∫ (−6+2e5x2−exx2 +60x2+ex(−12x2−6x3)) log(e−5x2+exx2 (e5x2−exx2 (−6−x)+3x))__________________________________________________________

3.35.32 \(\int \frac {(-6+2 e^{5 x^2-e^x x^2}+60 x^2+e^x (-12 x^2-6 x^3)) \log (e^{-5 x^2+e^x x^2} (e^{5 x^2-e^x x^2} (-6-x)+3 x))}{-3 x+e^{5 x^2-e^x x^2} (6+x)} \, dx\)

Optimal. Leaf size=37 \[ \log ^2\left (-5+\frac {-x-x^2+3 e^{-\left (\left (5-e^x\right ) x^2\right )} x^2}{x}\right ) \]

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Rubi [F] time = 59.58, 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 {\left (-6+2 e^{5 x^2-e^x x^2}+60 x^2+e^x \left (-12 x^2-6 x^3\right )\right ) \log \left (e^{-5 x^2+e^x x^2} \left (e^{5 x^2-e^x x^2} (-6-x)+3 x\right )\right )}{-3 x+e^{5 x^2-e^x x^2} (6+x)} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[((-6 + 2*E^(5*x^2 - E^x*x^2) + 60*x^2 + E^x*(-12*x^2 - 6*x^3))*Log[E^(-5*x^2 + E^x*x^2)*(E^(5*x^2 - E^x*x^

2)*(-6 - x) + 3*x)])/(-3*x + E^(5*x^2 - E^x*x^2)*(6 + x)),x]

[Out]

2*E^x - 2*E^x*x + 5*x^2 - 25*x^4 + 10*E^x*x^4 - E^(2*x)*x^4 - 10*x^2*Log[-6 - (1 - 3/E^((5 - E^x)*x^2))*x] + 2

*E^x*x^2*Log[-6 - (1 - 3/E^((5 - E^x)*x^2))*x] - 12*Log[-6 - (1 - 3/E^((5 - E^x)*x^2))*x]*Defer[Int][E^(5*x^2)

/(x*(6*E^(5*x^2) + E^(5*x^2)*x - 3*E^(E^x*x^2)*x)), x] + 120*Log[-6 - (1 - 3/E^((5 - E^x)*x^2))*x]*Defer[Int][

(E^(5*x^2)*x)/(6*E^(5*x^2) + E^(5*x^2)*x - 3*E^(E^x*x^2)*x), x] - 24*Log[-6 - (1 - 3/E^((5 - E^x)*x^2))*x]*Def

er[Int][(E^(x + 5*x^2)*x)/(6*E^(5*x^2) + E^(5*x^2)*x - 3*E^(E^x*x^2)*x), x] + 20*Log[-6 - (1 - 3/E^((5 - E^x)*

x^2))*x]*Defer[Int][(E^(5*x^2)*x^2)/(6*E^(5*x^2) + E^(5*x^2)*x - 3*E^(E^x*x^2)*x), x] - 16*Log[-6 - (1 - 3/E^(

(5 - E^x)*x^2))*x]*Defer[Int][(E^(x + 5*x^2)*x^2)/(6*E^(5*x^2) + E^(5*x^2)*x - 3*E^(E^x*x^2)*x), x] - 2*Log[-6

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

x] + 60*Defer[Int][x/(-6 - x + 3*E^((-5 + E^x)*x^2)*x), x] - 12*Defer[Int][(E^x*x)/(-6 - x + 3*E^((-5 + E^x)*x

^2)*x), x] - 600*Defer[Int][x^3/(-6 - x + 3*E^((-5 + E^x)*x^2)*x), x] + 240*Defer[Int][(E^x*x^3)/(-6 - x + 3*E

^((-5 + E^x)*x^2)*x), x] - 24*Defer[Int][(E^(2*x)*x^3)/(-6 - x + 3*E^((-5 + E^x)*x^2)*x), x] - 100*Defer[Int][

x^4/(-6 - x + 3*E^((-5 + E^x)*x^2)*x), x] + 100*Defer[Int][(E^x*x^4)/(-6 - x + 3*E^((-5 + E^x)*x^2)*x), x] - 1

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

+ E^x)*x^2)*x), x] - 2*Defer[Int][(E^(2*x)*x^5)/(-6 - x + 3*E^((-5 + E^x)*x^2)*x), x] + 2*Defer[Int][Log[-6 +

