3.94.57 \(\int (125000+30000 x+8 e^{4 x^2} x+2400 x^2+64 x^3+(150000+24000 x+960 x^2) \log (2)+(75000+7200 x+96 x^2) \log ^2(2)+(20000+960 x) \log ^3(2)+(3000+48 x) \log ^4(2)+240 \log ^5(2)+8 \log ^6(2)+e^{3 x^2} (-8-600 x-48 x^2-240 x \log (2)-24 x \log ^2(2))+e^{2 x^2} (600+15048 x+2400 x^2+96 x^3+(240+12000 x+960 x^2) \log (2)+(24+3600 x+96 x^2) \log ^2(2)+480 x \log ^3(2)+24 x \log ^4(2))+e^{x^2} (-15000-127400 x-30096 x^2-2400 x^3-64 x^4+(-12000-150960 x-24000 x^2-960 x^3) \log (2)+(-3600-75096 x-7200 x^2-96 x^3) \log ^2(2)+(-480-20000 x-960 x^2) \log ^3(2)+(-24-3000 x-48 x^2) \log ^4(2)-240 x \log ^5(2)-8 x \log ^6(2))) \, dx\)

Optimal. Leaf size=19 \[ \left (-e^{x^2}+2 x+(5+\log (2))^2\right )^4 \]

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Rubi [C]  time = 0.49, antiderivative size = 370, normalized size of antiderivative = 19.47, number of steps used = 35, number of rules used = 5, integrand size = 288, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.017, Rules used = {2209, 6, 2226, 2204, 2212} \begin {gather*} -24 \sqrt {\pi } \text {erfi}(x)+12 \sqrt {\pi } \left (627+\log ^4(2)+20 \log ^3(2)+150 \log ^2(2)+500 \log (2)\right ) \text {erfi}(x)-12 \sqrt {\pi } (5+\log (2))^4 \text {erfi}(x)+16 x^4+800 x^3+32 x^3 \log ^2(2)+320 x^3 \log (2)+24 e^{2 x^2} x^2+15000 x^2+48 e^{x^2} x-8 e^{3 x^2} x-12 e^{2 x^2}+e^{4 x^2}+3600 x^2 \log ^2(2)-24 e^{x^2} x \left (627+\log ^4(2)+20 \log ^3(2)+150 \log ^2(2)+500 \log (2)\right )-4 e^{x^2} (5+\log (2))^2 \left (637+\log ^4(2)+20 \log ^3(2)+150 \log ^2(2)+500 \log (2)\right )+6 e^{2 x^2} \left (627+\log ^4(2)+20 \log ^3(2)+150 \log ^2(2)+500 \log (2)\right )-48 e^{x^2} x^2 (5+\log (2))^2+12000 x^2 \log (2)+24 e^{2 x^2} x (5+\log (2))^2+48 e^{x^2} (5+\log (2))^2-4 e^{3 x^2} (5+\log (2))^2-32 e^{x^2} x^3+6 (2 x+125)^2 \log ^4(2)+\frac {40}{3} (6 x+125)^2 \log ^3(2)+75000 x \log ^2(2)+8 x \left (15625+\log ^6(2)+30 \log ^5(2)\right )+150000 x \log (2) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[125000 + 30000*x + 8*E^(4*x^2)*x + 2400*x^2 + 64*x^3 + (150000 + 24000*x + 960*x^2)*Log[2] + (75000 + 7200
*x + 96*x^2)*Log[2]^2 + (20000 + 960*x)*Log[2]^3 + (3000 + 48*x)*Log[2]^4 + 240*Log[2]^5 + 8*Log[2]^6 + E^(3*x
^2)*(-8 - 600*x - 48*x^2 - 240*x*Log[2] - 24*x*Log[2]^2) + E^(2*x^2)*(600 + 15048*x + 2400*x^2 + 96*x^3 + (240
+ 12000*x + 960*x^2)*Log[2] + (24 + 3600*x + 96*x^2)*Log[2]^2 + 480*x*Log[2]^3 + 24*x*Log[2]^4) + E^x^2*(-150
00 - 127400*x - 30096*x^2 - 2400*x^3 - 64*x^4 + (-12000 - 150960*x - 24000*x^2 - 960*x^3)*Log[2] + (-3600 - 75
096*x - 7200*x^2 - 96*x^3)*Log[2]^2 + (-480 - 20000*x - 960*x^2)*Log[2]^3 + (-24 - 3000*x - 48*x^2)*Log[2]^4 -
240*x*Log[2]^5 - 8*x*Log[2]^6),x]

[Out]

-12*E^(2*x^2) + E^(4*x^2) + 48*E^x^2*x - 8*E^(3*x^2)*x + 15000*x^2 + 24*E^(2*x^2)*x^2 + 800*x^3 - 32*E^x^2*x^3
+ 16*x^4 - 24*Sqrt[Pi]*Erfi[x] + 150000*x*Log[2] + 12000*x^2*Log[2] + 320*x^3*Log[2] + 75000*x*Log[2]^2 + 360
0*x^2*Log[2]^2 + 32*x^3*Log[2]^2 + (40*(125 + 6*x)^2*Log[2]^3)/3 + 6*(125 + 2*x)^2*Log[2]^4 + 48*E^x^2*(5 + Lo
g[2])^2 - 4*E^(3*x^2)*(5 + Log[2])^2 + 24*E^(2*x^2)*x*(5 + Log[2])^2 - 48*E^x^2*x^2*(5 + Log[2])^2 - 12*Sqrt[P
i]*Erfi[x]*(5 + Log[2])^4 + 6*E^(2*x^2)*(627 + 500*Log[2] + 150*Log[2]^2 + 20*Log[2]^3 + Log[2]^4) - 24*E^x^2*
x*(627 + 500*Log[2] + 150*Log[2]^2 + 20*Log[2]^3 + Log[2]^4) + 12*Sqrt[Pi]*Erfi[x]*(627 + 500*Log[2] + 150*Log
[2]^2 + 20*Log[2]^3 + Log[2]^4) - 4*E^x^2*(5 + Log[2])^2*(637 + 500*Log[2] + 150*Log[2]^2 + 20*Log[2]^3 + Log[
2]^4) + 8*x*(15625 + 30*Log[2]^5 + Log[2]^6)

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 2204

Int[(F_)^((a_.) + (b_.)*((c_.) + (d_.)*(x_))^2), x_Symbol] :> Simp[(F^a*Sqrt[Pi]*Erfi[(c + d*x)*Rt[b*Log[F], 2
]])/(2*d*Rt[b*Log[F], 2]), x] /; FreeQ[{F, a, b, c, d}, x] && PosQ[b]

