\(\int \frac {7776-48 e^{\frac {5}{3} (-15+x \log (4))}+e^{\frac {4}{3} (-15+x \log (4))} (672-240 x)-14256 x+10368 x^2-3744 x^3+672 x^4-48 x^5+e^{-15+x \log (4)} (-3744+2688 x-480 x^2)+e^{\frac {2}{3} (-15+x \log (4))} (10368-11232 x+4032 x^2-480 x^3)+e^{\frac {1}{3} (-15+x \log (4))} (-14256+20736 x-11232 x^2+2688 x^3-240 x^4)+(31104-192 e^{\frac {5}{3} (-15+x \log (4))}-62208 x+46656 x^2-16704 x^3+2880 x^4-192 x^5+e^{\frac {4}{3} (-15+x \log (4))} (2688-960 x+64 x \log (4))+e^{-15+x \log (4)} (-14976+10944 x-1920 x^2+(-576 x+192 x^2) \log (4))+e^{\frac {2}{3} (-15+x \log (4))} (41472-46656 x+16704 x^2-1920 x^3+(1728 x-1152 x^2+192 x^3) \log (4))+e^{\frac {1}{3} (-15+x \log (4))} (-57024+88128 x-48384 x^2+11328 x^3-960 x^4+(-1728 x+1728 x^2-576 x^3+64 x^4) \log (4))) \log (x)}{(-96 x^5+3 e^{\frac {5}{3} (-15+x \log (4))} x^5+240 x^6-240 x^7+120 x^8-30 x^9+3 x^{10}+e^{\frac {4}{3} (-15+x \log (4))} (-30 x^5+15 x^6)+e^{-15+x \log (4)} (120 x^5-120 x^6+30 x^7)+e^{\frac {2}{3} (-15+x \log (4))} (-240 x^5+360 x^6-180 x^7+30 x^8)+e^{\frac {1}{3} (-15+x \log (4))} (240 x^5-480 x^6+360 x^7-120 x^8+15 x^9)) \log ^2(x)} \, dx\) [2616]

Optimal result

Integrand size = 510, antiderivative size = 28 \[ \int \frac {7776-48 e^{\frac {5}{3} (-15+x \log (4))}+e^{\frac {4}{3} (-15+x \log (4))} (672-240 x)-14256 x+10368 x^2-3744 x^3+672 x^4-48 x^5+e^{-15+x \log (4)} \left (-3744+2688 x-480 x^2\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (10368-11232 x+4032 x^2-480 x^3\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-14256+20736 x-11232 x^2+2688 x^3-240 x^4\right )+\left (31104-192 e^{\frac {5}{3} (-15+x \log (4))}-62208 x+46656 x^2-16704 x^3+2880 x^4-192 x^5+e^{\frac {4}{3} (-15+x \log (4))} (2688-960 x+64 x \log (4))+e^{-15+x \log (4)} \left (-14976+10944 x-1920 x^2+\left (-576 x+192 x^2\right ) \log (4)\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (41472-46656 x+16704 x^2-1920 x^3+\left (1728 x-1152 x^2+192 x^3\right ) \log (4)\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-57024+88128 x-48384 x^2+11328 x^3-960 x^4+\left (-1728 x+1728 x^2-576 x^3+64 x^4\right ) \log (4)\right )\right ) \log (x)}{\left (-96 x^5+3 e^{\frac {5}{3} (-15+x \log (4))} x^5+240 x^6-240 x^7+120 x^8-30 x^9+3 x^{10}+e^{\frac {4}{3} (-15+x \log (4))} \left (-30 x^5+15 x^6\right )+e^{-15+x \log (4)} \left (120 x^5-120 x^6+30 x^7\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (-240 x^5+360 x^6-180 x^7+30 x^8\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (240 x^5-480 x^6+360 x^7-120 x^8+15 x^9\right )\right ) \log ^2(x)} \, dx=\frac {16}{\left (x+\frac {x}{-3+e^{-5+\frac {1}{3} x \log (4)}+x}\right )^4 \log (x)} \] Output:

16/(x+x/(x+exp(2/3*x*ln(2)-5)-3))^4/ln(x)
 

Mathematica [A] (verified)

Time = 0.19 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.54 \[ \int \frac {7776-48 e^{\frac {5}{3} (-15+x \log (4))}+e^{\frac {4}{3} (-15+x \log (4))} (672-240 x)-14256 x+10368 x^2-3744 x^3+672 x^4-48 x^5+e^{-15+x \log (4)} \left (-3744+2688 x-480 x^2\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (10368-11232 x+4032 x^2-480 x^3\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-14256+20736 x-11232 x^2+2688 x^3-240 x^4\right )+\left (31104-192 e^{\frac {5}{3} (-15+x \log (4))}-62208 x+46656 x^2-16704 x^3+2880 x^4-192 x^5+e^{\frac {4}{3} (-15+x \log (4))} (2688-960 x+64 x \log (4))+e^{-15+x \log (4)} \left (-14976+10944 x-1920 x^2+\left (-576 x+192 x^2\right ) \log (4)\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (41472-46656 x+16704 x^2-1920 x^3+\left (1728 x-1152 x^2+192 x^3\right ) \log (4)\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-57024+88128 x-48384 x^2+11328 x^3-960 x^4+\left (-1728 x+1728 x^2-576 x^3+64 x^4\right ) \log (4)\right )\right ) \log (x)}{\left (-96 x^5+3 e^{\frac {5}{3} (-15+x \log (4))} x^5+240 x^6-240 x^7+120 x^8-30 x^9+3 x^{10}+e^{\frac {4}{3} (-15+x \log (4))} \left (-30 x^5+15 x^6\right )+e^{-15+x \log (4)} \left (120 x^5-120 x^6+30 x^7\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (-240 x^5+360 x^6-180 x^7+30 x^8\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (240 x^5-480 x^6+360 x^7-120 x^8+15 x^9\right )\right ) \log ^2(x)} \, dx=\frac {16 \left (2^{2 x/3}+e^5 (-3+x)\right )^4}{\left (2^{2 x/3}+e^5 (-2+x)\right )^4 x^4 \log (x)} \] Input:

Integrate[(7776 - 48*E^((5*(-15 + x*Log[4]))/3) + E^((4*(-15 + x*Log[4]))/ 
3)*(672 - 240*x) - 14256*x + 10368*x^2 - 3744*x^3 + 672*x^4 - 48*x^5 + E^( 
-15 + x*Log[4])*(-3744 + 2688*x - 480*x^2) + E^((2*(-15 + x*Log[4]))/3)*(1 
0368 - 11232*x + 4032*x^2 - 480*x^3) + E^((-15 + x*Log[4])/3)*(-14256 + 20 
736*x - 11232*x^2 + 2688*x^3 - 240*x^4) + (31104 - 192*E^((5*(-15 + x*Log[ 
4]))/3) - 62208*x + 46656*x^2 - 16704*x^3 + 2880*x^4 - 192*x^5 + E^((4*(-1 
5 + x*Log[4]))/3)*(2688 - 960*x + 64*x*Log[4]) + E^(-15 + x*Log[4])*(-1497 
6 + 10944*x - 1920*x^2 + (-576*x + 192*x^2)*Log[4]) + E^((2*(-15 + x*Log[4 
]))/3)*(41472 - 46656*x + 16704*x^2 - 1920*x^3 + (1728*x - 1152*x^2 + 192* 
x^3)*Log[4]) + E^((-15 + x*Log[4])/3)*(-57024 + 88128*x - 48384*x^2 + 1132 
8*x^3 - 960*x^4 + (-1728*x + 1728*x^2 - 576*x^3 + 64*x^4)*Log[4]))*Log[x]) 
/((-96*x^5 + 3*E^((5*(-15 + x*Log[4]))/3)*x^5 + 240*x^6 - 240*x^7 + 120*x^ 
8 - 30*x^9 + 3*x^10 + E^((4*(-15 + x*Log[4]))/3)*(-30*x^5 + 15*x^6) + E^(- 
15 + x*Log[4])*(120*x^5 - 120*x^6 + 30*x^7) + E^((2*(-15 + x*Log[4]))/3)*( 
-240*x^5 + 360*x^6 - 180*x^7 + 30*x^8) + E^((-15 + x*Log[4])/3)*(240*x^5 - 
 480*x^6 + 360*x^7 - 120*x^8 + 15*x^9))*Log[x]^2),x]
 

Output:

(16*(2^((2*x)/3) + E^5*(-3 + x))^4)/((2^((2*x)/3) + E^5*(-2 + x))^4*x^4*Lo 
g[x])
 

Rubi [F]

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.

