3.77.99 \(\int \frac {-4+256 x^3-160 x^4+24 x^5+e^{x^2} (1+8 x-64 x^3+40 x^4-38 x^5+16 x^6-2 x^7)+(8-256 x^3+160 x^4-24 x^5+e^{x^2} (-2+64 x^3-40 x^4+6 x^5)) \log (4-e^{x^2})+(-4+e^{x^2}) \log ^2(4-e^{x^2})}{-4+e^{x^2}+(8-2 e^{x^2}) \log (4-e^{x^2})+(-4+e^{x^2}) \log ^2(4-e^{x^2})} \, dx\)

Optimal. Leaf size=34 \[ -4+x-\frac {-4+(4-x)^2 x^4}{1-\log \left (4-e^{x^2}\right )} \]

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Rubi [F]  time = 4.59, 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 {-4+256 x^3-160 x^4+24 x^5+e^{x^2} \left (1+8 x-64 x^3+40 x^4-38 x^5+16 x^6-2 x^7\right )+\left (8-256 x^3+160 x^4-24 x^5+e^{x^2} \left (-2+64 x^3-40 x^4+6 x^5\right )\right ) \log \left (4-e^{x^2}\right )+\left (-4+e^{x^2}\right ) \log ^2\left (4-e^{x^2}\right )}{-4+e^{x^2}+\left (8-2 e^{x^2}\right ) \log \left (4-e^{x^2}\right )+\left (-4+e^{x^2}\right ) \log ^2\left (4-e^{x^2}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-4 + 256*x^3 - 160*x^4 + 24*x^5 + E^x^2*(1 + 8*x - 64*x^3 + 40*x^4 - 38*x^5 + 16*x^6 - 2*x^7) + (8 - 256*
x^3 + 160*x^4 - 24*x^5 + E^x^2*(-2 + 64*x^3 - 40*x^4 + 6*x^5))*Log[4 - E^x^2] + (-4 + E^x^2)*Log[4 - E^x^2]^2)
/(-4 + E^x^2 + (8 - 2*E^x^2)*Log[4 - E^x^2] + (-4 + E^x^2)*Log[4 - E^x^2]^2),x]

[Out]

