∫ e16x−e4+xx+(−98e16−112e16x log(3)−60e16x2 log2(3)−16e16x3 log3(3)−2e16x4 log4(3)+e4+x(98+98x+(112x+112x2) log(3)+(60x2+60x3) log2(3)+(16x3+16x4) log3(3)+(2x4+2x5) log4(3))) log(e16x−e4+xx)+(−56e16x log(3)−60e16x2 log2(3)−24e16x3 log3(3)−4e16x4 log4(3)+e4+x(56x log(3)+60x2 log2(3)+24x3 log3(3)+4x4 log4(3))) log2(e16x−e4+xx)__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

3.91.71 \(\int \frac {e^{16} x-e^{4+x} x+(-98 e^{16}-112 e^{16} x \log (3)-60 e^{16} x^2 \log ^2(3)-16 e^{16} x^3 \log ^3(3)-2 e^{16} x^4 \log ^4(3)+e^{4+x} (98+98 x+(112 x+112 x^2) \log (3)+(60 x^2+60 x^3) \log ^2(3)+(16 x^3+16 x^4) \log ^3(3)+(2 x^4+2 x^5) \log ^4(3))) \log (e^{16} x-e^{4+x} x)+(-56 e^{16} x \log (3)-60 e^{16} x^2 \log ^2(3)-24 e^{16} x^3 \log ^3(3)-4 e^{16} x^4 \log ^4(3)+e^{4+x} (56 x \log (3)+60 x^2 \log ^2(3)+24 x^3 \log ^3(3)+4 x^4 \log ^4(3))) \log ^2(e^{16} x-e^{4+x} x)}{-e^{16} x+e^{4+x} x} \, dx\)

Optimal. Leaf size=33 \[ -x+\left (3+(2+x \log (3))^2\right )^2 \log ^2\left (\left (e^{16}-e^{4+x}\right ) x\right ) \]

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Rubi [F] time = 8.71, 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 {e^{16} x-e^{4+x} x+\left (-98 e^{16}-112 e^{16} x \log (3)-60 e^{16} x^2 \log ^2(3)-16 e^{16} x^3 \log ^3(3)-2 e^{16} x^4 \log ^4(3)+e^{4+x} \left (98+98 x+\left (112 x+112 x^2\right ) \log (3)+\left (60 x^2+60 x^3\right ) \log ^2(3)+\left (16 x^3+16 x^4\right ) \log ^3(3)+\left (2 x^4+2 x^5\right ) \log ^4(3)\right )\right ) \log \left (e^{16} x-e^{4+x} x\right )+\left (-56 e^{16} x \log (3)-60 e^{16} x^2 \log ^2(3)-24 e^{16} x^3 \log ^3(3)-4 e^{16} x^4 \log ^4(3)+e^{4+x} \left (56 x \log (3)+60 x^2 \log ^2(3)+24 x^3 \log ^3(3)+4 x^4 \log ^4(3)\right )\right ) \log ^2\left (e^{16} x-e^{4+x} x\right )}{-e^{16} x+e^{4+x} x} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[(E^16*x - E^(4 + x)*x + (-98*E^16 - 112*E^16*x*Log[3] - 60*E^16*x^2*Log[3]^2 - 16*E^16*x^3*Log[3]^3 - 2*E^

16*x^4*Log[3]^4 + E^(4 + x)*(98 + 98*x + (112*x + 112*x^2)*Log[3] + (60*x^2 + 60*x^3)*Log[3]^2 + (16*x^3 + 16*

x^4)*Log[3]^3 + (2*x^4 + 2*x^5)*Log[3]^4))*Log[E^16*x - E^(4 + x)*x] + (-56*E^16*x*Log[3] - 60*E^16*x^2*Log[3]

^2 - 24*E^16*x^3*Log[3]^3 - 4*E^16*x^4*Log[3]^4 + E^(4 + x)*(56*x*Log[3] + 60*x^2*Log[3]^2 + 24*x^3*Log[3]^3 +

4*x^4*Log[3]^4))*Log[E^16*x - E^(4 + x)*x]^2)/(-(E^16*x) + E^(4 + x)*x),x]

[Out]

-x - (2*x^5*Log[3]^4)/25 - (2*x^3*(Log[81]^2 + 2*Log[3]^2*(7 + Log[81])))/9 - (x^2*(14*Log[3]^2 + Log[81]*(14

+ Log[81])))/2 - 14*x*(7 + Log[6561]) - (x^4*Log[3]^2*(Log[3]^2 + Log[6561]))/8 - (2*x^5*Log[3]^4*Log[1 - E^(-

12 + x)])/5 - (2*x^3*(Log[81]^2 + 2*Log[3]^2*(7 + Log[81]))*Log[1 - E^(-12 + x)])/3 - x^2*(14*Log[3]^2 + Log[8

1]*(14 + Log[81]))*Log[1 - E^(-12 + x)] - 14*x*(7 + Log[6561])*Log[1 - E^(-12 + x)] - (x^4*Log[3]^2*(Log[3]^2

+ Log[6561])*Log[1 - E^(-12 + x)])/2 + (2*x^5*Log[3]^4*Log[E^4*(E^12 - E^x)*x])/5 + (2*x^3*(Log[81]^2 + 2*Log[

3]^2*(7 + Log[81]))*Log[E^4*(E^12 - E^x)*x])/3 + x^2*(14*Log[3]^2 + Log[81]*(14 + Log[81]))*Log[E^4*(E^12 - E^

x)*x] + 14*x*(7 + Log[6561])*Log[E^4*(E^12 - E^x)*x] + (x^4*Log[3]^2*(Log[3]^2 + Log[6561])*Log[E^4*(E^12 - E^

x)*x])/2 - 2*x^4*Log[3]^4*PolyLog[2, E^(-12 + x)] - 2*x^2*(Log[81]^2 + 2*Log[3]^2*(7 + Log[81]))*PolyLog[2, E^

(-12 + x)] - 2*x*(14*Log[3]^2 + Log[81]*(14 + Log[81]))*PolyLog[2, E^(-12 + x)] - 14*(7 + Log[6561])*PolyLog[2

, E^(-12 + x)] - 2*x^3*Log[3]^2*(Log[3]^2 + Log[6561])*PolyLog[2, E^(-12 + x)] + 8*x^3*Log[3]^4*PolyLog[3, E^(