\(\displaystyle \int \frac {-48 x^5+672 x^4-3744 x^3+10368 x^2+\left (-480 x^2+2688 x-3744\right ) e^{x \log (4)-15}+\left (-480 x^3+4032 x^2-11232 x+10368\right ) e^{\frac {2}{3} (x \log (4)-15)}+\left (-240 x^4+2688 x^3-11232 x^2+20736 x-14256\right ) e^{\frac {1}{3} (x \log (4)-15)}+\left (-192 x^5+2880 x^4-16704 x^3+46656 x^2+e^{x \log (4)-15} \left (-1920 x^2+\left (192 x^2-576 x\right ) \log (4)+10944 x-14976\right )+e^{\frac {2}{3} (x \log (4)-15)} \left (-1920 x^3+16704 x^2+\left (192 x^3-1152 x^2+1728 x\right ) \log (4)-46656 x+41472\right )+e^{\frac {1}{3} (x \log (4)-15)} \left (-960 x^4+11328 x^3-48384 x^2+\left (64 x^4-576 x^3+1728 x^2-1728 x\right ) \log (4)+88128 x-57024\right )-62208 x-192 e^{\frac {5}{3} (x \log (4)-15)}+e^{\frac {4}{3} (x \log (4)-15)} (-960 x+64 x \log (4)+2688)+31104\right ) \log (x)-14256 x-48 e^{\frac {5}{3} (x \log (4)-15)}+(672-240 x) e^{\frac {4}{3} (x \log (4)-15)}+7776}{\left (3 x^{10}-30 x^9+120 x^8-240 x^7+240 x^6-96 x^5+3 x^5 e^{\frac {5}{3} (x \log (4)-15)}+\left (15 x^6-30 x^5\right ) e^{\frac {4}{3} (x \log (4)-15)}+\left (30 x^7-120 x^6+120 x^5\right ) e^{x \log (4)-15}+\left (30 x^8-180 x^7+360 x^6-240 x^5\right ) e^{\frac {2}{3} (x \log (4)-15)}+\left (15 x^9-120 x^8+360 x^7-480 x^6+240 x^5\right ) e^{\frac {1}{3} (x \log (4)-15)}\right ) \log ^2(x)} \, dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {16 \left (e^5 (x-3)+2^{2 x/3}\right )^3 \left (-3 \left (e^{10} \left (x^2-5 x+6\right )+e^5 2^{2 x/3} (2 x-5)+2^{4 x/3}\right )-4 \left (3 e^{10} \left (x^2-6 x+6\right )+3\ 2^{4 x/3}-e^5 2^{2 x/3} (x (\log (4)-6)+15)\right ) \log (x)\right )}{3 \left (e^5 (x-2)+2^{2 x/3}\right )^5 x^5 \log ^2(x)}dx\)

\(\Big \downarrow \) 27

\(\displaystyle \frac {16}{3} \int -\frac {\left (2^{2 x/3}-e^5 (3-x)\right )^3 \left (3 \left (-2^{2 x/3} e^5 (5-2 x)+2^{4 x/3}+e^{10} \left (x^2-5 x+6\right )\right )+4 \left (3 e^{10} \left (x^2-6 x+6\right )+3\ 2^{4 x/3}-2^{2 x/3} e^5 (15-x (6-\log (4)))\right ) \log (x)\right )}{\left (2^{2 x/3}-e^5 (2-x)\right )^5 x^5 \log ^2(x)}dx\)

\(\Big \downarrow \) 25

\(\displaystyle -\frac {16}{3} \int \frac {\left (2^{2 x/3}-e^5 (3-x)\right )^3 \left (3 \left (-2^{2 x/3} e^5 (5-2 x)+2^{4 x/3}+e^{10} \left (x^2-5 x+6\right )\right )+4 \left (3 e^{10} \left (x^2-6 x+6\right )+3\ 2^{4 x/3}-2^{2 x/3} e^5 (15-x (6-\log (4)))\right ) \log (x)\right )}{\left (2^{2 x/3}-e^5 (2-x)\right )^5 x^5 \log ^2(x)}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -\frac {16}{3} \int \left (-\frac {4 e^{25} (\log (4) x-\log (16)-3)}{x^4 \left (e^5 x+2^{2 x/3}-2 e^5\right )^5 \log (x)}+\frac {3 (4 \log (x)+1)}{x^5 \log ^2(x)}-\frac {4 e^5 (x \log (4) \log (x)+12 \log (x)+3)}{x^5 \left (e^5 x+2^{2 x/3}-2 e^5\right ) \log ^2(x)}+\frac {12 e^{15} \left (-\log (4) \log (x) x^2+3 \left (1+\frac {2 \log (2)}{3}\right ) \log (x) x-4 \log (x)-1\right )}{x^5 \left (e^5 x+2^{2 x/3}-2 e^5\right )^3 \log ^2(x)}+\frac {2 e^{10} \left (2 \log (4) \log (x) x^2-6 \left (1-\frac {2 \log (2)}{3}\right ) \log (x) x+36 \log (x)+9\right )}{x^5 \left (e^5 x+2^{2 x/3}-2 e^5\right )^2 \log ^2(x)}+\frac {e^{20} \left (4 \log (64) \log (x) x^2-36 \left (1+\frac {5 \log (4)}{9}\right ) \log (x) x+12 \log (x)+3\right )}{x^5 \left (e^5 x+2^{2 x/3}-2 e^5\right )^4 \log ^2(x)}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle -\frac {16}{3} \left (3 e^{20} \int \frac {1}{x^5 \left (e^5 x+2^{2 x/3}-2 e^5\right )^4 \log ^2(x)}dx-12 e^{15} \int \frac {1}{x^5 \left (e^5 x+2^{2 x/3}-2 e^5\right )^3 \log ^2(x)}dx+18 e^{10} \int \frac {1}{x^5 \left (e^5 x+2^{2 x/3}-2 e^5\right )^2 \log ^2(x)}dx-12 e^5 \int \frac {1}{x^5 \left (e^5 x+2^{2 x/3}-2 e^5\right ) \log ^2(x)}dx+12 e^{20} \int \frac {1}{x^5 \left (e^5 x+2^{2 x/3}-2 e^5\right )^4 \log (x)}dx-48 e^{15} \int \frac {1}{x^5 \left (e^5 x+2^{2 x/3}-2 e^5\right )^3 \log (x)}dx+72 e^{10} \int \frac {1}{x^5 \left (e^5 x+2^{2 x/3}-2 e^5\right )^2 \log (x)}dx-48 e^5 \int \frac {1}{x^5 \left (e^5 x+2^{2 x/3}-2 e^5\right ) \log (x)}dx+4 e^{25} (3+\log (16)) \int \frac {1}{x^4 \left (e^5 x+2^{2 x/3}-2 e^5\right )^5 \log (x)}dx-4 e^{20} (9+5 \log (4)) \int \frac {1}{x^4 \left (e^5 x+2^{2 x/3}-2 e^5\right )^4 \log (x)}dx+12 e^{15} (3+\log (4)) \int \frac {1}{x^4 \left (e^5 x+2^{2 x/3}-2 e^5\right )^3 \log (x)}dx-2 e^{10} (6-\log (16)) \int \frac {1}{x^4 \left (e^5 x+2^{2 x/3}-2 e^5\right )^2 \log (x)}dx-4 e^5 \log (4) \int \frac {1}{x^4 \left (e^5 x+2^{2 x/3}-2 e^5\right ) \log (x)}dx-4 e^{25} \log (4) \int \frac {1}{x^3 \left (e^5 x+2^{2 x/3}-2 e^5\right )^5 \log (x)}dx+4 e^{20} \log (64) \int \frac {1}{x^3 \left (e^5 x+2^{2 x/3}-2 e^5\right )^4 \log (x)}dx-12 e^{15} \log (4) \int \frac {1}{x^3 \left (e^5 x+2^{2 x/3}-2 e^5\right )^3 \log (x)}dx+2 e^{10} \log (16) \int \frac {1}{x^3 \left (e^5 x+2^{2 x/3}-2 e^5\right )^2 \log (x)}dx+48 \log (x) \operatorname {ExpIntegralEi}(-4 \log (x))-12 (4 \log (x)+1) \operatorname {ExpIntegralEi}(-4 \log (x))+12 \operatorname {ExpIntegralEi}(-4 \log (x))+\frac {12}{x^4}-\frac {3 (4 \log (x)+1)}{x^4 \log (x)}\right )\)