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 2212

Int[(F_)^((a_.) + (b_.)*((c_.) + (d_.)*(x_))^(n_))*((c_.) + (d_.)*(x_))^(m_.), x_Symbol] :> Simp[((c + d*x)^(m
- n + 1)*F^(a + b*(c + d*x)^n))/(b*d*n*Log[F]), x] - Dist[(m - n + 1)/(b*n*Log[F]), Int[(c + d*x)^(m - n)*F^(
a + b*(c + d*x)^n), x], x] /; FreeQ[{F, a, b, c, d}, x] && IntegerQ[(2*(m + 1))/n] && LtQ[0, (m + 1)/n, 5] &&
IntegerQ[n] && (LtQ[0, n, m + 1] || LtQ[m, n, 0])

Rule 2226

Int[(F_)^((a_.) + (b_.)*((c_.) + (d_.)*(x_))^(n_))*(u_), x_Symbol] :> Int[ExpandLinearProduct[F^(a + b*(c + d*
x)^n), u, c, d, x], x] /; FreeQ[{F, a, b, c, d, n}, x] && PolynomialQ[u, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=15000 x^2+800 x^3+16 x^4+\frac {40}{3} (125+6 x)^2 \log ^3(2)+6 (125+2 x)^2 \log ^4(2)+8 x \left (15625+30 \log ^5(2)+\log ^6(2)\right )+8 \int e^{4 x^2} x \, dx+\log (2) \int \left (150000+24000 x+960 x^2\right ) \, dx+\log ^2(2) \int \left (75000+7200 x+96 x^2\right ) \, dx+\int e^{3 x^2} \left (-8-600 x-48 x^2-240 x \log (2)-24 x \log ^2(2)\right ) \, dx+\int e^{2 x^2} \left (600+15048 x+2400 x^2+96 x^3+\left (240+12000 x+960 x^2\right ) \log (2)+\left (24+3600 x+96 x^2\right ) \log ^2(2)+480 x \log ^3(2)+24 x \log ^4(2)\right ) \, dx+\int e^{x^2} \left (-15000-127400 x-30096 x^2-2400 x^3-64 x^4+\left (-12000-150960 x-24000 x^2-960 x^3\right ) \log (2)+\left (-3600-75096 x-7200 x^2-96 x^3\right ) \log ^2(2)+\left (-480-20000 x-960 x^2\right ) \log ^3(2)+\left (-24-3000 x-48 x^2\right ) \log ^4(2)-240 x \log ^5(2)-8 x \log ^6(2)\right ) \, dx\\ &=e^{4 x^2}+15000 x^2+800 x^3+16 x^4+150000 x \log (2)+12000 x^2 \log (2)+320 x^3 \log (2)+75000 x \log ^2(2)+3600 x^2 \log ^2(2)+32 x^3 \log ^2(2)+\frac {40}{3} (125+6 x)^2 \log ^3(2)+6 (125+2 x)^2 \log ^4(2)+8 x \left (15625+30 \log ^5(2)+\log ^6(2)\right )+\int e^{3 x^2} \left (-8-48 x^2+x (-600-240 \log (2))-24 x \log ^2(2)\right ) \, dx+\int e^{2 x^2} \left (600+2400 x^2+96 x^3+\left (240+12000 x+960 x^2\right ) \log (2)+\left (24+3600 x+96 x^2\right ) \log ^2(2)+24 x \log ^4(2)+x \left (15048+480 \log ^3(2)\right )\right ) \, dx+\int e^{x^2} \left (-15000-30096 x^2-2400 x^3-64 x^4+\left (-12000-150960 x-24000 x^2-960 x^3\right ) \log (2)+\left (-3600-75096 x-7200 x^2-96 x^3\right ) \log ^2(2)+\left (-480-20000 x-960 x^2\right ) \log ^3(2)+\left (-24-3000 x-48 x^2\right ) \log ^4(2)-8 x \log ^6(2)+x \left (-127400-240 \log ^5(2)\right )\right ) \, dx\\ &=e^{4 x^2}+15000 x^2+800 x^3+16 x^4+150000 x \log (2)+12000 x^2 \log (2)+320 x^3 \log (2)+75000 x \log ^2(2)+3600 x^2 \log ^2(2)+32 x^3 \log ^2(2)+\frac {40}{3} (125+6 x)^2 \log ^3(2)+6 (125+2 x)^2 \log ^4(2)+8 x \left (15625+30 \log ^5(2)+\log ^6(2)\right )+\int e^{3 x^2} \left (-8-48 x^2+x \left (-600-240 \log (2)-24 \log ^2(2)\right )\right ) \, dx+\int e^{2 x^2} \left (600+2400 x^2+96 x^3+\left (240+12000 x+960 x^2\right ) \log (2)+\left (24+3600 x+96 x^2\right ) \log ^2(2)+x \left (15048+480 \log ^3(2)+24 \log ^4(2)\right )\right ) \, dx+\int e^{x^2} \left (-15000-30096 x^2-2400 x^3-64 x^4+\left (-12000-150960 x-24000 x^2-960 x^3\right ) \log (2)+\left (-3600-75096 x-7200 x^2-96 x^3\right ) \log ^2(2)+\left (-480-20000 x-960 x^2\right ) \log ^3(2)+\left (-24-3000 x-48 x^2\right ) \log ^4(2)+x \left (-127400-240 \log ^5(2)-8 \log ^6(2)\right )\right ) \, dx\\ &=e^{4 x^2}+15000 x^2+800 x^3+16 x^4+150000 x \log (2)+12000 x^2 \log (2)+320 x^3 \log (2)+75000 x \log ^2(2)+3600 x^2 \log ^2(2)+32 x^3 \log ^2(2)+\frac {40}{3} (125+6 x)^2 \log ^3(2)+6 (125+2 x)^2 \log ^4(2)+8 x \left (15625+30 \log ^5(2)+\log ^6(2)\right )+\int \left (-8 e^{3 x^2}-48 e^{3 x^2} x^2-24 e^{3 x^2} x (5+\log (2))^2\right ) \, dx+\int \left (96 e^{2 x^2} x^3+24 e^{2 x^2} (5+\log (2))^2+96 e^{2 x^2} x^2 (5+\log (2))^2+24 e^{2 x^2} x \left (627+500 \log (2)+150 \log ^2(2)+20 \log ^3(2)+\log ^4(2)\right )\right ) \, dx+\int \left (-64 e^{x^2} x^4-96 e^{x^2} x^3 (5+\log (2))^2-24 e^{x^2} (5+\log (2))^4-48 e^{x^2} x^2 \left (627+500 \log (2)+150 \log ^2(2)+20 \log ^3(2)+\log ^4(2)\right )-8 e^{x^2} x (5+\log (2))^2 \left (637+500 \log (2)+150 \log ^2(2)+20 \log ^3(2)+\log ^4(2)\right )\right ) \, dx\\ &=e^{4 x^2}+15000 x^2+800 x^3+16 x^4+150000 x \log (2)+12000 x^2 \log (2)+320 x^3 \log (2)+75000 x \log ^2(2)+3600 x^2 \log ^2(2)+32 x^3 \log ^2(2)+\frac {40}{3} (125+6 x)^2 \log ^3(2)+6 (125+2 x)^2 \log ^4(2)+8 x \left (15625+30 \log ^5(2)+\log ^6(2)\right )-8 \int e^{3 x^2} \, dx-48 \int e^{3 x^2} x^2 \, dx-64 \int e^{x^2} x^4 \, dx+96 \int