x + 4/(1 - Log[4 - E^x^2]) + 16*Defer[Int][x^6/(-1 + Log[4 - E^x^2])^2, x] + 64*Defer[Int][x^6/((-4 + E^x^2)*(
-1 + Log[4 - E^x^2])^2), x] - 40*Defer[Int][x^4/(-1 + Log[4 - E^x^2]), x] - 16*Defer[Subst][Defer[Int][x^2/(-1
+ Log[4 - E^x])^2, x], x, x^2] - 64*Defer[Subst][Defer[Int][x^2/((-4 + E^x)*(-1 + Log[4 - E^x])^2), x], x, x^
2] - Defer[Subst][Defer[Int][x^3/(-1 + Log[4 - E^x])^2, x], x, x^2] - 4*Defer[Subst][Defer[Int][x^3/((-4 + E^x
)*(-1 + Log[4 - E^x])^2), x], x, x^2] + 32*Defer[Subst][Defer[Int][x/(-1 + Log[4 - E^x]), x], x, x^2] + 3*Defe
r[Subst][Defer[Int][x^2/(-1 + Log[4 - E^x]), x], x, x^2]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4-256 x^3+160 x^4-24 x^5-e^{x^2} \left (1+8 x-64 x^3+40 x^4-38 x^5+16 x^6-2 x^7\right )-\left (8-256 x^3+160 x^4-24 x^5+e^{x^2} \left (-2+64 x^3-40 x^4+6 x^5\right )\right ) \log \left (4-e^{x^2}\right )-\left (-4+e^{x^2}\right ) \log ^2\left (4-e^{x^2}\right )}{\left (4-e^{x^2}\right ) \left (1-\log \left (4-e^{x^2}\right )\right )^2} \, dx\\ &=\int \left (-\frac {8 x \left (-4+16 x^4-8 x^5+x^6\right )}{\left (-4+e^{x^2}\right ) \left (-1+\log \left (4-e^{x^2}\right )\right )^2}+\frac {1+8 x-64 x^3+40 x^4-38 x^5+16 x^6-2 x^7-2 \log \left (4-e^{x^2}\right )+64 x^3 \log \left (4-e^{x^2}\right )-40 x^4 \log \left (4-e^{x^2}\right )+6 x^5 \log \left (4-e^{x^2}\right )+\log ^2\left (4-e^{x^2}\right )}{\left (-1+\log \left (4-e^{x^2}\right )\right )^2}\right ) \, dx\\ &=-\left (8 \int \frac {x \left (-4+16 x^4-8 x^5+x^6\right )}{\left (-4+e^{x^2}\right ) \left (-1+\log \left (4-e^{x^2}\right )\right )^2} \, dx\right )+\int \frac {1+8 x-64 x^3+40 x^4-38 x^5+16 x^6-2 x^7-2 \log \left (4-e^{x^2}\right )+64 x^3 \log \left (4-e^{x^2}\right )-40 x^4 \log \left (4-e^{x^2}\right )+6 x^5 \log \left (4-e^{x^2}\right )+\log ^2\left (4-e^{x^2}\right )}{\left (-1+\log \left (4-e^{x^2}\right )\right )^2} \, dx\\ &=-\left (8 \int \left (-\frac {4 x}{\left (-4+e^{x^2}\right ) \left (-1+\log \left (4-e^{x^2}\right )\right )^2}+\frac {16 x^5}{\left (-4+e^{x^2}\right ) \left (-1+\log \left (4-e^{x^2}\right )\right )^2}-\frac {8 x^6}{\left (-4+e^{x^2}\right ) \left (-1+\log \left (4-e^{x^2}\right )\right )^2}+\frac {x^7}{\left (-4+e^{x^2}\right ) \left (-1+\log \left (4-e^{x^2}\right )\right )^2}\right ) \, dx\right )+\int \left (1-\frac {2 x \left (-4+16 x^4-8 x^5+x^6\right )}{\left (-1+\log \left (4-e^{x^2}\right )\right )^2}+\frac {2 x^3 \left (32-20 x+3 x^2\right )}{-1+\log \left (4-e^{x^2}\right )}\right ) \, dx\\ &=x-2 \int \frac {x \left (-4+16 x^4-8 x^5+x^6\right )}{\left (-1+\log \left (4-e^{x^2}\right )\right )^2} \, dx+2 \int \frac {x^3 \left (32-20 x+3 x^2\right )}{-1+\log \left (4-e^{x^2}\right )} \, dx-8 \int \frac {x^7}{\left (-4+e^{x^2}\right ) \left (-1+\log \left (4-e^{x^2}\right )\right )^2} \, dx+32 \int \frac {x}{\left (-4+e^{x^2}\right ) \left (-1+\log \left (4-e^{x^2}\right )\right )^2} \, dx+64 \int \frac {x^6}{\left (-4+e^{x^2}\right ) \left (-1+\log \left (4-e^{x^2}\right )\right )^2} \, dx-128 \int \frac {x^5}{\left (-4+e^{x^2}\right ) \left (-1+\log \left (4-e^{x^2}\right )\right )^2} \, dx\\ &=x-2 \int \left (-\frac {4 x}{\left (-1+\log \left (4-e^{x^2}\right )\right )^2}+\frac {16 x^5}{\left (-1+\log \left (4-e^{x^2}\right )\right )^2}-\frac {8 x^6}{\left (-1+\log \left (4-e^{x^2}\right )\right )^2}+\frac {x^7}{\left (-1+\log \left (4-e^{x^2}\right )\right )^2}\right ) \, dx+2 \int \left (\frac {32 x^3}{-1+\log \left (4-e^{x^2}\right )}-\frac {20 x^4}{-1+\log \left (4-e^{x^2}\right )}+\frac {3 x^5}{-1+\log \left (4-e^{x^2}\right )}\right ) \, dx-4 \operatorname {Subst}\left (\int \frac {x^3}{\left (-4+e^x\right ) \left (-1+\log \left (4-e^x\right )\right )^2} \, dx,x,x^2\right )+16 \operatorname {Subst}\left (\int \frac {1}{\left (-4+e^x\right ) \left (-1+\log \left (4-e^x\right )\right )^2} \, dx,x,x^2\right )+64 \int \frac {x^6}{\left (-4+e^{x^2}\right ) \left (-1+\log \left (4-e^{x^2}\right )\right )^2} \, dx-64 \operatorname {Subst}\left (\int \frac {x^2}{\left (-4+e^x\right ) \left (-1+\log \left (4-e^x\right )\right )^2} \, dx,x,x^2\right )\\ &=x-2 \int \frac {x^7}{\left (-1+\log \left (4-e^{x^2}\right )\right )^2} \, dx-4 \operatorname {Subst}\left (\int \frac {x^3}{\left (-4+e^x\right ) \left (-1+\log \left (4-e^x\right )\right )^2} \, dx,x,x^2\right )+6 \int \frac {x^5}{-1+\log \left (4-e^{x^2}\right )} \, dx+8 \int \frac {x}{\left (-1+\log \left (4-e^{x^2}\right )\right )^2} \, dx+16 \int \frac {x^6}{\left (-1+\log \left (4-e^{x^2}\right )\right )^2} \, dx+16 \operatorname {Subst}\left (\int \frac {1}{(-4+x) x (-1+\log (4-x))^2} \, dx,x,e^{x^2}\right )-32 \int \frac {x^5}{\left (-1+\log \left (4-e^{x^2}\right )\right )^2} \, dx-40 \int \frac {x^4}{-1+\log \left (4-e^{x^2}\right )} \, dx+64 \int \frac {x^6}{\left (-4+e^{x^2}\right ) \left (-1+\log \left (4-e^{x^2}\right )\right )^2} \, dx+64 \int \frac {x^3}{-1+\log \left (4-e^{x^2}\right )} \, dx-64 \operatorname {Subst}\left (\int \frac {x^2}{\left (-4+e^x\right ) \left (-1+\log \left (4-e^x\right )\right )^2} \, dx,x,x^2\right )\\ &=x+3 \operatorname {Subst}\left (\int \frac {x^2}{-1+\log \left (4-e^x\right )} \, dx,x,x^2\right )+4 \operatorname {Subst}\left (\int \frac {1}{\left (-1+\log \left (4-e^x\right )\right )^2} \, dx,x,x^2\right )-4 \operatorname {Subst}\left (\int \frac {x^3}{\left (-4+e^x\right ) \left (-1+\log \left (4-e^x\right )\right )^2} \, dx,x,x^2\right )+16 \int \frac {x^6}{\left (-1+\log \left (4-e^{x^2}\right )\right )^2} \, dx-16 \operatorname {Subst}\left (\int \frac {x^2}{\left (-1+\log \left (4-e^x\right )\right )^2} \, dx,x,x^2\right )+16 \operatorname {Subst}\left (\int \left (\frac {1}{4 (-4+x) (-1+\log (4-x))^2}-\frac {1}{4 x (-1+\log (4-x))^2}\right ) \, dx,x,e^{x^2}\right )+32 \operatorname {Subst}\left (\int \frac {x}{-1+\log \left (4-e^x\right )} \, dx,x,x^2\right )-40 \int \frac {x^4}{-1+\log \left (4-e^{x^2}\right )} \, dx+64 \int \frac {x^6}{\left (-4+e^{x^2}\right ) \left (-1+\log \left (4-e^{x^2}\right )\right )^2} \, dx-64 \operatorname {Subst}\left (\int \frac {x^2}{\left (-4+e^x\right ) \left (-1+\log \left (4-e^x\right )\right )^2} \, dx,x,x^2\right )-\operatorname {Subst}\left (\int \frac {x^3}{\left (-1+\log \left (4-e^x\right )\right )^2} \, dx,x,x^2\right )\\ &=x+3 \operatorname {Subst}\left (\int \frac {x^2}{-1+\log \left (4-e^x\right )} \, dx,x,x^2\right )-4 \operatorname {Subst}\left (\int \frac {x^3}{\left (-4+e^x\right ) \left (-1+\log \left (4-e^x\right )\right )^2} \, dx,x,x^2\right )+4 \operatorname {Subst}\left (\int \frac {1}{(-4+x) (-1+\log (4-x))^2} \, dx,x,e^{x^2}\right )+16 \int \frac {x^6}{\left (-1+\log \left (4-e^{x^2}\right )\right )^2} \, dx-16 \operatorname {Subst}\left (\int \frac {x^2}{\left (-1+\log \left (4-e^x\right )\right )^2} \, dx,x,x^2\right )+32 \operatorname {Subst}\left (\int \frac {x}{-1+\log \left (4-e^x\right )} \, dx,x,x^2\right )-40 \int \frac {x^4}{-1+\log \left (4-e^{x^2}\right )} \, dx+64 \int \frac {x^6}{\left (-4+e^{x^2}\right ) \left (-1+\log \left (4-e^{x^2}\right )\right )^2} \, dx-64 \operatorname {Subst}\left (\int \frac {x^2}{\left (-4+e^x\right ) \left (-1+\log \left (4-e^x\right )\right )^2} \, dx,x,x^2\right )-\operatorname {Subst}\left (\int \frac {x^3}{\left (-1+\log \left (4-e^x\right )\right )^2} \, dx,x,x^2\right )\\ &=x+3 \operatorname {Subst}\left (\int \frac {x^2}{-1+\log \left (4-e^x\right )} \, dx,x,x^2\right )-4 \operatorname {Subst}\left (\int \frac {x^3}{\left (-4+e^x\right ) \left (-1+\log \left (4-e^x\right )\right )^2} \, dx,x,x^2\right )+4 \operatorname {Subst}\left (\int \frac {1}{x (-1+\log (x))^2} \, dx,x,4-e^{x^2}\right )+16 \int \frac {x^6}{\left (-1+\log \left (4-e^{x^2}\right )\right )^2} \, dx-16 \operatorname {Subst}\left (\int \frac {x^2}{\left (-1+\log \left (4-e^x\right )\right )^2} \, dx,x,x^2\right )+32 \operatorname {Subst}\left (\int \frac {x}{-1+\log \left (4-e^x\right )} \, dx,x,x^2\right )-40 \int \frac {x^4}{-1+\log \left (4-e^{x^2}\right )} \, dx+64 \int \frac {x^6}{\left (-4+e^{x^2}\right ) \left (-1+\log \left (4-e^{x^2}\right )\right )^2} \, dx-64 \operatorname {Subst}\left (\int \frac {x^2}{\left (-4+e^x\right ) \left (-1+\log \left (4-e^x\right )\right )^2} \, dx,x,x^2\right )-\operatorname {Subst}\left (\int \frac {x^3}{\left (-1+\log \left (4-e^x\right )\right )^2} \, dx,x,x^2\right )\\ &=x+3 \operatorname {Subst}\left (\int \frac {x^2}{-1+\log \left (4-e^x\right )} \, dx,x,x^2\right )+4 \operatorname {Subst}\left (\int \frac {1}{x^2} \, dx,x,-1+\log \left (4-e^{x^2}\right )\right )-4 \operatorname {Subst}\left (\int \frac {x^3}{\left (-4+e^x\right ) \left (-1+\log \left (4-e^x\right )\right )^2} \, dx,x,x^2\right )+16 \int \frac {x^6}{\left (-1+\log \left (4-e^{x^2}\right )\right )^2} \, dx-16 \operatorname {Subst}\left (\int \frac {x^2}{\left (-1+\log \left (4-e^x\right )\right )^2} \, dx,x,x^2\right )+32 \operatorname {Subst}\left (\int \frac {x}{-1+\log \left (4-e^x\right )} \, dx,x,x^2\right )-40 \int \frac {x^4}{-1+\log \left (4-e^{x^2}\right )} \, dx+64 \int \frac {x^6}{\left (-4+e^{x^2}\right ) \left (-1+\log \left (4-e^{x^2}\right )\right )^2} \, dx-64 \operatorname {Subst}\left (\int \frac {x^2}{\left (-4+e^x\right ) \left (-1+\log \left (4-e^x\right )\right )^2} \, dx,x,x^2\right )-\operatorname {Subst}\left (\int \frac {x^3}{\left (-1+\log \left (4-e^x\right )\right )^2} \, dx,x,x^2\right )\\ &=x+\frac {4}{1-\log \left (4-e^{x^2}\right )}+3 \operatorname {Subst}\left (\int \frac {x^2}{-1+\log \left (4-e^x\right )} \, dx,x,x^2\right )-4 \operatorname {Subst}\left (\int \frac {x^3}{\left (-4+e^x\right ) \left (-1+\log \left (4-e^x\right )\right )^2} \, dx,x,x^2\right )+16 \int \frac {x^6}{\left (-1+\log \left (4-e^{x^2}\right )\right )^2} \, dx-16 \operatorname {Subst}\left (\int \frac {x^2}{\left (-1+\log \left (4-e^x\right )\right )^2} \, dx,x,x^2\right )+32 \operatorname {Subst}\left (\int \frac {x}{-1+\log \left (4-e^x\right )} \, dx,x,x^2\right )-40 \int \frac {x^4}{-1+\log \left (4-e^{x^2}\right )} \, dx+64 \int \frac {x^6}{\left (-4+e^{x^2}\right ) \left (-1+\log \left (4-e^{x^2}\right )\right )^2} \, dx-64 \operatorname {Subst}\left (\int \frac {x^2}{\left (-4+e^x\right ) \left (-1+\log \left (4-e^x\right )\right )^2} \, dx,x,x^2\right )-\operatorname {Subst}\left (\int \frac {x^3}{\left (-1+\log \left (4-e^x\right )\right )^2} \, dx,x,x^2\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.10, size = 32, normalized size = 0.94 \begin {gather*} x+\frac {-4+16 x^4-8 x^5+x^6}{-1+\log \left (4-e^{x^2}\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-4 + 256*x^3 - 160*x^4 + 24*x^5 + E^x^2*(1 + 8*x - 64*x^3 + 40*x^4 - 38*x^5 + 16*x^6 - 2*x^7) + (8
- 256*x^3 + 160*x^4 - 24*x^5 + E^x^2*(-2 + 64*x^3 - 40*x^4 + 6*x^5))*Log[4 - E^x^2] + (-4 + E^x^2)*Log[4 - E^x
^2]^2)/(-4 + E^x^2 + (8 - 2*E^x^2)*Log[4 - E^x^2] + (-4 + E^x^2)*Log[4 - E^x^2]^2),x]

