3.50.54 \(\int \frac {100+560 x+960 x^2+504 x^3-48 x^4-96 x^5-64 x^6+e^{3 x^2} (8 x^3-x^6)+(-130-464 x-384 x^2+12 x^3+48 x^4+48 x^5) \log ^2(5)+(56+96 x-6 x^3-12 x^4) \log ^4(5)+(-8+x^3) \log ^6(5)+e^{2 x^2} (60 x^2+96 x^3+8 x^4-6 x^5-12 x^6+(-24 x^2+3 x^5) \log ^2(5))+e^{x^2} (140 x+480 x^2+404 x^3+20 x^4-48 x^5-48 x^6+(-116 x-192 x^2-8 x^3+12 x^4+24 x^5) \log ^2(5)+(24 x-3 x^4) \log ^4(5))}{8 x^3+48 x^4+96 x^5+64 x^6+e^{3 x^2} x^6+(-12 x^3-48 x^4-48 x^5) \log ^2(5)+(6 x^3+12 x^4) \log ^4(5)-x^3 \log ^6(5)+e^{2 x^2} (6 x^5+12 x^6-3 x^5 \log ^2(5))+e^{x^2} (12 x^4+48 x^5+48 x^6+(-12 x^4-24 x^5) \log ^2(5)+3 x^4 \log ^4(5))} \, dx\)

Optimal. Leaf size=34 \[ 5-x-\frac {\left (2+\frac {1}{2+4 x+e^{x^2} x-\log ^2(5)}\right )^2}{x^2} \]

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Rubi [F]  time = 6.89, 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+560 x+960 x^2+504 x^3-48 x^4-96 x^5-64 x^6+e^{3 x^2} \left (8 x^3-x^6\right )+\left (-130-464 x-384 x^2+12 x^3+48 x^4+48 x^5\right ) \log ^2(5)+\left (56+96 x-6 x^3-12 x^4\right ) \log ^4(5)+\left (-8+x^3\right ) \log ^6(5)+e^{2 x^2} \left (60 x^2+96 x^3+8 x^4-6 x^5-12 x^6+\left (-24 x^2+3 x^5\right ) \log ^2(5)\right )+e^{x^2} \left (140 x+480 x^2+404 x^3+20 x^4-48 x^5-48 x^6+\left (-116 x-192 x^2-8 x^3+12 x^4+24 x^5\right ) \log ^2(5)+\left (24 x-3 x^4\right ) \log ^4(5)\right )}{8 x^3+48 x^4+96 x^5+64 x^6+e^{3 x^2} x^6+\left (-12 x^3-48 x^4-48 x^5\right ) \log ^2(5)+\left (6 x^3+12 x^4\right ) \log ^4(5)-x^3 \log ^6(5)+e^{2 x^2} \left (6 x^5+12 x^6-3 x^5 \log ^2(5)\right )+e^{x^2} \left (12 x^4+48 x^5+48 x^6+\left (-12 x^4-24 x^5\right ) \log ^2(5)+3 x^4 \log ^4(5)\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(100 + 560*x + 960*x^2 + 504*x^3 - 48*x^4 - 96*x^5 - 64*x^6 + E^(3*x^2)*(8*x^3 - x^6) + (-130 - 464*x - 38
4*x^2 + 12*x^3 + 48*x^4 + 48*x^5)*Log[5]^2 + (56 + 96*x - 6*x^3 - 12*x^4)*Log[5]^4 + (-8 + x^3)*Log[5]^6 + E^(
2*x^2)*(60*x^2 + 96*x^3 + 8*x^4 - 6*x^5 - 12*x^6 + (-24*x^2 + 3*x^5)*Log[5]^2) + E^x^2*(140*x + 480*x^2 + 404*
x^3 + 20*x^4 - 48*x^5 - 48*x^6 + (-116*x - 192*x^2 - 8*x^3 + 12*x^4 + 24*x^5)*Log[5]^2 + (24*x - 3*x^4)*Log[5]
^4))/(8*x^3 + 48*x^4 + 96*x^5 + 64*x^6 + E^(3*x^2)*x^6 + (-12*x^3 - 48*x^4 - 48*x^5)*Log[5]^2 + (6*x^3 + 12*x^
4)*Log[5]^4 - x^3*Log[5]^6 + E^(2*x^2)*(6*x^5 + 12*x^6 - 3*x^5*Log[5]^2) + E^x^2*(12*x^4 + 48*x^5 + 48*x^6 + (
-12*x^4 - 24*x^5)*Log[5]^2 + 3*x^4*Log[5]^4)),x]