e^{2 x^2} x^3 \, dx+\left (24 (5+\log (2))^2\right ) \int e^{2 x^2} \, dx-\left (24 (5+\log (2))^2\right ) \int e^{3 x^2} x \, dx+\left (96 (5+\log (2))^2\right ) \int e^{2 x^2} x^2 \, dx-\left (96 (5+\log (2))^2\right ) \int e^{x^2} x^3 \, dx-\left (24 (5+\log (2))^4\right ) \int e^{x^2} \, dx+\left (24 \left (627+500 \log (2)+150 \log ^2(2)+20 \log ^3(2)+\log ^4(2)\right )\right ) \int e^{2 x^2} x \, dx-\left (48 \left (627+500 \log (2)+150 \log ^2(2)+20 \log ^3(2)+\log ^4(2)\right )\right ) \int e^{x^2} x^2 \, dx-\left (8 (5+\log (2))^2 \left (637+500 \log (2)+150 \log ^2(2)+20 \log ^3(2)+\log ^4(2)\right )\right ) \int e^{x^2} x \, dx\\ &=e^{4 x^2}-8 e^{3 x^2} x+15000 x^2+24 e^{2 x^2} x^2+800 x^3-32 e^{x^2} x^3+16 x^4-4 \sqrt {\frac {\pi }{3}} \text {erfi}\left (\sqrt {3} x\right )+150000 x \log (2)+12000 x^2 \log (2)+320 x^3 \log (2)+75000 x \log ^2(2)+3600 x^2 \log ^2(2)+32 x^3 \log ^2(2)+\frac {40}{3} (125+6 x)^2 \log ^3(2)+6 (125+2 x)^2 \log ^4(2)-4 e^{3 x^2} (5+\log (2))^2+24 e^{2 x^2} x (5+\log (2))^2-48 e^{x^2} x^2 (5+\log (2))^2+6 \sqrt {2 \pi } \text {erfi}\left (\sqrt {2} x\right ) (5+\log (2))^2-12 \sqrt {\pi } \text {erfi}(x) (5+\log (2))^4+6 e^{2 x^2} \left (627+500 \log (2)+150 \log ^2(2)+20 \log ^3(2)+\log ^4(2)\right )-24 e^{x^2} x \left (627+500 \log (2)+150 \log ^2(2)+20 \log ^3(2)+\log ^4(2)\right )-4 e^{x^2} (5+\log (2))^2 \left (637+500 \log (2)+150 \log ^2(2)+20 \log ^3(2)+\log ^4(2)\right )+8 x \left (15625+30 \log ^5(2)+\log ^6(2)\right )+8 \int e^{3 x^2} \, dx-48 \int e^{2 x^2} x \, dx+96 \int e^{x^2} x^2 \, dx-\left (24 (5+\log (2))^2\right ) \int e^{2 x^2} \, dx+\left (96 (5+\log (2))^2\right ) \int e^{x^2} x \, dx+\left (24 \left (627+500 \log (2)+150 \log ^2(2)+20 \log ^3(2)+\log ^4(2)\right )\right ) \int e^{x^2} \, dx\\ &=-12 e^{2 x^2}+e^{4 x^2}+48 e^{x^2} x-8 e^{3 x^2} x+15000 x^2+24 e^{2 x^2} x^2+800 x^3-32 e^{x^2} x^3+16 x^4+150000 x \log (2)+12000 x^2 \log (2)+320 x^3 \log (2)+75000 x \log ^2(2)+3600 x^2 \log ^2(2)+32 x^3 \log ^2(2)+\frac {40}{3} (125+6 x)^2 \log ^3(2)+6 (125+2 x)^2 \log ^4(2)+48 e^{x^2} (5+\log (2))^2-4 e^{3 x^2} (5+\log (2))^2+24 e^{2 x^2} x (5+\log (2))^2-48 e^{x^2} x^2 (5+\log (2))^2-12 \sqrt {\pi } \text {erfi}(x) (5+\log (2))^4+6 e^{2 x^2} \left (627+500 \log (2)+150 \log ^2(2)+20 \log ^3(2)+\log ^4(2)\right )-24 e^{x^2} x \left (627+500 \log (2)+150 \log ^2(2)+20 \log ^3(2)+\log ^4(2)\right )+12 \sqrt {\pi } \text {erfi}(x) \left (627+500 \log (2)+150 \log ^2(2)+20 \log ^3(2)+\log ^4(2)\right )-4 e^{x^2} (5+\log (2))^2 \left (637+500 \log (2)+150 \log ^2(2)+20 \log ^3(2)+\log ^4(2)\right )+8 x \left (15625+30 \log ^5(2)+\log ^6(2)\right )-48 \int e^{x^2} \, dx\\ &=-12 e^{2 x^2}+e^{4 x^2}+48 e^{x^2} x-8 e^{3 x^2} x+15000 x^2+24 e^{2 x^2} x^2+800 x^3-32 e^{x^2} x^3+16 x^4-24 \sqrt {\pi } \text {erfi}(x)+150000 x \log (2)+12000 x^2 \log (2)+320 x^3 \log (2)+75000 x \log ^2(2)+3600 x^2 \log ^2(2)+32 x^3 \log ^2(2)+\frac {40}{3} (125+6 x)^2 \log ^3(2)+6 (125+2 x)^2 \log ^4(2)+48 e^{x^2} (5+\log (2))^2-4 e^{3 x^2} (5+\log (2))^2+24 e^{2 x^2} x (5+\log (2))^2-48 e^{x^2} x^2 (5+\log (2))^2-12 \sqrt {\pi } \text {erfi}(x) (5+\log (2))^4+6 e^{2 x^2} \left (627+500 \log (2)+150 \log ^2(2)+20 \log ^3(2)+\log ^4(2)\right )-24 e^{x^2} x \left (627+500 \log (2)+150 \log ^2(2)+20 \log ^3(2)+\log ^4(2)\right )+12 \sqrt {\pi } \text {erfi}(x) \left (627+500 \log (2)+150 \log ^2(2)+20 \log ^3(2)+\log ^4(2)\right )-4 e^{x^2} (5+\log (2))^2 \left (637+500 \log (2)+150 \log ^2(2)+20 \log ^3(2)+\log ^4(2)\right )+8 x \left (15625+30 \log ^5(2)+\log ^6(2)\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.07, size = 19, normalized size = 1.00 \begin {gather*} \left (-e^{x^2}+2 x+(5+\log (2))^2\right )^4 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[125000 + 30000*x + 8*E^(4*x^2)*x + 2400*x^2 + 64*x^3 + (150000 + 24000*x + 960*x^2)*Log[2] + (75000
+ 7200*x + 96*x^2)*Log[2]^2 + (20000 + 960*x)*Log[2]^3 + (3000 + 48*x)*Log[2]^4 + 240*Log[2]^5 + 8*Log[2]^6 +
E^(3*x^2)*(-8 - 600*x - 48*x^2 - 240*x*Log[2] - 24*x*Log[2]^2) + E^(2*x^2)*(600 + 15048*x + 2400*x^2 + 96*x^3
+ (240 + 12000*x + 960*x^2)*Log[2] + (24 + 3600*x + 96*x^2)*Log[2]^2 + 480*x*Log[2]^3 + 24*x*Log[2]^4) + E^x^2
*(-15000 - 127400*x - 30096*x^2 - 2400*x^3 - 64*x^4 + (-12000 - 150960*x - 24000*x^2 - 960*x^3)*Log[2] + (-360
0 - 75096*x - 7200*x^2 - 96*x^3)*Log[2]^2 + (-480 - 20000*x - 960*x^2)*Log[2]^3 + (-24 - 3000*x - 48*x^2)*Log[
2]^4 - 240*x*Log[2]^5 - 8*x*Log[2]^6),x]

