3.42.45 \(\int \frac {e^{\frac {1}{10} (-x+10 x^2)} (e^{2 x+\frac {1}{10} (x-10 x^2)} (-10+10 x+20 x^3+10 x^4+10 x^5)+e^{2 e^{\frac {1}{10} (-x+10 x^2)} x} (10 x^3-x^4+20 x^5)+e^{x+e^{\frac {1}{10} (-x+10 x^2)} x} (-10 x^2+x^3-30 x^4+x^5-20 x^6+e^{\frac {1}{10} (x-10 x^2)} (10 x-10 x^2-10 x^3-10 x^4)))}{5 x^3} \, dx\)

Optimal. Leaf size=32 \[ \left (e^{e^{-\frac {x}{10}+x^2} x}-\frac {e^x}{x}-e^x x\right )^2 \]

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Rubi [F]  time = 17.27, 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^{\frac {1}{10} \left (-x+10 x^2\right )} \left (e^{2 x+\frac {1}{10} \left (x-10 x^2\right )} \left (-10+10 x+20 x^3+10 x^4+10 x^5\right )+e^{2 e^{\frac {1}{10} \left (-x+10 x^2\right )} x} \left (10 x^3-x^4+20 x^5\right )+e^{x+e^{\frac {1}{10} \left (-x+10 x^2\right )} x} \left (-10 x^2+x^3-30 x^4+x^5-20 x^6+e^{\frac {1}{10} \left (x-10 x^2\right )} \left (10 x-10 x^2-10 x^3-10 x^4\right )\right )\right )}{5 x^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^((-x + 10*x^2)/10)*(E^(2*x + (x - 10*x^2)/10)*(-10 + 10*x + 20*x^3 + 10*x^4 + 10*x^5) + E^(2*E^((-x + 1
0*x^2)/10)*x)*(10*x^3 - x^4 + 20*x^5) + E^(x + E^((-x + 10*x^2)/10)*x)*(-10*x^2 + x^3 - 30*x^4 + x^5 - 20*x^6
+ E^((x - 10*x^2)/10)*(10*x - 10*x^2 - 10*x^3 - 10*x^4))))/(5*x^3),x]

[Out]

