Integrand size = 254, antiderivative size = 28 \[ \int \left (18 x+e^{25} \left (288 x+432 x^2+48 x^3-120 x^4-36 x^5+e^{10} \left (-48 x-72 x^2-24 x^3\right )+e^5 \left (-144 x^2-192 x^3-60 x^4\right )\right )+e^{50} \left (1152 x+3456 x^2+2688 x^3-480 x^4-1416 x^5-448 x^6+96 x^7+72 x^8+10 x^9+e^{20} \left (32 x+96 x^2+96 x^3+40 x^4+6 x^5\right )+e^{15} \left (192 x^2+512 x^3+480 x^4+192 x^5+28 x^6\right )+e^{10} \left (-384 x-1152 x^2-768 x^3+480 x^4+792 x^5+336 x^6+48 x^7\right )+e^5 \left (-1152 x^2-3072 x^3-2560 x^4-384 x^5+504 x^6+256 x^7+36 x^8\right )\right )\right ) \, dx=x^2 \left (3+e^{25} (2+x)^2 \left (6-\left (e^5+x\right )^2\right )\right )^2 \] Output:
(3+(2+x)^2*exp(25)*(6-(exp(5)+x)^2))^2*x^2
Time = 0.04 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.50 \[ \int \left (18 x+e^{25} \left (288 x+432 x^2+48 x^3-120 x^4-36 x^5+e^{10} \left (-48 x-72 x^2-24 x^3\right )+e^5 \left (-144 x^2-192 x^3-60 x^4\right )\right )+e^{50} \left (1152 x+3456 x^2+2688 x^3-480 x^4-1416 x^5-448 x^6+96 x^7+72 x^8+10 x^9+e^{20} \left (32 x+96 x^2+96 x^3+40 x^4+6 x^5\right )+e^{15} \left (192 x^2+512 x^3+480 x^4+192 x^5+28 x^6\right )+e^{10} \left (-384 x-1152 x^2-768 x^3+480 x^4+792 x^5+336 x^6+48 x^7\right )+e^5 \left (-1152 x^2-3072 x^3-2560 x^4-384 x^5+504 x^6+256 x^7+36 x^8\right )\right )\right ) \, dx=x^2 \left (-3+e^{35} (2+x)^2+2 e^{30} x (2+x)^2+e^{25} (2+x)^2 \left (-6+x^2\right )\right )^2 \] Input:
Integrate[18*x + E^25*(288*x + 432*x^2 + 48*x^3 - 120*x^4 - 36*x^5 + E^10* (-48*x - 72*x^2 - 24*x^3) + E^5*(-144*x^2 - 192*x^3 - 60*x^4)) + E^50*(115 2*x + 3456*x^2 + 2688*x^3 - 480*x^4 - 1416*x^5 - 448*x^6 + 96*x^7 + 72*x^8 + 10*x^9 + E^20*(32*x + 96*x^2 + 96*x^3 + 40*x^4 + 6*x^5) + E^15*(192*x^2 + 512*x^3 + 480*x^4 + 192*x^5 + 28*x^6) + E^10*(-384*x - 1152*x^2 - 768*x ^3 + 480*x^4 + 792*x^5 + 336*x^6 + 48*x^7) + E^5*(-1152*x^2 - 3072*x^3 - 2 560*x^4 - 384*x^5 + 504*x^6 + 256*x^7 + 36*x^8)),x]
Output:
x^2*(-3 + E^35*(2 + x)^2 + 2*E^30*x*(2 + x)^2 + E^25*(2 + x)^2*(-6 + x^2)) ^2
Leaf count is larger than twice the leaf count of optimal. \(356\) vs. \(2(28)=56\).
Time = 0.43 (sec) , antiderivative size = 356, normalized size of antiderivative = 12.71, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.004, 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.
| \(\displaystyle \int \left (e^{25} \left (-36 x^5-120 x^4+48 x^3+432 x^2+e^{10} \left (-24 x^3-72 x^2-48 x\right )+e^5 \left (-60 x^4-192 x^3-144 x^2\right )+288 x\right )+e^{50} \left (10 x^9+72 x^8+96 x^7-448 x^6-1416 x^5-480 x^4+2688 x^3+3456 x^2+e^{20} \left (6 x^5+40 x^4+96 x^3+96 x^2+32 x\right )+e^{15} \left (28 x^6+192 x^5+480 x^4+512 x^3+192 x^2\right )+e^{10} \left (48 x^7+336 x^6+792 x^5+480 x^4-768 x^3-1152 x^2-384 x\right )+e^5 \left (36 x^8+256 x^7+504 x^6-384 x^5-2560 x^4-3072 x^3-1152 x^2\right )+1152 x\right )+18 x\right ) \, dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle e^{50} x^{10}+4 e^{55} x^9+8 e^{50} x^9+6 e^{60} x^8+32 e^{55} x^8+12 e^{50} x^8+4 e^{65} x^7+48 e^{60} x^7+72 e^{55} x^7-64 e^{50} x^7+e^{70} x^6+32 e^{65} x^6+132 e^{60} x^6-64 e^{55} x^6-236 e^{50} x^6-6 e^{25} x^6+8 e^{70} x^5+96 e^{65} x^5+96 e^{60} x^5-512 e^{55} x^5-96 e^{50} x^5-12 e^{30} x^5-24 e^{25} x^5+24 e^{70} x^4+128 e^{65} x^4-192 e^{60} x^4-768 e^{55} x^4+672 e^{50} x^4-6 e^{35} x^4-48 e^{30} x^4+12 e^{25} x^4+32 e^{70} x^3+64 e^{65} x^3-384 e^{60} x^3-384 e^{55} x^3+1152 e^{50} x^3-24 e^{35} x^3-48 e^{30} x^3+144 e^{25} x^3+16 e^{70} x^2-192 e^{60} x^2+576 e^{50} x^2-24 e^{35} x^2+144 e^{25} x^2+9 x^2\) |
Input:
Int[18*x + E^25*(288*x + 432*x^2 + 48*x^3 - 120*x^4 - 36*x^5 + E^10*(-48*x - 72*x^2 - 24*x^3) + E^5*(-144*x^2 - 192*x^3 - 60*x^4)) + E^50*(1152*x + 3456*x^2 + 2688*x^3 - 480*x^4 - 1416*x^5 - 448*x^6 + 96*x^7 + 72*x^8 + 10* x^9 + E^20*(32*x + 96*x^2 + 96*x^3 + 40*x^4 + 6*x^5) + E^15*(192*x^2 + 512 *x^3 + 480*x^4 + 192*x^5 + 28*x^6) + E^10*(-384*x - 1152*x^2 - 768*x^3 + 4 80*x^4 + 792*x^5 + 336*x^6 + 48*x^7) + E^5*(-1152*x^2 - 3072*x^3 - 2560*x^ 4 - 384*x^5 + 504*x^6 + 256*x^7 + 36*x^8)),x]
Output:
9*x^2 + 144*E^25*x^2 - 24*E^35*x^2 + 576*E^50*x^2 - 192*E^60*x^2 + 16*E^70 *x^2 + 144*E^25*x^3 - 48*E^30*x^3 - 24*E^35*x^3 + 1152*E^50*x^3 - 384*E^55 *x^3 - 384*E^60*x^3 + 64*E^65*x^3 + 32*E^70*x^3 + 12*E^25*x^4 - 48*E^30*x^ 4 - 6*E^35*x^4 + 672*E^50*x^4 - 768*E^55*x^4 - 192*E^60*x^4 + 128*E^65*x^4 + 24*E^70*x^4 - 24*E^25*x^5 - 12*E^30*x^5 - 96*E^50*x^5 - 512*E^55*x^5 + 96*E^60*x^5 + 96*E^65*x^5 + 8*E^70*x^5 - 6*E^25*x^6 - 236*E^50*x^6 - 64*E^ 55*x^6 + 132*E^60*x^6 + 32*E^65*x^6 + E^70*x^6 - 64*E^50*x^7 + 72*E^55*x^7 + 48*E^60*x^7 + 4*E^65*x^7 + 12*E^50*x^8 + 32*E^55*x^8 + 6*E^60*x^8 + 8*E ^50*x^9 + 4*E^55*x^9 + E^50*x^10
Leaf count of result is larger than twice the leaf count of optimal. \(372\) vs. \(2(26)=52\).