Input:

Int[(7776 - 48*E^((5*(-15 + x*Log[4]))/3) + E^((4*(-15 + x*Log[4]))/3)*(67 
2 - 240*x) - 14256*x + 10368*x^2 - 3744*x^3 + 672*x^4 - 48*x^5 + E^(-15 + 
x*Log[4])*(-3744 + 2688*x - 480*x^2) + E^((2*(-15 + x*Log[4]))/3)*(10368 - 
 11232*x + 4032*x^2 - 480*x^3) + E^((-15 + x*Log[4])/3)*(-14256 + 20736*x 
- 11232*x^2 + 2688*x^3 - 240*x^4) + (31104 - 192*E^((5*(-15 + x*Log[4]))/3 
) - 62208*x + 46656*x^2 - 16704*x^3 + 2880*x^4 - 192*x^5 + E^((4*(-15 + x* 
Log[4]))/3)*(2688 - 960*x + 64*x*Log[4]) + E^(-15 + x*Log[4])*(-14976 + 10 
944*x - 1920*x^2 + (-576*x + 192*x^2)*Log[4]) + E^((2*(-15 + x*Log[4]))/3) 
*(41472 - 46656*x + 16704*x^2 - 1920*x^3 + (1728*x - 1152*x^2 + 192*x^3)*L 
og[4]) + E^((-15 + x*Log[4])/3)*(-57024 + 88128*x - 48384*x^2 + 11328*x^3 
- 960*x^4 + (-1728*x + 1728*x^2 - 576*x^3 + 64*x^4)*Log[4]))*Log[x])/((-96 
*x^5 + 3*E^((5*(-15 + x*Log[4]))/3)*x^5 + 240*x^6 - 240*x^7 + 120*x^8 - 30 
*x^9 + 3*x^10 + E^((4*(-15 + x*Log[4]))/3)*(-30*x^5 + 15*x^6) + E^(-15 + x 
*Log[4])*(120*x^5 - 120*x^6 + 30*x^7) + E^((2*(-15 + x*Log[4]))/3)*(-240*x 
^5 + 360*x^6 - 180*x^7 + 30*x^8) + E^((-15 + x*Log[4])/3)*(240*x^5 - 480*x 
^6 + 360*x^7 - 120*x^8 + 15*x^9))*Log[x]^2),x]
 

Output:

$Aborted
 

Maple [B] (warning: unable to verify)

Leaf count of result is larger than twice the leaf count of optimal. \(273\) vs. \(2(25)=50\).

Time = 0.16 (sec) , antiderivative size = 274, normalized size of antiderivative = 9.79

\[\frac {16 x^{4}+64 \,2^{\frac {2 x}{3}} {\mathrm e}^{-5} x^{3}+96 \,2^{\frac {4 x}{3}} {\mathrm e}^{-10} x^{2}+64 \,2^{2 x} {\mathrm e}^{-15} x +16 \,2^{\frac {8 x}{3}} {\mathrm e}^{-20}-192 x^{3}-576 \,2^{\frac {2 x}{3}} {\mathrm e}^{-5} x^{2}-576 \,2^{\frac {4 x}{3}} {\mathrm e}^{-10} x -192 \,2^{2 x} {\mathrm e}^{-15}+864 x^{2}+1728 \,2^{\frac {2 x}{3}} {\mathrm e}^{-5} x +864 \,2^{\frac {4 x}{3}} {\mathrm e}^{-10}-1728 x -1728 \,2^{\frac {2 x}{3}} {\mathrm e}^{-5}+1296}{x^{4} \left (x^{4}+4 \,2^{\frac {2 x}{3}} {\mathrm e}^{-5} x^{3}+6 \,2^{\frac {4 x}{3}} {\mathrm e}^{-10} x^{2}+4 \,2^{2 x} {\mathrm e}^{-15} x +2^{\frac {8 x}{3}} {\mathrm e}^{-20}-8 x^{3}-24 \,2^{\frac {2 x}{3}} {\mathrm e}^{-5} x^{2}-24 \,2^{\frac {4 x}{3}} {\mathrm e}^{-10} x -8 \,2^{2 x} {\mathrm e}^{-15}+24 x^{2}+48 \,2^{\frac {2 x}{3}} {\mathrm e}^{-5} x +24 \,2^{\frac {4 x}{3}} {\mathrm e}^{-10}-32 x -32 \,2^{\frac {2 x}{3}} {\mathrm e}^{-5}+16\right ) \ln \left (x \right )}\]

Input:

int(((-192*exp(2/3*x*ln(2)-5)^5+(128*x*ln(2)-960*x+2688)*exp(2/3*x*ln(2)-5 
)^4+(2*(192*x^2-576*x)*ln(2)-1920*x^2+10944*x-14976)*exp(2/3*x*ln(2)-5)^3+ 
(2*(192*x^3-1152*x^2+1728*x)*ln(2)-1920*x^3+16704*x^2-46656*x+41472)*exp(2 
/3*x*ln(2)-5)^2+(2*(64*x^4-576*x^3+1728*x^2-1728*x)*ln(2)-960*x^4+11328*x^ 
3-48384*x^2+88128*x-57024)*exp(2/3*x*ln(2)-5)-192*x^5+2880*x^4-16704*x^3+4 
6656*x^2-62208*x+31104)*ln(x)-48*exp(2/3*x*ln(2)-5)^5+(-240*x+672)*exp(2/3 
*x*ln(2)-5)^4+(-480*x^2+2688*x-3744)*exp(2/3*x*ln(2)-5)^3+(-480*x^3+4032*x 
^2-11232*x+10368)*exp(2/3*x*ln(2)-5)^2+(-240*x^4+2688*x^3-11232*x^2+20736* 
x-14256)*exp(2/3*x*ln(2)-5)-48*x^5+672*x^4-3744*x^3+10368*x^2-14256*x+7776 
)/(3*x^5*exp(2/3*x*ln(2)-5)^5+(15*x^6-30*x^5)*exp(2/3*x*ln(2)-5)^4+(30*x^7 
-120*x^6+120*x^5)*exp(2/3*x*ln(2)-5)^3+(30*x^8-180*x^7+360*x^6-240*x^5)*ex 
p(2/3*x*ln(2)-5)^2+(15*x^9-120*x^8+360*x^7-480*x^6+240*x^5)*exp(2/3*x*ln(2 
)-5)+3*x^10-30*x^9+120*x^8-240*x^7+240*x^6-96*x^5)/ln(x)^2,x)
 

Output:

16/x^4*(x^4+4*2^(2/3*x)*exp(-5)*x^3+6*(2^(2/3*x))^2*exp(-10)*x^2+4*(2^(2/3 
*x))^3*exp(-15)*x+(2^(2/3*x))^4*exp(-20)-12*x^3-36*2^(2/3*x)*exp(-5)*x^2-3 
6*(2^(2/3*x))^2*exp(-10)*x-12*(2^(2/3*x))^3*exp(-15)+54*x^2+108*2^(2/3*x)* 
exp(-5)*x+54*(2^(2/3*x))^2*exp(-10)-108*x-108*2^(2/3*x)*exp(-5)+81)/(x^4+4 
*2^(2/3*x)*exp(-5)*x^3+6*(2^(2/3*x))^2*exp(-10)*x^2+4*(2^(2/3*x))^3*exp(-1 
5)*x+(2^(2/3*x))^4*exp(-20)-8*x^3-24*2^(2/3*x)*exp(-5)*x^2-24*(2^(2/3*x))^ 
2*exp(-10)*x-8*(2^(2/3*x))^3*exp(-15)+24*x^2+48*2^(2/3*x)*exp(-5)*x+24*(2^ 
(2/3*x))^2*exp(-10)-32*x-32*2^(2/3*x)*exp(-5)+16)/ln(x)
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 196 vs. \(2 (25) = 50\).

