3.62.79 \(\int \frac {-50+e^{12} (-5-2 x)+20 x+5 x^3+2 x^4+e^{3 x^2} (5+2 e^{20}+2 x)+e^8 (-10+15 x+6 x^2)+e^4 (-20+10 x-15 x^2-6 x^3)+e^{2 x^2} (-10+e^4 (-15-6 x)+55 x+26 x^2+e^{20} (-6 e^4+26 x))+e^{20} (-2 e^{12}+10 x+6 e^8 x+2 x^3+e^4 (-10-6 x^2))+e^{x^2} (20-110 x+55 x^2+26 x^3+e^8 (15+6 x)+e^4 (20-70 x-32 x^2)+e^{20} (10+6 e^8-32 e^4 x+26 x^2))}{-e^{12}+e^{3 x^2}+3 e^8 x-3 e^4 x^2+x^3+e^{2 x^2} (-3 e^4+3 x)+e^{x^2} (3 e^8-6 e^4 x+3 x^2)} \, dx\)

Optimal. Leaf size=27 \[ 3+x+\left (2+e^{20}+x-\frac {5}{-e^4+e^{x^2}+x}\right )^2 \]

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Rubi [F]  time = 5.41, 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 {-50+e^{12} (-5-2 x)+20 x+5 x^3+2 x^4+e^{3 x^2} \left (5+2 e^{20}+2 x\right )+e^8 \left (-10+15 x+6 x^2\right )+e^4 \left (-20+10 x-15 x^2-6 x^3\right )+e^{2 x^2} \left (-10+e^4 (-15-6 x)+55 x+26 x^2+e^{20} \left (-6 e^4+26 x\right )\right )+e^{20} \left (-2 e^{12}+10 x+6 e^8 x+2 x^3+e^4 \left (-10-6 x^2\right )\right )+e^{x^2} \left (20-110 x+55 x^2+26 x^3+e^8 (15+6 x)+e^4 \left (20-70 x-32 x^2\right )+e^{20} \left (10+6 e^8-32 e^4 x+26 x^2\right )\right )}{-e^{12}+e^{3 x^2}+3 e^8 x-3 e^4 x^2+x^3+e^{2 x^2} \left (-3 e^4+3 x\right )+e^{x^2} \left (3 e^8-6 e^4 x+3 x^2\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-50 + E^12*(-5 - 2*x) + 20*x + 5*x^3 + 2*x^4 + E^(3*x^2)*(5 + 2*E^20 + 2*x) + E^8*(-10 + 15*x + 6*x^2) +
E^4*(-20 + 10*x - 15*x^2 - 6*x^3) + E^(2*x^2)*(-10 + E^4*(-15 - 6*x) + 55*x + 26*x^2 + E^20*(-6*E^4 + 26*x)) +
E^20*(-2*E^12 + 10*x + 6*E^8*x + 2*x^3 + E^4*(-10 - 6*x^2)) + E^x^2*(20 - 110*x + 55*x^2 + 26*x^3 + E^8*(15 +
6*x) + E^4*(20 - 70*x - 32*x^2) + E^20*(10 + 6*E^8 - 32*E^4*x + 26*x^2)))/(-E^12 + E^(3*x^2) + 3*E^8*x - 3*E^
4*x^2 + x^3 + E^(2*x^2)*(-3*E^4 + 3*x) + E^x^2*(3*E^8 - 6*E^4*x + 3*x^2)),x]

[Out]

