Integrand size = 198, antiderivative size = 28 \[ \int \left (36-24 e^5+18 x+\left (72+32 e^{10}+e^5 (-96-80 x)+120 x+36 x^2\right ) \log (4)+\left (72 x+32 e^{10} x+72 x^2+16 x^3+e^5 \left (-96 x-48 x^2\right )\right ) \log ^2(4)+e^{2 x} \left (2 e^{10}+e^{10} (2+4 x) \log (4)+e^{10} \left (2 x+2 x^2\right ) \log ^2(4)\right )+e^x \left (8 e^{10}+e^5 (-18-6 x)+\left (e^{10} (16+16 x)+e^5 \left (-24-44 x-10 x^2\right )\right ) \log (4)+\left (e^{10} \left (16 x+8 x^2\right )+e^5 \left (-24 x-24 x^2-4 x^3\right )\right ) \log ^2(4)\right )\right ) \, dx=\left (x+x \left (-e^5 \left (4+e^x\right )+2 (3+x)\right ) \left (\frac {1}{x}+\log (4)\right )\right )^2 \] Output:
(x*(2*x+6-exp(5)*(exp(x)+4))*(2*ln(2)+1/x)+x)^2
Leaf count is larger than twice the leaf count of optimal. \(147\) vs. \(2(28)=56\).
Time = 6.14 (sec) , antiderivative size = 147, normalized size of antiderivative = 5.25 \[ \int \left (36-24 e^5+18 x+\left (72+32 e^{10}+e^5 (-96-80 x)+120 x+36 x^2\right ) \log (4)+\left (72 x+32 e^{10} x+72 x^2+16 x^3+e^5 \left (-96 x-48 x^2\right )\right ) \log ^2(4)+e^{2 x} \left (2 e^{10}+e^{10} (2+4 x) \log (4)+e^{10} \left (2 x+2 x^2\right ) \log ^2(4)\right )+e^x \left (8 e^{10}+e^5 (-18-6 x)+\left (e^{10} (16+16 x)+e^5 \left (-24-44 x-10 x^2\right )\right ) \log (4)+\left (e^{10} \left (16 x+8 x^2\right )+e^5 \left (-24 x-24 x^2-4 x^3\right )\right ) \log ^2(4)\right )\right ) \, dx=e^{2 (5+x)} (1+x \log (4))^2+8 e^{10+x} (1+x \log (4))^2+16 e^{10} x \log (4) (2+x \log (4))-8 e^5 x \left (3+12 \log (4)+2 x^2 \log ^2(4)+x \log (4) (5+6 \log (4))\right )-2 e^{5+x} (1+x \log (4)) \left (6+x^2 \log (16)+3 x (1+\log (16))\right )+x \left (36+72 \log (4)+4 x^3 \log ^2(4)+x \left (9+60 \log (4)+36 \log ^2(4)\right )+12 x^2 \log (4) (1+\log (16))\right ) \] Input:
Integrate[36 - 24*E^5 + 18*x + (72 + 32*E^10 + E^5*(-96 - 80*x) + 120*x + 36*x^2)*Log[4] + (72*x + 32*E^10*x + 72*x^2 + 16*x^3 + E^5*(-96*x - 48*x^2 ))*Log[4]^2 + E^(2*x)*(2*E^10 + E^10*(2 + 4*x)*Log[4] + E^10*(2*x + 2*x^2) *Log[4]^2) + E^x*(8*E^10 + E^5*(-18 - 6*x) + (E^10*(16 + 16*x) + E^5*(-24 - 44*x - 10*x^2))*Log[4] + (E^10*(16*x + 8*x^2) + E^5*(-24*x - 24*x^2 - 4* x^3))*Log[4]^2),x]
Output:
E^(2*(5 + x))*(1 + x*Log[4])^2 + 8*E^(10 + x)*(1 + x*Log[4])^2 + 16*E^10*x *Log[4]*(2 + x*Log[4]) - 8*E^5*x*(3 + 12*Log[4] + 2*x^2*Log[4]^2 + x*Log[4 ]*(5 + 6*Log[4])) - 2*E^(5 + x)*(1 + x*Log[4])*(6 + x^2*Log[16] + 3*x*(1 + Log[16])) + x*(36 + 72*Log[4] + 4*x^3*Log[4]^2 + x*(9 + 60*Log[4] + 36*Lo g[4]^2) + 12*x^2*Log[4]*(1 + Log[16]))
Leaf count is larger than twice the leaf count of optimal. \(414\) vs. \(2(28)=56\).
Time = 0.85 (sec) , antiderivative size = 414, normalized size of antiderivative = 14.79, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.005, Rules used = {2009}
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.