[Out]

(-E^x^2 + 2*x + (5 + Log[2])^2)^4

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fricas [B]  time = 0.47, size = 257, normalized size = 13.53 \begin {gather*} 8 \, x \log \relax (2)^{6} + 240 \, x \log \relax (2)^{5} + 24 \, {\left (x^{2} + 125 \, x\right )} \log \relax (2)^{4} + 16 \, x^{4} + 160 \, {\left (3 \, x^{2} + 125 \, x\right )} \log \relax (2)^{3} + 800 \, x^{3} + 8 \, {\left (4 \, x^{3} + 450 \, x^{2} + 9375 \, x\right )} \log \relax (2)^{2} + 15000 \, x^{2} - 4 \, {\left (\log \relax (2)^{2} + 2 \, x + 10 \, \log \relax (2) + 25\right )} e^{\left (3 \, x^{2}\right )} + 6 \, {\left (\log \relax (2)^{4} + 2 \, {\left (2 \, x + 75\right )} \log \relax (2)^{2} + 20 \, \log \relax (2)^{3} + 4 \, x^{2} + 20 \, {\left (2 \, x + 25\right )} \log \relax (2) + 100 \, x + 625\right )} e^{\left (2 \, x^{2}\right )} - 4 \, {\left (\log \relax (2)^{6} + 3 \, {\left (2 \, x + 125\right )} \log \relax (2)^{4} + 30 \, \log \relax (2)^{5} + 20 \, {\left (6 \, x + 125\right )} \log \relax (2)^{3} + 8 \, x^{3} + 3 \, {\left (4 \, x^{2} + 300 \, x + 3125\right )} \log \relax (2)^{2} + 300 \, x^{2} + 30 \, {\left (4 \, x^{2} + 100 \, x + 625\right )} \log \relax (2) + 3750 \, x + 15625\right )} e^{\left (x^{2}\right )} + 80 \, {\left (4 \, x^{3} + 150 \, x^{2} + 1875 \, x\right )} \log \relax (2) + 125000 \, x + e^{\left (4 \, x^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*x*exp(x^2)^4+(-24*x*log(2)^2-240*x*log(2)-48*x^2-600*x-8)*exp(x^2)^3+(24*x*log(2)^4+480*x*log(2)^3
+(96*x^2+3600*x+24)*log(2)^2+(960*x^2+12000*x+240)*log(2)+96*x^3+2400*x^2+15048*x+600)*exp(x^2)^2+(-8*x*log(2)
^6-240*x*log(2)^5+(-48*x^2-3000*x-24)*log(2)^4+(-960*x^2-20000*x-480)*log(2)^3+(-96*x^3-7200*x^2-75096*x-3600)
*log(2)^2+(-960*x^3-24000*x^2-150960*x-12000)*log(2)-64*x^4-2400*x^3-30096*x^2-127400*x-15000)*exp(x^2)+8*log(
2)^6+240*log(2)^5+(48*x+3000)*log(2)^4+(960*x+20000)*log(2)^3+(96*x^2+7200*x+75000)*log(2)^2+(960*x^2+24000*x+
150000)*log(2)+64*x^3+2400*x^2+30000*x+125000,x, algorithm="fricas")

[Out]

8*x*log(2)^6 + 240*x*log(2)^5 + 24*(x^2 + 125*x)*log(2)^4 + 16*x^4 + 160*(3*x^2 + 125*x)*log(2)^3 + 800*x^3 +
8*(4*x^3 + 450*x^2 + 9375*x)*log(2)^2 + 15000*x^2 - 4*(log(2)^2 + 2*x + 10*log(2) + 25)*e^(3*x^2) + 6*(log(2)^
4 + 2*(2*x + 75)*log(2)^2 + 20*log(2)^3 + 4*x^2 + 20*(2*x + 25)*log(2) + 100*x + 625)*e^(2*x^2) - 4*(log(2)^6
+ 3*(2*x + 125)*log(2)^4 + 30*log(2)^5 + 20*(6*x + 125)*log(2)^3 + 8*x^3 + 3*(4*x^2 + 300*x + 3125)*log(2)^2 +
300*x^2 + 30*(4*x^2 + 100*x + 625)*log(2) + 3750*x + 15625)*e^(x^2) + 80*(4*x^3 + 150*x^2 + 1875*x)*log(2) +
125000*x + e^(4*x^2)