Time = 1.35 (sec) , antiderivative size = 373, normalized size of antiderivative = 13.32
| method | result | size |
| risch | \(144 x^{3} {\mathrm e}^{25}+144 x^{2} {\mathrm e}^{25}+9 x^{2}+1152 \,{\mathrm e}^{50} x^{3}-48 \,{\mathrm e}^{5} {\mathrm e}^{25} x^{3}+672 \,{\mathrm e}^{50} x^{4}-24 \,{\mathrm e}^{25} x^{5}+12 \,{\mathrm e}^{50} x^{8}+12 \,{\mathrm e}^{25} x^{4}+4 \,{\mathrm e}^{50} x^{9} {\mathrm e}^{5}+16 \,{\mathrm e}^{50} x^{2} {\mathrm e}^{20}-192 \,{\mathrm e}^{50} x^{2} {\mathrm e}^{10}-24 \,{\mathrm e}^{25} x^{2} {\mathrm e}^{10}-6 \,{\mathrm e}^{25} x^{6}+8 \,{\mathrm e}^{50} x^{9}+6 \,{\mathrm e}^{50} x^{8} {\mathrm e}^{10}+32 \,{\mathrm e}^{50} x^{8} {\mathrm e}^{5}+48 \,{\mathrm e}^{50} x^{7} {\mathrm e}^{10}+4 \,{\mathrm e}^{50} x^{7} {\mathrm e}^{15}+72 \,{\mathrm e}^{50} x^{7} {\mathrm e}^{5}+{\mathrm e}^{50} x^{6} {\mathrm e}^{20}+132 \,{\mathrm e}^{50} x^{6} {\mathrm e}^{10}+32 \,{\mathrm e}^{50} x^{6} {\mathrm e}^{15}-64 \,{\mathrm e}^{50} x^{6} {\mathrm e}^{5}+8 \,{\mathrm e}^{50} x^{5} {\mathrm e}^{20}+96 \,{\mathrm e}^{50} x^{5} {\mathrm e}^{10}+96 \,{\mathrm e}^{50} x^{5} {\mathrm e}^{15}-512 \,{\mathrm e}^{50} x^{5} {\mathrm e}^{5}-12 \,{\mathrm e}^{25} x^{5} {\mathrm e}^{5}+24 \,{\mathrm e}^{50} x^{4} {\mathrm e}^{20}-192 \,{\mathrm e}^{50} x^{4} {\mathrm e}^{10}+128 \,{\mathrm e}^{50} x^{4} {\mathrm e}^{15}-768 \,{\mathrm e}^{50} x^{4} {\mathrm e}^{5}-6 \,{\mathrm e}^{25} x^{4} {\mathrm e}^{10}+32 \,{\mathrm e}^{50} x^{3} {\mathrm e}^{20}-384 \,{\mathrm e}^{50} x^{3} {\mathrm e}^{10}+64 \,{\mathrm e}^{50} x^{3} {\mathrm e}^{15}-384 \,{\mathrm e}^{50} x^{3} {\mathrm e}^{5}-24 \,{\mathrm e}^{25} x^{3} {\mathrm e}^{10}-96 \,{\mathrm e}^{50} x^{5}+576 \,{\mathrm e}^{50} x^{2}+{\mathrm e}^{50} x^{10}-236 \,{\mathrm e}^{50} x^{6}-48 \,{\mathrm e}^{5} {\mathrm e}^{25} x^{4}-64 \,{\mathrm e}^{50} x^{7}\) | \(373\) |
| norman | \(\left (4 \,{\mathrm e}^{50} {\mathrm e}^{5}+8 \,{\mathrm e}^{50}\right ) x^{9}+\left (6 \,{\mathrm e}^{50} {\mathrm e}^{10}+32 \,{\mathrm e}^{50} {\mathrm e}^{5}+12 \,{\mathrm e}^{50}\right ) x^{8}+\left (4 \,{\mathrm e}^{50} {\mathrm e}^{15}+48 \,{\mathrm e}^{50} {\mathrm e}^{10}+72 \,{\mathrm e}^{50} {\mathrm e}^{5}-64 \,{\mathrm e}^{50}\right ) x^{7}+\left ({\mathrm e}^{50} {\mathrm e}^{20}+32 \,{\mathrm e}^{50} {\mathrm e}^{15}+132 \,{\mathrm e}^{50} {\mathrm e}^{10}-64 \,{\mathrm e}^{50} {\mathrm e}^{5}-236 \,{\mathrm e}^{50}-6 \,{\mathrm e}^{25}\right ) x^{6}+\left (16 \,{\mathrm e}^{50} {\mathrm e}^{20}-192 \,{\mathrm e}^{50} {\mathrm e}^{10}-24 \,{\mathrm e}^{25} {\mathrm e}^{10}+576 \,{\mathrm e}^{50}+144 \,{\mathrm e}^{25}+9\right ) x^{2}+\left (8 \,{\mathrm e}^{50} {\mathrm e}^{20}+96 \,{\mathrm e}^{50} {\mathrm e}^{15}+96 \,{\mathrm e}^{50} {\mathrm e}^{10}-512 \,{\mathrm e}^{50} {\mathrm e}^{5}-12 \,{\mathrm e}^{5} {\mathrm e}^{25}-96 \,{\mathrm e}^{50}-24 \,{\mathrm e}^{25}\right ) x^{5}+\left (24 \,{\mathrm e}^{50} {\mathrm e}^{20}+128 \,{\mathrm e}^{50} {\mathrm e}^{15}-192 \,{\mathrm e}^{50} {\mathrm e}^{10}-6 \,{\mathrm e}^{25} {\mathrm e}^{10}-768 \,{\mathrm e}^{50} {\mathrm e}^{5}-48 \,{\mathrm e}^{5} {\mathrm e}^{25}+672 \,{\mathrm e}^{50}+12 \,{\mathrm e}^{25}\right ) x^{4}+\left (32 \,{\mathrm e}^{50} {\mathrm e}^{20}+64 \,{\mathrm e}^{50} {\mathrm e}^{15}-384 \,{\mathrm e}^{50} {\mathrm e}^{10}-24 \,{\mathrm e}^{25} {\mathrm e}^{10}-384 \,{\mathrm e}^{50} {\mathrm e}^{5}-48 \,{\mathrm e}^{5} {\mathrm e}^{25}+1152 \,{\mathrm e}^{50}+144 \,{\mathrm e}^{25}\right ) x^{3}+{\mathrm e}^{50} x^{10}\) | \(386\) |