(-1 + 3*E^((-5 + E^x)*x^2))*x]/x, x] + 12*Defer[Int][Defer[Int][E^(5*x^2)/(x*(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6

+ x))), x]/x, x] - 120*Defer[Int][x*Defer[Int][E^(5*x^2)/(x*(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x))), x], x] +

24*Defer[Int][E^x*x*Defer[Int][E^(5*x^2)/(x*(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x))), x], x] + 12*Defer[Int][E^

x*x^2*Defer[Int][E^(5*x^2)/(x*(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x))), x], x] + 72*Defer[Int][Defer[Int][E^(5*

x^2)/(x*(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x))), x]/(x*(-6 - x + 3*E^((-5 + E^x)*x^2)*x)), x] - 720*Defer[Int]

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

+ 144*Defer[Int][(E^x*x*Defer[Int][E^(5*x^2)/(x*(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x))), x])/(-6 - x + 3*E^((

-5 + E^x)*x^2)*x), x] - 120*Defer[Int][(x^2*Defer[Int][E^(5*x^2)/(x*(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x))), x

])/(-6 - x + 3*E^((-5 + E^x)*x^2)*x), x] + 96*Defer[Int][(E^x*x^2*Defer[Int][E^(5*x^2)/(x*(-3*E^(E^x*x^2)*x +

E^(5*x^2)*(6 + x))), x])/(-6 - x + 3*E^((-5 + E^x)*x^2)*x), x] + 12*Defer[Int][(E^x*x^3*Defer[Int][E^(5*x^2)/(

x*(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x))), x])/(-6 - x + 3*E^((-5 + E^x)*x^2)*x), x] - 120*Defer[Int][Defer[In

t][(E^(5*x^2)*x)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x]/x, x] + 1200*Defer[Int][x*Defer[Int][(E^(5*x^2)*x)

/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x], x] - 240*Defer[Int][E^x*x*Defer[Int][(E^(5*x^2)*x)/(-3*E^(E^x*x^2

)*x + E^(5*x^2)*(6 + x)), x], x] - 120*Defer[Int][E^x*x^2*Defer[Int][(E^(5*x^2)*x)/(-3*E^(E^x*x^2)*x + E^(5*x^

2)*(6 + x)), x], x] - 720*Defer[Int][Defer[Int][(E^(5*x^2)*x)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x]/(x*(-

6 - x + 3*E^((-5 + E^x)*x^2)*x)), x] + 7200*Defer[Int][(x*Defer[Int][(E^(5*x^2)*x)/(-3*E^(E^x*x^2)*x + E^(5*x^

2)*(6 + x)), x])/(-6 - x + 3*E^((-5 + E^x)*x^2)*x), x] - 1440*Defer[Int][(E^x*x*Defer[Int][(E^(5*x^2)*x)/(-3*E

^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x])/(-6 - x + 3*E^((-5 + E^x)*x^2)*x), x] + 1200*Defer[Int][(x^2*Defer[Int]

[(E^(5*x^2)*x)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x])/(-6 - x + 3*E^((-5 + E^x)*x^2)*x), x] - 960*Defer[I

nt][(E^x*x^2*Defer[Int][(E^(5*x^2)*x)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x])/(-6 - x + 3*E^((-5 + E^x)*x^

2)*x), x] - 120*Defer[Int][(E^x*x^3*Defer[Int][(E^(5*x^2)*x)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x])/(-6 -

x + 3*E^((-5 + E^x)*x^2)*x), x] + 24*Defer[Int][Defer[Int][(E^(x + 5*x^2)*x)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6

+ x)), x]/x, x] - 240*Defer[Int][x*Defer[Int][(E^(x + 5*x^2)*x)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x], x

] + 48*Defer[Int][E^x*x*Defer[Int][(E^(x + 5*x^2)*x)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x], x] + 24*Defer

[Int][E^x*x^2*Defer[Int][(E^(x + 5*x^2)*x)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x], x] + 144*Defer[Int][Def

er[Int][(E^(x + 5*x^2)*x)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x]/(x*(-6 - x + 3*E^((-5 + E^x)*x^2)*x)), x]

