3.1.11 \(\int \frac {24 x+48 x^2+8 x^3+e^x (-4 x-44 x^2-28 x^3-4 x^4)+e^{2 x} (-4 x+10 x^2+12 x^3+2 x^4)+(-40-68 x-12 x^2+e^{2 x} (-15 x-13 x^2-2 x^3)+e^x (20+64 x+32 x^2+4 x^3)) \log (5+x)+\log ^2(x^2) (-4 x+(-5 x-x^2) \log (5+x))+\log (x^2) (4 x+24 x^2+4 x^3+e^x (8 x-10 x^2-12 x^3-2 x^4)+(-20-44 x-8 x^2+e^x (20 x+14 x^2+2 x^3)) \log (5+x))}{5 x^3+x^4+(-10 x^2-2 x^3) \log (5+x)+(5 x+x^2) \log ^2(5+x)} \, dx\)

Optimal. Leaf size=29 \[ 2+\frac {(1+x) \left (-2+e^x-\log \left (x^2\right )\right )^2}{x-\log (5+x)} \]

________________________________________________________________________________________

Rubi [F]  time = 116.87, 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 {24 x+48 x^2+8 x^3+e^x \left (-4 x-44 x^2-28 x^3-4 x^4\right )+e^{2 x} \left (-4 x+10 x^2+12 x^3+2 x^4\right )+\left (-40-68 x-12 x^2+e^{2 x} \left (-15 x-13 x^2-2 x^3\right )+e^x \left (20+64 x+32 x^2+4 x^3\right )\right ) \log (5+x)+\log ^2\left (x^2\right ) \left (-4 x+\left (-5 x-x^2\right ) \log (5+x)\right )+\log \left (x^2\right ) \left (4 x+24 x^2+4 x^3+e^x \left (8 x-10 x^2-12 x^3-2 x^4\right )+\left (-20-44 x-8 x^2+e^x \left (20 x+14 x^2+2 x^3\right )\right ) \log (5+x)\right )}{5 x^3+x^4+\left (-10 x^2-2 x^3\right ) \log (5+x)+\left (5 x+x^2\right ) \log ^2(5+x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(24*x + 48*x^2 + 8*x^3 + E^x*(-4*x - 44*x^2 - 28*x^3 - 4*x^4) + E^(2*x)*(-4*x + 10*x^2 + 12*x^3 + 2*x^4) +
(-40 - 68*x - 12*x^2 + E^(2*x)*(-15*x - 13*x^2 - 2*x^3) + E^x*(20 + 64*x + 32*x^2 + 4*x^3))*Log[5 + x] + Log[
x^2]^2*(-4*x + (-5*x - x^2)*Log[5 + x]) + Log[x^2]*(4*x + 24*x^2 + 4*x^3 + E^x*(8*x - 10*x^2 - 12*x^3 - 2*x^4)
+ (-20 - 44*x - 8*x^2 + E^x*(20*x + 14*x^2 + 2*x^3))*Log[5 + x]))/(5*x^3 + x^4 + (-10*x^2 - 2*x^3)*Log[5 + x]
+ (5*x + x^2)*Log[5 + x]^2),x]

[Out]