(5 + 2*E^20)*x + x^2 + 10*(2 + E^20)*Defer[Int][(E^4 - E^x^2 - x)^(-2), x] + 100*E^4*Defer[Int][x/(E^4 - E^x^2
- x)^3, x] - 20*(2 + E^20)*Defer[Int][x/(E^4 - E^x^2 - x), x] - 20*(2 - E^4 + E^20)*Defer[Int][x^2/(E^4 - E^x
^2 - x)^2, x] - 50*Defer[Int][(-E^4 + E^x^2 + x)^(-3), x] + 100*Defer[Int][x^2/(-E^4 + E^x^2 + x)^3, x] - 10*(
9 - 4*E^4 - 2*E^24)*Defer[Int][x/(-E^4 + E^x^2 + x)^2, x] - 20*Defer[Int][x^3/(-E^4 + E^x^2 + x)^2, x] - 10*De
fer[Int][(-E^4 + E^x^2 + x)^(-1), x] + 20*Defer[Int][x^2/(-E^4 + E^x^2 + x), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {50-e^{12} (-5-2 x)-20 x-5 x^3-2 x^4-e^{3 x^2} \left (5+2 e^{20}+2 x\right )-e^8 \left (-10+15 x+6 x^2\right )-e^4 \left (-20+10 x-15 x^2-6 x^3\right )-e^{2 x^2} \left (-10+e^4 (-15-6 x)+55 x+26 x^2+e^{20} \left (-6 e^4+26 x\right )\right )-e^{20} \left (-2 e^{12}+10 x+6 e^8 x+2 x^3+e^4 \left (-10-6 x^2\right )\right )-e^{x^2} \left (20-110 x+55 x^2+26 x^3+e^8 (15+6 x)+e^4 \left (20-70 x-32 x^2\right )+e^{20} \left (10+6 e^8-32 e^4 x+26 x^2\right )\right )}{\left (e^4-e^{x^2}-x\right )^3} \, dx\\ &=\int \left (5 \left (1+\frac {2 e^{20}}{5}\right )+2 x-\frac {50 \left (1+2 e^4 x-2 x^2\right )}{\left (-e^4+e^{x^2}+x\right )^3}+\frac {10 \left (1-2 \left (2+e^{20}\right ) x-2 x^2\right )}{e^4-e^{x^2}-x}+\frac {10 \left (2+e^{20}-\left (9-4 e^4-2 e^{24}\right ) x-2 \left (2-e^4+e^{20}\right ) x^2-2 x^3\right )}{\left (e^4-e^{x^2}-x\right )^2}\right ) \, dx\\ &=\left (5+2 e^{20}\right ) x+x^2+10 \int \frac {1-2 \left (2+e^{20}\right ) x-2 x^2}{e^4-e^{x^2}-x} \, dx+10 \int \frac {2+e^{20}-\left (9-4 e^4-2 e^{24}\right ) x-2 \left (2-e^4+e^{20}\right ) x^2-2 x^3}{\left (e^4-e^{x^2}-x\right )^2} \, dx-50 \int \frac {1+2 e^4 x-2 x^2}{\left (-e^4+e^{x^2}+x\right )^3} \, dx\\ &=\left (5+2 e^{20}\right ) x+x^2+10 \int \left (\frac {\left (1+\frac {2}{e^{20}}\right ) e^{20}}{\left (e^4-e^{x^2}-x\right )^2}-\frac {2 \left (2-e^4+e^{20}\right ) x^2}{\left (e^4-e^{x^2}-x\right )^2}+\frac {\left (-9+4 e^4+2 e^{24}\right ) x}{\left (-e^4+e^{x^2}+x\right )^2}-\frac {2 x^3}{\left (-e^4+e^{x^2}+x\right )^2}\right ) \, dx+10 \int \left (-\frac {2 \left (2+e^{20}\right ) x}{e^4-e^{x^2}-x}-\frac {1}{-e^4+e^{x^2}+x}+\frac {2 x^2}{-e^4+e^{x^2}+x}\right ) \, dx-50 \int \left (-\frac {2 e^4 x}{\left (e^4-e^{x^2}-x\right )^3}+\frac {1}{\left (-e^4+e^{x^2}+x\right )^3}-\frac {2 x^2}{\left (-e^4+e^{x^2}+x\right )^3}\right ) \, dx\\ &=\left (5+2 e^{20}\right ) x+x^2-10 \int \frac {1}{-e^4+e^{x^2}+x} \, dx-20 \int \frac {x^3}{\left (-e^4+e^{x^2}+x\right )^2} \, dx+20 \int \frac {x^2}{-e^4+e^{x^2}+x} \, dx-50 \int \frac {1}{\left (-e^4+e^{x^2}+x\right )^3} \, dx+100 \int \frac {x^2}{\left (-e^4+e^{x^2}+x\right )^3} \, dx+\left (100 e^4\right ) \int \frac {x}{\left (e^4-e^{x^2}-x\right )^3} \, dx+\left (10 \left (2+e^{20}\right )\right ) \int \frac {1}{\left (e^4-e^{x^2}-x\right )^2} \, dx-\left (20 \left (2+e^{20}\right )\right ) \int \frac {x}{e^4-e^{x^2}-x} \, dx-\left (20 \left (2-e^4+e^{20}\right )\right ) \int \frac {x^2}{\left (e^4-e^{x^2}-x\right )^2} \, dx-\left (10 \left (9-4 e^4-2 e^{24}\right )\right ) \int \frac {x}{\left (-e^4+e^{x^2}+x\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.12, size = 51, normalized size = 1.89 \begin {gather*} \left (5+2 e^{20}\right ) x+x^2+\frac {25}{\left (-e^4+e^{x^2}+x\right )^2}-\frac {10 \left (2+e^{20}+x\right )}{-e^4+e^{x^2}+x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-50 + E^12*(-5 - 2*x) + 20*x + 5*x^3 + 2*x^4 + E^(3*x^2)*(5 + 2*E^20 + 2*x) + E^8*(-10 + 15*x + 6*x
^2) + E^4*(-20 + 10*x - 15*x^2 - 6*x^3) + E^(2*x^2)*(-10 + E^4*(-15 - 6*x) + 55*x + 26*x^2 + E^20*(-6*E^4 + 26
*x)) + E^20*(-2*E^12 + 10*x + 6*E^8*x + 2*x^3 + E^4*(-10 - 6*x^2)) + E^x^2*(20 - 110*x + 55*x^2 + 26*x^3 + E^8
*(15 + 6*x) + E^4*(20 - 70*x - 32*x^2) + E^20*(10 + 6*E^8 - 32*E^4*x + 26*x^2)))/(-E^12 + E^(3*x^2) + 3*E^8*x
- 3*E^4*x^2 + x^3 + E^(2*x^2)*(-3*E^4 + 3*x) + E^x^2*(3*E^8 - 6*E^4*x + 3*x^2)),x]