[Out]

-4/x^2 - x + 16*Defer[Int][(-4*x - E^x^2*x - 2*(1 - Log[5]^2/2))^(-3), x] - 2*(2 - Log[5]^2)*Defer[Int][1/(x^3
*(4*x + E^x^2*x + 2*(1 - Log[5]^2/2))^3), x] - 4*(2 - Log[5]^2)*Defer[Int][1/(x*(4*x + E^x^2*x + 2*(1 - Log[5]
^2/2))^3), x] - 32*Defer[Int][(4*x + E^x^2*x + 2*(1 - Log[5]^2/2))^(-2), x] - 4*(1 - Log[5]^2)*Defer[Int][1/(x
^3*(4*x + E^x^2*x + 2*(1 - Log[5]^2/2))^2), x] - 4*(3 - 2*Log[5]^2)*Defer[Int][1/(x*(4*x + E^x^2*x + 2*(1 - Lo
g[5]^2/2))^2), x] + 12*Defer[Int][1/(x^3*(4*x + E^x^2*x + 2*(1 - Log[5]^2/2))), x] + 8*Defer[Int][1/(x*(4*x +
E^x^2*x + 2*(1 - Log[5]^2/2))), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {100+560 x+960 x^2+504 x^3-48 x^4-96 x^5-64 x^6+e^{3 x^2} \left (8 x^3-x^6\right )+\left (-130-464 x-384 x^2+12 x^3+48 x^4+48 x^5\right ) \log ^2(5)+\left (56+96 x-6 x^3-12 x^4\right ) \log ^4(5)+\left (-8+x^3\right ) \log ^6(5)+e^{2 x^2} \left (60 x^2+96 x^3+8 x^4-6 x^5-12 x^6+\left (-24 x^2+3 x^5\right ) \log ^2(5)\right )+e^{x^2} \left (140 x+480 x^2+404 x^3+20 x^4-48 x^5-48 x^6+\left (-116 x-192 x^2-8 x^3+12 x^4+24 x^5\right ) \log ^2(5)+\left (24 x-3 x^4\right ) \log ^4(5)\right )}{48 x^4+96 x^5+64 x^6+e^{3 x^2} x^6+\left (-12 x^3-48 x^4-48 x^5\right ) \log ^2(5)+\left (6 x^3+12 x^4\right ) \log ^4(5)+e^{2 x^2} \left (6 x^5+12 x^6-3 x^5 \log ^2(5)\right )+e^{x^2} \left (12 x^4+48 x^5+48 x^6+\left (-12 x^4-24 x^5\right ) \log ^2(5)+3 x^4 \log ^4(5)\right )+x^3 \left (8-\log ^6(5)\right )} \, dx\\ &=\int \frac {-\left (4+e^{x^2}\right )^3 x^6+3 \left (4+e^{x^2}\right )^2 x^5 \left (-2+\log ^2(5)\right )-2 \left (5-2 \log ^2(5)\right )^2 \left (-2+\log ^2(5)\right )-12 \left (4+e^{x^2}\right )^2 x^2 \left (-5+2 \log ^2(5)\right )+4 \left (4+e^{x^2}\right ) x \left (35-29 \log ^2(5)+6 \log ^4(5)\right )+x^3 \left (504+96 e^{2 x^2}+8 e^{3 x^2}+12 \log ^2(5)-6 \log ^4(5)+\log ^6(5)+e^{x^2} \left (404-8 \log ^2(5)\right )\right )+x^4 \left (8 e^{2 x^2}-12 \left (-2+\log ^2(5)\right )^2+e^{x^2} \left (20+12 \log ^2(5)-3 \log ^4(5)\right )\right )}{x^3 \left (\left (4+e^{x^2}\right ) x+2 \left (1-\frac {\log ^2(5)}{2}\right )\right )^3} \, dx\\ &=\int \left (\frac {8-x^3}{x^3}+\frac {2 \left (-2-8 x^3+\log ^2(5)-2 x^2 \left (2-\log ^2(5)\right )\right )}{x^3 \left (4 x+e^{x^2} x+2 \left (1-\frac {\log ^2(5)}{2}\right )\right )^3}+\frac {4 \left (-1-8 x^3+\log ^2(5)-x^2 \left (3-2 \log ^2(5)\right )\right )}{x^3 \left (4 x+e^{x^2} x+2 \left (1-\frac {\log ^2(5)}{2}\right )\right )^2}+\frac {4 \left (3+2 x^2\right )}{x^3 \left (4 x+e^{x^2} x+2 \left (1-\frac {\log ^2(5)}{2}\right )\right )}\right ) \, dx\\ &=2 \int \frac {-2-8 x^3+\log ^2(5)-2 x^2 \left (2-\log ^2(5)\right )}{x^3 \left (4 x+e^{x^2} x+2 \left (1-\frac {\log ^2(5)}{2}\right )\right )^3} \, dx+4 \int \frac {-1-8 x^3+\log ^2(5)-x^2 \left (3-2 \log ^2(5)\right )}{x^3 \left (4 x+e^{x^2} x+2 \left (1-\frac {\log ^2(5)}{2}\right )\right )^2} \, dx+4 \int \frac {3+2 x^2}{x^3 \left (4 x+e^{x^2} x+2 \left (1-\frac {\log ^2(5)}{2}\right )\right )} \, dx+\int \frac {8-x^3}{x^3} \, dx\\ &=2 \int \left (\frac {8}{\left (-4 x-e^{x^2} x-2 \left (1-\frac {\log ^2(5)}{2}\right )\right )^3}+\frac {-2+\log ^2(5)}{x^3 \left (4 x+e^{x^2} x+2 \left (1-\frac {\log ^2(5)}{2}\right )\right )^3}+\frac {2 \left (-2+\log ^2(5)\right )}{x \left (4 x+e^{x^2} x+2 \left (1-\frac {\log ^2(5)}{2}\right )\right )^3}\right ) \, dx+4 \int \left (-\frac {8}{\left (4 x+e^{x^2} x+2 \left (1-\frac {\log ^2(5)}{2}\right )\right )^2}+\frac {-1+\log ^2(5)}{x^3 \left (4 x+e^{x^2} x+2 \left (1-\frac {\log ^2(5)}{2}\right )\right )^2}+\frac {-3+2 \log ^2(5)}{x \left (4 x+e^{x^2} x+2 \left (1-\frac {\log ^2(5)}{2}\right )\right )^2}\right ) \, dx+4 \int \left (\frac {3}{x^3 \left (4 x+e^{x^2} x+2 \left (1-\frac {\log ^2(5)}{2}\right )\right )}+\frac {2}{x \left (4 x+e^{x^2} x+2 \left (1-\frac {\log ^2(5)}{2}\right )\right )}\right ) \, dx+\int \left (-1+\frac {8}{x^3}\right ) \, dx\\ &=-\frac {4}{x^2}-x+8 \int \frac {1}{x \left (4 x+e^{x^2} x+2 \left (1-\frac {\log ^2(5)}{2}\right )\right )} \, dx+12 \int \frac {1}{x^3 \left (4 x+e^{x^2} x+2 \left (1-\frac {\log ^2(5)}{2}\right )\right )} \, dx+16 \int \frac {1}{\left (-4 x-e^{x^2} x-2 \left (1-\frac {\log ^2(5)}{2}\right )\right )^3} \, dx-32 \int \frac {1}{\left (4 x+e^{x^2} x+2 \left (1-\frac {\log ^2(5)}{2}\right )\right )^2} \, dx-\left (4 \left (3-2 \log ^2(5)\right )\right ) \int \frac {1}{x \left (4 x+e^{x^2} x+2 \left (1-\frac {\log ^2(5)}{2}\right )\right )^2} \, dx-\left (4 \left (1-\log ^2(5)\right )\right ) \int \frac {1}{x^3 \left (4 x+e^{x^2} x+2 \left (1-\frac {\log ^2(5)}{2}\right )\right )^2} \, dx-\left (2 \left (2-\log ^2(5)\right )\right ) \int \frac {1}{x^3 \left (4 x+e^{x^2} x+2 \left (1-\frac {\log ^2(5)}{2}\right )\right )^3} \, dx-\left (4 \left (2-\log ^2(5)\right )\right ) \int \frac {1}{x \left (4 x+e^{x^2} x+2 \left (1-\frac {\log ^2(5)}{2}\right )\right )^3} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.26, size = 49, normalized size = 1.44 \begin {gather*} -\frac {x^3+\frac {\left (5+2 \left (4+e^{x^2}\right ) x-2 \log ^2(5)\right )^2}{\left (2+\left (4+e^{x^2}\right ) x-\log ^2(5)\right )^2}}{x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(100 + 560*x + 960*x^2 + 504*x^3 - 48*x^4 - 96*x^5 - 64*x^6 + E^(3*x^2)*(8*x^3 - x^6) + (-130 - 464*
x - 384*x^2 + 12*x^3 + 48*x^4 + 48*x^5)*Log[5]^2 + (56 + 96*x - 6*x^3 - 12*x^4)*Log[5]^4 + (-8 + x^3)*Log[5]^6
+ E^(2*x^2)*(60*x^2 + 96*x^3 + 8*x^4 - 6*x^5 - 12*x^6 + (-24*x^2 + 3*x^5)*Log[5]^2) + E^x^2*(140*x + 480*x^2
+ 404*x^3 + 20*x^4 - 48*x^5 - 48*x^6 + (-116*x - 192*x^2 - 8*x^3 + 12*x^4 + 24*x^5)*Log[5]^2 + (24*x - 3*x^4)*
Log[5]^4))/(8*x^3 + 48*x^4 + 96*x^5 + 64*x^6 + E^(3*x^2)*x^6 + (-12*x^3 - 48*x^4 - 48*x^5)*Log[5]^2 + (6*x^3 +
12*x^4)*Log[5]^4 - x^3*Log[5]^6 + E^(2*x^2)*(6*x^5 + 12*x^6 - 3*x^5*Log[5]^2) + E^x^2*(12*x^4 + 48*x^5 + 48*x
^6 + (-12*x^4 - 24*x^5)*Log[5]^2 + 3*x^4*Log[5]^4)),x]