-12 + x)] + 4*x*(Log[81]^2 + 2*Log[3]^2*(7 + Log[81]))*PolyLog[3, E^(-12 + x)] + 2*(14*Log[3]^2 + Log[81]*(14

+ Log[81]))*PolyLog[3, E^(-12 + x)] + 6*x^2*Log[3]^2*(Log[3]^2 + Log[6561])*PolyLog[3, E^(-12 + x)] - 24*x^2*L

og[3]^4*PolyLog[4, E^(-12 + x)] - 4*(Log[81]^2 + 2*Log[3]^2*(7 + Log[81]))*PolyLog[4, E^(-12 + x)] - 12*x*Log[

3]^2*(Log[3]^2 + Log[6561])*PolyLog[4, E^(-12 + x)] + 48*x*Log[3]^4*PolyLog[5, E^(-12 + x)] + 12*Log[3]^2*(Log

[3]^2 + Log[6561])*PolyLog[5, E^(-12 + x)] - 48*Log[3]^4*PolyLog[6, E^(-12 + x)] + 98*E^12*Defer[Int][Log[E^4*

(E^12 - E^x)*x]/(-E^12 + E^x), x] + 98*Defer[Int][Log[E^4*(E^12 - E^x)*x]/x, x] + 28*E^12*Log[81]*Defer[Int][(

x*Log[E^4*(E^12 - E^x)*x])/(-E^12 + E^x), x] + 2*E^12*(14*Log[3]^2 + Log[81]^2)*Defer[Int][(x^2*Log[E^4*(E^12

- E^x)*x])/(-E^12 + E^x), x] + 4*E^12*Log[3]^2*Log[81]*Defer[Int][(x^3*Log[E^4*(E^12 - E^x)*x])/(-E^12 + E^x),

x] + 2*E^12*Log[3]^4*Defer[Int][(x^4*Log[E^4*(E^12 - E^x)*x])/(-E^12 + E^x), x] + 56*Log[3]*Defer[Int][Log[E^

4*(E^12 - E^x)*x]^2, x] + 60*Log[3]^2*Defer[Int][x*Log[E^4*(E^12 - E^x)*x]^2, x] + 24*Log[3]^3*Defer[Int][x^2*

