∫ −2−x+8x3+x4+e2e4x−x log(x)x (1+e4x−x log(x)(4+12x−4x log(x)))+ee4x−x log(x)x (8x+2x2+e4x−x log(x)(4x2+12x3−4x3 log(x)))___________________________________________________________________________________________ e2e4x−x log(x)x −x+2ee4x−x log(x)x x2+x4 dx

3.27.10 \(\int \frac {-2-x+8 x^3+x^4+e^{2 e^{4 x-x \log (x)} x} (1+e^{4 x-x \log (x)} (4+12 x-4 x \log (x)))+e^{e^{4 x-x \log (x)} x} (8 x+2 x^2+e^{4 x-x \log (x)} (4 x^2+12 x^3-4 x^3 \log (x)))}{e^{2 e^{4 x-x \log (x)} x}-x+2 e^{e^{4 x-x \log (x)} x} x^2+x^4} \, dx\)

Optimal. Leaf size=29 \[ x+\log \left (\left (x-\left (e^{e^{x (4-\log (x))} x}+x^2\right )^2\right )^2\right ) \]

________________________________________________________________________________________

Rubi [F] time = 11.51, 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 {-2-x+8 x^3+x^4+e^{2 e^{4 x-x \log (x)} x} \left (1+e^{4 x-x \log (x)} (4+12 x-4 x \log (x))\right )+e^{e^{4 x-x \log (x)} x} \left (8 x+2 x^2+e^{4 x-x \log (x)} \left (4 x^2+12 x^3-4 x^3 \log (x)\right )\right )}{e^{2 e^{4 x-x \log (x)} x}-x+2 e^{e^{4 x-x \log (x)} x} x^2+x^4} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[(-2 - x + 8*x^3 + x^4 + E^(2*E^(4*x - x*Log[x])*x)*(1 + E^(4*x - x*Log[x])*(4 + 12*x - 4*x*Log[x])) + E^(E

^(4*x - x*Log[x])*x)*(8*x + 2*x^2 + E^(4*x - x*Log[x])*(4*x^2 + 12*x^3 - 4*x^3*Log[x])))/(E^(2*E^(4*x - x*Log[

x])*x) - x + 2*E^(E^(4*x - x*Log[x])*x)*x^2 + x^4),x]

[Out]

-2*Defer[Int][(E^(2*E^(4*x)*x^(1 - x)) - x + 2*E^(E^(4*x)*x^(1 - x))*x^2 + x^4)^(-1), x] + Defer[Int][E^(2*E^(

4*x)*x^(1 - x))/(E^(2*E^(4*x)*x^(1 - x)) - x + 2*E^(E^(4*x)*x^(1 - x))*x^2 + x^4), x] - Defer[Int][x/(E^(2*E^(

4*x)*x^(1 - x)) - x + 2*E^(E^(4*x)*x^(1 - x))*x^2 + x^4), x] + 8*Defer[Int][(E^(E^(4*x)*x^(1 - x))*x)/(E^(2*E^

(4*x)*x^(1 - x)) - x + 2*E^(E^(4*x)*x^(1 - x))*x^2 + x^4), x] + 2*Defer[Int][(E^(E^(4*x)*x^(1 - x))*x^2)/(E^(2

*E^(4*x)*x^(1 - x)) - x + 2*E^(E^(4*x)*x^(1 - x))*x^2 + x^4), x] + 8*Defer[Int][x^3/(E^(2*E^(4*x)*x^(1 - x)) -

x + 2*E^(E^(4*x)*x^(1 - x))*x^2 + x^4), x] + Defer[Int][x^4/(E^(2*E^(4*x)*x^(1 - x)) - x + 2*E^(E^(4*x)*x^(1

- x))*x^2 + x^4), x] + 12*Defer[Int][(E^(2*x*(2 + E^(4*x)/x^x))*x^(1 - x))/(E^(2*E^(4*x)*x^(1 - x)) - x + 2*E^

(E^(4*x)*x^(1 - x))*x^2 + x^4), x] - 4*Log[x]*Defer[Int][(E^(2*x*(2 + E^(4*x)/x^x))*x^(1 - x))/(E^(2*E^(4*x)*x

^(1 - x)) - x + 2*E^(E^(4*x)*x^(1 - x))*x^2 + x^4), x] + 4*Defer[Int][(E^(x^(1 - x)*(E^(4*x) + 4*x^x))*x^(2 -

x))/(E^(2*E^(4*x)*x^(1 - x)) - x + 2*E^(E^(4*x)*x^(1 - x))*x^2 + x^4), x] + 12*Defer[Int][(E^(x^(1 - x)*(E^(4*

x) + 4*x^x))*x^(3 - x))/(E^(2*E^(4*x)*x^(1 - x)) - x + 2*E^(E^(4*x)*x^(1 - x))*x^2 + x^4), x] - 4*Log[x]*Defer