[Out]

x + (-4 + 16*x^4 - 8*x^5 + x^6)/(-1 + Log[4 - E^x^2])

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fricas [A]  time = 0.81, size = 43, normalized size = 1.26 \begin {gather*} \frac {x^{6} - 8 \, x^{5} + 16 \, x^{4} + x \log \left (-e^{\left (x^{2}\right )} + 4\right ) - x - 4}{\log \left (-e^{\left (x^{2}\right )} + 4\right ) - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((exp(x^2)-4)*log(4-exp(x^2))^2+((6*x^5-40*x^4+64*x^3-2)*exp(x^2)-24*x^5+160*x^4-256*x^3+8)*log(4-ex
p(x^2))+(-2*x^7+16*x^6-38*x^5+40*x^4-64*x^3+8*x+1)*exp(x^2)+24*x^5-160*x^4+256*x^3-4)/((exp(x^2)-4)*log(4-exp(
x^2))^2+(-2*exp(x^2)+8)*log(4-exp(x^2))+exp(x^2)-4),x, algorithm="fricas")

[Out]

(x^6 - 8*x^5 + 16*x^4 + x*log(-e^(x^2) + 4) - x - 4)/(log(-e^(x^2) + 4) - 1)

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giac [A]  time = 0.23, size = 43, normalized size = 1.26 \begin {gather*} \frac {x^{6} - 8 \, x^{5} + 16 \, x^{4} + x \log \left (-e^{\left (x^{2}\right )} + 4\right ) - x - 4}{\log \left (-e^{\left (x^{2}\right )} + 4\right ) - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((exp(x^2)-4)*log(4-exp(x^2))^2+((6*x^5-40*x^4+64*x^3-2)*exp(x^2)-24*x^5+160*x^4-256*x^3+8)*log(4-ex
p(x^2))+(-2*x^7+16*x^6-38*x^5+40*x^4-64*x^3+8*x+1)*exp(x^2)+24*x^5-160*x^4+256*x^3-4)/((exp(x^2)-4)*log(4-exp(
x^2))^2+(-2*exp(x^2)+8)*log(4-exp(x^2))+exp(x^2)-4),x, algorithm="giac")

[Out]

(x^6 - 8*x^5 + 16*x^4 + x*log(-e^(x^2) + 4) - x - 4)/(log(-e^(x^2) + 4) - 1)

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maple [A]  time = 0.03, size = 32, normalized size = 0.94

method	result	size
risch	\(x +\frac {x^{6}-8 x^{5}+16 x^{4}-4}{\ln \left (4-{\mathrm e}^{x^{2}}\right )-1}\)	\(32\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((exp(x^2)-4)*ln(4-exp(x^2))^2+((6*x^5-40*x^4+64*x^3-2)*exp(x^2)-24*x^5+160*x^4-256*x^3+8)*ln(4-exp(x^2))+
(-2*x^7+16*x^6-38*x^5+40*x^4-64*x^3+8*x+1)*exp(x^2)+24*x^5-160*x^4+256*x^3-4)/((exp(x^2)-4)*ln(4-exp(x^2))^2+(
-2*exp(x^2)+8)*ln(4-exp(x^2))+exp(x^2)-4),x,method=_RETURNVERBOSE)

[Out]

x+(x^6-8*x^5+16*x^4-4)/(ln(4-exp(x^2))-1)