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-e^{12} x+e^x x-2 \left (-e^{12}+e^x (1+x)\right ) \left (7+x^2 \log ^2(3)+x \log (81)\right )^2 \log \left (e^{16} x-e^{4+x} x\right )-4 \left (-e^{12}+e^x\right ) x \log (3) \left (14+15 x \log (3)+6 x^2 \log ^2(3)+x^3 \log ^3(3)\right ) \log ^2\left (e^{16} x-e^{4+x} x\right )}{\left (e^{12}-e^x\right ) x} \, dx\\ &=\int \left (\frac {2 e^{12} \left (7+x^2 \log ^2(3)+x \log (81)\right )^2 \log \left (e^4 \left (e^{12}-e^x\right ) x\right )}{-e^{12}+e^x}+\frac {-x+98 \log \left (e^{16} x-e^{4+x} x\right )+2 x^5 \log ^4(3) \log \left (e^{16} x-e^{4+x} x\right )+98 x \left (1+\frac {2 \log (81)}{7}\right ) \log \left (e^{16} x-e^{4+x} x\right )+2 x^4 \log ^4(3) \left (1+\frac {2 \log (81)}{\log ^2(3)}\right ) \log \left (e^{16} x-e^{4+x} x\right )+28 x^2 \log ^2(3) \left (1+\frac {(7+\log (9)) \log (81)}{7 \log ^2(3)}\right ) \log \left (e^{16} x-e^{4+x} x\right )+28 x^3 \log ^2(3) \left (1+\frac {1}{7} \log (81) \left (1+\frac {\log (81)}{2 \log ^2(3)}\right )\right ) \log \left (e^{16} x-e^{4+x} x\right )+56 x \log (3) \log ^2\left (e^{16} x-e^{4+x} x\right )+60 x^2 \log ^2(3) \log ^2\left (e^{16} x-e^{4+x} x\right )+24 x^3 \log ^3(3) \log ^2\left (e^{16} x-e^{4+x} x\right )+4 x^4 \log ^4(3) \log ^2\left (e^{16} x-e^{4+x} x\right )}{x}\right ) \, dx\\ &=\left (2 e^{12}\right ) \int \frac {\left (7+x^2 \log ^2(3)+x \log (81)\right )^2 \log \left (e^4 \left (e^{12}-e^x\right ) x\right )}{-e^{12}+e^x} \, dx+\int \frac {-x+98 \log \left (e^{16} x-e^{4+x} x\right )+2 x^5 \log ^4(3) \log \left (e^{16} x-e^{4+x} x\right )+98 x \left (1+\frac {2 \log (81)}{7}\right ) \log \left (e^{16} x-e^{4+x} x\right )+2 x^4 \log ^4(3) \left (1+\frac {2 \log (81)}{\log ^2(3)}\right ) \log \left (e^{16} x-e^{4+x} x\right )+28 x^2 \log ^2(3) \left (1+\frac {(7+\log (9)) \log (81)}{7 \log ^2(3)}\right ) \log \left (e^{16} x-e^{4+x} x\right )+28 x^3 \log ^2(3) \left (1+\frac {1}{7} \log (81) \left (1+\frac {\log (81)}{2 \log ^2(3)}\right )\right ) \log \left (e^{16} x-e^{4+x} x\right )+56 x \log (3) \log ^2\left (e^{16} x-e^{4+x} x\right )+60 x^2 \log ^2(3) \log ^2\left (e^{16} x-e^{4+x} x\right )+24 x^3 \log ^3(3) \log ^2\left (e^{16} x-e^{4+x} x\right )+4 x^4 \log ^4(3) \log ^2\left (e^{16} x-e^{4+x} x\right )}{x} \, dx\\ &=\left (2 e^{12}\right ) \int \left (\frac {49 \log \left (e^4 \left (e^{12}-e^x\right ) x\right )}{-e^{12}+e^x}+\frac {x^4 \log ^4(3) \log \left (e^4 \left (e^{12}-e^x\right ) x\right )}{-e^{12}+e^x}+\frac {14 x \log (81) \log \left (e^4 \left (e^{12}-e^x\right ) x\right )}{-e^{12}+e^x}+\frac {2 x^3 \log ^2(3) \log (81) \log \left (e^4 \left (e^{12}-e^x\right ) x\right )}{-e^{12}+e^x}+\frac {x^2 \left (14 \log ^2(3)+\log ^2(81)\right ) \log \left (e^4 \left (e^{12}-e^x\right ) x\right )}{-e^{12}+e^x}\right ) \, dx+\int \left (-1+\frac {2 (1+x) \left (7+x^2 \log ^2(3)+x \log (81)\right )^2 \log \left (e^4 \left (e^{12}-e^x\right ) x\right )}{x}+4 \log (3) \left (14+15 x \log (3)+6 x^2 \log ^2(3)+x^3 \log ^3(3)\right ) \log ^2\left (e^4 \left (e^{12}-e^x\right ) x\right )\right ) \, dx\\ &=-x+2 \int \frac {(1+x) \left (7+x^2 \log ^2(3)+x \log (81)\right )^2 \log \left (e^4 \left (e^{12}-e^x\right ) x\right )}{x} \, dx+\left (98 e^{12}\right ) \int \frac {\log \left (e^4 \left (e^{12}-e^x\right ) x\right )}{-e^{12}+e^x} \, dx+(4 \log (3)) \int \left (14+15 x \log (3)+6 x^2 \log ^2(3)+x^3 \log ^3(3)\right ) \log ^2\left (e^4 \left (e^{12}-e^x\right ) x\right ) \, dx+\left (2 e^{12} \log ^4(3)\right ) \int \frac {x^4 \log \left (e^4 \left (e^{12}-e^x\right ) x\right )}{-e^{12}+e^x} \, dx+\left (28 e^{12} \log (81)\right ) \int \frac {x \log \left (e^4 \left (e^{12}-e^x\right ) x\right )}{-e^{12}+e^x} \, dx+\left (4 e^{12} \log ^2(3) \log (81)\right ) \int \frac {x^3 \log \left (e^4 \left (e^{12}-e^x\right ) x\right )}{-e^{12}+e^x} \, dx+\left (2 e^{12} \left (14 \log ^2(3)+\log ^2(81)\right )\right ) \int \frac {x^2 \log \left (e^4 \left (e^{12}-e^x\right ) x\right )}{-e^{12}+e^x} \, dx\\ &=-x+2 \int \left (\frac {49 \log \left (e^4 \left (e^{12}-e^x\right ) x\right )}{x}+x^4 \log ^4(3) \log \left (e^4 \left (e^{12}-e^x\right ) x\right )+x^2 \left (\log ^2(81)+2 \log ^2(3) (7+\log (81))\right ) \log \left (e^4 \left (e^{12}-e^x\right ) x\right )+x \left (14 \log ^2(3)+\log (81) (14+\log (81))\right ) \log \left (e^4 \left (e^{12}-e^x\right ) x\right )+7 (7+\log (6561)) \log \left (e^4 \left (e^{12}-e^x\right ) x\right )+x^3 \log ^2(3) \left (\log ^2(3)+\log (6561)\right ) \log \left (e^4 \left (e^{12}-e^x\right ) x\right )\right ) \, dx+\left (98 e^{12}\right ) \int \frac {\log \left (e^4 \left (e^{12}-e^x\right ) x\right )}{-e^{12}+e^x} \, dx+(4 \log (3)) \int \left (14 \log ^2\left (e^4 \left (e^{12}-e^x\right ) x\right )+15 x \log (3) \log ^2\left (e^4 \left (e^{12}-e^x\right ) x\right )+6 x^2 \log ^2(3) \log ^2\left (e^4 \left (e^{12}-e^x\right ) x\right )+x^3 \log ^3(3) \log ^2\left (e^4 \left (e^{12}-e^x\right ) x\right )\right ) \, dx+\left (2 e^{12} \log ^4(3)\right ) \int \frac {x^4 \log \left (e^4 \left (e^{12}-e^x\right ) x\right )}{-e^{12}+e^x} \, dx+\left (28 e^{12} \log (81)\right ) \int \frac {x \log \left (e^4 \left (e^{12}-e^x\right ) x\right )}{-e^{12}+e^x} \, dx+\left (4 e^{12} \log ^2(3) \log (81)\right ) \int \frac {x^3 \log \left (e^4 \left (e^{12}-e^x\right ) x\right )}{-e^{12}+e^x} \, dx+\left (2 e^{12} \left (14 \log ^2(3)+\log ^2(81)\right )\right ) \int \frac {x^2 \log \left (e^4 \left (e^{12}-e^x\right ) x\right )}{-e^{12}+e^x} \, dx\\ &=-x+98 \int \frac {\log \left (e^4 \left (e^{12}-e^x\right ) x\right )}{x} \, dx+\left (98 e^{12}\right ) \int \frac {\log \left (e^4 \left (e^{12}-e^x\right ) x\right )}{-e^{12}+e^x} \, dx+(56 \log (3)) \int \log ^2\left (e^4 \left (e^{12}-e^x\right ) x\right ) \, dx+\left (60 \log ^2(3)\right ) \int x \log ^2\left (e^4 \left (e^{12}-e^x\right ) x\right ) \, dx+\left (24 \log ^3(3)\right ) \int x^2 \log ^2\left (e^4 \left (e^{12}-e^x\right ) x\right ) \, dx+\left (2 \log ^4(3)\right ) \int x^4 \log \left (e^4 \left (e^{12}-e^x\right ) x\right ) \, dx+\left (4 \log ^4(3)\right ) \int x^3 \log ^2\left (e^4 \left (e^{12}-e^x\right ) x\right ) \, dx+\left (2 e^{12} \log ^4(3)\right ) \int \frac {x^4 \log \left (e^4 \left (e^{12}-e^x\right ) x\right )}{-e^{12}+e^x} \, dx+\left (28 e^{12} \log (81)\right ) \int \frac {x \log \left (e^4 \left (e^{12}-e^x\right ) x\right )}{-e^{12}+e^x} \, dx+\left (4 e^{12} \log ^2(3) \log (81)\right ) \int \frac {x^3 \log \left (e^4 \left (e^{12}-e^x\right ) x\right )}{-e^{12}+e^x} \, dx+\left (2 e^{12} \left (14 \log ^2(3)+\log ^2(81)\right )\right ) \int \frac {x^2 \log \left (e^4 \left (e^{12}-e^x\right ) x\right )}{-e^{12}+e^x} \, dx+\left (2 \left (\log ^2(81)+2 \log ^2(3) (7+\log (81))\right )\right ) \int x^2 \log \left (e^4 \left (e^{12}-e^x\right ) x\right ) \, dx+\left (2 \left (14 \log ^2(3)+\log (81) (14+\log (81))\right )\right ) \int x \log \left (e^4 \left (e^{12}-e^x\right ) x\right ) \, dx+(14 (7+\log (6561))) \int \log \left (e^4 \left (e^{12}-e^x\right ) x\right ) \, dx+\left (2 \log ^2(3) \left (\log ^2(3)+\log (6561)\right )\right ) \int x^3 \log \left (e^4 \left (e^{12}-e^x\right ) x\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [F] time = 1.40, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{16} x-e^{4+x} x+\left (-98 e^{16}-112 e^{16} x \log (3)-60 e^{16} x^2 \log ^2(3)-16 e^{16} x^3 \log ^3(3)-2 e^{16} x^4 \log ^4(3)+e^{4+x} \left (98+98 x+\left (112 x+112 x^2\right ) \log (3)+\left (60 x^2+60 x^3\right ) \log ^2(3)+\left (16 x^3+16 x^4\right ) \log ^3(3)+\left (2 x^4+2 x^5\right ) \log ^4(3)\right )\right ) \log \left (e^{16} x-e^{4+x} x\right )+\left (-56 e^{16} x \log (3)-60 e^{16} x^2 \log ^2(3)-24 e^{16} x^3 \log ^3(3)-4 e^{16} x^4 \log ^4(3)+e^{4+x} \left (56 x \log (3)+60 x^2 \log ^2(3)+24 x^3 \log ^3(3)+4 x^4 \log ^4(3)\right )\right ) \log ^2\left (e^{16} x-e^{4+x} x\right )}{-e^{16} x+e^{4+x} x} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Integrate[(E^16*x - E^(4 + x)*x + (-98*E^16 - 112*E^16*x*Log[3] - 60*E^16*x^2*Log[3]^2 - 16*E^16*x^3*Log[3]^3

