3.59.64 \(\int \frac {-54912-63380 x-37053 x^2-232575 x^3-256350 x^4-148575 x^5-51525 x^6-11400 x^7-1500 x^8-100 x^9+(-21970-25350 x-14820 x^2-93030 x^3-102540 x^4-59430 x^5-20610 x^6-4560 x^7-600 x^8-40 x^9) \log (2)+(-2197-2535 x-1482 x^2-9303 x^3-10254 x^4-5943 x^5-2061 x^6-456 x^7-60 x^8-4 x^9) \log ^2(2)+e^{3 x} (25+100 x^3+(10+40 x^3) \log (2)+(1+4 x^3) \log ^2(2))+e^{2 x} (-975-375 x-75 x^2-3900 x^3-1500 x^4-300 x^5+(-390-150 x-30 x^2-1560 x^3-600 x^4-120 x^5) \log (2)+(-39-15 x-3 x^2-156 x^3-60 x^4-12 x^5) \log ^2(2))+e^x (12674+9752 x+3825 x^2+51450 x^3+39075 x^4+15300 x^5+3000 x^6+300 x^7+(5070+3900 x+1530 x^2+20580 x^3+15630 x^4+6120 x^5+1200 x^6+120 x^7) \log (2)+(507+390 x+153 x^2+2058 x^3+1563 x^4+612 x^5+120 x^6+12 x^7) \log ^2(2))}{-54925-63375 x-37050 x^2-12875 x^3-2850 x^4-375 x^5-25 x^6+(-21970-25350 x-14820 x^2-5150 x^3-1140 x^4-150 x^5-10 x^6) \log (2)+(-2197-2535 x-1482 x^2-515 x^3-114 x^4-15 x^5-x^6) \log ^2(2)+e^{3 x} (25+10 \log (2)+\log ^2(2))+e^{2 x} (-975-375 x-75 x^2+(-390-150 x-30 x^2) \log (2)+(-39-15 x-3 x^2) \log ^2(2))+e^x (12675+9750 x+3825 x^2+750 x^3+75 x^4+(5070+3900 x+1530 x^2+300 x^3+30 x^4) \log (2)+(507+390 x+153 x^2+30 x^3+3 x^4) \log ^2(2))} \, dx\)

Optimal. Leaf size=29 \[ x+x^4-\frac {x}{\left (-4+e^x+x-(3+x)^2\right )^2 (5+\log (2))^2} \]

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Rubi [F]  time = 8.08, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {-54912-63380 x-37053 x^2-232575 x^3-256350 x^4-148575 x^5-51525 x^6-11400 x^7-1500 x^8-100 x^9+\left (-21970-25350 x-14820 x^2-93030 x^3-102540 x^4-59430 x^5-20610 x^6-4560 x^7-600 x^8-40 x^9\right ) \log (2)+\left (-2197-2535 x-1482 x^2-9303 x^3-10254 x^4-5943 x^5-2061 x^6-456 x^7-60 x^8-4 x^9\right ) \log ^2(2)+e^{3 x} \left (25+100 x^3+\left (10+40 x^3\right ) \log (2)+\left (1+4 x^3\right ) \log ^2(2)\right )+e^{2 x} \left (-975-375 x-75 x^2-3900 x^3-1500 x^4-300 x^5+\left (-390-150 x-30 x^2-1560 x^3-600 x^4-120 x^5\right ) \log (2)+\left (-39-15 x-3 x^2-156 x^3-60 x^4-12 x^5\right ) \log ^2(2)\right )+e^x \left (12674+9752 x+3825 x^2+51450 x^3+39075 x^4+15300 x^5+3000 x^6+300 x^7+\left (5070+3900 x+1530 x^2+20580 x^3+15630 x^4+6120 x^5+1200 x^6+120 x^7\right ) \log (2)+\left (507+390 x+153 x^2+2058 x^3+1563 x^4+612 x^5+120 x^6+12 x^7\right ) \log ^2(2)\right )}{-54925-63375 x-37050 x^2-12875 x^3-2850 x^4-375 x^5-25 x^6+\left (-21970-25350 x-14820 x^2-5150 x^3-1140 x^4-150 x^5-10 x^6\right ) \log (2)+\left (-2197-2535 x-1482 x^2-515 x^3-114 x^4-15 x^5-x^6\right ) \log ^2(2)+e^{3 x} \left (25+10 \log (2)+\log ^2(2)\right )+e^{2 x} \left (-975-375 x-75 x^2+\left (-390-150 x-30 x^2\right ) \log (2)+\left (-39-15 x-3 x^2\right ) \log ^2(2)\right )+e^x \left (12675+9750 x+3825 x^2+750 x^3+75 x^4+\left (5070+3900 x+1530 x^2+300 x^3+30 x^4\right ) \log (2)+\left (507+390 x+153 x^2+30 x^3+3 x^4\right ) \log ^2(2)\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-54912 - 63380*x - 37053*x^2 - 232575*x^3 - 256350*x^4 - 148575*x^5 - 51525*x^6 - 11400*x^7 - 1500*x^8 -
100*x^9 + (-21970 - 25350*x - 14820*x^2 - 93030*x^3 - 102540*x^4 - 59430*x^5 - 20610*x^6 - 4560*x^7 - 600*x^8
- 40*x^9)*Log[2] + (-2197 - 2535*x - 1482*x^2 - 9303*x^3 - 10254*x^4 - 5943*x^5 - 2061*x^6 - 456*x^7 - 60*x^8
- 4*x^9)*Log[2]^2 + E^(3*x)*(25 + 100*x^3 + (10 + 40*x^3)*Log[2] + (1 + 4*x^3)*Log[2]^2) + E^(2*x)*(-975 - 375
*x - 75*x^2 - 3900*x^3 - 1500*x^4 - 300*x^5 + (-390 - 150*x - 30*x^2 - 1560*x^3 - 600*x^4 - 120*x^5)*Log[2] +
(-39 - 15*x - 3*x^2 - 156*x^3 - 60*x^4 - 12*x^5)*Log[2]^2) + E^x*(12674 + 9752*x + 3825*x^2 + 51450*x^3 + 3907
5*x^4 + 15300*x^5 + 3000*x^6 + 300*x^7 + (5070 + 3900*x + 1530*x^2 + 20580*x^3 + 15630*x^4 + 6120*x^5 + 1200*x
^6 + 120*x^7)*Log[2] + (507 + 390*x + 153*x^2 + 2058*x^3 + 1563*x^4 + 612*x^5 + 120*x^6 + 12*x^7)*Log[2]^2))/(
-54925 - 63375*x - 37050*x^2 - 12875*x^3 - 2850*x^4 - 375*x^5 - 25*x^6 + (-21970 - 25350*x - 14820*x^2 - 5150*
x^3 - 1140*x^4 - 150*x^5 - 10*x^6)*Log[2] + (-2197 - 2535*x - 1482*x^2 - 515*x^3 - 114*x^4 - 15*x^5 - x^6)*Log
[2]^2 + E^(3*x)*(25 + 10*Log[2] + Log[2]^2) + E^(2*x)*(-975 - 375*x - 75*x^2 + (-390 - 150*x - 30*x^2)*Log[2]
+ (-39 - 15*x - 3*x^2)*Log[2]^2) + E^x*(12675 + 9750*x + 3825*x^2 + 750*x^3 + 75*x^4 + (5070 + 3900*x + 1530*x
^2 + 300*x^3 + 30*x^4)*Log[2] + (507 + 390*x + 153*x^2 + 30*x^3 + 3*x^4)*Log[2]^2)),x]

