Integrand size = 195, antiderivative size = 32 \[ \int \frac {-60 x+81 x^2+24 x^3+\frac {e^{-1+x} \left (-12+57 x+12 x^2\right )}{4+x}+\left (24-42 x-12 x^2+\frac {e^{-1+x} (-30-6 x)}{4+x}\right ) \log \left (x+\frac {e^{-1+x}}{4+x}\right )}{-4 x^2+15 x^3+4 x^4+\frac {e^{-1+x} \left (-4 x+15 x^2+4 x^3\right )}{4+x}+\left (-16 x^2-4 x^3+\frac {e^{-1+x} \left (-16 x-4 x^2\right )}{4+x}\right ) \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\left (e^{-1+x}+4 x+x^2\right ) \log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )} \, dx=3 \log \left (x-x^2 \left (-2+\frac {\log \left (x+\frac {e^{-1+x}}{4+x}\right )}{x}\right )^2\right ) \]
Time = 0.24 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.41 \[ \int \frac {-60 x+81 x^2+24 x^3+\frac {e^{-1+x} \left (-12+57 x+12 x^2\right )}{4+x}+\left (24-42 x-12 x^2+\frac {e^{-1+x} (-30-6 x)}{4+x}\right ) \log \left (x+\frac {e^{-1+x}}{4+x}\right )}{-4 x^2+15 x^3+4 x^4+\frac {e^{-1+x} \left (-4 x+15 x^2+4 x^3\right )}{4+x}+\left (-16 x^2-4 x^3+\frac {e^{-1+x} \left (-16 x-4 x^2\right )}{4+x}\right ) \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\left (e^{-1+x}+4 x+x^2\right ) \log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )} \, dx=3 \log \left (-x+4 x^2-4 x \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )\right ) \]
Integrate[(-60*x + 81*x^2 + 24*x^3 + (E^(-1 + x)*(-12 + 57*x + 12*x^2))/(4 + x) + (24 - 42*x - 12*x^2 + (E^(-1 + x)*(-30 - 6*x))/(4 + x))*Log[x + E^ (-1 + x)/(4 + x)])/(-4*x^2 + 15*x^3 + 4*x^4 + (E^(-1 + x)*(-4*x + 15*x^2 + 4*x^3))/(4 + x) + (-16*x^2 - 4*x^3 + (E^(-1 + x)*(-16*x - 4*x^2))/(4 + x) )*Log[x + E^(-1 + x)/(4 + x)] + (E^(-1 + x) + 4*x + x^2)*Log[x + E^(-1 + x )/(4 + x)]^2),x]
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {24 x^3+81 x^2+\frac {e^{x-1} \left (12 x^2+57 x-12\right )}{x+4}+\left (-12 x^2-42 x+\frac {e^{x-1} (-6 x-30)}{x+4}+24\right ) \log \left (x+\frac {e^{x-1}}{x+4}\right )-60 x}{4 x^4+15 x^3-4 x^2+\left (x^2+4 x+e^{x-1}\right ) \log ^2\left (x+\frac {e^{x-1}}{x+4}\right )+\frac {e^{x-1} \left (4 x^3+15 x^2-4 x\right )}{x+4}+\left (-4 x^3-16 x^2+\frac {e^{x-1} \left (-4 x^2-16 x\right )}{x+4}\right ) \log \left (x+\frac {e^{x-1}}{x+4}\right )} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {e \left (-24 x^3-81 x^2-\frac {e^{x-1} \left (12 x^2+57 x-12\right )}{x+4}-\left (-12 x^2-42 x+\frac {e^{x-1} (-6 