| \(\displaystyle \int \left (e^{2 x} \left (e^{10} \left (2 x^2+2 x\right ) \log ^2(4)+e^{10} (4 x+2) \log (4)+2 e^{10}\right )+\left (36 x^2+120 x+e^5 (-80 x-96)+32 e^{10}+72\right ) \log (4)+e^x \left (\left (e^5 \left (-10 x^2-44 x-24\right )+e^{10} (16 x+16)\right ) \log (4)+\left (e^{10} \left (8 x^2+16 x\right )+e^5 \left (-4 x^3-24 x^2-24 x\right )\right ) \log ^2(4)+e^5 (-6 x-18)+8 e^{10}\right )+\left (16 x^3+72 x^2+e^5 \left (-48 x^2-96 x\right )+32 e^{10} x+72 x\right ) \log ^2(4)+18 x-24 e^5+36\right ) \, dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 4 x^4 \log ^2(4)-4 e^{x+5} x^3 \log ^2(4)-16 e^5 x^3 \log ^2(4)+24 x^3 \log ^2(4)+12 x^3 \log (4)+9 x^2+12 e^{x+5} x^2 \log ^2(4)+e^{2 x+10} x^2 \log ^2(4)+4 \left (9+4 e^{10}\right ) x^2 \log ^2(4)-8 \left (3-e^5\right ) e^{x+5} x^2 \log ^2(4)-48 e^5 x^2 \log ^2(4)-10 e^{x+5} x^2 \log (4)+60 x^2 \log (4)+12 \left (3-2 e^5\right ) x+6 e^{x+5}+8 e^{x+10}+e^{2 x+10}-6 e^{x+5} (x+3)-24 e^{x+5} x \log ^2(4)+16 \left (3-e^5\right ) e^{x+5} x \log ^2(4)-8 \left (3-2 e^5\right ) e^{x+5} x \log ^2(4)+24 e^{x+5} \log ^2(4)-16 \left (3-e^5\right ) e^{x+5} \log ^2(4)+8 \left (3-2 e^5\right ) e^{x+5} \log ^2(4)+20 e^{x+5} x \log (4)+8 \left (9+4 e^{10}\right ) x \log (4)-4 \left (11-4 e^5\right ) e^{x+5} x \log (4)-20 e^{x+5} \log (4)-e^{2 x+10} \log (4)-\frac {8}{5} e^5 (5 x+6)^2 \log (4)+e^{2 x+10} (2 x+1) \log (4)-8 \left (3-2 e^5\right ) e^{x+5} \log (4)+4 \left (11-4 e^5\right ) e^{x+5} \log (4)\) |
Input:
Int[36 - 24*E^5 + 18*x + (72 + 32*E^10 + E^5*(-96 - 80*x) + 120*x + 36*x^2 )*Log[4] + (72*x + 32*E^10*x + 72*x^2 + 16*x^3 + E^5*(-96*x - 48*x^2))*Log [4]^2 + E^(2*x)*(2*E^10 + E^10*(2 + 4*x)*Log[4] + E^10*(2*x + 2*x^2)*Log[4 ]^2) + E^x*(8*E^10 + E^5*(-18 - 6*x) + (E^10*(16 + 16*x) + E^5*(-24 - 44*x - 10*x^2))*Log[4] + (E^10*(16*x + 8*x^2) + E^5*(-24*x - 24*x^2 - 4*x^3))* Log[4]^2),x]
Output:
6*E^(5 + x) + 8*E^(10 + x) + E^(10 + 2*x) + 12*(3 - 2*E^5)*x + 9*x^2 - 6*E ^(5 + x)*(3 + x) - 20*E^(5 + x)*Log[4] - E^(10 + 2*x)*Log[4] + 4*E^(5 + x) *(11 - 4*E^5)*Log[4] - 8*E^(5 + x)*(3 - 2*E^5)*Log[4] + 20*E^(5 + x)*x*Log [4] - 4*E^(5 + x)*(11 - 4*E^5)*x*Log[4] + 8*(9 + 4*E^10)*x*Log[4] + 60*x^2 *Log[4] - 10*E^(5 + x)*x^2*Log[4] + 12*x^3*Log[4] + E^(10 + 2*x)*(1 + 2*x) *Log[4] - (8*E^5*(6 + 5*x)^2*Log[4])/5 + 24*E^(5 + x)*Log[4]^2 + 8*E^(5 + x)*(3 - 2*E^5)*Log[4]^2 - 16*E^(5 + x)*(3 - E^5)*Log[4]^2 - 24*E^(5 + x)*x *Log[4]^2 - 8*E^(5 + x)*(3 - 2*E^5)*x*Log[4]^2 + 16*E^(5 + x)*(3 - E^5)*x* Log[4]^2 - 48*E^5*x^2*Log[4]^2 + 12*E^(5 + x)*x^2*Log[4]^2 + E^(10 + 2*x)* x^2*Log[4]^2 - 8*E^(5 + x)*(3 - E^5)*x^2*Log[4]^2 + 4*(9 + 4*E^10)*x^2*Log [4]^2 + 24*x^3*Log[4]^2 - 16*E^5*x^3*Log[4]^2 - 4*E^(5 + x)*x^3*Log[4]^2 + 4*x^4*Log[4]^2
Leaf count of result is larger than twice the leaf count of optimal. \(215\) vs. \(2(27)=54\).
Time = 15.29 (sec) , antiderivative size = 216, normalized size of antiderivative = 7.71
| method | result | size |