[Out]

x + x^4 - Defer[Int][(-13 + E^x - 5*x - x^2)^(-2), x]/(5 + Log[2])^2 - (16*Defer[Int][x/(13 - E^x + 5*x + x^2)
^3, x])/(5 + Log[2])^2 - (6*Defer[Int][x^2/(13 - E^x + 5*x + x^2)^3, x])/(5 + Log[2])^2 - (2*Defer[Int][x^3/(1
3 - E^x + 5*x + x^2)^3, x])/(5 + Log[2])^2 + (2*Defer[Int][x/(13 - E^x + 5*x + x^2)^2, x])/(5 + Log[2])^2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {9303 x^3 (5+\log (2))^2+10254 x^4 (5+\log (2))^2+5943 x^5 (5+\log (2))^2+2061 x^6 (5+\log (2))^2+456 x^7 (5+\log (2))^2+60 x^8 (5+\log (2))^2+4 x^9 (5+\log (2))^2-e^{3 x} \left (1+4 x^3\right ) (5+\log (2))^2+3 e^{2 x} \left (13+5 x+x^2+52 x^3+20 x^4+4 x^5\right ) (5+\log (2))^2+13 \left (4224+1690 \log (2)+169 \log ^2(2)\right )+3 x^2 \left (12351+4940 \log (2)+494 \log ^2(2)\right )+5 x \left (12676+5070 \log (2)+507 \log ^2(2)\right )-e^x \left (12674+5070 \log (2)+507 \log ^2(2)+153 x^2 (5+\log (2))^2+2058 x^3 (5+\log (2))^2+1563 x^4 (5+\log (2))^2+612 x^5 (5+\log (2))^2+120 x^6 (5+\log (2))^2+12 x^7 (5+\log (2))^2+x \left (9752+3900 \log (2)+390 \log ^2(2)\right )\right )}{\left (13-e^x+5 x+x^2\right )^3 (5+\log (2))^2} \, dx\\ &=\frac {\int \frac {9303 x^3 (5+\log (2))^2+10254 x^4 (5+\log (2))^2+5943 x^5 (5+\log (2))^2+2061 x^6 (5+\log (2))^2+456 x^7 (5+\log (2))^2+60 x^8 (5+\log (2))^2+4 x^9 (5+\log (2))^2-e^{3 x} \left (1+4 x^3\right ) (5+\log (2))^2+3 e^{2 x} \left (13+5 x+x^2+52 x^3+20 x^4+4 x^5\right ) (5+\log (2))^2+13 \left (4224+1690 \log (2)+169 \log ^2(2)\right )+3 x^2 \left (12351+4940 \log (2)+494 \log ^2(2)\right )+5 x \left (12676+5070 \log (2)+507 \log ^2(2)\right )-e^x \left (12674+5070 \log (2)+507 \log ^2(2)+153 x^2 (5+\log (2))^2+2058 x^3 (5+\log (2))^2+1563 x^4 (5+\log (2))^2+612 x^5 (5+\log (2))^2+120 x^6 (5+\log (2))^2+12 x^7 (5+\log (2))^2+x \left (9752+3900 \log (2)+390 \log ^2(2)\right )\right )}{\left (13-e^x+5 x+x^2\right )^3} \, dx}{(5+\log (2))^2}\\ &=\frac {\int \left (-\frac {2 x \left (8+3 x+x^2\right )}{\left (13-e^x+5 x+x^2\right )^3}+\frac {-1+2 x}{\left (13-e^x+5 x+x^2\right )^2}+\left (1+4 x^3\right ) (5+\log (2))^2\right ) \, dx}{(5+\log (2))^2}\\ &=\frac {\int \frac {-1+2 x}{\left (13-e^x+5 x+x^2\right )^2} \, dx}{(5+\log (2))^2}-\frac {2 \int \frac {x \left (8+3 x+x^2\right )}{\left (13-e^x+5 x+x^2\right )^3} \, dx}{(5+\log (2))^2}+\int \left (1+4 x^3\right ) \, dx\\ &=x+x^4+\frac {\int \left (-\frac {1}{\left (-13+e^x-5 x-x^2\right )^2}+\frac {2 x}{\left (13-e^x+5 x+x^2\right )^2}\right ) \, dx}{(5+\log (2))^2}-\frac {2 \int \left (\frac {8 x}{\left (13-e^x+5 x+x^2\right )^3}+\frac {3 x^2}{\left (13-e^x+5 x+x^2\right )^3}+\frac {x^3}{\left (13-e^x+5 x+x^2\right )^3}\right ) \, dx}{(5+\log (2))^2}\\ &=x+x^4-\frac {\int \frac {1}{\left (-13+e^x-5 x-x^2\right )^2} \, dx}{(5+\log (2))^2}-\frac {2 \int \frac {x^3}{\left (13-e^x+5 x+x^2\right )^3} \, dx}{(5+\log (2))^2}+\frac {2 \int \frac {x}{\left (13-e^x+5 x+x^2\right )^2} \, dx}{(5+\log (2))^2}-\frac {6 \int \frac {x^2}{\left (13-e^x+5 x+x^2\right )^3} \, dx}{(5+\log (2))^2}-\frac {16 \int \frac {x}{\left (13-e^x+5 x+x^2\right )^3} \, dx}{(5+\log (2))^2}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.26, size = 46, normalized size = 1.59 \begin {gather*} -\frac {\frac {x}{\left (-13+e^x-5 x-x^2\right )^2}-x (5+\log (2))^2-x^4 (5+\log (2))^2}{(5+\log (2))^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-54912 - 63380*x - 37053*x^2 - 232575*x^3 - 256350*x^4 - 148575*x^5 - 51525*x^6 - 11400*x^7 - 1500*
x^8 - 100*x^9 + (-21970 - 25350*x - 14820*x^2 - 93030*x^3 - 102540*x^4 - 59430*x^5 - 20610*x^6 - 4560*x^7 - 60
0*x^8 - 40*x^9)*Log[2] + (-2197 - 2535*x - 1482*x^2 - 9303*x^3 - 10254*x^4 - 5943*x^5 - 2061*x^6 - 456*x^7 - 6
0*x^8 - 4*x^9)*Log[2]^2 + E^(3*x)*(25 + 100*x^3 + (10 + 40*x^3)*Log[2] + (1 + 4*x^3)*Log[2]^2) + E^(2*x)*(-975
- 375*x - 75*x^2 - 3900*x^3 - 1500*x^4 - 300*x^5 + (-390 - 150*x - 30*x^2 - 1560*x^3 - 600*x^4 - 120*x^5)*Log
[2] + (-39 - 15*x - 3*x^2 - 156*x^3 - 60*x^4 - 12*x^5)*Log[2]^2) + E^x*(12674 + 9752*x + 3825*x^2 + 51450*x^3
+ 39075*x^4 + 15300*x^5 + 3000*x^6 + 300*x^7 + (5070 + 3900*x + 1530*x^2 + 20580*x^3 + 15630*x^4 + 6120*x^5 +
1200*x^6 + 120*x^7)*Log[2] + (507 + 390*x + 153*x^2 + 2058*x^3 + 1563*x^4 + 612*x^5 + 120*x^6 + 12*x^7)*Log[2]
^2))/(-54925 - 63375*x - 37050*x^2 - 12875*x^3 - 2850*x^4 - 375*x^5 - 25*x^6 + (-21970 - 25350*x - 14820*x^2 -
5150*x^3 - 1140*x^4 - 150*x^5 - 10*x^6)*Log[2] + (-2197 - 2535*x - 1482*x^2 - 515*x^3 - 114*x^4 - 15*x^5 - x^
6)*Log[2]^2 + E^(3*x)*(25 + 10*Log[2] + Log[2]^2) + E^(2*x)*(-975 - 375*x - 75*x^2 + (-390 - 150*x - 30*x^2)*L
og[2] + (-39 - 15*x - 3*x^2)*Log[2]^2) + E^x*(12675 + 9750*x + 3825*x^2 + 750*x^3 + 75*x^4 + (5070 + 3900*x +
1530*x^2 + 300*x^3 + 30*x^4)*Log[2] + (507 + 390*x + 153*x^2 + 30*x^3 + 3*x^4)*Log[2]^2)),x]

