3.78.55 \(\int \frac {-6 x+2 x^3+e^{10} (-6 x+2 x^3)+e^5 (-12 x+4 x^3)+e^{2-2 x} (-6 x+6 x^2+2 x^3-2 x^4)+e^{1-x} (-12 x+6 x^2+4 x^3-2 x^4+e^5 (-12 x+6 x^2+4 x^3-2 x^4))+(2 x+2 x^3+4 e^5 x^3+2 e^{10} x^3+2 e^{2-2 x} x^3+e^{1-x} (4 x^3+4 e^5 x^3)) \log (1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} (2 x^2+2 e^5 x^2))}{1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} (2 x^2+2 e^5 x^2)} \, dx\)

Optimal. Leaf size=27 \[ \left (-3+x^2\right ) \log \left (1+\left (1+e^5+e^{1-x}\right )^2 x^2\right ) \]

________________________________________________________________________________________

Rubi [F]  time = 96.42, 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 {-6 x+2 x^3+e^{10} \left (-6 x+2 x^3\right )+e^5 \left (-12 x+4 x^3\right )+e^{2-2 x} \left (-6 x+6 x^2+2 x^3-2 x^4\right )+e^{1-x} \left (-12 x+6 x^2+4 x^3-2 x^4+e^5 \left (-12 x+6 x^2+4 x^3-2 x^4\right )\right )+\left (2 x+2 x^3+4 e^5 x^3+2 e^{10} x^3+2 e^{2-2 x} x^3+e^{1-x} \left (4 x^3+4 e^5 x^3\right )\right ) \log \left (1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )\right )}{1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-6*x + 2*x^3 + E^10*(-6*x + 2*x^3) + E^5*(-12*x + 4*x^3) + E^(2 - 2*x)*(-6*x + 6*x^2 + 2*x^3 - 2*x^4) + E
^(1 - x)*(-12*x + 6*x^2 + 4*x^3 - 2*x^4 + E^5*(-12*x + 6*x^2 + 4*x^3 - 2*x^4)) + (2*x + 2*x^3 + 4*E^5*x^3 + 2*
E^10*x^3 + 2*E^(2 - 2*x)*x^3 + E^(1 - x)*(4*x^3 + 4*E^5*x^3))*Log[1 + x^2 + 2*E^5*x^2 + E^10*x^2 + E^(2 - 2*x)
*x^2 + E^(1 - x)*(2*x^2 + 2*E^5*x^2)])/(1 + x^2 + 2*E^5*x^2 + E^10*x^2 + E^(2 - 2*x)*x^2 + E^(1 - x)*(2*x^2 +
2*E^5*x^2)),x]

[Out]