[Out]

(5 + 2*E^20)*x + x^2 + 25/(-E^4 + E^x^2 + x)^2 - (10*(2 + E^20 + x))/(-E^4 + E^x^2 + x)

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fricas [B]  time = 0.71, size = 168, normalized size = 6.22 \begin {gather*} \frac {x^{4} + 5 \, x^{3} - 10 \, x^{2} + 2 \, x e^{28} - 2 \, {\left (2 \, x^{2} - 5\right )} e^{24} + 2 \, {\left (x^{3} - 5 \, x\right )} e^{20} + {\left (x^{2} + 5 \, x\right )} e^{8} - 2 \, {\left (x^{3} + 5 \, x^{2} - 5 \, x - 10\right )} e^{4} + {\left (x^{2} + 2 \, x e^{20} + 5 \, x\right )} e^{\left (2 \, x^{2}\right )} + 2 \, {\left (x^{3} + 5 \, x^{2} - 2 \, x e^{24} + {\left (2 \, x^{2} - 5\right )} e^{20} - {\left (x^{2} + 5 \, x\right )} e^{4} - 5 \, x - 10\right )} e^{\left (x^{2}\right )} - 20 \, x + 25}{x^{2} - 2 \, x e^{4} + 2 \, {\left (x - e^{4}\right )} e^{\left (x^{2}\right )} + e^{8} + e^{\left (2 \, x^{2}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*exp(20)+5+2*x)*exp(x^2)^3+((-6*exp(4)+26*x)*exp(20)+(-6*x-15)*exp(4)+26*x^2+55*x-10)*exp(x^2)^2+
((6*exp(4)^2-32*x*exp(4)+26*x^2+10)*exp(20)+(6*x+15)*exp(4)^2+(-32*x^2-70*x+20)*exp(4)+26*x^3+55*x^2-110*x+20)
*exp(x^2)+(-2*exp(4)^3+6*x*exp(4)^2+(-6*x^2-10)*exp(4)+2*x^3+10*x)*exp(20)+(-2*x-5)*exp(4)^3+(6*x^2+15*x-10)*e
xp(4)^2+(-6*x^3-15*x^2+10*x-20)*exp(4)+2*x^4+5*x^3+20*x-50)/(exp(x^2)^3+(-3*exp(4)+3*x)*exp(x^2)^2+(3*exp(4)^2
-6*x*exp(4)+3*x^2)*exp(x^2)-exp(4)^3+3*x*exp(4)^2-3*x^2*exp(4)+x^3),x, algorithm="fricas")

[Out]