| gosper | \(x^{2} \left (9-24 x^{3} {\mathrm e}^{25}+12 x^{2} {\mathrm e}^{25}+144 x \,{\mathrm e}^{25}+144 \,{\mathrm e}^{25}+1152 \,{\mathrm e}^{50} x -96 \,{\mathrm e}^{50} x^{3}-12 \,{\mathrm e}^{5} {\mathrm e}^{25} x^{3}-48 \,{\mathrm e}^{5} {\mathrm e}^{25} x^{2}-48 \,{\mathrm e}^{5} {\mathrm e}^{25} x -24 \,{\mathrm e}^{25} {\mathrm e}^{10}-192 \,{\mathrm e}^{50} {\mathrm e}^{10}-768 \,{\mathrm e}^{5} {\mathrm e}^{50} x^{2}-384 \,{\mathrm e}^{5} {\mathrm e}^{50} x -236 \,{\mathrm e}^{50} x^{4}+{\mathrm e}^{50} x^{8}-6 \,{\mathrm e}^{25} x^{4}+24 \,{\mathrm e}^{50} x^{2} {\mathrm e}^{20}-192 \,{\mathrm e}^{50} x^{2} {\mathrm e}^{10}-6 \,{\mathrm e}^{25} x^{2} {\mathrm e}^{10}+16 \,{\mathrm e}^{50} {\mathrm e}^{20}-384 \,{\mathrm e}^{10} {\mathrm e}^{50} x +4 \,{\mathrm e}^{50} x^{7} {\mathrm e}^{5}+6 \,{\mathrm e}^{50} x^{6} {\mathrm e}^{10}+32 \,{\mathrm e}^{50} x^{6} {\mathrm e}^{5}+48 \,{\mathrm e}^{50} x^{5} {\mathrm e}^{10}+4 \,{\mathrm e}^{50} x^{5} {\mathrm e}^{15}+72 \,{\mathrm e}^{50} x^{5} {\mathrm e}^{5}+{\mathrm e}^{50} x^{4} {\mathrm e}^{20}+132 \,{\mathrm e}^{50} x^{4} {\mathrm e}^{10}+32 \,{\mathrm e}^{50} x^{4} {\mathrm e}^{15}-64 \,{\mathrm e}^{50} x^{4} {\mathrm e}^{5}+8 \,{\mathrm e}^{50} x^{3} {\mathrm e}^{20}+96 \,{\mathrm e}^{50} x^{3} {\mathrm e}^{10}+96 \,{\mathrm e}^{50} x^{3} {\mathrm e}^{15}-512 \,{\mathrm e}^{50} x^{3} {\mathrm e}^{5}+128 \,{\mathrm e}^{15} {\mathrm e}^{50} x^{2}-24 \,{\mathrm e}^{10} {\mathrm e}^{25} x -64 \,{\mathrm e}^{50} x^{5}+672 \,{\mathrm e}^{50} x^{2}+12 \,{\mathrm e}^{50} x^{6}+64 \,{\mathrm e}^{15} {\mathrm e}^{50} x +32 \,{\mathrm e}^{20} {\mathrm e}^{50} x +8 \,{\mathrm e}^{50} x^{7}+576 \,{\mathrm e}^{50}\right )\) | \(448\) |
| parallelrisch | \(144 x^{3} {\mathrm e}^{25}+144 x^{2} {\mathrm e}^{25}+9 x^{2}+1152 \,{\mathrm e}^{50} x^{3}-48 \,{\mathrm e}^{5} {\mathrm e}^{25} x^{3}+672 \,{\mathrm e}^{50} x^{4}-24 \,{\mathrm e}^{25} x^{5}+12 \,{\mathrm e}^{50} x^{8}+12 \,{\mathrm e}^{25} x^{4}+4 \,{\mathrm e}^{50} x^{9} {\mathrm e}^{5}+16 \,{\mathrm e}^{50} x^{2} {\mathrm e}^{20}-192 \,{\mathrm e}^{50} x^{2} {\mathrm e}^{10}-24 \,{\mathrm e}^{25} x^{2} {\mathrm e}^{10}-6 \,{\mathrm e}^{25} x^{6}+8 \,{\mathrm e}^{50} x^{9}+6 \,{\mathrm e}^{50} x^{8} {\mathrm e}^{10}+32 \,{\mathrm e}^{50} x^{8} {\mathrm e}^{5}+48 \,{\mathrm e}^{50} x^{7} {\mathrm e}^{10}+4 \,{\mathrm e}^{50} x^{7} {\mathrm e}^{15}+72 \,{\mathrm e}^{50} x^{7} {\mathrm e}^{5}+{\mathrm e}^{50} x^{6} {\mathrm e}^{20}+132 \,{\mathrm e}^{50} x^{6} {\mathrm e}^{10}+32 \,{\mathrm e}^{50} x^{6} {\mathrm e}^{15}-64 \,{\mathrm e}^{50} x^{6} {\mathrm e}^{5}+8 \,{\mathrm e}^{50} x^{5} {\mathrm e}^{20}+96 \,{\mathrm e}^{50} x^{5} {\mathrm e}^{10}+96 \,{\mathrm e}^{50} x^{5} {\mathrm e}^{15}-512 \,{\mathrm e}^{50} x^{5} {\mathrm e}^{5}-12 \,{\mathrm e}^{25} x^{5} {\mathrm e}^{5}+24 \,{\mathrm e}^{50} x^{4} {\mathrm e}^{20}-192 \,{\mathrm e}^{50} x^{4} {\mathrm e}^{10}+128 \,{\mathrm e}^{50} x^{4} {\mathrm e}^{15}-768 \,{\mathrm e}^{50} x^{4} {\mathrm e}^{5}-6 \,{\mathrm e}^{25} x^{4} {\mathrm e}^{10}+32 \,{\mathrm e}^{50} x^{3} {\mathrm e}^{20}-384 \,{\mathrm e}^{50} x^{3} {\mathrm e}^{10}+64 \,{\mathrm e}^{50} x^{3} {\mathrm e}^{15}-384 \,{\mathrm e}^{50} x^{3} {\mathrm e}^{5}-24 \,{\mathrm e}^{25} x^{3} {\mathrm e}^{10}-96 \,{\mathrm e}^{50} x^{5}+576 \,{\mathrm e}^{50} x^{2}+{\mathrm e}^{50} x^{10}-236 \,{\mathrm e}^{50} x^{6}-48 \,{\mathrm e}^{5} {\mathrm e}^{25} x^{4}-64 \,{\mathrm e}^{50} x^{7}\) | \(479\) |