[Int][(E^(x^(1 - x)*(E^(4*x) + 4*x^x))*x^(3 - x))/(E^(2*E^(4*x)*x^(1 - x)) - x + 2*E^(E^(4*x)*x^(1 - x))*x^2 +

x^4), x] + 4*Defer[Int][E^(2*x*(2 + E^(4*x)/x^x))/(x^x*(E^(2*E^(4*x)*x^(1 - x)) - x + 2*E^(E^(4*x)*x^(1 - x))

*x^2 + x^4)), x] + 4*Defer[Int][Defer[Int][(E^(2*x*(2 + E^(4*x)/x^x))*x^(1 - x))/(E^(2*E^(4*x)*x^(1 - x)) - x

+ 2*E^(E^(4*x)*x^(1 - x))*x^2 + x^4), x]/x, x] + 4*Defer[Int][Defer[Int][(E^(x^(1 - x)*(E^(4*x) + 4*x^x))*x^(3

- x))/(E^(2*E^(4*x)*x^(1 - x)) - x + 2*E^(E^(4*x)*x^(1 - x))*x^2 + x^4), x]/x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {2}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4}+\frac {e^{2 e^{4 x} x^{1-x}}}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4}-\frac {x}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4}+\frac {8 e^{e^{4 x} x^{1-x}} x}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4}+\frac {2 e^{e^{4 x} x^{1-x}} x^2}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4}+\frac {8 x^3}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4}+\frac {x^4}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4}+\frac {4 e^{x^{1-x} \left (e^{4 x}+4 x^x\right )} x^{-x} \left (e^{e^{4 x} x^{1-x}}+x^2\right ) (1+3 x-x \log (x))}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4}\right ) \, dx\\ &=-\left (2 \int \frac {1}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx\right )+2 \int \frac {e^{e^{4 x} x^{1-x}} x^2}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx+4 \int \frac {e^{x^{1-x} \left (e^{4 x}+4 x^x\right )} x^{-x} \left (e^{e^{4 x} x^{1-x}}+x^2\right ) (1+3 x-x \log (x))}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx+8 \int \frac {e^{e^{4 x} x^{1-x}} x}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx+8 \int \frac {x^3}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx+\int \frac {e^{2 e^{4 x} x^{1-x}}}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx-\int \frac {x}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx+\int \frac {x^4}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx\\ &=-\left (2 \int \frac {1}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx\right )+2 \int \frac {e^{e^{4 x} x^{1-x}} x^2}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx+4 \int \left (\frac {3 e^{e^{4 x} x^{1-x}+x^{1-x} \left (e^{4 x}+4 x^x\right )} x^{1-x}}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4}+\frac {e^{x^{1-x} \left (e^{4 x}+4 x^x\right )} x^{2-x}}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4}+\frac {3 e^{x^{1-x} \left (e^{4 x}+4 x^x\right )} x^{3-x}}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4}+\frac {e^{e^{4 x} x^{1-x}+x^{1-x} \left (e^{4 x}+4 x^x\right )} x^{-x}}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4}-\frac {e^{e^{4 x} x^{1-x}+x^{1-x} \left (e^{4 x}+4 x^x\right )} x^{1-x} \log (x)}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4}-\frac {e^{x^{1-x} \left (e^{4 x}+4 x^x\right )} x^{3-x} \log (x)}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4}\right ) \, dx+8 \int \frac {e^{e^{4 x} x^{1-x}} x}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx+8 \int \frac {x^3}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx+\int \frac {e^{2 e^{4 x} x^{1-x}}}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx-\int \frac {x}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx+\int \frac {x^4}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx\\ &=-\left (2 \int \frac {1}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx\right )+2 \int \frac {e^{e^{4 x} x^{1-x}} x^2}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx+4 \int \frac {e^{x^{1-x} \left (e^{4 x}+4 x^x\right )} x^{2-x}}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx+4 \int \frac {e^{e^{4 x} x^{1-x}+x^{1-x} \left (e^{4 x}+4 x^x\right )} x^{-x}}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx-4 \int \frac {e^{e^{4 x} x^{1-x}+x^{1-x} \left (e^{4 x}+4 x^x\right )} x^{1-x} \log (x)}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx-4 \int \frac {e^{x^{1-x} \left (e^{4 x}+4 x^x\right )} x^{3-x} \log (x)}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx+8 \int \frac {e^{e^{4 x} x^{1-x}} x}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx+8 \int \frac {x^3}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx+12 \int \frac {e^{e^{4 x} x^{1-x}+x^{1-x} \left (e^{4 x}+4 x^x\right )} x^{1-x}}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx+12 \int \frac {e^{x^{1-x} \left (e^{4 x}+4 x^x\right )} x^{3-x}}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx+\int \frac {e^{2 e^{4 x} x^{1-x}}}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx-\int \frac {x}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx+\int \frac {x^4}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx\\ &=-\left (2 \int \frac {1}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx\right )+2 \int \frac {e^{e^{4 x} x^{1-x}} x^2}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx+4 \int \frac {e^{x^{1-x} \left (e^{4 x}+4 x^x\right )} x^{2-x}}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx+4 \int \frac {e^{2 x \left (2+e^{4 x} x^{-x}\right )} x^{-x}}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx+4 \int \frac {\int \frac {e^{2 x \left (2+e^{4 x} x^{-x}\right )} x^{1-x}}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx}{x} \, dx+4 \int \frac {\int \frac {e^{x^{1-x} \left (e^{4 x}+4 x^x\right )} x^{3-x}}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx}{x} \, dx+8 \int \frac {e^{e^{4 x} x^{1-x}} x}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx+8 \int \frac {x^3}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx+12 \int \frac {e^{2 x \left (2+e^{4 x} x^{-x}\right )} x^{1-x}}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx+12 \int \frac {e^{x^{1-x} \left (e^{4 x}+4 x^x\right )} x^{3-x}}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx-(4 \log (x)) \int \frac {e^{2 x \left (2+e^{4 x} x^{-x}\right )} x^{1-x}}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx-(4 \log (x)) \int \frac {e^{x^{1-x} \left (e^{4 x}+4 x^x\right )} x^{3-x}}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx+\int \frac {e^{2 e^{4 x} x^{1-x}}}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx-\int \frac {x}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx+\int \frac {x^4}{e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A] time = 2.97, size = 48, normalized size = 1.66 \begin {gather*} x+2 \log \left (e^{2 e^{4 x} x^{1-x}}-x+2 e^{e^{4 x} x^{1-x}} x^2+x^4\right ) \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(-2 - x + 8*x^3 + x^4 + E^(2*E^(4*x - x*Log[x])*x)*(1 + E^(4*x - x*Log[x])*(4 + 12*x - 4*x*Log[x]))