Time = 0.10 (sec) , antiderivative size = 196, normalized size of antiderivative = 7.00 \[ \int \frac {7776-48 e^{\frac {5}{3} (-15+x \log (4))}+e^{\frac {4}{3} (-15+x \log (4))} (672-240 x)-14256 x+10368 x^2-3744 x^3+672 x^4-48 x^5+e^{-15+x \log (4)} \left (-3744+2688 x-480 x^2\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (10368-11232 x+4032 x^2-480 x^3\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-14256+20736 x-11232 x^2+2688 x^3-240 x^4\right )+\left (31104-192 e^{\frac {5}{3} (-15+x \log (4))}-62208 x+46656 x^2-16704 x^3+2880 x^4-192 x^5+e^{\frac {4}{3} (-15+x \log (4))} (2688-960 x+64 x \log (4))+e^{-15+x \log (4)} \left (-14976+10944 x-1920 x^2+\left (-576 x+192 x^2\right ) \log (4)\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (41472-46656 x+16704 x^2-1920 x^3+\left (1728 x-1152 x^2+192 x^3\right ) \log (4)\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-57024+88128 x-48384 x^2+11328 x^3-960 x^4+\left (-1728 x+1728 x^2-576 x^3+64 x^4\right ) \log (4)\right )\right ) \log (x)}{\left (-96 x^5+3 e^{\frac {5}{3} (-15+x \log (4))} x^5+240 x^6-240 x^7+120 x^8-30 x^9+3 x^{10}+e^{\frac {4}{3} (-15+x \log (4))} \left (-30 x^5+15 x^6\right )+e^{-15+x \log (4)} \left (120 x^5-120 x^6+30 x^7\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (-240 x^5+360 x^6-180 x^7+30 x^8\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (240 x^5-480 x^6+360 x^7-120 x^8+15 x^9\right )\right ) \log ^2(x)} \, dx=\frac {16 \, {\left (x^{4} - 12 \, x^{3} + 54 \, x^{2} + 4 \, {\left (x - 3\right )} e^{\left (2 \, x \log \left (2\right ) - 15\right )} + 6 \, {\left (x^{2} - 6 \, x + 9\right )} e^{\left (\frac {4}{3} \, x \log \left (2\right ) - 10\right )} + 4 \, {\left (x^{3} - 9 \, x^{2} + 27 \, x - 27\right )} e^{\left (\frac {2}{3} \, x \log \left (2\right ) - 5\right )} - 108 \, x + e^{\left (\frac {8}{3} \, x \log \left (2\right ) - 20\right )} + 81\right )}}{{\left (x^{8} - 8 \, x^{7} + 24 \, x^{6} - 32 \, x^{5} + x^{4} e^{\left (\frac {8}{3} \, x \log \left (2\right ) - 20\right )} + 16 \, x^{4} + 4 \, {\left (x^{5} - 2 \, x^{4}\right )} e^{\left (2 \, x \log \left (2\right ) - 15\right )} + 6 \, {\left (x^{6} - 4 \, x^{5} + 4 \, x^{4}\right )} e^{\left (\frac {4}{3} \, x \log \left (2\right ) - 10\right )} + 4 \, {\left (x^{7} - 6 \, x^{6} + 12 \, x^{5} - 8 \, x^{4}\right )} e^{\left (\frac {2}{3} \, x \log \left (2\right ) - 5\right )}\right )} \log \left (x\right )} \] Input:

integrate(((-192*exp(2/3*x*log(2)-5)^5+(128*x*log(2)-960*x+2688)*exp(2/3*x 
*log(2)-5)^4+(2*(192*x^2-576*x)*log(2)-1920*x^2+10944*x-14976)*exp(2/3*x*l 
og(2)-5)^3+(2*(192*x^3-1152*x^2+1728*x)*log(2)-1920*x^3+16704*x^2-46656*x+ 
41472)*exp(2/3*x*log(2)-5)^2+(2*(64*x^4-576*x^3+1728*x^2-1728*x)*log(2)-96 
0*x^4+11328*x^3-48384*x^2+88128*x-57024)*exp(2/3*x*log(2)-5)-192*x^5+2880* 
x^4-16704*x^3+46656*x^2-62208*x+31104)*log(x)-48*exp(2/3*x*log(2)-5)^5+(-2 
40*x+672)*exp(2/3*x*log(2)-5)^4+(-480*x^2+2688*x-3744)*exp(2/3*x*log(2)-5) 
^3+(-480*x^3+4032*x^2-11232*x+10368)*exp(2/3*x*log(2)-5)^2+(-240*x^4+2688* 
x^3-11232*x^2+20736*x-14256)*exp(2/3*x*log(2)-5)-48*x^5+672*x^4-3744*x^3+1 
0368*x^2-14256*x+7776)/(3*x^5*exp(2/3*x*log(2)-5)^5+(15*x^6-30*x^5)*exp(2/ 
3*x*log(2)-5)^4+(30*x^7-120*x^6+120*x^5)*exp(2/3*x*log(2)-5)^3+(30*x^8-180 
*x^7+360*x^6-240*x^5)*exp(2/3*x*log(2)-5)^2+(15*x^9-120*x^8+360*x^7-480*x^ 
6+240*x^5)*exp(2/3*x*log(2)-5)+3*x^10-30*x^9+120*x^8-240*x^7+240*x^6-96*x^ 
5)/log(x)^2,x, algorithm="fricas")
 

Output:

16*(x^4 - 12*x^3 + 54*x^2 + 4*(x - 3)*e^(2*x*log(2) - 15) + 6*(x^2 - 6*x + 
 9)*e^(4/3*x*log(2) - 10) + 4*(x^3 - 9*x^2 + 27*x - 27)*e^(2/3*x*log(2) - 
5) - 108*x + e^(8/3*x*log(2) - 20) + 81)/((x^8 - 8*x^7 + 24*x^6 - 32*x^5 + 
 x^4*e^(8/3*x*log(2) - 20) + 16*x^4 + 4*(x^5 - 2*x^4)*e^(2*x*log(2) - 15) 
+ 6*(x^6 - 4*x^5 + 4*x^4)*e^(4/3*x*log(2) - 10) + 4*(x^7 - 6*x^6 + 12*x^5 
- 8*x^4)*e^(2/3*x*log(2) - 5))*log(x))
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 243 vs. \(2 (24) = 48\).

Time = 0.59 (sec) , antiderivative size = 243, normalized size of antiderivative = 8.68 \[ \int \frac {7776-48 e^{\frac {5}{3} (-15+x \log (4))}+e^{\frac {4}{3} (-15+x \log (4))} (672-240 x)-14256 x+10368 x^2-3744 x^3+672 x^4-48 x^5+e^{-15+x \log (4)} \left (-3744+2688 x-480 x^2\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (10368-11232 x+4032 x^2-480 x^3\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-14256+20736 x-11232 x^2+2688 x^3-240 x^4\right )+\left (31104-192 e^{\frac {5}{3} (-15+x \log (4))}-62208 x+46656 x^2-16704 x^3+2880 x^4-192 x^5+e^{\frac {4}{3} (-15+x \log (4))} (2688-960 x+64 x \log (4))+e^{-15+x \log (4)} \left (-14976+10944 x-1920 x^2+\left (-576 x+192 x^2\right ) \log (4)\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (41472-46656 x+16704 x^2-1920 x^3+\left (1728 x-1152 x^2+192 x^3\right ) \log (4)\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-57024+88128 x-48384 x^2+11328 x^3-960 x^4+\left (-1728 x+1728 x^2-576 x^3+64 x^4\right ) \log (4)\right )\right ) \log (x)}{\left (-96 x^5+3 e^{\frac {5}{3} (-15+x \log (4))} x^5+240 x^6-240 x^7+120 x^8-30 x^9+3 x^{10}+e^{\frac {4}{3} (-15+x \log (4))} \left (-30 x^5+15 x^6\right )+e^{-15+x \log (4)} \left (120 x^5-120 x^6+30 x^7\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (-240 x^5+360 x^6-180 x^7+30 x^8\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (240 x^5-480 x^6+360 x^7-120 x^8+15 x^9\right )\right ) \log ^2(x)} \, dx=\frac {- 64 x^{3} + 480 x^{2} - 1216 x + \left (480 - 192 x\right ) e^{\frac {4 x \log {\left (2 \right )}}{3} - 10} + \left (- 192 x^{2} + 960 x - 1216\right ) e^{\frac {2 x \log {\left (2 \right )}}{3} - 5} - 64 e^{2 x \log {\left (2 \right )} - 15} + 1040}{x^{8} \log {\left (x \right )} - 8 x^{7} \log {\left (x \right )} + 24 x^{6} \log {\left (x \right )} - 32 x^{5} \log {\left (x \right )} + x^{4} e^{\frac {8 x \log {\left (2 \right )}}{3} - 20} \log {\left (x \right )} + 16 x^{4} \log {\left (x \right )} + \left (4 x^{5} \log {\left (x \right )} - 8 x^{4} \log {\left (x \right )}\right ) e^{2 x \log {\left (2 \right )} - 15} + \left (6 x^{6} \log {\left (x \right )} - 24 x^{5} \log {\left (x \right )} + 24 x^{4} \log {\left (x \right )}\right ) e^{\frac {4 x \log {\left (2 \right )}}{3} - 10} + \left (4 x^{7} \log {\left (x \right )} - 24 x^{6} \log {\left (x \right )} + 48 x^{5} \log {\left (x \right )} - 32 x^{4} \log {\left (x \right )}\right ) e^{\frac {2 x \log {\left (2 \right )}}{3} - 5}} + \frac {16}{x^{4} \log {\left (x \right )}} \] Input:

integrate(((-192*exp(2/3*x*ln(2)-5)**5+(128*x*ln(2)-960*x+2688)*exp(2/3*x* 
ln(2)-5)**4+(2*(192*x**2-576*x)*ln(2)-1920*x**2+10944*x-14976)*exp(2/3*x*l 
n(2)-5)**3+(2*(192*x**3-1152*x**2+1728*x)*ln(2)-1920*x**3+16704*x**2-46656 
*x+41472)*exp(2/3*x*ln(2)-5)**2+(2*(64*x**4-576*x**3+1728*x**2-1728*x)*ln( 
2)-960*x**4+11328*x**3-48384*x**2+88128*x-57024)*exp(2/3*x*ln(2)-5)-192*x* 
*5+2880*x**4-16704*x**3+46656*x**2-62208*x+31104)*ln(x)-48*exp(2/3*x*ln(2) 
-5)**5+(-240*x+672)*exp(2/3*x*ln(2)-5)**4+(-480*x**2+2688*x-3744)*exp(2/3* 
x*ln(2)-5)**3+(-480*x**3+4032*x**2-11232*x+10368)*exp(2/3*x*ln(2)-5)**2+(- 
240*x**4+2688*x**3-11232*x**2+20736*x-14256)*exp(2/3*x*ln(2)-5)-48*x**5+67 
2*x**4-3744*x**3+10368*x**2-14256*x+7776)/(3*x**5*exp(2/3*x*ln(2)-5)**5+(1 
5*x**6-30*x**5)*exp(2/3*x*ln(2)-5)**4+(30*x**7-120*x**6+120*x**5)*exp(2/3* 
x*ln(2)-5)**3+(30*x**8-180*x**7+360*x**6-240*x**5)*exp(2/3*x*ln(2)-5)**2+( 
15*x**9-120*x**8+360*x**7-480*x**6+240*x**5)*exp(2/3*x*ln(2)-5)+3*x**10-30 
*x**9+120*x**8-240*x**7+240*x**6-96*x**5)/ln(x)**2,x)
 

Output:

(-64*x**3 + 480*x**2 - 1216*x + (480 - 192*x)*exp(4*x*log(2)/3 - 10) + (-1 
92*x**2 + 960*x - 1216)*exp(2*x*log(2)/3 - 5) - 64*exp(2*x*log(2) - 15) + 
1040)/(x**8*log(x) - 8*x**7*log(x) + 24*x**6*log(x) - 32*x**5*log(x) + x** 
4*exp(8*x*log(2)/3 - 20)*log(x) + 16*x**4*log(x) + (4*x**5*log(x) - 8*x**4 
*log(x))*exp(2*x*log(2) - 15) + (6*x**6*log(x) - 24*x**5*log(x) + 24*x**4* 
log(x))*exp(4*x*log(2)/3 - 10) + (4*x**7*log(x) - 24*x**6*log(x) + 48*x**5 
*log(x) - 32*x**4*log(x))*exp(2*x*log(2)/3 - 5)) + 16/(x**4*log(x))
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 248 vs. \(2 (25) = 50\).

Time = 0.68 (sec) , antiderivative size = 248, normalized size of antiderivative = 8.86 \[ \int \frac {7776-48 e^{\frac {5}{3} (-15+x \log (4))}+e^{\frac {4}{3} (-15+x \log (4))} (672-240 x)-14256 x+10368 x^2-3744 x^3+672 x^4-48 x^5+e^{-15+x \log (4)} \left (-3744+2688 x-480 x^2\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (10368-11232 x+4032 x^2-480 x^3\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-14256+20736 x-11232 x^2+2688 x^3-240 x^4\right )+\left (31104-192 e^{\frac {5}{3} (-15+x \log (4))}-62208 x+46656 x^2-16704 x^3+2880 x^4-192 x^5+e^{\frac {4}{3} (-15+x \log (4))} (2688-960 x+64 x \log (4))+e^{-15+x \log (4)} \left (-14976+10944 x-1920 x^2+\left (-576 x+192 x^2\right ) \log (4)\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (41472-46656 x+16704 x^2-1920 x^3+\left (1728 x-1152 x^2+192 x^3\right ) \log (4)\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-57024+88128 x-48384 x^2+11328 x^3-960 x^4+\left (-1728 x+1728 x^2-576 x^3+64 x^4\right ) \log (4)\right )\right ) \log (x)}{\left (-96 x^5+3 e^{\frac {5}{3} (-15+x \log (4))} x^5+240 x^6-240 x^7+120 x^8-30 x^9+3 x^{10}+e^{\frac {4}{3} (-15+x \log (4))} \left (-30 x^5+15 x^6\right )+e^{-15+x \log (4)} \left (120 x^5-120 x^6+30 x^7\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (-240 x^5+360 x^6-180 x^7+30 x^8\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (240 x^5-480 x^6+360 x^7-120 x^8+15 x^9\right )\right ) \log ^2(x)} \, dx=\frac {16 \, {\left (x^{4} e^{20} - 12 \, x^{3} e^{20} + 54 \, x^{2} e^{20} + 4 \, {\left (x e^{5} - 3 \, e^{5}\right )} 2^{2 \, x} + 6 \, {\left (x^{2} e^{10} - 6 \, x e^{10} + 9 \, e^{10}\right )} 2^{\frac {4}{3} \, x} + 4 \, {\left (x^{3} e^{15} - 9 \, x^{2} e^{15} + 27 \, x e^{15} - 27 \, e^{15}\right )} 2^{\frac {2}{3} \, x} - 108 \, x e^{20} + 2^{\frac {8}{3} \, x} + 81 \, e^{20}\right )}}{2^{\frac {8}{3} \, x} x^{4} \log \left (x\right ) + 4 \, {\left (x^{5} e^{5} - 2 \, x^{4} e^{5}\right )} 2^{2 \, x} \log \left (x\right ) + 6 \, {\left (x^{6} e^{10} - 4 \, x^{5} e^{10} + 4 \, x^{4} e^{10}\right )} 2^{\frac {4}{3} \, x} \log \left (x\right ) + 4 \, {\left (x^{7} e^{15} - 6 \, x^{6} e^{15} + 12 \, x^{5} e^{15} - 8 \, x^{4} e^{15}\right )} 2^{\frac {2}{3} \, x} \log \left (x\right ) + {\left (x^{8} e^{20} - 8 \, x^{7} e^{20} + 24 \, x^{6} e^{20} - 32 \, x^{5} e^{20} + 16 \, x^{4} e^{20}\right )} \log \left (x\right )} \] Input:

integrate(((-192*exp(2/3*x*log(2)-5)^5+(128*x*log(2)-960*x+2688)*exp(2/3*x 
*log(2)-5)^4+(2*(192*x^2-576*x)*log(2)-1920*x^2+10944*x-14976)*exp(2/3*x*l 
og(2)-5)^3+(2*(192*x^3-1152*x^2+1728*x)*log(2)-1920*x^3+16704*x^2-46656*x+ 
41472)*exp(2/3*x*log(2)-5)^2+(2*(64*x^4-576*x^3+1728*x^2-1728*x)*log(2)-96 
0*x^4+11328*x^3-48384*x^2+88128*x-57024)*exp(2/3*x*log(2)-5)-192*x^5+2880* 
x^4-16704*x^3+46656*x^2-62208*x+31104)*log(x)-48*exp(2/3*x*log(2)-5)^5+(-2 
40*x+672)*exp(2/3*x*log(2)-5)^4+(-480*x^2+2688*x-3744)*exp(2/3*x*log(2)-5) 
^3+(-480*x^3+4032*x^2-11232*x+10368)*exp(2/3*x*log(2)-5)^2+(-240*x^4+2688* 
x^3-11232*x^2+20736*x-14256)*exp(2/3*x*log(2)-5)-48*x^5+672*x^4-3744*x^3+1 
0368*x^2-14256*x+7776)/(3*x^5*exp(2/3*x*log(2)-5)^5+(15*x^6-30*x^5)*exp(2/ 
3*x*log(2)-5)^4+(30*x^7-120*x^6+120*x^5)*exp(2/3*x*log(2)-5)^3+(30*x^8-180 
*x^7+360*x^6-240*x^5)*exp(2/3*x*log(2)-5)^2+(15*x^9-120*x^8+360*x^7-480*x^ 
6+240*x^5)*exp(2/3*x*log(2)-5)+3*x^10-30*x^9+120*x^8-240*x^7+240*x^6-96*x^ 
5)/log(x)^2,x, algorithm="maxima")
 