(x^4 + 5*x^3 - 10*x^2 + 2*x*e^28 - 2*(2*x^2 - 5)*e^24 + 2*(x^3 - 5*x)*e^20 + (x^2 + 5*x)*e^8 - 2*(x^3 + 5*x^2
- 5*x - 10)*e^4 + (x^2 + 2*x*e^20 + 5*x)*e^(2*x^2) + 2*(x^3 + 5*x^2 - 2*x*e^24 + (2*x^2 - 5)*e^20 - (x^2 + 5*x
)*e^4 - 5*x - 10)*e^(x^2) - 20*x + 25)/(x^2 - 2*x*e^4 + 2*(x - e^4)*e^(x^2) + e^8 + e^(2*x^2))

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giac [B]  time = 1.51, size = 224, normalized size = 8.30 \begin {gather*} \frac {x^{4} + 2 \, x^{3} e^{20} - 2 \, x^{3} e^{4} + 2 \, x^{3} e^{\left (x^{2}\right )} + 5 \, x^{3} - 4 \, x^{2} e^{24} + x^{2} e^{8} - 10 \, x^{2} e^{4} + x^{2} e^{\left (2 \, x^{2}\right )} + 4 \, x^{2} e^{\left (x^{2} + 20\right )} - 2 \, x^{2} e^{\left (x^{2} + 4\right )} + 10 \, x^{2} e^{\left (x^{2}\right )} - 10 \, x^{2} + 2 \, x e^{28} - 10 \, x e^{20} + 5 \, x e^{8} + 10 \, x e^{4} + 5 \, x e^{\left (2 \, x^{2}\right )} + 2 \, x e^{\left (2 \, x^{2} + 20\right )} - 4 \, x e^{\left (x^{2} + 24\right )} - 10 \, x e^{\left (x^{2} + 4\right )} - 10 \, x e^{\left (x^{2}\right )} - 20 \, x + 10 \, e^{24} + 20 \, e^{4} - 10 \, e^{\left (x^{2} + 20\right )} - 20 \, e^{\left (x^{2}\right )} + 25}{x^{2} - 2 \, x e^{4} + 2 \, x e^{\left (x^{2}\right )} + e^{8} + e^{\left (2 \, x^{2}\right )} - 2 \, e^{\left (x^{2} + 4\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*exp(20)+5+2*x)*exp(x^2)^3+((-6*exp(4)+26*x)*exp(20)+(-6*x-15)*exp(4)+26*x^2+55*x-10)*exp(x^2)^2+
((6*exp(4)^2-32*x*exp(4)+26*x^2+10)*exp(20)+(6*x+15)*exp(4)^2+(-32*x^2-70*x+20)*exp(4)+26*x^3+55*x^2-110*x+20)
*exp(x^2)+(-2*exp(4)^3+6*x*exp(4)^2+(-6*x^2-10)*exp(4)+2*x^3+10*x)*exp(20)+(-2*x-5)*exp(4)^3+(6*x^2+15*x-10)*e
xp(4)^2+(-6*x^3-15*x^2+10*x-20)*exp(4)+2*x^4+5*x^3+20*x-50)/(exp(x^2)^3+(-3*exp(4)+3*x)*exp(x^2)^2+(3*exp(4)^2
-6*x*exp(4)+3*x^2)*exp(x^2)-exp(4)^3+3*x*exp(4)^2-3*x^2*exp(4)+x^3),x, algorithm="giac")

[Out]

(x^4 + 2*x^3*e^20 - 2*x^3*e^4 + 2*x^3*e^(x^2) + 5*x^3 - 4*x^2*e^24 + x^2*e^8 - 10*x^2*e^4 + x^2*e^(2*x^2) + 4*
x^2*e^(x^2 + 20) - 2*x^2*e^(x^2 + 4) + 10*x^2*e^(x^2) - 10*x^2 + 2*x*e^28 - 10*x*e^20 + 5*x*e^8 + 10*x*e^4 + 5
*x*e^(2*x^2) + 2*x*e^(2*x^2 + 20) - 4*x*e^(x^2 + 24) - 10*x*e^(x^2 + 4) - 10*x*e^(x^2) - 20*x + 10*e^24 + 20*e
^4 - 10*e^(x^2 + 20) - 20*e^(x^2) + 25)/(x^2 - 2*x*e^4 + 2*x*e^(x^2) + e^8 + e^(2*x^2) - 2*e^(x^2 + 4))