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giac [B]  time = 0.31, size = 271, normalized size = 14.26 \begin {gather*} 8 \, x \log \relax (2)^{6} + 240 \, x \log \relax (2)^{5} + 24 \, {\left (x^{2} + 125 \, x\right )} \log \relax (2)^{4} + 16 \, x^{4} + 160 \, {\left (3 \, x^{2} + 125 \, x\right )} \log \relax (2)^{3} + 800 \, x^{3} + 8 \, {\left (4 \, x^{3} + 450 \, x^{2} + 9375 \, x\right )} \log \relax (2)^{2} + 15000 \, x^{2} - 4 \, {\left (\log \relax (2)^{2} + 2 \, x + 10 \, \log \relax (2) + 25\right )} e^{\left (3 \, x^{2}\right )} + 6 \, {\left (\log \relax (2)^{4} + 4 \, x \log \relax (2)^{2} + 20 \, \log \relax (2)^{3} + 4 \, x^{2} + 40 \, x \log \relax (2) + 150 \, \log \relax (2)^{2} + 100 \, x + 500 \, \log \relax (2) + 625\right )} e^{\left (2 \, x^{2}\right )} - 4 \, {\left (\log \relax (2)^{6} + 6 \, x \log \relax (2)^{4} + 30 \, \log \relax (2)^{5} + 12 \, x^{2} \log \relax (2)^{2} + 120 \, x \log \relax (2)^{3} + 375 \, \log \relax (2)^{4} + 8 \, x^{3} + 120 \, x^{2} \log \relax (2) + 900 \, x \log \relax (2)^{2} + 2500 \, \log \relax (2)^{3} + 300 \, x^{2} + 3000 \, x \log \relax (2) + 9375 \, \log \relax (2)^{2} + 3750 \, x + 18750 \, \log \relax (2) + 15625\right )} e^{\left (x^{2}\right )} + 80 \, {\left (4 \, x^{3} + 150 \, x^{2} + 1875 \, x\right )} \log \relax (2) + 125000 \, x + e^{\left (4 \, x^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*x*exp(x^2)^4+(-24*x*log(2)^2-240*x*log(2)-48*x^2-600*x-8)*exp(x^2)^3+(24*x*log(2)^4+480*x*log(2)^3
+(96*x^2+3600*x+24)*log(2)^2+(960*x^2+12000*x+240)*log(2)+96*x^3+2400*x^2+15048*x+600)*exp(x^2)^2+(-8*x*log(2)
^6-240*x*log(2)^5+(-48*x^2-3000*x-24)*log(2)^4+(-960*x^2-20000*x-480)*log(2)^3+(-96*x^3-7200*x^2-75096*x-3600)
*log(2)^2+(-960*x^3-24000*x^2-150960*x-12000)*log(2)-64*x^4-2400*x^3-30096*x^2-127400*x-15000)*exp(x^2)+8*log(
2)^6+240*log(2)^5+(48*x+3000)*log(2)^4+(960*x+20000)*log(2)^3+(96*x^2+7200*x+75000)*log(2)^2+(960*x^2+24000*x+
150000)*log(2)+64*x^3+2400*x^2+30000*x+125000,x, algorithm="giac")

[Out]

8*x*log(2)^6 + 240*x*log(2)^5 + 24*(x^2 + 125*x)*log(2)^4 + 16*x^4 + 160*(3*x^2 + 125*x)*log(2)^3 + 800*x^3 +
8*(4*x^3 + 450*x^2 + 9375*x)*log(2)^2 + 15000*x^2 - 4*(log(2)^2 + 2*x + 10*log(2) + 25)*e^(3*x^2) + 6*(log(2)^
4 + 4*x*log(2)^2 + 20*log(2)^3 + 4*x^2 + 40*x*log(2) + 150*log(2)^2 + 100*x + 500*log(2) + 625)*e^(2*x^2) - 4*
(log(2)^6 + 6*x*log(2)^4 + 30*log(2)^5 + 12*x^2*log(2)^2 + 120*x*log(2)^3 + 375*log(2)^4 + 8*x^3 + 120*x^2*log
(2) + 900*x*log(2)^2 + 2500*log(2)^3 + 300*x^2 + 3000*x*log(2) + 9375*log(2)^2 + 3750*x + 18750*log(2) + 15625
)*e^(x^2) + 80*(4*x^3 + 150*x^2 + 1875*x)*log(2) + 125000*x + e^(4*x^2)

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maple [B]  time = 0.12, size = 285, normalized size = 15.00