[Out]

-((x^3 + (5 + 2*(4 + E^x^2)*x - 2*Log[5]^2)^2/(2 + (4 + E^x^2)*x - Log[5]^2)^2)/x^2)

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fricas [B]  time = 0.82, size = 186, normalized size = 5.47 \begin {gather*} -\frac {16 \, x^{5} + {\left (x^{3} + 4\right )} \log \relax (5)^{4} + 16 \, x^{4} + 4 \, x^{3} - 4 \, {\left (2 \, x^{4} + x^{3} + 8 \, x + 5\right )} \log \relax (5)^{2} + 64 \, x^{2} + {\left (x^{5} + 4 \, x^{2}\right )} e^{\left (2 \, x^{2}\right )} + 2 \, {\left (4 \, x^{5} + 2 \, x^{4} - {\left (x^{4} + 4 \, x\right )} \log \relax (5)^{2} + 16 \, x^{2} + 10 \, x\right )} e^{\left (x^{2}\right )} + 80 \, x + 25}{x^{2} \log \relax (5)^{4} + x^{4} e^{\left (2 \, x^{2}\right )} + 16 \, x^{4} + 16 \, x^{3} - 4 \, {\left (2 \, x^{3} + x^{2}\right )} \log \relax (5)^{2} + 4 \, x^{2} - 2 \, {\left (x^{3} \log \relax (5)^{2} - 4 \, x^{4} - 2 \, x^{3}\right )} e^{\left (x^{2}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x^6+8*x^3)*exp(x^2)^3+((3*x^5-24*x^2)*log(5)^2-12*x^6-6*x^5+8*x^4+96*x^3+60*x^2)*exp(x^2)^2+((-3*
x^4+24*x)*log(5)^4+(24*x^5+12*x^4-8*x^3-192*x^2-116*x)*log(5)^2-48*x^6-48*x^5+20*x^4+404*x^3+480*x^2+140*x)*ex
p(x^2)+(x^3-8)*log(5)^6+(-12*x^4-6*x^3+96*x+56)*log(5)^4+(48*x^5+48*x^4+12*x^3-384*x^2-464*x-130)*log(5)^2-64*
x^6-96*x^5-48*x^4+504*x^3+960*x^2+560*x+100)/(x^6*exp(x^2)^3+(-3*x^5*log(5)^2+12*x^6+6*x^5)*exp(x^2)^2+(3*x^4*
log(5)^4+(-24*x^5-12*x^4)*log(5)^2+48*x^6+48*x^5+12*x^4)*exp(x^2)-x^3*log(5)^6+(12*x^4+6*x^3)*log(5)^4+(-48*x^
5-48*x^4-12*x^3)*log(5)^2+64*x^6+96*x^5+48*x^4+8*x^3),x, algorithm="fricas")