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maple [B]  time = 0.53, size = 78, normalized size = 2.89

method	result	size
risch	\(2 x \,{\mathrm e}^{20}+x^{2}+5 x +\frac {10 \,{\mathrm e}^{24}-10 x \,{\mathrm e}^{20}-10 \,{\mathrm e}^{x^{2}+20}+10 x \,{\mathrm e}^{4}-10 x^{2}-10 \,{\mathrm e}^{x^{2}} x +20 \,{\mathrm e}^{4}-20 x -20 \,{\mathrm e}^{x^{2}}+25}{\left ({\mathrm e}^{4}-{\mathrm e}^{x^{2}}-x \right )^{2}}\)	\(78\)
norman	\(\frac {x^{4}+x^{2} {\mathrm e}^{2 x^{2}}+\left (5-2 \,{\mathrm e}^{4}+2 \,{\mathrm e}^{20}\right ) x^{3}+\left (-{\mathrm e}^{8}+4 \,{\mathrm e}^{20} {\mathrm e}^{4}+10 \,{\mathrm e}^{4}+10\right ) {\mathrm e}^{2 x^{2}}+\left (2 \,{\mathrm e}^{12}-6 \,{\mathrm e}^{20} {\mathrm e}^{8}-15 \,{\mathrm e}^{8}-10 \,{\mathrm e}^{4}-10 \,{\mathrm e}^{20}-20\right ) x +\left (2 \,{\mathrm e}^{12}-8 \,{\mathrm e}^{20} {\mathrm e}^{8}-20 \,{\mathrm e}^{8}-20 \,{\mathrm e}^{4}-10 \,{\mathrm e}^{20}-20\right ) {\mathrm e}^{x^{2}}+\left (2 \,{\mathrm e}^{20}+5\right ) x \,{\mathrm e}^{2 x^{2}}+\left (-2 \,{\mathrm e}^{4}+10+4 \,{\mathrm e}^{20}\right ) x^{2} {\mathrm e}^{x^{2}}+\left (-2 \,{\mathrm e}^{8}+4 \,{\mathrm e}^{20} {\mathrm e}^{4}+10 \,{\mathrm e}^{4}+10\right ) x \,{\mathrm e}^{x^{2}}+2 x^{3} {\mathrm e}^{x^{2}}+25-{\mathrm e}^{16}+4 \,{\mathrm e}^{12} {\mathrm e}^{20}+10 \,{\mathrm e}^{12}+10 \,{\mathrm e}^{8}+10 \,{\mathrm e}^{20} {\mathrm e}^{4}+20 \,{\mathrm e}^{4}}{\left ({\mathrm e}^{4}-{\mathrm e}^{x^{2}}-x \right )^{2}}\)	\(238\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((2*exp(20)+5+2*x)*exp(x^2)^3+((-6*exp(4)+26*x)*exp(20)+(-6*x-15)*exp(4)+26*x^2+55*x-10)*exp(x^2)^2+((6*ex
p(4)^2-32*x*exp(4)+26*x^2+10)*exp(20)+(6*x+15)*exp(4)^2+(-32*x^2-70*x+20)*exp(4)+26*x^3+55*x^2-110*x+20)*exp(x
^2)+(-2*exp(4)^3+6*x*exp(4)^2+(-6*x^2-10)*exp(4)+2*x^3+10*x)*exp(20)+(-2*x-5)*exp(4)^3+(6*x^2+15*x-10)*exp(4)^
2+(-6*x^3-15*x^2+10*x-20)*exp(4)+2*x^4+5*x^3+20*x-50)/(exp(x^2)^3+(-3*exp(4)+3*x)*exp(x^2)^2+(3*exp(4)^2-6*x*e
xp(4)+3*x^2)*exp(x^2)-exp(4)^3+3*x*exp(4)^2-3*x^2*exp(4)+x^3),x,method=_RETURNVERBOSE)

[Out]

2*x*exp(20)+x^2+5*x+5*(2*exp(24)-2*x*exp(20)-2*exp(x^2+20)+2*x*exp(4)-2*x^2-2*exp(x^2)*x+4*exp(4)-4*x-4*exp(x^
2)+5)/(exp(4)-exp(x^2)-x)^2