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\left (2-e^x+\log \left (x^2\right )\right ) \left (-2 x \left (-2 \left (3+6 x+x^2\right )+e^x \left (-2+5 x+6 x^2+x^3\right )\right )+(5+x) \left (-4+3 \left (-2+e^x\right ) x+2 e^x x^2\right ) \log (5+x)-x \log \left (x^2\right ) (4+(5+x) \log (5+x))\right )}{x (5+x) (x-\log (5+x))^2} \, dx\\ &=\int \left (\frac {8 \left (3+6 x+x^2\right )}{(5+x) (x-\log (5+x))^2}+\frac {4 \left (3+6 x+x^2\right ) \log \left (x^2\right )}{(5+x) (x-\log (5+x))^2}-\frac {12 \log (5+x)}{(x-\log (5+x))^2}-\frac {8 \log (5+x)}{x (x-\log (5+x))^2}-\frac {6 \log \left (x^2\right ) \log (5+x)}{(x-\log (5+x))^2}-\frac {4 \log \left (x^2\right ) \log (5+x)}{x (x-\log (5+x))^2}-\frac {2 \log \left (x^2\right ) (4+5 \log (5+x)+x \log (5+x))}{(5+x) (x-\log (5+x))^2}-\frac {\log ^2\left (x^2\right ) (4+5 \log (5+x)+x \log (5+x))}{(5+x) (x-\log (5+x))^2}+\frac {e^{2 x} \left (-4+10 x+12 x^2+2 x^3-15 \log (5+x)-13 x \log (5+x)-2 x^2 \log (5+x)\right )}{(5+x) (x-\log (5+x))^2}-\frac {2 e^x \left (2 x+22 x^2+14 x^3+2 x^4-4 x \log \left (x^2\right )+5 x^2 \log \left (x^2\right )+6 x^3 \log \left (x^2\right )+x^4 \log \left (x^2\right )-10 \log (5+x)-32 x \log (5+x)-16 x^2 \log (5+x)-2 x^3 \log (5+x)-10 x \log \left (x^2\right ) \log (5+x)-7 x^2 \log \left (x^2\right ) \log (5+x)-x^3 \log \left (x^2\right ) \log (5+x)\right )}{x (5+x) (x-\log (5+x))^2}\right ) \, dx\\ &=-\left (2 \int \frac {\log \left (x^2\right ) (4+5 \log (5+x)+x \log (5+x))}{(5+x) (x-\log (5+x))^2} \, dx\right )-2 \int \frac {e^x \left (2 x+22 x^2+14 x^3+2 x^4-4 x \log \left (x^2\right )+5 x^2 \log \left (x^2\right )+6 x^3 \log \left (x^2\right )+x^4 \log \left (x^2\right )-10 \log (5+x)-32 x \log (5+x)-16 x^2 \log (5+x)-2 x^3 \log (5+x)-10 x \log \left (x^2\right ) \log (5+x)-7 x^2 \log \left (x^2\right ) \log (5+x)-x^3 \log \left (x^2\right ) \log (5+x)\right )}{x (5+x) (x-\log (5+x))^2} \, dx+4 \int \frac {\left (3+6 x+x^2\right ) \log \left (x^2\right )}{(5+x) (x-\log (5+x))^2} \, dx-4 \int \frac {\log \left (x^2\right ) \log (5+x)}{x (x-\log (5+x))^2} \, dx-6 \int \frac {\log \left (x^2\right ) \log (5+x)}{(x-\log (5+x))^2} \, dx+8 \int \frac {3+6 x+x^2}{(5+x) (x-\log (5+x))^2} \, dx-8 \int \frac {\log (5+x)}{x (x-\log (5+x))^2} \, dx-12 \int \frac {\log (5+x)}{(x-\log (5+x))^2} \, dx-\int \frac {\log ^2\left (x^2\right ) (4+5 \log (5+x)+x \log (5+x))}{(5+x) (x-\log (5+x))^2} \, dx+\int \frac {e^{2 x} \left (-4+10 x+12 x^2+2 x^3-15 \log (5+x)-13 x \log (5+x)-2 x^2 \log (5+x)\right )}{(5+x) (x-\log (5+x))^2} \, dx\\ &=-\left (2 \int \frac {\log \left (x^2\right ) (4+(5+x) \log (5+x))}{(5+x) (x-\log (5+x))^2} \, dx\right )-2 \int \frac {e^x \left (2 x \left (1+11 x+7 x^2+x^3\right )-2 \left (5+16 x+8 x^2+x^3\right ) \log (5+x)+x \log \left (x^2\right ) \left (-4+5 x+6 x^2+x^3-\left (10+7 x+x^2\right ) \log (5+x)\right )\right )}{x (5+x) (x-\log (5+x))^2} \, dx+4 \int \left (\frac {\log \left (x^2\right )}{(x-\log (5+x))^2}+\frac {x \log \left (x^2\right )}{(x-\log (5+x))^2}-\frac {2 \log \left (x^2\right )}{(5+x) (x-\log (5+x))^2}\right ) \, dx-4 \int \left (\frac {\log \left (x^2\right )}{(x-\log (5+x))^2}-\frac {\log \left (x^2\right )}{x (x-\log (5+x))}\right ) \, dx-6 \int \left (\frac {x \log \left (x^2\right )}{(x-\log (5+x))^2}-\frac {\log \left (x^2\right )}{x-\log (5+x)}\right ) \, dx+8 \int \left (\frac {1}{(x-\log (5+x))^2}+\frac {x}{(x-\log (5+x))^2}-\frac {2}{(5+x) (x-\log (5+x))^2}\right ) \, dx-8 \int \left (\frac {1}{(x-\log (5+x))^2}-\frac {1}{x (x-\log (5+x))}\right ) \, dx-12 \int \left (\frac {x}{(x-\log (5+x))^2}+\frac {1}{-x+\log (5+x)}\right ) \, dx+\int \left (\frac {e^{2 x} \left (-4-5 x-x^2\right )}{(5+x) (x-\log (5+x))^2}+\frac {e^{2 x} (3+2 x)}{x-\log (5+x)}\right ) \, dx-\int \frac {\log ^2\left (x^2\right ) (4+(5+x) \log (5+x))}{(5+x) (x-\log (5+x))^2} \, dx\\ &=-\left (2 \int \left (\frac {\left (4+5 x+x^2\right ) \log \left (x^2\right )}{(5+x) (x-\log (5+x))^2}-\frac {\log \left (x^2\right )}{x-\log (5+x)}\right ) \, dx\right )-2 \int \left (-\frac {e^x \left (4+5 x+x^2\right ) \left (2+\log \left (x^2\right )\right )}{(5+x) (x-\log (5+x))^2}+\frac {e^x \left (2+6 x+2 x^2+2 x \log \left (x^2\right )+x^2 \log \left (x^2\right )\right )}{x (x-\log (5+x))}\right ) \, dx+4 \int \frac {x \log \left (x^2\right )}{(x-\log (5+x))^2} \, dx+4 \int \frac {\log \left (x^2\right )}{x (x-\log (5+x))} \, dx-6 \int \frac {x \log \left (x^2\right )}{(x-\log (5+x))^2} \, dx+6 \int \frac {\log \left (x^2\right )}{x-\log (5+x)} \, dx+8 \int \frac {x}{(x-\log (5+x))^2} \, dx-8 \int \frac {\log \left (x^2\right )}{(5+x) (x-\log (5+x))^2} \, dx+8 \int \frac {1}{x (x-\log (5+x))} \, dx-12 \int \frac {x}{(x-\log (5+x))^2} \, dx-12 \int \frac {1}{-x+\log (5+x)} \, dx-16 \int \frac {1}{(5+x) (x-\log (5+x))^2} \, dx-\int \left (\frac {\left (4+5 x+x^2\right ) \log ^2\left (x^2\right )}{(5+x) (x-\log (5+x))^2}-\frac {\log ^2\left (x^2\right )}{x-\log (5+x)}\right ) \, dx+\int \frac {e^{2 x} \left (-4-5 x-x^2\right )}{(5+x) (x-\log (5+x))^2} \, dx+\int \frac {e^{2 x} (3+2 x)}{x-\log (5+x)} \, dx\\ &=-\left (2 \int \frac {\left (4+5 x+x^2\right ) \log \left (x^2\right )}{(5+x) (x-\log (5+x))^2} \, dx\right )+2 \int \frac {e^x \left (4+5 x+x^2\right ) \left (2+\log \left (x^2\right )\right )}{(5+x) (x-\log (5+x))^2} \, dx+2 \int \frac {\log \left (x^2\right )}{x-\log (5+x)} \, dx-2 \int \frac {e^x \left (2+6 x+2 x^2+2 x \log \left (x^2\right )+x^2 \log \left (x^2\right )\right )}{x (x-\log (5+x))} \, dx+4 \int \frac {x \log \left (x^2\right )}{(x-\log (5+x))^2} \, dx+4 \int \frac {\log \left (x^2\right )}{x (x-\log (5+x))} \, dx-6 \int \frac {x \log \left (x^2\right )}{(x-\log (5+x))^2} \, dx+6 \int \frac {\log \left (x^2\right )}{x-\log (5+x)} \, dx+8 \int \frac {x}{(x-\log (5+x))^2} \, dx-8 \int \frac {\log \left (x^2\right )}{(5+x) (x-\log (5+x))^2} \, dx+8 \int \frac {1}{x (x-\log (5+x))} \, dx-12 \int \frac {x}{(x-\log (5+x))^2} \, dx-12 \int \frac {1}{-x+\log (5+x)} \, dx-16 \int \frac {1}{(5+x) (x-\log (5+x))^2} \, dx+\int \left (-\frac {e^{2 x} x}{(x-\log (5+x))^2}-\frac {4 e^{2 x}}{(5+x) (x-\log (5+x))^2}\right ) \, dx+\int \left (\frac {3 e^{2 x}}{x-\log (5+x)}+\frac {2 e^{2 x} x}{x-\log (5+x)}\right ) \, dx-\int \frac {\left (4+5 x+x^2\right ) \log ^2\left (x^2\right )}{(5+x) (x-\log (5+x))^2} \, dx+\int \frac {\log ^2\left (x^2\right )}{x-\log (5+x)} \, dx\\ &=-\left (2 \int \left (\frac {x \log \left (x^2\right )}{(x-\log (5+x))^2}+\frac {4 \log \left (x^2\right )}{(5+x) (x-\log (5+x))^2}\right ) \, dx\right )+2 \int \left (\frac {e^x x \left (2+\log \left (x^2\right )\right )}{(x-\log (5+x))^2}+\frac {4 e^x \left (2+\log \left (x^2\right )\right )}{(5+x) (x-\log (5+x))^2}\right ) \, dx-2 \int \left (\frac {6 e^x}{x-\log (5+x)}+\frac {2 e^x}{x (x-\log (5+x))}+\frac {2 e^x x}{x-\log (5+x)}+\frac {2 e^x \log \left (x^2\right )}{x-\log (5+x)}+\frac {e^x x \log \left (x^2\right )}{x-\log (5+x)}\right ) \, dx+2 \int \frac {e^{2 x} x}{x-\log (5+x)} \, dx+2 \int \frac {\log \left (x^2\right )}{x-\log (5+x)} \, dx+3 \int \frac {e^{2 x}}{x-\log (5+x)} \, dx-4 \int \frac {e^{2 x}}{(5+x) (x-\log (5+x))^2} \, dx+4 \int \frac {x \log \left (x^2\right )}{(x-\log (5+x))^2} \, dx+4 \int \frac {\log \left (x^2\right )}{x (x-\log (5+x))} \, dx-6 \int \frac {x \log \left (x^2\right )}{(x-\log (5+x))^2} \, dx+6 \int \frac {\log \left (x^2\right )}{x-\log (5+x)} \, dx+8 \int \frac {x}{(x-\log (5+x))^2} \, dx-8 \int \frac {\log \left (x^2\right )}{(5+x) (x-\log (5+x))^2} \, dx+8 \int \frac {1}{x (x-\log (5+x))} \, dx-12 \int \frac {x}{(x-\log (5+x))^2} \, dx-12 \int \frac {1}{-x+\log (5+x)} \, dx-16 \int \frac {1}{(5+x) (x-\log (5+x))^2} \, dx-\int \left (\frac {x \log ^2\left (x^2\right )}{(x-\log (5+x))^2}+\frac {4 \log ^2\left (x^2\right )}{(5+x) (x-\log (5+x))^2}\right ) \, dx-\int \frac {e^{2 x} x}{(x-\log (5+x))^2} \, dx+\int \frac {\log ^2\left (x^2\right )}{x-\log (5+x)} \, dx\\ &=-\left (2 \int \frac {x \log \left (x^2\right )}{(x-\log (5+x))^2} \, dx\right )+2 \int \frac {e^x x \left (2+\log \left (x^2\right )\right )}{(x-\log (5+x))^2} \, dx+2 \int \frac {e^{2 x} x}{x-\log (5+x)} \, dx+2 \int \frac {\log \left (x^2\right )}{x-\log (5+x)} \, dx-2 \int \frac {e^x x \log \left (x^2\right )}{x-\log (5+x)} \, dx+3 \int \frac {e^{2 x}}{x-\log (5+x)} \, dx-4 \int \frac {e^{2 x}}{(5+x) (x-\log (5+x))^2} \, dx+4 \int \frac {x \log \left (x^2\right )}{(x-\log (5+x))^2} \, dx-4 \int \frac {\log ^2\left (x^2\right )}{(5+x) (x-\log (5+x))^2} \, dx-4 \int \frac {e^x}{x (x-\log (5+x))} \, dx-4 \int \frac {e^x x}{x-\log (5+x)} \, dx-4 \int \frac {e^x \log \left (x^2\right )}{x-\log (5+x)} \, dx+4 \int \frac {\log \left (x^2\right )}{x (x-\log (5+x))} \, dx-6 \int \frac {x \log \left (x^2\right )}{(x-\log (5+x))^2} \, dx+6 \int \frac {\log \left (x^2\right )}{x-\log (5+x)} \, dx+8 \int \frac {x}{(x-\log (5+x))^2} \, dx-2 \left (8 \int \frac {\log \left (x^2\right )}{(5+x) (x-\log (5+x))^2} \, dx\right )+8 \int \frac {e^x \left (2+\log \left (x^2\right )\right )}{(5+x) (x-\log (5+x))^2} \, dx+8 \int \frac {1}{x (x-\log (5+x))} \, dx-12 \int \frac {x}{(x-\log (5+x))^2} \, dx-12 \int \frac {e^x}{x-\log (5+x)} \, dx-12 \int \frac {1}{-x+\log (5+x)} \, dx-16 \int \frac {1}{(5+x) (x-\log (5+x))^2} \, dx-\int \frac {e^{2 x} x}{(x-\log (5+x))^2} \, dx-\int \frac {x \log ^2\left (x^2\right )}{(x-\log (5+x))^2} \, dx+\int \frac {\log ^2\left (x^2\right )}{x-\log (5+x)} \, dx\\ &=2 \int \left (\frac {2 e^x x}{(x-\log (5+x))^2}+\frac {e^x x \log \left (x^2\right )}{(x-\log (5+x))^2}\right ) \, dx-2 \int \frac {x \log \left (x^2\right )}{(x-\log (5+x))^2} \, dx+2 \int \frac {e^{2 x} x}{x-\log (5+x)} \, dx+2 \int \frac {\log \left (x^2\right )}{x-\log (5+x)} \, dx-2 \int \frac {e^x x \log \left (x^2\right )}{x-\log (5+x)} \, dx+3 \int \frac {e^{2 x}}{x-\log (5+x)} \, dx-4 \int \frac {e^{2 x}}{(5+x) (x-\log (5+x))^2} \, dx+4 \int \frac {x \log \left (x^2\right )}{(x-\log (5+x))^2} \, dx-4 \int \frac {\log ^2\left (x^2\right )}{(5+x) (x-\log (5+x))^2} \, dx-4 \int \frac {e^x}{x (x-\log (5+x))} \, dx-4 \int \frac {e^x x}{x-\log (5+x)} \, dx-4 \int \frac {e^x \log \left (x^2\right )}{x-\log (5+x)} \, dx+4 \int \frac {\log \left (x^2\right )}{x (x-\log (5+x))} \, dx-6 \int \frac {x \log \left (x^2\right )}{(x-\log (5+x))^2} \, dx+6 \int \frac {\log \left (x^2\right )}{x-\log (5+x)} \, dx+8 \int \left (\frac {2 e^x}{(5+x) (x-\log (5+x))^2}+\frac {e^x \log \left (x^2\right )}{(5+x) (x-\log (5+x))^2}\right ) \, dx+8 \int \frac {x}{(x-\log (5+x))^2} \, dx-2 \left (8 \int \frac {\log \left (x^2\right )}{(5+x) (x-\log (5+x))^2} \, dx\right )+8 \int \frac {1}{x (x-\log (5+x))} \, dx-12 \int \frac {x}{(x-\log (5+x))^2} \, dx-12 \int \frac {e^x}{x-\log (5+x)} \, dx-12 \int \frac {1}{-x+\log (5+x)} \, dx-16 \int \frac {1}{(5+x) (x-\log (5+x))^2} \, dx-\int \frac {e^{2 x} x}{(x-\log (5+x))^2} \, dx-\int \frac {x \log ^2\left (x^2\right )}{(x-\log (5+x))^2} \, dx+\int \frac {\log ^2\left (x^2\right )}{x-\log (5+x)} \, dx\\ &=-\left (2 \int \frac {x \log \left (x^2\right )}{(x-\log (5+x))^2} \, dx\right )+2 \int \frac {e^x x \log \left (x^2\right )}{(x-\log (5+x))^2} \, dx+2 \int \frac {e^{2 x} x}{x-\log (5+x)} \, dx+2 \int \frac {\log \left (x^2\right )}{x-\log (5+x)} \, dx-2 \int \frac {e^x x \log \left (x^2\right )}{x-\log (5+x)} \, dx+3 \int \frac {e^{2 x}}{x-\log (5+x)} \, dx+4 \int \frac {e^x x}{(x-\log (5+x))^2} \, dx-4 \int \frac {e^{2 x}}{(5+x) (x-\log (5+x))^2} \, dx+4 \int \frac {x \log \left (x^2\right )}{(x-\log (5+x))^2} \, dx-4 \int \frac {\log ^2\left (x^2\right )}{(5+x) (x-\log (5+x))^2} \, dx-4 \int \frac {e^x}{x (x-\log (5+x))} \, dx-4 \int \frac {e^x x}{x-\log (5+x)} \, dx-4 \int \frac {e^x \log \left (x^2\right )}{x-\log (5+x)} \, dx+4 \int \frac {\log \left (x^2\right )}{x (x-\log (5+x))} \, dx-6 \int \frac {x \log \left (x^2\right )}{(x-\log (5+x))^2} \, dx+6 \int \frac {\log \left (x^2\right )}{x-\log (5+x)} \, dx+8 \int \frac {x}{(x-\log (5+x))^2} \, dx-2 \left (8 \int \frac {\log \left (x^2\right )}{(5+x) (x-\log (5+x))^2} \, dx\right )+8 \int \frac {e^x \log \left (x^2\right )}{(5+x) (x-\log (5+x))^2} \, dx+8 \int \frac {1}{x (x-\log (5+x))} \, dx-12 \int \frac {x}{(x-\log (5+x))^2} \, dx-12 \int \frac {e^x}{x-\log (5+x)} \, dx-12 \int \frac {1}{-x+\log (5+x)} \, dx-16 \int \frac {1}{(5+x) (x-\log (5+x))^2} \, dx+16 \int \frac {e^x}{(5+x) (x-\log (5+x))^2} \, dx-\int \frac {e^{2 x} x}{(x-\log (5+x))^2} \, dx-\int \frac {x \log ^2\left (x^2\right )}{(x-\log (5+x))^2} \, dx+\int \frac {\log ^2\left (x^2\right )}{x-\log (5+x)} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.15, size = 28, normalized size = 0.97 \begin {gather*} -\frac {(1+x) \left (-2+e^x-\log \left (x^2\right )\right )^2}{-x+\log (5+x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(24*x + 48*x^2 + 8*x^3 + E^x*(-4*x - 44*x^2 - 28*x^3 - 4*x^4) + E^(2*x)*(-4*x + 10*x^2 + 12*x^3 + 2*
x^4) + (-40 - 68*x - 12*x^2 + E^(2*x)*(-15*x - 13*x^2 - 2*x^3) + E^x*(20 + 64*x + 32*x^2 + 4*x^3))*Log[5 + x]
+ Log[x^2]^2*(-4*x + (-5*x - x^2)*Log[5 + x]) + Log[x^2]*(4*x + 24*x^2 + 4*x^3 + E^x*(8*x - 10*x^2 - 12*x^3 -
2*x^4) + (-20 - 44*x - 8*x^2 + E^x*(20*x + 14*x^2 + 2*x^3))*Log[5 + x]))/(5*x^3 + x^4 + (-10*x^2 - 2*x^3)*Log[
5 + x] + (5*x + x^2)*Log[5 + x]^2),x]