method	result	size
norman	\({\mathrm e}^{4 x^{2}}+\left (-4 \ln \relax (2)^{2}-40 \ln \relax (2)-100\right ) {\mathrm e}^{3 x^{2}}+\left (320 \ln \relax (2)+800+32 \ln \relax (2)^{2}\right ) x^{3}+\left (6 \ln \relax (2)^{4}+120 \ln \relax (2)^{3}+900 \ln \relax (2)^{2}+3000 \ln \relax (2)+3750\right ) {\mathrm e}^{2 x^{2}}+\left (24 \ln \relax (2)^{4}+480 \ln \relax (2)^{3}+3600 \ln \relax (2)^{2}+12000 \ln \relax (2)+15000\right ) x^{2}+\left (-62500-1500 \ln \relax (2)^{4}-37500 \ln \relax (2)^{2}-10000 \ln \relax (2)^{3}-75000 \ln \relax (2)-4 \ln \relax (2)^{6}-120 \ln \relax (2)^{5}\right ) {\mathrm e}^{x^{2}}+\left (125000+3000 \ln \relax (2)^{4}+75000 \ln \relax (2)^{2}+20000 \ln \relax (2)^{3}+150000 \ln \relax (2)+8 \ln \relax (2)^{6}+240 \ln \relax (2)^{5}\right ) x +\left (24 \ln \relax (2)^{2}+240 \ln \relax (2)+600\right ) x \,{\mathrm e}^{2 x^{2}}+\left (-480 \ln \relax (2)-1200-48 \ln \relax (2)^{2}\right ) x^{2} {\mathrm e}^{x^{2}}+\left (-24 \ln \relax (2)^{4}-480 \ln \relax (2)^{3}-3600 \ln \relax (2)^{2}-12000 \ln \relax (2)-15000\right ) x \,{\mathrm e}^{x^{2}}+16 x^{4}+24 \,{\mathrm e}^{2 x^{2}} x^{2}-32 x^{3} {\mathrm e}^{x^{2}}-8 x \,{\mathrm e}^{3 x^{2}}\)	\(285\)
risch	\({\mathrm e}^{4 x^{2}}+\left (-4 \ln \relax (2)^{2}-40 \ln \relax (2)-8 x -100\right ) {\mathrm e}^{3 x^{2}}+\left (6 \ln \relax (2)^{4}+120 \ln \relax (2)^{3}+24 x \ln \relax (2)^{2}+900 \ln \relax (2)^{2}+240 x \ln \relax (2)+24 x^{2}+3000 \ln \relax (2)+600 x +3750\right ) {\mathrm e}^{2 x^{2}}+\left (-4 \ln \relax (2)^{6}-120 \ln \relax (2)^{5}-24 x \ln \relax (2)^{4}-1500 \ln \relax (2)^{4}-480 x \ln \relax (2)^{3}-48 x^{2} \ln \relax (2)^{2}-10000 \ln \relax (2)^{3}-3600 x \ln \relax (2)^{2}-480 x^{2} \ln \relax (2)-32 x^{3}-37500 \ln \relax (2)^{2}-12000 x \ln \relax (2)-1200 x^{2}-75000 \ln \relax (2)-15000 x -62500\right ) {\mathrm e}^{x^{2}}+8 x \ln \relax (2)^{6}+240 x \ln \relax (2)^{5}+24 x^{2} \ln \relax (2)^{4}+3000 x \ln \relax (2)^{4}+480 x^{2} \ln \relax (2)^{3}+20000 x \ln \relax (2)^{3}+32 x^{3} \ln \relax (2)^{2}+3600 x^{2} \ln \relax (2)^{2}+75000 x \ln \relax (2)^{2}+320 x^{3} \ln \relax (2)+12000 x^{2} \ln \relax (2)+150000 x \ln \relax (2)+16 x^{4}+800 x^{3}+15000 x^{2}+125000 x\)	\(285\)
default	\(125000 x +24 x^{2} \ln \relax (2)^{4}-1200 x^{2} {\mathrm e}^{x^{2}}+3750 \,{\mathrm e}^{2 x^{2}}-12000 x \ln \relax (2) {\mathrm e}^{x^{2}}-62500 \,{\mathrm e}^{x^{2}}+16 x^{4}+800 x^{3}+15000 x^{2}+480 x^{2} \ln \relax (2)^{3}-8 x \,{\mathrm e}^{3 x^{2}}+20000 x \ln \relax (2)^{3}+8 x \ln \relax (2)^{6}-75000 \ln \relax (2) {\mathrm e}^{x^{2}}+3000 x \ln \relax (2)^{4}-32 x^{3} {\mathrm e}^{x^{2}}+32 x^{3} \ln \relax (2)^{2}+600 x \,{\mathrm e}^{2 x^{2}}+75000 x \ln \relax (2)^{2}-15000 \,{\mathrm e}^{x^{2}} x +3600 x^{2} \ln \relax (2)^{2}+150000 x \ln \relax (2)+12000 x^{2} \ln \relax (2)+320 x^{3} \ln \relax (2)-100 \,{\mathrm e}^{3 x^{2}}+{\mathrm e}^{4 x^{2}}+240 x \ln \relax (2)^{5}-37500 \ln \relax (2)^{2} {\mathrm e}^{x^{2}}+24 \,{\mathrm e}^{2 x^{2}} x^{2}+240 \,{\mathrm e}^{2 x^{2}} x \ln \relax (2)+24 \,{\mathrm e}^{2 x^{2}} x \ln \relax (2)^{2}-480 \ln \relax (2) {\mathrm e}^{x^{2}} x^{2}-3600 \ln \relax (2)^{2} {\mathrm e}^{x^{2}} x -10000 \,{\mathrm e}^{x^{2}} \ln \relax (2)^{3}-1500 \,{\mathrm e}^{x^{2}} \ln \relax (2)^{4}-120 \ln \relax (2)^{5} {\mathrm e}^{x^{2}}-4 \ln \relax (2)^{6} {\mathrm e}^{x^{2}}-480 \,{\mathrm e}^{x^{2}} x \ln \relax (2)^{3}-24 \,{\mathrm e}^{x^{2}} x \ln \relax (2)^{4}-48 \ln \relax (2)^{2} {\mathrm e}^{x^{2}} x^{2}-40 \ln \relax (2) {\mathrm e}^{3 x^{2}}-4 \ln \relax (2)^{2} {\mathrm e}^{3 x^{2}}+3000 \,{\mathrm e}^{2 x^{2}} \ln \relax (2)+900 \,{\mathrm e}^{2 x^{2}} \ln \relax (2)^{2}+120 \ln \relax (2)^{3} {\mathrm e}^{2 x^{2}}+6 \ln \relax (2)^{4} {\mathrm e}^{2 x^{2}}\)	\(408\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(8*x*exp(x^2)^4+(-24*x*ln(2)^2-240*x*ln(2)-48*x^2-600*x-8)*exp(x^2)^3+(24*x*ln(2)^4+480*x*ln(2)^3+(96*x^2+3
600*x+24)*ln(2)^2+(960*x^2+12000*x+240)*ln(2)+96*x^3+2400*x^2+15048*x+600)*exp(x^2)^2+(-8*x*ln(2)^6-240*x*ln(2
)^5+(-48*x^2-3000*x-24)*ln(2)^4+(-960*x^2-20000*x-480)*ln(2)^3+(-96*x^3-7200*x^2-75096*x-3600)*ln(2)^2+(-960*x
^3-24000*x^2-150960*x-12000)*ln(2)-64*x^4-2400*x^3-30096*x^2-127400*x-15000)*exp(x^2)+8*ln(2)^6+240*ln(2)^5+(4
8*x+3000)*ln(2)^4+(960*x+20000)*ln(2)^3+(96*x^2+7200*x+75000)*ln(2)^2+(960*x^2+24000*x+150000)*ln(2)+64*x^3+24
00*x^2+30000*x+125000,x,method=_RETURNVERBOSE)

[Out]

exp(x^2)^4+(-4*ln(2)^2-40*ln(2)-100)*exp(x^2)^3+(320*ln(2)+800+32*ln(2)^2)*x^3+(6*ln(2)^4+120*ln(2)^3+900*ln(2
)^2+3000*ln(2)+3750)*exp(x^2)^2+(24*ln(2)^4+480*ln(2)^3+3600*ln(2)^2+12000*ln(2)+15000)*x^2+(-62500-1500*ln(2)
^4-37500*ln(2)^2-10000*ln(2)^3-75000*ln(2)-4*ln(2)^6-120*ln(2)^5)*exp(x^2)+(125000+3000*ln(2)^4+75000*ln(2)^2+
20000*ln(2)^3+150000*ln(2)+8*ln(2)^6+240*ln(2)^5)*x+(24*ln(2)^2+240*ln(2)+600)*x*exp(x^2)^2+(-480*ln(2)-1200-4
8*ln(2)^2)*x^2*exp(x^2)+(-24*ln(2)^4-480*ln(2)^3-3600*ln(2)^2-12000*ln(2)-15000)*x*exp(x^2)+16*x^4+24*x^2*exp(
x^2)^2-32*x^3*exp(x^2)-8*exp(x^2)^3*x