2*E^(2*x) + E^(2*x)/x^2 + E^(2*x)*x^2 - 2*Defer[Int][E^(x + E^(-1/10*x + x^2)*x), x] + Defer[Int][E^((9*x)/10
+ E^(-1/10*x + x^2)*x + x^2), x]/5 + 2*Defer[Int][E^(-1/10*x + 2*E^(-1/10*x + x^2)*x + x^2), x] + 2*Defer[Int]
[E^(x + E^(-1/10*x + x^2)*x)/x^2, x] - 2*Defer[Int][E^(x + E^(-1/10*x + x^2)*x)/x, x] - 2*Defer[Int][E^((9*x)/
10 + E^(-1/10*x + x^2)*x + x^2)/x, x] - 2*Defer[Int][E^(x + E^(-1/10*x + x^2)*x)*x, x] - 6*Defer[Int][E^((9*x)
/10 + E^(-1/10*x + x^2)*x + x^2)*x, x] - Defer[Int][E^(-1/10*x + 2*E^(-1/10*x + x^2)*x + x^2)*x, x]/5 + Defer[
Int][E^((9*x)/10 + E^(-1/10*x + x^2)*x + x^2)*x^2, x]/5 + 4*Defer[Int][E^(-1/10*x + 2*E^(-1/10*x + x^2)*x + x^
2)*x^2, x] - 4*Defer[Int][E^((9*x)/10 + E^(-1/10*x + x^2)*x + x^2)*x^3, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {e^{\frac {1}{10} \left (-x+10 x^2\right )} \left (e^{2 x+\frac {1}{10} \left (x-10 x^2\right )} \left (-10+10 x+20 x^3+10 x^4+10 x^5\right )+e^{2 e^{\frac {1}{10} \left (-x+10 x^2\right )} x} \left (10 x^3-x^4+20 x^5\right )+e^{x+e^{\frac {1}{10} \left (-x+10 x^2\right )} x} \left (-10 x^2+x^3-30 x^4+x^5-20 x^6+e^{\frac {1}{10} \left (x-10 x^2\right )} \left (10 x-10 x^2-10 x^3-10 x^4\right )\right )\right )}{x^3} \, dx\\ &=\frac {1}{5} \int \frac {e^{-x^2+\frac {1}{10} x (-1+10 x)} \left (e^x-e^{e^{-\frac {x}{10}+x^2} x} x+e^x x^2\right ) \left (-10 e^{11 x/10}+10 e^{11 x/10} x+10 e^{11 x/10} x^2-10 e^{x \left (e^{-\frac {x}{10}+x^2}+x\right )} x^2+10 e^{11 x/10} x^3+e^{x \left (e^{-\frac {x}{10}+x^2}+x\right )} x^3-20 e^{x \left (e^{-\frac {x}{10}+x^2}+x\right )} x^4\right )}{x^3} \, dx\\ &=\frac {1}{5} \int \frac {e^{-x/10} \left (e^{e^{-\frac {x}{10}+x^2} x} x-e^x \left (1+x^2\right )\right ) \left (e^{x \left (e^{-\frac {x}{10}+x^2}+x\right )} x^2 \left (10-x+20 x^2\right )-10 e^{11 x/10} \left (-1+x+x^2+x^3\right )\right )}{x^3} \, dx\\ &=\frac {1}{5} \int \left (\frac {e^{-\frac {x}{10}+e^{-\frac {x}{10}+x^2} x+x^2} \left (10-x+20 x^2\right ) \left (-e^x+e^{e^{-\frac {x}{10}+x^2} x} x-e^x x^2\right )}{x}+\frac {10 e^x \left (e^x-e^{e^{-\frac {x}{10}+x^2} x} x+e^x x^2\right ) \left (-1+x+x^2+x^3\right )}{x^3}\right ) \, dx\\ &=\frac {1}{5} \int \frac {e^{-\frac {x}{10}+e^{-\frac {x}{10}+x^2} x+x^2} \left (10-x+20 x^2\right ) \left (-e^x+e^{e^{-\frac {x}{10}+x^2} x} x-e^x x^2\right )}{x} \, dx+2 \int \frac {e^x \left (e^x-e^{e^{-\frac {x}{10}+x^2} x} x+e^x x^2\right ) \left (-1+x+x^2+x^3\right )}{x^3} \, dx\\ &=\frac {1}{5} \int \left (e^{-\frac {x}{10}+2 e^{-\frac {x}{10}+x^2} x+x^2} \left (10-x+20 x^2\right )-\frac {e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2} \left (10-x+30 x^2-x^3+20 x^4\right )}{x}\right ) \, dx+2 \int \left (-\frac {e^{x+e^{-\frac {x}{10}+x^2} x} \left (-1+x+x^2+x^3\right )}{x^2}+\frac {e^{2 x} \left (1+x^2\right ) \left (-1+x+x^2+x^3\right )}{x^3}\right ) \, dx\\ &=\frac {1}{5} \int e^{-\frac {x}{10}+2 e^{-\frac {x}{10}+x^2} x+x^2} \left (10-x+20 x^2\right ) \, dx-\frac {1}{5} \int \frac {e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2} \left (10-x+30 x^2-x^3+20 x^4\right )}{x} \, dx-2 \int \frac {e^{x+e^{-\frac {x}{10}+x^2} x} \left (-1+x+x^2+x^3\right )}{x^2} \, dx+2 \int \frac {e^{2 x} \left (1+x^2\right ) \left (-1+x+x^2+x^3\right )}{x^3} \, dx\\ &=\frac {1}{5} \int \left (10 e^{-\frac {x}{10}+2 e^{-\frac {x}{10}+x^2} x+x^2}-e^{-\frac {x}{10}+2 e^{-\frac {x}{10}+x^2} x+x^2} x+20 e^{-\frac {x}{10}+2 e^{-\frac {x}{10}+x^2} x+x^2} x^2\right ) \, dx-\frac {1}{5} \int \left (-e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2}+\frac {10 e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2}}{x}+30 e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2} x-e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2} x^2+20 e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2} x^3\right ) \, dx-2 \int \left (e^{x+e^{-\frac {x}{10}+x^2} x}-\frac {e^{x+e^{-\frac {x}{10}+x^2} x}}{x^2}+\frac {e^{x+e^{-\frac {x}{10}+x^2} x}}{x}+e^{x+e^{-\frac {x}{10}+x^2} x} x\right ) \, dx+2 \int \left (2 e^{2 x}-\frac {e^{2 x}}{x^3}+\frac {e^{2 x}}{x^2}+e^{2 x} x+e^{2 x} x^2\right ) \, dx\\ &=\frac {1}{5} \int e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2} \, dx-\frac {1}{5} \int e^{-\frac {x}{10}+2 e^{-\frac {x}{10}+x^2} x+x^2} x \, dx+\frac {1}{5} \int e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2} x^2 \, dx-2 \int e^{x+e^{-\frac {x}{10}+x^2} x} \, dx+2 \int e^{-\frac {x}{10}+2 e^{-\frac {x}{10}+x^2} x+x^2} \, dx-2 \int \frac {e^{2 x}}{x^3} \, dx+2 \int \frac {e^{2 x}}{x^2} \, dx+2 \int \frac {e^{x+e^{-\frac {x}{10}+x^2} x}}{x^2} \, dx-2 \int \frac {e^{x+e^{-\frac {x}{10}+x^2} x}}{x} \, dx-2 \int \frac {e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2}}{x} \, dx+2 \int e^{2 x} x \, dx-2 \int e^{x+e^{-\frac {x}{10}+x^2} x} x \, dx+2 \int e^{2 x} x^2 \, dx+4 \int e^{2 x} \, dx+4 \int e^{-\frac {x}{10}+2 e^{-\frac {x}{10}+x^2} x+x^2} x^2 \, dx-4 \int e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2} x^3 \, dx-6 \int e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2} x \, dx\\ &=2 e^{2 x}+\frac {e^{2 x}}{x^2}-\frac {2 e^{2 x}}{x}+e^{2 x} x+e^{2 x} x^2+\frac {1}{5} \int e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2} \, dx-\frac {1}{5} \int e^{-\frac {x}{10}+2 e^{-\frac {x}{10}+x^2} x+x^2} x \, dx+\frac {1}{5} \int e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2} x^2 \, dx-2 \int e^{x+e^{-\frac {x}{10}+x^2} x} \, dx+2 \int e^{-\frac {x}{10}+2 e^{-\frac {x}{10}+x^2} x+x^2} \, dx-2 \int \frac {e^{2 x}}{x^2} \, dx+2 \int \frac {e^{x+e^{-\frac {x}{10}+x^2} x}}{x^2} \, dx-2 \int \frac {e^{x+e^{-\frac {x}{10}+x^2} x}}{x} \, dx-2 \int \frac {e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2}}{x} \, dx-2 \int e^{2 x} x \, dx-2 \int e^{x+e^{-\frac {x}{10}+x^2} x} x \, dx+4 \int \frac {e^{2 x}}{x} \, dx+4 \int e^{-\frac {x}{10}+2 e^{-\frac {x}{10}+x^2} x+x^2} x^2 \, dx-4 \int e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2} x^3 \, dx-6 \int e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2} x \, dx-\int e^{2 x} \, dx\\ &=\frac {3 e^{2 x}}{2}+\frac {e^{2 x}}{x^2}+e^{2 x} x^2+4 \text {Ei}(2 x)+\frac {1}{5} \int e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2} \, dx-\frac {1}{5} \int e^{-\frac {x}{10}+2 e^{-\frac {x}{10}+x^2} x+x^2} x \, dx+\frac {1}{5} \int e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2} x^2 \, dx-2 \int e^{x+e^{-\frac {x}{10}+x^2} x} \, dx+2 \int e^{-\frac {x}{10}+2 e^{-\frac {x}{10}+x^2} x+x^2} \, dx+2 \int \frac {e^{x+e^{-\frac {x}{10}+x^2} x}}{x^2} \, dx-2 \int \frac {e^{x+e^{-\frac {x}{10}+x^2} x}}{x} \, dx-2 \int \frac {e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2}}{x} \, dx-2 \int e^{x+e^{-\frac {x}{10}+x^2} x} x \, dx-4 \int \frac {e^{2 x}}{x} \, dx+4 \int e^{-\frac {x}{10}+2 e^{-\frac {x}{10}+x^2} x+x^2} x^2 \, dx-4 \int e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2} x^3 \, dx-6 \int e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2} x \, dx+\int e^{2 x} \, dx\\ &=2 e^{2 x}+\frac {e^{2 x}}{x^2}+e^{2 x} x^2+\frac {1}{5} \int e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2} \, dx-\frac {1}{5} \int e^{-\frac {x}{10}+2 e^{-\frac {x}{10}+x^2} x+x^2} x \, dx+\frac {1}{5} \int e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2} x^2 \, dx-2 \int e^{x+e^{-\frac {x}{10}+x^2} x} \, dx+2 \int e^{-\frac {x}{10}+2 e^{-\frac {x}{10}+x^2} x+x^2} \, dx+2 \int \frac {e^{x+e^{-\frac {x}{10}+x^2} x}}{x^2} \, dx-2 \int \frac {e^{x+e^{-\frac {x}{10}+x^2} x}}{x} \, dx-2 \int \frac {e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2}}{x} \, dx-2 \int e^{x+e^{-\frac {x}{10}+x^2} x} x \, dx+4 \int e^{-\frac {x}{10}+2 e^{-\frac {x}{10}+x^2} x+x^2} x^2 \, dx-4 \int e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2} x^3 \, dx-6 \int e^{\frac {9 x}{10}+e^{-\frac {x}{10}+x^2} x+x^2} x \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 1.80, size = 34, normalized size = 1.06 \begin {gather*} \frac {\left (e^{e^{-\frac {x}{10}+x^2} x} x-e^x \left (1+x^2\right )\right )^2}{x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((-x + 10*x^2)/10)*(E^(2*x + (x - 10*x^2)/10)*(-10 + 10*x + 20*x^3 + 10*x^4 + 10*x^5) + E^(2*E^((
-x + 10*x^2)/10)*x)*(10*x^3 - x^4 + 20*x^5) + E^(x + E^((-x + 10*x^2)/10)*x)*(-10*x^2 + x^3 - 30*x^4 + x^5 - 2
0*x^6 + E^((x - 10*x^2)/10)*(10*x - 10*x^2 - 10*x^3 - 10*x^4))))/(5*x^3),x]