Log[1 + (1 + E^5)^2*x^2]/(1 + E^5)^2 - ((4 + 6*E^5 + 3*E^10)*Log[1 + (1 + E^5)^2*x^2])/(1 + E^5)^2 + x^2*Log[1
+ ((E + E^x + E^(5 + x))^2*x^2)/E^(2*x)] - (E*Defer[Int][1/((I + (1 + E^5)*x)*(E^x + I*E*x + I*E^x*(1 + E^5)*
x)), x])/(1 + E^5)^2 + (E*(4 + 6*E^5 + 3*E^10)*Defer[Int][1/((I + (1 + E^5)*x)*(E^x + I*E*x + I*E^x*(1 + E^5)*
x)), x])/(1 + E^5)^2 - (2*E*Defer[Int][E^(-1 + x)/((I + (1 + E^5)*x)*(E^x + I*E*x + I*E^x*(1 + E^5)*x)), x])/(
1 + E^5) + (2*E*(4 + 6*E^5 + 3*E^10)*Defer[Int][E^(-1 + x)/((I + (1 + E^5)*x)*(E^x + I*E*x + I*E^x*(1 + E^5)*x
)), x])/(1 + E^5) + (E*Defer[Int][1/((1 + I*(1 + E^5)*x)*(I*E^x + E*x + E^x*(1 + E^5)*x)), x])/(1 + E^5)^2 - (
E*(4 + 6*E^5 + 3*E^10)*Defer[Int][1/((1 + I*(1 + E^5)*x)*(I*E^x + E*x + E^x*(1 + E^5)*x)), x])/(1 + E^5)^2 + (
2*E*Defer[Int][E^(-1 + x)/((1 + I*(1 + E^5)*x)*(I*E^x + E*x + E^x*(1 + E^5)*x)), x])/(1 + E^5) - (2*E*(4 + 6*E
^5 + 3*E^10)*Defer[Int][E^(-1 + x)/((1 + I*(1 + E^5)*x)*(I*E^x + E*x + E^x*(1 + E^5)*x)), x])/(1 + E^5) - (2*E
^2*Defer[Int][(-E^(2*x) - E^2*x^2 - 2*E^(1 + x)*(1 + E^5)*x^2 - E^(2*x)*(1 + E^5*(2 + E^5))*x^2)^(-1), x])/(1
+ E^5)^4 + (2*E^2*(4 + 6*E^5 + 3*E^10)*Defer[Int][(-E^(2*x) - E^2*x^2 - 2*E^(1 + x)*(1 + E^5)*x^2 - E^(2*x)*(1
+ E^5*(2 + E^5))*x^2)^(-1), x])/(1 + E^5)^4 - (2*E*Defer[Int][E^x/(-E^(2*x) - E^2*x^2 - 2*E^(1 + x)*(1 + E^5)
*x^2 - E^(2*x)*(1 + E^5*(2 + E^5))*x^2), x])/(1 + E^5)^3 + (2*E*(4 + 6*E^5 + 3*E^10)*Defer[Int][E^x/(-E^(2*x)
- E^2*x^2 - 2*E^(1 + x)*(1 + E^5)*x^2 - E^(2*x)*(1 + E^5*(2 + E^5))*x^2), x])/(1 + E^5)^3 - (2*E^2*Defer[Int][
(E^(2*x) + E^2*x^2 + 2*E^(1 + x)*(1 + E^5)*x^2 + E^(2*x)*(1 + E^5*(2 + E^5))*x^2)^(-1), x])/(1 + E^5)^4 + (2*E
^2*(4 + 6*E^5 + 3*E^10)*Defer[Int][(E^(2*x) + E^2*x^2 + 2*E^(1 + x)*(1 + E^5)*x^2 + E^(2*x)*(1 + E^5*(2 + E^5)
)*x^2)^(-1), x])/(1 + E^5)^4 - (2*E*Defer[Int][E^x/(E^(2*x) + E^2*x^2 + 2*E^(1 + x)*(1 + E^5)*x^2 + E^(2*x)*(1
+ E^5*(2 + E^5))*x^2), x])/(1 + E^5)^3 + (2*E*(4 + 6*E^5 + 3*E^10)*Defer[Int][E^x/(E^(2*x) + E^2*x^2 + 2*E^(1
+ x)*(1 + E^5)*x^2 + E^(2*x)*(1 + E^5*(2 + E^5))*x^2), x])/(1 + E^5)^3 - (2*E^2*Defer[Int][x^2/(E^(2*x) + E^2
*x^2 + 2*E^(1 + x)*(1 + E^5)*x^2 + E^(2*x)*(1 + E^5*(2 + E^5))*x^2), x])/(1 + E^5)^2 + (2*E^2*(4 + 6*E^5 + 3*E
^10)*Defer[Int][x^2/(E^(2*x) + E^2*x^2 + 2*E^(1 + x)*(1 + E^5)*x^2 + E^(2*x)*(1 + E^5*(2 + E^5))*x^2), x])/(1
+ E^5)^2 - (2*E*Defer[Int][(E^x*x^2)/(E^(2*x) + E^2*x^2 + 2*E^(1 + x)*(1 + E^5)*x^2 + E^(2*x)*(1 + E^5*(2 + E^
5))*x^2), x])/(1 + E^5) + (2*E*(4 + 6*E^5 + 3*E^10)*Defer[Int][(E^x*x^2)/(E^(2*x) + E^2*x^2 + 2*E^(1 + x)*(1 +
E^5)*x^2 + E^(2*x)*(1 + E^5*(2 + E^5))*x^2), x])/(1 + E^5)

