3.69.49 $\int \frac{200+100x+e^{6x^2-2x^3}(8+4x)+e^{3x^2-x^3}(80+40x)+e^{\frac{2(39x+8e^{3x^2-x^3}x)}{20+4e^{3x^2-x^3}}}(100x+195x^2+e^{6x^2-2x^3}(4x+8x^2)+e^{3x^2-x^3}(40x+79x^2+6x^4-3x^5))+e^{\frac{39x+8e^{3x^2-x^3}x}{20+4e^{3x^2-x^3}}}(-200-590x-195x^2+e^{6x^2-2x^3}(-8-24x-8x^2)+e^{3x^2-x^3}(-80-238x-79x^2-12x^3+3x^5))}{50+2e^{6x^2-2x^3}+20e^{3x^2-x^3}}dx$

Optimal. Leaf size=34 $${(2+x-e^{2x-\frac{x}{4(5+e^{(3-x)x^2})}}x)}^2$$

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Rubi [F]  time = 157.70, 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 = {} $$\begin{array}{c}\int \frac{200+100x+e^{6x^2-2x^3}(8+4x)+e^{3x^2-x^3}(80+40x)+\exp \left(\frac{2(39x+8e^{3x^2-x^3}x)}{20+4e^{3x^2-x^3}}\right)(100x+195x^2+e^{6x^2-2x^3}(4x+8x^2)+e^{3x^2-x^3}(40x+79x^2+6x^4-3x^5))+\exp \left(\frac{39x+8e^{3x^2-x^3}x}{20+4e^{3x^2-x^3}}\right)(-200-590x-195x^2+e^{6x^2-2x^3}(-8-24x-8x^2)+e^{3x^2-x^3}(-80-238x-79x^2-12x^3+3x^5))}{50+2e^{6x^2-2x^3}+20e^{3x^2-x^3}}dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[(200 + 100*x + E^(6*x^2 - 2*x^3)*(8 + 4*x) + E^(3*x^2 - x^3)*(80 + 40*x) + E^((2*(39*x + 8*E^(3*x^2 - x^3)
*x))/(20 + 4*E^(3*x^2 - x^3)))*(100*x + 195*x^2 + E^(6*x^2 - 2*x^3)*(4*x + 8*x^2) + E^(3*x^2 - x^3)*(40*x + 79
*x^2 + 6*x^4 - 3*x^5)) + E^((39*x + 8*E^(3*x^2 - x^3)*x)/(20 + 4*E^(3*x^2 - x^3)))*(-200 - 590*x - 195*x^2 + E
^(6*x^2 - 2*x^3)*(-8 - 24*x - 8*x^2) + E^(3*x^2 - x^3)*(-80 - 238*x - 79*x^2 - 12*x^3 + 3*x^5)))/(50 + 2*E^(6*
x^2 - 2*x^3) + 20*E^(3*x^2 - x^3)),x]

[Out]

