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3.83.56 \(\int \frac {37968750000+16 e^{20 x^2}-31104 x+7593750000 x^2+607500000 x^4+24300000 x^6+486000 x^8+3888 x^{10}+e^{16 x^2} (6000+240 x^2)+e^{12 x^2} (900000+72000 x^2+1440 x^4)+e^{8 x^2} (67500000+8100000 x^2+324000 x^4+4320 x^6)+e^{4 x^2} (2531250000-41472 x+405000000 x^2+24300000 x^4+648000 x^6+6480 x^8)}{2373046875+e^{20 x^2}+474609375 x^2+37968750 x^4+1518750 x^6+30375 x^8+243 x^{10}+e^{16 x^2} (375+15 x^2)+e^{12 x^2} (56250+4500 x^2+90 x^4)+e^{8 x^2} (4218750+506250 x^2+20250 x^4+270 x^6)+e^{4 x^2} (158203125+25312500 x^2+1518750 x^4+40500 x^6+405 x^8)} \, dx\)

Optimal. Leaf size=22 \[ 16 \left (x+\frac {1}{\left (25+\frac {e^{4 x^2}}{3}+x^2\right )^4}\right ) \]

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Rubi [F]  time = 1.36, 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 {37968750000+16 e^{20 x^2}-31104 x+7593750000 x^2+607500000 x^4+24300000 x^6+486000 x^8+3888 x^{10}+e^{16 x^2} \left (6000+240 x^2\right )+e^{12 x^2} \left (900000+72000 x^2+1440 x^4\right )+e^{8 x^2} \left (67500000+8100000 x^2+324000 x^4+4320 x^6\right )+e^{4 x^2} \left (2531250000-41472 x+405000000 x^2+24300000 x^4+648000 x^6+6480 x^8\right )}{2373046875+e^{20 x^2}+474609375 x^2+37968750 x^4+1518750 x^6+30375 x^8+243 x^{10}+e^{16 x^2} \left (375+15 x^2\right )+e^{12 x^2} \left (56250+4500 x^2+90 x^4\right )+e^{8 x^2} \left (4218750+506250 x^2+20250 x^4+270 x^6\right )+e^{4 x^2} \left (158203125+25312500 x^2+1518750 x^4+40500 x^6+405 x^8\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(37968750000 + 16*E^(20*x^2) - 31104*x + 7593750000*x^2 + 607500000*x^4 + 24300000*x^6 + 486000*x^8 + 3888
*x^10 + E^(16*x^2)*(6000 + 240*x^2) + E^(12*x^2)*(900000 + 72000*x^2 + 1440*x^4) + E^(8*x^2)*(67500000 + 81000
00*x^2 + 324000*x^4 + 4320*x^6) + E^(4*x^2)*(2531250000 - 41472*x + 405000000*x^2 + 24300000*x^4 + 648000*x^6
+ 6480*x^8))/(2373046875 + E^(20*x^2) + 474609375*x^2 + 37968750*x^4 + 1518750*x^6 + 30375*x^8 + 243*x^10 + E^
(16*x^2)*(375 + 15*x^2) + E^(12*x^2)*(56250 + 4500*x^2 + 90*x^4) + E^(8*x^2)*(4218750 + 506250*x^2 + 20250*x^4
 + 270*x^6) + E^(4*x^2)*(158203125 + 25312500*x^2 + 1518750*x^4 + 40500*x^6 + 405*x^8)),x]

[Out]