| risch | \(\left (4 \,{\mathrm e}^{10} \ln \left (2\right )^{2} x^{2}+4 \,{\mathrm e}^{10} \ln \left (2\right ) x +{\mathrm e}^{10}\right ) {\mathrm e}^{2 x}+\left (32 \,{\mathrm e}^{10} \ln \left (2\right )^{2} x^{2}-16 \,{\mathrm e}^{5} \ln \left (2\right )^{2} x^{3}-48 \,{\mathrm e}^{5} \ln \left (2\right )^{2} x^{2}+32 \,{\mathrm e}^{10} \ln \left (2\right ) x -20 \,{\mathrm e}^{5} \ln \left (2\right ) x^{2}-48 \,{\mathrm e}^{5} \ln \left (2\right ) x +8 \,{\mathrm e}^{10}-6 x \,{\mathrm e}^{5}-12 \,{\mathrm e}^{5}\right ) {\mathrm e}^{x}+16 x^{4} \ln \left (2\right )^{2}-64 \,{\mathrm e}^{5} \ln \left (2\right )^{2} x^{3}+96 x^{3} \ln \left (2\right )^{2}-192 \,{\mathrm e}^{5} \ln \left (2\right )^{2} x^{2}+64 \,{\mathrm e}^{10} \ln \left (2\right )^{2} x^{2}+144 x^{2} \ln \left (2\right )^{2}+64 \,{\mathrm e}^{10} \ln \left (2\right ) x -80 \,{\mathrm e}^{5} \ln \left (2\right ) x^{2}+24 x^{3} \ln \left (2\right )-192 \,{\mathrm e}^{5} \ln \left (2\right ) x +120 x^{2} \ln \left (2\right )+144 x \ln \left (2\right )-24 x \,{\mathrm e}^{5}+9 x^{2}+36 x\) | \(216\) |
| default | \(36 x +{\mathrm e}^{10} {\mathrm e}^{2 x}+4 \,{\mathrm e}^{10} \ln \left (2\right ) {\mathrm e}^{2 x} x +4 \,{\mathrm e}^{10} \ln \left (2\right )^{2} {\mathrm e}^{2 x} x^{2}+8 \,{\mathrm e}^{10} {\mathrm e}^{x}-6 x \,{\mathrm e}^{5} {\mathrm e}^{x}-48 \,{\mathrm e}^{5} \ln \left (2\right )^{2} {\mathrm e}^{x} x^{2}+32 \,{\mathrm e}^{10} \ln \left (2\right ) {\mathrm e}^{x} x -20 \,{\mathrm e}^{5} \ln \left (2\right ) {\mathrm e}^{x} x^{2}-48 \,{\mathrm e}^{5} \ln \left (2\right ) {\mathrm e}^{x} x +32 \,{\mathrm e}^{10} \ln \left (2\right )^{2} {\mathrm e}^{x} x^{2}-16 \,{\mathrm e}^{5} \ln \left (2\right )^{2} {\mathrm e}^{x} x^{3}-12 \,{\mathrm e}^{5} {\mathrm e}^{x}+9 x^{2}+2 \ln \left (2\right ) \left (32 \,{\mathrm e}^{10} x -40 x^{2} {\mathrm e}^{5}+12 x^{3}-96 x \,{\mathrm e}^{5}+60 x^{2}+72 x \right )+4 \ln \left (2\right )^{2} \left (4 x^{4}+\frac {8 \left (-6 \,{\mathrm e}^{5}+9\right ) x^{3}}{3}+4 \left (2 \,{\mathrm e}^{5}-3\right )^{2} x^{2}\right )-24 x \,{\mathrm e}^{5}\) | \(220\) |
| norman | \(\left (-12 \,{\mathrm e}^{5}+8 \,{\mathrm e}^{10}\right ) {\mathrm e}^{x}+\left (-64 \,{\mathrm e}^{5} \ln \left (2\right )^{2}+96 \ln \left (2\right )^{2}+24 \ln \left (2\right )\right ) x^{3}+\left (36+64 \,{\mathrm e}^{10} \ln \left (2\right )-192 \,{\mathrm e}^{5} \ln \left (2\right )+144 \ln \left (2\right )-24 \,{\mathrm e}^{5}\right ) x +\left (64 \,{\mathrm e}^{10} \ln \left (2\right )^{2}-192 \,{\mathrm e}^{5} \ln \left (2\right )^{2}-80 \,{\mathrm e}^{5} \ln \left (2\right )+144 \ln \left (2\right )^{2}+120 \ln \left (2\right )+9\right ) x^{2}+{\mathrm e}^{10} {\mathrm e}^{2 x}+\left (-48 \,{\mathrm e}^{5} \ln \left (2\right )+32 \,{\mathrm e}^{10} \ln \left (2\right )-6 \,{\mathrm e}^{5}\right ) x \,{\mathrm e}^{x}+\left (-48 \,{\mathrm e}^{5} \ln \left (2\right )^{2}+32 \,{\mathrm e}^{10} \ln \left (2\right )^{2}-20 \,{\mathrm e}^{5} \ln \left (2\right )\right ) x^{2} {\mathrm e}^{x}+16 x^{4} \ln \left (2\right )^{2}-16 \,{\mathrm e}^{5} \ln \left (2\right )^{2} {\mathrm e}^{x} x^{3}+4 \,{\mathrm e}^{10} \ln \left (2\right ) {\mathrm e}^{2 x} x +4 \,{\mathrm e}^{10} \ln \left (2\right )^{2} {\mathrm e}^{2 x} x^{2}\) | \(220\) |