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-6 x+2 x^3+e^{10} \left (-6 x+2 x^3\right )+e^5 \left (-12 x+4 x^3\right )+e^{2-2 x} \left (-6 x+6 x^2+2 x^3-2 x^4\right )+e^{1-x} \left (-12 x+6 x^2+4 x^3-2 x^4+e^5 \left (-12 x+6 x^2+4 x^3-2 x^4\right )\right )+\left (2 x+2 x^3+4 e^5 x^3+2 e^{10} x^3+2 e^{2-2 x} x^3+e^{1-x} \left (4 x^3+4 e^5 x^3\right )\right ) \log \left (1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )\right )}{1+e^{10} x^2+e^{2-2 x} x^2+\left (1+2 e^5\right ) x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )} \, dx\\ &=\int \frac {-6 x+2 x^3+e^{10} \left (-6 x+2 x^3\right )+e^5 \left (-12 x+4 x^3\right )+e^{2-2 x} \left (-6 x+6 x^2+2 x^3-2 x^4\right )+e^{1-x} \left (-12 x+6 x^2+4 x^3-2 x^4+e^5 \left (-12 x+6 x^2+4 x^3-2 x^4\right )\right )+\left (2 x+2 x^3+4 e^5 x^3+2 e^{10} x^3+2 e^{2-2 x} x^3+e^{1-x} \left (4 x^3+4 e^5 x^3\right )\right ) \log \left (1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )\right )}{1+e^{2-2 x} x^2+\left (1+2 e^5+e^{10}\right ) x^2+e^{1-x} \left (2 x^2+2 e^5 x^2\right )} \, dx\\ &=\int \frac {2 x \left (-3+x^2+2 e^5 \left (1+\frac {e^5}{2}\right ) \left (-3+x^2\right )+e^{2-2 x} \left (-3+3 x+x^2-x^3\right )-e^{1-x} \left (1+e^5\right ) \left (6-3 x-2 x^2+x^3\right )+e^{-2 x} \left (e^2 x^2+2 e^{1+x} x^2+e^{2 (5+x)} x^2+2 e^{6+x} x^2+2 e^{5+2 x} x^2+e^{2 x} \left (1+x^2\right )\right ) \log \left (1+e^{-2 x} \left (e+e^x+e^{5+x}\right )^2 x^2\right )\right )}{1+e^{-2 x} \left (e+e^x+e^{5+x}\right )^2 x^2} \, dx\\ &=2 \int \frac {x \left (-3+x^2+2 e^5 \left (1+\frac {e^5}{2}\right ) \left (-3+x^2\right )+e^{2-2 x} \left (-3+3 x+x^2-x^3\right )-e^{1-x} \left (1+e^5\right ) \left (6-3 x-2 x^2+x^3\right )+e^{-2 x} \left (e^2 x^2+2 e^{1+x} x^2+e^{2 (5+x)} x^2+2 e^{6+x} x^2+2 e^{5+2 x} x^2+e^{2 x} \left (1+x^2\right )\right ) \log \left (1+e^{-2 x} \left (e+e^x+e^{5+x}\right )^2 x^2\right )\right )}{1+e^{-2 x} \left (e+e^x+e^{5+x}\right )^2 x^2} \, dx\\ &=2 \int \left (\frac {e x \left (3-x^2\right ) \left (-e-2 e^x \left (1+e^5\right )+e x+e^x \left (1+e^5\right ) x+e \left (1+e^5 \left (2+e^5\right )\right ) x^3+e^x \left (1+e^5 \left (3+3 e^5+e^{10}\right )\right ) x^3\right )}{\left (1+\left (1+e^5\right )^2 x^2\right ) \left (e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2\right )}+\frac {x \left (-3 \left (1+e^5 \left (2+e^5\right )\right )+\left (1+e^5 \left (2+e^5\right )\right ) x^2+\log \left (1+e^{-2 x} \left (e+e^x+e^{5+x}\right )^2 x^2\right )+\left (1+e^5 \left (2+e^5\right )\right ) x^2 \log \left (1+e^{-2 x} \left (e+e^x+e^{5+x}\right )^2 x^2\right )\right )}{1+\left (1+e^5\right )^2 x^2}\right ) \, dx\\ &=2 \int \frac {x \left (-3 \left (1+e^5 \left (2+e^5\right )\right )+\left (1+e^5 \left (2+e^5\right )\right ) x^2+\log \left (1+e^{-2 x} \left (e+e^x+e^{5+x}\right )^2 x^2\right )+\left (1+e^5 \left (2+e^5\right )\right ) x^2 \log \left (1+e^{-2 x} \left (e+e^x+e^{5+x}\right )^2 x^2\right )\right )}{1+\left (1+e^5\right )^2 