[Out]

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

________________________________________________________________________________________

fricas [B]  time = 0.86, size = 58, normalized size = 2.00 \begin {gather*} \frac {{\left (x + 1\right )} \log \left (x^{2}\right )^{2} + {\left (x + 1\right )} e^{\left (2 \, x\right )} - 4 \, {\left (x + 1\right )} e^{x} - 2 \, {\left ({\left (x + 1\right )} e^{x} - 2 \, x - 2\right )} \log \left (x^{2}\right ) + 4 \, x + 4}{x - \log \left (x + 5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x^2-5*x)*log(5+x)-4*x)*log(x^2)^2+(((2*x^3+14*x^2+20*x)*exp(x)-8*x^2-44*x-20)*log(5+x)+(-2*x^4-1
2*x^3-10*x^2+8*x)*exp(x)+4*x^3+24*x^2+4*x)*log(x^2)+((-2*x^3-13*x^2-15*x)*exp(x)^2+(4*x^3+32*x^2+64*x+20)*exp(
x)-12*x^2-68*x-40)*log(5+x)+(2*x^4+12*x^3+10*x^2-4*x)*exp(x)^2+(-4*x^4-28*x^3-44*x^2-4*x)*exp(x)+8*x^3+48*x^2+
24*x)/((x^2+5*x)*log(5+x)^2+(-2*x^3-10*x^2)*log(5+x)+x^4+5*x^3),x, algorithm="fricas")

[Out]

((x + 1)*log(x^2)^2 + (x + 1)*e^(2*x) - 4*(x + 1)*e^x - 2*((x + 1)*e^x - 2*x - 2)*log(x^2) + 4*x + 4)/(x - log
(x + 5))

________________________________________________________________________________________

giac [B]  time = 0.37, size = 86, normalized size = 2.97 \begin {gather*} -\frac {2 \, x e^{x} \log \left (x^{2}\right ) - x \log \left (x^{2}\right )^{2} - x e^{\left (2 \, x\right )} + 4 \, x e^{x} - 4 \, x \log \left (x^{2}\right ) + 2 \, e^{x} \log \left (x^{2}\right ) - \log \left (x^{2}\right )^{2} - 4 \, x - e^{\left (2 \, x\right )} + 4 \, e^{x} - 4 \, \log \left (x^{2}\right ) - 4}{x - \log \left (x + 5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x^2-5*x)*log(5+x)-4*x)*log(x^2)^2+(((2*x^3+14*x^2+20*x)*exp(x)-8*x^2-44*x-20)*log(5+x)+(-2*x^4-1
2*x^3-10*x^2+8*x)*exp(x)+4*x^3+24*x^2+4*x)*log(x^2)+((-2*x^3-13*x^2-15*x)*exp(x)^2+(4*x^3+32*x^2+64*x+20)*exp(
x)-12*x^2-68*x-40)*log(5+x)+(2*x^4+12*x^3+10*x^2-4*x)*exp(x)^2+(-4*x^4-28*x^3-44*x^2-4*x)*exp(x)+8*x^3+48*x^2+
24*x)/((x^2+5*x)*log(5+x)^2+(-2*x^3-10*x^2)*log(5+x)+x^4+5*x^3),x, algorithm="giac")

[Out]

-(2*x*e^x*log(x^2) - x*log(x^2)^2 - x*e^(2*x) + 4*x*e^x - 4*x*log(x^2) + 2*e^x*log(x^2) - log(x^2)^2 - 4*x - e
^(2*x) + 4*e^x - 4*log(x^2) - 4)/(x - log(x + 5))