+ E^(E^(4*x - x*Log[x])*x)*(8*x + 2*x^2 + E^(4*x - x*Log[x])*(4*x^2 + 12*x^3 - 4*x^3*Log[x])))/(E^(2*E^(4*x -

x*Log[x])*x) - x + 2*E^(E^(4*x - x*Log[x])*x)*x^2 + x^4),x]

[Out]

x + 2*Log[E^(2*E^(4*x)*x^(1 - x)) - x + 2*E^(E^(4*x)*x^(1 - x))*x^2 + x^4]

________________________________________________________________________________________

fricas [A] time = 0.49, size = 44, normalized size = 1.52 \begin {gather*} x + 2 \, \log \left (x^{4} + 2 \, x^{2} e^{\left (x e^{\left (-x \log \relax (x) + 4 \, x\right )}\right )} - x + e^{\left (2 \, x e^{\left (-x \log \relax (x) + 4 \, x\right )}\right )}\right ) \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x*log(x)+12*x+4)*exp(-x*log(x)+4*x)+1)*exp(x*exp(-x*log(x)+4*x))^2+((-4*x^3*log(x)+12*x^3+4*x^

2)*exp(-x*log(x)+4*x)+2*x^2+8*x)*exp(x*exp(-x*log(x)+4*x))+x^4+8*x^3-x-2)/(exp(x*exp(-x*log(x)+4*x))^2+2*x^2*e

xp(x*exp(-x*log(x)+4*x))+x^4-x),x, algorithm="fricas")

[Out]

x + 2*log(x^4 + 2*x^2*e^(x*e^(-x*log(x) + 4*x)) - x + e^(2*x*e^(-x*log(x) + 4*x)))

________________________________________________________________________________________

giac [A] time = 1.95, size = 44, normalized size = 1.52 \begin {gather*} x + 2 \, \log \left (x^{4} + 2 \, x^{2} e^{\left (x e^{\left (-x \log \relax (x) + 4 \, x\right )}\right )} - x + e^{\left (2 \, x e^{\left (-x \log \relax (x) + 4 \, x\right )}\right )}\right ) \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x*log(x)+12*x+4)*exp(-x*log(x)+4*x)+1)*exp(x*exp(-x*log(x)+4*x))^2+((-4*x^3*log(x)+12*x^3+4*x^

2)*exp(-x*log(x)+4*x)+2*x^2+8*x)*exp(x*exp(-x*log(x)+4*x))+x^4+8*x^3-x-2)/(exp(x*exp(-x*log(x)+4*x))^2+2*x^2*e

xp(x*exp(-x*log(x)+4*x))+x^4-x),x, algorithm="giac")