[Out]

(E^(E^(-1/10*x + x^2)*x)*x - E^x*(1 + x^2))^2/x^2

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fricas [B]  time = 0.54, size = 66, normalized size = 2.06 \begin {gather*} \frac {{\left (x^{2} e^{\left (2 \, x e^{\left (x^{2} - \frac {1}{10} \, x\right )} + 2 \, x\right )} - 2 \, {\left (x^{3} + x\right )} e^{\left (x e^{\left (x^{2} - \frac {1}{10} \, x\right )} + 3 \, x\right )} + {\left (x^{4} + 2 \, x^{2} + 1\right )} e^{\left (4 \, x\right )}\right )} e^{\left (-2 \, x\right )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*((20*x^5-x^4+10*x^3)*exp(x/exp(-x^2+1/10*x))^2+((-10*x^4-10*x^3-10*x^2+10*x)*exp(-x^2+1/10*x)-20
*x^6+x^5-30*x^4+x^3-10*x^2)*exp(x)*exp(x/exp(-x^2+1/10*x))+(10*x^5+10*x^4+20*x^3+10*x-10)*exp(-x^2+1/10*x)*exp
(x)^2)/x^3/exp(-x^2+1/10*x),x, algorithm="fricas")

[Out]

(x^2*e^(2*x*e^(x^2 - 1/10*x) + 2*x) - 2*(x^3 + x)*e^(x*e^(x^2 - 1/10*x) + 3*x) + (x^4 + 2*x^2 + 1)*e^(4*x))*e^
(-2*x)/x^2

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (10 \, {\left (x^{5} + x^{4} + 2 \, x^{3} + x - 1\right )} e^{\left (-x^{2} + \frac {21}{10} \, x\right )} + {\left (20 \, x^{5} - x^{4} + 10 \, x^{3}\right )} e^{\left (2 \, x e^{\left (x^{2} - \frac {1}{10} \, x\right )}\right )} - {\left (20 \, x^{6} - x^{5} + 30 \, x^{4} - x^{3} + 10 \, x^{2} + 10 \, {\left (x^{4} + x^{3} + x^{2} - x\right )} e^{\left (-x^{2} + \frac {1}{10} \, x\right )}\right )} e^{\left (x e^{\left (x^{2} - \frac {1}{10} \, x\right )} + x\right )}\right )} e^{\left (x^{2} - \frac {1}{10} \, x\right )}}{5 \, x^{3}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*((20*x^5-x^4+10*x^3)*exp(x/exp(-x^2+1/10*x))^2+((-10*x^4-10*x^3-10*x^2+10*x)*exp(-x^2+1/10*x)-20
*x^6+x^5-30*x^4+x^3-10*x^2)*exp(x)*exp(x/exp(-x^2+1/10*x))+(10*x^5+10*x^4+20*x^3+10*x-10)*exp(-x^2+1/10*x)*exp
(x)^2)/x^3/exp(-x^2+1/10*x),x, algorithm="giac")

[Out]

integrate(1/5*(10*(x^5 + x^4 + 2*x^3 + x - 1)*e^(-x^2 + 21/10*x) + (20*x^5 - x^4 + 10*x^3)*e^(2*x*e^(x^2 - 1/1
0*x)) - (20*x^6 - x^5 + 30*x^4 - x^3 + 10*x^2 + 10*(x^4 + x^3 + x^2 - x)*e^(-x^2 + 1/10*x))*e^(x*e^(x^2 - 1/10
*x) + x))*e^(x^2 - 1/10*x)/x^3, x)

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maple [A]  time = 0.07, size = 57, normalized size = 1.78

method	result	size
risch	\(\frac {\left (x^{4}+2 x^{2}+1\right ) {\mathrm e}^{2 x}}{x^{2}}+{\mathrm e}^{2 x \,{\mathrm e}^{\frac {x \left (10 x -1\right )}{10}}}-\frac {2 \left (x^{2}+1\right ) {\mathrm e}^{x \left ({\mathrm e}^{\frac {x \left (10 x -1\right )}{10}}+1\right )}}{x}\)	\(57\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/5*((20*x^5-x^4+10*x^3)*exp(x/exp(-x^2+1/10*x))^2+((-10*x^4-10*x^3-10*x^2+10*x)*exp(-x^2+1/10*x)-20*x^6+x
^5-30*x^4+x^3-10*x^2)*exp(x)*exp(x/exp(-x^2+1/10*x))+(10*x^5+10*x^4+20*x^3+10*x-10)*exp(-x^2+1/10*x)*exp(x)^2)
/x^3/exp(-x^2+1/10*x),x,method=_RETURNVERBOSE)

[Out]

(x^4+2*x^2+1)/x^2*exp(2*x)+exp(2*x*exp(1/10*x*(10*x-1)))-2*(x^2+1)/x*exp(x*(exp(1/10*x*(10*x-1))+1))