[Out]

-((x/(-13 + E^x - 5*x - x^2)^2 - x*(5 + Log[2])^2 - x^4*(5 + Log[2])^2)/(5 + Log[2])^2)

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fricas [B]  time = 0.68, size = 369, normalized size = 12.72 \begin {gather*} \frac {25 \, x^{8} + 250 \, x^{7} + 1275 \, x^{6} + 3275 \, x^{5} + 4475 \, x^{4} + 1275 \, x^{3} + {\left (x^{8} + 10 \, x^{7} + 51 \, x^{6} + 131 \, x^{5} + 179 \, x^{4} + 51 \, x^{3} + 130 \, x^{2} + 169 \, x\right )} \log \relax (2)^{2} + 3250 \, x^{2} + {\left (25 \, x^{4} + {\left (x^{4} + x\right )} \log \relax (2)^{2} + 10 \, {\left (x^{4} + x\right )} \log \relax (2) + 25 \, x\right )} e^{\left (2 \, x\right )} - 2 \, {\left (25 \, x^{6} + 125 \, x^{5} + 325 \, x^{4} + 25 \, x^{3} + {\left (x^{6} + 5 \, x^{5} + 13 \, x^{4} + x^{3} + 5 \, x^{2} + 13 \, x\right )} \log \relax (2)^{2} + 125 \, x^{2} + 10 \, {\left (x^{6} + 5 \, x^{5} + 13 \, x^{4} + x^{3} + 5 \, x^{2} + 13 \, x\right )} \log \relax (2) + 325 \, x\right )} e^{x} + 10 \, {\left (x^{8} + 10 \, x^{7} + 51 \, x^{6} + 131 \, x^{5} + 179 \, x^{4} + 51 \, x^{3} + 130 \, x^{2} + 169 \, x\right )} \log \relax (2) + 4224 \, x}{25 \, x^{4} + 250 \, x^{3} + {\left (x^{4} + 10 \, x^{3} + 51 \, x^{2} + 130 \, x + 169\right )} \log \relax (2)^{2} + 1275 \, x^{2} + {\left (\log \relax (2)^{2} + 10 \, \log \relax (2) + 25\right )} e^{\left (2 \, x\right )} - 2 \, {\left ({\left (x^{2} + 5 \, x + 13\right )} \log \relax (2)^{2} + 25 \, x^{2} + 10 \, {\left (x^{2} + 5 \, x + 13\right )} \log \relax (2) + 125 \, x + 325\right )} e^{x} + 10 \, {\left (x^{4} + 10 \, x^{3} + 51 \, x^{2} + 130 \, x + 169\right )} \log \relax (2) + 3250 \, x + 4225} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^3+1)*log(2)^2+(40*x^3+10)*log(2)+100*x^3+25)*exp(x)^3+((-12*x^5-60*x^4-156*x^3-3*x^2-15*x-39)
*log(2)^2+(-120*x^5-600*x^4-1560*x^3-30*x^2-150*x-390)*log(2)-300*x^5-1500*x^4-3900*x^3-75*x^2-375*x-975)*exp(
x)^2+((12*x^7+120*x^6+612*x^5+1563*x^4+2058*x^3+153*x^2+390*x+507)*log(2)^2+(120*x^7+1200*x^6+6120*x^5+15630*x
^4+20580*x^3+1530*x^2+3900*x+5070)*log(2)+300*x^7+3000*x^6+15300*x^5+39075*x^4+51450*x^3+3825*x^2+9752*x+12674
)*exp(x)+(-4*x^9-60*x^8-456*x^7-2061*x^6-5943*x^5-10254*x^4-9303*x^3-1482*x^2-2535*x-2197)*log(2)^2+(-40*x^9-6
00*x^8-4560*x^7-20610*x^6-59430*x^5-102540*x^4-93030*x^3-14820*x^2-25350*x-21970)*log(2)-100*x^9-1500*x^8-1140
0*x^7-51525*x^6-148575*x^5-256350*x^4-232575*x^3-37053*x^2-63380*x-54912)/((log(2)^2+10*log(2)+25)*exp(x)^3+((
-3*x^2-15*x-39)*log(2)^2+(-30*x^2-150*x-390)*log(2)-75*x^2-375*x-975)*exp(x)^2+((3*x^4+30*x^3+153*x^2+390*x+50
7)*log(2)^2+(30*x^4+300*x^3+1530*x^2+3900*x+5070)*log(2)+75*x^4+750*x^3+3825*x^2+9750*x+12675)*exp(x)+(-x^6-15
*x^5-114*x^4-515*x^3-1482*x^2-2535*x-2197)*log(2)^2+(-10*x^6-150*x^5-1140*x^4-5150*x^3-14820*x^2-25350*x-21970
)*log(2)-25*x^6-375*x^5-2850*x^4-12875*x^3-37050*x^2-63375*x-54925),x, algorithm="fricas")

