Integrand size = 211, antiderivative size = 30 \[ \int \frac {-4800+e^{4 x} (-3-12 x)-7680 x-1584 x^2+384 x^3-15 x^4+\left (-3840 x-2304 x^2+192 x^3\right ) \log (2)+\left (3840+3072 x-864 x^2\right ) \log ^2(2)+1536 x \log ^3(2)-768 \log ^4(2)+e^{3 x} \left (24 x+36 x^2+(-48-144 x) \log (2)\right )+e^{2 x} \left (240+672 x+138 x^2-36 x^3+\left (288 x+288 x^2\right ) \log (2)+(-288-576 x) \log ^2(2)\right )+e^x \left (-960 x-1056 x^2-144 x^3+12 x^4+\left (1920+3456 x+336 x^2-144 x^3\right ) \log (2)+\left (1152 x+576 x^2\right ) \log ^2(2)+(-768-768 x) \log ^3(2)\right )}{4096} \, dx=-\frac {3}{16} x \left (\frac {5}{2}+x-\left (\frac {1}{4} \left (e^x-x\right )+\log (2)\right )^2\right )^2 \]
Leaf count is larger than twice the leaf count of optimal. \(206\) vs. \(2(30)=60\).
Time = 6.81 (sec) , antiderivative size = 206, normalized size of antiderivative = 6.87 \[ \int \frac {-4800+e^{4 x} (-3-12 x)-7680 x-1584 x^2+384 x^3-15 x^4+\left (-3840 x-2304 x^2+192 x^3\right ) \log (2)+\left (3840+3072 x-864 x^2\right ) \log ^2(2)+1536 x \log ^3(2)-768 \log ^4(2)+e^{3 x} \left (24 x+36 x^2+(-48-144 x) \log (2)\right )+e^{2 x} \left (240+672 x+138 x^2-36 x^3+\left (288 x+288 x^2\right ) \log (2)+(-288-576 x) \log ^2(2)\right )+e^x \left (-960 x-1056 x^2-144 x^3+12 x^4+\left (1920+3456 x+336 x^2-144 x^3\right ) \log (2)+\left (1152 x+576 x^2\right ) \log ^2(2)+(-768-768 x) \log ^3(2)\right )}{4096} \, dx=-\frac {3 \left (e^{4 x} x+x^5-16 x^4 (2+\log (2))+64 x \left (5-2 \log ^2(2)\right )^2+16 x^3 \left (11+16 \log (2)+6 \log ^2(2)\right )-128 x^2 \left (-10-5 \log (2)+4 \log ^2(2)+2 \log ^3(2)\right )+2 e^{2 x} \left (3 x^3-8 x^2 (2+3 \log (2))+8 x \left (-5+3 \log (2)+6 \log ^2(2)-\log (8)\right )\right )-\frac {4}{3} e^{3 x} \left (3 x^2-2 x \log (64)\right )-4 e^x \left (x^4-4 x^3 (4+3 \log (2))-8 (7 \log (2)-\log (128))+4 x^2 \left (-10+9 \log (2)+12 \log ^2(2)+\log (128)\right )-8 x \left (-27 \log (2)+8 \log ^3(2)+\log (128)\right )\right )\right )}{4096} \]
Integrate[(-4800 + E^(4*x)*(-3 - 12*x) - 7680*x - 1584*x^2 + 384*x^3 - 15* x^4 + (-3840*x - 2304*x^2 + 192*x^3)*Log[2] + (3840 + 3072*x - 864*x^2)*Lo g[2]^2 + 1536*x*Log[2]^3 - 768*Log[2]^4 + E^(3*x)*(24*x + 36*x^2 + (-48 - 144*x)*Log[2]) + E^(2*x)*(240 + 672*x + 138*x^2 - 36*x^3 + (288*x + 288*x^ 2)*Log[2] + (-288 - 576*x)*Log[2]^2) + E^x*(-960*x - 1056*x^2 - 144*x^3 + 12*x^4 + (1920 + 3456*x + 336*x^2 - 144*x^3)*Log[2] + (1152*x + 576*x^2)*L og[2]^2 + (-768 - 768*x)*Log[2]^3))/4096,x]
(-3*(E^(4*x)*x + x^5 - 16*x^4*(2 + Log[2]) + 64*x*(5 - 2*Log[2]^2)^2 + 16* x^3*(11 + 16*Log[2] + 6*Log[2]^2) - 128*x^2*(-10 - 5*Log[2] + 4*Log[2]^2 + 2*Log[2]^3) + 2*E^(2*x)*(3*x^3 - 8*x^2*(2 + 3*Log[2]) + 8*x*(-5 + 3*Log[2 ] + 6*Log[2]^2 - Log[8])) - (4*E^(3*x)*(3*x^2 - 2*x*Log[64]))/3 - 4*E^x*(x ^4 - 4*x^3*(4 + 3*Log[2]) - 8*(7*Log[2] - Log[128]) + 4*x^2*(-10 + 9*Log[2 ] + 12*Log[2]^2 + Log[128]) - 8*x*(-27*Log[2] + 8*Log[2]^3 + Log[128]))))/ 4096
Leaf count is larger than twice the leaf count of optimal. \(298\) vs. \(2(30)=60\).