- 2*E^16*x^4*Log[3]^4 + E^(4 + x)*(98 + 98*x + (112*x + 112*x^2)*Log[3] + (60*x^2 + 60*x^3)*Log[3]^2 + (16*x^3

+ 16*x^4)*Log[3]^3 + (2*x^4 + 2*x^5)*Log[3]^4))*Log[E^16*x - E^(4 + x)*x] + (-56*E^16*x*Log[3] - 60*E^16*x^2*

Log[3]^2 - 24*E^16*x^3*Log[3]^3 - 4*E^16*x^4*Log[3]^4 + E^(4 + x)*(56*x*Log[3] + 60*x^2*Log[3]^2 + 24*x^3*Log[

3]^3 + 4*x^4*Log[3]^4))*Log[E^16*x - E^(4 + x)*x]^2)/(-(E^16*x) + E^(4 + x)*x),x]

[Out]

Integrate[(E^16*x - E^(4 + x)*x + (-98*E^16 - 112*E^16*x*Log[3] - 60*E^16*x^2*Log[3]^2 - 16*E^16*x^3*Log[3]^3

- 2*E^16*x^4*Log[3]^4 + E^(4 + x)*(98 + 98*x + (112*x + 112*x^2)*Log[3] + (60*x^2 + 60*x^3)*Log[3]^2 + (16*x^3

+ 16*x^4)*Log[3]^3 + (2*x^4 + 2*x^5)*Log[3]^4))*Log[E^16*x - E^(4 + x)*x] + (-56*E^16*x*Log[3] - 60*E^16*x^2*

Log[3]^2 - 24*E^16*x^3*Log[3]^3 - 4*E^16*x^4*Log[3]^4 + E^(4 + x)*(56*x*Log[3] + 60*x^2*Log[3]^2 + 24*x^3*Log[

3]^3 + 4*x^4*Log[3]^4))*Log[E^16*x - E^(4 + x)*x]^2)/(-(E^16*x) + E^(4 + x)*x), x]

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fricas [A] time = 1.39, size = 53, normalized size = 1.61 \begin {gather*} {\left (x^{4} \log \relax (3)^{4} + 8 \, x^{3} \log \relax (3)^{3} + 30 \, x^{2} \log \relax (3)^{2} + 56 \, x \log \relax (3) + 49\right )} \log \left (x e^{16} - x e^{\left (x + 4\right )}\right )^{2} - x \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^4*log(3)^4+24*x^3*log(3)^3+60*x^2*log(3)^2+56*x*log(3))*exp(4+x)-4*x^4*exp(16)*log(3)^4-24*x^

3*exp(16)*log(3)^3-60*x^2*exp(16)*log(3)^2-56*x*exp(16)*log(3))*log(-x*exp(4+x)+x*exp(16))^2+(((2*x^5+2*x^4)*l

og(3)^4+(16*x^4+16*x^3)*log(3)^3+(60*x^3+60*x^2)*log(3)^2+(112*x^2+112*x)*log(3)+98*x+98)*exp(4+x)-2*x^4*exp(1

6)*log(3)^4-16*x^3*exp(16)*log(3)^3-60*x^2*exp(16)*log(3)^2-112*x*exp(16)*log(3)-98*exp(16))*log(-x*exp(4+x)+x

*exp(16))-x*exp(4+x)+x*exp(16))/(x*exp(4+x)-x*exp(16)),x, algorithm="fricas")

[Out]

(x^4*log(3)^4 + 8*x^3*log(3)^3 + 30*x^2*log(3)^2 + 56*x*log(3) + 49)*log(x*e^16 - x*e^(x + 4))^2 - x