| parallelrisch | \(64 \,{\mathrm e}^{10} \ln \left (2\right ) x +64 \,{\mathrm e}^{10} \ln \left (2\right )^{2} x^{2}+16 x^{4} \ln \left (2\right )^{2}+24 x^{3} \ln \left (2\right )+144 x \ln \left (2\right )+144 x^{2} \ln \left (2\right )^{2}+96 x^{3} \ln \left (2\right )^{2}-12 \,{\mathrm e}^{5} {\mathrm e}^{x}-20 \,{\mathrm e}^{5} \ln \left (2\right ) {\mathrm e}^{x} x^{2}-48 \,{\mathrm e}^{5} \ln \left (2\right ) {\mathrm e}^{x} x -48 \,{\mathrm e}^{5} \ln \left (2\right )^{2} {\mathrm e}^{x} x^{2}-16 \,{\mathrm e}^{5} \ln \left (2\right )^{2} {\mathrm e}^{x} x^{3}+120 x^{2} \ln \left (2\right )+9 x^{2}-6 x \,{\mathrm e}^{5} {\mathrm e}^{x}-192 \,{\mathrm e}^{5} \ln \left (2\right )^{2} x^{2}-80 \,{\mathrm e}^{5} \ln \left (2\right ) x^{2}-192 \,{\mathrm e}^{5} \ln \left (2\right ) x +\left (36-24 \,{\mathrm e}^{5}\right ) x -64 \,{\mathrm e}^{5} \ln \left (2\right )^{2} x^{3}+4 \,{\mathrm e}^{10} \ln \left (2\right ) {\mathrm e}^{2 x} x +4 \,{\mathrm e}^{10} \ln \left (2\right )^{2} {\mathrm e}^{2 x} x^{2}+32 \,{\mathrm e}^{10} \ln \left (2\right ) {\mathrm e}^{x} x +32 \,{\mathrm e}^{10} \ln \left (2\right )^{2} {\mathrm e}^{x} x^{2}+{\mathrm e}^{10} {\mathrm e}^{2 x}+8 \,{\mathrm e}^{10} {\mathrm e}^{x}\) | \(253\) |
| parts | \(36 x +64 \,{\mathrm e}^{10} \ln \left (2\right ) x +64 \,{\mathrm e}^{10} \ln \left (2\right )^{2} x^{2}+16 x^{4} \ln \left (2\right )^{2}-24 x \,{\mathrm e}^{5}+24 x^{3} \ln \left (2\right )+144 x \ln \left (2\right )+144 x^{2} \ln \left (2\right )^{2}+96 x^{3} \ln \left (2\right )^{2}-12 \,{\mathrm e}^{5} {\mathrm e}^{x}-20 \,{\mathrm e}^{5} \ln \left (2\right ) {\mathrm e}^{x} x^{2}-48 \,{\mathrm e}^{5} \ln \left (2\right ) {\mathrm e}^{x} x -48 \,{\mathrm e}^{5} \ln \left (2\right )^{2} {\mathrm e}^{x} x^{2}-16 \,{\mathrm e}^{5} \ln \left (2\right )^{2} {\mathrm e}^{x} x^{3}+120 x^{2} \ln \left (2\right )+9 x^{2}-6 x \,{\mathrm e}^{5} {\mathrm e}^{x}-192 \,{\mathrm e}^{5} \ln \left (2\right )^{2} x^{2}-80 \,{\mathrm e}^{5} \ln \left (2\right ) x^{2}-192 \,{\mathrm e}^{5} \ln \left (2\right ) x -64 \,{\mathrm e}^{5} \ln \left (2\right )^{2} x^{3}+4 \,{\mathrm e}^{10} \ln \left (2\right ) {\mathrm e}^{2 x} x +4 \,{\mathrm e}^{10} \ln \left (2\right )^{2} {\mathrm e}^{2 x} x^{2}+32 \,{\mathrm e}^{10} \ln \left (2\right ) {\mathrm e}^{x} x +32 \,{\mathrm e}^{10} \ln \left (2\right )^{2} {\mathrm e}^{x} x^{2}+{\mathrm e}^{10} {\mathrm e}^{2 x}+8 \,{\mathrm e}^{10} {\mathrm e}^{x}\) | \(253\) |
Input:
int((4*(2*x^2+2*x)*exp(5)^2*ln(2)^2+2*(4*x+2)*exp(5)^2*ln(2)+2*exp(5)^2)*e xp(x)^2+(4*((8*x^2+16*x)*exp(5)^2+(-4*x^3-24*x^2-24*x)*exp(5))*ln(2)^2+2*( (16*x+16)*exp(5)^2+(-10*x^2-44*x-24)*exp(5))*ln(2)+8*exp(5)^2+(-6*x-18)*ex p(5))*exp(x)+4*(32*x*exp(5)^2+(-48*x^2-96*x)*exp(5)+16*x^3+72*x^2+72*x)*ln (2)^2+2*(32*exp(5)^2+(-80*x-96)*exp(5)+36*x^2+120*x+72)*ln(2)-24*exp(5)+18 *x+36,x,method=_RETURNVERBOSE)
Output:
(4*exp(10)*ln(2)^2*x^2+4*exp(10)*ln(2)*x+exp(10))*exp(2*x)+(32*exp(10)*ln( 2)^2*x^2-16*exp(5)*ln(2)^2*x^3-48*exp(5)*ln(2)^2*x^2+32*exp(10)*ln(2)*x-20 *exp(5)*ln(2)*x^2-48*exp(5)*ln(2)*x+8*exp(10)-6*x*exp(5)-12*exp(5))*exp(x) +16*x^4*ln(2)^2-64*exp(5)*ln(2)^2*x^3+96*x^3*ln(2)^2-192*exp(5)*ln(2)^2*x^ 2+64*exp(10)*ln(2)^2*x^2+144*x^2*ln(2)^2+64*exp(10)*ln(2)*x-80*exp(5)*ln(2 )*x^2+24*x^3*ln(2)-192*exp(5)*ln(2)*x+120*x^2*ln(2)+144*x*ln(2)-24*x*exp(5 )+9*x^2+36*x
Leaf count of result is larger than twice the leaf count of optimal. 182 vs. \(2 (28) = 56\).