x-30)}{x+4}+24\right ) \log \left (x+\frac {e^{x-1}}{x+4}\right )+60 x\right )}{\left (e x^2+4 e x+e^x\right ) \left (-4 x^2+x-\log ^2\left (x+\frac {e^{x-1}}{x+4}\right )+4 x \log \left (x+\frac {e^{x-1}}{x+4}\right )\right )}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle e \int \frac {3 \left (-8 x^3-27 x^2+20 x+\frac {e^{x-1} \left (-4 x^2-19 x+4\right )}{x+4}-2 \left (-2 x^2-7 x-\frac {e^{x-1} (x+5)}{x+4}+4\right ) \log \left (x+\frac {e^{x-1}}{x+4}\right )\right )}{\left (e x^2+4 e x+e^x\right ) \left (-4 x^2+4 \log \left (x+\frac {e^{x-1}}{x+4}\right ) x+x-\log ^2\left (x+\frac {e^{x-1}}{x+4}\right )\right )}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 3 e \int \frac {-8 x^3-27 x^2+20 x+\frac {e^{x-1} \left (-4 x^2-19 x+4\right )}{x+4}-2 \left (-2 x^2-7 x-\frac {e^{x-1} (x+5)}{x+4}+4\right ) \log \left (x+\frac {e^{x-1}}{x+4}\right )}{\left (e x^2+4 e x+e^x\right ) \left (-4 x^2+4 \log \left (x+\frac {e^{x-1}}{x+4}\right ) x+x-\log ^2\left (x+\frac {e^{x-1}}{x+4}\right )\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 3 e \int \left (\frac {2 \left (x^2+2 x-4\right ) \left (2 x-\log \left (x+\frac {e^{x-1}}{x+4}\right )\right )}{\left (e x^2+4 e x+e^x\right ) \left (4 x^2-4 \log \left (x+\frac {e^{x-1}}{x+4}\right ) x-x+\log ^2\left (x+\frac {e^{x-1}}{x+4}\right )\right )}+\frac {4 x^2-2 \log \left (x+\frac {e^{x-1}}{x+4}\right ) x+19 x-10 \log \left (x+\frac {e^{x-1}}{x+4}\right )-4}{e (x+4) \left (4 x^2-4 \log \left (x+\frac {e^{x-1}}{x+4}\right ) x-x+\log ^2\left (x+\frac {e^{x-1}}{x+4}\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 3 e \left (\frac {3 \int \frac {1}{4 x^2-4 \log \left (x+\frac {e^{x-1}}{x+4}\right ) x-x+\log ^2\left (x+\frac {e^{x-1}}{x+4}\right )}dx}{e}+\frac {4 \int \frac {x}{4 x^2-4 \log \left (x+\frac {e^{x-1}}{x+4}\right ) x-x+\log ^2\left (x+\frac {e^{x-1}}{x+4}\right )}dx}{e}-\frac {16 \int \frac {1}{(x+4) \left (4 x^2-4 \log \left (x+\frac {e^{x-1}}{x+4}\right ) x-x+\log ^2\left (x+\frac {e^{x-1}}{x+4}\right )\right )}dx}{e}-16 \int \frac {x}{\left (e x^2+4 e x+e^x\right ) \left (4 x^2-4 \log \left (x+\frac {e^{x-1}}{x+4}\right ) x-x+\log ^2\left (x+\frac {e^{x-1}}{x+4}\right )\right )}dx+8 \int \frac {x^2}{\left (e x^2+4 e x+e^x\right ) \left (4 x^2-4 \log \left (x+\frac {e^{x-1}}{x+4}\right ) x-x+\log ^2\left (x+\frac {e^{x-1}}{x+4}\right )\right )}dx-\frac {2 \int \frac {\log \left (x+\frac {e^{x-1}}{x+4}\right )}{4 x^2-4 \log \left (x+\frac {e^{x-1}}{x+4}\right ) x-x+\log ^2\left (x+\frac {e^{x-1}}{x+4}\right )}dx}{e}-\frac {2 \int \frac {\log \left (x+\frac {e^{x-1}}{x+4}\right )}{(x+4) \left (4 x^2-4 \log \left (x+\frac {e^{x-1}}{x+4}\right ) x-x+\log ^2\left (x+\frac {e^{x-1}}{x+4}\right )\right )}dx}{e}+8 \int \frac {\log \left (x+\frac {e^{x-1}}{x+4}\right )}{\left (e x^2+4 e x+e^x\right ) \left (4 x^2-4 \log \left (x+\frac {e^{x-1}}{x+4}\right ) x-x+\log ^2\left (x+\frac {e^{x-1}}{x+4}\right )\right )}dx-4 \int \frac {x \log \left (x+\frac {e^{x-1}}{x+4}\right )}{\left (e x^2+4 e x+e^x\right ) \left (4 x^2-4 \log \left (x+\frac {e^{x-1}}{x+4}\right ) x-x+\log ^2\left (x+\frac {e^{x-1}}{x+4}\right )\right )}dx-2 \int \frac {x^2 \log \left (x+\frac {e^{x-1}}{x+4}\right )}{\left (e x^2+4 e x+e^x\right ) \left (4 x^2-4 \log \left (x+\frac {e^{x-1}}{x+4}\right ) x-x+\log ^2\left (x+\frac {e^{x-1}}{x+4}\right )\right )}dx+4 \int \frac {x^3}{\left (e x^2+4 e x+e^x\right ) \left (4 x^2-4 \log \left (x+\frac {e^{x-1}}{x+4}\right ) x-x+\log ^2\left (x+\frac {e^{x-1}}{x+4}\right )\right )}dx\right )\) |
Int[(-60*x + 81*x^2 + 24*x^3 + (E^(-1 + x)*(-12 + 57*x + 12*x^2))/(4 + x) + (24 - 42*x - 12*x^2 + (E^(-1 + x)*(-30 - 6*x))/(4 + x))*Log[x + E^(-1 + x)/(4 + x)])/(-4*x^2 + 15*x^3 + 4*x^4 + (E^(-1 + x)*(-4*x + 15*x^2 + 4*x^3 ))/(4 + x) + (-16*x^2 - 4*x^3 + (E^(-1 + x)*(-16*x - 4*x^2))/(4 + x))*Log[ x + E^(-1 + x)/(4 + x)] + (E^(-1 + x) + 4*x + x^2)*Log[x + E^(-1 + x)/(4 + x)]^2),x]
3.20.6.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Time = 3.52 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.34
| method | result | size |
| risch | \(3 \ln \left (\ln \left (\frac {{\mathrm e}^{-1+x}}{4+x}+x \right )^{2}-4 \ln \left (\frac {{\mathrm e}^{-1+x}}{4+x}+x \right ) x +x \left (-1+4 x \right )\right )\) | \(43\) |
| parallelrisch | \(3 \ln \left (x^{2}-\ln \left ({\mathrm e}^{-\ln \left (4+x \right )+x -1}+x \right ) x +\frac {\ln \left ({\mathrm e}^{-\ln \left (4+x \right )+x -1}+x \right )^{2}}{4}-\frac {x}{4}\right )\) | \(44\) |
int((((-6*x-30)*exp(-ln(4+x)+x-1)-12*x^2-42*x+24)*ln(exp(-ln(4+x)+x-1)+x)+ (12*x^2+57*x-12)*exp(-ln(4+x)+x-1)+24*x^3+81*x^2-60*x)/(((4+x)*exp(-ln(4+x )+x-1)+x^2+4*x)*ln(exp(-ln(4+x)+x-1)+x)^2+((-4*x^2-16*x)*exp(-ln(4+x)+x-1) -4*x^3-16*x^2)*ln(exp(-ln(4+x)+x-1)+x)+(4*x^3+15*x^2-4*x)*exp(-ln(4+x)+x-1 )+4*x^4+15*x^3-4*x^2),x,method=_RETURNVERBOSE)