[Out]

-(16*x^5 + (x^3 + 4)*log(5)^4 + 16*x^4 + 4*x^3 - 4*(2*x^4 + x^3 + 8*x + 5)*log(5)^2 + 64*x^2 + (x^5 + 4*x^2)*e
^(2*x^2) + 2*(4*x^5 + 2*x^4 - (x^4 + 4*x)*log(5)^2 + 16*x^2 + 10*x)*e^(x^2) + 80*x + 25)/(x^2*log(5)^4 + x^4*e
^(2*x^2) + 16*x^4 + 16*x^3 - 4*(2*x^3 + x^2)*log(5)^2 + 4*x^2 - 2*(x^3*log(5)^2 - 4*x^4 - 2*x^3)*e^(x^2))

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giac [B]  time = 0.72, size = 240, normalized size = 7.06 \begin {gather*} -\frac {2 \, x^{4} e^{\left (x^{2}\right )} \log \relax (5)^{2} - x^{3} \log \relax (5)^{4} - x^{5} e^{\left (2 \, x^{2}\right )} - 8 \, x^{5} e^{\left (x^{2}\right )} + 8 \, x^{4} \log \relax (5)^{2} - 16 \, x^{5} - 4 \, x^{4} e^{\left (x^{2}\right )} + 4 \, x^{3} \log \relax (5)^{2} - 16 \, x^{4} + 8 \, x e^{\left (x^{2}\right )} \log \relax (5)^{2} - 4 \, \log \relax (5)^{4} - 4 \, x^{3} - 4 \, x^{2} e^{\left (2 \, x^{2}\right )} - 32 \, x^{2} e^{\left (x^{2}\right )} + 32 \, x \log \relax (5)^{2} - 64 \, x^{2} - 20 \, x e^{\left (x^{2}\right )} + 20 \, \log \relax (5)^{2} - 80 \, x - 25}{2 \, x^{3} e^{\left (x^{2}\right )} \log \relax (5)^{2} - x^{2} \log \relax (5)^{4} - x^{4} e^{\left (2 \, x^{2}\right )} - 8 \, x^{4} e^{\left (x^{2}\right )} + 8 \, x^{3} \log \relax (5)^{2} - 16 \, x^{4} - 4 \, x^{3} e^{\left (x^{2}\right )} + 4 \, x^{2} \log \relax (5)^{2} - 16 \, x^{3} - 4 \, x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x^6+8*x^3)*exp(x^2)^3+((3*x^5-24*x^2)*log(5)^2-12*x^6-6*x^5+8*x^4+96*x^3+60*x^2)*exp(x^2)^2+((-3*
x^4+24*x)*log(5)^4+(24*x^5+12*x^4-8*x^3-192*x^2-116*x)*log(5)^2-48*x^6-48*x^5+20*x^4+404*x^3+480*x^2+140*x)*ex
p(x^2)+(x^3-8)*log(5)^6+(-12*x^4-6*x^3+96*x+56)*log(5)^4+(48*x^5+48*x^4+12*x^3-384*x^2-464*x-130)*log(5)^2-64*
x^6-96*x^5-48*x^4+504*x^3+960*x^2+560*x+100)/(x^6*exp(x^2)^3+(-3*x^5*log(5)^2+12*x^6+6*x^5)*exp(x^2)^2+(3*x^4*
log(5)^4+(-24*x^5-12*x^4)*log(5)^2+48*x^6+48*x^5+12*x^4)*exp(x^2)-x^3*log(5)^6+(12*x^4+6*x^3)*log(5)^4+(-48*x^
5-48*x^4-12*x^3)*log(5)^2+64*x^6+96*x^5+48*x^4+8*x^3),x, algorithm="giac")

[Out]