16*x + 1539648*Defer[Subst][Defer[Int][(75 + E^(4*x) + 3*x)^(-5), x], x, x^2] + 62208*Defer[Subst][Defer[Int][
x/(75 + E^(4*x) + 3*x)^5, x], x, x^2] - 20736*Defer[Subst][Defer[Int][(75 + E^(4*x) + 3*x)^(-4), x], x, x^2]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {16 \left (e^{20 x^2}+15 e^{16 x^2} \left (25+x^2\right )+90 e^{12 x^2} \left (25+x^2\right )^2+270 e^{8 x^2} \left (25+x^2\right )^3+81 e^{4 x^2} \left (1953125-32 x+312500 x^2+18750 x^4+500 x^6+5 x^8\right )+243 \left (9765625-8 x+1953125 x^2+156250 x^4+6250 x^6+125 x^8+x^{10}\right )\right )}{\left (75+e^{4 x^2}+3 x^2\right )^5} \, dx\\ &=16 \int \frac {e^{20 x^2}+15 e^{16 x^2} \left (25+x^2\right )+90 e^{12 x^2} \left (25+x^2\right )^2+270 e^{8 x^2} \left (25+x^2\right )^3+81 e^{4 x^2} \left (1953125-32 x+312500 x^2+18750 x^4+500 x^6+5 x^8\right )+243 \left (9765625-8 x+1953125 x^2+156250 x^4+6250 x^6+125 x^8+x^{10}\right )}{\left (75+e^{4 x^2}+3 x^2\right )^5} \, dx\\ &=16 \int \left (1-\frac {2592 x}{\left (75+e^{4 x^2}+3 x^2\right )^4}+\frac {1944 x \left (99+4 x^2\right )}{\left (75+e^{4 x^2}+3 x^2\right )^5}\right ) \, dx\\ &=16 x+31104 \int \frac {x \left (99+4 x^2\right )}{\left (75+e^{4 x^2}+3 x^2\right )^5} \, dx-41472 \int \frac {x}{\left (75+e^{4 x^2}+3 x^2\right )^4} \, dx\\ &=16 x+15552 \operatorname {Subst}\left (\int \frac {99+4 x}{\left (75+e^{4 x}+3 x\right )^5} \, dx,x,x^2\right )-20736 \operatorname {Subst}\left (\int \frac {1}{\left (75+e^{4 x}+3 x\right )^4} \, dx,x,x^2\right )\\ &=16 x+15552 \operatorname {Subst}\left (\int \left (\frac {99}{\left (75+e^{4 x}+3 x\right )^5}+\frac {4 x}{\left (75+e^{4 x}+3 x\right )^5}\right ) \, dx,x,x^2\right )-20736 \operatorname {Subst}\left (\int \frac {1}{\left (75+e^{4 x}+3 x\right )^4} \, dx,x,x^2\right )\\ &=16 x-20736 \operatorname {Subst}\left (\int \frac {1}{\left (75+e^{4 x}+3 x\right )^4} \, dx,x,x^2\right )+62208 \operatorname {Subst}\left (\int \frac {x}{\left (75+e^{4 x}+3 x\right )^5} \, dx,x,x^2\right )+1539648 \operatorname {Subst}\left (\int \frac {1}{\left (75+e^{4 x}+3 x\right )^5} \, dx,x,x^2\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.07, size = 22, normalized size = 1.00 \begin {gather*} 16 \left (x+\frac {81}{\left (75+e^{4 x^2}+3 x^2\right )^4}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(37968750000 + 16*E^(20*x^2) - 31104*x + 7593750000*x^2 + 607500000*x^4 + 24300000*x^6 + 486000*x^8
+ 3888*x^10 + E^(16*x^2)*(6000 + 240*x^2) + E^(12*x^2)*(900000 + 72000*x^2 + 1440*x^4) + E^(8*x^2)*(67500000 +
 8100000*x^2 + 324000*x^4 + 4320*x^6) + E^(4*x^2)*(2531250000 - 41472*x + 405000000*x^2 + 24300000*x^4 + 64800
0*x^6 + 6480*x^8))/(2373046875 + E^(20*x^2) + 474609375*x^2 + 37968750*x^4 + 1518750*x^6 + 30375*x^8 + 243*x^1
0 + E^(16*x^2)*(375 + 15*x^2) + E^(12*x^2)*(56250 + 4500*x^2 + 90*x^4) + E^(8*x^2)*(4218750 + 506250*x^2 + 202
50*x^4 + 270*x^6) + E^(4*x^2)*(158203125 + 25312500*x^2 + 1518750*x^4 + 40500*x^6 + 405*x^8)),x]

[Out]

16*(x + 81/(75 + E^(4*x^2) + 3*x^2)^4)