Time = 0.79 (sec) , antiderivative size = 298, normalized size of antiderivative = 9.93, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.014, Rules used = {6, 27, 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.
| \(\displaystyle \int \frac {-15 x^4+384 x^3-1584 x^2+\left (-864 x^2+3072 x+3840\right ) \log ^2(2)+e^{3 x} \left (36 x^2+24 x+(-144 x-48) \log (2)\right )+e^{2 x} \left (-36 x^3+138 x^2+\left (288 x^2+288 x\right ) \log (2)+672 x+(-576 x-288) \log ^2(2)+240\right )+\left (192 x^3-2304 x^2-3840 x\right ) \log (2)+e^x \left (12 x^4-144 x^3-1056 x^2+\left (576 x^2+1152 x\right ) \log ^2(2)+\left (-144 x^3+336 x^2+3456 x+1920\right ) \log (2)-960 x+(-768 x-768) \log ^3(2)\right )-7680 x+e^{4 x} (-12 x-3)+1536 x \log ^3(2)-4800-768 \log ^4(2)}{4096} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {-15 x^4+384 x^3-1584 x^2+\left (-864 x^2+3072 x+3840\right ) \log ^2(2)+e^{3 x} \left (36 x^2+24 x+(-144 x-48) \log (2)\right )+e^{2 x} \left (-36 x^3+138 x^2+\left (288 x^2+288 x\right ) \log (2)+672 x+(-576 x-288) \log ^2(2)+240\right )+\left (192 x^3-2304 x^2-3840 x\right ) \log (2)+e^x \left (12 x^4-144 x^3-1056 x^2+\left (576 x^2+1152 x\right ) \log ^2(2)+\left (-144 x^3+336 x^2+3456 x+1920\right ) \log (2)-960 x+(-768 x-768) \log ^3(2)\right )+e^{4 x} (-12 x-3)+x \left (1536 \log ^3(2)-7680\right )-4800-768 \log ^4(2)}{4096}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {\int \left (-15 x^4+384 x^3-1584 x^2-1536 \left (5-\log ^3(2)\right ) x-3 e^{4 x} (4 x+1)+12 e^{3 x} \left (3 x^2+2 x-4 (3 x+1) \log (2)\right )+6 e^{2 x} \left (-6 x^3+23 x^2+112 x-48 (2 x+1) \log ^2(2)+48 \left (x^2+x\right ) \log (2)+40\right )-12 e^x \left (-x^4+12 x^3+88 x^2+80 x+64 (x+1) \log ^3(2)-48 \left (x^2+2 x\right ) \log ^2(2)-4 \left (-3 x^3+7 x^2+72 x+40\right ) \log (2)\right )-192 \left (25+4 \log ^4(2)\right )+96 \left (-9 x^2+32 x+40\right ) \log ^2(2)-192 \left (-x^3+12 x^2+20 x\right ) \log (2)\right )dx}{4096}\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {-3 x^5+12 e^x x^4+96 x^4+48 x^4 \log (2)-192 e^x x^3-18 e^{2 x} x^3-528 x^3-288 x^3 \log ^2(2)-144 e^x x^3 \log (2)-768 x^3 \log (2)-480 e^x x^2+96 e^{2 x} x^2+12 e^{3 x} x^2-768 x^2 \left (5-\log ^3(2)\right )+576 e^x x^2 \log ^2(2)+1536 x^2 \log ^2(2)+768 e^x x^2 \log (2)+144 e^{2 x} x^2 \log (2)-1920 x^2 \log (2)+240 e^{2 x} x+\frac {3 e^{4 x}}{4}-\frac {3}{4} e^{4 x} (4 x+1)-192 x \left (25+4 \log ^4(2)\right )+768 e^x \log ^3(2)-768 e^x (x+1) \log ^3(2)+3840 x \log ^2(2)+144 e^{2 x} \log ^2(2)-144 e^{2 x} (2 x+1) \log ^2(2)+1920 e^x x \log (2)+16 e^{3 x} \log (2)-16 e^{3 x} (3 x+1) \log (2)}{4096}\) |
Int[(-4800 + E^(4*x)*(-3 - 12*x) - 7680*x - 1584*x^2 + 384*x^3 - 15*x^4 + (-3840*x - 2304*x^2 + 192*x^3)*Log[2] + (3840 + 3072*x - 864*x^2)*Log[2]^2 + 1536*x*Log[2]^3 - 768*Log[2]^4 + E^(3*x)*(24*x + 36*x^2 + (-48 - 144*x) *Log[2]) + E^(2*x)*(240 + 672*x + 138*x^2 - 36*x^3 + (288*x + 288*x^2)*Log [2] + (-288 - 576*x)*Log[2]^2) + E^x*(-960*x - 1056*x^2 - 144*x^3 + 12*x^4 + (1920 + 3456*x + 336*x^2 - 144*x^3)*Log[2] + (1152*x + 576*x^2)*Log[2]^ 2 + (-768 - 768*x)*Log[2]^3))/4096,x]
((3*E^(4*x))/4 + 240*E^(2*x)*x - 480*E^x*x^2 + 96*E^(2*x)*x^2 + 12*E^(3*x) *x^2 - 528*x^3 - 192*E^x*x^3 - 18*E^(2*x)*x^3 + 96*x^4 + 12*E^x*x^4 - 3*x^ 5 - (3*E^(4*x)*(1 + 4*x))/4 + 16*E^(3*x)*Log[2] + 1920*E^x*x*Log[2] - 1920 *x^2*Log[2] + 768*E^x*x^2*Log[2] + 144*E^(2*x)*x^2*Log[2] - 768*x^3*Log[2] - 144*E^x*x^3*Log[2] + 48*x^4*Log[2] - 16*E^(3*x)*(1 + 3*x)*Log[2] + 144* E^(2*x)*Log[2]^2 + 3840*x*Log[2]^2 + 1536*x^2*Log[2]^2 + 576*E^x*x^2*Log[2 ]^2 - 288*x^3*Log[2]^2 - 144*E^(2*x)*(1 + 2*x)*Log[2]^2 + 768*E^x*Log[2]^3 - 768*E^x*(1 + x)*Log[2]^3 - 768*x^2*(5 - Log[2]^3) - 192*x*(25 + 4*Log[2 ]^4))/4096
3.6.9.3.1 Defintions of rubi rules used
Int[(u_.)*((v_.) + (a_.)*(Fx_) + (b_.)*(Fx_))^(p_.), x_Symbol] :> Int[u*(v + (a + b)*Fx)^p, x] /; FreeQ[{a, b}, x] && !FreeQ[Fx, x]
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(184\) vs. \(2(22)=44\).