| parts | \(144 x^{3} {\mathrm e}^{25}+144 x^{2} {\mathrm e}^{25}+9 x^{2}+1152 \,{\mathrm e}^{50} x^{3}-48 \,{\mathrm e}^{5} {\mathrm e}^{25} x^{3}+672 \,{\mathrm e}^{50} x^{4}-24 \,{\mathrm e}^{25} x^{5}+12 \,{\mathrm e}^{50} x^{8}+12 \,{\mathrm e}^{25} x^{4}+4 \,{\mathrm e}^{50} x^{9} {\mathrm e}^{5}+16 \,{\mathrm e}^{50} x^{2} {\mathrm e}^{20}-192 \,{\mathrm e}^{50} x^{2} {\mathrm e}^{10}-24 \,{\mathrm e}^{25} x^{2} {\mathrm e}^{10}-6 \,{\mathrm e}^{25} x^{6}+8 \,{\mathrm e}^{50} x^{9}+6 \,{\mathrm e}^{50} x^{8} {\mathrm e}^{10}+32 \,{\mathrm e}^{50} x^{8} {\mathrm e}^{5}+48 \,{\mathrm e}^{50} x^{7} {\mathrm e}^{10}+4 \,{\mathrm e}^{50} x^{7} {\mathrm e}^{15}+72 \,{\mathrm e}^{50} x^{7} {\mathrm e}^{5}+{\mathrm e}^{50} x^{6} {\mathrm e}^{20}+132 \,{\mathrm e}^{50} x^{6} {\mathrm e}^{10}+32 \,{\mathrm e}^{50} x^{6} {\mathrm e}^{15}-64 \,{\mathrm e}^{50} x^{6} {\mathrm e}^{5}+8 \,{\mathrm e}^{50} x^{5} {\mathrm e}^{20}+96 \,{\mathrm e}^{50} x^{5} {\mathrm e}^{10}+96 \,{\mathrm e}^{50} x^{5} {\mathrm e}^{15}-512 \,{\mathrm e}^{50} x^{5} {\mathrm e}^{5}-12 \,{\mathrm e}^{25} x^{5} {\mathrm e}^{5}+24 \,{\mathrm e}^{50} x^{4} {\mathrm e}^{20}-192 \,{\mathrm e}^{50} x^{4} {\mathrm e}^{10}+128 \,{\mathrm e}^{50} x^{4} {\mathrm e}^{15}-768 \,{\mathrm e}^{50} x^{4} {\mathrm e}^{5}-6 \,{\mathrm e}^{25} x^{4} {\mathrm e}^{10}+32 \,{\mathrm e}^{50} x^{3} {\mathrm e}^{20}-384 \,{\mathrm e}^{50} x^{3} {\mathrm e}^{10}+64 \,{\mathrm e}^{50} x^{3} {\mathrm e}^{15}-384 \,{\mathrm e}^{50} x^{3} {\mathrm e}^{5}-24 \,{\mathrm e}^{25} x^{3} {\mathrm e}^{10}-96 \,{\mathrm e}^{50} x^{5}+576 \,{\mathrm e}^{50} x^{2}+{\mathrm e}^{50} x^{10}-236 \,{\mathrm e}^{50} x^{6}-48 \,{\mathrm e}^{5} {\mathrm e}^{25} x^{4}-64 \,{\mathrm e}^{50} x^{7}\) | \(479\) |
| default | \(\text {Expression too large to display}\) | \(695\) |
Input:
int(((6*x^5+40*x^4+96*x^3+96*x^2+32*x)*exp(5)^4+(28*x^6+192*x^5+480*x^4+51 2*x^3+192*x^2)*exp(5)^3+(48*x^7+336*x^6+792*x^5+480*x^4-768*x^3-1152*x^2-3 84*x)*exp(5)^2+(36*x^8+256*x^7+504*x^6-384*x^5-2560*x^4-3072*x^3-1152*x^2) *exp(5)+10*x^9+72*x^8+96*x^7-448*x^6-1416*x^5-480*x^4+2688*x^3+3456*x^2+11 52*x)*exp(25)^2+((-24*x^3-72*x^2-48*x)*exp(5)^2+(-60*x^4-192*x^3-144*x^2)* exp(5)-36*x^5-120*x^4+48*x^3+432*x^2+288*x)*exp(25)+18*x,x,method=_RETURNV ERBOSE)
Output:
144*x^3*exp(25)+144*x^2*exp(25)+9*x^2+1152*exp(50)*x^3-48*exp(5)*exp(25)*x ^3+672*exp(50)*x^4-24*exp(25)*x^5+12*exp(50)*x^8+12*exp(25)*x^4+4*exp(50)* x^9*exp(5)+16*exp(50)*x^2*exp(20)-192*exp(50)*x^2*exp(10)-24*exp(25)*x^2*e xp(10)-6*exp(25)*x^6+8*exp(50)*x^9+6*exp(50)*x^8*exp(10)+32*exp(50)*x^8*ex p(5)+48*exp(50)*x^7*exp(10)+4*exp(50)*x^7*exp(15)+72*exp(50)*x^7*exp(5)+ex p(50)*x^6*exp(20)+132*exp(50)*x^6*exp(10)+32*exp(50)*x^6*exp(15)-64*exp(50 )*x^6*exp(5)+8*exp(50)*x^5*exp(20)+96*exp(50)*x^5*exp(10)+96*exp(50)*x^5*e xp(15)-512*exp(50)*x^5*exp(5)-12*exp(25)*x^5*exp(5)+24*exp(50)*x^4*exp(20) -192*exp(50)*x^4*exp(10)+128*exp(50)*x^4*exp(15)-768*exp(50)*x^4*exp(5)-6* exp(25)*x^4*exp(10)+32*exp(50)*x^3*exp(20)-384*exp(50)*x^3*exp(10)+64*exp( 50)*x^3*exp(15)-384*exp(50)*x^3*exp(5)-24*exp(25)*x^3*exp(10)-96*exp(50)*x ^5+576*exp(50)*x^2+exp(50)*x^10-236*exp(50)*x^6-48*exp(5)*exp(25)*x^4-64*e xp(50)*x^7
Leaf count of result is larger than twice the leaf count of optimal. 248 vs. \(2 (24) = 48\).