- 1440*Defer[Int][(x*Defer[Int][(E^(x + 5*x^2)*x)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x])/(-6 - x + 3*E^(

(-5 + E^x)*x^2)*x), x] + 288*Defer[Int][(E^x*x*Defer[Int][(E^(x + 5*x^2)*x)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 +

x)), x])/(-6 - x + 3*E^((-5 + E^x)*x^2)*x), x] - 240*Defer[Int][(x^2*Defer[Int][(E^(x + 5*x^2)*x)/(-3*E^(E^x*

x^2)*x + E^(5*x^2)*(6 + x)), x])/(-6 - x + 3*E^((-5 + E^x)*x^2)*x), x] + 192*Defer[Int][(E^x*x^2*Defer[Int][(E

^(x + 5*x^2)*x)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x])/(-6 - x + 3*E^((-5 + E^x)*x^2)*x), x] + 24*Defer[I

nt][(E^x*x^3*Defer[Int][(E^(x + 5*x^2)*x)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x])/(-6 - x + 3*E^((-5 + E^x

)*x^2)*x), x] - 20*Defer[Int][Defer[Int][(E^(5*x^2)*x^2)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x]/x, x] + 20

0*Defer[Int][x*Defer[Int][(E^(5*x^2)*x^2)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x], x] - 40*Defer[Int][E^x*x

*Defer[Int][(E^(5*x^2)*x^2)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x], x] - 20*Defer[Int][E^x*x^2*Defer[Int][

(E^(5*x^2)*x^2)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x], x] - 120*Defer[Int][Defer[Int][(E^(5*x^2)*x^2)/(-3

*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x]/(x*(-6 - x + 3*E^((-5 + E^x)*x^2)*x)), x] + 1200*Defer[Int][(x*Defer[I

nt][(E^(5*x^2)*x^2)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x])/(-6 - x + 3*E^((-5 + E^x)*x^2)*x), x] - 240*De

fer[Int][(E^x*x*Defer[Int][(E^(5*x^2)*x^2)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x])/(-6 - x + 3*E^((-5 + E^

x)*x^2)*x), x] + 200*Defer[Int][(x^2*Defer[Int][(E^(5*x^2)*x^2)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x])/(-

6 - x + 3*E^((-5 + E^x)*x^2)*x), x] - 160*Defer[Int][(E^x*x^2*Defer[Int][(E^(5*x^2)*x^2)/(-3*E^(E^x*x^2)*x + E

^(5*x^2)*(6 + x)), x])/(-6 - x + 3*E^((-5 + E^x)*x^2)*x), x] - 20*Defer[Int][(E^x*x^3*Defer[Int][(E^(5*x^2)*x^

2)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x])/(-6 - x + 3*E^((-5 + E^x)*x^2)*x), x] + 16*Defer[Int][Defer[Int

][(E^(x + 5*x^2)*x^2)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x]/x, x] - 160*Defer[Int][x*Defer[Int][(E^(x + 5

*x^2)*x^2)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x], x] + 32*Defer[Int][E^x*x*Defer[Int][(E^(x + 5*x^2)*x^2)

/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x], x] + 16*Defer[Int][E^x*x^2*Defer[Int][(E^(x + 5*x^2)*x^2)/(-3*E^(

E^x*x^2)*x + E^(5*x^2)*(6 + x)), x], x] + 96*Defer[Int][Defer[Int][(E^(x + 5*x^2)*x^2)/(-3*E^(E^x*x^2)*x + E^(

5*x^2)*(6 + x)), x]/(x*(-6 - x + 3*E^((-5 + E^x)*x^2)*x)), x] - 960*Defer[Int][(x*Defer[Int][(E^(x + 5*x^2)*x^

2)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x])/(-6 - x + 3*E^((-5 + E^x)*x^2)*x), x] + 192*Defer[Int][(E^x*x*D

efer[Int][(E^(x + 5*x^2)*x^2)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x])/(-6 - x + 3*E^((-5 + E^x)*x^2)*x), x

] - 160*Defer[Int][(x^2*Defer[Int][(E^(x + 5*x^2)*x^2)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x])/(-6 - x + 3

*E^((-5 + E^x)*x^2)*x), x] + 128*Defer[Int][(E^x*x^2*Defer[Int][(E^(x + 5*x^2)*x^2)/(-3*E^(E^x*x^2)*x + E^(5*x

