3.93.61 \(\int \frac {e^{\frac {x^2+2 e x^2+e^2 x^2+(-2 e x^2-2 e^2 x^2) \log (2)+e^2 x^2 \log ^2(2)}{1-2 e \log (2)+e^2 \log ^2(2)}} (2 x+4 e x+2 e^2 x+(-4 e x-4 e^2 x) \log (2)+2 e^2 x \log ^2(2))}{1-2 e \log (2)+e^2 \log ^2(2)} \, dx\)

Optimal. Leaf size=18 \[ e^{\left (x+\frac {x}{\frac {1}{e}-\log (2)}\right )^2} \]

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Rubi [A]  time = 0.22, antiderivative size = 27, normalized size of antiderivative = 1.50, number of steps used = 7, number of rules used = 4, integrand size = 122, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.033, Rules used = {6, 12, 2225, 2209} \begin {gather*} \exp \left (\frac {x^2 (1+e (1-\log (2)))^2}{(1-e \log (2))^2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^((x^2 + 2*E*x^2 + E^2*x^2 + (-2*E*x^2 - 2*E^2*x^2)*Log[2] + E^2*x^2*Log[2]^2)/(1 - 2*E*Log[2] + E^2*Log
[2]^2))*(2*x + 4*E*x + 2*E^2*x + (-4*E*x - 4*E^2*x)*Log[2] + 2*E^2*x*Log[2]^2))/(1 - 2*E*Log[2] + E^2*Log[2]^2
),x]

[Out]

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

Rule 6

Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] :> Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x
] &&  !FreeQ[v, x]

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 2209

Int[(F_)^((a_.) + (b_.)*((c_.) + (d_.)*(x_))^(n_))*((e_.) + (f_.)*(x_))^(m_.), x_Symbol] :> Simp[((e + f*x)^n*
F^(a + b*(c + d*x)^n))/(b*f*n*(c + d*x)^n*Log[F]), x] /; FreeQ[{F, a, b, c, d, e, f, n}, x] && EqQ[m, n - 1] &
& EqQ[d*e - c*f, 0]

Rule 2225

Int[(F_)^(v_)*(u_)^(m_.), x_Symbol] :> Int[ExpandToSum[u, x]^m*F^ExpandToSum[v, x], x] /; FreeQ[{F, m}, x] &&
LinearQ[u, x] && BinomialQ[v, x] &&  !(LinearMatchQ[u, x] && BinomialMatchQ[v, x])

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (\frac {x^2+2 e x^2+e^2 x^2+\left (-2 e x^2-2 e^2 x^2\right ) \log (2)+e^2 x^2 \log ^2(2)}{1-2 e \log (2)+e^2 \log ^2(2)}\right ) \left (2 e^2 x+(2+4 e) x+\left (-4 e x-4 e^2 x\right ) \log (2)+2 e^2 x \log ^2(2)\right )}{1-2 e \log (2)+e^2 \log ^2(2)} \, dx\\ &=\int \frac {\exp \left (\frac {x^2+2 e x^2+e^2 x^2+\left (-2 e x^2-2 e^2 x^2\right ) \log (2)+e^2 x^2 \log ^2(2)}{1-2 e \log (2)+e^2 \log ^2(2)}\right ) \left (\left (2+4 e+2 e^2\right ) x+\left (-4 e x-4 e^2 x\right ) \log (2)+2 e^2 x \log ^2(2)\right )}{1-2 e \log (2)+e^2 \log ^2(2)} \, dx\\ &=\int \frac {\exp \left (\frac {x^2+2 e x^2+e^2 x^2+\left (-2 e x^2-2 e^2 x^2\right ) \log (2)+e^2 x^2 \log ^2(2)}{1-2 e \log (2)+e^2 \log ^2(2)}\right ) \left (\left (-4 e x-4 e^2 x\right ) \log (2)+x \left (2+4 e+2 e^2+2 e^2 \log ^2(2)\right )\right )}{1-2 e \log (2)+e^2 \log ^2(2)} \, dx\\ &=\frac {\int \exp \left (\frac {x^2+2 e x^2+e^2 x^2+\left (-2 e x^2-2 e^2 x^2\right ) \log (2)+e^2 x^2 \log ^2(2)}{1-2 e \log (2)+e^2 \log ^2(2)}\right ) \left (\left (-4 e x-4 e^2 x\right ) \log (2)+x \left (2+4 e+2 e^2+2 e^2 \log ^2(2)\right )\right ) \, dx}{1-2 e \log (2)+e^2 \log ^2(2)}\\ &=\frac {\int 2 \exp \left (\frac {x^2 (1+e (1-\log (2)))^2}{(1-e \log (2))^2}\right ) x (1+e (1-\log (2)))^2 \, dx}{1-2 e \log (2)+e^2 \log ^2(2)}\\ &=\frac {\left (2 (1+e (1-\log (2)))^2\right ) \int \exp \left (\frac {x^2 (1+e (1-\log (2)))^2}{(1-e \log (2))^2}\right ) x \, dx}{(1-e \log (2))^2}\\ &=\exp \left (\frac {x^2 (1+e (1-\log (2)))^2}{(1-e \log (2))^2}\right )\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.22, size = 64, normalized size = 3.56 \begin {gather*} 2^{-1+\frac {1}{(-1+e \log (2))^2}} e^{\frac {e \log ^2(2) (-2+e \log (2))+x^2 \left (1+e^2 \left (1+\log ^2(2)-\log (4)\right )-e (-2+\log (4))\right )}{(-1+e \log (2))^2}} \end {gather*}