[Out]

(25*x^8 + 250*x^7 + 1275*x^6 + 3275*x^5 + 4475*x^4 + 1275*x^3 + (x^8 + 10*x^7 + 51*x^6 + 131*x^5 + 179*x^4 + 5
1*x^3 + 130*x^2 + 169*x)*log(2)^2 + 3250*x^2 + (25*x^4 + (x^4 + x)*log(2)^2 + 10*(x^4 + x)*log(2) + 25*x)*e^(2
*x) - 2*(25*x^6 + 125*x^5 + 325*x^4 + 25*x^3 + (x^6 + 5*x^5 + 13*x^4 + x^3 + 5*x^2 + 13*x)*log(2)^2 + 125*x^2
+ 10*(x^6 + 5*x^5 + 13*x^4 + x^3 + 5*x^2 + 13*x)*log(2) + 325*x)*e^x + 10*(x^8 + 10*x^7 + 51*x^6 + 131*x^5 + 1
79*x^4 + 51*x^3 + 130*x^2 + 169*x)*log(2) + 4224*x)/(25*x^4 + 250*x^3 + (x^4 + 10*x^3 + 51*x^2 + 130*x + 169)*
log(2)^2 + 1275*x^2 + (log(2)^2 + 10*log(2) + 25)*e^(2*x) - 2*((x^2 + 5*x + 13)*log(2)^2 + 25*x^2 + 10*(x^2 +
5*x + 13)*log(2) + 125*x + 325)*e^x + 10*(x^4 + 10*x^3 + 51*x^2 + 130*x + 169)*log(2) + 3250*x + 4225)

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giac [B]  time = 0.52, size = 557, normalized size = 19.21 \begin {gather*} \frac {x^{8} \log \relax (2)^{2} + 10 \, x^{8} \log \relax (2) + 10 \, x^{7} \log \relax (2)^{2} - 2 \, x^{6} e^{x} \log \relax (2)^{2} + 25 \, x^{8} + 100 \, x^{7} \log \relax (2) - 20 \, x^{6} e^{x} \log \relax (2) + 51 \, x^{6} \log \relax (2)^{2} - 10 \, x^{5} e^{x} \log \relax (2)^{2} + 250 \, x^{7} - 50 \, x^{6} e^{x} + 510 \, x^{6} \log \relax (2) - 100 \, x^{5} e^{x} \log \relax (2) + 131 \, x^{5} \log \relax (2)^{2} + x^{4} e^{\left (2 \, x\right )} \log \relax (2)^{2} - 26 \, x^{4} e^{x} \log \relax (2)^{2} + 1275 \, x^{6} - 250 \, x^{5} e^{x} + 1310 \, x^{5} \log \relax (2) + 10 \, x^{4} e^{\left (2 \, x\right )} \log \relax (2) - 260 \, x^{4} e^{x} \log \relax (2) + 179 \, x^{4} \log \relax (2)^{2} - 2 \, x^{3} e^{x} \log \relax (2)^{2} + 3275 \, x^{5} + 25 \, x^{4} e^{\left (2 \, x\right )} - 650 \, x^{4} e^{x} + 1790 \, x^{4} \log \relax (2) - 20 \, x^{3} e^{x} \log \relax (2) + 51 \, x^{3} \log \relax (2)^{2} - 10 \, x^{2} e^{x} \log \relax (2)^{2} + 4475 \, x^{4} - 50 \, x^{3} e^{x} + 510 \, x^{3} \log \relax (2) - 100 \, x^{2} e^{x} \log \relax (2) + 130 \, x^{2} \log \relax (2)^{2} + x e^{\left (2 \, x\right )} \log \relax (2)^{2} - 26 \, x e^{x} \log \relax (2)^{2} + 1275 \, x^{3} - 250 \, x^{2} e^{x} + 1300 \, x^{2} \log \relax (2) + 10 \, x e^{\left (2 \, x\right )} \log \relax (2) - 260 \, x e^{x} \log \relax (2) + 169 \, x \log \relax (2)^{2} + 3250 \, x^{2} + 25 \, x e^{\left (2 \, x\right )} - 650 \, x e^{x} + 1690 \, x \log \relax (2) + 4224 \, x}{x^{4} \log \relax (2)^{2} + 10 \, x^{4} \log \relax (2) + 10 \, x^{3} \log \relax (2)^{2} - 2 \, x^{2} e^{x} \log \relax (2)^{2} + 25 \, x^{4} + 100 \, x^{3} \log \relax (2) - 20 \, x^{2} e^{x} \log \relax (2) + 51 \, x^{2} \log \relax (2)^{2} - 10 \, x e^{x} \log \relax (2)^{2} + 250 \, x^{3} - 50 \, x^{2} e^{x} + 510 \, x^{2} \log \relax (2) - 100 \, x e^{x} \log \relax (2) + 130 \, x \log \relax (2)^{2} + e^{\left (2 \, x\right )} \log \relax (2)^{2} - 26 \, e^{x} \log \relax (2)^{2} + 1275 \, x^{2} - 250 \, x e^{x} + 1300 \, x \log \relax (2) + 10 \, e^{\left (2 \, x\right )} \log \relax (2) - 260 \, e^{x} \log \relax (2) + 169 \, \log \relax (2)^{2} + 3250 \, x + 25 \, e^{\left (2 \, x\right )} - 650 \, e^{x} + 1690 \, \log \relax (2) + 4225} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^3+1)*log(2)^2+(40*x^3+10)*log(2)+100*x^3+25)*exp(x)^3+((-12*x^5-60*x^4-156*x^3-3*x^2-15*x-39)
*log(2)^2+(-120*x^5-600*x^4-1560*x^3-30*x^2-150*x-390)*log(2)-300*x^5-1500*x^4-3900*x^3-75*x^2-375*x-975)*exp(
x)^2+((12*x^7+120*x^6+612*x^5+1563*x^4+2058*x^3+153*x^2+390*x+507)*log(2)^2+(120*x^7+1200*x^6+6120*x^5+15630*x
^4+20580*x^3+1530*x^2+3900*x+5070)*log(2)+300*x^7+3000*x^6+15300*x^5+39075*x^4+51450*x^3+3825*x^2+9752*x+12674
)*exp(x)+(-4*x^9-60*x^8-456*x^7-2061*x^6-5943*x^5-10254*x^4-9303*x^3-1482*x^2-2535*x-2197)*log(2)^2+(-40*x^9-6
00*x^8-4560*x^7-20610*x^6-59430*x^5-102540*x^4-93030*x^3-14820*x^2-25350*x-21970)*log(2)-100*x^9-1500*x^8-1140
0*x^7-51525*x^6-148575*x^5-256350*x^4-232575*x^3-37053*x^2-63380*x-54912)/((log(2)^2+10*log(2)+25)*exp(x)^3+((
-3*x^2-15*x-39)*log(2)^2+(-30*x^2-150*x-390)*log(2)-75*x^2-375*x-975)*exp(x)^2+((3*x^4+30*x^3+153*x^2+390*x+50
7)*log(2)^2+(30*x^4+300*x^3+1530*x^2+3900*x+5070)*log(2)+75*x^4+750*x^3+3825*x^2+9750*x+12675)*exp(x)+(-x^6-15
*x^5-114*x^4-515*x^3-1482*x^2-2535*x-2197)*log(2)^2+(-10*x^6-150*x^5-1140*x^4-5150*x^3-14820*x^2-25350*x-21970
)*log(2)-25*x^6-375*x^5-2850*x^4-12875*x^3-37050*x^2-63375*x-54925),x, algorithm="giac")