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maxima [A]  time = 0.40, size = 43, normalized size = 1.26 \begin {gather*} \frac {x^{6} - 8 \, x^{5} + 16 \, x^{4} + x \log \left (-e^{\left (x^{2}\right )} + 4\right ) - x - 4}{\log \left (-e^{\left (x^{2}\right )} + 4\right ) - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((exp(x^2)-4)*log(4-exp(x^2))^2+((6*x^5-40*x^4+64*x^3-2)*exp(x^2)-24*x^5+160*x^4-256*x^3+8)*log(4-ex
p(x^2))+(-2*x^7+16*x^6-38*x^5+40*x^4-64*x^3+8*x+1)*exp(x^2)+24*x^5-160*x^4+256*x^3-4)/((exp(x^2)-4)*log(4-exp(
x^2))^2+(-2*exp(x^2)+8)*log(4-exp(x^2))+exp(x^2)-4),x, algorithm="maxima")

[Out]

(x^6 - 8*x^5 + 16*x^4 + x*log(-e^(x^2) + 4) - x - 4)/(log(-e^(x^2) + 4) - 1)

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mupad [B]  time = 5.06, size = 169, normalized size = 4.97 \begin {gather*} x-\frac {{\mathrm {e}}^{-x^2}\,\left (4\,{\mathrm {e}}^{x^2}-32\,x^2\,{\mathrm {e}}^{x^2}+20\,x^3\,{\mathrm {e}}^{x^2}-19\,x^4\,{\mathrm {e}}^{x^2}+8\,x^5\,{\mathrm {e}}^{x^2}-x^6\,{\mathrm {e}}^{x^2}+128\,x^2-80\,x^3+12\,x^4\right )+{\mathrm {e}}^{-x^2}\,\ln \left (4-{\mathrm {e}}^{x^2}\right )\,\left ({\mathrm {e}}^{x^2}-4\right )\,\left (3\,x^4-20\,x^3+32\,x^2\right )}{\ln \left (4-{\mathrm {e}}^{x^2}\right )-1}+32\,x^2-20\,x^3+3\,x^4-{\mathrm {e}}^{-x^2}\,\left (12\,x^4-80\,x^3+128\,x^2\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(4 - exp(x^2))*(exp(x^2)*(64*x^3 - 40*x^4 + 6*x^5 - 2) - 256*x^3 + 160*x^4 - 24*x^5 + 8) + log(4 - exp
(x^2))^2*(exp(x^2) - 4) + 256*x^3 - 160*x^4 + 24*x^5 + exp(x^2)*(8*x - 64*x^3 + 40*x^4 - 38*x^5 + 16*x^6 - 2*x
^7 + 1) - 4)/(exp(x^2) - log(4 - exp(x^2))*(2*exp(x^2) - 8) + log(4 - exp(x^2))^2*(exp(x^2) - 4) - 4),x)

[Out]

x - (exp(-x^2)*(4*exp(x^2) - 32*x^2*exp(x^2) + 20*x^3*exp(x^2) - 19*x^4*exp(x^2) + 8*x^5*exp(x^2) - x^6*exp(x^
2) + 128*x^2 - 80*x^3 + 12*x^4) + exp(-x^2)*log(4 - exp(x^2))*(exp(x^2) - 4)*(32*x^2 - 20*x^3 + 3*x^4))/(log(4
- exp(x^2)) - 1) + 32*x^2 - 20*x^3 + 3*x^4 - exp(-x^2)*(128*x^2 - 80*x^3 + 12*x^4)

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sympy [A]  time = 0.34, size = 26, normalized size = 0.76 \begin {gather*} x + \frac {x^{6} - 8 x^{5} + 16 x^{4} - 4}{\log {\left (4 - e^{x^{2}} \right )} - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((exp(x**2)-4)*ln(4-exp(x**2))**2+((6*x**5-40*x**4+64*x**3-2)*exp(x**2)-24*x**5+160*x**4-256*x**3+8)
*ln(4-exp(x**2))+(-2*x**7+16*x**6-38*x**5+40*x**4-64*x**3+8*x+1)*exp(x**2)+24*x**5-160*x**4+256*x**3-4)/((exp(
x**2)-4)*ln(4-exp(x**2))**2+(-2*exp(x**2)+8)*ln(4-exp(x**2))+exp(x**2)-4),x)

[Out]

x + (x**6 - 8*x**5 + 16*x**4 - 4)/(log(4 - exp(x**2)) - 1)

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