-(2*x^4*e^(x^2)*log(5)^2 - x^3*log(5)^4 - x^5*e^(2*x^2) - 8*x^5*e^(x^2) + 8*x^4*log(5)^2 - 16*x^5 - 4*x^4*e^(x
^2) + 4*x^3*log(5)^2 - 16*x^4 + 8*x*e^(x^2)*log(5)^2 - 4*log(5)^4 - 4*x^3 - 4*x^2*e^(2*x^2) - 32*x^2*e^(x^2) +
32*x*log(5)^2 - 64*x^2 - 20*x*e^(x^2) + 20*log(5)^2 - 80*x - 25)/(2*x^3*e^(x^2)*log(5)^2 - x^2*log(5)^4 - x^4
*e^(2*x^2) - 8*x^4*e^(x^2) + 8*x^3*log(5)^2 - 16*x^4 - 4*x^3*e^(x^2) + 4*x^2*log(5)^2 - 16*x^3 - 4*x^2)

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maple [A]  time = 0.79, size = 50, normalized size = 1.47

method	result	size
risch	\(-x -\frac {4}{x^{2}}+\frac {4 \ln \relax (5)^{2}-4 \,{\mathrm e}^{x^{2}} x -16 x -9}{x^{2} \left (\ln \relax (5)^{2}-{\mathrm e}^{x^{2}} x -4 x -2\right )^{2}}\)	\(50\)
norman	\(\frac {\left (-80+32 \ln \relax (5)^{2}\right ) x -64 x^{2}+\left (8 \ln \relax (5)^{2}-16\right ) x^{4}+\left (-\ln \relax (5)^{4}+4 \ln \relax (5)^{2}-4\right ) x^{3}+\left (-20+8 \ln \relax (5)^{2}\right ) x \,{\mathrm e}^{x^{2}}+\left (2 \ln \relax (5)^{2}-4\right ) x^{4} {\mathrm e}^{x^{2}}-25-16 x^{5}-32 x^{2} {\mathrm e}^{x^{2}}-4 x^{2} {\mathrm e}^{2 x^{2}}-8 \,{\mathrm e}^{x^{2}} x^{5}-{\mathrm e}^{2 x^{2}} x^{5}-4 \ln \relax (5)^{4}+20 \ln \relax (5)^{2}}{x^{2} \left (\ln \relax (5)^{2}-{\mathrm e}^{x^{2}} x -4 x -2\right )^{2}}\)	\(157\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-x^6+8*x^3)*exp(x^2)^3+((3*x^5-24*x^2)*ln(5)^2-12*x^6-6*x^5+8*x^4+96*x^3+60*x^2)*exp(x^2)^2+((-3*x^4+24*
x)*ln(5)^4+(24*x^5+12*x^4-8*x^3-192*x^2-116*x)*ln(5)^2-48*x^6-48*x^5+20*x^4+404*x^3+480*x^2+140*x)*exp(x^2)+(x
^3-8)*ln(5)^6+(-12*x^4-6*x^3+96*x+56)*ln(5)^4+(48*x^5+48*x^4+12*x^3-384*x^2-464*x-130)*ln(5)^2-64*x^6-96*x^5-4
8*x^4+504*x^3+960*x^2+560*x+100)/(x^6*exp(x^2)^3+(-3*x^5*ln(5)^2+12*x^6+6*x^5)*exp(x^2)^2+(3*x^4*ln(5)^4+(-24*
x^5-12*x^4)*ln(5)^2+48*x^6+48*x^5+12*x^4)*exp(x^2)-x^3*ln(5)^6+(12*x^4+6*x^3)*ln(5)^4+(-48*x^5-48*x^4-12*x^3)*
ln(5)^2+64*x^6+96*x^5+48*x^4+8*x^3),x,method=_RETURNVERBOSE)

[Out]