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maxima [B]  time = 0.41, size = 159, normalized size = 5.89 \begin {gather*} \frac {x^{4} + x^{3} {\left (2 \, e^{20} - 2 \, e^{4} + 5\right )} - x^{2} {\left (4 \, e^{24} - e^{8} + 10 \, e^{4} + 10\right )} + x {\left (2 \, e^{28} - 10 \, e^{20} + 5 \, e^{8} + 10 \, e^{4} - 20\right )} + {\left (x^{2} + x {\left (2 \, e^{20} + 5\right )}\right )} e^{\left (2 \, x^{2}\right )} + 2 \, {\left (x^{3} + x^{2} {\left (2 \, e^{20} - e^{4} + 5\right )} - x {\left (2 \, e^{24} + 5 \, e^{4} + 5\right )} - 5 \, e^{20} - 10\right )} e^{\left (x^{2}\right )} + 10 \, e^{24} + 20 \, e^{4} + 25}{x^{2} - 2 \, x e^{4} + 2 \, {\left (x - e^{4}\right )} e^{\left (x^{2}\right )} + e^{8} + e^{\left (2 \, x^{2}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*exp(20)+5+2*x)*exp(x^2)^3+((-6*exp(4)+26*x)*exp(20)+(-6*x-15)*exp(4)+26*x^2+55*x-10)*exp(x^2)^2+
((6*exp(4)^2-32*x*exp(4)+26*x^2+10)*exp(20)+(6*x+15)*exp(4)^2+(-32*x^2-70*x+20)*exp(4)+26*x^3+55*x^2-110*x+20)
*exp(x^2)+(-2*exp(4)^3+6*x*exp(4)^2+(-6*x^2-10)*exp(4)+2*x^3+10*x)*exp(20)+(-2*x-5)*exp(4)^3+(6*x^2+15*x-10)*e
xp(4)^2+(-6*x^3-15*x^2+10*x-20)*exp(4)+2*x^4+5*x^3+20*x-50)/(exp(x^2)^3+(-3*exp(4)+3*x)*exp(x^2)^2+(3*exp(4)^2
-6*x*exp(4)+3*x^2)*exp(x^2)-exp(4)^3+3*x*exp(4)^2-3*x^2*exp(4)+x^3),x, algorithm="maxima")

[Out]

(x^4 + x^3*(2*e^20 - 2*e^4 + 5) - x^2*(4*e^24 - e^8 + 10*e^4 + 10) + x*(2*e^28 - 10*e^20 + 5*e^8 + 10*e^4 - 20
) + (x^2 + x*(2*e^20 + 5))*e^(2*x^2) + 2*(x^3 + x^2*(2*e^20 - e^4 + 5) - x*(2*e^24 + 5*e^4 + 5) - 5*e^20 - 10)
*e^(x^2) + 10*e^24 + 20*e^4 + 25)/(x^2 - 2*x*e^4 + 2*(x - e^4)*e^(x^2) + e^8 + e^(2*x^2))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {20\,x+{\mathrm {e}}^{2\,x^2}\,\left (55\,x+{\mathrm {e}}^{20}\,\left (26\,x-6\,{\mathrm {e}}^4\right )+26\,x^2-{\mathrm {e}}^4\,\left (6\,x+15\right )-10\right )+{\mathrm {e}}^8\,\left (6\,x^2+15\,x-10\right )-{\mathrm {e}}^4\,\left (6\,x^3+15\,x^2-10\,x+20\right )+{\mathrm {e}}^{20}\,\left (10\,x-2\,{\mathrm {e}}^{12}+6\,x\,{\mathrm {e}}^8-{\mathrm {e}}^4\,\left (6\,x^2+10\right )+2\,x^3\right )+{\mathrm {e}}^{x^2}\,\left ({\mathrm {e}}^{20}\,\left (26\,x^2-32\,{\mathrm {e}}^4\,x+6\,{\mathrm {e}}^8+10\right )-{\mathrm {e}}^4\,\left (32\,x^2+70\,x-20\right )-110\,x+55\,x^2+26\,x^3+{\mathrm {e}}^8\,\left (6\,x+15\right )+20\right )+5\,x^3+2\,x^4+{\mathrm {e}}^{3\,x^2}\,\left (2\,x+2\,{\mathrm {e}}^{20}+5\right )-{\mathrm {e}}^{12}\,\left (2\,x+5\right )-50}{{\mathrm {e}}^{3\,x^2}-{\mathrm {e}}^{12}+{\mathrm {e}}^{x^2}\,\left (3\,x^2-6\,{\mathrm {e}}^4\,x+3\,{\mathrm {e}}^8\right )+3\,x\,{\mathrm {e}}^8-3\,x^2\,{\mathrm {e}}^4+x^3+{\mathrm {e}}^{2\,x^2}\,\left (3\,x-3\,{\mathrm {e}}^4\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((20*x + exp(2*x^2)*(55*x + exp(20)*(26*x - 6*exp(4)) + 26*x^2 - exp(4)*(6*x + 15) - 10) + exp(8)*(15*x + 6
*x^2 - 10) - exp(4)*(15*x^2 - 10*x + 6*x^3 + 20) + exp(20)*(10*x - 2*exp(12) + 6*x*exp(8) - exp(4)*(6*x^2 + 10
) + 2*x^3) + exp(x^2)*(exp(20)*(6*exp(8) - 32*x*exp(4) + 26*x^2 + 10) - exp(4)*(70*x + 32*x^2 - 20) - 110*x +
55*x^2 + 26*x^3 + exp(8)*(6*x + 15) + 20) + 5*x^3 + 2*x^4 + exp(3*x^2)*(2*x + 2*exp(20) + 5) - exp(12)*(2*x +
5) - 50)/(exp(3*x^2) - exp(12) + exp(x^2)*(3*exp(8) - 6*x*exp(4) + 3*x^2) + 3*x*exp(8) - 3*x^2*exp(4) + x^3 +
exp(2*x^2)*(3*x - 3*exp(4))),x)