[Out]

(x^8*log(2)^2 + 10*x^8*log(2) + 10*x^7*log(2)^2 - 2*x^6*e^x*log(2)^2 + 25*x^8 + 100*x^7*log(2) - 20*x^6*e^x*lo
g(2) + 51*x^6*log(2)^2 - 10*x^5*e^x*log(2)^2 + 250*x^7 - 50*x^6*e^x + 510*x^6*log(2) - 100*x^5*e^x*log(2) + 13
1*x^5*log(2)^2 + x^4*e^(2*x)*log(2)^2 - 26*x^4*e^x*log(2)^2 + 1275*x^6 - 250*x^5*e^x + 1310*x^5*log(2) + 10*x^
4*e^(2*x)*log(2) - 260*x^4*e^x*log(2) + 179*x^4*log(2)^2 - 2*x^3*e^x*log(2)^2 + 3275*x^5 + 25*x^4*e^(2*x) - 65
0*x^4*e^x + 1790*x^4*log(2) - 20*x^3*e^x*log(2) + 51*x^3*log(2)^2 - 10*x^2*e^x*log(2)^2 + 4475*x^4 - 50*x^3*e^
x + 510*x^3*log(2) - 100*x^2*e^x*log(2) + 130*x^2*log(2)^2 + x*e^(2*x)*log(2)^2 - 26*x*e^x*log(2)^2 + 1275*x^3
- 250*x^2*e^x + 1300*x^2*log(2) + 10*x*e^(2*x)*log(2) - 260*x*e^x*log(2) + 169*x*log(2)^2 + 3250*x^2 + 25*x*e
^(2*x) - 650*x*e^x + 1690*x*log(2) + 4224*x)/(x^4*log(2)^2 + 10*x^4*log(2) + 10*x^3*log(2)^2 - 2*x^2*e^x*log(2
)^2 + 25*x^4 + 100*x^3*log(2) - 20*x^2*e^x*log(2) + 51*x^2*log(2)^2 - 10*x*e^x*log(2)^2 + 250*x^3 - 50*x^2*e^x
+ 510*x^2*log(2) - 100*x*e^x*log(2) + 130*x*log(2)^2 + e^(2*x)*log(2)^2 - 26*e^x*log(2)^2 + 1275*x^2 - 250*x*
e^x + 1300*x*log(2) + 10*e^(2*x)*log(2) - 260*e^x*log(2) + 169*log(2)^2 + 3250*x + 25*e^(2*x) - 650*e^x + 1690
*log(2) + 4225)

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maple [A]  time = 0.71, size = 35, normalized size = 1.21

method	result	size
risch	\(x^{4}+x -\frac {x}{\left (\ln \relax (2)^{2}+10 \ln \relax (2)+25\right ) \left (x^{2}+5 x -{\mathrm e}^{x}+13\right )^{2}}\)	\(35\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((4*x^3+1)*ln(2)^2+(40*x^3+10)*ln(2)+100*x^3+25)*exp(x)^3+((-12*x^5-60*x^4-156*x^3-3*x^2-15*x-39)*ln(2)^2
+(-120*x^5-600*x^4-1560*x^3-30*x^2-150*x-390)*ln(2)-300*x^5-1500*x^4-3900*x^3-75*x^2-375*x-975)*exp(x)^2+((12*
x^7+120*x^6+612*x^5+1563*x^4+2058*x^3+153*x^2+390*x+507)*ln(2)^2+(120*x^7+1200*x^6+6120*x^5+15630*x^4+20580*x^
3+1530*x^2+3900*x+5070)*ln(2)+300*x^7+3000*x^6+15300*x^5+39075*x^4+51450*x^3+3825*x^2+9752*x+12674)*exp(x)+(-4
*x^9-60*x^8-456*x^7-2061*x^6-5943*x^5-10254*x^4-9303*x^3-1482*x^2-2535*x-2197)*ln(2)^2+(-40*x^9-600*x^8-4560*x
^7-20610*x^6-59430*x^5-102540*x^4-93030*x^3-14820*x^2-25350*x-21970)*ln(2)-100*x^9-1500*x^8-11400*x^7-51525*x^
6-148575*x^5-256350*x^4-232575*x^3-37053*x^2-63380*x-54912)/((ln(2)^2+10*ln(2)+25)*exp(x)^3+((-3*x^2-15*x-39)*
ln(2)^2+(-30*x^2-150*x-390)*ln(2)-75*x^2-375*x-975)*exp(x)^2+((3*x^4+30*x^3+153*x^2+390*x+507)*ln(2)^2+(30*x^4
+300*x^3+1530*x^2+3900*x+5070)*ln(2)+75*x^4+750*x^3+3825*x^2+9750*x+12675)*exp(x)+(-x^6-15*x^5-114*x^4-515*x^3
-1482*x^2-2535*x-2197)*ln(2)^2+(-10*x^6-150*x^5-1140*x^4-5150*x^3-14820*x^2-25350*x-21970)*ln(2)-25*x^6-375*x^
5-2850*x^4-12875*x^3-37050*x^2-63375*x-54925),x,method=_RETURNVERBOSE)