4*x + x^2 - 4*Defer[Int][E^(((8*E^(3*x^2) + 39*E^x^3)*x)/(4*(E^(3*x^2) + 5*E^x^3))), x] - 12*Defer[Int][E^(((8
*E^(3*x^2) + 39*E^x^3)*x)/(4*(E^(3*x^2) + 5*E^x^3)))*x, x] + 2*Defer[Int][E^(((8*E^(3*x^2) + 39*E^x^3)*x)/(2*(
E^(3*x^2) + 5*E^x^3)))*x, x] + Defer[Int][E^(2*x^3 - (x*(4*E^(3*x^2)*(-2 + 3*x + x^2) + E^x^3*(-39 + 60*x + 20
*x^2)))/(4*(E^(3*x^2) + 5*E^x^3)))*x, x] - 5*Defer[Int][(E^(2*x^3 - (x*(4*E^(3*x^2)*(-2 + 3*x) + E^x^3*(-39 +
60*x)))/(4*(E^(3*x^2) + 5*E^x^3)))*x)/(E^(3*x^2) + 5*E^x^3), x] - 4*Defer[Int][E^(((8*E^(3*x^2) + 39*E^x^3)*x)
/(4*(E^(3*x^2) + 5*E^x^3)))*x^2, x] + 4*Defer[Int][E^(((8*E^(3*x^2) + 39*E^x^3)*x)/(2*(E^(3*x^2) + 5*E^x^3)))*
x^2, x] - Defer[Int][E^((x*(2*E^(3*x^2)*(4 - 3*x + x^2) + E^x^3*(39 - 30*x + 10*x^2)))/(2*(E^(3*x^2) + 5*E^x^3
)))*x^2, x]/2 + Defer[Int][E^(2*x^3 - (x*(4*E^(3*x^2)*(-2 + 3*x + x^2) + E^x^3*(-39 + 60*x + 20*x^2)))/(4*(E^(
3*x^2) + 5*E^x^3)))*x^2, x]/2 + (5*Defer[Int][(E^((x*(E^(3*x^2)*(8 - 6*x + 4*x^2) + E^x^3*(39 - 30*x + 20*x^2)
))/(2*(E^(3*x^2) + 5*E^x^3)))*x^2)/(E^(3*x^2) + 5*E^x^3), x])/2 - (5*Defer[Int][(E^(2*x^3 - (x*(4*E^(3*x^2)*(-
2 + 3*x) + E^x^3*(-39 + 60*x)))/(4*(E^(3*x^2) + 5*E^x^3)))*x^2)/(E^(3*x^2) + 5*E^x^3), x])/2 - 6*Defer[Int][E^
(2*x^3 - (x*(4*E^(3*x^2)*(-2 + 3*x + x^2) + E^x^3*(-39 + 60*x + 20*x^2)))/(4*(E^(3*x^2) + 5*E^x^3)))*x^3, x] +
30*Defer[Int][(E^(((8*E^(3*x^2) + 39*E^x^3)*x)/(4*(E^(3*x^2) + 5*E^x^3)) + 2*x^3)*x^3)/(E^(3*x^2) + 5*E^x^3)^
2, x] + 30*Defer[Int][(E^(2*x^3 - (x*(4*E^(3*x^2)*(-2 + 3*x) + E^x^3*(-39 + 60*x)))/(4*(E^(3*x^2) + 5*E^x^3)))
*x^3)/(E^(3*x^2) + 5*E^x^3), x] + 3*Defer[Int][E^((x*(2*E^(3*x^2)*(4 - 3*x + x^2) + E^x^3*(39 - 30*x + 10*x^2)
))/(2*(E^(3*x^2) + 5*E^x^3)))*x^4, x] - 15*Defer[Int][(E^(((8*E^(3*x^2) + 39*E^x^3)*x)/(2*(E^(3*x^2) + 5*E^x^3
)) + 2*x^3)*x^4)/(E^(3*x^2) + 5*E^x^3)^2, x] - 15*Defer[Int][(E^((x*(E^(3*x^2)*(8 - 6*x + 4*x^2) + E^x^3*(39 -
30*x + 20*x^2)))/(2*(E^(3*x^2) + 5*E^x^3)))*x^4)/(E^(3*x^2) + 5*E^x^3), x] - (3*Defer[Int][E^((x*(2*E^(3*x^2)
*(4 - 3*x + x^2) + E^x^3*(39 - 30*x + 10*x^2)))/(2*(E^(3*x^2) + 5*E^x^3)))*x^5, x])/2 + (3*Defer[Int][E^(2*x^3
- (x*(4*E^(3*x^2)*(-2 + 3*x + x^2) + E^x^3*(-39 + 60*x + 20*x^2)))/(4*(E^(3*x^2) + 5*E^x^3)))*x^5, x])/2 - (1
5*Defer[Int][(E^(((8*E^(3*x^2) + 39*E^x^3)*x)/(4*(E^(3*x^2) + 5*E^x^3)) + 2*x^3)*x^5)/(E^(3*x^2) + 5*E^x^3)^2,
x])/2 + (15*Defer[Int][(E^(((8*E^(3*x^2) + 39*E^x^3)*x)/(2*(E^(3*x^2) + 5*E^x^3)) + 2*x^3)*x^5)/(E^(3*x^2) +
5*E^x^3)^2, x])/2 + (15*Defer[Int][(E^((x*(E^(3*x^2)*(8 - 6*x + 4*x^2) + E^x^3*(39 - 30*x + 20*x^2)))/(2*(E^(3
*x^2) + 5*E^x^3)))*x^5)/(E^(3*x^2) + 5*E^x^3), x])/2 - (15*Defer[Int][(E^(2*x^3 - (x*(4*E^(3*x^2)*(-2 + 3*x) +
E^x^3*(-39 + 60*x)))/(4*(E^(3*x^2) + 5*E^x^3)))*x^5)/(E^(3*x^2) + 5*E^x^3), x])/2