Time = 0.25 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.34 \[ \int \frac {-60 x+81 x^2+24 x^3+\frac {e^{-1+x} \left (-12+57 x+12 x^2\right )}{4+x}+\left (24-42 x-12 x^2+\frac {e^{-1+x} (-30-6 x)}{4+x}\right ) \log \left (x+\frac {e^{-1+x}}{4+x}\right )}{-4 x^2+15 x^3+4 x^4+\frac {e^{-1+x} \left (-4 x+15 x^2+4 x^3\right )}{4+x}+\left (-16 x^2-4 x^3+\frac {e^{-1+x} \left (-16 x-4 x^2\right )}{4+x}\right ) \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\left (e^{-1+x}+4 x+x^2\right ) \log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )} \, dx=3 \, \log \left (4 \, x^{2} - 4 \, x \log \left (x + e^{\left (x - \log \left (x + 4\right ) - 1\right )}\right ) + \log \left (x + e^{\left (x - \log \left (x + 4\right ) - 1\right )}\right )^{2} - x\right ) \]
integrate((((-6*x-30)*exp(-log(4+x)+x-1)-12*x^2-42*x+24)*log(exp(-log(4+x) +x-1)+x)+(12*x^2+57*x-12)*exp(-log(4+x)+x-1)+24*x^3+81*x^2-60*x)/(((4+x)*e xp(-log(4+x)+x-1)+x^2+4*x)*log(exp(-log(4+x)+x-1)+x)^2+((-4*x^2-16*x)*exp( -log(4+x)+x-1)-4*x^3-16*x^2)*log(exp(-log(4+x)+x-1)+x)+(4*x^3+15*x^2-4*x)* exp(-log(4+x)+x-1)+4*x^4+15*x^3-4*x^2),x, algorithm=\
Time = 0.82 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.16 \[ \int \frac {-60 x+81 x^2+24 x^3+\frac {e^{-1+x} \left (-12+57 x+12 x^2\right )}{4+x}+\left (24-42 x-12 x^2+\frac {e^{-1+x} (-30-6 x)}{4+x}\right ) \log \left (x+\frac {e^{-1+x}}{4+x}\right )}{-4 x^2+15 x^3+4 x^4+\frac {e^{-1+x} \left (-4 x+15 x^2+4 x^3\right )}{4+x}+\left (-16 x^2-4 x^3+\frac {e^{-1+x} \left (-16 x-4 x^2\right )}{4+x}\right ) \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\left (e^{-1+x}+4 x+x^2\right ) \log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )} \, dx=3 \log {\left (4 x^{2} - 4 x \log {\left (x + \frac {e^{x - 1}}{x + 4} \right )} - x + \log {\left (x + \frac {e^{x - 1}}{x + 4} \right )}^{2} \right )} \]
integrate((((-6*x-30)*exp(-ln(4+x)+x-1)-12*x**2-42*x+24)*ln(exp(-ln(4+x)+x -1)+x)+(12*x**2+57*x-12)*exp(-ln(4+x)+x-1)+24*x**3+81*x**2-60*x)/(((4+x)*e xp(-ln(4+x)+x-1)+x**2+4*x)*ln(exp(-ln(4+x)+x-1)+x)**2+((-4*x**2-16*x)*exp( -ln(4+x)+x-1)-4*x**3-16*x**2)*ln(exp(-ln(4+x)+x-1)+x)+(4*x**3+15*x**2-4*x) *exp(-ln(4+x)+x-1)+4*x**4+15*x**3-4*x**2),x)
Leaf count of result is larger than twice the leaf count of optimal. 73 vs. \(2 (31) = 62\).