[Out]

x^4+x-x/(ln(2)^2+10*ln(2)+25)/(x^2+5*x-exp(x)+13)^2

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maxima [B]  time = 1.17, size = 372, normalized size = 12.83 \begin {gather*} \frac {{\left (\log \relax (2)^{2} + 10 \, \log \relax (2) + 25\right )} x^{8} + 10 \, {\left (\log \relax (2)^{2} + 10 \, \log \relax (2) + 25\right )} x^{7} + 51 \, {\left (\log \relax (2)^{2} + 10 \, \log \relax (2) + 25\right )} x^{6} + 131 \, {\left (\log \relax (2)^{2} + 10 \, \log \relax (2) + 25\right )} x^{5} + 179 \, {\left (\log \relax (2)^{2} + 10 \, \log \relax (2) + 25\right )} x^{4} + 51 \, {\left (\log \relax (2)^{2} + 10 \, \log \relax (2) + 25\right )} x^{3} + 130 \, {\left (\log \relax (2)^{2} + 10 \, \log \relax (2) + 25\right )} x^{2} + {\left (169 \, \log \relax (2)^{2} + 1690 \, \log \relax (2) + 4224\right )} x + {\left ({\left (\log \relax (2)^{2} + 10 \, \log \relax (2) + 25\right )} x^{4} + {\left (\log \relax (2)^{2} + 10 \, \log \relax (2) + 25\right )} x\right )} e^{\left (2 \, x\right )} - 2 \, {\left ({\left (\log \relax (2)^{2} + 10 \, \log \relax (2) + 25\right )} x^{6} + 5 \, {\left (\log \relax (2)^{2} + 10 \, \log \relax (2) + 25\right )} x^{5} + 13 \, {\left (\log \relax (2)^{2} + 10 \, \log \relax (2) + 25\right )} x^{4} + {\left (\log \relax (2)^{2} + 10 \, \log \relax (2) + 25\right )} x^{3} + 5 \, {\left (\log \relax (2)^{2} + 10 \, \log \relax (2) + 25\right )} x^{2} + 13 \, {\left (\log \relax (2)^{2} + 10 \, \log \relax (2) + 25\right )} x\right )} e^{x}}{{\left (\log \relax (2)^{2} + 10 \, \log \relax (2) + 25\right )} x^{4} + 10 \, {\left (\log \relax (2)^{2} + 10 \, \log \relax (2) + 25\right )} x^{3} + 51 \, {\left (\log \relax (2)^{2} + 10 \, \log \relax (2) + 25\right )} x^{2} + 130 \, {\left (\log \relax (2)^{2} + 10 \, \log \relax (2) + 25\right )} x + {\left (\log \relax (2)^{2} + 10 \, \log \relax (2) + 25\right )} e^{\left (2 \, x\right )} - 2 \, {\left ({\left (\log \relax (2)^{2} + 10 \, \log \relax (2) + 25\right )} x^{2} + 5 \, {\left (\log \relax (2)^{2} + 10 \, \log \relax (2) + 25\right )} x + 13 \, \log \relax (2)^{2} + 130 \, \log \relax (2) + 325\right )} e^{x} + 169 \, \log \relax (2)^{2} + 1690 \, \log \relax (2) + 4225} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x^3+1)*log(2)^2+(40*x^3+10)*log(2)+100*x^3+25)*exp(x)^3+((-12*x^5-60*x^4-156*x^3-3*x^2-15*x-39)
*log(2)^2+(-120*x^5-600*x^4-1560*x^3-30*x^2-150*x-390)*log(2)-300*x^5-1500*x^4-3900*x^3-75*x^2-375*x-975)*exp(
x)^2+((12*x^7+120*x^6+612*x^5+1563*x^4+2058*x^3+153*x^2+390*x+507)*log(2)^2+(120*x^7+1200*x^6+6120*x^5+15630*x
^4+20580*x^3+1530*x^2+3900*x+5070)*log(2)+300*x^7+3000*x^6+15300*x^5+39075*x^4+51450*x^3+3825*x^2+9752*x+12674
)*exp(x)+(-4*x^9-60*x^8-456*x^7-2061*x^6-5943*x^5-10254*x^4-9303*x^3-1482*x^2-2535*x-2197)*log(2)^2+(-40*x^9-6
00*x^8-4560*x^7-20610*x^6-59430*x^5-102540*x^4-93030*x^3-14820*x^2-25350*x-21970)*log(2)-100*x^9-1500*x^8-1140
0*x^7-51525*x^6-148575*x^5-256350*x^4-232575*x^3-37053*x^2-63380*x-54912)/((log(2)^2+10*log(2)+25)*exp(x)^3+((
-3*x^2-15*x-39)*log(2)^2+(-30*x^2-150*x-390)*log(2)-75*x^2-375*x-975)*exp(x)^2+((3*x^4+30*x^3+153*x^2+390*x+50
7)*log(2)^2+(30*x^4+300*x^3+1530*x^2+3900*x+5070)*log(2)+75*x^4+750*x^3+3825*x^2+9750*x+12675)*exp(x)+(-x^6-15
*x^5-114*x^4-515*x^3-1482*x^2-2535*x-2197)*log(2)^2+(-10*x^6-150*x^5-1140*x^4-5150*x^3-14820*x^2-25350*x-21970
)*log(2)-25*x^6-375*x^5-2850*x^4-12875*x^3-37050*x^2-63375*x-54925),x, algorithm="maxima")

[Out]