Time = 1.05 (sec) , antiderivative size = 185, normalized size of antiderivative = 6.17
| method | result | size |
| norman | \(\left (\frac {3 \ln \left (2\right )}{256}+\frac {3}{128}\right ) x^{4}+\left (-\frac {9 \ln \left (2\right )^{2}}{128}-\frac {3 \ln \left (2\right )}{16}-\frac {33}{256}\right ) x^{3}+\left (-\frac {3 \ln \left (2\right )^{4}}{16}+\frac {15 \ln \left (2\right )^{2}}{16}-\frac {75}{64}\right ) x +\left (\frac {3 \ln \left (2\right )^{3}}{16}+\frac {3 \ln \left (2\right )^{2}}{8}-\frac {15 \ln \left (2\right )}{32}-\frac {15}{16}\right ) x^{2}+\left (-\frac {3}{64}-\frac {9 \ln \left (2\right )}{256}\right ) x^{3} {\mathrm e}^{x}+\left (\frac {3}{128}+\frac {9 \ln \left (2\right )}{256}\right ) x^{2} {\mathrm e}^{2 x}+\left (\frac {15}{256}-\frac {9 \ln \left (2\right )^{2}}{128}\right ) x \,{\mathrm e}^{2 x}+\left (-\frac {3 \ln \left (2\right )^{3}}{16}+\frac {15 \ln \left (2\right )}{32}\right ) x \,{\mathrm e}^{x}+\left (-\frac {15}{128}+\frac {3 \ln \left (2\right )}{16}+\frac {9 \ln \left (2\right )^{2}}{64}\right ) x^{2} {\mathrm e}^{x}-\frac {3 x^{5}}{4096}-\frac {3 x \,{\mathrm e}^{4 x}}{4096}+\frac {3 x^{2} {\mathrm e}^{3 x}}{1024}+\frac {3 \,{\mathrm e}^{x} x^{4}}{1024}-\frac {9 \,{\mathrm e}^{2 x} x^{3}}{2048}-\frac {3 \ln \left (2\right ) {\mathrm e}^{3 x} x}{256}\) | \(185\) |
| risch | \(-\frac {3 x \,{\mathrm e}^{4 x}}{4096}+\frac {\left (-48 x \ln \left (2\right )+12 x^{2}\right ) {\mathrm e}^{3 x}}{4096}+\frac {\left (-288 x \ln \left (2\right )^{2}+144 x^{2} \ln \left (2\right )-18 x^{3}+96 x^{2}+240 x \right ) {\mathrm e}^{2 x}}{4096}+\frac {\left (-768 x \ln \left (2\right )^{3}+576 x^{2} \ln \left (2\right )^{2}-144 x^{3} \ln \left (2\right )+12 x^{4}+768 x^{2} \ln \left (2\right )-192 x^{3}+1920 x \ln \left (2\right )-480 x^{2}\right ) {\mathrm e}^{x}}{4096}-\frac {3 x \ln \left (2\right )^{4}}{16}+\frac {3 x^{2} \ln \left (2\right )^{3}}{16}-\frac {9 x^{3} \ln \left (2\right )^{2}}{128}+\frac {3 x^{2} \ln \left (2\right )^{2}}{8}+\frac {15 x \ln \left (2\right )^{2}}{16}+\frac {3 x^{4} \ln \left (2\right )}{256}-\frac {3 x^{3} \ln \left (2\right )}{16}-\frac {15 x^{2} \ln \left (2\right )}{32}-\frac {3 x^{5}}{4096}+\frac {3 x^{4}}{128}-\frac {33 x^{3}}{256}-\frac {15 x^{2}}{16}-\frac {75 x}{64}\) | \(200\) |
| default | \(-\frac {9 x \ln \left (2\right )^{2} {\mathrm e}^{2 x}}{128}-\frac {75 x}{64}+\frac {3 x^{2} {\mathrm e}^{3 x}}{1024}-\frac {9 \,{\mathrm e}^{2 x} x^{3}}{2048}+\frac {3 x^{2} \ln \left (2\right )^{3}}{16}-\frac {3 x \ln \left (2\right )^{4}}{16}+\frac {3 \,{\mathrm e}^{2 x} x^{2}}{128}+\frac {15 x \,{\mathrm e}^{2 x}}{256}+\frac {3 \,{\mathrm e}^{x} x^{4}}{1024}-\frac {15 \,{\mathrm e}^{x} x^{2}}{128}-\frac {3 \,{\mathrm e}^{x} x^{3}}{64}-\frac {3 x \,{\mathrm e}^{4 x}}{4096}+\frac {15 x \ln \left (2\right ) {\mathrm e}^{x}}{32}-\frac {9 x^{3} \ln \left (2\right ) {\mathrm e}^{x}}{256}+\frac {3 x^{2} \ln \left (2\right ) {\mathrm e}^{x}}{16}+\frac {9 \ln \left (2\right ) {\mathrm e}^{2 x} x^{2}}{256}+\frac {3 x^{4}}{128}-\frac {33 x^{3}}{256}-\frac {15 x^{2}}{16}-\frac {3 x^{5}}{4096}-\frac {3 \ln \left (2\right )^{3} {\mathrm e}^{x} x}{16}+\frac {9 \,{\mathrm e}^{x} \ln \left (2\right )^{2} x^{2}}{64}+\frac {3 \ln \left (2\right )^{2} \left (-3 x^{3}+16 x^{2}+40 x \right )}{128}+\frac {3 \ln \left (2\right ) \left (\frac {1}{4} x^{4}-4 x^{3}-10 x^{2}\right )}{64}-\frac {3 \ln \left (2\right ) {\mathrm e}^{3 x} x}{256}\) | \(219\) |