Time = 0.08 (sec) , antiderivative size = 182, normalized size of antiderivative = 6.50 \[ \int \left (36-24 e^5+18 x+\left (72+32 e^{10}+e^5 (-96-80 x)+120 x+36 x^2\right ) \log (4)+\left (72 x+32 e^{10} x+72 x^2+16 x^3+e^5 \left (-96 x-48 x^2\right )\right ) \log ^2(4)+e^{2 x} \left (2 e^{10}+e^{10} (2+4 x) \log (4)+e^{10} \left (2 x+2 x^2\right ) \log ^2(4)\right )+e^x \left (8 e^{10}+e^5 (-18-6 x)+\left (e^{10} (16+16 x)+e^5 \left (-24-44 x-10 x^2\right )\right ) \log (4)+\left (e^{10} \left (16 x+8 x^2\right )+e^5 \left (-24 x-24 x^2-4 x^3\right )\right ) \log ^2(4)\right )\right ) \, dx=16 \, {\left (x^{4} + 6 \, x^{3} + 4 \, x^{2} e^{10} + 9 \, x^{2} - 4 \, {\left (x^{3} + 3 \, x^{2}\right )} e^{5}\right )} \log \left (2\right )^{2} + 9 \, x^{2} - 24 \, x e^{5} + {\left (4 \, x^{2} e^{10} \log \left (2\right )^{2} + 4 \, x e^{10} \log \left (2\right ) + e^{10}\right )} e^{\left (2 \, x\right )} + 2 \, {\left (8 \, {\left (2 \, x^{2} e^{10} - {\left (x^{3} + 3 \, x^{2}\right )} e^{5}\right )} \log \left (2\right )^{2} - 3 \, {\left (x + 2\right )} e^{5} + 2 \, {\left (8 \, x e^{10} - {\left (5 \, x^{2} + 12 \, x\right )} e^{5}\right )} \log \left (2\right ) + 4 \, e^{10}\right )} e^{x} + 8 \, {\left (3 \, x^{3} + 15 \, x^{2} + 8 \, x e^{10} - 2 \, {\left (5 \, x^{2} + 12 \, x\right )} e^{5} + 18 \, x\right )} \log \left (2\right ) + 36 \, x \] Input:
integrate((4*(2*x^2+2*x)*exp(5)^2*log(2)^2+2*(2+4*x)*exp(5)^2*log(2)+2*exp (5)^2)*exp(x)^2+(4*((8*x^2+16*x)*exp(5)^2+(-4*x^3-24*x^2-24*x)*exp(5))*log (2)^2+2*((16*x+16)*exp(5)^2+(-10*x^2-44*x-24)*exp(5))*log(2)+8*exp(5)^2+(- 6*x-18)*exp(5))*exp(x)+4*(32*x*exp(5)^2+(-48*x^2-96*x)*exp(5)+16*x^3+72*x^ 2+72*x)*log(2)^2+2*(32*exp(5)^2+(-80*x-96)*exp(5)+36*x^2+120*x+72)*log(2)- 24*exp(5)+18*x+36,x, algorithm="fricas")
Output:
16*(x^4 + 6*x^3 + 4*x^2*e^10 + 9*x^2 - 4*(x^3 + 3*x^2)*e^5)*log(2)^2 + 9*x ^2 - 24*x*e^5 + (4*x^2*e^10*log(2)^2 + 4*x*e^10*log(2) + e^10)*e^(2*x) + 2 *(8*(2*x^2*e^10 - (x^3 + 3*x^2)*e^5)*log(2)^2 - 3*(x + 2)*e^5 + 2*(8*x*e^1 0 - (5*x^2 + 12*x)*e^5)*log(2) + 4*e^10)*e^x + 8*(3*x^3 + 15*x^2 + 8*x*e^1 0 - 2*(5*x^2 + 12*x)*e^5 + 18*x)*log(2) + 36*x
Leaf count of result is larger than twice the leaf count of optimal. 236 vs. \(2 (26) = 52\).
Time = 0.17 (sec) , antiderivative size = 236, normalized size of antiderivative = 8.43 \[ \int \left (36-24 e^5+18 x+\left (72+32 e^{10}+e^5 (-96-80 x)+120 x+36 x^2\right ) \log (4)+\left (72 x+32 e^{10} x+72 x^2+16 x^3+e^5 \left (-96 x-48 x^2\right )\right ) \log ^2(4)+e^{2 x} \left (2 e^{10}+e^{10} (2+4 x) \log (4)+e^{10} \left (2 x+2 x^2\right ) \log ^2(4)\right )+e^x \left (8 e^{10}+e^5 (-18-6 x)+\left (e^{10} (16+16 x)+e^5 \left (-24-44 x-10 x^2\right )\right ) \log (4)+\left (e^{10} \left (16 x+8 x^2\right )+e^5 \left (-24 x-24 x^2-4 x^3\right )\right ) \log ^2(4)\right )\right ) \, dx=16 x^{4} \log {\left (2 \right )}^{2} + x^{3} \left (- 64 e^{5} \log {\left (2 \right )}^{2} + 24 \log {\left (2 \right )} + 96 \log {\left (2 \right )}^{2}\right ) + x^{2} \left (- 192 e^{5} \log {\left (2 \right )}^{2} - 80 e^{5} \log {\left (2 \right )} + 9 + 144 \log {\left (2 \right )}^{2} + 120 \log {\left (2 \right )} + 64 e^{10} \log {\left (2 \right )}^{2}\right ) + x \left (- 192 e^{5} \log {\left (2 \right )} - 24 e^{5} + 36 + 144 \log {\left (2 \right )} + 64 e^{10} \log {\left (2 \right )}\right ) + \left (4 x^{2} e^{10} \log {\left (2 \right )}^{2} + 4 x e^{10} \log {\left (2 \right )} + e^{10}\right ) e^{2 x} + \left (- 16 x^{3} e^{5} \log {\left (2 \right )}^{2} - 48 x^{2} e^{5} \log {\left (2 \right )}^{2} - 20 x^{2} e^{5} \log {\left (2 \right )} + 32 x^{2} e^{10} \log {\left (2 \right )}^{2} - 48 x e^{5} \log {\left (2 \right )} - 6 x e^{5} + 32 x e^{10} \log {\left (2 \right )} - 12 e^{5} + 8 e^{10}\right ) e^{x} \] Input:
integrate((4*(2*x**2+2*x)*exp(5)**2*ln(2)**2+2*(2+4*x)*exp(5)**2*ln(2)+2*e xp(5)**2)*exp(x)**2+(4*((8*x**2+16*x)*exp(5)**2+(-4*x**3-24*x**2-24*x)*exp (5))*ln(2)**2+2*((16*x+16)*exp(5)**2+(-10*x**2-44*x-24)*exp(5))*ln(2)+8*ex p(5)**2+(-6*x-18)*exp(5))*exp(x)+4*(32*x*exp(5)**2+(-48*x**2-96*x)*exp(5)+ 16*x**3+72*x**2+72*x)*ln(2)**2+2*(32*exp(5)**2+(-80*x-96)*exp(5)+36*x**2+1 20*x+72)*ln(2)-24*exp(5)+18*x+36,x)
Output:
16*x**4*log(2)**2 + x**3*(-64*exp(5)*log(2)**2 + 24*log(2) + 96*log(2)**2) + x**2*(-192*exp(5)*log(2)**2 - 80*exp(5)*log(2) + 9 + 144*log(2)**2 + 12 0*log(2) + 64*exp(10)*log(2)**2) + x*(-192*exp(5)*log(2) - 24*exp(5) + 36 + 144*log(2) + 64*exp(10)*log(2)) + (4*x**2*exp(10)*log(2)**2 + 4*x*exp(10 )*log(2) + exp(10))*exp(2*x) + (-16*x**3*exp(5)*log(2)**2 - 48*x**2*exp(5) *log(2)**2 - 20*x**2*exp(5)*log(2) + 32*x**2*exp(10)*log(2)**2 - 48*x*exp( 5)*log(2) - 6*x*exp(5) + 32*x*exp(10)*log(2) - 12*exp(5) + 8*exp(10))*exp( x)
Leaf count of result is larger than twice the leaf count of optimal. 188 vs. \(2 (28) = 56\).