Warning: Unable to verify antiderivative.

[In]

Integrate[(E^((x^2 + 2*E*x^2 + E^2*x^2 + (-2*E*x^2 - 2*E^2*x^2)*Log[2] + E^2*x^2*Log[2]^2)/(1 - 2*E*Log[2] + E
^2*Log[2]^2))*(2*x + 4*E*x + 2*E^2*x + (-4*E*x - 4*E^2*x)*Log[2] + 2*E^2*x*Log[2]^2))/(1 - 2*E*Log[2] + E^2*Lo
g[2]^2),x]

[Out]

2^(-1 + (-1 + E*Log[2])^(-2))*E^((E*Log[2]^2*(-2 + E*Log[2]) + x^2*(1 + E^2*(1 + Log[2]^2 - Log[4]) - E*(-2 +
Log[4])))/(-1 + E*Log[2])^2)

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fricas [B]  time = 1.08, size = 63, normalized size = 3.50 \begin {gather*} e^{\left (\frac {x^{2} e^{2} \log \relax (2)^{2} + x^{2} e^{2} + 2 \, x^{2} e + x^{2} - 2 \, {\left (x^{2} e^{2} + x^{2} e\right )} \log \relax (2)}{e^{2} \log \relax (2)^{2} - 2 \, e \log \relax (2) + 1}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x*exp(1)^2*log(2)^2+(-4*x*exp(1)^2-4*x*exp(1))*log(2)+2*x*exp(1)^2+4*x*exp(1)+2*x)*exp((x^2*exp(1
)^2*log(2)^2+(-2*x^2*exp(1)^2-2*x^2*exp(1))*log(2)+x^2*exp(1)^2+2*x^2*exp(1)+x^2)/(exp(1)^2*log(2)^2-2*exp(1)*
log(2)+1))/(exp(1)^2*log(2)^2-2*exp(1)*log(2)+1),x, algorithm="fricas")

[Out]

e^((x^2*e^2*log(2)^2 + x^2*e^2 + 2*x^2*e + x^2 - 2*(x^2*e^2 + x^2*e)*log(2))/(e^2*log(2)^2 - 2*e*log(2) + 1))