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{e^{2x^3}(200+100x+e^{6x^2-2x^3}(8+4x)+e^{3x^2-x^3}(80+40x)+\exp \left(\frac{2(39x+8e^{3x^2-x^3}x)}{20+4e^{3x^2-x^3}}\right)(100x+195x^2+e^{6x^2-2x^3}(4x+8x^2)+e^{3x^2-x^3}(40x+79x^2+6x^4-3x^5))+\exp \left(\frac{39x+8e^{3x^2-x^3}x}{20+4e^{3x^2-x^3}}\right)(-200-590x-195x^2+e^{6x^2-2x^3}(-8-24x-8x^2)+e^{3x^2-x^3}(-80-238x-79x^2-12x^3+3x^5)))}{2{(e^{3x^2}+5e^{x^3})}^2}dx\\ & =\frac{1}{2}\int \frac{e^{2x^3}(200+100x+e^{6x^2-2x^3}(8+4x)+e^{3x^2-x^3}(80+40x)+\exp \left(\frac{2(39x+8e^{3x^2-x^3}x)}{20+4e^{3x^2-x^3}}\right)(100x+195x^2+e^{6x^2-2x^3}(4x+8x^2)+e^{3x^2-x^3}(40x+79x^2+6x^4-3x^5))+\exp \left(\frac{39x+8e^{3x^2-x^3}x}{20+4e^{3x^2-x^3}}\right)(-200-590x-195x^2+e^{6x^2-2x^3}(-8-24x-8x^2)+e^{3x^2-x^3}(-80-238x-79x^2-12x^3+3x^5)))}{{(e^{3x^2}+5e^{x^3})}^2}dx\\ & =\frac{1}{2}\int (\frac{15\exp (\frac{(8e^{3x^2}+39e^{x^3})x}{4(e^{3x^2}+5e^{x^3})}+2x^3)(-2+x)x^3(-2-x+\exp \left(\frac{(8e^{3x^2}+39e^{x^3})x}{4(e^{3x^2}+5e^{x^3})}\right)x)}{{(e^{3x^2}+5e^{x^3})}^2}+4(-2-x+\exp \left(\frac{(8e^{3x^2}+39e^{x^3})x}{4(e^{3x^2}+5e^{x^3})}\right)x)(-1+\exp \left(\frac{(8e^{3x^2}+39e^{x^3})x}{4(e^{3x^2}+5e^{x^3})}\right)+2\exp \left(\frac{(8e^{3x^2}+39e^{x^3})x}{4(e^{3x^2}+5e^{x^3})}\right)x)-\exp (2x^3-\frac{x(4e^{3x^2}(-2+3x+x^2)+e^{x^3}(-39+60x+20x^2))}{4(e^{3x^2}+5e^{x^3})})x(-2-x+\exp \left(\frac{(8e^{3x^2}+39e^{x^3})x}{4(e^{3x^2}+5e^{x^3})}\right)x)(1-6x^2+3x^3)+\frac{5\exp (2x^3-\frac{x(4e^{3x^2}(-2+3x)+e^{x^3}(-39+60x))}{4(e^{3x^2}+5e^{x^3})})x(-2-x+\exp \left(\frac{(8e^{3x^2}+39e^{x^3})x}{4(e^{3x^2}+5e^{x^3})}\right)x)(1-6x^2+3x^3)}{e^{3x^2}+5e^{x^3}})dx\\ & =-(\frac{1}{2}\int \exp (2x^3-\frac{x(4e^{3x^2}(-2+3x+x^2)+e^{x^3}(-39+60x+20x^2))}{4(e^{3x^2}+5e^{x^3})})x(-2-x+\exp \left(\frac{(8e^{3x^2}+39e^{x^3})x}{4(e^{3x^2}+5e^{x^3})}\right)x)(1-6x^2+3x^3)dx)+2\int (-2-x+\exp \left(\frac{(8e^{3x^2}+39e^{x^3})x}{4(e^{3x^2}+5e^{x^3})}\right)x)(-1+\exp \left(\frac{(8e^{3x^2}+39e^{x^3})x}{4(e^{3x^2}+5e^{x^3})}\right)+2\exp \left(\frac{(8e^{3x^2}+39e^{x^3})x}{4(e^{3x^2}+5e^{x^3})}\right)x)dx+\frac{5}{2}\int \frac{\exp (2x^3-\frac{x(4e^{3x^2}(-2+3x)+e^{x^3}(-39+60x))}{4(e^{3x^2}+5e^{x^3})})x(-2-x+\exp \left(\frac{(8e^{3x^2}+39e^{x^3})x}{4(e^{3x^2}+5e^{x^3})}\right)x)(1-6x^2+3x^3)}{e^{3x^2}+5e^{x^3}}dx+\frac{15}{2}\int \frac{\exp (\frac{(8e^{3x^2}+39e^{x^3})x}{4(e^{3x^2}+5e^{x^3})}+2x^3)(-2+x)x^3(-2-x+\exp \left(\frac{(8e^{3x^2}+39e^{x^3})x}{4(e^{3x^2}+5e^{x^3})}\right)x)}{{(e^{3x^2}+5e^{x^3})}^2}dx\\ & =\text{Rest of rules removed due to large latex content}\end{array}\end{array}$$

