3.39.59 \(\int \frac {-100 x+40 x^2+e^{12 x^4} (-100 x+20 x^2+2400 x^5-960 x^6+96 x^7)+e^{6 x^4} (-200 x+60 x^2+2400 x^5-1440 x^6+192 x^7)}{625-1000 x+350 x^2+40 x^3+x^4+e^{6 x^4} (2500-3500 x+1300 x^2-100 x^3-8 x^4)+e^{24 x^4} (625-500 x+150 x^2-20 x^3+x^4)+e^{18 x^4} (2500-2500 x+900 x^2-140 x^3+8 x^4)+e^{12 x^4} (3750-4500 x+1700 x^2-260 x^3+14 x^4)} \, dx\)

Optimal. Leaf size=31 \[ \frac {2}{5-\left (-3+\frac {5-e^{6 x^4} (-5+x)+x}{x}\right )^2} \]

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Rubi [F]  time = 66.12, 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 {-100 x+40 x^2+e^{12 x^4} \left (-100 x+20 x^2+2400 x^5-960 x^6+96 x^7\right )+e^{6 x^4} \left (-200 x+60 x^2+2400 x^5-1440 x^6+192 x^7\right )}{625-1000 x+350 x^2+40 x^3+x^4+e^{6 x^4} \left (2500-3500 x+1300 x^2-100 x^3-8 x^4\right )+e^{24 x^4} \left (625-500 x+150 x^2-20 x^3+x^4\right )+e^{18 x^4} \left (2500-2500 x+900 x^2-140 x^3+8 x^4\right )+e^{12 x^4} \left (3750-4500 x+1700 x^2-260 x^3+14 x^4\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-100*x + 40*x^2 + E^(12*x^4)*(-100*x + 20*x^2 + 2400*x^5 - 960*x^6 + 96*x^7) + E^(6*x^4)*(-200*x + 60*x^2
+ 2400*x^5 - 1440*x^6 + 192*x^7))/(625 - 1000*x + 350*x^2 + 40*x^3 + x^4 + E^(6*x^4)*(2500 - 3500*x + 1300*x^
2 - 100*x^3 - 8*x^4) + E^(24*x^4)*(625 - 500*x + 150*x^2 - 20*x^3 + x^4) + E^(18*x^4)*(2500 - 2500*x + 900*x^2
- 140*x^3 + 8*x^4) + E^(12*x^4)*(3750 - 4500*x + 1700*x^2 - 260*x^3 + 14*x^4)),x]

[Out]