| parallelrisch | \(-\frac {9 x \ln \left (2\right )^{2} {\mathrm e}^{2 x}}{128}+\frac {3 x^{2} {\mathrm e}^{3 x}}{1024}-\frac {9 \,{\mathrm e}^{2 x} x^{3}}{2048}+\frac {3 x^{2} \ln \left (2\right )^{3}}{16}-\frac {9 x^{3} \ln \left (2\right )^{2}}{128}+\frac {3 \,{\mathrm e}^{2 x} x^{2}}{128}+\frac {15 x \,{\mathrm e}^{2 x}}{256}+\frac {15 x \ln \left (2\right )^{2}}{16}+\frac {3 x^{4} \ln \left (2\right )}{256}+\frac {3 x^{2} \ln \left (2\right )^{2}}{8}+\frac {3 \,{\mathrm e}^{x} x^{4}}{1024}-\frac {15 x^{2} \ln \left (2\right )}{32}-\frac {3 x^{3} \ln \left (2\right )}{16}-\frac {15 \,{\mathrm e}^{x} x^{2}}{128}-\frac {3 \,{\mathrm e}^{x} x^{3}}{64}-\frac {3 x \,{\mathrm e}^{4 x}}{4096}+\frac {15 x \ln \left (2\right ) {\mathrm e}^{x}}{32}-\frac {9 x^{3} \ln \left (2\right ) {\mathrm e}^{x}}{256}+\frac {3 x^{2} \ln \left (2\right ) {\mathrm e}^{x}}{16}+\frac {9 \ln \left (2\right ) {\mathrm e}^{2 x} x^{2}}{256}+\frac {3 x^{4}}{128}-\frac {33 x^{3}}{256}-\frac {15 x^{2}}{16}-\frac {3 x^{5}}{4096}-\frac {3 \ln \left (2\right )^{3} {\mathrm e}^{x} x}{16}+\frac {9 \,{\mathrm e}^{x} \ln \left (2\right )^{2} x^{2}}{64}+\left (-\frac {75}{64}-\frac {3 \ln \left (2\right )^{4}}{16}\right ) x -\frac {3 \ln \left (2\right ) {\mathrm e}^{3 x} x}{256}\) | \(225\) |
| parts | \(-\frac {9 x \ln \left (2\right )^{2} {\mathrm e}^{2 x}}{128}-\frac {75 x}{64}+\frac {3 x^{2} {\mathrm e}^{3 x}}{1024}-\frac {9 \,{\mathrm e}^{2 x} x^{3}}{2048}+\frac {3 x^{2} \ln \left (2\right )^{3}}{16}-\frac {3 x \ln \left (2\right )^{4}}{16}-\frac {9 x^{3} \ln \left (2\right )^{2}}{128}+\frac {3 \,{\mathrm e}^{2 x} x^{2}}{128}+\frac {15 x \,{\mathrm e}^{2 x}}{256}+\frac {15 x \ln \left (2\right )^{2}}{16}+\frac {3 x^{4} \ln \left (2\right )}{256}+\frac {3 x^{2} \ln \left (2\right )^{2}}{8}+\frac {3 \,{\mathrm e}^{x} x^{4}}{1024}-\frac {15 x^{2} \ln \left (2\right )}{32}-\frac {3 x^{3} \ln \left (2\right )}{16}-\frac {15 \,{\mathrm e}^{x} x^{2}}{128}-\frac {3 \,{\mathrm e}^{x} x^{3}}{64}-\frac {3 x \,{\mathrm e}^{4 x}}{4096}+\frac {15 x \ln \left (2\right ) {\mathrm e}^{x}}{32}-\frac {9 x^{3} \ln \left (2\right ) {\mathrm e}^{x}}{256}+\frac {3 x^{2} \ln \left (2\right ) {\mathrm e}^{x}}{16}+\frac {9 \ln \left (2\right ) {\mathrm e}^{2 x} x^{2}}{256}+\frac {3 x^{4}}{128}-\frac {33 x^{3}}{256}-\frac {15 x^{2}}{16}-\frac {3 x^{5}}{4096}-\frac {3 \ln \left (2\right )^{3} {\mathrm e}^{x} x}{16}+\frac {9 \,{\mathrm e}^{x} \ln \left (2\right )^{2} x^{2}}{64}-\frac {3 \ln \left (2\right ) {\mathrm e}^{3 x} x}{256}\) | \(225\) |
int(1/4096*(-12*x-3)*exp(x)^4+1/4096*((-144*x-48)*ln(2)+36*x^2+24*x)*exp(x )^3+1/4096*((-576*x-288)*ln(2)^2+(288*x^2+288*x)*ln(2)-36*x^3+138*x^2+672* x+240)*exp(x)^2+1/4096*((-768*x-768)*ln(2)^3+(576*x^2+1152*x)*ln(2)^2+(-14 4*x^3+336*x^2+3456*x+1920)*ln(2)+12*x^4-144*x^3-1056*x^2-960*x)*exp(x)-3/1 6*ln(2)^4+3/8*x*ln(2)^3+1/4096*(-864*x^2+3072*x+3840)*ln(2)^2+1/4096*(192* x^3-2304*x^2-3840*x)*ln(2)-15/4096*x^4+3/32*x^3-99/256*x^2-15/8*x-75/64,x, method=_RETURNVERBOSE)