[Out]

x + 2*log(x^4 + 2*x^2*e^(x*e^(-x*log(x) + 4*x)) - x + e^(2*x*e^(-x*log(x) + 4*x)))

________________________________________________________________________________________

maple [A] time = 0.05, size = 43, normalized size = 1.48


method	result	size

risch	\(x +2 \ln \left ({\mathrm e}^{2 x \,x^{-x} {\mathrm e}^{4 x}}+2 x^{2} {\mathrm e}^{x \,x^{-x} {\mathrm e}^{4 x}}+x^{4}-x \right )\)	\(43\)

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((((-4*x*ln(x)+12*x+4)*exp(-x*ln(x)+4*x)+1)*exp(x*exp(-x*ln(x)+4*x))^2+((-4*x^3*ln(x)+12*x^3+4*x^2)*exp(-x*

ln(x)+4*x)+2*x^2+8*x)*exp(x*exp(-x*ln(x)+4*x))+x^4+8*x^3-x-2)/(exp(x*exp(-x*ln(x)+4*x))^2+2*x^2*exp(x*exp(-x*l

n(x)+4*x))+x^4-x),x,method=_RETURNVERBOSE)

[Out]

x+2*ln(exp(2*x*x^(-x)*exp(4*x))+2*x^2*exp(x*x^(-x)*exp(4*x))+x^4-x)

________________________________________________________________________________________

maxima [A] time = 0.56, size = 44, normalized size = 1.52 \begin {gather*} x + 2 \, \log \left (x^{4} + 2 \, x^{2} e^{\left (x e^{\left (-x \log \relax (x) + 4 \, x\right )}\right )} - x + e^{\left (2 \, x e^{\left (-x \log \relax (x) + 4 \, x\right )}\right )}\right ) \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x*log(x)+12*x+4)*exp(-x*log(x)+4*x)+1)*exp(x*exp(-x*log(x)+4*x))^2+((-4*x^3*log(x)+12*x^3+4*x^

2)*exp(-x*log(x)+4*x)+2*x^2+8*x)*exp(x*exp(-x*log(x)+4*x))+x^4+8*x^3-x-2)/(exp(x*exp(-x*log(x)+4*x))^2+2*x^2*e

xp(x*exp(-x*log(x)+4*x))+x^4-x),x, algorithm="maxima")

[Out]

x + 2*log(x^4 + 2*x^2*e^(x*e^(-x*log(x) + 4*x)) - x + e^(2*x*e^(-x*log(x) + 4*x)))

________________________________________________________________________________________

mupad [B] time = 2.24, size = 44, normalized size = 1.52 \begin {gather*} x+2\,\ln \left ({\mathrm {e}}^{2\,x^{1-x}\,{\mathrm {e}}^{4\,x}}-x+2\,x^2\,{\mathrm {e}}^{x^{1-x}\,{\mathrm {e}}^{4\,x}}+x^4\right ) \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((exp(x*exp(4*x - x*log(x)))*(8*x + exp(4*x - x*log(x))*(4*x^2 - 4*x^3*log(x) + 12*x^3) + 2*x^2) - x + 8*x^

3 + x^4 + exp(2*x*exp(4*x - x*log(x)))*(exp(4*x - x*log(x))*(12*x - 4*x*log(x) + 4) + 1) - 2)/(exp(2*x*exp(4*x

- x*log(x))) - x + 2*x^2*exp(x*exp(4*x - x*log(x))) + x^4),x)

[Out]

x + 2*log(exp(2*x^(1 - x)*exp(4*x)) - x + 2*x^2*exp(x^(1 - x)*exp(4*x)) + x^4)

________________________________________________________________________________________

sympy [A] time = 0.80, size = 42, normalized size = 1.45 \begin {gather*} x + 2 \log {\left (x^{4} + 2 x^{2} e^{x e^{- x \log {\relax (x )} + 4 x}} - x + e^{2 x e^{- x \log {\relax (x )} + 4 x}} \right )} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x*ln(x)+12*x+4)*exp(-x*ln(x)+4*x)+1)*exp(x*exp(-x*ln(x)+4*x))**2+((-4*x**3*ln(x)+12*x**3+4*x**

2)*exp(-x*ln(x)+4*x)+2*x**2+8*x)*exp(x*exp(-x*ln(x)+4*x))+x**4+8*x**3-x-2)/(exp(x*exp(-x*ln(x)+4*x))**2+2*x**2

*exp(x*exp(-x*ln(x)+4*x))+x**4-x),x)

[Out]

x + 2*log(x**4 + 2*x**2*exp(x*exp(-x*log(x) + 4*x)) - x + exp(2*x*exp(-x*log(x) + 4*x)))

________________________________________________________________________________________

[next] [prev] [prev-tail] [front] [up]