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Mathematica [F]  time = 177.60, size = 0, normalized size = 0.00 $$\begin{array}{c}\int \frac{200+100x+e^{6x^2-2x^3}(8+4x)+e^{3x^2-x^3}(80+40x)+e^{\frac{2(39x+8e^{3x^2-x^3}x)}{20+4e^{3x^2-x^3}}}(100x+195x^2+e^{6x^2-2x^3}(4x+8x^2)+e^{3x^2-x^3}(40x+79x^2+6x^4-3x^5))+e^{\frac{39x+8e^{3x^2-x^3}x}{20+4e^{3x^2-x^3}}}(-200-590x-195x^2+e^{6x^2-2x^3}(-8-24x-8x^2)+e^{3x^2-x^3}(-80-238x-79x^2-12x^3+3x^5))}{50+2e^{6x^2-2x^3}+20e^{3x^2-x^3}}dx\end{array}$$

Verification is not applicable to the result.

[In]

Integrate[(200 + 100*x + E^(6*x^2 - 2*x^3)*(8 + 4*x) + E^(3*x^2 - x^3)*(80 + 40*x) + E^((2*(39*x + 8*E^(3*x^2
- x^3)*x))/(20 + 4*E^(3*x^2 - x^3)))*(100*x + 195*x^2 + E^(6*x^2 - 2*x^3)*(4*x + 8*x^2) + E^(3*x^2 - x^3)*(40*
x + 79*x^2 + 6*x^4 - 3*x^5)) + E^((39*x + 8*E^(3*x^2 - x^3)*x)/(20 + 4*E^(3*x^2 - x^3)))*(-200 - 590*x - 195*x
^2 + E^(6*x^2 - 2*x^3)*(-8 - 24*x - 8*x^2) + E^(3*x^2 - x^3)*(-80 - 238*x - 79*x^2 - 12*x^3 + 3*x^5)))/(50 + 2
*E^(6*x^2 - 2*x^3) + 20*E^(3*x^2 - x^3)),x]