(3/256*ln(2)+3/128)*x^4+(-9/128*ln(2)^2-3/16*ln(2)-33/256)*x^3+(-3/16*ln(2 )^4+15/16*ln(2)^2-75/64)*x+(3/16*ln(2)^3+3/8*ln(2)^2-15/32*ln(2)-15/16)*x^ 2+(-3/64-9/256*ln(2))*x^3*exp(x)+(3/128+9/256*ln(2))*x^2*exp(x)^2+(15/256- 9/128*ln(2)^2)*x*exp(x)^2+(-3/16*ln(2)^3+15/32*ln(2))*x*exp(x)+(-15/128+3/ 16*ln(2)+9/64*ln(2)^2)*x^2*exp(x)-3/4096*x^5-3/4096*x*exp(x)^4+3/1024*x^2* exp(x)^3+3/1024*exp(x)*x^4-9/2048*exp(x)^2*x^3-3/256*x*ln(2)*exp(x)^3
Leaf count of result is larger than twice the leaf count of optimal. 186 vs. \(2 (22) = 44\).
Time = 0.24 (sec) , antiderivative size = 186, normalized size of antiderivative = 6.20 \[ \int \frac {-4800+e^{4 x} (-3-12 x)-7680 x-1584 x^2+384 x^3-15 x^4+\left (-3840 x-2304 x^2+192 x^3\right ) \log (2)+\left (3840+3072 x-864 x^2\right ) \log ^2(2)+1536 x \log ^3(2)-768 \log ^4(2)+e^{3 x} \left (24 x+36 x^2+(-48-144 x) \log (2)\right )+e^{2 x} \left (240+672 x+138 x^2-36 x^3+\left (288 x+288 x^2\right ) \log (2)+(-288-576 x) \log ^2(2)\right )+e^x \left (-960 x-1056 x^2-144 x^3+12 x^4+\left (1920+3456 x+336 x^2-144 x^3\right ) \log (2)+\left (1152 x+576 x^2\right ) \log ^2(2)+(-768-768 x) \log ^3(2)\right )}{4096} \, dx=-\frac {3}{4096} \, x^{5} + \frac {3}{16} \, x^{2} \log \left (2\right )^{3} - \frac {3}{16} \, x \log \left (2\right )^{4} + \frac {3}{128} \, x^{4} - \frac {33}{256} \, x^{3} - \frac {3}{128} \, {\left (3 \, x^{3} - 16 \, x^{2} - 40 \, x\right )} \log \left (2\right )^{2} - \frac {15}{16} \, x^{2} - \frac {3}{4096} \, x e^{\left (4 \, x\right )} + \frac {3}{1024} \, {\left (x^{2} - 4 \, x \log \left (2\right )\right )} e^{\left (3 \, x\right )} - \frac {3}{2048} \, {\left (3 \, x^{3} - 24 \, x^{2} \log \left (2\right ) + 48 \, x \log \left (2\right )^{2} - 16 \, x^{2} - 40 \, x\right )} e^{\left (2 \, x\right )} + \frac {3}{1024} \, {\left (x^{4} + 48 \, x^{2} \log \left (2\right )^{2} - 64 \, x \log \left (2\right )^{3} - 16 \, x^{3} - 40 \, x^{2} - 4 \, {\left (3 \, x^{3} - 16 \, x^{2} - 40 \, x\right )} \log \left (2\right )\right )} e^{x} + \frac {3}{256} \, {\left (x^{4} - 16 \, x^{3} - 40 \, x^{2}\right )} \log \left (2\right ) - \frac {75}{64} \, x \]
integrate(1/4096*(-12*x-3)*exp(x)^4+1/4096*((-144*x-48)*log(2)+36*x^2+24*x )*exp(x)^3+1/4096*((-576*x-288)*log(2)^2+(288*x^2+288*x)*log(2)-36*x^3+138 *x^2+672*x+240)*exp(x)^2+1/4096*((-768*x-768)*log(2)^3+(576*x^2+1152*x)*lo g(2)^2+(-144*x^3+336*x^2+3456*x+1920)*log(2)+12*x^4-144*x^3-1056*x^2-960*x )*exp(x)-3/16*log(2)^4+3/8*x*log(2)^3+1/4096*(-864*x^2+3072*x+3840)*log(2) ^2+1/4096*(192*x^3-2304*x^2-3840*x)*log(2)-15/4096*x^4+3/32*x^3-99/256*x^2 -15/8*x-75/64,x, algorithm=\
-3/4096*x^5 + 3/16*x^2*log(2)^3 - 3/16*x*log(2)^4 + 3/128*x^4 - 33/256*x^3 - 3/128*(3*x^3 - 16*x^2 - 40*x)*log(2)^2 - 15/16*x^2 - 3/4096*x*e^(4*x) + 3/1024*(x^2 - 4*x*log(2))*e^(3*x) - 3/2048*(3*x^3 - 24*x^2*log(2) + 48*x* log(2)^2 - 16*x^2 - 40*x)*e^(2*x) + 3/1024*(x^4 + 48*x^2*log(2)^2 - 64*x*l og(2)^3 - 16*x^3 - 40*x^2 - 4*(3*x^3 - 16*x^2 - 40*x)*log(2))*e^x + 3/256* (x^4 - 16*x^3 - 40*x^2)*log(2) - 75/64*x
Leaf count of result is larger than twice the leaf count of optimal. 224 vs. \(2 (26) = 52\).