-x-4/x^2+(4*ln(5)^2-4*exp(x^2)*x-16*x-9)/x^2/(ln(5)^2-exp(x^2)*x-4*x-2)^2

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maxima [B]  time = 0.65, size = 186, normalized size = 5.47 \begin {gather*} \frac {8 \, {\left (\log \relax (5)^{2} - 2\right )} x^{4} - 16 \, x^{5} - {\left (\log \relax (5)^{4} - 4 \, \log \relax (5)^{2} + 4\right )} x^{3} - 4 \, \log \relax (5)^{4} + 16 \, {\left (2 \, \log \relax (5)^{2} - 5\right )} x - 64 \, x^{2} - {\left (x^{5} + 4 \, x^{2}\right )} e^{\left (2 \, x^{2}\right )} + 2 \, {\left ({\left (\log \relax (5)^{2} - 2\right )} x^{4} - 4 \, x^{5} + 2 \, {\left (2 \, \log \relax (5)^{2} - 5\right )} x - 16 \, x^{2}\right )} e^{\left (x^{2}\right )} + 20 \, \log \relax (5)^{2} - 25}{x^{4} e^{\left (2 \, x^{2}\right )} - 8 \, {\left (\log \relax (5)^{2} - 2\right )} x^{3} + 16 \, x^{4} + {\left (\log \relax (5)^{4} - 4 \, \log \relax (5)^{2} + 4\right )} x^{2} - 2 \, {\left ({\left (\log \relax (5)^{2} - 2\right )} x^{3} - 4 \, x^{4}\right )} e^{\left (x^{2}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x^6+8*x^3)*exp(x^2)^3+((3*x^5-24*x^2)*log(5)^2-12*x^6-6*x^5+8*x^4+96*x^3+60*x^2)*exp(x^2)^2+((-3*
x^4+24*x)*log(5)^4+(24*x^5+12*x^4-8*x^3-192*x^2-116*x)*log(5)^2-48*x^6-48*x^5+20*x^4+404*x^3+480*x^2+140*x)*ex
p(x^2)+(x^3-8)*log(5)^6+(-12*x^4-6*x^3+96*x+56)*log(5)^4+(48*x^5+48*x^4+12*x^3-384*x^2-464*x-130)*log(5)^2-64*
x^6-96*x^5-48*x^4+504*x^3+960*x^2+560*x+100)/(x^6*exp(x^2)^3+(-3*x^5*log(5)^2+12*x^6+6*x^5)*exp(x^2)^2+(3*x^4*
log(5)^4+(-24*x^5-12*x^4)*log(5)^2+48*x^6+48*x^5+12*x^4)*exp(x^2)-x^3*log(5)^6+(12*x^4+6*x^3)*log(5)^4+(-48*x^
5-48*x^4-12*x^3)*log(5)^2+64*x^6+96*x^5+48*x^4+8*x^3),x, algorithm="maxima")

[Out]

(8*(log(5)^2 - 2)*x^4 - 16*x^5 - (log(5)^4 - 4*log(5)^2 + 4)*x^3 - 4*log(5)^4 + 16*(2*log(5)^2 - 5)*x - 64*x^2
- (x^5 + 4*x^2)*e^(2*x^2) + 2*((log(5)^2 - 2)*x^4 - 4*x^5 + 2*(2*log(5)^2 - 5)*x - 16*x^2)*e^(x^2) + 20*log(5
)^2 - 25)/(x^4*e^(2*x^2) - 8*(log(5)^2 - 2)*x^3 + 16*x^4 + (log(5)^4 - 4*log(5)^2 + 4)*x^2 - 2*((log(5)^2 - 2)
*x^3 - 4*x^4)*e^(x^2))

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mupad [B]  time = 4.20, size = 213, normalized size = 6.26 \begin {gather*} -x-\frac {4}{x^2}-\frac {4\,\left (4\,x^2-{\ln \relax (5)}^2-2\,x^2\,{\ln \relax (5)}^2+8\,x^3+2\right )}{x\,\left ({\mathrm {e}}^{x^2}+\frac {4\,x-{\ln \relax (5)}^2+2}{x}\right )\,\left (2\,x^2-2\,x^4\,{\ln \relax (5)}^2-x^2\,{\ln \relax (5)}^2+4\,x^4+8\,x^5\right )}-\frac {4\,x^2-{\ln \relax (5)}^2-2\,x^2\,{\ln \relax (5)}^2+8\,x^3+2}{x^2\,\left ({\mathrm {e}}^{2\,x^2}+\frac {{\left (4\,x-{\ln \relax (5)}^2+2\right )}^2}{x^2}+\frac {2\,{\mathrm {e}}^{x^2}\,\left (4\,x-{\ln \relax (5)}^2+2\right )}{x}\right )\,\left (2\,x^2-2\,x^4\,{\ln \relax (5)}^2-x^2\,{\ln \relax (5)}^2+4\,x^4+8\,x^5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((560*x - log(5)^2*(464*x + 384*x^2 - 12*x^3 - 48*x^4 - 48*x^5 + 130) + log(5)^6*(x^3 - 8) + exp(2*x^2)*(60
*x^2 + 96*x^3 + 8*x^4 - 6*x^5 - 12*x^6 - log(5)^2*(24*x^2 - 3*x^5)) + exp(x^2)*(140*x - log(5)^2*(116*x + 192*
x^2 + 8*x^3 - 12*x^4 - 24*x^5) + log(5)^4*(24*x - 3*x^4) + 480*x^2 + 404*x^3 + 20*x^4 - 48*x^5 - 48*x^6) + exp
(3*x^2)*(8*x^3 - x^6) + log(5)^4*(96*x - 6*x^3 - 12*x^4 + 56) + 960*x^2 + 504*x^3 - 48*x^4 - 96*x^5 - 64*x^6 +
100)/(exp(x^2)*(3*x^4*log(5)^4 + 12*x^4 + 48*x^5 + 48*x^6 - log(5)^2*(12*x^4 + 24*x^5)) - log(5)^2*(12*x^3 +
48*x^4 + 48*x^5) - x^3*log(5)^6 + exp(2*x^2)*(6*x^5 - 3*x^5*log(5)^2 + 12*x^6) + x^6*exp(3*x^2) + 8*x^3 + 48*x
^4 + 96*x^5 + 64*x^6 + log(5)^4*(6*x^3 + 12*x^4)),x)