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giac [B]  time = 0.22, size = 149, normalized size = 8.28 \begin {gather*} e^{\left (\frac {x^{2} e^{2} \log \relax (2)^{2}}{e^{2} \log \relax (2)^{2} - 2 \, e \log \relax (2) + 1} - \frac {2 \, x^{2} e^{2} \log \relax (2)}{e^{2} \log \relax (2)^{2} - 2 \, e \log \relax (2) + 1} - \frac {2 \, x^{2} e \log \relax (2)}{e^{2} \log \relax (2)^{2} - 2 \, e \log \relax (2) + 1} + \frac {x^{2} e^{2}}{e^{2} \log \relax (2)^{2} - 2 \, e \log \relax (2) + 1} + \frac {2 \, x^{2} e}{e^{2} \log \relax (2)^{2} - 2 \, e \log \relax (2) + 1} + \frac {x^{2}}{e^{2} \log \relax (2)^{2} - 2 \, e \log \relax (2) + 1}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x*exp(1)^2*log(2)^2+(-4*x*exp(1)^2-4*x*exp(1))*log(2)+2*x*exp(1)^2+4*x*exp(1)+2*x)*exp((x^2*exp(1
)^2*log(2)^2+(-2*x^2*exp(1)^2-2*x^2*exp(1))*log(2)+x^2*exp(1)^2+2*x^2*exp(1)+x^2)/(exp(1)^2*log(2)^2-2*exp(1)*
log(2)+1))/(exp(1)^2*log(2)^2-2*exp(1)*log(2)+1),x, algorithm="giac")

[Out]

e^(x^2*e^2*log(2)^2/(e^2*log(2)^2 - 2*e*log(2) + 1) - 2*x^2*e^2*log(2)/(e^2*log(2)^2 - 2*e*log(2) + 1) - 2*x^2
*e*log(2)/(e^2*log(2)^2 - 2*e*log(2) + 1) + x^2*e^2/(e^2*log(2)^2 - 2*e*log(2) + 1) + 2*x^2*e/(e^2*log(2)^2 -
2*e*log(2) + 1) + x^2/(e^2*log(2)^2 - 2*e*log(2) + 1))

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maple [B]  time = 0.13, size = 54, normalized size = 3.00

method	result	size
risch	\({\mathrm e}^{\frac {x^{2} \left (-{\mathrm e}^{2} \ln \relax (2)^{2}+2 \,{\mathrm e}^{2} \ln \relax (2)-{\mathrm e}^{2}+2 \,{\mathrm e} \ln \relax (2)-2 \,{\mathrm e}-1\right )}{-{\mathrm e}^{2} \ln \relax (2)^{2}+2 \,{\mathrm e} \ln \relax (2)-1}}\)	\(54\)
gosper	\({\mathrm e}^{\frac {x^{2} \left ({\mathrm e}^{2} \ln \relax (2)^{2}-2 \,{\mathrm e}^{2} \ln \relax (2)-2 \,{\mathrm e} \ln \relax (2)+{\mathrm e}^{2}+2 \,{\mathrm e}+1\right )}{{\mathrm e}^{2} \ln \relax (2)^{2}-2 \,{\mathrm e} \ln \relax (2)+1}}\)	\(58\)
derivativedivides	\({\mathrm e}^{\frac {x^{2} {\mathrm e}^{2} \ln \relax (2)^{2}+\left (-2 x^{2} {\mathrm e}^{2}-2 x^{2} {\mathrm e}\right ) \ln \relax (2)+x^{2} {\mathrm e}^{2}+2 x^{2} {\mathrm e}+x^{2}}{{\mathrm e}^{2} \ln \relax (2)^{2}-2 \,{\mathrm e} \ln \relax (2)+1}}\)	\(73\)
default	\({\mathrm e}^{\frac {x^{2} {\mathrm e}^{2} \ln \relax (2)^{2}+\left (-2 x^{2} {\mathrm e}^{2}-2 x^{2} {\mathrm e}\right ) \ln \relax (2)+x^{2} {\mathrm e}^{2}+2 x^{2} {\mathrm e}+x^{2}}{{\mathrm e}^{2} \ln \relax (2)^{2}-2 \,{\mathrm e} \ln \relax (2)+1}}\)	\(73\)
norman	\({\mathrm e}^{\frac {x^{2} {\mathrm e}^{2} \ln \relax (2)^{2}+\left (-2 x^{2} {\mathrm e}^{2}-2 x^{2} {\mathrm e}\right ) \ln \relax (2)+x^{2} {\mathrm e}^{2}+2 x^{2} {\mathrm e}+x^{2}}{{\mathrm e}^{2} \ln \relax (2)^{2}-2 \,{\mathrm e} \ln \relax (2)+1}}\)	\(73\)
meijerg	\(-\frac {\left (2 \,{\mathrm e}^{2} \ln \relax (2)^{2}-4 \,{\mathrm e}^{2} \ln \relax (2)+2 \,{\mathrm e}^{2}-4 \,{\mathrm e} \ln \relax (2)+4 \,{\mathrm e}+2\right ) \left (1-{\mathrm e}^{\frac {x^{2} \left ({\mathrm e}^{2} \ln \relax (2)^{2}+\ln \relax (2) \left (-2 \,{\mathrm e}^{2}-2 \,{\mathrm e}\right )+{\mathrm e}^{2}+2 \,{\mathrm e}+1\right )}{{\mathrm e}^{2} \ln \relax (2)^{2}-2 \,{\mathrm e} \ln \relax (2)+1}}\right )}{2 \left ({\mathrm e}^{2} \ln \relax (2)^{2}+\ln \relax (2) \left (-2 \,{\mathrm e}^{2}-2 \,{\mathrm e}\right )+{\mathrm e}^{2}+2 \,{\mathrm e}+1\right )}\)	\(115\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x*exp(1)^2*ln(2)^2+(-4*x*exp(1)^2-4*x*exp(1))*ln(2)+2*x*exp(1)^2+4*x*exp(1)+2*x)*exp((x^2*exp(1)^2*ln(2
)^2+(-2*x^2*exp(1)^2-2*x^2*exp(1))*ln(2)+x^2*exp(1)^2+2*x^2*exp(1)+x^2)/(exp(1)^2*ln(2)^2-2*exp(1)*ln(2)+1))/(
exp(1)^2*ln(2)^2-2*exp(1)*ln(2)+1),x,method=_RETURNVERBOSE)