Time = 0.11 (sec) , antiderivative size = 188, normalized size of antiderivative = 6.71 \[ \int \left (36-24 e^5+18 x+\left (72+32 e^{10}+e^5 (-96-80 x)+120 x+36 x^2\right ) \log (4)+\left (72 x+32 e^{10} x+72 x^2+16 x^3+e^5 \left (-96 x-48 x^2\right )\right ) \log ^2(4)+e^{2 x} \left (2 e^{10}+e^{10} (2+4 x) \log (4)+e^{10} \left (2 x+2 x^2\right ) \log ^2(4)\right )+e^x \left (8 e^{10}+e^5 (-18-6 x)+\left (e^{10} (16+16 x)+e^5 \left (-24-44 x-10 x^2\right )\right ) \log (4)+\left (e^{10} \left (16 x+8 x^2\right )+e^5 \left (-24 x-24 x^2-4 x^3\right )\right ) \log ^2(4)\right )\right ) \, dx=16 \, {\left (x^{4} + 6 \, x^{3} + 4 \, x^{2} e^{10} + 9 \, x^{2} - 4 \, {\left (x^{3} + 3 \, x^{2}\right )} e^{5}\right )} \log \left (2\right )^{2} + 9 \, x^{2} - 24 \, x e^{5} + {\left (4 \, x^{2} e^{10} \log \left (2\right )^{2} + 4 \, x e^{10} \log \left (2\right ) + e^{10}\right )} e^{\left (2 \, x\right )} - 2 \, {\left (8 \, x^{3} e^{5} \log \left (2\right )^{2} - 2 \, {\left (8 \, e^{10} \log \left (2\right )^{2} - {\left (12 \, \log \left (2\right )^{2} + 5 \, \log \left (2\right )\right )} e^{5}\right )} x^{2} + {\left (3 \, {\left (8 \, \log \left (2\right ) + 1\right )} e^{5} - 16 \, e^{10} \log \left (2\right )\right )} x - 4 \, e^{10} + 6 \, e^{5}\right )} e^{x} + 8 \, {\left (3 \, x^{3} + 15 \, x^{2} + 8 \, x e^{10} - 2 \, {\left (5 \, x^{2} + 12 \, x\right )} e^{5} + 18 \, x\right )} \log \left (2\right ) + 36 \, x \] Input:
integrate((4*(2*x^2+2*x)*exp(5)^2*log(2)^2+2*(2+4*x)*exp(5)^2*log(2)+2*exp (5)^2)*exp(x)^2+(4*((8*x^2+16*x)*exp(5)^2+(-4*x^3-24*x^2-24*x)*exp(5))*log (2)^2+2*((16*x+16)*exp(5)^2+(-10*x^2-44*x-24)*exp(5))*log(2)+8*exp(5)^2+(- 6*x-18)*exp(5))*exp(x)+4*(32*x*exp(5)^2+(-48*x^2-96*x)*exp(5)+16*x^3+72*x^ 2+72*x)*log(2)^2+2*(32*exp(5)^2+(-80*x-96)*exp(5)+36*x^2+120*x+72)*log(2)- 24*exp(5)+18*x+36,x, algorithm="maxima")
Output:
16*(x^4 + 6*x^3 + 4*x^2*e^10 + 9*x^2 - 4*(x^3 + 3*x^2)*e^5)*log(2)^2 + 9*x ^2 - 24*x*e^5 + (4*x^2*e^10*log(2)^2 + 4*x*e^10*log(2) + e^10)*e^(2*x) - 2 *(8*x^3*e^5*log(2)^2 - 2*(8*e^10*log(2)^2 - (12*log(2)^2 + 5*log(2))*e^5)* x^2 + (3*(8*log(2) + 1)*e^5 - 16*e^10*log(2))*x - 4*e^10 + 6*e^5)*e^x + 8* (3*x^3 + 15*x^2 + 8*x*e^10 - 2*(5*x^2 + 12*x)*e^5 + 18*x)*log(2) + 36*x
Leaf count of result is larger than twice the leaf count of optimal. 176 vs. \(2 (28) = 56\).