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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {4 \, {\left (x^{4} e^{16} \log \relax (3)^{4} + 6 \, x^{3} e^{16} \log \relax (3)^{3} + 15 \, x^{2} e^{16} \log \relax (3)^{2} + 14 \, x e^{16} \log \relax (3) - {\left (x^{4} \log \relax (3)^{4} + 6 \, x^{3} \log \relax (3)^{3} + 15 \, x^{2} \log \relax (3)^{2} + 14 \, x \log \relax (3)\right )} e^{\left (x + 4\right )}\right )} \log \left (x e^{16} - x e^{\left (x + 4\right )}\right )^{2} - x e^{16} + x e^{\left (x + 4\right )} + 2 \, {\left (x^{4} e^{16} \log \relax (3)^{4} + 8 \, x^{3} e^{16} \log \relax (3)^{3} + 30 \, x^{2} e^{16} \log \relax (3)^{2} + 56 \, x e^{16} \log \relax (3) - {\left ({\left (x^{5} + x^{4}\right )} \log \relax (3)^{4} + 8 \, {\left (x^{4} + x^{3}\right )} \log \relax (3)^{3} + 30 \, {\left (x^{3} + x^{2}\right )} \log \relax (3)^{2} + 56 \, {\left (x^{2} + x\right )} \log \relax (3) + 49 \, x + 49\right )} e^{\left (x + 4\right )} + 49 \, e^{16}\right )} \log \left (x e^{16} - x e^{\left (x + 4\right )}\right )}{x e^{16} - x e^{\left (x + 4\right )}}\,{d x} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^4*log(3)^4+24*x^3*log(3)^3+60*x^2*log(3)^2+56*x*log(3))*exp(4+x)-4*x^4*exp(16)*log(3)^4-24*x^

3*exp(16)*log(3)^3-60*x^2*exp(16)*log(3)^2-56*x*exp(16)*log(3))*log(-x*exp(4+x)+x*exp(16))^2+(((2*x^5+2*x^4)*l

og(3)^4+(16*x^4+16*x^3)*log(3)^3+(60*x^3+60*x^2)*log(3)^2+(112*x^2+112*x)*log(3)+98*x+98)*exp(4+x)-2*x^4*exp(1

6)*log(3)^4-16*x^3*exp(16)*log(3)^3-60*x^2*exp(16)*log(3)^2-112*x*exp(16)*log(3)-98*exp(16))*log(-x*exp(4+x)+x

*exp(16))-x*exp(4+x)+x*exp(16))/(x*exp(4+x)-x*exp(16)),x, algorithm="giac")

[Out]

integrate((4*(x^4*e^16*log(3)^4 + 6*x^3*e^16*log(3)^3 + 15*x^2*e^16*log(3)^2 + 14*x*e^16*log(3) - (x^4*log(3)^

4 + 6*x^3*log(3)^3 + 15*x^2*log(3)^2 + 14*x*log(3))*e^(x + 4))*log(x*e^16 - x*e^(x + 4))^2 - x*e^16 + x*e^(x +

4) + 2*(x^4*e^16*log(3)^4 + 8*x^3*e^16*log(3)^3 + 30*x^2*e^16*log(3)^2 + 56*x*e^16*log(3) - ((x^5 + x^4)*log(

3)^4 + 8*(x^4 + x^3)*log(3)^3 + 30*(x^3 + x^2)*log(3)^2 + 56*(x^2 + x)*log(3) + 49*x + 49)*e^(x + 4) + 49*e^16

)*log(x*e^16 - x*e^(x + 4)))/(x*e^16 - x*e^(x + 4)), x)

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maple [C] time = 0.57, size = 3152, normalized size = 95.52


method	result	size

risch	\(\text {Expression too large to display}\)	\(3152\)

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((((4*x^4*ln(3)^4+24*x^3*ln(3)^3+60*x^2*ln(3)^2+56*x*ln(3))*exp(4+x)-4*x^4*exp(16)*ln(3)^4-24*x^3*exp(16)*l

n(3)^3-60*x^2*exp(16)*ln(3)^2-56*x*exp(16)*ln(3))*ln(-x*exp(4+x)+x*exp(16))^2+(((2*x^5+2*x^4)*ln(3)^4+(16*x^4+

16*x^3)*ln(3)^3+(60*x^3+60*x^2)*ln(3)^2+(112*x^2+112*x)*ln(3)+98*x+98)*exp(4+x)-2*x^4*exp(16)*ln(3)^4-16*x^3*e

xp(16)*ln(3)^3-60*x^2*exp(16)*ln(3)^2-112*x*exp(16)*ln(3)-98*exp(16))*ln(-x*exp(4+x)+x*exp(16))-x*exp(4+x)+x*e

xp(16))/(x*exp(4+x)-x*exp(16)),x,method=_RETURNVERBOSE)

[Out]

-1568-x+56*x*ln(3)*ln(x)^2+49*ln(x)^2-1/4*Pi^2*ln(3)^4*x^4*csgn(I*x*(exp(16)-exp(4+x)))^6-2*Pi^2*ln(3)^3*x^3*c

sgn(I*x*(exp(16)-exp(4+x)))^6-15/2*Pi^2*ln(3)^2*x^2*csgn(I*x*(exp(16)-exp(4+x)))^6-14*Pi^2*ln(3)*x*csgn(I*x*(e

xp(16)-exp(4+x)))^6-49*I*Pi*ln(x)*csgn(I*x*(exp(16)-exp(4+x)))^3-196*I*Pi*csgn(I*x)*csgn(I*x*(exp(16)-exp(4+x)

))^2-196*I*Pi*csgn(I*(exp(16)-exp(4+x)))*csgn(I*x*(exp(16)-exp(4+x)))^2-49*I*Pi*ln(exp(4+x)-exp(16))*csgn(I*x*

(exp(16)-exp(4+x)))^3-30*I*Pi*ln(3)^2*x^2*csgn(I*x*(exp(16)-exp(4+x)))^3*ln(x)-49*I*Pi*ln(exp(4+x)-exp(16))*cs

gn(I*x)*csgn(I*(exp(16)-exp(4+x)))*csgn(I*x*(exp(16)-exp(4+x)))-49*I*Pi*ln(x)*csgn(I*x)*csgn(I*(exp(16)-exp(4+

x)))*csgn(I*x*(exp(16)-exp(4+x)))-56*I*Pi*ln(3)*x*csgn(I*x*(exp(16)-exp(4+x)))^3*ln(x)-I*Pi*ln(3)^4*x^4*csgn(I

*x*(exp(16)-exp(4+x)))^3*ln(x)-8*I*Pi*ln(3)^3*x^3*csgn(I*x*(exp(16)-exp(4+x)))^3*ln(x)+4*Pi^2*ln(3)^3*x^3*csgn

(I*x)^2*csgn(I*(exp(16)-exp(4+x)))*csgn(I*x*(exp(16)-exp(4+x)))^3+4*Pi^2*ln(3)^3*x^3*csgn(I*x)*csgn(I*(exp(16)