Output:

16*(x^4*e^20 - 12*x^3*e^20 + 54*x^2*e^20 + 4*(x*e^5 - 3*e^5)*2^(2*x) + 6*( 
x^2*e^10 - 6*x*e^10 + 9*e^10)*2^(4/3*x) + 4*(x^3*e^15 - 9*x^2*e^15 + 27*x* 
e^15 - 27*e^15)*2^(2/3*x) - 108*x*e^20 + 2^(8/3*x) + 81*e^20)/(2^(8/3*x)*x 
^4*log(x) + 4*(x^5*e^5 - 2*x^4*e^5)*2^(2*x)*log(x) + 6*(x^6*e^10 - 4*x^5*e 
^10 + 4*x^4*e^10)*2^(4/3*x)*log(x) + 4*(x^7*e^15 - 6*x^6*e^15 + 12*x^5*e^1 
5 - 8*x^4*e^15)*2^(2/3*x)*log(x) + (x^8*e^20 - 8*x^7*e^20 + 24*x^6*e^20 - 
32*x^5*e^20 + 16*x^4*e^20)*log(x))
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 314 vs. \(2 (25) = 50\).

Time = 1.77 (sec) , antiderivative size = 314, normalized size of antiderivative = 11.21 \[ \int \frac {7776-48 e^{\frac {5}{3} (-15+x \log (4))}+e^{\frac {4}{3} (-15+x \log (4))} (672-240 x)-14256 x+10368 x^2-3744 x^3+672 x^4-48 x^5+e^{-15+x \log (4)} \left (-3744+2688 x-480 x^2\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (10368-11232 x+4032 x^2-480 x^3\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-14256+20736 x-11232 x^2+2688 x^3-240 x^4\right )+\left (31104-192 e^{\frac {5}{3} (-15+x \log (4))}-62208 x+46656 x^2-16704 x^3+2880 x^4-192 x^5+e^{\frac {4}{3} (-15+x \log (4))} (2688-960 x+64 x \log (4))+e^{-15+x \log (4)} \left (-14976+10944 x-1920 x^2+\left (-576 x+192 x^2\right ) \log (4)\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (41472-46656 x+16704 x^2-1920 x^3+\left (1728 x-1152 x^2+192 x^3\right ) \log (4)\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-57024+88128 x-48384 x^2+11328 x^3-960 x^4+\left (-1728 x+1728 x^2-576 x^3+64 x^4\right ) \log (4)\right )\right ) \log (x)}{\left (-96 x^5+3 e^{\frac {5}{3} (-15+x \log (4))} x^5+240 x^6-240 x^7+120 x^8-30 x^9+3 x^{10}+e^{\frac {4}{3} (-15+x \log (4))} \left (-30 x^5+15 x^6\right )+e^{-15+x \log (4)} \left (120 x^5-120 x^6+30 x^7\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (-240 x^5+360 x^6-180 x^7+30 x^8\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (240 x^5-480 x^6+360 x^7-120 x^8+15 x^9\right )\right ) \log ^2(x)} \, dx=\frac {16 \, {\left (x^{4} e^{20} + 4 \cdot 2^{\frac {2}{3} \, x} x^{3} e^{15} - 12 \, x^{3} e^{20} - 36 \cdot 2^{\frac {2}{3} \, x} x^{2} e^{15} + 6 \cdot 2^{\frac {4}{3} \, x} x^{2} e^{10} + 54 \, x^{2} e^{20} + 108 \cdot 2^{\frac {2}{3} \, x} x e^{15} - 36 \cdot 2^{\frac {4}{3} \, x} x e^{10} + 4 \cdot 2^{2 \, x} x e^{5} - 108 \, x e^{20} - 108 \cdot 2^{\frac {2}{3} \, x} e^{15} + 54 \cdot 2^{\frac {4}{3} \, x} e^{10} - 12 \cdot 2^{2 \, x} e^{5} + 2^{\frac {8}{3} \, x} + 81 \, e^{20}\right )}}{x^{8} e^{20} \log \left (x\right ) + 4 \cdot 2^{\frac {2}{3} \, x} x^{7} e^{15} \log \left (x\right ) - 8 \, x^{7} e^{20} \log \left (x\right ) - 24 \cdot 2^{\frac {2}{3} \, x} x^{6} e^{15} \log \left (x\right ) + 6 \cdot 2^{\frac {4}{3} \, x} x^{6} e^{10} \log \left (x\right ) + 24 \, x^{6} e^{20} \log \left (x\right ) + 48 \cdot 2^{\frac {2}{3} \, x} x^{5} e^{15} \log \left (x\right ) - 24 \cdot 2^{\frac {4}{3} \, x} x^{5} e^{10} \log \left (x\right ) + 4 \cdot 2^{2 \, x} x^{5} e^{5} \log \left (x\right ) - 32 \, x^{5} e^{20} \log \left (x\right ) - 32 \cdot 2^{\frac {2}{3} \, x} x^{4} e^{15} \log \left (x\right ) + 24 \cdot 2^{\frac {4}{3} \, x} x^{4} e^{10} \log \left (x\right ) - 8 \cdot 2^{2 \, x} x^{4} e^{5} \log \left (x\right ) + 2^{\frac {8}{3} \, x} x^{4} \log \left (x\right ) + 16 \, x^{4} e^{20} \log \left (x\right )} \] Input:

integrate(((-192*exp(2/3*x*log(2)-5)^5+(128*x*log(2)-960*x+2688)*exp(2/3*x 
*log(2)-5)^4+(2*(192*x^2-576*x)*log(2)-1920*x^2+10944*x-14976)*exp(2/3*x*l 
og(2)-5)^3+(2*(192*x^3-1152*x^2+1728*x)*log(2)-1920*x^3+16704*x^2-46656*x+ 
41472)*exp(2/3*x*log(2)-5)^2+(2*(64*x^4-576*x^3+1728*x^2-1728*x)*log(2)-96 
0*x^4+11328*x^3-48384*x^2+88128*x-57024)*exp(2/3*x*log(2)-5)-192*x^5+2880* 
x^4-16704*x^3+46656*x^2-62208*x+31104)*log(x)-48*exp(2/3*x*log(2)-5)^5+(-2 
40*x+672)*exp(2/3*x*log(2)-5)^4+(-480*x^2+2688*x-3744)*exp(2/3*x*log(2)-5) 
^3+(-480*x^3+4032*x^2-11232*x+10368)*exp(2/3*x*log(2)-5)^2+(-240*x^4+2688* 
x^3-11232*x^2+20736*x-14256)*exp(2/3*x*log(2)-5)-48*x^5+672*x^4-3744*x^3+1 
0368*x^2-14256*x+7776)/(3*x^5*exp(2/3*x*log(2)-5)^5+(15*x^6-30*x^5)*exp(2/ 
3*x*log(2)-5)^4+(30*x^7-120*x^6+120*x^5)*exp(2/3*x*log(2)-5)^3+(30*x^8-180 
*x^7+360*x^6-240*x^5)*exp(2/3*x*log(2)-5)^2+(15*x^9-120*x^8+360*x^7-480*x^ 
6+240*x^5)*exp(2/3*x*log(2)-5)+3*x^10-30*x^9+120*x^8-240*x^7+240*x^6-96*x^ 
5)/log(x)^2,x, algorithm="giac")
 

Output:

16*(x^4*e^20 + 4*2^(2/3*x)*x^3*e^15 - 12*x^3*e^20 - 36*2^(2/3*x)*x^2*e^15 
+ 6*2^(4/3*x)*x^2*e^10 + 54*x^2*e^20 + 108*2^(2/3*x)*x*e^15 - 36*2^(4/3*x) 
*x*e^10 + 4*2^(2*x)*x*e^5 - 108*x*e^20 - 108*2^(2/3*x)*e^15 + 54*2^(4/3*x) 
*e^10 - 12*2^(2*x)*e^5 + 2^(8/3*x) + 81*e^20)/(x^8*e^20*log(x) + 4*2^(2/3* 
x)*x^7*e^15*log(x) - 8*x^7*e^20*log(x) - 24*2^(2/3*x)*x^6*e^15*log(x) + 6* 
2^(4/3*x)*x^6*e^10*log(x) + 24*x^6*e^20*log(x) + 48*2^(2/3*x)*x^5*e^15*log 
(x) - 24*2^(4/3*x)*x^5*e^10*log(x) + 4*2^(2*x)*x^5*e^5*log(x) - 32*x^5*e^2 
0*log(x) - 32*2^(2/3*x)*x^4*e^15*log(x) + 24*2^(4/3*x)*x^4*e^10*log(x) - 8 
*2^(2*x)*x^4*e^5*log(x) + 2^(8/3*x)*x^4*log(x) + 16*x^4*e^20*log(x))
 

Mupad [F(-1)]

Timed out. \[ \int \frac {7776-48 e^{\frac {5}{3} (-15+x \log (4))}+e^{\frac {4}{3} (-15+x \log (4))} (672-240 x)-14256 x+10368 x^2-3744 x^3+672 x^4-48 x^5+e^{-15+x \log (4)} \left (-3744+2688 x-480 x^2\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (10368-11232 x+4032 x^2-480 x^3\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-14256+20736 x-11232 x^2+2688 x^3-240 x^4\right )+\left (31104-192 e^{\frac {5}{3} (-15+x \log (4))}-62208 x+46656 x^2-16704 x^3+2880 x^4-192 x^5+e^{\frac {4}{3} (-15+x \log (4))} (2688-960 x+64 x \log (4))+e^{-15+x \log (4)} \left (-14976+10944 x-1920 x^2+\left (-576 x+192 x^2\right ) \log (4)\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (41472-46656 x+16704 x^2-1920 x^3+\left (1728 x-1152 x^2+192 x^3\right ) \log (4)\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-57024+88128 x-48384 x^2+11328 x^3-960 x^4+\left (-1728 x+1728 x^2-576 x^3+64 x^4\right ) \log (4)\right )\right ) \log (x)}{\left (-96 x^5+3 e^{\frac {5}{3} (-15+x \log (4))} x^5+240 x^6-240 x^7+120 x^8-30 x^9+3 x^{10}+e^{\frac {4}{3} (-15+x \log (4))} \left (-30 x^5+15 x^6\right )+e^{-15+x \log (4)} \left (120 x^5-120 x^6+30 x^7\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (-240 x^5+360 x^6-180 x^7+30 x^8\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (240 x^5-480 x^6+360 x^7-120 x^8+15 x^9\right )\right ) \log ^2(x)} \, dx=\int -\frac {14256\,x+48\,{\mathrm {e}}^{\frac {10\,x\,\ln \left (2\right )}{3}-25}+{\mathrm {e}}^{\frac {4\,x\,\ln \left (2\right )}{3}-10}\,\left (480\,x^3-4032\,x^2+11232\,x-10368\right )+\ln \left (x\right )\,\left (62208\,x+192\,{\mathrm {e}}^{\frac {10\,x\,\ln \left (2\right )}{3}-25}+{\mathrm {e}}^{2\,x\,\ln \left (2\right )-15}\,\left (2\,\ln \left (2\right )\,\left (576\,x-192\,x^2\right )-10944\,x+1920\,x^2+14976\right )-{\mathrm {e}}^{\frac {4\,x\,\ln \left (2\right )}{3}-10}\,\left (2\,\ln \left (2\right )\,\left (192\,x^3-1152\,x^2+1728\,x\right )-46656\,x+16704\,x^2-1920\,x^3+41472\right )-46656\,x^2+16704\,x^3-2880\,x^4+192\,x^5-{\mathrm {e}}^{\frac {8\,x\,\ln \left (2\right )}{3}-20}\,\left (128\,x\,\ln \left (2\right )-960\,x+2688\right )+{\mathrm {e}}^{\frac {2\,x\,\ln \left (2\right )}{3}-5}\,\left (2\,\ln \left (2\right )\,\left (-64\,x^4+576\,x^3-1728\,x^2+1728\,x\right )-88128\,x+48384\,x^2-11328\,x^3+960\,x^4+57024\right )-31104\right )+{\mathrm {e}}^{\frac {2\,x\,\ln \left (2\right )}{3}-5}\,\left (240\,x^4-2688\,x^3+11232\,x^2-20736\,x+14256\right )+{\mathrm {e}}^{\frac {8\,x\,\ln \left (2\right )}{3}-20}\,\left (240\,x-672\right )+{\mathrm {e}}^{2\,x\,\ln \left (2\right )-15}\,\left (480\,x^2-2688\,x+3744\right )-10368\,x^2+3744\,x^3-672\,x^4+48\,x^5-7776}{{\ln \left (x\right )}^2\,\left (3\,x^5\,{\mathrm {e}}^{\frac {10\,x\,\ln \left (2\right )}{3}-25}-{\mathrm {e}}^{\frac {8\,x\,\ln \left (2\right )}{3}-20}\,\left (30\,x^5-15\,x^6\right )+{\mathrm {e}}^{2\,x\,\ln \left (2\right )-15}\,\left (30\,x^7-120\,x^6+120\,x^5\right )-{\mathrm {e}}^{\frac {4\,x\,\ln \left (2\right )}{3}-10}\,\left (-30\,x^8+180\,x^7-360\,x^6+240\,x^5\right )-96\,x^5+240\,x^6-240\,x^7+120\,x^8-30\,x^9+3\,x^{10}+{\mathrm {e}}^{\frac {2\,x\,\ln \left (2\right )}{3}-5}\,\left (15\,x^9-120\,x^8+360\,x^7-480\,x^6+240\,x^5\right )\right )} \,d x \] Input:

int(-(14256*x + 48*exp((10*x*log(2))/3 - 25) + exp((4*x*log(2))/3 - 10)*(1 
1232*x - 4032*x^2 + 480*x^3 - 10368) + log(x)*(62208*x + 192*exp((10*x*log 
(2))/3 - 25) + exp(2*x*log(2) - 15)*(2*log(2)*(576*x - 192*x^2) - 10944*x 
+ 1920*x^2 + 14976) - exp((4*x*log(2))/3 - 10)*(2*log(2)*(1728*x - 1152*x^ 
2 + 192*x^3) - 46656*x + 16704*x^2 - 1920*x^3 + 41472) - 46656*x^2 + 16704 
*x^3 - 2880*x^4 + 192*x^5 - exp((8*x*log(2))/3 - 20)*(128*x*log(2) - 960*x 
 + 2688) + exp((2*x*log(2))/3 - 5)*(2*log(2)*(1728*x - 1728*x^2 + 576*x^3 
- 64*x^4) - 88128*x + 48384*x^2 - 11328*x^3 + 960*x^4 + 57024) - 31104) + 
exp((2*x*log(2))/3 - 5)*(11232*x^2 - 20736*x - 2688*x^3 + 240*x^4 + 14256) 
 + exp((8*x*log(2))/3 - 20)*(240*x - 672) + exp(2*x*log(2) - 15)*(480*x^2 
- 2688*x + 3744) - 10368*x^2 + 3744*x^3 - 672*x^4 + 48*x^5 - 7776)/(log(x) 
^2*(3*x^5*exp((10*x*log(2))/3 - 25) - exp((8*x*log(2))/3 - 20)*(30*x^5 - 1 
5*x^6) + exp(2*x*log(2) - 15)*(120*x^5 - 120*x^6 + 30*x^7) - exp((4*x*log( 
2))/3 - 10)*(240*x^5 - 360*x^6 + 180*x^7 - 30*x^8) - 96*x^5 + 240*x^6 - 24 
0*x^7 + 120*x^8 - 30*x^9 + 3*x^10 + exp((2*x*log(2))/3 - 5)*(240*x^5 - 480 
*x^6 + 360*x^7 - 120*x^8 + 15*x^9))),x)
 