[Out]

Integrate[(200 + 100*x + E^(6*x^2 - 2*x^3)*(8 + 4*x) + E^(3*x^2 - x^3)*(80 + 40*x) + E^((2*(39*x + 8*E^(3*x^2
- x^3)*x))/(20 + 4*E^(3*x^2 - x^3)))*(100*x + 195*x^2 + E^(6*x^2 - 2*x^3)*(4*x + 8*x^2) + E^(3*x^2 - x^3)*(40*
x + 79*x^2 + 6*x^4 - 3*x^5)) + E^((39*x + 8*E^(3*x^2 - x^3)*x)/(20 + 4*E^(3*x^2 - x^3)))*(-200 - 590*x - 195*x
^2 + E^(6*x^2 - 2*x^3)*(-8 - 24*x - 8*x^2) + E^(3*x^2 - x^3)*(-80 - 238*x - 79*x^2 - 12*x^3 + 3*x^5)))/(50 + 2
*E^(6*x^2 - 2*x^3) + 20*E^(3*x^2 - x^3)), x]

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fricas [B]  time = 0.56, size = 96, normalized size = 2.82 $$\begin{array}{c}{x}^2{e}^{\left(\frac{8x{e}^{(-x^3+3x^2)}+39x}{2(e^{(-x^3+3x^2)}+5)}\right)}+x^2-2(x^2+2x)e^{\left(\frac{8x{e}^{(-x^3+3x^2)}+39x}{4(e^{(-x^3+3x^2)}+5)}\right)}+4x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x^2+4*x)*exp(-x^3+3*x^2)^2+(-3*x^5+6*x^4+79*x^2+40*x)*exp(-x^3+3*x^2)+195*x^2+100*x)*exp((8*x*e
xp(-x^3+3*x^2)+39*x)/(4*exp(-x^3+3*x^2)+20))^2+((-8*x^2-24*x-8)*exp(-x^3+3*x^2)^2+(3*x^5-12*x^3-79*x^2-238*x-8
0)*exp(-x^3+3*x^2)-195*x^2-590*x-200)*exp((8*x*exp(-x^3+3*x^2)+39*x)/(4*exp(-x^3+3*x^2)+20))+(4*x+8)*exp(-x^3+
3*x^2)^2+(40*x+80)*exp(-x^3+3*x^2)+100*x+200)/(2*exp(-x^3+3*x^2)^2+20*exp(-x^3+3*x^2)+50),x, algorithm="fricas
")

[Out]

x^2*e^(1/2*(8*x*e^(-x^3 + 3*x^2) + 39*x)/(e^(-x^3 + 3*x^2) + 5)) + x^2 - 2*(x^2 + 2*x)*e^(1/4*(8*x*e^(-x^3 + 3
*x^2) + 39*x)/(e^(-x^3 + 3*x^2) + 5)) + 4*x

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giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 $$\begin{array}{c}\text{Timed out}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x^2+4*x)*exp(-x^3+3*x^2)^2+(-3*x^5+6*x^4+79*x^2+40*x)*exp(-x^3+3*x^2)+195*x^2+100*x)*exp((8*x*e
xp(-x^3+3*x^2)+39*x)/(4*exp(-x^3+3*x^2)+20))^2+((-8*x^2-24*x-8)*exp(-x^3+3*x^2)^2+(3*x^5-12*x^3-79*x^2-238*x-8
0)*exp(-x^3+3*x^2)-195*x^2-590*x-200)*exp((8*x*exp(-x^3+3*x^2)+39*x)/(4*exp(-x^3+3*x^2)+20))+(4*x+8)*exp(-x^3+
3*x^2)^2+(40*x+80)*exp(-x^3+3*x^2)+100*x+200)/(2*exp(-x^3+3*x^2)^2+20*exp(-x^3+3*x^2)+50),x, algorithm="giac")

[Out]