-exp(4+x)))^2*csgn(I*x*(exp(16)-exp(4+x)))^3-8*Pi^2*ln(3)^3*x^3*csgn(I*x)*csgn(I*(exp(16)-exp(4+x)))*csgn(I*x*

(exp(16)-exp(4+x)))^4-1/4*Pi^2*ln(3)^4*x^4*csgn(I*x)^2*csgn(I*(exp(16)-exp(4+x)))^2*csgn(I*x*(exp(16)-exp(4+x)

))^2-14*Pi^2*ln(3)*x*csgn(I*x)^2*csgn(I*(exp(16)-exp(4+x)))^2*csgn(I*x*(exp(16)-exp(4+x)))^2+28*Pi^2*ln(3)*x*c

sgn(I*x)^2*csgn(I*(exp(16)-exp(4+x)))*csgn(I*x*(exp(16)-exp(4+x)))^3+30*ln(3)^2*ln(x)^2*x^2+28*Pi^2*ln(3)*x*cs

gn(I*(exp(16)-exp(4+x)))*csgn(I*x*(exp(16)-exp(4+x)))^5+49*I*Pi*ln(x)*csgn(I*(exp(16)-exp(4+x)))*csgn(I*x*(exp

(16)-exp(4+x)))^2+196*I*Pi*csgn(I*x)*csgn(I*(exp(16)-exp(4+x)))*csgn(I*x*(exp(16)-exp(4+x)))+49*I*Pi*ln(exp(4+

x)-exp(16))*csgn(I*x)*csgn(I*x*(exp(16)-exp(4+x)))^2+49*I*Pi*ln(exp(4+x)-exp(16))*csgn(I*(exp(16)-exp(4+x)))*c

sgn(I*x*(exp(16)-exp(4+x)))^2+49*I*Pi*ln(x)*csgn(I*x)*csgn(I*x*(exp(16)-exp(4+x)))^2-1/4*Pi^2*ln(3)^4*x^4*csgn

(I*x)^2*csgn(I*x*(exp(16)-exp(4+x)))^4+1/2*Pi^2*ln(3)^4*x^4*csgn(I*x)*csgn(I*x*(exp(16)-exp(4+x)))^5-1/4*Pi^2*

ln(3)^4*x^4*csgn(I*(exp(16)-exp(4+x)))^2*csgn(I*x*(exp(16)-exp(4+x)))^4+1/2*Pi^2*ln(3)^4*x^4*csgn(I*(exp(16)-e

xp(4+x)))*csgn(I*x*(exp(16)-exp(4+x)))^5-2*Pi^2*ln(3)^3*x^3*csgn(I*x)^2*csgn(I*x*(exp(16)-exp(4+x)))^4+4*Pi^2*

ln(3)^3*x^3*csgn(I*x)*csgn(I*x*(exp(16)-exp(4+x)))^5-2*Pi^2*ln(3)^3*x^3*csgn(I*(exp(16)-exp(4+x)))^2*csgn(I*x*

(exp(16)-exp(4+x)))^4+4*Pi^2*ln(3)^3*x^3*csgn(I*(exp(16)-exp(4+x)))*csgn(I*x*(exp(16)-exp(4+x)))^5-15/2*Pi^2*l

n(3)^2*x^2*csgn(I*x)^2*csgn(I*x*(exp(16)-exp(4+x)))^4+15*Pi^2*ln(3)^2*x^2*csgn(I*x)*csgn(I*x*(exp(16)-exp(4+x)

))^5-15/2*Pi^2*ln(3)^2*x^2*csgn(I*(exp(16)-exp(4+x)))^2*csgn(I*x*(exp(16)-exp(4+x)))^4+15*Pi^2*ln(3)^2*x^2*csg

n(I*(exp(16)-exp(4+x)))*csgn(I*x*(exp(16)-exp(4+x)))^5-14*Pi^2*ln(3)*x*csgn(I*x)^2*csgn(I*x*(exp(16)-exp(4+x))

)^4+28*Pi^2*ln(3)*x*csgn(I*x)*csgn(I*x*(exp(16)-exp(4+x)))^5-14*Pi^2*ln(3)*x*csgn(I*(exp(16)-exp(4+x)))^2*csgn

(I*x*(exp(16)-exp(4+x)))^4+392*ln(exp(4+x)-exp(16))+ln(3)^4*x^4*ln(x)^2+8*ln(3)^3*x^3*ln(x)^2+(8*I*Pi*ln(3)^3*

x^3*csgn(I*(exp(16)-exp(4+x)))*csgn(I*x*(exp(16)-exp(4+x)))^2+I*Pi*ln(3)^4*x^4*csgn(I*x)*csgn(I*x*(exp(16)-exp

(4+x)))^2-56*I*Pi*ln(3)*x*csgn(I*x)*csgn(I*(exp(16)-exp(4+x)))*csgn(I*x*(exp(16)-exp(4+x)))+I*Pi*ln(3)^4*x^4*c

sgn(I*(exp(16)-exp(4+x)))*csgn(I*x*(exp(16)-exp(4+x)))^2-I*Pi*ln(3)^4*x^4*csgn(I*x)*csgn(I*(exp(16)-exp(4+x)))

*csgn(I*x*(exp(16)-exp(4+x)))+30*I*Pi*ln(3)^2*x^2*csgn(I*(exp(16)-exp(4+x)))*csgn(I*x*(exp(16)-exp(4+x)))^2-30

*I*Pi*ln(3)^2*x^2*csgn(I*x*(exp(16)-exp(4+x)))^3-8*I*Pi*ln(3)^3*x^3*csgn(I*x*(exp(16)-exp(4+x)))^3+56*I*Pi*ln(

3)*x*csgn(I*(exp(16)-exp(4+x)))*csgn(I*x*(exp(16)-exp(4+x)))^2+30*I*Pi*ln(3)^2*x^2*csgn(I*x)*csgn(I*x*(exp(16)

-exp(4+x)))^2+56*I*Pi*ln(3)*x*csgn(I*x)*csgn(I*x*(exp(16)-exp(4+x)))^2-8*I*Pi*ln(3)^3*x^3*csgn(I*x)*csgn(I*(ex

p(16)-exp(4+x)))*csgn(I*x*(exp(16)-exp(4+x)))+2*ln(3)^4*x^4*ln(x)-I*Pi*ln(3)^4*x^4*csgn(I*x*(exp(16)-exp(4+x))