Time = 0.24 (sec) , antiderivative size = 224, normalized size of antiderivative = 7.47 \[ \int \frac {-4800+e^{4 x} (-3-12 x)-7680 x-1584 x^2+384 x^3-15 x^4+\left (-3840 x-2304 x^2+192 x^3\right ) \log (2)+\left (3840+3072 x-864 x^2\right ) \log ^2(2)+1536 x \log ^3(2)-768 \log ^4(2)+e^{3 x} \left (24 x+36 x^2+(-48-144 x) \log (2)\right )+e^{2 x} \left (240+672 x+138 x^2-36 x^3+\left (288 x+288 x^2\right ) \log (2)+(-288-576 x) \log ^2(2)\right )+e^x \left (-960 x-1056 x^2-144 x^3+12 x^4+\left (1920+3456 x+336 x^2-144 x^3\right ) \log (2)+\left (1152 x+576 x^2\right ) \log ^2(2)+(-768-768 x) \log ^3(2)\right )}{4096} \, dx=- \frac {3 x^{5}}{4096} + x^{4} \cdot \left (\frac {3 \log {\left (2 \right )}}{256} + \frac {3}{128}\right ) + x^{3} \left (- \frac {3 \log {\left (2 \right )}}{16} - \frac {33}{256} - \frac {9 \log {\left (2 \right )}^{2}}{128}\right ) + x^{2} \left (- \frac {15}{16} - \frac {15 \log {\left (2 \right )}}{32} + \frac {3 \log {\left (2 \right )}^{3}}{16} + \frac {3 \log {\left (2 \right )}^{2}}{8}\right ) - \frac {3 x e^{4 x}}{4096} + x \left (- \frac {75}{64} - \frac {3 \log {\left (2 \right )}^{4}}{16} + \frac {15 \log {\left (2 \right )}^{2}}{16}\right ) + \frac {\left (25769803776 x^{2} - 103079215104 x \log {\left (2 \right )}\right ) e^{3 x}}{8796093022208} + \frac {\left (- 38654705664 x^{3} + 206158430208 x^{2} + 309237645312 x^{2} \log {\left (2 \right )} - 618475290624 x \log {\left (2 \right )}^{2} + 515396075520 x\right ) e^{2 x}}{8796093022208} + \frac {\left (25769803776 x^{4} - 412316860416 x^{3} - 309237645312 x^{3} \log {\left (2 \right )} - 1030792151040 x^{2} + 1236950581248 x^{2} \log {\left (2 \right )}^{2} + 1649267441664 x^{2} \log {\left (2 \right )} - 1649267441664 x \log {\left (2 \right )}^{3} + 4123168604160 x \log {\left (2 \right )}\right ) e^{x}}{8796093022208} \]
integrate(1/4096*(-12*x-3)*exp(x)**4+1/4096*((-144*x-48)*ln(2)+36*x**2+24* x)*exp(x)**3+1/4096*((-576*x-288)*ln(2)**2+(288*x**2+288*x)*ln(2)-36*x**3+ 138*x**2+672*x+240)*exp(x)**2+1/4096*((-768*x-768)*ln(2)**3+(576*x**2+1152 *x)*ln(2)**2+(-144*x**3+336*x**2+3456*x+1920)*ln(2)+12*x**4-144*x**3-1056* x**2-960*x)*exp(x)-3/16*ln(2)**4+3/8*x*ln(2)**3+1/4096*(-864*x**2+3072*x+3 840)*ln(2)**2+1/4096*(192*x**3-2304*x**2-3840*x)*ln(2)-15/4096*x**4+3/32*x **3-99/256*x**2-15/8*x-75/64,x)
-3*x**5/4096 + x**4*(3*log(2)/256 + 3/128) + x**3*(-3*log(2)/16 - 33/256 - 9*log(2)**2/128) + x**2*(-15/16 - 15*log(2)/32 + 3*log(2)**3/16 + 3*log(2 )**2/8) - 3*x*exp(4*x)/4096 + x*(-75/64 - 3*log(2)**4/16 + 15*log(2)**2/16 ) + (25769803776*x**2 - 103079215104*x*log(2))*exp(3*x)/8796093022208 + (- 38654705664*x**3 + 206158430208*x**2 + 309237645312*x**2*log(2) - 61847529 0624*x*log(2)**2 + 515396075520*x)*exp(2*x)/8796093022208 + (25769803776*x **4 - 412316860416*x**3 - 309237645312*x**3*log(2) - 1030792151040*x**2 + 1236950581248*x**2*log(2)**2 + 1649267441664*x**2*log(2) - 1649267441664*x *log(2)**3 + 4123168604160*x*log(2))*exp(x)/8796093022208
Leaf count of result is larger than twice the leaf count of optimal. 184 vs. \(2 (22) = 44\).
