}}^{x+42}-3\,x^2\,{\mathrm {e}}^{x+42}+2\,x^4\,{\mathrm {e}}^{x+42}-x^4+2\,x^6\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(x^2)*(exp(3*x + 126)*(2*x - 4*x^3) + exp(x + 42)*(6*x^5 - 12*x^7) + exp(2*x + 84)*(6*x^3 - 12*x^5) +
2*x^7 - 4*x^9) + exp(x + 42)*(4*x^6 - 2*x^7) + exp(2*x + 84)*(4*x^4 - 2*x^5))/(exp(3*x^2)*(exp(3*x + 126) + 3*
x^4*exp(x + 42) + 3*x^2*exp(2*x + 84) + x^6) + exp(x^2)*(3*x^6*exp(x + 42) + 3*x^8) - x^9 - exp(2*x^2)*(6*x^5*
exp(x + 42) + 3*x^3*exp(2*x + 84) + 3*x^7)),x)

[Out]

(exp(x + 42)*(x^9 - 5*x^8 + 6*x^10) - 7*x^6*exp(2*x + 84) + 2*x^7*exp(2*x + 84) + 6*x^8*exp(2*x + 84) - 3*x^4*
exp(3*x + 126) + x^5*exp(3*x + 126) + 2*x^6*exp(3*x + 126) - x^10 + 2*x^12)/((exp(2*x^2)*(exp(x + 42) + x^2)^2
+ x^6 - 2*x^3*exp(x^2)*(exp(x + 42) + x^2))*(x^3*exp(x + 42) - 3*x^2*exp(x + 42) + 2*x^4*exp(x + 42) - x^4 +
2*x^6))

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sympy [B]  time = 0.50, size = 112, normalized size = 3.86 \begin {gather*} x^{2} e^{- 2 x^{2}} + \frac {- x^{8} + 2 x^{7} e^{x^{2}} + 2 x^{5} e^{x^{2}} e^{x + 42}}{x^{6} e^{2 x^{2}} - 2 x^{5} e^{3 x^{2}} + x^{4} e^{4 x^{2}} + \left (- 2 x^{3} e^{3 x^{2}} + 2 x^{2} e^{4 x^{2}}\right ) e^{x + 42} + e^{4 x^{2}} e^{2 x + 84}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x**3+2*x)*exp(x+42)**3+(-12*x**5+6*x**3)*exp(x+42)**2+(-12*x**7+6*x**5)*exp(x+42)-4*x**9+2*x**
7)*exp(x**2)+(-2*x**5+4*x**4)*exp(x+42)**2+(-2*x**7+4*x**6)*exp(x+42))/((exp(x+42)**3+3*x**2*exp(x+42)**2+3*x*
*4*exp(x+42)+x**6)*exp(x**2)**3+(-3*x**3*exp(x+42)**2-6*x**5*exp(x+42)-3*x**7)*exp(x**2)**2+(3*x**6*exp(x+42)+
3*x**8)*exp(x**2)-x**9),x)

[Out]

x**2*exp(-2*x**2) + (-x**8 + 2*x**7*exp(x**2) + 2*x**5*exp(x**2)*exp(x + 42))/(x**6*exp(2*x**2) - 2*x**5*exp(3
*x**2) + x**4*exp(4*x**2) + (-2*x**3*exp(3*x**2) + 2*x**2*exp(4*x**2))*exp(x + 42) + exp(4*x**2)*exp(2*x + 84)
)

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