Time = 0.10 (sec) , antiderivative size = 248, normalized size of antiderivative = 8.86 \[ \int \left (18 x+e^{25} \left (288 x+432 x^2+48 x^3-120 x^4-36 x^5+e^{10} \left (-48 x-72 x^2-24 x^3\right )+e^5 \left (-144 x^2-192 x^3-60 x^4\right )\right )+e^{50} \left (1152 x+3456 x^2+2688 x^3-480 x^4-1416 x^5-448 x^6+96 x^7+72 x^8+10 x^9+e^{20} \left (32 x+96 x^2+96 x^3+40 x^4+6 x^5\right )+e^{15} \left (192 x^2+512 x^3+480 x^4+192 x^5+28 x^6\right )+e^{10} \left (-384 x-1152 x^2-768 x^3+480 x^4+792 x^5+336 x^6+48 x^7\right )+e^5 \left (-1152 x^2-3072 x^3-2560 x^4-384 x^5+504 x^6+256 x^7+36 x^8\right )\right )\right ) \, dx=9 \, x^{2} + {\left (x^{6} + 8 \, x^{5} + 24 \, x^{4} + 32 \, x^{3} + 16 \, x^{2}\right )} e^{70} + 4 \, {\left (x^{7} + 8 \, x^{6} + 24 \, x^{5} + 32 \, x^{4} + 16 \, x^{3}\right )} e^{65} + 6 \, {\left (x^{8} + 8 \, x^{7} + 22 \, x^{6} + 16 \, x^{5} - 32 \, x^{4} - 64 \, x^{3} - 32 \, x^{2}\right )} e^{60} + 4 \, {\left (x^{9} + 8 \, x^{8} + 18 \, x^{7} - 16 \, x^{6} - 128 \, x^{5} - 192 \, x^{4} - 96 \, x^{3}\right )} e^{55} + {\left (x^{10} + 8 \, x^{9} + 12 \, x^{8} - 64 \, x^{7} - 236 \, x^{6} - 96 \, x^{5} + 672 \, x^{4} + 1152 \, x^{3} + 576 \, x^{2}\right )} e^{50} - 6 \, {\left (x^{4} + 4 \, x^{3} + 4 \, x^{2}\right )} e^{35} - 12 \, {\left (x^{5} + 4 \, x^{4} + 4 \, x^{3}\right )} e^{30} - 6 \, {\left (x^{6} + 4 \, x^{5} - 2 \, x^{4} - 24 \, x^{3} - 24 \, x^{2}\right )} e^{25} \] Input:
integrate(((6*x^5+40*x^4+96*x^3+96*x^2+32*x)*exp(5)^4+(28*x^6+192*x^5+480* x^4+512*x^3+192*x^2)*exp(5)^3+(48*x^7+336*x^6+792*x^5+480*x^4-768*x^3-1152 *x^2-384*x)*exp(5)^2+(36*x^8+256*x^7+504*x^6-384*x^5-2560*x^4-3072*x^3-115 2*x^2)*exp(5)+10*x^9+72*x^8+96*x^7-448*x^6-1416*x^5-480*x^4+2688*x^3+3456* x^2+1152*x)*exp(25)^2+((-24*x^3-72*x^2-48*x)*exp(5)^2+(-60*x^4-192*x^3-144 *x^2)*exp(5)-36*x^5-120*x^4+48*x^3+432*x^2+288*x)*exp(25)+18*x,x, algorith m="fricas")
Output:
9*x^2 + (x^6 + 8*x^5 + 24*x^4 + 32*x^3 + 16*x^2)*e^70 + 4*(x^7 + 8*x^6 + 2 4*x^5 + 32*x^4 + 16*x^3)*e^65 + 6*(x^8 + 8*x^7 + 22*x^6 + 16*x^5 - 32*x^4 - 64*x^3 - 32*x^2)*e^60 + 4*(x^9 + 8*x^8 + 18*x^7 - 16*x^6 - 128*x^5 - 192 *x^4 - 96*x^3)*e^55 + (x^10 + 8*x^9 + 12*x^8 - 64*x^7 - 236*x^6 - 96*x^5 + 672*x^4 + 1152*x^3 + 576*x^2)*e^50 - 6*(x^4 + 4*x^3 + 4*x^2)*e^35 - 12*(x ^5 + 4*x^4 + 4*x^3)*e^30 - 6*(x^6 + 4*x^5 - 2*x^4 - 24*x^3 - 24*x^2)*e^25
Leaf count of result is larger than twice the leaf count of optimal. 252 vs. \(2 (22) = 44\).
Time = 0.07 (sec) , antiderivative size = 252, normalized size of antiderivative = 9.00 \[ \int \left (18 x+e^{25} \left (288 x+432 x^2+48 x^3-120 x^4-36 x^5+e^{10} \left (-48 x-72 x^2-24 x^3\right )+e^5 \left (-144 x^2-192 x^3-60 x^4\right )\right )+e^{50} \left (1152 x+3456 x^2+2688 x^3-480 x^4-1416 x^5-448 x^6+96 x^7+72 x^8+10 x^9+e^{20} \left (32 x+96 x^2+96 x^3+40 x^4+6 x^5\right )+e^{15} \left (192 x^2+512 x^3+480 x^4+192 x^5+28 x^6\right )+e^{10} \left (-384 x-1152 x^2-768 x^3+480 x^4+792 x^5+336 x^6+48 x^7\right )+e^5 \left (-1152 x^2-3072 x^3-2560 x^4-384 x^5+504 x^6+256 x^7+36 x^8\right )\right )\right ) \, dx=x^{10} e^{50} + x^{9} \cdot \left (8 e^{50} + 4 e^{55}\right ) + x^{8} \cdot \left (12 e^{50} + 32 e^{55} + 6 e^{60}\right ) + x^{7} \left (- 64 e^{50} + 72 e^{55} + 48 e^{60} + 4 e^{65}\right ) + x^{6} \left (- 64 e^{55} - 236 e^{50} - 6 e^{25} + 132 e^{60} + 32 e^{65} + e^{70}\right ) + x^{5} \left (- 512 e^{55} - 96 e^{50} - 12 e^{30} - 24 e^{25} + 96 e^{60} + 96 e^{65} + 8 e^{70}\right ) + x^{4} \left (- 192 e^{60} - 768 e^{55} - 6 e^{35} - 48 e^{30} + 12 e^{25} + 672 e^{50} + 128 e^{65} + 24 e^{70}\right ) + x^{3} \left (- 384 e^{60} - 384 e^{55} - 24 e^{35} - 48 e^{30} + 144 e^{25} + 1152 e^{50} + 64 e^{65} + 32 e^{70}\right ) + x^{2} \left (- 192 e^{60} - 24 e^{35} + 9 + 144 e^{25} + 576 e^{50} + 16 e^{70}\right ) \] Input:
integrate(((6*x**5+40*x**4+96*x**3+96*x**2+32*x)*exp(5)**4+(28*x**6+192*x* *5+480*x**4+512*x**3+192*x**2)*exp(5)**3+(48*x**7+336*x**6+792*x**5+480*x* *4-768*x**3-1152*x**2-384*x)*exp(5)**2+(36*x**8+256*x**7+504*x**6-384*x**5 -2560*x**4-3072*x**3-1152*x**2)*exp(5)+10*x**9+72*x**8+96*x**7-448*x**6-14 16*x**5-480*x**4+2688*x**3+3456*x**2+1152*x)*exp(25)**2+((-24*x**3-72*x**2 -48*x)*exp(5)**2+(-60*x**4-192*x**3-144*x**2)*exp(5)-36*x**5-120*x**4+48*x **3+432*x**2+288*x)*exp(25)+18*x,x)
Output:
x**10*exp(50) + x**9*(8*exp(50) + 4*exp(55)) + x**8*(12*exp(50) + 32*exp(5 5) + 6*exp(60)) + x**7*(-64*exp(50) + 72*exp(55) + 48*exp(60) + 4*exp(65)) + x**6*(-64*exp(55) - 236*exp(50) - 6*exp(25) + 132*exp(60) + 32*exp(65) + exp(70)) + x**5*(-512*exp(55) - 96*exp(50) - 12*exp(30) - 24*exp(25) + 9 6*exp(60) + 96*exp(65) + 8*exp(70)) + x**4*(-192*exp(60) - 768*exp(55) - 6 *exp(35) - 48*exp(30) + 12*exp(25) + 672*exp(50) + 128*exp(65) + 24*exp(70 )) + x**3*(-384*exp(60) - 384*exp(55) - 24*exp(35) - 48*exp(30) + 144*exp( 25) + 1152*exp(50) + 64*exp(65) + 32*exp(70)) + x**2*(-192*exp(60) - 24*ex p(35) + 9 + 144*exp(25) + 576*exp(50) + 16*exp(70))
Leaf count of result is larger than twice the leaf count of optimal. 247 vs. \(2 (24) = 48\).