2000*Defer[Int][(25 + E^(12*x^4)*(-5 + x)^2 - 20*x - x^2 + E^(6*x^4)*(50 - 30*x + 4*x^2))^(-2), x] + 10000*Def
er[Int][1/((-5 + x)*(25 + E^(12*x^4)*(-5 + x)^2 - 20*x - x^2 + E^(6*x^4)*(50 - 30*x + 4*x^2))^2), x] + 400*Def
er[Int][x/(25 + E^(12*x^4)*(-5 + x)^2 - 20*x - x^2 + E^(6*x^4)*(50 - 30*x + 4*x^2))^2, x] + 60*Defer[Int][x^2/
(25 + E^(12*x^4)*(-5 + x)^2 - 20*x - x^2 + E^(6*x^4)*(50 - 30*x + 4*x^2))^2, x] - 20*Defer[Int][(E^(6*x^4)*x^2
)/(25 + E^(12*x^4)*(-5 + x)^2 - 20*x - x^2 + E^(6*x^4)*(50 - 30*x + 4*x^2))^2, x] - 2400*Defer[Int][x^5/(25 +
E^(12*x^4)*(-5 + x)^2 - 20*x - x^2 + E^(6*x^4)*(50 - 30*x + 4*x^2))^2, x] - 2400*Defer[Int][(E^(6*x^4)*x^5)/(2
5 + E^(12*x^4)*(-5 + x)^2 - 20*x - x^2 + E^(6*x^4)*(50 - 30*x + 4*x^2))^2, x] + 1920*Defer[Int][x^6/(25 + E^(1
2*x^4)*(-5 + x)^2 - 20*x - x^2 + E^(6*x^4)*(50 - 30*x + 4*x^2))^2, x] + 1440*Defer[Int][(E^(6*x^4)*x^6)/(25 +
E^(12*x^4)*(-5 + x)^2 - 20*x - x^2 + E^(6*x^4)*(50 - 30*x + 4*x^2))^2, x] + 96*Defer[Int][x^7/(25 + E^(12*x^4)
*(-5 + x)^2 - 20*x - x^2 + E^(6*x^4)*(50 - 30*x + 4*x^2))^2, x] - 192*Defer[Int][(E^(6*x^4)*x^7)/(25 + E^(12*x
^4)*(-5 + x)^2 - 20*x - x^2 + E^(6*x^4)*(50 - 30*x + 4*x^2))^2, x] + 20*Defer[Int][(25 + E^(12*x^4)*(-5 + x)^2
- 20*x - x^2 + E^(6*x^4)*(50 - 30*x + 4*x^2))^(-1), x] + 100*Defer[Int][1/((-5 + x)*(25 + E^(12*x^4)*(-5 + x)
^2 - 20*x - x^2 + E^(6*x^4)*(50 - 30*x + 4*x^2))), x] + 96*Defer[Int][x^5/(25 + E^(12*x^4)*(-5 + x)^2 - 20*x -
x^2 + E^(6*x^4)*(50 - 30*x + 4*x^2)), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 x \left (5 (-5+2 x)+e^{12 x^4} \left (-25+5 x+600 x^4-240 x^5+24 x^6\right )+e^{6 x^4} \left (-50+15 x+600 x^4-360 x^5+48 x^6\right )\right )}{\left (25+e^{12 x^4} (-5+x)^2-20 x-x^2+e^{6 x^4} \left (50-30 x+4 x^2\right )\right )^2} \, dx\\ &=4 \int \frac {x \left (5 (-5+2 x)+e^{12 x^4} \left (-25+5 x+600 x^4-240 x^5+24 x^6\right )+e^{6 x^4} \left (-50+15 x+600 x^4-360 x^5+48 x^6\right )\right )}{\left (25+e^{12 x^4} (-5+x)^2-20 x-x^2+e^{6 x^4} \left (50-30 x+4 x^2\right )\right )^2} \, dx\\ &=4 \int \left (\frac {x \left (5-120 x^4+24 x^5\right )}{(-5+x) \left (25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2\right )}-\frac {x^2 \left (-25-25 e^{6 x^4}-15 x+5 e^{6 x^4} x-3000 x^3-3000 e^{6 x^4} x^3+3000 x^4+2400 e^{6 x^4} x^4-360 x^5-600 e^{6 x^4} x^5-24 x^6+48 e^{6 x^4} x^6\right )}{(-5+x) \left (25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2\right )^2}\right ) \, dx\\ &=4 \int \frac {x \left (5-120 x^4+24 x^5\right )}{(-5+x) \left (25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2\right )} \, dx-4 \int \frac {x^2 \left (-25-25 e^{6 x^4}-15 x+5 e^{6 x^4} x-3000 x^3-3000 e^{6 x^4} x^3+3000 x^4+2400 e^{6 x^4} x^4-360 x^5-600 e^{6 x^4} x^5-24 x^6+48 e^{6 x^4} x^6\right )}{(-5+x) \left (25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2\right )^2} \, dx\\ &=4 \int \frac {x \left (-5+120 x^4-24 x^5\right )}{(5-x) \left (25+e^{12 x^4} (-5+x)^2-20 x-x^2+e^{6 x^4} \left (50-30 x+4 x^2\right )\right )} \, dx-4 \int \frac {x^2 \left (25+15 x+3000 x^3-3000 x^4+360 x^5+24 x^6-e^{6 x^4} \left (-25+5 x-3000 x^3+2400 x^4-600 x^5+48 x^6\right )\right )}{(5-x) \left (25+e^{12 x^4} (-5+x)^2-20 x-x^2+e^{6 x^4} \left (50-30 x+4 x^2\right )\right )^2} \, dx\\ &=4 \int \left (\frac {5}{25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2}+\frac {25}{(-5+x) \left (25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2\right )}+\frac {24 x^5}{25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2}\right ) \, dx-4 \int \left (\frac {5 \left (-25-25 e^{6 x^4}-15 x+5 e^{6 x^4} x-3000 x^3-3000 e^{6 x^4} x^3+3000 x^4+2400 e^{6 x^4} x^4-360 x^5-600 e^{6 x^4} x^5-24 x^6+48 e^{6 x^4} x^6\right )}{\left (25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2\right )^2}+\frac {25 \left (-25-25 e^{6 x^4}-15 x+5 e^{6 x^4} x-3000 x^3-3000 e^{6 x^4} x^3+3000 x^4+2400 e^{6 x^4} x^4-360 x^5-600 e^{6 x^4} x^5-24 x^6+48 e^{6 x^4} x^6\right )}{(-5+x) \left (25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2\right )^2}+\frac {x \left (-25-25 e^{6 x^4}-15 x+5 e^{6 x^4} x-3000 x^3-3000 e^{6 x^4} x^3+3000 x^4+2400 e^{6 x^4} x^4-360 x^5-600 e^{6 x^4} x^5-24 x^6+48 e^{6 x^4} x^6\right )}{\left (25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2\right )^2}\right ) \, dx\\ &=-\left (4 \int \frac {x \left (-25-25 e^{6 x^4}-15 x+5 e^{6 x^4} x-3000 x^3-3000 e^{6 x^4} x^3+3000 x^4+2400 e^{6 x^4} x^4-360 x^5-600 e^{6 x^4} x^5-24 x^6+48 e^{6 x^4} x^6\right )}{\left (25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2\right )^2} \, dx\right )+20 \int \frac {1}{25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2} \, dx-20 \int \frac {-25-25 e^{6 x^4}-15 x+5 e^{6 x^4} x-3000 x^3-3000 e^{6 x^4} x^3+3000 x^4+2400 e^{6 x^4} x^4-360 x^5-600 e^{6 x^4} x^5-24 x^6+48 e^{6 x^4} x^6}{\left (25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2\right )^2} \, dx+96 \int \frac {x^5}{25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2} \, dx+100 \int \frac {1}{(-5+x) \left (25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2\right )} \, dx-100 \int \frac {-25-25 e^{6 x^4}-15 x+5 e^{6 x^4} x-3000 x^3-3000 e^{6 x^4} x^3+3000 x^4+2400 e^{6 x^4} x^4-360 x^5-600 e^{6 x^4} x^5-24 x^6+48 e^{6 x^4} x^6}{(-5+x) \left (25+50 e^{6 x^4}+25 e^{12 x^4}-20 x-30 e^{6 x^4} x-10 e^{12 x^4} x-x^2+4 e^{6 x^4} x^2+e^{12 x^4} x^2\right )^2} \, dx\\ &=-\left (4 \int \frac {x \left (-25-15 x-3000 x^3+3000 x^4-360 x^5-24 x^6+e^{6 x^4} \left (-25+5 x-3000 x^3+2400 x^4-600 x^5+48 x^6\right )\right )}{\left (25+e^{12 x^4} (-5+x)^2-20 x-x^2+e^{6 x^4} \left (50-30 x+4 x^2\right )\right )^2} \, dx\right )+20 \int \frac {1}{25+e^{12 x^4} (-5+x)^2-20 x-x^2+e^{6 x^4} \left (50-30 x+4 x^2\right )} \, dx-20 \int \frac {-25-15 x-3000 x^3+3000 x^4-360 x^5-24 x^6+e^{6 x^4} \left (-25+5 x-3000 x^3+2400 x^4-600 x^5+48 x^6\right )}{\left (25+e^{12 x^4} (-5+x)^2-20 x-x^2+e^{6 x^4} \left (50-30 x+4 x^2\right )\right )^2} \, dx+96 \int \frac {x^5}{25+e^{12 x^4} (-5+x)^2-20 x-x^2+e^{6 x^4} \left (50-30 x+4 x^2\right )} \, dx+100 \int \frac {1}{(-5+x) \left (25+e^{12 x^4} (-5+x)^2-20 x-x^2+e^{6 x^4} \left (50-30 x+4 x^2\right )\right )} \, dx-100 \int \frac {25+15 x+3000 x^3-3000 x^4+360 x^5+24 x^6-e^{6 x^4} \left (-25+5 x-3000 x^3+2400 x^4-600 x^5+48 x^6\right )}{(5-x) \left (25+e^{12 x^4} (-5+x)^2-20 x-x^2+e^{6 x^4} \left (50-30 x+4 x^2\right )\right )^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.10, size = 48, normalized size = 1.55 \begin {gather*} -\frac {2 x^2}{25+e^{12 x^4} (-5+x)^2-20 x-x^2+e^{6 x^4} \left (50-30 x+4 x^2\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-100*x + 40*x^2 + E^(12*x^4)*(-100*x + 20*x^2 + 2400*x^5 - 960*x^6 + 96*x^7) + E^(6*x^4)*(-200*x +
60*x^2 + 2400*x^5 - 1440*x^6 + 192*x^7))/(625 - 1000*x + 350*x^2 + 40*x^3 + x^4 + E^(6*x^4)*(2500 - 3500*x + 1
300*x^2 - 100*x^3 - 8*x^4) + E^(24*x^4)*(625 - 500*x + 150*x^2 - 20*x^3 + x^4) + E^(18*x^4)*(2500 - 2500*x + 9
00*x^2 - 140*x^3 + 8*x^4) + E^(12*x^4)*(3750 - 4500*x + 1700*x^2 - 260*x^3 + 14*x^4)),x]