x^2} \, dx+(2 e) \int \frac {x \left (3-x^2\right ) \left (-e-2 e^x \left (1+e^5\right )+e x+e^x \left (1+e^5\right ) x+e \left (1+e^5 \left (2+e^5\right )\right ) x^3+e^x \left (1+e^5 \left (3+3 e^5+e^{10}\right )\right ) x^3\right )}{\left (1+\left (1+e^5\right )^2 x^2\right ) \left (e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2\right )} \, dx\\ &=2 \int x \left (\frac {\left (1+e^5\right )^2 \left (-3+x^2\right )}{1+\left (1+e^5\right )^2 x^2}+\log \left (1+e^{-2 x} \left (e+e^x+e^{5+x}\right )^2 x^2\right )\right ) \, dx+(2 e) \int \left (\frac {x \left (e+2 e^x \left (1+e^5\right )-e x-e^x \left (1+e^5\right ) x-e \left (1+e^5 \left (2+e^5\right )\right ) x^3-e^x \left (1+e^5 \left (3+3 e^5+e^{10}\right )\right ) x^3\right )}{\left (1+e^5\right )^2 \left (e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2\right )}+\frac {\left (4+6 e^5+3 e^{10}\right ) x \left (-e-2 e^x \left (1+e^5\right )+e x+e^x \left (1+e^5\right ) x+e \left (1+e^5 \left (2+e^5\right )\right ) x^3+e^x \left (1+e^5 \left (3+3 e^5+e^{10}\right )\right ) x^3\right )}{\left (1+e^5\right )^2 \left (1+\left (1+e^5\right )^2 x^2\right ) \left (e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2\right )}\right ) \, dx\\ &=2 \int \left (\frac {\left (1+e^5\right )^2 x \left (-3+x^2\right )}{1+\left (1+e^5\right )^2 x^2}+x \log \left (1+e^{-2 x} \left (e+e^x+e^{5+x}\right )^2 x^2\right )\right ) \, dx+\frac {(2 e) \int \frac {x \left (e+2 e^x \left (1+e^5\right )-e x-e^x \left (1+e^5\right ) x-e \left (1+e^5 \left (2+e^5\right )\right ) x^3-e^x \left (1+e^5 \left (3+3 e^5+e^{10}\right )\right ) x^3\right )}{e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2} \, dx}{\left (1+e^5\right )^2}+\frac {\left (2 e \left (4+6 e^5+3 e^{10}\right )\right ) \int \frac {x \left (-e-2 e^x \left (1+e^5\right )+e x+e^x \left (1+e^5\right ) x+e \left (1+e^5 \left (2+e^5\right )\right ) x^3+e^x \left (1+e^5 \left (3+3 e^5+e^{10}\right )\right ) x^3\right )}{\left (1+\left (1+e^5\right )^2 x^2\right ) \left (e^{2 x}+e^2 x^2+2 e^{1+x} \left (1+e^5\right ) x^2+e^{2 x} \left (1+e^5 \left (2+e^5\right )\right ) x^2\right )} \, dx}{\left (1+e^5\right )^2}\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [B]  time = 0.26, size = 94, normalized size = 3.48 \begin {gather*} 2 \left (-\frac {3}{2} \log \left (1+x^2+2 e^5 x^2+e^{10} x^2+e^{2-2 x} x^2+2 e^{1-x} x^2+2 e^{6-x} x^2\right )+\frac {1}{2} x^2 \log \left (1+e^{-2 x} \left (e+e^x+e^{5+x}\right )^2 x^2\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-6*x + 2*x^3 + E^10*(-6*x + 2*x^3) + E^5*(-12*x + 4*x^3) + E^(2 - 2*x)*(-6*x + 6*x^2 + 2*x^3 - 2*x^
4) + E^(1 - x)*(-12*x + 6*x^2 + 4*x^3 - 2*x^4 + E^5*(-12*x + 6*x^2 + 4*x^3 - 2*x^4)) + (2*x + 2*x^3 + 4*E^5*x^
3 + 2*E^10*x^3 + 2*E^(2 - 2*x)*x^3 + E^(1 - x)*(4*x^3 + 4*E^5*x^3))*Log[1 + x^2 + 2*E^5*x^2 + E^10*x^2 + E^(2
- 2*x)*x^2 + E^(1 - x)*(2*x^2 + 2*E^5*x^2)])/(1 + x^2 + 2*E^5*x^2 + E^10*x^2 + E^(2 - 2*x)*x^2 + E^(1 - x)*(2*
x^2 + 2*E^5*x^2)),x]