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maxima [B]  time = 0.49, size = 259, normalized size = 13.63 \begin {gather*} 8 \, x \log \relax (2)^{6} + 240 \, x \log \relax (2)^{5} + 24 \, {\left (x^{2} + 125 \, x\right )} \log \relax (2)^{4} + 16 \, x^{4} + 160 \, {\left (3 \, x^{2} + 125 \, x\right )} \log \relax (2)^{3} + 800 \, x^{3} + 8 \, {\left (4 \, x^{3} + 450 \, x^{2} + 9375 \, x\right )} \log \relax (2)^{2} + 15000 \, x^{2} - 4 \, {\left (\log \relax (2)^{2} + 2 \, x + 10 \, \log \relax (2) + 25\right )} e^{\left (3 \, x^{2}\right )} + 6 \, {\left (\log \relax (2)^{4} + 20 \, \log \relax (2)^{3} + 4 \, {\left (\log \relax (2)^{2} + 10 \, \log \relax (2) + 25\right )} x + 4 \, x^{2} + 150 \, \log \relax (2)^{2} + 500 \, \log \relax (2) + 625\right )} e^{\left (2 \, x^{2}\right )} - 4 \, {\left (\log \relax (2)^{6} + 30 \, \log \relax (2)^{5} + 375 \, \log \relax (2)^{4} + 12 \, {\left (\log \relax (2)^{2} + 10 \, \log \relax (2) + 25\right )} x^{2} + 8 \, x^{3} + 2500 \, \log \relax (2)^{3} + 6 \, {\left (\log \relax (2)^{4} + 20 \, \log \relax (2)^{3} + 150 \, \log \relax (2)^{2} + 500 \, \log \relax (2) + 625\right )} x + 9375 \, \log \relax (2)^{2} + 18750 \, \log \relax (2) + 15625\right )} e^{\left (x^{2}\right )} + 80 \, {\left (4 \, x^{3} + 150 \, x^{2} + 1875 \, x\right )} \log \relax (2) + 125000 \, x + e^{\left (4 \, x^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*x*exp(x^2)^4+(-24*x*log(2)^2-240*x*log(2)-48*x^2-600*x-8)*exp(x^2)^3+(24*x*log(2)^4+480*x*log(2)^3
+(96*x^2+3600*x+24)*log(2)^2+(960*x^2+12000*x+240)*log(2)+96*x^3+2400*x^2+15048*x+600)*exp(x^2)^2+(-8*x*log(2)
^6-240*x*log(2)^5+(-48*x^2-3000*x-24)*log(2)^4+(-960*x^2-20000*x-480)*log(2)^3+(-96*x^3-7200*x^2-75096*x-3600)
*log(2)^2+(-960*x^3-24000*x^2-150960*x-12000)*log(2)-64*x^4-2400*x^3-30096*x^2-127400*x-15000)*exp(x^2)+8*log(
2)^6+240*log(2)^5+(48*x+3000)*log(2)^4+(960*x+20000)*log(2)^3+(96*x^2+7200*x+75000)*log(2)^2+(960*x^2+24000*x+
150000)*log(2)+64*x^3+2400*x^2+30000*x+125000,x, algorithm="maxima")

[Out]

8*x*log(2)^6 + 240*x*log(2)^5 + 24*(x^2 + 125*x)*log(2)^4 + 16*x^4 + 160*(3*x^2 + 125*x)*log(2)^3 + 800*x^3 +
8*(4*x^3 + 450*x^2 + 9375*x)*log(2)^2 + 15000*x^2 - 4*(log(2)^2 + 2*x + 10*log(2) + 25)*e^(3*x^2) + 6*(log(2)^
4 + 20*log(2)^3 + 4*(log(2)^2 + 10*log(2) + 25)*x + 4*x^2 + 150*log(2)^2 + 500*log(2) + 625)*e^(2*x^2) - 4*(lo
g(2)^6 + 30*log(2)^5 + 375*log(2)^4 + 12*(log(2)^2 + 10*log(2) + 25)*x^2 + 8*x^3 + 2500*log(2)^3 + 6*(log(2)^4
+ 20*log(2)^3 + 150*log(2)^2 + 500*log(2) + 625)*x + 9375*log(2)^2 + 18750*log(2) + 15625)*e^(x^2) + 80*(4*x^
3 + 150*x^2 + 1875*x)*log(2) + 125000*x + e^(4*x^2)

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mupad [B]  time = 0.41, size = 231, normalized size = 12.16 \begin {gather*} {\mathrm {e}}^{4\,x^2}-4\,{\mathrm {e}}^{3\,x^2}\,{\left (\ln \relax (2)+5\right )}^2+6\,{\mathrm {e}}^{2\,x^2}\,{\left (\ln \relax (2)+5\right )}^4+32\,x^3\,{\left (\ln \relax (2)+5\right )}^2-8\,x\,{\mathrm {e}}^{3\,x^2}-32\,x^3\,{\mathrm {e}}^{x^2}-{\mathrm {e}}^{x^2}\,\left (75000\,\ln \relax (2)+37500\,{\ln \relax (2)}^2+10000\,{\ln \relax (2)}^3+1500\,{\ln \relax (2)}^4+120\,{\ln \relax (2)}^5+4\,{\ln \relax (2)}^6+62500\right )+24\,x^2\,{\mathrm {e}}^{2\,x^2}+16\,x^4+x\,\left (150000\,\ln \relax (2)+75000\,{\ln \relax (2)}^2+20000\,{\ln \relax (2)}^3+3000\,{\ln \relax (2)}^4+240\,{\ln \relax (2)}^5+8\,{\ln \relax (2)}^6+125000\right )+x^2\,\left (12000\,\ln \relax (2)+3600\,{\ln \relax (2)}^2+480\,{\ln \relax (2)}^3+24\,{\ln \relax (2)}^4+15000\right )-24\,x\,{\mathrm {e}}^{x^2}\,{\left (\ln \relax (2)+5\right )}^4+24\,x\,{\mathrm {e}}^{2\,x^2}\,{\left (\ln \relax (2)+5\right )}^2-48\,x^2\,{\mathrm {e}}^{x^2}\,{\left (\ln \relax (2)+5\right )}^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(30000*x - exp(x^2)*(127400*x + log(2)*(150960*x + 24000*x^2 + 960*x^3 + 12000) + log(2)^4*(3000*x + 48*x^2
+ 24) + log(2)^3*(20000*x + 960*x^2 + 480) + 240*x*log(2)^5 + 8*x*log(2)^6 + log(2)^2*(75096*x + 7200*x^2 + 9
6*x^3 + 3600) + 30096*x^2 + 2400*x^3 + 64*x^4 + 15000) + log(2)*(24000*x + 960*x^2 + 150000) - exp(3*x^2)*(600
*x + 240*x*log(2) + 24*x*log(2)^2 + 48*x^2 + 8) + log(2)^4*(48*x + 3000) + log(2)^3*(960*x + 20000) + 8*x*exp(
4*x^2) + log(2)^2*(7200*x + 96*x^2 + 75000) + exp(2*x^2)*(15048*x + log(2)*(12000*x + 960*x^2 + 240) + log(2)^
2*(3600*x + 96*x^2 + 24) + 480*x*log(2)^3 + 24*x*log(2)^4 + 2400*x^2 + 96*x^3 + 600) + 240*log(2)^5 + 8*log(2)
^6 + 2400*x^2 + 64*x^3 + 125000,x)