[Out]

(-2*x^2)/(25 + E^(12*x^4)*(-5 + x)^2 - 20*x - x^2 + E^(6*x^4)*(50 - 30*x + 4*x^2))

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fricas [A]  time = 0.61, size = 49, normalized size = 1.58 \begin {gather*} \frac {2 \, x^{2}}{x^{2} - {\left (x^{2} - 10 \, x + 25\right )} e^{\left (12 \, x^{4}\right )} - 2 \, {\left (2 \, x^{2} - 15 \, x + 25\right )} e^{\left (6 \, x^{4}\right )} + 20 \, x - 25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((96*x^7-960*x^6+2400*x^5+20*x^2-100*x)*exp(6*x^4)^2+(192*x^7-1440*x^6+2400*x^5+60*x^2-200*x)*exp(6*
x^4)+40*x^2-100*x)/((x^4-20*x^3+150*x^2-500*x+625)*exp(6*x^4)^4+(8*x^4-140*x^3+900*x^2-2500*x+2500)*exp(6*x^4)
^3+(14*x^4-260*x^3+1700*x^2-4500*x+3750)*exp(6*x^4)^2+(-8*x^4-100*x^3+1300*x^2-3500*x+2500)*exp(6*x^4)+x^4+40*
x^3+350*x^2-1000*x+625),x, algorithm="fricas")

[Out]

2*x^2/(x^2 - (x^2 - 10*x + 25)*e^(12*x^4) - 2*(2*x^2 - 15*x + 25)*e^(6*x^4) + 20*x - 25)

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giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((96*x^7-960*x^6+2400*x^5+20*x^2-100*x)*exp(6*x^4)^2+(192*x^7-1440*x^6+2400*x^5+60*x^2-200*x)*exp(6*
x^4)+40*x^2-100*x)/((x^4-20*x^3+150*x^2-500*x+625)*exp(6*x^4)^4+(8*x^4-140*x^3+900*x^2-2500*x+2500)*exp(6*x^4)
^3+(14*x^4-260*x^3+1700*x^2-4500*x+3750)*exp(6*x^4)^2+(-8*x^4-100*x^3+1300*x^2-3500*x+2500)*exp(6*x^4)+x^4+40*
x^3+350*x^2-1000*x+625),x, algorithm="giac")

[Out]

Timed out

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maple [B]  time = 0.06, size = 73, normalized size = 2.35

method	result	size
risch	\(-\frac {2 x^{2}}{{\mathrm e}^{12 x^{4}} x^{2}-10 \,{\mathrm e}^{12 x^{4}} x +4 \,{\mathrm e}^{6 x^{4}} x^{2}+25 \,{\mathrm e}^{12 x^{4}}-30 \,{\mathrm e}^{6 x^{4}} x -x^{2}+50 \,{\mathrm e}^{6 x^{4}}-20 x +25}\)	\(73\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((96*x^7-960*x^6+2400*x^5+20*x^2-100*x)*exp(6*x^4)^2+(192*x^7-1440*x^6+2400*x^5+60*x^2-200*x)*exp(6*x^4)+4
0*x^2-100*x)/((x^4-20*x^3+150*x^2-500*x+625)*exp(6*x^4)^4+(8*x^4-140*x^3+900*x^2-2500*x+2500)*exp(6*x^4)^3+(14
*x^4-260*x^3+1700*x^2-4500*x+3750)*exp(6*x^4)^2+(-8*x^4-100*x^3+1300*x^2-3500*x+2500)*exp(6*x^4)+x^4+40*x^3+35
0*x^2-1000*x+625),x,method=_RETURNVERBOSE)

[Out]

-2*x^2/(exp(12*x^4)*x^2-10*exp(12*x^4)*x+4*exp(6*x^4)*x^2+25*exp(12*x^4)-30*exp(6*x^4)*x-x^2+50*exp(6*x^4)-20*
x+25)

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maxima [A]  time = 0.43, size = 49, normalized size = 1.58 \begin {gather*} \frac {2 \, x^{2}}{x^{2} - {\left (x^{2} - 10 \, x + 25\right )} e^{\left (12 \, x^{4}\right )} - 2 \, {\left (2 \, x^{2} - 15 \, x + 25\right )} e^{\left (6 \, x^{4}\right )} + 20 \, x - 25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((96*x^7-960*x^6+2400*x^5+20*x^2-100*x)*exp(6*x^4)^2+(192*x^7-1440*x^6+2400*x^5+60*x^2-200*x)*exp(6*
x^4)+40*x^2-100*x)/((x^4-20*x^3+150*x^2-500*x+625)*exp(6*x^4)^4+(8*x^4-140*x^3+900*x^2-2500*x+2500)*exp(6*x^4)
^3+(14*x^4-260*x^3+1700*x^2-4500*x+3750)*exp(6*x^4)^2+(-8*x^4-100*x^3+1300*x^2-3500*x+2500)*exp(6*x^4)+x^4+40*
x^3+350*x^2-1000*x+625),x, algorithm="maxima")