[Out]

2*((-3*Log[1 + x^2 + 2*E^5*x^2 + E^10*x^2 + E^(2 - 2*x)*x^2 + 2*E^(1 - x)*x^2 + 2*E^(6 - x)*x^2])/2 + (x^2*Log
[1 + ((E + E^x + E^(5 + x))^2*x^2)/E^(2*x)])/2)

________________________________________________________________________________________

fricas [B]  time = 1.08, size = 53, normalized size = 1.96 \begin {gather*} {\left (x^{2} - 3\right )} \log \left (x^{2} e^{10} + 2 \, x^{2} e^{5} + x^{2} e^{\left (-2 \, x + 2\right )} + x^{2} + 2 \, {\left (x^{2} e^{5} + x^{2}\right )} e^{\left (-x + 1\right )} + 1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^3*exp(-x+1)^2+(4*x^3*exp(5)+4*x^3)*exp(-x+1)+2*x^3*exp(5)^2+4*x^3*exp(5)+2*x^3+2*x)*log(x^2*ex
p(-x+1)^2+(2*x^2*exp(5)+2*x^2)*exp(-x+1)+x^2*exp(5)^2+2*x^2*exp(5)+x^2+1)+(-2*x^4+2*x^3+6*x^2-6*x)*exp(-x+1)^2
+((-2*x^4+4*x^3+6*x^2-12*x)*exp(5)-2*x^4+4*x^3+6*x^2-12*x)*exp(-x+1)+(2*x^3-6*x)*exp(5)^2+(4*x^3-12*x)*exp(5)+
2*x^3-6*x)/(x^2*exp(-x+1)^2+(2*x^2*exp(5)+2*x^2)*exp(-x+1)+x^2*exp(5)^2+2*x^2*exp(5)+x^2+1),x, algorithm="fric
as")

[Out]

(x^2 - 3)*log(x^2*e^10 + 2*x^2*e^5 + x^2*e^(-2*x + 2) + x^2 + 2*(x^2*e^5 + x^2)*e^(-x + 1) + 1)