((log(2)^2 + 10*log(2) + 25)*x^8 + 10*(log(2)^2 + 10*log(2) + 25)*x^7 + 51*(log(2)^2 + 10*log(2) + 25)*x^6 + 1
31*(log(2)^2 + 10*log(2) + 25)*x^5 + 179*(log(2)^2 + 10*log(2) + 25)*x^4 + 51*(log(2)^2 + 10*log(2) + 25)*x^3
+ 130*(log(2)^2 + 10*log(2) + 25)*x^2 + (169*log(2)^2 + 1690*log(2) + 4224)*x + ((log(2)^2 + 10*log(2) + 25)*x
^4 + (log(2)^2 + 10*log(2) + 25)*x)*e^(2*x) - 2*((log(2)^2 + 10*log(2) + 25)*x^6 + 5*(log(2)^2 + 10*log(2) + 2
5)*x^5 + 13*(log(2)^2 + 10*log(2) + 25)*x^4 + (log(2)^2 + 10*log(2) + 25)*x^3 + 5*(log(2)^2 + 10*log(2) + 25)*
x^2 + 13*(log(2)^2 + 10*log(2) + 25)*x)*e^x)/((log(2)^2 + 10*log(2) + 25)*x^4 + 10*(log(2)^2 + 10*log(2) + 25)
*x^3 + 51*(log(2)^2 + 10*log(2) + 25)*x^2 + 130*(log(2)^2 + 10*log(2) + 25)*x + (log(2)^2 + 10*log(2) + 25)*e^
(2*x) - 2*((log(2)^2 + 10*log(2) + 25)*x^2 + 5*(log(2)^2 + 10*log(2) + 25)*x + 13*log(2)^2 + 130*log(2) + 325)
*e^x + 169*log(2)^2 + 1690*log(2) + 4225)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {63380\,x+{\ln \relax (2)}^2\,\left (4\,x^9+60\,x^8+456\,x^7+2061\,x^6+5943\,x^5+10254\,x^4+9303\,x^3+1482\,x^2+2535\,x+2197\right )-{\mathrm {e}}^{3\,x}\,\left (\ln \relax (2)\,\left (40\,x^3+10\right )+{\ln \relax (2)}^2\,\left (4\,x^3+1\right )+100\,x^3+25\right )-{\mathrm {e}}^x\,\left (9752\,x+\ln \relax (2)\,\left (120\,x^7+1200\,x^6+6120\,x^5+15630\,x^4+20580\,x^3+1530\,x^2+3900\,x+5070\right )+{\ln \relax (2)}^2\,\left (12\,x^7+120\,x^6+612\,x^5+1563\,x^4+2058\,x^3+153\,x^2+390\,x+507\right )+3825\,x^2+51450\,x^3+39075\,x^4+15300\,x^5+3000\,x^6+300\,x^7+12674\right )+\ln \relax (2)\,\left (40\,x^9+600\,x^8+4560\,x^7+20610\,x^6+59430\,x^5+102540\,x^4+93030\,x^3+14820\,x^2+25350\,x+21970\right )+{\mathrm {e}}^{2\,x}\,\left (375\,x+{\ln \relax (2)}^2\,\left (12\,x^5+60\,x^4+156\,x^3+3\,x^2+15\,x+39\right )+75\,x^2+3900\,x^3+1500\,x^4+300\,x^5+\ln \relax (2)\,\left (120\,x^5+600\,x^4+1560\,x^3+30\,x^2+150\,x+390\right )+975\right )+37053\,x^2+232575\,x^3+256350\,x^4+148575\,x^5+51525\,x^6+11400\,x^7+1500\,x^8+100\,x^9+54912}{63375\,x+\ln \relax (2)\,\left (10\,x^6+150\,x^5+1140\,x^4+5150\,x^3+14820\,x^2+25350\,x+21970\right )+{\ln \relax (2)}^2\,\left (x^6+15\,x^5+114\,x^4+515\,x^3+1482\,x^2+2535\,x+2197\right )-{\mathrm {e}}^{3\,x}\,\left (10\,\ln \relax (2)+{\ln \relax (2)}^2+25\right )-{\mathrm {e}}^x\,\left (9750\,x+{\ln \relax (2)}^2\,\left (3\,x^4+30\,x^3+153\,x^2+390\,x+507\right )+\ln \relax (2)\,\left (30\,x^4+300\,x^3+1530\,x^2+3900\,x+5070\right )+3825\,x^2+750\,x^3+75\,x^4+12675\right )+37050\,x^2+12875\,x^3+2850\,x^4+375\,x^5+25\,x^6+{\mathrm {e}}^{2\,x}\,\left (375\,x+\ln \relax (2)\,\left (30\,x^2+150\,x+390\right )+{\ln \relax (2)}^2\,\left (3\,x^2+15\,x+39\right )+75\,x^2+975\right )+54925} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((63380*x + log(2)^2*(2535*x + 1482*x^2 + 9303*x^3 + 10254*x^4 + 5943*x^5 + 2061*x^6 + 456*x^7 + 60*x^8 + 4
*x^9 + 2197) - exp(3*x)*(log(2)*(40*x^3 + 10) + log(2)^2*(4*x^3 + 1) + 100*x^3 + 25) - exp(x)*(9752*x + log(2)
*(3900*x + 1530*x^2 + 20580*x^3 + 15630*x^4 + 6120*x^5 + 1200*x^6 + 120*x^7 + 5070) + log(2)^2*(390*x + 153*x^
2 + 2058*x^3 + 1563*x^4 + 612*x^5 + 120*x^6 + 12*x^7 + 507) + 3825*x^2 + 51450*x^3 + 39075*x^4 + 15300*x^5 + 3
000*x^6 + 300*x^7 + 12674) + log(2)*(25350*x + 14820*x^2 + 93030*x^3 + 102540*x^4 + 59430*x^5 + 20610*x^6 + 45
60*x^7 + 600*x^8 + 40*x^9 + 21970) + exp(2*x)*(375*x + log(2)^2*(15*x + 3*x^2 + 156*x^3 + 60*x^4 + 12*x^5 + 39
) + 75*x^2 + 3900*x^3 + 1500*x^4 + 300*x^5 + log(2)*(150*x + 30*x^2 + 1560*x^3 + 600*x^4 + 120*x^5 + 390) + 97
5) + 37053*x^2 + 232575*x^3 + 256350*x^4 + 148575*x^5 + 51525*x^6 + 11400*x^7 + 1500*x^8 + 100*x^9 + 54912)/(6
3375*x + log(2)*(25350*x + 14820*x^2 + 5150*x^3 + 1140*x^4 + 150*x^5 + 10*x^6 + 21970) + log(2)^2*(2535*x + 14
82*x^2 + 515*x^3 + 114*x^4 + 15*x^5 + x^6 + 2197) - exp(3*x)*(10*log(2) + log(2)^2 + 25) - exp(x)*(9750*x + lo
g(2)^2*(390*x + 153*x^2 + 30*x^3 + 3*x^4 + 507) + log(2)*(3900*x + 1530*x^2 + 300*x^3 + 30*x^4 + 5070) + 3825*
x^2 + 750*x^3 + 75*x^4 + 12675) + 37050*x^2 + 12875*x^3 + 2850*x^4 + 375*x^5 + 25*x^6 + exp(2*x)*(375*x + log(
2)*(150*x + 30*x^2 + 390) + log(2)^2*(15*x + 3*x^2 + 39) + 75*x^2 + 975) + 54925),x)