[Out]

exp(4*x^2) - 4*exp(3*x^2)*(log(2) + 5)^2 + 6*exp(2*x^2)*(log(2) + 5)^4 + 32*x^3*(log(2) + 5)^2 - 8*x*exp(3*x^2
) - 32*x^3*exp(x^2) - exp(x^2)*(75000*log(2) + 37500*log(2)^2 + 10000*log(2)^3 + 1500*log(2)^4 + 120*log(2)^5
+ 4*log(2)^6 + 62500) + 24*x^2*exp(2*x^2) + 16*x^4 + x*(150000*log(2) + 75000*log(2)^2 + 20000*log(2)^3 + 3000
*log(2)^4 + 240*log(2)^5 + 8*log(2)^6 + 125000) + x^2*(12000*log(2) + 3600*log(2)^2 + 480*log(2)^3 + 24*log(2)
^4 + 15000) - 24*x*exp(x^2)*(log(2) + 5)^4 + 24*x*exp(2*x^2)*(log(2) + 5)^2 - 48*x^2*exp(x^2)*(log(2) + 5)^2

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sympy [B]  time = 0.47, size = 296, normalized size = 15.58 \begin {gather*} 16 x^{4} + x^{3} \left (32 \log {\relax (2 )}^{2} + 320 \log {\relax (2 )} + 800\right ) + x^{2} \left (24 \log {\relax (2 )}^{4} + 480 \log {\relax (2 )}^{3} + 3600 \log {\relax (2 )}^{2} + 12000 \log {\relax (2 )} + 15000\right ) + x \left (8 \log {\relax (2 )}^{6} + 240 \log {\relax (2 )}^{5} + 3000 \log {\relax (2 )}^{4} + 20000 \log {\relax (2 )}^{3} + 75000 \log {\relax (2 )}^{2} + 150000 \log {\relax (2 )} + 125000\right ) + \left (- 8 x - 100 - 40 \log {\relax (2 )} - 4 \log {\relax (2 )}^{2}\right ) e^{3 x^{2}} + \left (24 x^{2} + 24 x \log {\relax (2 )}^{2} + 240 x \log {\relax (2 )} + 600 x + 6 \log {\relax (2 )}^{4} + 120 \log {\relax (2 )}^{3} + 900 \log {\relax (2 )}^{2} + 3000 \log {\relax (2 )} + 3750\right ) e^{2 x^{2}} + \left (- 32 x^{3} - 1200 x^{2} - 480 x^{2} \log {\relax (2 )} - 48 x^{2} \log {\relax (2 )}^{2} - 15000 x - 12000 x \log {\relax (2 )} - 3600 x \log {\relax (2 )}^{2} - 480 x \log {\relax (2 )}^{3} - 24 x \log {\relax (2 )}^{4} - 62500 - 75000 \log {\relax (2 )} - 37500 \log {\relax (2 )}^{2} - 10000 \log {\relax (2 )}^{3} - 1500 \log {\relax (2 )}^{4} - 120 \log {\relax (2 )}^{5} - 4 \log {\relax (2 )}^{6}\right ) e^{x^{2}} + e^{4 x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(8*x*exp(x**2)**4+(-24*x*ln(2)**2-240*x*ln(2)-48*x**2-600*x-8)*exp(x**2)**3+(24*x*ln(2)**4+480*x*ln(2
)**3+(96*x**2+3600*x+24)*ln(2)**2+(960*x**2+12000*x+240)*ln(2)+96*x**3+2400*x**2+15048*x+600)*exp(x**2)**2+(-8
*x*ln(2)**6-240*x*ln(2)**5+(-48*x**2-3000*x-24)*ln(2)**4+(-960*x**2-20000*x-480)*ln(2)**3+(-96*x**3-7200*x**2-
75096*x-3600)*ln(2)**2+(-960*x**3-24000*x**2-150960*x-12000)*ln(2)-64*x**4-2400*x**3-30096*x**2-127400*x-15000
)*exp(x**2)+8*ln(2)**6+240*ln(2)**5+(48*x+3000)*ln(2)**4+(960*x+20000)*ln(2)**3+(96*x**2+7200*x+75000)*ln(2)**
2+(960*x**2+24000*x+150000)*ln(2)+64*x**3+2400*x**2+30000*x+125000,x)

[Out]

16*x**4 + x**3*(32*log(2)**2 + 320*log(2) + 800) + x**2*(24*log(2)**4 + 480*log(2)**3 + 3600*log(2)**2 + 12000
*log(2) + 15000) + x*(8*log(2)**6 + 240*log(2)**5 + 3000*log(2)**4 + 20000*log(2)**3 + 75000*log(2)**2 + 15000
0*log(2) + 125000) + (-8*x - 100 - 40*log(2) - 4*log(2)**2)*exp(3*x**2) + (24*x**2 + 24*x*log(2)**2 + 240*x*lo
g(2) + 600*x + 6*log(2)**4 + 120*log(2)**3 + 900*log(2)**2 + 3000*log(2) + 3750)*exp(2*x**2) + (-32*x**3 - 120
0*x**2 - 480*x**2*log(2) - 48*x**2*log(2)**2 - 15000*x - 12000*x*log(2) - 3600*x*log(2)**2 - 480*x*log(2)**3 -
24*x*log(2)**4 - 62500 - 75000*log(2) - 37500*log(2)**2 - 10000*log(2)**3 - 1500*log(2)**4 - 120*log(2)**5 -
4*log(2)**6)*exp(x**2) + exp(4*x**2)

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