^2)*(6 + x)), x])/(-6 - x + 3*E^((-5 + E^x)*x^2)*x), x] + 16*Defer[Int][(E^x*x^3*Defer[Int][(E^(x + 5*x^2)*x^2

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

(E^(x + 5*x^2)*x^3)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x]/x, x] - 20*Defer[Int][x*Defer[Int][(E^(x + 5*x^

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

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

^2)*x + E^(5*x^2)*(6 + x)), x], x] + 12*Defer[Int][Defer[Int][(E^(x + 5*x^2)*x^3)/(-3*E^(E^x*x^2)*x + E^(5*x^2

)*(6 + x)), x]/(x*(-6 - x + 3*E^((-5 + E^x)*x^2)*x)), x] - 120*Defer[Int][(x*Defer[Int][(E^(x + 5*x^2)*x^3)/(-

3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x])/(-6 - x + 3*E^((-5 + E^x)*x^2)*x), x] + 24*Defer[Int][(E^x*x*Defer[I

nt][(E^(x + 5*x^2)*x^3)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)), x])/(-6 - x + 3*E^((-5 + E^x)*x^2)*x), x] - 20

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

+ E^x)*x^2)*x), x] + 16*Defer[Int][(E^x*x^2*Defer[Int][(E^(x + 5*x^2)*x^3)/(-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 +

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

E^x*x^2)*x + E^(5*x^2)*(6 + x)), x])/(-6 - x + 3*E^((-5 + E^x)*x^2)*x), x]

Rubi steps

Aborted

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Mathematica [B] time = 0.28, size = 152, normalized size = 4.11 \begin {gather*} 2 \left (-\frac {1}{2} \left (5 x^2-\log \left (3 e^{e^x x^2} x-e^{5 x^2} (6+x)\right )\right ) \left (5 x^2+\log \left (3 e^{e^x x^2} x-e^{5 x^2} (6+x)\right )-2 \log \left (-3 e^{e^x x^2} x+e^{5 x^2} (6+x)\right )\right )+\log \left (-6+\left (-1+3 e^{\left (-5+e^x\right ) x^2}\right ) x\right ) \left (-5 x^2+\log \left (-3 e^{e^x x^2} x+e^{5 x^2} (6+x)\right )\right )\right ) \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[((-6 + 2*E^(5*x^2 - E^x*x^2) + 60*x^2 + E^x*(-12*x^2 - 6*x^3))*Log[E^(-5*x^2 + E^x*x^2)*(E^(5*x^2 -

E^x*x^2)*(-6 - x) + 3*x)])/(-3*x + E^(5*x^2 - E^x*x^2)*(6 + x)),x]

[Out]

2*(-1/2*((5*x^2 - Log[3*E^(E^x*x^2)*x - E^(5*x^2)*(6 + x)])*(5*x^2 + Log[3*E^(E^x*x^2)*x - E^(5*x^2)*(6 + x)]

- 2*Log[-3*E^(E^x*x^2)*x + E^(5*x^2)*(6 + x)])) + Log[-6 + (-1 + 3*E^((-5 + E^x)*x^2))*x]*(-5*x^2 + Log[-3*E^(

E^x*x^2)*x + E^(5*x^2)*(6 + x)]))

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fricas [A] time = 0.73, size = 24, normalized size = 0.65 \begin {gather*} \log \left (3 \, x e^{\left (x^{2} e^{x} - 5 \, x^{2}\right )} - x - 6\right )^{2} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*exp(-exp(x)*x^2+5*x^2)+(-6*x^3-12*x^2)*exp(x)+60*x^2-6)*log(((-x-6)*exp(-exp(x)*x^2+5*x^2)+3*x)/e

xp(-exp(x)*x^2+5*x^2))/((x+6)*exp(-exp(x)*x^2+5*x^2)-3*x),x, algorithm="fricas")

[Out]

log(3*x*e^(x^2*e^x - 5*x^2) - x - 6)^2

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*exp(-exp(x)*x^2+5*x^2)+(-6*x^3-12*x^2)*exp(x)+60*x^2-6)*log(((-x-6)*exp(-exp(x)*x^2+5*x^2)+3*x)/e

xp(-exp(x)*x^2+5*x^2))/((x+6)*exp(-exp(x)*x^2+5*x^2)-3*x),x, algorithm="giac")