[Out]

exp(x^2*(-exp(2)*ln(2)^2+2*exp(2)*ln(2)-exp(2)+2*exp(1)*ln(2)-2*exp(1)-1)/(-exp(2)*ln(2)^2+2*exp(1)*ln(2)-1))

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maxima [B]  time = 0.37, size = 1721, normalized size = 95.61 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x*exp(1)^2*log(2)^2+(-4*x*exp(1)^2-4*x*exp(1))*log(2)+2*x*exp(1)^2+4*x*exp(1)+2*x)*exp((x^2*exp(1
)^2*log(2)^2+(-2*x^2*exp(1)^2-2*x^2*exp(1))*log(2)+x^2*exp(1)^2+2*x^2*exp(1)+x^2)/(exp(1)^2*log(2)^2-2*exp(1)*
log(2)+1))/(exp(1)^2*log(2)^2-2*exp(1)*log(2)+1),x, algorithm="maxima")

[Out]

(e^(x^2*e^2*log(2)^2/(e^2*log(2)^2 - 2*e*log(2) + 1) - 2*x^2*e^2*log(2)/(e^2*log(2)^2 - 2*e*log(2) + 1) - 2*x^
2*e*log(2)/(e^2*log(2)^2 - 2*e*log(2) + 1) + x^2*e^2/(e^2*log(2)^2 - 2*e*log(2) + 1) + 2*x^2*e/(e^2*log(2)^2 -
2*e*log(2) + 1) + x^2/(e^2*log(2)^2 - 2*e*log(2) + 1) + 2)*log(2)^2/(e^2*log(2)^2/(e^2*log(2)^2 - 2*e*log(2)
+ 1) - 2*e^2*log(2)/(e^2*log(2)^2 - 2*e*log(2) + 1) - 2*e*log(2)/(e^2*log(2)^2 - 2*e*log(2) + 1) + e^2/(e^2*lo
g(2)^2 - 2*e*log(2) + 1) + 2*e/(e^2*log(2)^2 - 2*e*log(2) + 1) + 1/(e^2*log(2)^2 - 2*e*log(2) + 1)) - 2*e^(x^2
*e^2*log(2)^2/(e^2*log(2)^2 - 2*e*log(2) + 1) - 2*x^2*e^2*log(2)/(e^2*log(2)^2 - 2*e*log(2) + 1) - 2*x^2*e*log
(2)/(e^2*log(2)^2 - 2*e*log(2) + 1) + x^2*e^2/(e^2*log(2)^2 - 2*e*log(2) + 1) + 2*x^2*e/(e^2*log(2)^2 - 2*e*lo
g(2) + 1) + x^2/(e^2*log(2)^2 - 2*e*log(2) + 1) + 2)*log(2)/(e^2*log(2)^2/(e^2*log(2)^2 - 2*e*log(2) + 1) - 2*
e^2*log(2)/(e^2*log(2)^2 - 2*e*log(2) + 1) - 2*e*log(2)/(e^2*log(2)^2 - 2*e*log(2) + 1) + e^2/(e^2*log(2)^2 -
2*e*log(2) + 1) + 2*e/(e^2*log(2)^2 - 2*e*log(2) + 1) + 1/(e^2*log(2)^2 - 2*e*log(2) + 1)) - 2*e^(x^2*e^2*log(
2)^2/(e^2*log(2)^2 - 2*e*log(2) + 1) - 2*x^2*e^2*log(2)/(e^2*log(2)^2 - 2*e*log(2) + 1) - 2*x^2*e*log(2)/(e^2*
log(2)^2 - 2*e*log(2) + 1) + x^2*e^2/(e^2*log(2)^2 - 2*e*log(2) + 1) + 2*x^2*e/(e^2*log(2)^2 - 2*e*log(2) + 1)