Time = 0.12 (sec) , antiderivative size = 176, normalized size of antiderivative = 6.29 \[ \int \left (36-24 e^5+18 x+\left (72+32 e^{10}+e^5 (-96-80 x)+120 x+36 x^2\right ) \log (4)+\left (72 x+32 e^{10} x+72 x^2+16 x^3+e^5 \left (-96 x-48 x^2\right )\right ) \log ^2(4)+e^{2 x} \left (2 e^{10}+e^{10} (2+4 x) \log (4)+e^{10} \left (2 x+2 x^2\right ) \log ^2(4)\right )+e^x \left (8 e^{10}+e^5 (-18-6 x)+\left (e^{10} (16+16 x)+e^5 \left (-24-44 x-10 x^2\right )\right ) \log (4)+\left (e^{10} \left (16 x+8 x^2\right )+e^5 \left (-24 x-24 x^2-4 x^3\right )\right ) \log ^2(4)\right )\right ) \, dx=16 \, {\left (x^{4} + 6 \, x^{3} + 4 \, x^{2} e^{10} + 9 \, x^{2} - 4 \, {\left (x^{3} + 3 \, x^{2}\right )} e^{5}\right )} \log \left (2\right )^{2} + 9 \, x^{2} - 24 \, x e^{5} + {\left (4 \, x^{2} \log \left (2\right )^{2} + 4 \, x \log \left (2\right ) + 1\right )} e^{\left (2 \, x + 10\right )} + 8 \, {\left (4 \, x^{2} \log \left (2\right )^{2} + 4 \, x \log \left (2\right ) + 1\right )} e^{\left (x + 10\right )} - 2 \, {\left (8 \, x^{3} \log \left (2\right )^{2} + 24 \, x^{2} \log \left (2\right )^{2} + 10 \, x^{2} \log \left (2\right ) + 24 \, x \log \left (2\right ) + 3 \, x + 6\right )} e^{\left (x + 5\right )} + 8 \, {\left (3 \, x^{3} + 15 \, x^{2} + 8 \, x e^{10} - 2 \, {\left (5 \, x^{2} + 12 \, x\right )} e^{5} + 18 \, x\right )} \log \left (2\right ) + 36 \, x \] Input:
integrate((4*(2*x^2+2*x)*exp(5)^2*log(2)^2+2*(2+4*x)*exp(5)^2*log(2)+2*exp (5)^2)*exp(x)^2+(4*((8*x^2+16*x)*exp(5)^2+(-4*x^3-24*x^2-24*x)*exp(5))*log (2)^2+2*((16*x+16)*exp(5)^2+(-10*x^2-44*x-24)*exp(5))*log(2)+8*exp(5)^2+(- 6*x-18)*exp(5))*exp(x)+4*(32*x*exp(5)^2+(-48*x^2-96*x)*exp(5)+16*x^3+72*x^ 2+72*x)*log(2)^2+2*(32*exp(5)^2+(-80*x-96)*exp(5)+36*x^2+120*x+72)*log(2)- 24*exp(5)+18*x+36,x, algorithm="giac")
Output:
16*(x^4 + 6*x^3 + 4*x^2*e^10 + 9*x^2 - 4*(x^3 + 3*x^2)*e^5)*log(2)^2 + 9*x ^2 - 24*x*e^5 + (4*x^2*log(2)^2 + 4*x*log(2) + 1)*e^(2*x + 10) + 8*(4*x^2* log(2)^2 + 4*x*log(2) + 1)*e^(x + 10) - 2*(8*x^3*log(2)^2 + 24*x^2*log(2)^ 2 + 10*x^2*log(2) + 24*x*log(2) + 3*x + 6)*e^(x + 5) + 8*(3*x^3 + 15*x^2 + 8*x*e^10 - 2*(5*x^2 + 12*x)*e^5 + 18*x)*log(2) + 36*x
Time = 0.24 (sec) , antiderivative size = 189, normalized size of antiderivative = 6.75 \[ \int \left (36-24 e^5+18 x+\left (72+32 e^{10}+e^5 (-96-80 x)+120 x+36 x^2\right ) \log (4)+\left (72 x+32 e^{10} x+72 x^2+16 x^3+e^5 \left (-96 x-48 x^2\right )\right ) \log ^2(4)+e^{2 x} \left (2 e^{10}+e^{10} (2+4 x) \log (4)+e^{10} \left (2 x+2 x^2\right ) \log ^2(4)\right )+e^x \left (8 e^{10}+e^5 (-18-6 x)+\left (e^{10} (16+16 x)+e^5 \left (-24-44 x-10 x^2\right )\right ) \log (4)+\left (e^{10} \left (16 x+8 x^2\right )+e^5 \left (-24 x-24 x^2-4 x^3\right )\right ) \log ^2(4)\right )\right ) \, dx={\mathrm {e}}^{2\,x+10}+16\,x^4\,{\ln \left (2\right )}^2+x\,\left (144\,\ln \left (2\right )-24\,{\mathrm {e}}^5-192\,{\mathrm {e}}^5\,\ln \left (2\right )+64\,{\mathrm {e}}^{10}\,\ln \left (2\right )+36\right )+{\mathrm {e}}^{x+5}\,\left (8\,{\mathrm {e}}^5-12\right )+x^2\,\left (120\,\ln \left (2\right )-80\,{\mathrm {e}}^5\,\ln \left (2\right )-192\,{\mathrm {e}}^5\,{\ln \left (2\right )}^2+64\,{\mathrm {e}}^{10}\,{\ln \left (2\right )}^2+144\,{\ln \left (2\right )}^2+9\right )-16\,x^3\,{\mathrm {e}}^{x+5}\,{\ln \left (2\right )}^2-2\,x\,{\mathrm {e}}^{x+5}\,\left (24\,\ln \left (2\right )-16\,{\mathrm {e}}^5\,\ln \left (2\right )+3\right )+4\,x^2\,{\mathrm {e}}^{2\,x+10}\,{\ln \left (2\right )}^2+4\,x\,{\mathrm {e}}^{2\,x+10}\,\ln \left (2\right )+8\,x^3\,\ln \left (2\right )\,\left (12\,\ln \left (2\right )-8\,{\mathrm {e}}^5\,\ln \left (2\right )+3\right )-4\,x^2\,{\mathrm {e}}^{x+5}\,\ln \left (2\right )\,\left (12\,\ln \left (2\right )-8\,{\mathrm {e}}^5\,\ln \left (2\right )+5\right ) \] Input:
int(18*x - 24*exp(5) + exp(2*x)*(2*exp(10) + 2*exp(10)*log(2)*(4*x + 2) + 4*exp(10)*log(2)^2*(2*x + 2*x^2)) + 4*log(2)^2*(72*x - exp(5)*(96*x + 48*x ^2) + 32*x*exp(10) + 72*x^2 + 16*x^3) + exp(x)*(8*exp(10) + 4*log(2)^2*(ex p(10)*(16*x + 8*x^2) - exp(5)*(24*x + 24*x^2 + 4*x^3)) - 2*log(2)*(exp(5)* (44*x + 10*x^2 + 24) - exp(10)*(16*x + 16)) - exp(5)*(6*x + 18)) + 2*log(2 )*(120*x + 32*exp(10) + 36*x^2 - exp(5)*(80*x + 96) + 72) + 36,x)
Output:
exp(2*x + 10) + 16*x^4*log(2)^2 + x*(144*log(2) - 24*exp(5) - 192*exp(5)*l og(2) + 64*exp(10)*log(2) + 36) + exp(x + 5)*(8*exp(5) - 12) + x^2*(120*lo g(2) - 80*exp(5)*log(2) - 192*exp(5)*log(2)^2 + 64*exp(10)*log(2)^2 + 144* log(2)^2 + 9) - 16*x^3*exp(x + 5)*log(2)^2 - 2*x*exp(x + 5)*(24*log(2) - 1 6*exp(5)*log(2) + 3) + 4*x^2*exp(2*x + 10)*log(2)^2 + 4*x*exp(2*x + 10)*lo g(2) + 8*x^3*log(2)*(12*log(2) - 8*exp(5)*log(2) + 3) - 4*x^2*exp(x + 5)*l og(2)*(12*log(2) - 8*exp(5)*log(2) + 5)
Time = 0.17 (sec) , antiderivative size = 267, normalized size of antiderivative = 9.54 \[ \int \left (36-24 e^5+18 x+\left (72+32 e^{10}+e^5 (-96-80 x)+120 x+36 x^2\right ) \log (4)+\left (72 x+32 e^{10} x+72 x^2+16 x^3+e^5 \left (-96 x-48 x^2\right )\right ) \log ^2(4)+e^{2 x} \left (2 e^{10}+e^{10} (2+4 x) \log (4)+e^{10} \left (2 x+2 x^2\right ) \log ^2(4)\right )+e^x \left (8 e^{10}+e^5 (-18-6 x)+\left (e^{10} (16+16 x)+e^5 \left (-24-44 x-10 x^2\right )\right ) \log (4)+\left (e^{10} \left (16 x+8 x^2\right )+e^5 \left (-24 x-24 x^2-4 x^3\right )\right ) \log ^2(4)\right )\right ) \, dx=36 x +96 \mathrm {log}\left (2\right )^{2} x^{3}+120 \,\mathrm {log}\left (2\right ) x^{2}+144 \,\mathrm {log}\left (2\right ) x +9 x^{2}+4 e^{2 x} \mathrm {log}\left (2\right )^{2} e^{10} x^{2}+4 e^{2 x} \mathrm {log}\left (2\right ) e^{10} x +32 e^{x} \mathrm {log}\left (2\right )^{2} e^{10} x^{2}-16 e^{x} \mathrm {log}\left (2\right )^{2} e^{5} x^{3}-48 e^{x} \mathrm {log}\left (2\right )^{2} e^{5} x^{2}+32 e^{x} \mathrm {log}\left (2\right ) e^{10} x -20 e^{x} \mathrm {log}\left (2\right ) e^{5} x^{2}-48 e^{x} \mathrm {log}\left (2\right ) e^{5} x +16 \mathrm {log}\left (2\right )^{2} x^{4}+64 \mathrm {log}\left (2\right )^{2} e^{10} x^{2}-64 \mathrm {log}\left (2\right )^{2} e^{5} x^{3}-192 \mathrm {log}\left (2\right )^{2} e^{5} x^{2}+64 \,\mathrm {log}\left (2\right ) e^{10} x -80 \,\mathrm {log}\left (2\right ) e^{5} x^{2}-192 \,\mathrm {log}\left (2\right ) e^{5} x +8 e^{x} e^{10}-12 e^{x} e^{5}+24 \,\mathrm {log}\left (2\right ) x^{3}+144 \mathrm {log}\left (2\right )^{2} x^{2}-6 e^{x} e^{5} x +e^{2 x} e^{10}-24 e^{5} x \] Input:
int((4*(2*x^2+2*x)*exp(5)^2*log(2)^2+2*(2+4*x)*exp(5)^2*log(2)+2*exp(5)^2) *exp(x)^2+(4*((8*x^2+16*x)*exp(5)^2+(-4*x^3-24*x^2-24*x)*exp(5))*log(2)^2+ 2*((16*x+16)*exp(5)^2+(-10*x^2-44*x-24)*exp(5))*log(2)+8*exp(5)^2+(-6*x-18 )*exp(5))*exp(x)+4*(32*x*exp(5)^2+(-48*x^2-96*x)*exp(5)+16*x^3+72*x^2+72*x )*log(2)^2+2*(32*exp(5)^2+(-80*x-96)*exp(5)+36*x^2+120*x+72)*log(2)-24*exp (5)+18*x+36,x)
Output:
4*e**(2*x)*log(2)**2*e**10*x**2 + 4*e**(2*x)*log(2)*e**10*x + e**(2*x)*e** 10 + 32*e**x*log(2)**2*e**10*x**2 - 16*e**x*log(2)**2*e**5*x**3 - 48*e**x* log(2)**2*e**5*x**2 + 32*e**x*log(2)*e**10*x - 20*e**x*log(2)*e**5*x**2 - 48*e**x*log(2)*e**5*x + 8*e**x*e**10 - 6*e**x*e**5*x - 12*e**x*e**5 + 64*l og(2)**2*e**10*x**2 - 64*log(2)**2*e**5*x**3 - 192*log(2)**2*e**5*x**2 + 1 6*log(2)**2*x**4 + 96*log(2)**2*x**3 + 144*log(2)**2*x**2 + 64*log(2)*e**1 0*x - 80*log(2)*e**5*x**2 - 192*log(2)*e**5*x + 24*log(2)*x**3 + 120*log(2 )*x**2 + 144*log(2)*x - 24*e**5*x + 9*x**2 + 36*x