)^3-56*I*Pi*ln(3)*x*csgn(I*x*(exp(16)-exp(4+x)))^3+8*I*Pi*ln(3)^3*x^3*csgn(I*x)*csgn(I*x*(exp(16)-exp(4+x)))^2

-30*I*Pi*ln(3)^2*x^2*csgn(I*x)*csgn(I*(exp(16)-exp(4+x)))*csgn(I*x*(exp(16)-exp(4+x)))+16*ln(3)^3*x^3*ln(x)+60

*x^2*ln(3)^2*ln(x)+112*x*ln(3)*ln(x)+98*ln(x)-392)*ln(exp(16)-exp(4+x))-56*I*Pi*ln(3)*x*csgn(I*x)*csgn(I*(exp(

16)-exp(4+x)))*csgn(I*x*(exp(16)-exp(4+x)))*ln(x)-8*I*Pi*ln(3)^3*x^3*csgn(I*x)*csgn(I*(exp(16)-exp(4+x)))*csgn

(I*x*(exp(16)-exp(4+x)))*ln(x)-30*I*Pi*ln(3)^2*x^2*csgn(I*x)*csgn(I*(exp(16)-exp(4+x)))*csgn(I*x*(exp(16)-exp(

4+x)))*ln(x)-I*Pi*ln(3)^4*x^4*csgn(I*x)*csgn(I*(exp(16)-exp(4+x)))*csgn(I*x*(exp(16)-exp(4+x)))*ln(x)+196*I*Pi

*csgn(I*x*(exp(16)-exp(4+x)))^3+(x^4*ln(3)^4+8*x^3*ln(3)^3+30*x^2*ln(3)^2+56*x*ln(3)+49)*ln(exp(16)-exp(4+x))^

2+28*Pi^2*ln(3)*x*csgn(I*x)*csgn(I*(exp(16)-exp(4+x)))^2*csgn(I*x*(exp(16)-exp(4+x)))^3-56*Pi^2*ln(3)*x*csgn(I

*x)*csgn(I*(exp(16)-exp(4+x)))*csgn(I*x*(exp(16)-exp(4+x)))^4+15*Pi^2*ln(3)^2*x^2*csgn(I*x)*csgn(I*(exp(16)-ex

p(4+x)))^2*csgn(I*x*(exp(16)-exp(4+x)))^3-30*Pi^2*ln(3)^2*x^2*csgn(I*x)*csgn(I*(exp(16)-exp(4+x)))*csgn(I*x*(e

xp(16)-exp(4+x)))^4+1/2*Pi^2*ln(3)^4*x^4*csgn(I*x)^2*csgn(I*(exp(16)-exp(4+x)))*csgn(I*x*(exp(16)-exp(4+x)))^3

+1/2*Pi^2*ln(3)^4*x^4*csgn(I*x)*csgn(I*(exp(16)-exp(4+x)))^2*csgn(I*x*(exp(16)-exp(4+x)))^3-Pi^2*ln(3)^4*x^4*c

sgn(I*x)*csgn(I*(exp(16)-exp(4+x)))*csgn(I*x*(exp(16)-exp(4+x)))^4-2*Pi^2*ln(3)^3*x^3*csgn(I*x)^2*csgn(I*(exp(

16)-exp(4+x)))^2*csgn(I*x*(exp(16)-exp(4+x)))^2-15/2*Pi^2*ln(3)^2*x^2*csgn(I*x)^2*csgn(I*(exp(16)-exp(4+x)))^2

*csgn(I*x*(exp(16)-exp(4+x)))^2+15*Pi^2*ln(3)^2*x^2*csgn(I*x)^2*csgn(I*(exp(16)-exp(4+x)))*csgn(I*x*(exp(16)-e

xp(4+x)))^3+8*I*Pi*ln(3)^3*x^3*csgn(I*x)*csgn(I*x*(exp(16)-exp(4+x)))^2*ln(x)+8*I*Pi*ln(3)^3*x^3*csgn(I*(exp(1

6)-exp(4+x)))*csgn(I*x*(exp(16)-exp(4+x)))^2*ln(x)+30*I*Pi*ln(3)^2*x^2*csgn(I*x)*csgn(I*x*(exp(16)-exp(4+x)))^

2*ln(x)+30*I*Pi*ln(3)^2*x^2*csgn(I*(exp(16)-exp(4+x)))*csgn(I*x*(exp(16)-exp(4+x)))^2*ln(x)+56*I*Pi*ln(3)*x*cs

gn(I*x)*csgn(I*x*(exp(16)-exp(4+x)))^2*ln(x)+56*I*Pi*ln(3)*x*csgn(I*(exp(16)-exp(4+x)))*csgn(I*x*(exp(16)-exp(

4+x)))^2*ln(x)+I*Pi*ln(3)^4*x^4*csgn(I*x)*csgn(I*x*(exp(16)-exp(4+x)))^2*ln(x)+I*Pi*ln(3)^4*x^4*csgn(I*(exp(16

)-exp(4+x)))*csgn(I*x*(exp(16)-exp(4+x)))^2*ln(x)

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maxima [B] time = 0.53, size = 263, normalized size = 7.97 \begin {gather*} 16 \, x^{4} \log \relax (3)^{4} + 128 \, x^{3} \log \relax (3)^{3} + 480 \, x^{2} \log \relax (3)^{2} + {\left (x^{4} \log \relax (3)^{4} + 8 \, x^{3} \log \relax (3)^{3} + 30 \, x^{2} \log \relax (3)^{2} + 56 \, x \log \relax (3) + 49\right )} \log \relax (x)^{2} + {\left (x^{4} \log \relax (3)^{4} + 8 \, x^{3} \log \relax (3)^{3} + 30 \, x^{2} \log \relax (3)^{2} + 56 \, x \log \relax (3) + 49\right )} \log \left (e^{12} - e^{x}\right )^{2} - {\left (x e^{\left (-16\right )} - e^{\left (-16\right )} \log \left (-e^{12} + e^{x}\right )\right )} e^{16} + 896 \, x \log \relax (3) + 8 \, {\left (x^{4} \log \relax (3)^{4} + 8 \, x^{3} \log \relax (3)^{3} + 30 \, x^{2} \log \relax (3)^{2} + 56 \, x \log \relax (3) + 49\right )} \log \relax (x) + 2 \, {\left (4 \, x^{4} \log \relax (3)^{4} + 32 \, x^{3} \log \relax (3)^{3} + 120 \, x^{2} \log \relax (3)^{2} + 224 \, x \log \relax (3) + {\left (x^{4} \log \relax (3)^{4} + 8 \, x^{3} \log \relax (3)^{3} + 30 \, x^{2} \log \relax (3)^{2} + 56 \, x \log \relax (3) + 49\right )} \log \relax (x) + 196\right )} \log \left (e^{12} - e^{x}\right ) - \log \left (-e^{12} + e^{x}\right ) \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^4*log(3)^4+24*x^3*log(3)^3+60*x^2*log(3)^2+56*x*log(3))*exp(4+x)-4*x^4*exp(16)*log(3)^4-24*x^