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {1}{2} \, {\left (2 \, x^{2} - 2 \, x + 1\right )} e^{\left (2 \, x\right )} + \frac {1}{2} \, {\left (2 \, x - 1\right )} e^{\left (2 \, x\right )} + e^{\left (2 \, x e^{\left (x^{2} - \frac {1}{10} \, x\right )}\right )} + 2 \, e^{\left (2 \, x\right )} + 4 \, \Gamma \left (-1, -2 \, x\right ) + 8 \, \Gamma \left (-2, -2 \, x\right ) - \frac {1}{5} \, \int \frac {{\left ({\left (20 \, x^{5} - x^{4} + 30 \, x^{3} - x^{2} + 10 \, x\right )} e^{\left (x^{2} + \frac {9}{10} \, x\right )} + 10 \, {\left (x^{3} + x^{2} + x - 1\right )} e^{x}\right )} e^{\left (x e^{\left (x^{2} - \frac {1}{10} \, x\right )}\right )}}{x^{2}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*((20*x^5-x^4+10*x^3)*exp(x/exp(-x^2+1/10*x))^2+((-10*x^4-10*x^3-10*x^2+10*x)*exp(-x^2+1/10*x)-20
*x^6+x^5-30*x^4+x^3-10*x^2)*exp(x)*exp(x/exp(-x^2+1/10*x))+(10*x^5+10*x^4+20*x^3+10*x-10)*exp(-x^2+1/10*x)*exp
(x)^2)/x^3/exp(-x^2+1/10*x),x, algorithm="maxima")

[Out]

1/2*(2*x^2 - 2*x + 1)*e^(2*x) + 1/2*(2*x - 1)*e^(2*x) + e^(2*x*e^(x^2 - 1/10*x)) + 2*e^(2*x) + 4*gamma(-1, -2*
x) + 8*gamma(-2, -2*x) - 1/5*integrate(((20*x^5 - x^4 + 30*x^3 - x^2 + 10*x)*e^(x^2 + 9/10*x) + 10*(x^3 + x^2
+ x - 1)*e^x)*e^(x*e^(x^2 - 1/10*x))/x^2, x)

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mupad [B]  time = 0.48, size = 29, normalized size = 0.91 \begin {gather*} \frac {{\left ({\mathrm {e}}^x+x^2\,{\mathrm {e}}^x-x\,{\mathrm {e}}^{x\,{\mathrm {e}}^{-\frac {x}{10}}\,{\mathrm {e}}^{x^2}}\right )}^2}{x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(x^2 - x/10)*((exp(2*x*exp(x^2 - x/10))*(10*x^3 - x^4 + 20*x^5))/5 + (exp(2*x)*exp(x/10 - x^2)*(10*x +
20*x^3 + 10*x^4 + 10*x^5 - 10))/5 - (exp(x*exp(x^2 - x/10))*exp(x)*(exp(x/10 - x^2)*(10*x^2 - 10*x + 10*x^3 +
10*x^4) + 10*x^2 - x^3 + 30*x^4 - x^5 + 20*x^6))/5))/x^3,x)

[Out]

(exp(x) + x^2*exp(x) - x*exp(x*exp(-x/10)*exp(x^2)))^2/x^2

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sympy [B]  time = 0.41, size = 61, normalized size = 1.91 \begin {gather*} \frac {x e^{2 x e^{x^{2} - \frac {x}{10}}} + \left (- 2 x^{2} e^{x} - 2 e^{x}\right ) e^{x e^{x^{2} - \frac {x}{10}}}}{x} + \frac {\left (x^{4} + 2 x^{2} + 1\right ) e^{2 x}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/5*((20*x**5-x**4+10*x**3)*exp(x/exp(-x**2+1/10*x))**2+((-10*x**4-10*x**3-10*x**2+10*x)*exp(-x**2+1
/10*x)-20*x**6+x**5-30*x**4+x**3-10*x**2)*exp(x)*exp(x/exp(-x**2+1/10*x))+(10*x**5+10*x**4+20*x**3+10*x-10)*ex
p(-x**2+1/10*x)*exp(x)**2)/x**3/exp(-x**2+1/10*x),x)

[Out]

(x*exp(2*x*exp(x**2 - x/10)) + (-2*x**2*exp(x) - 2*exp(x))*exp(x*exp(x**2 - x/10)))/x + (x**4 + 2*x**2 + 1)*ex
p(2*x)/x**2

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