+ x^2/(e^2*log(2)^2 - 2*e*log(2) + 1) + 1)*log(2)/(e^2*log(2)^2/(e^2*log(2)^2 - 2*e*log(2) + 1) - 2*e^2*log(2
)/(e^2*log(2)^2 - 2*e*log(2) + 1) - 2*e*log(2)/(e^2*log(2)^2 - 2*e*log(2) + 1) + e^2/(e^2*log(2)^2 - 2*e*log(2
) + 1) + 2*e/(e^2*log(2)^2 - 2*e*log(2) + 1) + 1/(e^2*log(2)^2 - 2*e*log(2) + 1)) + e^(x^2*e^2*log(2)^2/(e^2*l
og(2)^2 - 2*e*log(2) + 1) - 2*x^2*e^2*log(2)/(e^2*log(2)^2 - 2*e*log(2) + 1) - 2*x^2*e*log(2)/(e^2*log(2)^2 -
2*e*log(2) + 1) + x^2*e^2/(e^2*log(2)^2 - 2*e*log(2) + 1) + 2*x^2*e/(e^2*log(2)^2 - 2*e*log(2) + 1) + x^2/(e^2
*log(2)^2 - 2*e*log(2) + 1) + 2)/(e^2*log(2)^2/(e^2*log(2)^2 - 2*e*log(2) + 1) - 2*e^2*log(2)/(e^2*log(2)^2 -
2*e*log(2) + 1) - 2*e*log(2)/(e^2*log(2)^2 - 2*e*log(2) + 1) + e^2/(e^2*log(2)^2 - 2*e*log(2) + 1) + 2*e/(e^2*
log(2)^2 - 2*e*log(2) + 1) + 1/(e^2*log(2)^2 - 2*e*log(2) + 1)) + 2*e^(x^2*e^2*log(2)^2/(e^2*log(2)^2 - 2*e*lo
g(2) + 1) - 2*x^2*e^2*log(2)/(e^2*log(2)^2 - 2*e*log(2) + 1) - 2*x^2*e*log(2)/(e^2*log(2)^2 - 2*e*log(2) + 1)
+ x^2*e^2/(e^2*log(2)^2 - 2*e*log(2) + 1) + 2*x^2*e/(e^2*log(2)^2 - 2*e*log(2) + 1) + x^2/(e^2*log(2)^2 - 2*e*
log(2) + 1) + 1)/(e^2*log(2)^2/(e^2*log(2)^2 - 2*e*log(2) + 1) - 2*e^2*log(2)/(e^2*log(2)^2 - 2*e*log(2) + 1)
- 2*e*log(2)/(e^2*log(2)^2 - 2*e*log(2) + 1) + e^2/(e^2*log(2)^2 - 2*e*log(2) + 1) + 2*e/(e^2*log(2)^2 - 2*e*l
og(2) + 1) + 1/(e^2*log(2)^2 - 2*e*log(2) + 1)) + e^(x^2*e^2*log(2)^2/(e^2*log(2)^2 - 2*e*log(2) + 1) - 2*x^2*
e^2*log(2)/(e^2*log(2)^2 - 2*e*log(2) + 1) - 2*x^2*e*log(2)/(e^2*log(2)^2 - 2*e*log(2) + 1) + x^2*e^2/(e^2*log
(2)^2 - 2*e*log(2) + 1) + 2*x^2*e/(e^2*log(2)^2 - 2*e*log(2) + 1) + x^2/(e^2*log(2)^2 - 2*e*log(2) + 1))/(e^2*
log(2)^2/(e^2*log(2)^2 - 2*e*log(2) + 1) - 2*e^2*log(2)/(e^2*log(2)^2 - 2*e*log(2) + 1) - 2*e*log(2)/(e^2*log(
2)^2 - 2*e*log(2) + 1) + e^2/(e^2*log(2)^2 - 2*e*log(2) + 1) + 2*e/(e^2*log(2)^2 - 2*e*log(2) + 1) + 1/(e^2*lo
g(2)^2 - 2*e*log(2) + 1)))/(e^2*log(2)^2 - 2*e*log(2) + 1)