________________________________________________________________________________________

giac [B]  time = 0.31, size = 133, normalized size = 4.93 \begin {gather*} -2 \, x^{3} + x^{2} \log \left (x^{2} e^{2} + x^{2} e^{\left (2 \, x\right )} + x^{2} e^{\left (2 \, x + 10\right )} + 2 \, x^{2} e^{\left (2 \, x + 5\right )} + 2 \, x^{2} e^{\left (x + 6\right )} + 2 \, x^{2} e^{\left (x + 1\right )} + e^{\left (2 \, x\right )}\right ) + 6 \, x - 3 \, \log \left (x^{2} e^{2} + x^{2} e^{\left (2 \, x\right )} + x^{2} e^{\left (2 \, x + 10\right )} + 2 \, x^{2} e^{\left (2 \, x + 5\right )} + 2 \, x^{2} e^{\left (x + 6\right )} + 2 \, x^{2} e^{\left (x + 1\right )} + e^{\left (2 \, x\right )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^3*exp(-x+1)^2+(4*x^3*exp(5)+4*x^3)*exp(-x+1)+2*x^3*exp(5)^2+4*x^3*exp(5)+2*x^3+2*x)*log(x^2*ex
p(-x+1)^2+(2*x^2*exp(5)+2*x^2)*exp(-x+1)+x^2*exp(5)^2+2*x^2*exp(5)+x^2+1)+(-2*x^4+2*x^3+6*x^2-6*x)*exp(-x+1)^2
+((-2*x^4+4*x^3+6*x^2-12*x)*exp(5)-2*x^4+4*x^3+6*x^2-12*x)*exp(-x+1)+(2*x^3-6*x)*exp(5)^2+(4*x^3-12*x)*exp(5)+
2*x^3-6*x)/(x^2*exp(-x+1)^2+(2*x^2*exp(5)+2*x^2)*exp(-x+1)+x^2*exp(5)^2+2*x^2*exp(5)+x^2+1),x, algorithm="giac
")

[Out]

-2*x^3 + x^2*log(x^2*e^2 + x^2*e^(2*x) + x^2*e^(2*x + 10) + 2*x^2*e^(2*x + 5) + 2*x^2*e^(x + 6) + 2*x^2*e^(x +
1) + e^(2*x)) + 6*x - 3*log(x^2*e^2 + x^2*e^(2*x) + x^2*e^(2*x + 10) + 2*x^2*e^(2*x + 5) + 2*x^2*e^(x + 6) +
2*x^2*e^(x + 1) + e^(2*x))

________________________________________________________________________________________

maple [B]  time = 0.07, size = 105, normalized size = 3.89

method	result	size
risch	\(x^{2} \ln \left (x^{2} {\mathrm e}^{-2 x +2}+\left (2 x^{2} {\mathrm e}^{5}+2 x^{2}\right ) {\mathrm e}^{1-x}+x^{2} {\mathrm e}^{10}+2 x^{2} {\mathrm e}^{5}+x^{2}+1\right )-6 \ln \relax (x )+6-3 \ln \left ({\mathrm e}^{-2 x +2}+\left (2 \,{\mathrm e}^{5}+2\right ) {\mathrm e}^{1-x}+\frac {2 x^{2} {\mathrm e}^{5}+x^{2} {\mathrm e}^{10}+x^{2}+1}{x^{2}}\right )\)	\(105\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((2*x^3*exp(1-x)^2+(4*x^3*exp(5)+4*x^3)*exp(1-x)+2*x^3*exp(5)^2+4*x^3*exp(5)+2*x^3+2*x)*ln(x^2*exp(1-x)^2+
(2*x^2*exp(5)+2*x^2)*exp(1-x)+x^2*exp(5)^2+2*x^2*exp(5)+x^2+1)+(-2*x^4+2*x^3+6*x^2-6*x)*exp(1-x)^2+((-2*x^4+4*
x^3+6*x^2-12*x)*exp(5)-2*x^4+4*x^3+6*x^2-12*x)*exp(1-x)+(2*x^3-6*x)*exp(5)^2+(4*x^3-12*x)*exp(5)+2*x^3-6*x)/(x
^2*exp(1-x)^2+(2*x^2*exp(5)+2*x^2)*exp(1-x)+x^2*exp(5)^2+2*x^2*exp(5)+x^2+1),x,method=_RETURNVERBOSE)