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fricas [B]  time = 0.60, size = 179, normalized size = 8.14 \begin {gather*} \frac {16 \, {\left (81 \, x^{9} + 8100 \, x^{7} + 303750 \, x^{5} + 5062500 \, x^{3} + x e^{\left (16 \, x^{2}\right )} + 12 \, {\left (x^{3} + 25 \, x\right )} e^{\left (12 \, x^{2}\right )} + 54 \, {\left (x^{5} + 50 \, x^{3} + 625 \, x\right )} e^{\left (8 \, x^{2}\right )} + 108 \, {\left (x^{7} + 75 \, x^{5} + 1875 \, x^{3} + 15625 \, x\right )} e^{\left (4 \, x^{2}\right )} + 31640625 \, x + 81\right )}}{81 \, x^{8} + 8100 \, x^{6} + 303750 \, x^{4} + 5062500 \, x^{2} + 12 \, {\left (x^{2} + 25\right )} e^{\left (12 \, x^{2}\right )} + 54 \, {\left (x^{4} + 50 \, x^{2} + 625\right )} e^{\left (8 \, x^{2}\right )} + 108 \, {\left (x^{6} + 75 \, x^{4} + 1875 \, x^{2} + 15625\right )} e^{\left (4 \, x^{2}\right )} + e^{\left (16 \, x^{2}\right )} + 31640625} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*exp(4*x^2)^5+(240*x^2+6000)*exp(4*x^2)^4+(1440*x^4+72000*x^2+900000)*exp(4*x^2)^3+(4320*x^6+3240
00*x^4+8100000*x^2+67500000)*exp(4*x^2)^2+(6480*x^8+648000*x^6+24300000*x^4+405000000*x^2-41472*x+2531250000)*
exp(4*x^2)+3888*x^10+486000*x^8+24300000*x^6+607500000*x^4+7593750000*x^2-31104*x+37968750000)/(exp(4*x^2)^5+(
15*x^2+375)*exp(4*x^2)^4+(90*x^4+4500*x^2+56250)*exp(4*x^2)^3+(270*x^6+20250*x^4+506250*x^2+4218750)*exp(4*x^2
)^2+(405*x^8+40500*x^6+1518750*x^4+25312500*x^2+158203125)*exp(4*x^2)+243*x^10+30375*x^8+1518750*x^6+37968750*
x^4+474609375*x^2+2373046875),x, algorithm="fricas")

[Out]

16*(81*x^9 + 8100*x^7 + 303750*x^5 + 5062500*x^3 + x*e^(16*x^2) + 12*(x^3 + 25*x)*e^(12*x^2) + 54*(x^5 + 50*x^
3 + 625*x)*e^(8*x^2) + 108*(x^7 + 75*x^5 + 1875*x^3 + 15625*x)*e^(4*x^2) + 31640625*x + 81)/(81*x^8 + 8100*x^6
 + 303750*x^4 + 5062500*x^2 + 12*(x^2 + 25)*e^(12*x^2) + 54*(x^4 + 50*x^2 + 625)*e^(8*x^2) + 108*(x^6 + 75*x^4
 + 1875*x^2 + 15625)*e^(4*x^2) + e^(16*x^2) + 31640625)

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giac [B]  time = 0.36, size = 248, normalized size = 11.27 \begin {gather*} \frac {16 \, {\left (81 \, x^{9} + 108 \, x^{7} e^{\left (4 \, x^{2}\right )} + 8100 \, x^{7} + 54 \, x^{5} e^{\left (8 \, x^{2}\right )} + 8100 \, x^{5} e^{\left (4 \, x^{2}\right )} + 303750 \, x^{5} + 12 \, x^{3} e^{\left (12 \, x^{2}\right )} + 2700 \, x^{3} e^{\left (8 \, x^{2}\right )} + 202500 \, x^{3} e^{\left (4 \, x^{2}\right )} + 5062500 \, x^{3} + x e^{\left (16 \, x^{2}\right )} + 300 \, x e^{\left (12 \, x^{2}\right )} + 33750 \, x e^{\left (8 \, x^{2}\right )} + 1687500 \, x e^{\left (4 \, x^{2}\right )} + 31640625 \, x + 81\right )}}{81 \, x^{8} + 108 \, x^{6} e^{\left (4 \, x^{2}\right )} + 8100 \, x^{6} + 54 \, x^{4} e^{\left (8 \, x^{2}\right )} + 8100 \, x^{4} e^{\left (4 \, x^{2}\right )} + 303750 \, x^{4} + 12 \, x^{2} e^{\left (12 \, x^{2}\right )} + 2700 \, x^{2} e^{\left (8 \, x^{2}\right )} + 202500 \, x^{2} e^{\left (4 \, x^{2}\right )} + 5062500 \, x^{2} + e^{\left (16 \, x^{2}\right )} + 300 \, e^{\left (12 \, x^{2}\right )} + 33750 \, e^{\left (8 \, x^{2}\right )} + 1687500 \, e^{\left (4 \, x^{2}\right )} + 31640625} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*exp(4*x^2)^5+(240*x^2+6000)*exp(4*x^2)^4+(1440*x^4+72000*x^2+900000)*exp(4*x^2)^3+(4320*x^6+3240
00*x^4+8100000*x^2+67500000)*exp(4*x^2)^2+(6480*x^8+648000*x^6+24300000*x^4+405000000*x^2-41472*x+2531250000)*
exp(4*x^2)+3888*x^10+486000*x^8+24300000*x^6+607500000*x^4+7593750000*x^2-31104*x+37968750000)/(exp(4*x^2)^5+(
15*x^2+375)*exp(4*x^2)^4+(90*x^4+4500*x^2+56250)*exp(4*x^2)^3+(270*x^6+20250*x^4+506250*x^2+4218750)*exp(4*x^2
)^2+(405*x^8+40500*x^6+1518750*x^4+25312500*x^2+158203125)*exp(4*x^2)+243*x^10+30375*x^8+1518750*x^6+37968750*
x^4+474609375*x^2+2373046875),x, algorithm="giac")