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mupad [B]  time = 0.59, size = 133, normalized size = 7.39 \begin {gather*} {\left (\frac {1}{4}\right )}^{\frac {x^2\,\mathrm {e}+x^2\,{\mathrm {e}}^2}{{\mathrm {e}}^2\,{\ln \relax (2)}^2-2\,\mathrm {e}\,\ln \relax (2)+1}}\,{\mathrm {e}}^{\frac {x^2}{{\mathrm {e}}^2\,{\ln \relax (2)}^2-2\,\mathrm {e}\,\ln \relax (2)+1}}\,{\mathrm {e}}^{\frac {x^2\,{\mathrm {e}}^2\,{\ln \relax (2)}^2}{{\mathrm {e}}^2\,{\ln \relax (2)}^2-2\,\mathrm {e}\,\ln \relax (2)+1}}\,{\mathrm {e}}^{\frac {x^2\,{\mathrm {e}}^2}{{\mathrm {e}}^2\,{\ln \relax (2)}^2-2\,\mathrm {e}\,\ln \relax (2)+1}}\,{\mathrm {e}}^{\frac {2\,x^2\,\mathrm {e}}{{\mathrm {e}}^2\,{\ln \relax (2)}^2-2\,\mathrm {e}\,\ln \relax (2)+1}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp((2*x^2*exp(1) - log(2)*(2*x^2*exp(1) + 2*x^2*exp(2)) + x^2*exp(2) + x^2 + x^2*exp(2)*log(2)^2)/(exp(2
)*log(2)^2 - 2*exp(1)*log(2) + 1))*(2*x + 4*x*exp(1) + 2*x*exp(2) - log(2)*(4*x*exp(1) + 4*x*exp(2)) + 2*x*exp
(2)*log(2)^2))/(exp(2)*log(2)^2 - 2*exp(1)*log(2) + 1),x)

[Out]

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

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sympy [B]  time = 0.26, size = 71, normalized size = 3.94 \begin {gather*} e^{\frac {x^{2} + x^{2} e^{2} \log {\relax (2 )}^{2} + 2 e x^{2} + x^{2} e^{2} + \left (- 2 x^{2} e^{2} - 2 e x^{2}\right ) \log {\relax (2 )}}{- 2 e \log {\relax (2 )} + 1 + e^{2} \log {\relax (2 )}^{2}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x*exp(1)**2*ln(2)**2+(-4*x*exp(1)**2-4*x*exp(1))*ln(2)+2*x*exp(1)**2+4*x*exp(1)+2*x)*exp((x**2*ex
p(1)**2*ln(2)**2+(-2*x**2*exp(1)**2-2*x**2*exp(1))*ln(2)+x**2*exp(1)**2+2*x**2*exp(1)+x**2)/(exp(1)**2*ln(2)**
2-2*exp(1)*ln(2)+1))/(exp(1)**2*ln(2)**2-2*exp(1)*ln(2)+1),x)

[Out]

exp((x**2 + x**2*exp(2)*log(2)**2 + 2*E*x**2 + x**2*exp(2) + (-2*x**2*exp(2) - 2*E*x**2)*log(2))/(-2*E*log(2)
+ 1 + exp(2)*log(2)**2))

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