[Out]

int((20*x + exp(2*x^2)*(55*x + exp(20)*(26*x - 6*exp(4)) + 26*x^2 - exp(4)*(6*x + 15) - 10) + exp(8)*(15*x + 6
*x^2 - 10) - exp(4)*(15*x^2 - 10*x + 6*x^3 + 20) + exp(20)*(10*x - 2*exp(12) + 6*x*exp(8) - exp(4)*(6*x^2 + 10
) + 2*x^3) + exp(x^2)*(exp(20)*(6*exp(8) - 32*x*exp(4) + 26*x^2 + 10) - exp(4)*(70*x + 32*x^2 - 20) - 110*x +
55*x^2 + 26*x^3 + exp(8)*(6*x + 15) + 20) + 5*x^3 + 2*x^4 + exp(3*x^2)*(2*x + 2*exp(20) + 5) - exp(12)*(2*x +
5) - 50)/(exp(3*x^2) - exp(12) + exp(x^2)*(3*exp(8) - 6*x*exp(4) + 3*x^2) + 3*x*exp(8) - 3*x^2*exp(4) + x^3 +
exp(2*x^2)*(3*x - 3*exp(4))), x)

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sympy [B]  time = 0.30, size = 95, normalized size = 3.52 \begin {gather*} x^{2} + x \left (5 + 2 e^{20}\right ) + \frac {- 10 x^{2} - 10 x e^{20} - 20 x + 10 x e^{4} + \left (- 10 x - 10 e^{20} - 20\right ) e^{x^{2}} + 25 + 20 e^{4} + 10 e^{24}}{x^{2} - 2 x e^{4} + \left (2 x - 2 e^{4}\right ) e^{x^{2}} + e^{2 x^{2}} + e^{8}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*exp(20)+5+2*x)*exp(x**2)**3+((-6*exp(4)+26*x)*exp(20)+(-6*x-15)*exp(4)+26*x**2+55*x-10)*exp(x**2
)**2+((6*exp(4)**2-32*x*exp(4)+26*x**2+10)*exp(20)+(6*x+15)*exp(4)**2+(-32*x**2-70*x+20)*exp(4)+26*x**3+55*x**
2-110*x+20)*exp(x**2)+(-2*exp(4)**3+6*x*exp(4)**2+(-6*x**2-10)*exp(4)+2*x**3+10*x)*exp(20)+(-2*x-5)*exp(4)**3+
(6*x**2+15*x-10)*exp(4)**2+(-6*x**3-15*x**2+10*x-20)*exp(4)+2*x**4+5*x**3+20*x-50)/(exp(x**2)**3+(-3*exp(4)+3*
x)*exp(x**2)**2+(3*exp(4)**2-6*x*exp(4)+3*x**2)*exp(x**2)-exp(4)**3+3*x*exp(4)**2-3*x**2*exp(4)+x**3),x)

[Out]

x**2 + x*(5 + 2*exp(20)) + (-10*x**2 - 10*x*exp(20) - 20*x + 10*x*exp(4) + (-10*x - 10*exp(20) - 20)*exp(x**2)
+ 25 + 20*exp(4) + 10*exp(24))/(x**2 - 2*x*exp(4) + (2*x - 2*exp(4))*exp(x**2) + exp(2*x**2) + exp(8))

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