________________________________________________________________________________________

maple [C]  time = 0.28, size = 599, normalized size = 20.66

method	result	size
risch	\(\frac {16+16 x -16 x \,{\mathrm e}^{x} \ln \relax (x )+4 \,{\mathrm e}^{2 x}+32 \ln \relax (x )+16 \ln \relax (x )^{2}-16 \,{\mathrm e}^{x}+4 x \,{\mathrm e}^{2 x}-16 \,{\mathrm e}^{x} \ln \relax (x )+16 x \ln \relax (x )^{2}-16 \,{\mathrm e}^{x} x +32 x \ln \relax (x )+4 i \pi x \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right ) {\mathrm e}^{x}-8 i \pi x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2} {\mathrm e}^{x}-8 i \pi x \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right ) \ln \relax (x )+16 i \pi x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2} \ln \relax (x )-\pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{6}+4 i \pi \mathrm {csgn}\left (i x^{2}\right )^{3} {\mathrm e}^{x}-\pi ^{2} x \mathrm {csgn}\left (i x \right )^{4} \mathrm {csgn}\left (i x^{2}\right )^{2}+4 \pi ^{2} x \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i x^{2}\right )^{3}-6 \pi ^{2} x \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )^{4}+4 \pi ^{2} x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{5}-8 i \pi x \mathrm {csgn}\left (i x^{2}\right )^{3}-8 i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+16 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-8 i \ln \relax (x ) \pi \mathrm {csgn}\left (i x^{2}\right )^{3}-8 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2} {\mathrm e}^{x}-8 i \ln \relax (x ) \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+16 i \ln \relax (x ) \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-8 i \pi x \mathrm {csgn}\left (i x^{2}\right )^{3} \ln \relax (x )+4 i \pi x \mathrm {csgn}\left (i x^{2}\right )^{3} {\mathrm e}^{x}-8 i \pi x \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+16 i \pi x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+4 i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right ) {\mathrm e}^{x}-8 i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}-\pi ^{2} \mathrm {csgn}\left (i x \right )^{4} \mathrm {csgn}\left (i x^{2}\right )^{2}+4 \pi ^{2} \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i x^{2}\right )^{3}-6 \pi ^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )^{4}+4 \pi ^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{5}-\pi ^{2} x \mathrm {csgn}\left (i x^{2}\right )^{6}}{4 x -4 \ln \left (5+x \right )}\)	\(599\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-x^2-5*x)*ln(5+x)-4*x)*ln(x^2)^2+(((2*x^3+14*x^2+20*x)*exp(x)-8*x^2-44*x-20)*ln(5+x)+(-2*x^4-12*x^3-10*
x^2+8*x)*exp(x)+4*x^3+24*x^2+4*x)*ln(x^2)+((-2*x^3-13*x^2-15*x)*exp(x)^2+(4*x^3+32*x^2+64*x+20)*exp(x)-12*x^2-
68*x-40)*ln(5+x)+(2*x^4+12*x^3+10*x^2-4*x)*exp(x)^2+(-4*x^4-28*x^3-44*x^2-4*x)*exp(x)+8*x^3+48*x^2+24*x)/((x^2
+5*x)*ln(5+x)^2+(-2*x^3-10*x^2)*ln(5+x)+x^4+5*x^3),x,method=_RETURNVERBOSE)

[Out]

1/4*(16+16*x-16*x*exp(x)*ln(x)+4*exp(2*x)+32*ln(x)+16*ln(x)^2-16*exp(x)+4*x*exp(2*x)-16*exp(x)*ln(x)+16*x*ln(x
)^2-16*exp(x)*x+32*x*ln(x)+4*I*Pi*x*csgn(I*x)^2*csgn(I*x^2)*exp(x)-8*I*Pi*x*csgn(I*x)*csgn(I*x^2)^2*exp(x)-8*I
*Pi*x*csgn(I*x)^2*csgn(I*x^2)*ln(x)+16*I*Pi*x*csgn(I*x)*csgn(I*x^2)^2*ln(x)-Pi^2*csgn(I*x^2)^6-Pi^2*x*csgn(I*x
)^4*csgn(I*x^2)^2+4*Pi^2*x*csgn(I*x)^3*csgn(I*x^2)^3-6*Pi^2*x*csgn(I*x)^2*csgn(I*x^2)^4+4*Pi^2*x*csgn(I*x)*csg
n(I*x^2)^5-8*I*Pi*x*csgn(I*x^2)^3-8*I*Pi*csgn(I*x)^2*csgn(I*x^2)+16*I*Pi*csgn(I*x)*csgn(I*x^2)^2-8*I*ln(x)*Pi*
csgn(I*x^2)^3+4*I*Pi*csgn(I*x^2)^3*exp(x)-8*I*Pi*csgn(I*x^2)^3-Pi^2*csgn(I*x)^4*csgn(I*x^2)^2+4*Pi^2*csgn(I*x)
^3*csgn(I*x^2)^3-6*Pi^2*csgn(I*x)^2*csgn(I*x^2)^4+4*Pi^2*csgn(I*x)*csgn(I*x^2)^5-Pi^2*x*csgn(I*x^2)^6-8*I*Pi*c
sgn(I*x)*csgn(I*x^2)^2*exp(x)-8*I*ln(x)*Pi*csgn(I*x)^2*csgn(I*x^2)+16*I*ln(x)*Pi*csgn(I*x)*csgn(I*x^2)^2-8*I*P
i*x*csgn(I*x^2)^3*ln(x)+4*I*Pi*x*csgn(I*x^2)^3*exp(x)-8*I*Pi*x*csgn(I*x)^2*csgn(I*x^2)+16*I*Pi*x*csgn(I*x)*csg
n(I*x^2)^2+4*I*Pi*csgn(I*x)^2*csgn(I*x^2)*exp(x))/(x-ln(5+x))

________________________________________________________________________________________

maxima [A]  time = 0.53, size = 53, normalized size = 1.83 \begin {gather*} \frac {4 \, {\left (x + 1\right )} \log \relax (x)^{2} + {\left (x + 1\right )} e^{\left (2 \, x\right )} - 4 \, {\left ({\left (x + 1\right )} \log \relax (x) + x + 1\right )} e^{x} + 8 \, {\left (x + 1\right )} \log \relax (x) + 4 \, x + 4}{x - \log \left (x + 5\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x^2-5*x)*log(5+x)-4*x)*log(x^2)^2+(((2*x^3+14*x^2+20*x)*exp(x)-8*x^2-44*x-20)*log(5+x)+(-2*x^4-1
2*x^3-10*x^2+8*x)*exp(x)+4*x^3+24*x^2+4*x)*log(x^2)+((-2*x^3-13*x^2-15*x)*exp(x)^2+(4*x^3+32*x^2+64*x+20)*exp(
x)-12*x^2-68*x-40)*log(5+x)+(2*x^4+12*x^3+10*x^2-4*x)*exp(x)^2+(-4*x^4-28*x^3-44*x^2-4*x)*exp(x)+8*x^3+48*x^2+
24*x)/((x^2+5*x)*log(5+x)^2+(-2*x^3-10*x^2)*log(5+x)+x^4+5*x^3),x, algorithm="maxima")