[Out]

x^2*ln(x^2*exp(-2*x+2)+(2*x^2*exp(5)+2*x^2)*exp(1-x)+x^2*exp(10)+2*x^2*exp(5)+x^2+1)-6*ln(x)+6-3*ln(exp(-2*x+2
)+(2*exp(5)+2)*exp(1-x)+(2*x^2*exp(5)+x^2*exp(10)+x^2+1)/x^2)

________________________________________________________________________________________

maxima [B]  time = 0.46, size = 127, normalized size = 4.70 \begin {gather*} -2 \, x^{3} + x^{2} \log \left (2 \, x^{2} {\left (e^{6} + e\right )} e^{x} + x^{2} e^{2} + {\left (x^{2} {\left (e^{10} + 2 \, e^{5} + 1\right )} + 1\right )} e^{\left (2 \, x\right )}\right ) + 6 \, x - 3 \, \log \left (x^{2} {\left (e^{10} + 2 \, e^{5} + 1\right )} + 1\right ) - 3 \, \log \left (\frac {2 \, x^{2} {\left (e^{6} + e\right )} e^{x} + x^{2} e^{2} + {\left (x^{2} {\left (e^{10} + 2 \, e^{5} + 1\right )} + 1\right )} e^{\left (2 \, x\right )}}{x^{2} {\left (e^{10} + 2 \, e^{5} + 1\right )} + 1}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^3*exp(-x+1)^2+(4*x^3*exp(5)+4*x^3)*exp(-x+1)+2*x^3*exp(5)^2+4*x^3*exp(5)+2*x^3+2*x)*log(x^2*ex
p(-x+1)^2+(2*x^2*exp(5)+2*x^2)*exp(-x+1)+x^2*exp(5)^2+2*x^2*exp(5)+x^2+1)+(-2*x^4+2*x^3+6*x^2-6*x)*exp(-x+1)^2
+((-2*x^4+4*x^3+6*x^2-12*x)*exp(5)-2*x^4+4*x^3+6*x^2-12*x)*exp(-x+1)+(2*x^3-6*x)*exp(5)^2+(4*x^3-12*x)*exp(5)+
2*x^3-6*x)/(x^2*exp(-x+1)^2+(2*x^2*exp(5)+2*x^2)*exp(-x+1)+x^2*exp(5)^2+2*x^2*exp(5)+x^2+1),x, algorithm="maxi
ma")

[Out]

-2*x^3 + x^2*log(2*x^2*(e^6 + e)*e^x + x^2*e^2 + (x^2*(e^10 + 2*e^5 + 1) + 1)*e^(2*x)) + 6*x - 3*log(x^2*(e^10
+ 2*e^5 + 1) + 1) - 3*log((2*x^2*(e^6 + e)*e^x + x^2*e^2 + (x^2*(e^10 + 2*e^5 + 1) + 1)*e^(2*x))/(x^2*(e^10 +
2*e^5 + 1) + 1))