3*exp(16)*log(3)^3-60*x^2*exp(16)*log(3)^2-56*x*exp(16)*log(3))*log(-x*exp(4+x)+x*exp(16))^2+(((2*x^5+2*x^4)*l

og(3)^4+(16*x^4+16*x^3)*log(3)^3+(60*x^3+60*x^2)*log(3)^2+(112*x^2+112*x)*log(3)+98*x+98)*exp(4+x)-2*x^4*exp(1

6)*log(3)^4-16*x^3*exp(16)*log(3)^3-60*x^2*exp(16)*log(3)^2-112*x*exp(16)*log(3)-98*exp(16))*log(-x*exp(4+x)+x

*exp(16))-x*exp(4+x)+x*exp(16))/(x*exp(4+x)-x*exp(16)),x, algorithm="maxima")

[Out]

16*x^4*log(3)^4 + 128*x^3*log(3)^3 + 480*x^2*log(3)^2 + (x^4*log(3)^4 + 8*x^3*log(3)^3 + 30*x^2*log(3)^2 + 56*

x*log(3) + 49)*log(x)^2 + (x^4*log(3)^4 + 8*x^3*log(3)^3 + 30*x^2*log(3)^2 + 56*x*log(3) + 49)*log(e^12 - e^x)

^2 - (x*e^(-16) - e^(-16)*log(-e^12 + e^x))*e^16 + 896*x*log(3) + 8*(x^4*log(3)^4 + 8*x^3*log(3)^3 + 30*x^2*lo

g(3)^2 + 56*x*log(3) + 49)*log(x) + 2*(4*x^4*log(3)^4 + 32*x^3*log(3)^3 + 120*x^2*log(3)^2 + 224*x*log(3) + (x

^4*log(3)^4 + 8*x^3*log(3)^3 + 30*x^2*log(3)^2 + 56*x*log(3) + 49)*log(x) + 196)*log(e^12 - e^x) - log(-e^12 +

e^x)

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mupad [B] time = 7.59, size = 53, normalized size = 1.61 \begin {gather*} {\ln \left (x\,{\mathrm {e}}^{16}-x\,{\mathrm {e}}^4\,{\mathrm {e}}^x\right )}^2\,\left ({\ln \relax (3)}^4\,x^4+8\,{\ln \relax (3)}^3\,x^3+30\,{\ln \relax (3)}^2\,x^2+56\,\ln \relax (3)\,x+49\right )-x \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(-(x*exp(x + 4) - x*exp(16) + log(x*exp(16) - x*exp(x + 4))^2*(60*x^2*exp(16)*log(3)^2 - exp(x + 4)*(60*x^2

*log(3)^2 + 24*x^3*log(3)^3 + 4*x^4*log(3)^4 + 56*x*log(3)) + 24*x^3*exp(16)*log(3)^3 + 4*x^4*exp(16)*log(3)^4

+ 56*x*exp(16)*log(3)) + log(x*exp(16) - x*exp(x + 4))*(98*exp(16) - exp(x + 4)*(98*x + log(3)*(112*x + 112*x

^2) + log(3)^4*(2*x^4 + 2*x^5) + log(3)^3*(16*x^3 + 16*x^4) + log(3)^2*(60*x^2 + 60*x^3) + 98) + 60*x^2*exp(16

)*log(3)^2 + 16*x^3*exp(16)*log(3)^3 + 2*x^4*exp(16)*log(3)^4 + 112*x*exp(16)*log(3)))/(x*exp(x + 4) - x*exp(1

6)),x)

[Out]

log(x*exp(16) - x*exp(4)*exp(x))^2*(30*x^2*log(3)^2 + 8*x^3*log(3)^3 + x^4*log(3)^4 + 56*x*log(3) + 49) - x

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sympy [B] time = 0.66, size = 53, normalized size = 1.61 \begin {gather*} - x + \left (x^{4} \log {\relax (3 )}^{4} + 8 x^{3} \log {\relax (3 )}^{3} + 30 x^{2} \log {\relax (3 )}^{2} + 56 x \log {\relax (3 )} + 49\right ) \log {\left (- x e^{x + 4} + x e^{16} \right )}^{2} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x**4*ln(3)**4+24*x**3*ln(3)**3+60*x**2*ln(3)**2+56*x*ln(3))*exp(4+x)-4*x**4*exp(16)*ln(3)**4-24

*x**3*exp(16)*ln(3)**3-60*x**2*exp(16)*ln(3)**2-56*x*exp(16)*ln(3))*ln(-x*exp(4+x)+x*exp(16))**2+(((2*x**5+2*x

**4)*ln(3)**4+(16*x**4+16*x**3)*ln(3)**3+(60*x**3+60*x**2)*ln(3)**2+(112*x**2+112*x)*ln(3)+98*x+98)*exp(4+x)-2

*x**4*exp(16)*ln(3)**4-16*x**3*exp(16)*ln(3)**3-60*x**2*exp(16)*ln(3)**2-112*x*exp(16)*ln(3)-98*exp(16))*ln(-x

*exp(4+x)+x*exp(16))-x*exp(4+x)+x*exp(16))/(x*exp(4+x)-x*exp(16)),x)

[Out]

-x + (x**4*log(3)**4 + 8*x**3*log(3)**3 + 30*x**2*log(3)**2 + 56*x*log(3) + 49)*log(-x*exp(x + 4) + x*exp(16))

**2

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