[Out]

16*(81*x^9 + 108*x^7*e^(4*x^2) + 8100*x^7 + 54*x^5*e^(8*x^2) + 8100*x^5*e^(4*x^2) + 303750*x^5 + 12*x^3*e^(12*
x^2) + 2700*x^3*e^(8*x^2) + 202500*x^3*e^(4*x^2) + 5062500*x^3 + x*e^(16*x^2) + 300*x*e^(12*x^2) + 33750*x*e^(
8*x^2) + 1687500*x*e^(4*x^2) + 31640625*x + 81)/(81*x^8 + 108*x^6*e^(4*x^2) + 8100*x^6 + 54*x^4*e^(8*x^2) + 81
00*x^4*e^(4*x^2) + 303750*x^4 + 12*x^2*e^(12*x^2) + 2700*x^2*e^(8*x^2) + 202500*x^2*e^(4*x^2) + 5062500*x^2 +
e^(16*x^2) + 300*e^(12*x^2) + 33750*e^(8*x^2) + 1687500*e^(4*x^2) + 31640625)

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maple [A]  time = 0.06, size = 22, normalized size = 1.00

method result size
risch \(16 x +\frac {1296}{\left (3 x^{2}+{\mathrm e}^{4 x^{2}}+75\right )^{4}}\) \(22\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((16*exp(4*x^2)^5+(240*x^2+6000)*exp(4*x^2)^4+(1440*x^4+72000*x^2+900000)*exp(4*x^2)^3+(4320*x^6+324000*x^4
+8100000*x^2+67500000)*exp(4*x^2)^2+(6480*x^8+648000*x^6+24300000*x^4+405000000*x^2-41472*x+2531250000)*exp(4*
x^2)+3888*x^10+486000*x^8+24300000*x^6+607500000*x^4+7593750000*x^2-31104*x+37968750000)/(exp(4*x^2)^5+(15*x^2
+375)*exp(4*x^2)^4+(90*x^4+4500*x^2+56250)*exp(4*x^2)^3+(270*x^6+20250*x^4+506250*x^2+4218750)*exp(4*x^2)^2+(4
05*x^8+40500*x^6+1518750*x^4+25312500*x^2+158203125)*exp(4*x^2)+243*x^10+30375*x^8+1518750*x^6+37968750*x^4+47
4609375*x^2+2373046875),x,method=_RETURNVERBOSE)

[Out]