________________________________________________________________________________________

mupad [B]  time = 0.88, size = 119, normalized size = 4.41 \begin {gather*} x^2\,\ln \left (2\,x^2\,{\mathrm {e}}^5+x^2\,{\mathrm {e}}^{10}+x^2+2\,x^2\,{\mathrm {e}}^{-x}\,\mathrm {e}+x^2\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^2+2\,x^2\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^6+1\right )-3\,\ln \left (2\,x^2\,{\mathrm {e}}^5+x^2\,{\mathrm {e}}^{10}+x^2+2\,x^2\,{\mathrm {e}}^{-x}\,\mathrm {e}+x^2\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^2+2\,x^2\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^6+1\right )-6\,\ln \relax (x)-3\,\ln \left (\frac {1}{x^2}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(6*x + exp(10)*(6*x - 2*x^3) + exp(5)*(12*x - 4*x^3) + exp(1 - x)*(12*x + exp(5)*(12*x - 6*x^2 - 4*x^3 +
2*x^4) - 6*x^2 - 4*x^3 + 2*x^4) + exp(2 - 2*x)*(6*x - 6*x^2 - 2*x^3 + 2*x^4) - 2*x^3 - log(exp(1 - x)*(2*x^2*e
xp(5) + 2*x^2) + 2*x^2*exp(5) + x^2*exp(10) + x^2*exp(2 - 2*x) + x^2 + 1)*(2*x + exp(1 - x)*(4*x^3*exp(5) + 4*
x^3) + 4*x^3*exp(5) + 2*x^3*exp(10) + 2*x^3*exp(2 - 2*x) + 2*x^3))/(exp(1 - x)*(2*x^2*exp(5) + 2*x^2) + 2*x^2*
exp(5) + x^2*exp(10) + x^2*exp(2 - 2*x) + x^2 + 1),x)

[Out]

x^2*log(2*x^2*exp(5) + x^2*exp(10) + x^2 + 2*x^2*exp(-x)*exp(1) + x^2*exp(-2*x)*exp(2) + 2*x^2*exp(-x)*exp(6)
+ 1) - 3*log(2*x^2*exp(5) + x^2*exp(10) + x^2 + 2*x^2*exp(-x)*exp(1) + x^2*exp(-2*x)*exp(2) + 2*x^2*exp(-x)*ex
p(6) + 1) - 6*log(x) - 3*log(1/x^2)

________________________________________________________________________________________

sympy [B]  time = 1.07, size = 104, normalized size = 3.85 \begin {gather*} x^{2} \log {\left (x^{2} e^{2 - 2 x} + x^{2} + 2 x^{2} e^{5} + x^{2} e^{10} + \left (2 x^{2} + 2 x^{2} e^{5}\right ) e^{1 - x} + 1 \right )} - 6 \log {\relax (x )} - 3 \log {\left (\left (2 + 2 e^{5}\right ) e^{1 - x} + e^{2 - 2 x} + \frac {x^{2} + 2 x^{2} e^{5} + x^{2} e^{10} + 1}{x^{2}} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x**3*exp(-x+1)**2+(4*x**3*exp(5)+4*x**3)*exp(-x+1)+2*x**3*exp(5)**2+4*x**3*exp(5)+2*x**3+2*x)*ln
(x**2*exp(-x+1)**2+(2*x**2*exp(5)+2*x**2)*exp(-x+1)+x**2*exp(5)**2+2*x**2*exp(5)+x**2+1)+(-2*x**4+2*x**3+6*x**
2-6*x)*exp(-x+1)**2+((-2*x**4+4*x**3+6*x**2-12*x)*exp(5)-2*x**4+4*x**3+6*x**2-12*x)*exp(-x+1)+(2*x**3-6*x)*exp
(5)**2+(4*x**3-12*x)*exp(5)+2*x**3-6*x)/(x**2*exp(-x+1)**2+(2*x**2*exp(5)+2*x**2)*exp(-x+1)+x**2*exp(5)**2+2*x
**2*exp(5)+x**2+1),x)

[Out]

x**2*log(x**2*exp(2 - 2*x) + x**2 + 2*x**2*exp(5) + x**2*exp(10) + (2*x**2 + 2*x**2*exp(5))*exp(1 - x) + 1) -
6*log(x) - 3*log((2 + 2*exp(5))*exp(1 - x) + exp(2 - 2*x) + (x**2 + 2*x**2*exp(5) + x**2*exp(10) + 1)/x**2)

________________________________________________________________________________________