[Out]

(4*(x + 1)*log(x)^2 + (x + 1)*e^(2*x) - 4*((x + 1)*log(x) + x + 1)*e^x + 8*(x + 1)*log(x) + 4*x + 4)/(x - log(
x + 5))

________________________________________________________________________________________

mupad [B]  time = 2.11, size = 743, normalized size = 25.62 \begin {gather*} 16\,\ln \relax (x)+\frac {4}{x+4}+\frac {\frac {2\,\left (2\,{\mathrm {e}}^{2\,x}-8\,{\mathrm {e}}^x-5\,x\,{\mathrm {e}}^{2\,x}+12\,x^2\,{\mathrm {e}}^x+2\,x^3\,{\mathrm {e}}^x-6\,x^2\,{\mathrm {e}}^{2\,x}-x^3\,{\mathrm {e}}^{2\,x}+10\,x\,{\mathrm {e}}^x+8\right )}{x+4}+\frac {\ln \left (x+5\right )\,\left (x+5\right )\,\left (3\,{\mathrm {e}}^{2\,x}-8\,{\mathrm {e}}^x+2\,x\,{\mathrm {e}}^{2\,x}-4\,x\,{\mathrm {e}}^x+4\right )}{x+4}}{x-\ln \left (x+5\right )}+{\ln \left (x^2\right )}^2\,\left (\frac {\frac {4}{x+4}+\ln \left (x+5\right )\,\left (\frac {x+5}{x+4}-\frac {x^3+9\,x^2+20\,x}{x\,{\left (x+4\right )}^2\,\left (x+5\right )}\right )+\frac {x^3+9\,x^2+20\,x}{{\left (x+4\right )}^2\,\left (x+5\right )}}{x-\ln \left (x+5\right )}+1\right )+\frac {{\mathrm {e}}^{2\,x}\,\left (2\,x^2+13\,x+15\right )}{x+4}+\frac {\ln \left (x^2\right )\,\left (\frac {2\,\left (6\,x^2\,{\mathrm {e}}^x-4\,{\mathrm {e}}^x-10\,x+x^3\,{\mathrm {e}}^x+5\,x\,{\mathrm {e}}^x-2\,x^2+8\right )}{x+4}-x\,\left (\frac {4\,x^3+36\,x^2+80\,x}{x\,{\left (x+4\right )}^2\,\left (x+5\right )}-\frac {2\,\left (2\,x^4+34\,x^3+184\,x^2+320\,x\right )}{x\,{\left (x+4\right )}^2\,\left (x+5\right )}+\frac {4\,x^4+56\,x^3+260\,x^2+400\,x}{x\,{\left (x+4\right )}^2\,\left (x+5\right )}-\frac {{\mathrm {e}}^x\,\left (4\,x^3+36\,x^2+80\,x\right )}{x\,{\left (x+4\right )}^2\,\left (x+5\right )}+\frac {{\mathrm {e}}^x\,\left (2\,x^5+32\,x^4+190\,x^3+496\,x^2+480\,x\right )}{x\,{\left (x+4\right )}^2\,\left (x+5\right )}\right )+{\ln \left (x+5\right )}^2\,\left (\frac {4\,x^3+36\,x^2+80\,x}{x^2\,{\left (x+4\right )}^2}-\frac {4\,\left (x+5\right )}{x\,\left (x+4\right )}\right )-\ln \left (x+5\right )\,\left (\frac {4\,x^3+36\,x^2+80\,x}{x\,{\left (x+4\right )}^2}+\frac {2\,\left (x+5\right )\,\left (2\,{\mathrm {e}}^x+x\,{\mathrm {e}}^x-6\right )}{x+4}-\frac {4\,x^3+36\,x^2+80\,x}{x\,{\left (x+4\right )}^2\,\left (x+5\right )}+\frac {2\,\left (2\,x^4+34\,x^3+184\,x^2+320\,x\right )}{x\,{\left (x+4\right )}^2\,\left (x+5\right )}-\frac {4\,x^4+56\,x^3+260\,x^2+400\,x}{x\,{\left (x+4\right )}^2\,\left (x+5\right )}+\frac {{\mathrm {e}}^x\,\left (4\,x^3+36\,x^2+80\,x\right )}{x\,{\left (x+4\right )}^2\,\left (x+5\right )}-\frac {{\mathrm {e}}^x\,\left (2\,x^5+32\,x^4+190\,x^3+496\,x^2+480\,x\right )}{x\,{\left (x+4\right )}^2\,\left (x+5\right )}\right )\right )}{x-\ln \left (x+5\right )}-\frac {{\mathrm {e}}^x\,\left (4\,x^2+28\,x+40\right )}{x+4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((24*x - exp(x)*(4*x + 44*x^2 + 28*x^3 + 4*x^4) - log(x + 5)*(68*x + exp(2*x)*(15*x + 13*x^2 + 2*x^3) + 12*
x^2 - exp(x)*(64*x + 32*x^2 + 4*x^3 + 20) + 40) + log(x^2)*(4*x - exp(x)*(10*x^2 - 8*x + 12*x^3 + 2*x^4) + 24*
x^2 + 4*x^3 - log(x + 5)*(44*x + 8*x^2 - exp(x)*(20*x + 14*x^2 + 2*x^3) + 20)) + exp(2*x)*(10*x^2 - 4*x + 12*x
^3 + 2*x^4) + 48*x^2 + 8*x^3 - log(x^2)^2*(4*x + log(x + 5)*(5*x + x^2)))/(log(x + 5)^2*(5*x + x^2) - log(x +
5)*(10*x^2 + 2*x^3) + 5*x^3 + x^4),x)