[Out]

int((63380*x + log(2)^2*(2535*x + 1482*x^2 + 9303*x^3 + 10254*x^4 + 5943*x^5 + 2061*x^6 + 456*x^7 + 60*x^8 + 4
*x^9 + 2197) - exp(3*x)*(log(2)*(40*x^3 + 10) + log(2)^2*(4*x^3 + 1) + 100*x^3 + 25) - exp(x)*(9752*x + log(2)
*(3900*x + 1530*x^2 + 20580*x^3 + 15630*x^4 + 6120*x^5 + 1200*x^6 + 120*x^7 + 5070) + log(2)^2*(390*x + 153*x^
2 + 2058*x^3 + 1563*x^4 + 612*x^5 + 120*x^6 + 12*x^7 + 507) + 3825*x^2 + 51450*x^3 + 39075*x^4 + 15300*x^5 + 3
000*x^6 + 300*x^7 + 12674) + log(2)*(25350*x + 14820*x^2 + 93030*x^3 + 102540*x^4 + 59430*x^5 + 20610*x^6 + 45
60*x^7 + 600*x^8 + 40*x^9 + 21970) + exp(2*x)*(375*x + log(2)^2*(15*x + 3*x^2 + 156*x^3 + 60*x^4 + 12*x^5 + 39
) + 75*x^2 + 3900*x^3 + 1500*x^4 + 300*x^5 + log(2)*(150*x + 30*x^2 + 1560*x^3 + 600*x^4 + 120*x^5 + 390) + 97
5) + 37053*x^2 + 232575*x^3 + 256350*x^4 + 148575*x^5 + 51525*x^6 + 11400*x^7 + 1500*x^8 + 100*x^9 + 54912)/(6
3375*x + log(2)*(25350*x + 14820*x^2 + 5150*x^3 + 1140*x^4 + 150*x^5 + 10*x^6 + 21970) + log(2)^2*(2535*x + 14
82*x^2 + 515*x^3 + 114*x^4 + 15*x^5 + x^6 + 2197) - exp(3*x)*(10*log(2) + log(2)^2 + 25) - exp(x)*(9750*x + lo
g(2)^2*(390*x + 153*x^2 + 30*x^3 + 3*x^4 + 507) + log(2)*(3900*x + 1530*x^2 + 300*x^3 + 30*x^4 + 5070) + 3825*
x^2 + 750*x^3 + 75*x^4 + 12675) + 37050*x^2 + 12875*x^3 + 2850*x^4 + 375*x^5 + 25*x^6 + exp(2*x)*(375*x + log(
2)*(150*x + 30*x^2 + 390) + log(2)^2*(15*x + 3*x^2 + 39) + 75*x^2 + 975) + 54925), x)

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sympy [B]  time = 0.85, size = 185, normalized size = 6.38 \begin {gather*} x^{4} + x - \frac {x}{x^{4} \log {\relax (2 )}^{2} + 10 x^{4} \log {\relax (2 )} + 25 x^{4} + 10 x^{3} \log {\relax (2 )}^{2} + 100 x^{3} \log {\relax (2 )} + 250 x^{3} + 51 x^{2} \log {\relax (2 )}^{2} + 510 x^{2} \log {\relax (2 )} + 1275 x^{2} + 130 x \log {\relax (2 )}^{2} + 1300 x \log {\relax (2 )} + 3250 x + \left (- 50 x^{2} - 20 x^{2} \log {\relax (2 )} - 2 x^{2} \log {\relax (2 )}^{2} - 250 x - 100 x \log {\relax (2 )} - 10 x \log {\relax (2 )}^{2} - 650 - 260 \log {\relax (2 )} - 26 \log {\relax (2 )}^{2}\right ) e^{x} + \left (\log {\relax (2 )}^{2} + 10 \log {\relax (2 )} + 25\right ) e^{2 x} + 169 \log {\relax (2 )}^{2} + 1690 \log {\relax (2 )} + 4225} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((4*x**3+1)*ln(2)**2+(40*x**3+10)*ln(2)+100*x**3+25)*exp(x)**3+((-12*x**5-60*x**4-156*x**3-3*x**2-1
5*x-39)*ln(2)**2+(-120*x**5-600*x**4-1560*x**3-30*x**2-150*x-390)*ln(2)-300*x**5-1500*x**4-3900*x**3-75*x**2-3
75*x-975)*exp(x)**2+((12*x**7+120*x**6+612*x**5+1563*x**4+2058*x**3+153*x**2+390*x+507)*ln(2)**2+(120*x**7+120
0*x**6+6120*x**5+15630*x**4+20580*x**3+1530*x**2+3900*x+5070)*ln(2)+300*x**7+3000*x**6+15300*x**5+39075*x**4+5
1450*x**3+3825*x**2+9752*x+12674)*exp(x)+(-4*x**9-60*x**8-456*x**7-2061*x**6-5943*x**5-10254*x**4-9303*x**3-14
82*x**2-2535*x-2197)*ln(2)**2+(-40*x**9-600*x**8-4560*x**7-20610*x**6-59430*x**5-102540*x**4-93030*x**3-14820*
x**2-25350*x-21970)*ln(2)-100*x**9-1500*x**8-11400*x**7-51525*x**6-148575*x**5-256350*x**4-232575*x**3-37053*x
**2-63380*x-54912)/((ln(2)**2+10*ln(2)+25)*exp(x)**3+((-3*x**2-15*x-39)*ln(2)**2+(-30*x**2-150*x-390)*ln(2)-75
*x**2-375*x-975)*exp(x)**2+((3*x**4+30*x**3+153*x**2+390*x+507)*ln(2)**2+(30*x**4+300*x**3+1530*x**2+3900*x+50
70)*ln(2)+75*x**4+750*x**3+3825*x**2+9750*x+12675)*exp(x)+(-x**6-15*x**5-114*x**4-515*x**3-1482*x**2-2535*x-21
97)*ln(2)**2+(-10*x**6-150*x**5-1140*x**4-5150*x**3-14820*x**2-25350*x-21970)*ln(2)-25*x**6-375*x**5-2850*x**4
-12875*x**3-37050*x**2-63375*x-54925),x)

[Out]

x**4 + x - x/(x**4*log(2)**2 + 10*x**4*log(2) + 25*x**4 + 10*x**3*log(2)**2 + 100*x**3*log(2) + 250*x**3 + 51*
x**2*log(2)**2 + 510*x**2*log(2) + 1275*x**2 + 130*x*log(2)**2 + 1300*x*log(2) + 3250*x + (-50*x**2 - 20*x**2*
log(2) - 2*x**2*log(2)**2 - 250*x - 100*x*log(2) - 10*x*log(2)**2 - 650 - 260*log(2) - 26*log(2)**2)*exp(x) +
(log(2)**2 + 10*log(2) + 25)*exp(2*x) + 169*log(2)**2 + 1690*log(2) + 4225)

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