[Out]

- x - 4/x^2 - (4*(4*x^2 - log(5)^2 - 2*x^2*log(5)^2 + 8*x^3 + 2))/(x*(exp(x^2) + (4*x - log(5)^2 + 2)/x)*(2*x^
2 - 2*x^4*log(5)^2 - x^2*log(5)^2 + 4*x^4 + 8*x^5)) - (4*x^2 - log(5)^2 - 2*x^2*log(5)^2 + 8*x^3 + 2)/(x^2*(ex
p(2*x^2) + (4*x - log(5)^2 + 2)^2/x^2 + (2*exp(x^2)*(4*x - log(5)^2 + 2))/x)*(2*x^2 - 2*x^4*log(5)^2 - x^2*log
(5)^2 + 4*x^4 + 8*x^5))

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sympy [B]  time = 0.53, size = 105, normalized size = 3.09 \begin {gather*} - x + \frac {- 4 x e^{x^{2}} - 16 x - 9 + 4 \log {\relax (5 )}^{2}}{x^{4} e^{2 x^{2}} + 16 x^{4} - 8 x^{3} \log {\relax (5 )}^{2} + 16 x^{3} - 4 x^{2} \log {\relax (5 )}^{2} + 4 x^{2} + x^{2} \log {\relax (5 )}^{4} + \left (8 x^{4} - 2 x^{3} \log {\relax (5 )}^{2} + 4 x^{3}\right ) e^{x^{2}}} - \frac {4}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x**6+8*x**3)*exp(x**2)**3+((3*x**5-24*x**2)*ln(5)**2-12*x**6-6*x**5+8*x**4+96*x**3+60*x**2)*exp(x
**2)**2+((-3*x**4+24*x)*ln(5)**4+(24*x**5+12*x**4-8*x**3-192*x**2-116*x)*ln(5)**2-48*x**6-48*x**5+20*x**4+404*
x**3+480*x**2+140*x)*exp(x**2)+(x**3-8)*ln(5)**6+(-12*x**4-6*x**3+96*x+56)*ln(5)**4+(48*x**5+48*x**4+12*x**3-3
84*x**2-464*x-130)*ln(5)**2-64*x**6-96*x**5-48*x**4+504*x**3+960*x**2+560*x+100)/(x**6*exp(x**2)**3+(-3*x**5*l
n(5)**2+12*x**6+6*x**5)*exp(x**2)**2+(3*x**4*ln(5)**4+(-24*x**5-12*x**4)*ln(5)**2+48*x**6+48*x**5+12*x**4)*exp
(x**2)-x**3*ln(5)**6+(12*x**4+6*x**3)*ln(5)**4+(-48*x**5-48*x**4-12*x**3)*ln(5)**2+64*x**6+96*x**5+48*x**4+8*x
**3),x)

[Out]

-x + (-4*x*exp(x**2) - 16*x - 9 + 4*log(5)**2)/(x**4*exp(2*x**2) + 16*x**4 - 8*x**3*log(5)**2 + 16*x**3 - 4*x*
*2*log(5)**2 + 4*x**2 + x**2*log(5)**4 + (8*x**4 - 2*x**3*log(5)**2 + 4*x**3)*exp(x**2)) - 4/x**2

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