[Out]

16*log(x) + 4/(x + 4) + ((2*(2*exp(2*x) - 8*exp(x) - 5*x*exp(2*x) + 12*x^2*exp(x) + 2*x^3*exp(x) - 6*x^2*exp(2
*x) - x^3*exp(2*x) + 10*x*exp(x) + 8))/(x + 4) + (log(x + 5)*(x + 5)*(3*exp(2*x) - 8*exp(x) + 2*x*exp(2*x) - 4
*x*exp(x) + 4))/(x + 4))/(x - log(x + 5)) + log(x^2)^2*((4/(x + 4) + log(x + 5)*((x + 5)/(x + 4) - (20*x + 9*x
^2 + x^3)/(x*(x + 4)^2*(x + 5))) + (20*x + 9*x^2 + x^3)/((x + 4)^2*(x + 5)))/(x - log(x + 5)) + 1) + (exp(2*x)
*(13*x + 2*x^2 + 15))/(x + 4) + (log(x^2)*((2*(6*x^2*exp(x) - 4*exp(x) - 10*x + x^3*exp(x) + 5*x*exp(x) - 2*x^
2 + 8))/(x + 4) - x*((80*x + 36*x^2 + 4*x^3)/(x*(x + 4)^2*(x + 5)) - (2*(320*x + 184*x^2 + 34*x^3 + 2*x^4))/(x
*(x + 4)^2*(x + 5)) + (400*x + 260*x^2 + 56*x^3 + 4*x^4)/(x*(x + 4)^2*(x + 5)) - (exp(x)*(80*x + 36*x^2 + 4*x^
3))/(x*(x + 4)^2*(x + 5)) + (exp(x)*(480*x + 496*x^2 + 190*x^3 + 32*x^4 + 2*x^5))/(x*(x + 4)^2*(x + 5))) + log
(x + 5)^2*((80*x + 36*x^2 + 4*x^3)/(x^2*(x + 4)^2) - (4*(x + 5))/(x*(x + 4))) - log(x + 5)*((80*x + 36*x^2 + 4
*x^3)/(x*(x + 4)^2) + (2*(x + 5)*(2*exp(x) + x*exp(x) - 6))/(x + 4) - (80*x + 36*x^2 + 4*x^3)/(x*(x + 4)^2*(x
+ 5)) + (2*(320*x + 184*x^2 + 34*x^3 + 2*x^4))/(x*(x + 4)^2*(x + 5)) - (400*x + 260*x^2 + 56*x^3 + 4*x^4)/(x*(
x + 4)^2*(x + 5)) + (exp(x)*(80*x + 36*x^2 + 4*x^3))/(x*(x + 4)^2*(x + 5)) - (exp(x)*(480*x + 496*x^2 + 190*x^
3 + 32*x^4 + 2*x^5))/(x*(x + 4)^2*(x + 5)))))/(x - log(x + 5)) - (exp(x)*(28*x + 4*x^2 + 40))/(x + 4)

________________________________________________________________________________________

sympy [B]  time = 0.62, size = 155, normalized size = 5.34 \begin {gather*} \frac {\left (x^{2} - x \log {\left (x + 5 \right )} + x - \log {\left (x + 5 \right )}\right ) e^{2 x} + \left (- 2 x^{2} \log {\left (x^{2} \right )} - 4 x^{2} + 2 x \log {\left (x^{2} \right )} \log {\left (x + 5 \right )} - 2 x \log {\left (x^{2} \right )} + 4 x \log {\left (x + 5 \right )} - 4 x + 2 \log {\left (x^{2} \right )} \log {\left (x + 5 \right )} + 4 \log {\left (x + 5 \right )}\right ) e^{x}}{x^{2} - 2 x \log {\left (x + 5 \right )} + \log {\left (x + 5 \right )}^{2}} + \frac {- x \log {\left (x^{2} \right )}^{2} - 4 x \log {\left (x^{2} \right )} - 4 x - \log {\left (x^{2} \right )}^{2} - 4 \log {\left (x^{2} \right )} - 4}{- x + \log {\left (x + 5 \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x**2-5*x)*ln(5+x)-4*x)*ln(x**2)**2+(((2*x**3+14*x**2+20*x)*exp(x)-8*x**2-44*x-20)*ln(5+x)+(-2*x*
*4-12*x**3-10*x**2+8*x)*exp(x)+4*x**3+24*x**2+4*x)*ln(x**2)+((-2*x**3-13*x**2-15*x)*exp(x)**2+(4*x**3+32*x**2+
64*x+20)*exp(x)-12*x**2-68*x-40)*ln(5+x)+(2*x**4+12*x**3+10*x**2-4*x)*exp(x)**2+(-4*x**4-28*x**3-44*x**2-4*x)*
exp(x)+8*x**3+48*x**2+24*x)/((x**2+5*x)*ln(5+x)**2+(-2*x**3-10*x**2)*ln(5+x)+x**4+5*x**3),x)

[Out]

((x**2 - x*log(x + 5) + x - log(x + 5))*exp(2*x) + (-2*x**2*log(x**2) - 4*x**2 + 2*x*log(x**2)*log(x + 5) - 2*
x*log(x**2) + 4*x*log(x + 5) - 4*x + 2*log(x**2)*log(x + 5) + 4*log(x + 5))*exp(x))/(x**2 - 2*x*log(x + 5) + l
og(x + 5)**2) + (-x*log(x**2)**2 - 4*x*log(x**2) - 4*x - log(x**2)**2 - 4*log(x**2) - 4)/(-x + log(x + 5))

________________________________________________________________________________________