Time = 0.30 (sec) , antiderivative size = 184, normalized size of antiderivative = 6.13 \[ \int \frac {-4800+e^{4 x} (-3-12 x)-7680 x-1584 x^2+384 x^3-15 x^4+\left (-3840 x-2304 x^2+192 x^3\right ) \log (2)+\left (3840+3072 x-864 x^2\right ) \log ^2(2)+1536 x \log ^3(2)-768 \log ^4(2)+e^{3 x} \left (24 x+36 x^2+(-48-144 x) \log (2)\right )+e^{2 x} \left (240+672 x+138 x^2-36 x^3+\left (288 x+288 x^2\right ) \log (2)+(-288-576 x) \log ^2(2)\right )+e^x \left (-960 x-1056 x^2-144 x^3+12 x^4+\left (1920+3456 x+336 x^2-144 x^3\right ) \log (2)+\left (1152 x+576 x^2\right ) \log ^2(2)+(-768-768 x) \log ^3(2)\right )}{4096} \, dx=-\frac {3}{4096} \, x^{5} + \frac {3}{16} \, x^{2} \log \left (2\right )^{3} - \frac {3}{16} \, x \log \left (2\right )^{4} + \frac {3}{128} \, x^{4} - \frac {33}{256} \, x^{3} - \frac {3}{128} \, {\left (3 \, x^{3} - 16 \, x^{2} - 40 \, x\right )} \log \left (2\right )^{2} - \frac {15}{16} \, x^{2} - \frac {3}{4096} \, x e^{\left (4 \, x\right )} + \frac {3}{1024} \, {\left (x^{2} - 4 \, x \log \left (2\right )\right )} e^{\left (3 \, x\right )} - \frac {3}{2048} \, {\left (3 \, x^{3} - 8 \, x^{2} {\left (3 \, \log \left (2\right ) + 2\right )} + 8 \, {\left (6 \, \log \left (2\right )^{2} - 5\right )} x\right )} e^{\left (2 \, x\right )} + \frac {3}{1024} \, {\left (x^{4} - 4 \, x^{3} {\left (3 \, \log \left (2\right ) + 4\right )} + 8 \, {\left (6 \, \log \left (2\right )^{2} + 8 \, \log \left (2\right ) - 5\right )} x^{2} - 32 \, {\left (2 \, \log \left (2\right )^{3} - 5 \, \log \left (2\right )\right )} x\right )} e^{x} + \frac {3}{256} \, {\left (x^{4} - 16 \, x^{3} - 40 \, x^{2}\right )} \log \left (2\right ) - \frac {75}{64} \, x \]
integrate(1/4096*(-12*x-3)*exp(x)^4+1/4096*((-144*x-48)*log(2)+36*x^2+24*x )*exp(x)^3+1/4096*((-576*x-288)*log(2)^2+(288*x^2+288*x)*log(2)-36*x^3+138 *x^2+672*x+240)*exp(x)^2+1/4096*((-768*x-768)*log(2)^3+(576*x^2+1152*x)*lo g(2)^2+(-144*x^3+336*x^2+3456*x+1920)*log(2)+12*x^4-144*x^3-1056*x^2-960*x )*exp(x)-3/16*log(2)^4+3/8*x*log(2)^3+1/4096*(-864*x^2+3072*x+3840)*log(2) ^2+1/4096*(192*x^3-2304*x^2-3840*x)*log(2)-15/4096*x^4+3/32*x^3-99/256*x^2 -15/8*x-75/64,x, algorithm=\
-3/4096*x^5 + 3/16*x^2*log(2)^3 - 3/16*x*log(2)^4 + 3/128*x^4 - 33/256*x^3 - 3/128*(3*x^3 - 16*x^2 - 40*x)*log(2)^2 - 15/16*x^2 - 3/4096*x*e^(4*x) + 3/1024*(x^2 - 4*x*log(2))*e^(3*x) - 3/2048*(3*x^3 - 8*x^2*(3*log(2) + 2) + 8*(6*log(2)^2 - 5)*x)*e^(2*x) + 3/1024*(x^4 - 4*x^3*(3*log(2) + 4) + 8*( 6*log(2)^2 + 8*log(2) - 5)*x^2 - 32*(2*log(2)^3 - 5*log(2))*x)*e^x + 3/256 *(x^4 - 16*x^3 - 40*x^2)*log(2) - 75/64*x
Leaf count of result is larger than twice the leaf count of optimal. 187 vs. \(2 (22) = 44\).