Timed out

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maple [B]  time = 0.10, size = 82, normalized size = 2.41

method	result	size
risch	$x^2{\mathrm{e}}^{\frac{(8{\mathrm{e}}^{-x^2(x-3)}+39)x}{2{\mathrm{e}}^{-x^2(x-3)}+10}}+x^2+4x+(-2x^2-4x){\mathrm{e}}^{\frac{(8{\mathrm{e}}^{-x^2(x-3)}+39)x}{4{\mathrm{e}}^{-x^2(x-3)}+20}}$	$82$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((8*x^2+4*x)*exp(-x^3+3*x^2)^2+(-3*x^5+6*x^4+79*x^2+40*x)*exp(-x^3+3*x^2)+195*x^2+100*x)*exp((8*x*exp(-x^
3+3*x^2)+39*x)/(4*exp(-x^3+3*x^2)+20))^2+((-8*x^2-24*x-8)*exp(-x^3+3*x^2)^2+(3*x^5-12*x^3-79*x^2-238*x-80)*exp
(-x^3+3*x^2)-195*x^2-590*x-200)*exp((8*x*exp(-x^3+3*x^2)+39*x)/(4*exp(-x^3+3*x^2)+20))+(4*x+8)*exp(-x^3+3*x^2)
^2+(40*x+80)*exp(-x^3+3*x^2)+100*x+200)/(2*exp(-x^3+3*x^2)^2+20*exp(-x^3+3*x^2)+50),x,method=_RETURNVERBOSE)

[Out]

x^2*exp(1/2*x*(8*exp(-x^2*(x-3))+39)/(exp(-x^2*(x-3))+5))+x^2+4*x+(-2*x^2-4*x)*exp(1/4*x*(8*exp(-x^2*(x-3))+39
)/(exp(-x^2*(x-3))+5))

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maxima [B]  time = 0.46, size = 116, normalized size = 3.41 $$\begin{array}{c}{x}^2{e}^{(\frac{39x{e}^{\left(x^3\right)}}{2(5e^{\left(x^3\right)}+e^{\left(3x^2\right)})}+\frac{4x{e}^{\left(3x^2\right)}}{5e^{\left(x^3\right)}+e^{\left(3x^2\right)}})}+x^2-2(x^2+2x)e^{(\frac{39x{e}^{\left(x^3\right)}}{4(5e^{\left(x^3\right)}+e^{\left(3x^2\right)})}+\frac{2x{e}^{\left(3x^2\right)}}{5e^{\left(x^3\right)}+e^{\left(3x^2\right)}})}+4x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x^2+4*x)*exp(-x^3+3*x^2)^2+(-3*x^5+6*x^4+79*x^2+40*x)*exp(-x^3+3*x^2)+195*x^2+100*x)*exp((8*x*e
xp(-x^3+3*x^2)+39*x)/(4*exp(-x^3+3*x^2)+20))^2+((-8*x^2-24*x-8)*exp(-x^3+3*x^2)^2+(3*x^5-12*x^3-79*x^2-238*x-8
0)*exp(-x^3+3*x^2)-195*x^2-590*x-200)*exp((8*x*exp(-x^3+3*x^2)+39*x)/(4*exp(-x^3+3*x^2)+20))+(4*x+8)*exp(-x^3+
3*x^2)^2+(40*x+80)*exp(-x^3+3*x^2)+100*x+200)/(2*exp(-x^3+3*x^2)^2+20*exp(-x^3+3*x^2)+50),x, algorithm="maxima
")

[Out]

x^2*e^(39/2*x*e^(x^3)/(5*e^(x^3) + e^(3*x^2)) + 4*x*e^(3*x^2)/(5*e^(x^3) + e^(3*x^2))) + x^2 - 2*(x^2 + 2*x)*e
^(39/4*x*e^(x^3)/(5*e^(x^3) + e^(3*x^2)) + 2*x*e^(3*x^2)/(5*e^(x^3) + e^(3*x^2))) + 4*x