[Out]

2*x^2/(x^2 - (x^2 - 10*x + 25)*e^(12*x^4) - 2*(2*x^2 - 15*x + 25)*e^(6*x^4) + 20*x - 25)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {{\mathrm {e}}^{12\,x^4}\,\left (96\,x^7-960\,x^6+2400\,x^5+20\,x^2-100\,x\right )-100\,x+{\mathrm {e}}^{6\,x^4}\,\left (192\,x^7-1440\,x^6+2400\,x^5+60\,x^2-200\,x\right )+40\,x^2}{{\mathrm {e}}^{24\,x^4}\,\left (x^4-20\,x^3+150\,x^2-500\,x+625\right )-1000\,x+{\mathrm {e}}^{18\,x^4}\,\left (8\,x^4-140\,x^3+900\,x^2-2500\,x+2500\right )-{\mathrm {e}}^{6\,x^4}\,\left (8\,x^4+100\,x^3-1300\,x^2+3500\,x-2500\right )+{\mathrm {e}}^{12\,x^4}\,\left (14\,x^4-260\,x^3+1700\,x^2-4500\,x+3750\right )+350\,x^2+40\,x^3+x^4+625} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(12*x^4)*(20*x^2 - 100*x + 2400*x^5 - 960*x^6 + 96*x^7) - 100*x + exp(6*x^4)*(60*x^2 - 200*x + 2400*x^
5 - 1440*x^6 + 192*x^7) + 40*x^2)/(exp(24*x^4)*(150*x^2 - 500*x - 20*x^3 + x^4 + 625) - 1000*x + exp(18*x^4)*(
900*x^2 - 2500*x - 140*x^3 + 8*x^4 + 2500) - exp(6*x^4)*(3500*x - 1300*x^2 + 100*x^3 + 8*x^4 - 2500) + exp(12*
x^4)*(1700*x^2 - 4500*x - 260*x^3 + 14*x^4 + 3750) + 350*x^2 + 40*x^3 + x^4 + 625),x)

[Out]

int((exp(12*x^4)*(20*x^2 - 100*x + 2400*x^5 - 960*x^6 + 96*x^7) - 100*x + exp(6*x^4)*(60*x^2 - 200*x + 2400*x^
5 - 1440*x^6 + 192*x^7) + 40*x^2)/(exp(24*x^4)*(150*x^2 - 500*x - 20*x^3 + x^4 + 625) - 1000*x + exp(18*x^4)*(
900*x^2 - 2500*x - 140*x^3 + 8*x^4 + 2500) - exp(6*x^4)*(3500*x - 1300*x^2 + 100*x^3 + 8*x^4 - 2500) + exp(12*
x^4)*(1700*x^2 - 4500*x - 260*x^3 + 14*x^4 + 3750) + 350*x^2 + 40*x^3 + x^4 + 625), x)

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sympy [B]  time = 0.54, size = 46, normalized size = 1.48 \begin {gather*} - \frac {2 x^{2}}{- x^{2} - 20 x + \left (x^{2} - 10 x + 25\right ) e^{12 x^{4}} + \left (4 x^{2} - 30 x + 50\right ) e^{6 x^{4}} + 25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((96*x**7-960*x**6+2400*x**5+20*x**2-100*x)*exp(6*x**4)**2+(192*x**7-1440*x**6+2400*x**5+60*x**2-200
*x)*exp(6*x**4)+40*x**2-100*x)/((x**4-20*x**3+150*x**2-500*x+625)*exp(6*x**4)**4+(8*x**4-140*x**3+900*x**2-250
0*x+2500)*exp(6*x**4)**3+(14*x**4-260*x**3+1700*x**2-4500*x+3750)*exp(6*x**4)**2+(-8*x**4-100*x**3+1300*x**2-3
500*x+2500)*exp(6*x**4)+x**4+40*x**3+350*x**2-1000*x+625),x)

[Out]

-2*x**2/(-x**2 - 20*x + (x**2 - 10*x + 25)*exp(12*x**4) + (4*x**2 - 30*x + 50)*exp(6*x**4) + 25)

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