16*x+1296/(3*x^2+exp(4*x^2)+75)^4

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maxima [B]  time = 0.43, size = 179, normalized size = 8.14 \begin {gather*} \frac {16 \, {\left (81 \, x^{9} + 8100 \, x^{7} + 303750 \, x^{5} + 5062500 \, x^{3} + x e^{\left (16 \, x^{2}\right )} + 12 \, {\left (x^{3} + 25 \, x\right )} e^{\left (12 \, x^{2}\right )} + 54 \, {\left (x^{5} + 50 \, x^{3} + 625 \, x\right )} e^{\left (8 \, x^{2}\right )} + 108 \, {\left (x^{7} + 75 \, x^{5} + 1875 \, x^{3} + 15625 \, x\right )} e^{\left (4 \, x^{2}\right )} + 31640625 \, x + 81\right )}}{81 \, x^{8} + 8100 \, x^{6} + 303750 \, x^{4} + 5062500 \, x^{2} + 12 \, {\left (x^{2} + 25\right )} e^{\left (12 \, x^{2}\right )} + 54 \, {\left (x^{4} + 50 \, x^{2} + 625\right )} e^{\left (8 \, x^{2}\right )} + 108 \, {\left (x^{6} + 75 \, x^{4} + 1875 \, x^{2} + 15625\right )} e^{\left (4 \, x^{2}\right )} + e^{\left (16 \, x^{2}\right )} + 31640625} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*exp(4*x^2)^5+(240*x^2+6000)*exp(4*x^2)^4+(1440*x^4+72000*x^2+900000)*exp(4*x^2)^3+(4320*x^6+3240
00*x^4+8100000*x^2+67500000)*exp(4*x^2)^2+(6480*x^8+648000*x^6+24300000*x^4+405000000*x^2-41472*x+2531250000)*
exp(4*x^2)+3888*x^10+486000*x^8+24300000*x^6+607500000*x^4+7593750000*x^2-31104*x+37968750000)/(exp(4*x^2)^5+(
15*x^2+375)*exp(4*x^2)^4+(90*x^4+4500*x^2+56250)*exp(4*x^2)^3+(270*x^6+20250*x^4+506250*x^2+4218750)*exp(4*x^2
)^2+(405*x^8+40500*x^6+1518750*x^4+25312500*x^2+158203125)*exp(4*x^2)+243*x^10+30375*x^8+1518750*x^6+37968750*
x^4+474609375*x^2+2373046875),x, algorithm="maxima")

[Out]

16*(81*x^9 + 8100*x^7 + 303750*x^5 + 5062500*x^3 + x*e^(16*x^2) + 12*(x^3 + 25*x)*e^(12*x^2) + 54*(x^5 + 50*x^
3 + 625*x)*e^(8*x^2) + 108*(x^7 + 75*x^5 + 1875*x^3 + 15625*x)*e^(4*x^2) + 31640625*x + 81)/(81*x^8 + 8100*x^6
 + 303750*x^4 + 5062500*x^2 + 12*(x^2 + 25)*e^(12*x^2) + 54*(x^4 + 50*x^2 + 625)*e^(8*x^2) + 108*(x^6 + 75*x^4
 + 1875*x^2 + 15625)*e^(4*x^2) + e^(16*x^2) + 31640625)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {16\,{\mathrm {e}}^{20\,x^2}-31104\,x+{\mathrm {e}}^{8\,x^2}\,\left (4320\,x^6+324000\,x^4+8100000\,x^2+67500000\right )+{\mathrm {e}}^{16\,x^2}\,\left (240\,x^2+6000\right )+{\mathrm {e}}^{4\,x^2}\,\left (6480\,x^8+648000\,x^6+24300000\,x^4+405000000\,x^2-41472\,x+2531250000\right )+{\mathrm {e}}^{12\,x^2}\,\left (1440\,x^4+72000\,x^2+900000\right )+7593750000\,x^2+607500000\,x^4+24300000\,x^6+486000\,x^8+3888\,x^{10}+37968750000}{{\mathrm {e}}^{20\,x^2}+{\mathrm {e}}^{8\,x^2}\,\left (270\,x^6+20250\,x^4+506250\,x^2+4218750\right )+{\mathrm {e}}^{4\,x^2}\,\left (405\,x^8+40500\,x^6+1518750\,x^4+25312500\,x^2+158203125\right )+{\mathrm {e}}^{16\,x^2}\,\left (15\,x^2+375\right )+{\mathrm {e}}^{12\,x^2}\,\left (90\,x^4+4500\,x^2+56250\right )+474609375\,x^2+37968750\,x^4+1518750\,x^6+30375\,x^8+243\,x^{10}+2373046875} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((16*exp(20*x^2) - 31104*x + exp(8*x^2)*(8100000*x^2 + 324000*x^4 + 4320*x^6 + 67500000) + exp(16*x^2)*(240
*x^2 + 6000) + exp(4*x^2)*(405000000*x^2 - 41472*x + 24300000*x^4 + 648000*x^6 + 6480*x^8 + 2531250000) + exp(
12*x^2)*(72000*x^2 + 1440*x^4 + 900000) + 7593750000*x^2 + 607500000*x^4 + 24300000*x^6 + 486000*x^8 + 3888*x^
10 + 37968750000)/(exp(20*x^2) + exp(8*x^2)*(506250*x^2 + 20250*x^4 + 270*x^6 + 4218750) + exp(4*x^2)*(2531250
0*x^2 + 1518750*x^4 + 40500*x^6 + 405*x^8 + 158203125) + exp(16*x^2)*(15*x^2 + 375) + exp(12*x^2)*(4500*x^2 +
90*x^4 + 56250) + 474609375*x^2 + 37968750*x^4 + 1518750*x^6 + 30375*x^8 + 243*x^10 + 2373046875),x)