Output:

int(-(14256*x + 48*exp((10*x*log(2))/3 - 25) + exp((4*x*log(2))/3 - 10)*(1 
1232*x - 4032*x^2 + 480*x^3 - 10368) + log(x)*(62208*x + 192*exp((10*x*log 
(2))/3 - 25) + exp(2*x*log(2) - 15)*(2*log(2)*(576*x - 192*x^2) - 10944*x 
+ 1920*x^2 + 14976) - exp((4*x*log(2))/3 - 10)*(2*log(2)*(1728*x - 1152*x^ 
2 + 192*x^3) - 46656*x + 16704*x^2 - 1920*x^3 + 41472) - 46656*x^2 + 16704 
*x^3 - 2880*x^4 + 192*x^5 - exp((8*x*log(2))/3 - 20)*(128*x*log(2) - 960*x 
 + 2688) + exp((2*x*log(2))/3 - 5)*(2*log(2)*(1728*x - 1728*x^2 + 576*x^3 
- 64*x^4) - 88128*x + 48384*x^2 - 11328*x^3 + 960*x^4 + 57024) - 31104) + 
exp((2*x*log(2))/3 - 5)*(11232*x^2 - 20736*x - 2688*x^3 + 240*x^4 + 14256) 
 + exp((8*x*log(2))/3 - 20)*(240*x - 672) + exp(2*x*log(2) - 15)*(480*x^2 
- 2688*x + 3744) - 10368*x^2 + 3744*x^3 - 672*x^4 + 48*x^5 - 7776)/(log(x) 
^2*(3*x^5*exp((10*x*log(2))/3 - 25) - exp((8*x*log(2))/3 - 20)*(30*x^5 - 1 
5*x^6) + exp(2*x*log(2) - 15)*(120*x^5 - 120*x^6 + 30*x^7) - exp((4*x*log( 
2))/3 - 10)*(240*x^5 - 360*x^6 + 180*x^7 - 30*x^8) - 96*x^5 + 240*x^6 - 24 
0*x^7 + 120*x^8 - 30*x^9 + 3*x^10 + exp((2*x*log(2))/3 - 5)*(240*x^5 - 480 
*x^6 + 360*x^7 - 120*x^8 + 15*x^9))), x)
 

Reduce [B] (verification not implemented)

Time = 0.19 (sec) , antiderivative size = 295, normalized size of antiderivative = 10.54 \[ \int \frac {7776-48 e^{\frac {5}{3} (-15+x \log (4))}+e^{\frac {4}{3} (-15+x \log (4))} (672-240 x)-14256 x+10368 x^2-3744 x^3+672 x^4-48 x^5+e^{-15+x \log (4)} \left (-3744+2688 x-480 x^2\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (10368-11232 x+4032 x^2-480 x^3\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-14256+20736 x-11232 x^2+2688 x^3-240 x^4\right )+\left (31104-192 e^{\frac {5}{3} (-15+x \log (4))}-62208 x+46656 x^2-16704 x^3+2880 x^4-192 x^5+e^{\frac {4}{3} (-15+x \log (4))} (2688-960 x+64 x \log (4))+e^{-15+x \log (4)} \left (-14976+10944 x-1920 x^2+\left (-576 x+192 x^2\right ) \log (4)\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (41472-46656 x+16704 x^2-1920 x^3+\left (1728 x-1152 x^2+192 x^3\right ) \log (4)\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (-57024+88128 x-48384 x^2+11328 x^3-960 x^4+\left (-1728 x+1728 x^2-576 x^3+64 x^4\right ) \log (4)\right )\right ) \log (x)}{\left (-96 x^5+3 e^{\frac {5}{3} (-15+x \log (4))} x^5+240 x^6-240 x^7+120 x^8-30 x^9+3 x^{10}+e^{\frac {4}{3} (-15+x \log (4))} \left (-30 x^5+15 x^6\right )+e^{-15+x \log (4)} \left (120 x^5-120 x^6+30 x^7\right )+e^{\frac {2}{3} (-15+x \log (4))} \left (-240 x^5+360 x^6-180 x^7+30 x^8\right )+e^{\frac {1}{3} (-15+x \log (4))} \left (240 x^5-480 x^6+360 x^7-120 x^8+15 x^9\right )\right ) \log ^2(x)} \, dx=\frac {16 \,2^{\frac {8 x}{3}}+96 \,2^{\frac {4 x}{3}} e^{10} x^{2}-576 \,2^{\frac {4 x}{3}} e^{10} x +864 \,2^{\frac {4 x}{3}} e^{10}+64 \,2^{\frac {2 x}{3}} e^{15} x^{3}-576 \,2^{\frac {2 x}{3}} e^{15} x^{2}+1728 \,2^{\frac {2 x}{3}} e^{15} x -1728 \,2^{\frac {2 x}{3}} e^{15}+64 \,2^{2 x} e^{5} x -192 \,2^{2 x} e^{5}+16 e^{20} x^{4}-192 e^{20} x^{3}+864 e^{20} x^{2}-1728 e^{20} x +1296 e^{20}}{\mathrm {log}\left (x \right ) x^{4} \left (2^{\frac {8 x}{3}}+6 \,2^{\frac {4 x}{3}} e^{10} x^{2}-24 \,2^{\frac {4 x}{3}} e^{10} x +24 \,2^{\frac {4 x}{3}} e^{10}+4 \,2^{\frac {2 x}{3}} e^{15} x^{3}-24 \,2^{\frac {2 x}{3}} e^{15} x^{2}+48 \,2^{\frac {2 x}{3}} e^{15} x -32 \,2^{\frac {2 x}{3}} e^{15}+4 \,2^{2 x} e^{5} x -8 \,2^{2 x} e^{5}+e^{20} x^{4}-8 e^{20} x^{3}+24 e^{20} x^{2}-32 e^{20} x +16 e^{20}\right )} \] Input:

int(((-192*exp(2/3*x*log(2)-5)^5+(128*x*log(2)-960*x+2688)*exp(2/3*x*log(2 
)-5)^4+(2*(192*x^2-576*x)*log(2)-1920*x^2+10944*x-14976)*exp(2/3*x*log(2)- 
5)^3+(2*(192*x^3-1152*x^2+1728*x)*log(2)-1920*x^3+16704*x^2-46656*x+41472) 
*exp(2/3*x*log(2)-5)^2+(2*(64*x^4-576*x^3+1728*x^2-1728*x)*log(2)-960*x^4+ 
11328*x^3-48384*x^2+88128*x-57024)*exp(2/3*x*log(2)-5)-192*x^5+2880*x^4-16 
704*x^3+46656*x^2-62208*x+31104)*log(x)-48*exp(2/3*x*log(2)-5)^5+(-240*x+6 
72)*exp(2/3*x*log(2)-5)^4+(-480*x^2+2688*x-3744)*exp(2/3*x*log(2)-5)^3+(-4 
80*x^3+4032*x^2-11232*x+10368)*exp(2/3*x*log(2)-5)^2+(-240*x^4+2688*x^3-11 
232*x^2+20736*x-14256)*exp(2/3*x*log(2)-5)-48*x^5+672*x^4-3744*x^3+10368*x 
^2-14256*x+7776)/(3*x^5*exp(2/3*x*log(2)-5)^5+(15*x^6-30*x^5)*exp(2/3*x*lo 
g(2)-5)^4+(30*x^7-120*x^6+120*x^5)*exp(2/3*x*log(2)-5)^3+(30*x^8-180*x^7+3 
60*x^6-240*x^5)*exp(2/3*x*log(2)-5)^2+(15*x^9-120*x^8+360*x^7-480*x^6+240* 
x^5)*exp(2/3*x*log(2)-5)+3*x^10-30*x^9+120*x^8-240*x^7+240*x^6-96*x^5)/log 
(x)^2,x)
 

Output:

(16*(2**((8*x)/3) + 6*2**((4*x)/3)*e**10*x**2 - 36*2**((4*x)/3)*e**10*x + 
54*2**((4*x)/3)*e**10 + 4*2**((2*x)/3)*e**15*x**3 - 36*2**((2*x)/3)*e**15* 
x**2 + 108*2**((2*x)/3)*e**15*x - 108*2**((2*x)/3)*e**15 + 4*2**(2*x)*e**5 
*x - 12*2**(2*x)*e**5 + e**20*x**4 - 12*e**20*x**3 + 54*e**20*x**2 - 108*e 
**20*x + 81*e**20))/(log(x)*x**4*(2**((8*x)/3) + 6*2**((4*x)/3)*e**10*x**2 
 - 24*2**((4*x)/3)*e**10*x + 24*2**((4*x)/3)*e**10 + 4*2**((2*x)/3)*e**15* 
x**3 - 24*2**((2*x)/3)*e**15*x**2 + 48*2**((2*x)/3)*e**15*x - 32*2**((2*x) 
/3)*e**15 + 4*2**(2*x)*e**5*x - 8*2**(2*x)*e**5 + e**20*x**4 - 8*e**20*x** 
3 + 24*e**20*x**2 - 32*e**20*x + 16*e**20))