Time = 0.26 (sec) , antiderivative size = 187, normalized size of antiderivative = 6.23 \[ \int \frac {-4800+e^{4 x} (-3-12 x)-7680 x-1584 x^2+384 x^3-15 x^4+\left (-3840 x-2304 x^2+192 x^3\right ) \log (2)+\left (3840+3072 x-864 x^2\right ) \log ^2(2)+1536 x \log ^3(2)-768 \log ^4(2)+e^{3 x} \left (24 x+36 x^2+(-48-144 x) \log (2)\right )+e^{2 x} \left (240+672 x+138 x^2-36 x^3+\left (288 x+288 x^2\right ) \log (2)+(-288-576 x) \log ^2(2)\right )+e^x \left (-960 x-1056 x^2-144 x^3+12 x^4+\left (1920+3456 x+336 x^2-144 x^3\right ) \log (2)+\left (1152 x+576 x^2\right ) \log ^2(2)+(-768-768 x) \log ^3(2)\right )}{4096} \, dx=-\frac {3}{4096} \, x^{5} + \frac {3}{16} \, x^{2} \log \left (2\right )^{3} - \frac {3}{16} \, x \log \left (2\right )^{4} + \frac {3}{128} \, x^{4} - \frac {33}{256} \, x^{3} - \frac {3}{128} \, {\left (3 \, x^{3} - 16 \, x^{2} - 40 \, x\right )} \log \left (2\right )^{2} - \frac {15}{16} \, x^{2} - \frac {3}{4096} \, x e^{\left (4 \, x\right )} + \frac {3}{1024} \, {\left (x^{2} - 4 \, x \log \left (2\right )\right )} e^{\left (3 \, x\right )} - \frac {3}{2048} \, {\left (3 \, x^{3} - 24 \, x^{2} \log \left (2\right ) + 48 \, x \log \left (2\right )^{2} - 16 \, x^{2} - 40 \, x\right )} e^{\left (2 \, x\right )} + \frac {3}{1024} \, {\left (x^{4} - 12 \, x^{3} \log \left (2\right ) + 48 \, x^{2} \log \left (2\right )^{2} - 64 \, x \log \left (2\right )^{3} - 16 \, x^{3} + 64 \, x^{2} \log \left (2\right ) - 40 \, x^{2} + 160 \, x \log \left (2\right )\right )} e^{x} + \frac {3}{256} \, {\left (x^{4} - 16 \, x^{3} - 40 \, x^{2}\right )} \log \left (2\right ) - \frac {75}{64} \, x \]
integrate(1/4096*(-12*x-3)*exp(x)^4+1/4096*((-144*x-48)*log(2)+36*x^2+24*x )*exp(x)^3+1/4096*((-576*x-288)*log(2)^2+(288*x^2+288*x)*log(2)-36*x^3+138 *x^2+672*x+240)*exp(x)^2+1/4096*((-768*x-768)*log(2)^3+(576*x^2+1152*x)*lo g(2)^2+(-144*x^3+336*x^2+3456*x+1920)*log(2)+12*x^4-144*x^3-1056*x^2-960*x )*exp(x)-3/16*log(2)^4+3/8*x*log(2)^3+1/4096*(-864*x^2+3072*x+3840)*log(2) ^2+1/4096*(192*x^3-2304*x^2-3840*x)*log(2)-15/4096*x^4+3/32*x^3-99/256*x^2 -15/8*x-75/64,x, algorithm=\
-3/4096*x^5 + 3/16*x^2*log(2)^3 - 3/16*x*log(2)^4 + 3/128*x^4 - 33/256*x^3 - 3/128*(3*x^3 - 16*x^2 - 40*x)*log(2)^2 - 15/16*x^2 - 3/4096*x*e^(4*x) + 3/1024*(x^2 - 4*x*log(2))*e^(3*x) - 3/2048*(3*x^3 - 24*x^2*log(2) + 48*x* log(2)^2 - 16*x^2 - 40*x)*e^(2*x) + 3/1024*(x^4 - 12*x^3*log(2) + 48*x^2*l og(2)^2 - 64*x*log(2)^3 - 16*x^3 + 64*x^2*log(2) - 40*x^2 + 160*x*log(2))* e^x + 3/256*(x^4 - 16*x^3 - 40*x^2)*log(2) - 75/64*x
Time = 9.29 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.43 \[ \int \frac {-4800+e^{4 x} (-3-12 x)-7680 x-1584 x^2+384 x^3-15 x^4+\left (-3840 x-2304 x^2+192 x^3\right ) \log (2)+\left (3840+3072 x-864 x^2\right ) \log ^2(2)+1536 x \log ^3(2)-768 \log ^4(2)+e^{3 x} \left (24 x+36 x^2+(-48-144 x) \log (2)\right )+e^{2 x} \left (240+672 x+138 x^2-36 x^3+\left (288 x+288 x^2\right ) \log (2)+(-288-576 x) \log ^2(2)\right )+e^x \left (-960 x-1056 x^2-144 x^3+12 x^4+\left (1920+3456 x+336 x^2-144 x^3\right ) \log (2)+\left (1152 x+576 x^2\right ) \log ^2(2)+(-768-768 x) \log ^3(2)\right )}{4096} \, dx=-\frac {3\,x\,{\left (16\,x-{\mathrm {e}}^{2\,x}+8\,x\,\ln \left (2\right )-8\,{\mathrm {e}}^x\,\ln \left (2\right )+2\,x\,{\mathrm {e}}^x-16\,{\ln \left (2\right )}^2-x^2+40\right )}^2}{4096} \]
int((exp(3*x)*(24*x - log(2)*(144*x + 48) + 36*x^2))/4096 - (15*x)/8 - (lo g(2)*(3840*x + 2304*x^2 - 192*x^3))/4096 - (exp(x)*(960*x + log(2)^3*(768* x + 768) - log(2)*(3456*x + 336*x^2 - 144*x^3 + 1920) - log(2)^2*(1152*x + 576*x^2) + 1056*x^2 + 144*x^3 - 12*x^4))/4096 + (log(2)^2*(3072*x - 864*x ^2 + 3840))/4096 + (3*x*log(2)^3)/8 - (3*log(2)^4)/16 - (exp(4*x)*(12*x + 3))/4096 - (99*x^2)/256 + (3*x^3)/32 - (15*x^4)/4096 + (exp(2*x)*(672*x + log(2)*(288*x + 288*x^2) - log(2)^2*(576*x + 288) + 138*x^2 - 36*x^3 + 240 ))/4096 - 75/64,x)