[Out]

integrate(2*(30*x^2 - 3*(x^3 + 2*x^2)*e^x + e^(-x^2*e^x + 5*x^2) - 3)*log(-((x + 6)*e^(-x^2*e^x + 5*x^2) - 3*x

)*e^(x^2*e^x - 5*x^2))/((x + 6)*e^(-x^2*e^x + 5*x^2) - 3*x), x)

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maple [F] time = 0.02, size = 0, normalized size = 0.00 \[\int \frac {\left (2 \,{\mathrm e}^{-{\mathrm e}^{x} x^{2}+5 x^{2}}+\left (-6 x^{3}-12 x^{2}\right ) {\mathrm e}^{x}+60 x^{2}-6\right ) \ln \left (\left (\left (-x -6\right ) {\mathrm e}^{-{\mathrm e}^{x} x^{2}+5 x^{2}}+3 x \right ) {\mathrm e}^{{\mathrm e}^{x} x^{2}-5 x^{2}}\right )}{\left (x +6\right ) {\mathrm e}^{-{\mathrm e}^{x} x^{2}+5 x^{2}}-3 x}\, dx\]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((2*exp(-exp(x)*x^2+5*x^2)+(-6*x^3-12*x^2)*exp(x)+60*x^2-6)*ln(((-x-6)*exp(-exp(x)*x^2+5*x^2)+3*x)/exp(-exp

(x)*x^2+5*x^2))/((x+6)*exp(-exp(x)*x^2+5*x^2)-3*x),x)

[Out]

int((2*exp(-exp(x)*x^2+5*x^2)+(-6*x^3-12*x^2)*exp(x)+60*x^2-6)*ln(((-x-6)*exp(-exp(x)*x^2+5*x^2)+3*x)/exp(-exp

(x)*x^2+5*x^2))/((x+6)*exp(-exp(x)*x^2+5*x^2)-3*x),x)

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

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*exp(-exp(x)*x^2+5*x^2)+(-6*x^3-12*x^2)*exp(x)+60*x^2-6)*log(((-x-6)*exp(-exp(x)*x^2+5*x^2)+3*x)/e

xp(-exp(x)*x^2+5*x^2))/((x+6)*exp(-exp(x)*x^2+5*x^2)-3*x),x, algorithm="maxima")

[Out]

2*integrate((30*x^2 - 3*(x^3 + 2*x^2)*e^x + e^(-x^2*e^x + 5*x^2) - 3)*log(-((x + 6)*e^(-x^2*e^x + 5*x^2) - 3*x

)*e^(x^2*e^x - 5*x^2))/((x + 6)*e^(-x^2*e^x + 5*x^2) - 3*x), x)

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mupad [B] time = 0.67, size = 24, normalized size = 0.65 \begin {gather*} {\ln \left (3\,x\,{\mathrm {e}}^{x^2\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-5\,x^2}-x-6\right )}^2 \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(exp(x^2*exp(x) - 5*x^2)*(3*x - exp(5*x^2 - x^2*exp(x))*(x + 6)))*(2*exp(5*x^2 - x^2*exp(x)) - exp(x)

*(12*x^2 + 6*x^3) + 60*x^2 - 6))/(3*x - exp(5*x^2 - x^2*exp(x))*(x + 6)),x)

[Out]

log(3*x*exp(x^2*exp(x))*exp(-5*x^2) - x - 6)^2

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sympy [A] time = 1.80, size = 37, normalized size = 1.00 \begin {gather*} \log {\left (\left (3 x + \left (- x - 6\right ) e^{- x^{2} e^{x} + 5 x^{2}}\right ) e^{x^{2} e^{x} - 5 x^{2}} \right )}^{2} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*exp(-exp(x)*x**2+5*x**2)+(-6*x**3-12*x**2)*exp(x)+60*x**2-6)*ln(((-x-6)*exp(-exp(x)*x**2+5*x**2)+

3*x)/exp(-exp(x)*x**2+5*x**2))/((x+6)*exp(-exp(x)*x**2+5*x**2)-3*x),x)

[Out]

log((3*x + (-x - 6)*exp(-x**2*exp(x) + 5*x**2))*exp(x**2*exp(x) - 5*x**2))**2

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