Time = 0.04 (sec) , antiderivative size = 247, normalized size of antiderivative = 8.82 \[ \int \left (18 x+e^{25} \left (288 x+432 x^2+48 x^3-120 x^4-36 x^5+e^{10} \left (-48 x-72 x^2-24 x^3\right )+e^5 \left (-144 x^2-192 x^3-60 x^4\right )\right )+e^{50} \left (1152 x+3456 x^2+2688 x^3-480 x^4-1416 x^5-448 x^6+96 x^7+72 x^8+10 x^9+e^{20} \left (32 x+96 x^2+96 x^3+40 x^4+6 x^5\right )+e^{15} \left (192 x^2+512 x^3+480 x^4+192 x^5+28 x^6\right )+e^{10} \left (-384 x-1152 x^2-768 x^3+480 x^4+792 x^5+336 x^6+48 x^7\right )+e^5 \left (-1152 x^2-3072 x^3-2560 x^4-384 x^5+504 x^6+256 x^7+36 x^8\right )\right )\right ) \, dx=9 \, x^{2} + {\left (x^{10} + 8 \, x^{9} + 12 \, x^{8} - 64 \, x^{7} - 236 \, x^{6} - 96 \, x^{5} + 672 \, x^{4} + 1152 \, x^{3} + 576 \, x^{2} + {\left (x^{6} + 8 \, x^{5} + 24 \, x^{4} + 32 \, x^{3} + 16 \, x^{2}\right )} e^{20} + 4 \, {\left (x^{7} + 8 \, x^{6} + 24 \, x^{5} + 32 \, x^{4} + 16 \, x^{3}\right )} e^{15} + 6 \, {\left (x^{8} + 8 \, x^{7} + 22 \, x^{6} + 16 \, x^{5} - 32 \, x^{4} - 64 \, x^{3} - 32 \, x^{2}\right )} e^{10} + 4 \, {\left (x^{9} + 8 \, x^{8} + 18 \, x^{7} - 16 \, x^{6} - 128 \, x^{5} - 192 \, x^{4} - 96 \, x^{3}\right )} e^{5}\right )} e^{50} - 6 \, {\left (x^{6} + 4 \, x^{5} - 2 \, x^{4} - 24 \, x^{3} - 24 \, x^{2} + {\left (x^{4} + 4 \, x^{3} + 4 \, x^{2}\right )} e^{10} + 2 \, {\left (x^{5} + 4 \, x^{4} + 4 \, x^{3}\right )} e^{5}\right )} e^{25} \] Input:
integrate(((6*x^5+40*x^4+96*x^3+96*x^2+32*x)*exp(5)^4+(28*x^6+192*x^5+480* x^4+512*x^3+192*x^2)*exp(5)^3+(48*x^7+336*x^6+792*x^5+480*x^4-768*x^3-1152 *x^2-384*x)*exp(5)^2+(36*x^8+256*x^7+504*x^6-384*x^5-2560*x^4-3072*x^3-115 2*x^2)*exp(5)+10*x^9+72*x^8+96*x^7-448*x^6-1416*x^5-480*x^4+2688*x^3+3456* x^2+1152*x)*exp(25)^2+((-24*x^3-72*x^2-48*x)*exp(5)^2+(-60*x^4-192*x^3-144 *x^2)*exp(5)-36*x^5-120*x^4+48*x^3+432*x^2+288*x)*exp(25)+18*x,x, algorith m="maxima")
Output:
9*x^2 + (x^10 + 8*x^9 + 12*x^8 - 64*x^7 - 236*x^6 - 96*x^5 + 672*x^4 + 115 2*x^3 + 576*x^2 + (x^6 + 8*x^5 + 24*x^4 + 32*x^3 + 16*x^2)*e^20 + 4*(x^7 + 8*x^6 + 24*x^5 + 32*x^4 + 16*x^3)*e^15 + 6*(x^8 + 8*x^7 + 22*x^6 + 16*x^5 - 32*x^4 - 64*x^3 - 32*x^2)*e^10 + 4*(x^9 + 8*x^8 + 18*x^7 - 16*x^6 - 128 *x^5 - 192*x^4 - 96*x^3)*e^5)*e^50 - 6*(x^6 + 4*x^5 - 2*x^4 - 24*x^3 - 24* x^2 + (x^4 + 4*x^3 + 4*x^2)*e^10 + 2*(x^5 + 4*x^4 + 4*x^3)*e^5)*e^25
Leaf count of result is larger than twice the leaf count of optimal. 247 vs. \(2 (24) = 48\).