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mupad [B]  time = 0.48, size = 134, normalized size = 3.94 $$\begin{array}{c}4x-{\mathrm{e}}^{\frac{39x}{4{\mathrm{e}}^{-x^3}{\mathrm{e}}^{3x^2}+20}+\frac{8x{\mathrm{e}}^{-x^3}{\mathrm{e}}^{3x^2}}{4{\mathrm{e}}^{-x^3}{\mathrm{e}}^{3x^2}+20}}(2x^2+4x)+x^2{\mathrm{e}}^{\frac{78x}{4{\mathrm{e}}^{-x^3}{\mathrm{e}}^{3x^2}+20}+\frac{16x{\mathrm{e}}^{-x^3}{\mathrm{e}}^{3x^2}}{4{\mathrm{e}}^{-x^3}{\mathrm{e}}^{3x^2}+20}}+x^2\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((100*x + exp((2*(39*x + 8*x*exp(3*x^2 - x^3)))/(4*exp(3*x^2 - x^3) + 20))*(100*x + exp(3*x^2 - x^3)*(40*x
+ 79*x^2 + 6*x^4 - 3*x^5) + 195*x^2 + exp(6*x^2 - 2*x^3)*(4*x + 8*x^2)) - exp((39*x + 8*x*exp(3*x^2 - x^3))/(4
*exp(3*x^2 - x^3) + 20))*(590*x + exp(3*x^2 - x^3)*(238*x + 79*x^2 + 12*x^3 - 3*x^5 + 80) + 195*x^2 + exp(6*x^
2 - 2*x^3)*(24*x + 8*x^2 + 8) + 200) + exp(6*x^2 - 2*x^3)*(4*x + 8) + exp(3*x^2 - x^3)*(40*x + 80) + 200)/(20*
exp(3*x^2 - x^3) + 2*exp(6*x^2 - 2*x^3) + 50),x)

[Out]

4*x - exp((39*x)/(4*exp(-x^3)*exp(3*x^2) + 20) + (8*x*exp(-x^3)*exp(3*x^2))/(4*exp(-x^3)*exp(3*x^2) + 20))*(4*
x + 2*x^2) + x^2*exp((78*x)/(4*exp(-x^3)*exp(3*x^2) + 20) + (16*x*exp(-x^3)*exp(3*x^2))/(4*exp(-x^3)*exp(3*x^2
) + 20)) + x^2

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sympy [B]  time = 71.71, size = 83, normalized size = 2.44 $$\begin{array}{c}{x}^2{e}^{\frac{2(8x{e}^{-x^3+3x^2}+39x)}{4e^{-x^3+3x^2}+20}}+x^2+4x+(-2x^2-4x)e^{\frac{8x{e}^{-x^3+3x^2}+39x}{4e^{-x^3+3x^2}+20}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((8*x**2+4*x)*exp(-x**3+3*x**2)**2+(-3*x**5+6*x**4+79*x**2+40*x)*exp(-x**3+3*x**2)+195*x**2+100*x)*
exp((8*x*exp(-x**3+3*x**2)+39*x)/(4*exp(-x**3+3*x**2)+20))**2+((-8*x**2-24*x-8)*exp(-x**3+3*x**2)**2+(3*x**5-1
2*x**3-79*x**2-238*x-80)*exp(-x**3+3*x**2)-195*x**2-590*x-200)*exp((8*x*exp(-x**3+3*x**2)+39*x)/(4*exp(-x**3+3
*x**2)+20))+(4*x+8)*exp(-x**3+3*x**2)**2+(40*x+80)*exp(-x**3+3*x**2)+100*x+200)/(2*exp(-x**3+3*x**2)**2+20*exp
(-x**3+3*x**2)+50),x)

[Out]

x**2*exp(2*(8*x*exp(-x**3 + 3*x**2) + 39*x)/(4*exp(-x**3 + 3*x**2) + 20)) + x**2 + 4*x + (-2*x**2 - 4*x)*exp((
8*x*exp(-x**3 + 3*x**2) + 39*x)/(4*exp(-x**3 + 3*x**2) + 20))

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