Time = 0.32 (sec) , antiderivative size = 73, normalized size of antiderivative = 2.28 \[ \int \frac {-60 x+81 x^2+24 x^3+\frac {e^{-1+x} \left (-12+57 x+12 x^2\right )}{4+x}+\left (24-42 x-12 x^2+\frac {e^{-1+x} (-30-6 x)}{4+x}\right ) \log \left (x+\frac {e^{-1+x}}{4+x}\right )}{-4 x^2+15 x^3+4 x^4+\frac {e^{-1+x} \left (-4 x+15 x^2+4 x^3\right )}{4+x}+\left (-16 x^2-4 x^3+\frac {e^{-1+x} \left (-16 x-4 x^2\right )}{4+x}\right ) \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\left (e^{-1+x}+4 x+x^2\right ) \log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )} \, dx=3 \, \log \left (4 \, x^{2} - 2 \, {\left (2 \, x + \log \left (x + 4\right ) + 1\right )} \log \left (x^{2} e + 4 \, x e + e^{x}\right ) + \log \left (x^{2} e + 4 \, x e + e^{x}\right )^{2} + 2 \, {\left (2 \, x + 1\right )} \log \left (x + 4\right ) + \log \left (x + 4\right )^{2} + 3 \, x + 1\right ) \]
integrate((((-6*x-30)*exp(-log(4+x)+x-1)-12*x^2-42*x+24)*log(exp(-log(4+x) +x-1)+x)+(12*x^2+57*x-12)*exp(-log(4+x)+x-1)+24*x^3+81*x^2-60*x)/(((4+x)*e xp(-log(4+x)+x-1)+x^2+4*x)*log(exp(-log(4+x)+x-1)+x)^2+((-4*x^2-16*x)*exp( -log(4+x)+x-1)-4*x^3-16*x^2)*log(exp(-log(4+x)+x-1)+x)+(4*x^3+15*x^2-4*x)* exp(-log(4+x)+x-1)+4*x^4+15*x^3-4*x^2),x, algorithm=\
3*log(4*x^2 - 2*(2*x + log(x + 4) + 1)*log(x^2*e + 4*x*e + e^x) + log(x^2* e + 4*x*e + e^x)^2 + 2*(2*x + 1)*log(x + 4) + log(x + 4)^2 + 3*x + 1)
Leaf count of result is larger than twice the leaf count of optimal. 105 vs. \(2 (31) = 62\).
Time = 0.88 (sec) , antiderivative size = 105, normalized size of antiderivative = 3.28 \[ \int \frac {-60 x+81 x^2+24 x^3+\frac {e^{-1+x} \left (-12+57 x+12 x^2\right )}{4+x}+\left (24-42 x-12 x^2+\frac {e^{-1+x} (-30-6 x)}{4+x}\right ) \log \left (x+\frac {e^{-1+x}}{4+x}\right )}{-4 x^2+15 x^3+4 x^4+\frac {e^{-1+x} \left (-4 x+15 x^2+4 x^3\right )}{4+x}+\left (-16 x^2-4 x^3+\frac {e^{-1+x} \left (-16 x-4 x^2\right )}{4+x}\right ) \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\left (e^{-1+x}+4 x+x^2\right ) \log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )} \, dx=3 \, \log \left (4 \, x^{2} - 4 \, x \log \left (x^{2} e + 4 \, x e + e^{x}\right ) + \log \left (x^{2} e + 4 \, x e + e^{x}\right )^{2} + 4 \, x \log \left (x + 4\right ) - 2 \, \log \left (x^{2} e + 4 \, x e + e^{x}\right ) \log \left (x + 4\right ) + \log \left (x + 4\right )^{2} + 3 \, x - 2 \, \log \left (x^{2} e + 4 \, x e + e^{x}\right ) + 2 \, \log \left (x + 4\right ) + 1\right ) \]