Time = 0.11 (sec) , antiderivative size = 247, normalized size of antiderivative = 8.82 \[ \int \left (18 x+e^{25} \left (288 x+432 x^2+48 x^3-120 x^4-36 x^5+e^{10} \left (-48 x-72 x^2-24 x^3\right )+e^5 \left (-144 x^2-192 x^3-60 x^4\right )\right )+e^{50} \left (1152 x+3456 x^2+2688 x^3-480 x^4-1416 x^5-448 x^6+96 x^7+72 x^8+10 x^9+e^{20} \left (32 x+96 x^2+96 x^3+40 x^4+6 x^5\right )+e^{15} \left (192 x^2+512 x^3+480 x^4+192 x^5+28 x^6\right )+e^{10} \left (-384 x-1152 x^2-768 x^3+480 x^4+792 x^5+336 x^6+48 x^7\right )+e^5 \left (-1152 x^2-3072 x^3-2560 x^4-384 x^5+504 x^6+256 x^7+36 x^8\right )\right )\right ) \, dx=9 \, x^{2} + {\left (x^{10} + 8 \, x^{9} + 12 \, x^{8} - 64 \, x^{7} - 236 \, x^{6} - 96 \, x^{5} + 672 \, x^{4} + 1152 \, x^{3} + 576 \, x^{2} + {\left (x^{6} + 8 \, x^{5} + 24 \, x^{4} + 32 \, x^{3} + 16 \, x^{2}\right )} e^{20} + 4 \, {\left (x^{7} + 8 \, x^{6} + 24 \, x^{5} + 32 \, x^{4} + 16 \, x^{3}\right )} e^{15} + 6 \, {\left (x^{8} + 8 \, x^{7} + 22 \, x^{6} + 16 \, x^{5} - 32 \, x^{4} - 64 \, x^{3} - 32 \, x^{2}\right )} e^{10} + 4 \, {\left (x^{9} + 8 \, x^{8} + 18 \, x^{7} - 16 \, x^{6} - 128 \, x^{5} - 192 \, x^{4} - 96 \, x^{3}\right )} e^{5}\right )} e^{50} - 6 \, {\left (x^{6} + 4 \, x^{5} - 2 \, x^{4} - 24 \, x^{3} - 24 \, x^{2} + {\left (x^{4} + 4 \, x^{3} + 4 \, x^{2}\right )} e^{10} + 2 \, {\left (x^{5} + 4 \, x^{4} + 4 \, x^{3}\right )} e^{5}\right )} e^{25} \] Input:
integrate(((6*x^5+40*x^4+96*x^3+96*x^2+32*x)*exp(5)^4+(28*x^6+192*x^5+480* x^4+512*x^3+192*x^2)*exp(5)^3+(48*x^7+336*x^6+792*x^5+480*x^4-768*x^3-1152 *x^2-384*x)*exp(5)^2+(36*x^8+256*x^7+504*x^6-384*x^5-2560*x^4-3072*x^3-115 2*x^2)*exp(5)+10*x^9+72*x^8+96*x^7-448*x^6-1416*x^5-480*x^4+2688*x^3+3456* x^2+1152*x)*exp(25)^2+((-24*x^3-72*x^2-48*x)*exp(5)^2+(-60*x^4-192*x^3-144 *x^2)*exp(5)-36*x^5-120*x^4+48*x^3+432*x^2+288*x)*exp(25)+18*x,x, algorith m="giac")
Output:
9*x^2 + (x^10 + 8*x^9 + 12*x^8 - 64*x^7 - 236*x^6 - 96*x^5 + 672*x^4 + 115 2*x^3 + 576*x^2 + (x^6 + 8*x^5 + 24*x^4 + 32*x^3 + 16*x^2)*e^20 + 4*(x^7 + 8*x^6 + 24*x^5 + 32*x^4 + 16*x^3)*e^15 + 6*(x^8 + 8*x^7 + 22*x^6 + 16*x^5 - 32*x^4 - 64*x^3 - 32*x^2)*e^10 + 4*(x^9 + 8*x^8 + 18*x^7 - 16*x^6 - 128 *x^5 - 192*x^4 - 96*x^3)*e^5)*e^50 - 6*(x^6 + 4*x^5 - 2*x^4 - 24*x^3 - 24* x^2 + (x^4 + 4*x^3 + 4*x^2)*e^10 + 2*(x^5 + 4*x^4 + 4*x^3)*e^5)*e^25
Time = 2.82 (sec) , antiderivative size = 239, normalized size of antiderivative = 8.54 \[ \int \left (18 x+e^{25} \left (288 x+432 x^2+48 x^3-120 x^4-36 x^5+e^{10} \left (-48 x-72 x^2-24 x^3\right )+e^5 \left (-144 x^2-192 x^3-60 x^4\right )\right )+e^{50} \left (1152 x+3456 x^2+2688 x^3-480 x^4-1416 x^5-448 x^6+96 x^7+72 x^8+10 x^9+e^{20} \left (32 x+96 x^2+96 x^3+40 x^4+6 x^5\right )+e^{15} \left (192 x^2+512 x^3+480 x^4+192 x^5+28 x^6\right )+e^{10} \left (-384 x-1152 x^2-768 x^3+480 x^4+792 x^5+336 x^6+48 x^7\right )+e^5 \left (-1152 x^2-3072 x^3-2560 x^4-384 x^5+504 x^6+256 x^7+36 x^8\right )\right )\right ) \, dx={\mathrm {e}}^{50}\,x^{10}+\frac {{\mathrm {e}}^{50}\,\left (36\,{\mathrm {e}}^5+72\right )\,x^9}{9}+\frac {{\mathrm {e}}^{50}\,\left (256\,{\mathrm {e}}^5+48\,{\mathrm {e}}^{10}+96\right )\,x^8}{8}+\frac {{\mathrm {e}}^{50}\,\left (504\,{\mathrm {e}}^5+336\,{\mathrm {e}}^{10}+28\,{\mathrm {e}}^{15}-448\right )\,x^7}{7}+\left (\frac {{\mathrm {e}}^{50}\,\left (792\,{\mathrm {e}}^{10}-384\,{\mathrm {e}}^5+192\,{\mathrm {e}}^{15}+6\,{\mathrm {e}}^{20}-1416\right )}{6}-6\,{\mathrm {e}}^{25}\right )\,x^6+\left (\frac {{\mathrm {e}}^{50}\,\left (480\,{\mathrm {e}}^{10}-2560\,{\mathrm {e}}^5+480\,{\mathrm {e}}^{15}+40\,{\mathrm {e}}^{20}-480\right )}{5}-\frac {{\mathrm {e}}^{25}\,\left (60\,{\mathrm {e}}^5+120\right )}{5}\right )\,x^5+\left (\frac {{\mathrm {e}}^{50}\,\left (512\,{\mathrm {e}}^{15}-768\,{\mathrm {e}}^{10}-3072\,{\mathrm {e}}^5+96\,{\mathrm {e}}^{20}+2688\right )}{4}-\frac {{\mathrm {e}}^{25}\,\left (192\,{\mathrm {e}}^5+24\,{\mathrm {e}}^{10}-48\right )}{4}\right )\,x^4+\left (\frac {{\mathrm {e}}^{50}\,\left (192\,{\mathrm {e}}^{15}-1152\,{\mathrm {e}}^{10}-1152\,{\mathrm {e}}^5+96\,{\mathrm {e}}^{20}+3456\right )}{3}-\frac {{\mathrm {e}}^{25}\,\left (144\,{\mathrm {e}}^5+72\,{\mathrm {e}}^{10}-432\right )}{3}\right )\,x^3+\left (\frac {{\mathrm {e}}^{50}\,\left (32\,{\mathrm {e}}^{20}-384\,{\mathrm {e}}^{10}+1152\right )}{2}-\frac {{\mathrm {e}}^{25}\,\left (48\,{\mathrm {e}}^{10}-288\right )}{2}+9\right )\,x^2 \] Input:
int(18*x - exp(25)*(exp(10)*(48*x + 72*x^2 + 24*x^3) - 288*x + exp(5)*(144 *x^2 + 192*x^3 + 60*x^4) - 432*x^2 - 48*x^3 + 120*x^4 + 36*x^5) + exp(50)* (1152*x + exp(15)*(192*x^2 + 512*x^3 + 480*x^4 + 192*x^5 + 28*x^6) + exp(1 0)*(480*x^4 - 1152*x^2 - 768*x^3 - 384*x + 792*x^5 + 336*x^6 + 48*x^7) - e xp(5)*(1152*x^2 + 3072*x^3 + 2560*x^4 + 384*x^5 - 504*x^6 - 256*x^7 - 36*x ^8) + exp(20)*(32*x + 96*x^2 + 96*x^3 + 40*x^4 + 6*x^5) + 3456*x^2 + 2688* x^3 - 480*x^4 - 1416*x^5 - 448*x^6 + 96*x^7 + 72*x^8 + 10*x^9),x)
Output:
x^2*((exp(50)*(32*exp(20) - 384*exp(10) + 1152))/2 - (exp(25)*(48*exp(10) - 288))/2 + 9) + x^3*((exp(50)*(192*exp(15) - 1152*exp(10) - 1152*exp(5) + 96*exp(20) + 3456))/3 - (exp(25)*(144*exp(5) + 72*exp(10) - 432))/3) + x^ 4*((exp(50)*(512*exp(15) - 768*exp(10) - 3072*exp(5) + 96*exp(20) + 2688)) /4 - (exp(25)*(192*exp(5) + 24*exp(10) - 48))/4) - x^6*(6*exp(25) - (exp(5 0)*(792*exp(10) - 384*exp(5) + 192*exp(15) + 6*exp(20) - 1416))/6) + x^10* exp(50) + x^5*((exp(50)*(480*exp(10) - 2560*exp(5) + 480*exp(15) + 40*exp( 20) - 480))/5 - (exp(25)*(60*exp(5) + 120))/5) + (x^7*exp(50)*(504*exp(5) + 336*exp(10) + 28*exp(15) - 448))/7 + (x^8*exp(50)*(256*exp(5) + 48*exp(1 0) + 96))/8 + (x^9*exp(50)*(36*exp(5) + 72))/9
Time = 0.17 (sec) , antiderivative size = 325, normalized size of antiderivative = 11.61 \[ \int \left (18 x+e^{25} \left (288 x+432 x^2+48 x^3-120 x^4-36 x^5+e^{10} \left (-48 x-72 x^2-24 x^3\right )+e^5 \left (-144 x^2-192 x^3-60 x^4\right )\right )+e^{50} \left (1152 x+3456 x^2+2688 x^3-480 x^4-1416 x^5-448 x^6+96 x^7+72 x^8+10 x^9+e^{20} \left (32 x+96 x^2+96 x^3+40 x^4+6 x^5\right )+e^{15} \left (192 x^2+512 x^3+480 x^4+192 x^5+28 x^6\right )+e^{10} \left (-384 x-1152 x^2-768 x^3+480 x^4+792 x^5+336 x^6+48 x^7\right )+e^5 \left (-1152 x^2-3072 x^3-2560 x^4-384 x^5+504 x^6+256 x^7+36 x^8\right )\right )\right ) \, dx=x^{2} \left (e^{70} x^{4}+8 e^{70} x^{3}+24 e^{70} x^{2}+32 e^{70} x +16 e^{70}+4 e^{65} x^{5}+32 e^{65} x^{4}+96 e^{65} x^{3}+128 e^{65} x^{2}+64 e^{65} x +6 e^{60} x^{6}+48 e^{60} x^{5}+132 e^{60} x^{4}+96 e^{60} x^{3}-192 e^{60} x^{2}+4 e^{55} x^{7}-384 e^{60} x +32 e^{55} x^{6}-192 e^{60}+72 e^{55} x^{5}-64 e^{55} x^{4}-512 e^{55} x^{3}+e^{50} x^{8}-768 e^{55} x^{2}+8 e^{50} x^{7}-384 e^{55} x +12 e^{50} x^{6}-64 e^{50} x^{5}-236 e^{50} x^{4}-96 e^{50} x^{3}+672 e^{50} x^{2}+1152 e^{50} x +576 e^{50}-6 e^{35} x^{2}-24 e^{35} x -24 e^{35}-12 e^{30} x^{3}-48 e^{30} x^{2}-48 e^{30} x -6 e^{25} x^{4}-24 e^{25} x^{3}+12 e^{25} x^{2}+144 e^{25} x +144 e^{25}+9\right ) \] Input:
int(((6*x^5+40*x^4+96*x^3+96*x^2+32*x)*exp(5)^4+(28*x^6+192*x^5+480*x^4+51 2*x^3+192*x^2)*exp(5)^3+(48*x^7+336*x^6+792*x^5+480*x^4-768*x^3-1152*x^2-3 84*x)*exp(5)^2+(36*x^8+256*x^7+504*x^6-384*x^5-2560*x^4-3072*x^3-1152*x^2) *exp(5)+10*x^9+72*x^8+96*x^7-448*x^6-1416*x^5-480*x^4+2688*x^3+3456*x^2+11 52*x)*exp(25)^2+((-24*x^3-72*x^2-48*x)*exp(5)^2+(-60*x^4-192*x^3-144*x^2)* exp(5)-36*x^5-120*x^4+48*x^3+432*x^2+288*x)*exp(25)+18*x,x)
Output:
x**2*(e**70*x**4 + 8*e**70*x**3 + 24*e**70*x**2 + 32*e**70*x + 16*e**70 + 4*e**65*x**5 + 32*e**65*x**4 + 96*e**65*x**3 + 128*e**65*x**2 + 64*e**65*x + 6*e**60*x**6 + 48*e**60*x**5 + 132*e**60*x**4 + 96*e**60*x**3 - 192*e** 60*x**2 - 384*e**60*x - 192*e**60 + 4*e**55*x**7 + 32*e**55*x**6 + 72*e**5 5*x**5 - 64*e**55*x**4 - 512*e**55*x**3 - 768*e**55*x**2 - 384*e**55*x + e **50*x**8 + 8*e**50*x**7 + 12*e**50*x**6 - 64*e**50*x**5 - 236*e**50*x**4 - 96*e**50*x**3 + 672*e**50*x**2 + 1152*e**50*x + 576*e**50 - 6*e**35*x**2 - 24*e**35*x - 24*e**35 - 12*e**30*x**3 - 48*e**30*x**2 - 48*e**30*x - 6* e**25*x**4 - 24*e**25*x**3 + 12*e**25*x**2 + 144*e**25*x + 144*e**25 + 9)