[Out]

int((16*exp(20*x^2) - 31104*x + exp(8*x^2)*(8100000*x^2 + 324000*x^4 + 4320*x^6 + 67500000) + exp(16*x^2)*(240
*x^2 + 6000) + exp(4*x^2)*(405000000*x^2 - 41472*x + 24300000*x^4 + 648000*x^6 + 6480*x^8 + 2531250000) + exp(
12*x^2)*(72000*x^2 + 1440*x^4 + 900000) + 7593750000*x^2 + 607500000*x^4 + 24300000*x^6 + 486000*x^8 + 3888*x^
10 + 37968750000)/(exp(20*x^2) + exp(8*x^2)*(506250*x^2 + 20250*x^4 + 270*x^6 + 4218750) + exp(4*x^2)*(2531250
0*x^2 + 1518750*x^4 + 40500*x^6 + 405*x^8 + 158203125) + exp(16*x^2)*(15*x^2 + 375) + exp(12*x^2)*(4500*x^2 +
90*x^4 + 56250) + 474609375*x^2 + 37968750*x^4 + 1518750*x^6 + 30375*x^8 + 243*x^10 + 2373046875), x)

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sympy [B]  time = 0.42, size = 88, normalized size = 4.00 \begin {gather*} 16 x + \frac {1296}{81 x^{8} + 8100 x^{6} + 303750 x^{4} + 5062500 x^{2} + \left (12 x^{2} + 300\right ) e^{12 x^{2}} + \left (54 x^{4} + 2700 x^{2} + 33750\right ) e^{8 x^{2}} + \left (108 x^{6} + 8100 x^{4} + 202500 x^{2} + 1687500\right ) e^{4 x^{2}} + e^{16 x^{2}} + 31640625} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((16*exp(4*x**2)**5+(240*x**2+6000)*exp(4*x**2)**4+(1440*x**4+72000*x**2+900000)*exp(4*x**2)**3+(4320
*x**6+324000*x**4+8100000*x**2+67500000)*exp(4*x**2)**2+(6480*x**8+648000*x**6+24300000*x**4+405000000*x**2-41
472*x+2531250000)*exp(4*x**2)+3888*x**10+486000*x**8+24300000*x**6+607500000*x**4+7593750000*x**2-31104*x+3796
8750000)/(exp(4*x**2)**5+(15*x**2+375)*exp(4*x**2)**4+(90*x**4+4500*x**2+56250)*exp(4*x**2)**3+(270*x**6+20250
*x**4+506250*x**2+4218750)*exp(4*x**2)**2+(405*x**8+40500*x**6+1518750*x**4+25312500*x**2+158203125)*exp(4*x**
2)+243*x**10+30375*x**8+1518750*x**6+37968750*x**4+474609375*x**2+2373046875),x)

[Out]

16*x + 1296/(81*x**8 + 8100*x**6 + 303750*x**4 + 5062500*x**2 + (12*x**2 + 300)*exp(12*x**2) + (54*x**4 + 2700
*x**2 + 33750)*exp(8*x**2) + (108*x**6 + 8100*x**4 + 202500*x**2 + 1687500)*exp(4*x**2) + exp(16*x**2) + 31640
625)

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