integrate((((-6*x-30)*exp(-log(4+x)+x-1)-12*x^2-42*x+24)*log(exp(-log(4+x) +x-1)+x)+(12*x^2+57*x-12)*exp(-log(4+x)+x-1)+24*x^3+81*x^2-60*x)/(((4+x)*e xp(-log(4+x)+x-1)+x^2+4*x)*log(exp(-log(4+x)+x-1)+x)^2+((-4*x^2-16*x)*exp( -log(4+x)+x-1)-4*x^3-16*x^2)*log(exp(-log(4+x)+x-1)+x)+(4*x^3+15*x^2-4*x)* exp(-log(4+x)+x-1)+4*x^4+15*x^3-4*x^2),x, algorithm=\
3*log(4*x^2 - 4*x*log(x^2*e + 4*x*e + e^x) + log(x^2*e + 4*x*e + e^x)^2 + 4*x*log(x + 4) - 2*log(x^2*e + 4*x*e + e^x)*log(x + 4) + log(x + 4)^2 + 3* x - 2*log(x^2*e + 4*x*e + e^x) + 2*log(x + 4) + 1)
Timed out. \[ \int \frac {-60 x+81 x^2+24 x^3+\frac {e^{-1+x} \left (-12+57 x+12 x^2\right )}{4+x}+\left (24-42 x-12 x^2+\frac {e^{-1+x} (-30-6 x)}{4+x}\right ) \log \left (x+\frac {e^{-1+x}}{4+x}\right )}{-4 x^2+15 x^3+4 x^4+\frac {e^{-1+x} \left (-4 x+15 x^2+4 x^3\right )}{4+x}+\left (-16 x^2-4 x^3+\frac {e^{-1+x} \left (-16 x-4 x^2\right )}{4+x}\right ) \log \left (x+\frac {e^{-1+x}}{4+x}\right )+\left (e^{-1+x}+4 x+x^2\right ) \log ^2\left (x+\frac {e^{-1+x}}{4+x}\right )} \, dx=\int \frac {{\mathrm {e}}^{x-\ln \left (x+4\right )-1}\,\left (12\,x^2+57\,x-12\right )-\ln \left (x+{\mathrm {e}}^{x-\ln \left (x+4\right )-1}\right )\,\left (42\,x+{\mathrm {e}}^{x-\ln \left (x+4\right )-1}\,\left (6\,x+30\right )+12\,x^2-24\right )-60\,x+81\,x^2+24\,x^3}{{\ln \left (x+{\mathrm {e}}^{x-\ln \left (x+4\right )-1}\right )}^2\,\left (4\,x+{\mathrm {e}}^{x-\ln \left (x+4\right )-1}\,\left (x+4\right )+x^2\right )-4\,x^2+15\,x^3+4\,x^4+{\mathrm {e}}^{x-\ln \left (x+4\right )-1}\,\left (4\,x^3+15\,x^2-4\,x\right )-\ln \left (x+{\mathrm {e}}^{x-\ln \left (x+4\right )-1}\right )\,\left ({\mathrm {e}}^{x-\ln \left (x+4\right )-1}\,\left (4\,x^2+16\,x\right )+16\,x^2+4\,x^3\right )} \,d x \]
int((exp(x - log(x + 4) - 1)*(57*x + 12*x^2 - 12) - log(x + exp(x - log(x + 4) - 1))*(42*x + exp(x - log(x + 4) - 1)*(6*x + 30) + 12*x^2 - 24) - 60* x + 81*x^2 + 24*x^3)/(log(x + exp(x - log(x + 4) - 1))^2*(4*x + exp(x - lo g(x + 4) - 1)*(x + 4) + x^2) - 4*x^2 + 15*x^3 + 4*x^4 + exp(x - log(x + 4) - 1)*(15*x^2 - 4*x + 4*x^3) - log(x + exp(x - log(x + 4) - 1))*(exp(x - l og(x + 4) - 1)*(16*x + 4*x^2) + 16*x^2 + 4*x^3)),x)
int((exp(x - log(x + 4) - 1)*(57*x + 12*x^2 - 12) - log(x + exp(x - log(x + 4) - 1))*(42*x + exp(x - log(x + 4) - 1)*(6*x + 30) + 12*x^2 - 24) - 60* x + 81*x^2 + 24*x^3)/(log(x + exp(x - log(x + 4) - 1))^2*(4*x + exp(x - lo g(x + 4) - 1)*(x + 4) + x^2) - 4*x^2 + 15*x^3 + 4*x^4 + exp(x - log(x + 4) - 1)*(15*x^2 - 4*x + 4*x^3) - log(x + exp(x - log(x + 4) - 1))*(exp(x - l og(x + 4) - 1)*(16*x + 4*x^2) + 16*x^2 + 4*x^3)), x)