3.842 \(\int x^m (d+e x) \left (1+2 x+x^2\right )^5 \, dx\)
Optimal. Leaf size=209 \[ \frac{(10 d+e) x^{m+2}}{m+2}+\frac{5 (9 d+2 e) x^{m+3}}{m+3}+\frac{15 (8 d+3 e) x^{m+4}}{m+4}+\frac{30 (7 d+4 e) x^{m+5}}{m+5}+\frac{42 (6 d+5 e) x^{m+6}}{m+6}+\frac{42 (5 d+6 e) x^{m+7}}{m+7}+\frac{30 (4 d+7 e) x^{m+8}}{m+8}+\frac{15 (3 d+8 e) x^{m+9}}{m+9}+\frac{5 (2 d+9 e) x^{m+10}}{m+10}+\frac{(d+10 e) x^{m+11}}{m+11}+\frac{d x^{m+1}}{m+1}+\frac{e x^{m+12}}{m+12} \]
[Out]
(d*x^(1 + m))/(1 + m) + ((10*d + e)*x^(2 + m))/(2 + m) + (5*(9*d + 2*e)*x^(3 + m
))/(3 + m) + (15*(8*d + 3*e)*x^(4 + m))/(4 + m) + (30*(7*d + 4*e)*x^(5 + m))/(5
+ m) + (42*(6*d + 5*e)*x^(6 + m))/(6 + m) + (42*(5*d + 6*e)*x^(7 + m))/(7 + m) +
(30*(4*d + 7*e)*x^(8 + m))/(8 + m) + (15*(3*d + 8*e)*x^(9 + m))/(9 + m) + (5*(2
*d + 9*e)*x^(10 + m))/(10 + m) + ((d + 10*e)*x^(11 + m))/(11 + m) + (e*x^(12 + m
))/(12 + m)
_______________________________________________________________________________________
Rubi [A] time = 0.228288, antiderivative size = 209, normalized size of antiderivative = 1.,
number of steps used = 3, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105
\[ \frac{(10 d+e) x^{m+2}}{m+2}+\frac{5 (9 d+2 e) x^{m+3}}{m+3}+\frac{15 (8 d+3 e) x^{m+4}}{m+4}+\frac{30 (7 d+4 e) x^{m+5}}{m+5}+\frac{42 (6 d+5 e) x^{m+6}}{m+6}+\frac{42 (5 d+6 e) x^{m+7}}{m+7}+\frac{30 (4 d+7 e) x^{m+8}}{m+8}+\frac{15 (3 d+8 e) x^{m+9}}{m+9}+\frac{5 (2 d+9 e) x^{m+10}}{m+10}+\frac{(d+10 e) x^{m+11}}{m+11}+\frac{d x^{m+1}}{m+1}+\frac{e x^{m+12}}{m+12} \]
Antiderivative was successfully verified.
[In] Int[x^m*(d + e*x)*(1 + 2*x + x^2)^5,x]
[Out]
(d*x^(1 + m))/(1 + m) + ((10*d + e)*x^(2 + m))/(2 + m) + (5*(9*d + 2*e)*x^(3 + m
))/(3 + m) + (15*(8*d + 3*e)*x^(4 + m))/(4 + m) + (30*(7*d + 4*e)*x^(5 + m))/(5
+ m) + (42*(6*d + 5*e)*x^(6 + m))/(6 + m) + (42*(5*d + 6*e)*x^(7 + m))/(7 + m) +
(30*(4*d + 7*e)*x^(8 + m))/(8 + m) + (15*(3*d + 8*e)*x^(9 + m))/(9 + m) + (5*(2
*d + 9*e)*x^(10 + m))/(10 + m) + ((d + 10*e)*x^(11 + m))/(11 + m) + (e*x^(12 + m
))/(12 + m)
_______________________________________________________________________________________
Rubi in Sympy [A] time = 33.2927, size = 182, normalized size = 0.87 \[ \frac{d x^{m + 1}}{m + 1} + \frac{e x^{m + 12}}{m + 12} + \frac{x^{m + 2} \left (10 d + e\right )}{m + 2} + \frac{5 x^{m + 3} \left (9 d + 2 e\right )}{m + 3} + \frac{15 x^{m + 4} \left (8 d + 3 e\right )}{m + 4} + \frac{30 x^{m + 5} \left (7 d + 4 e\right )}{m + 5} + \frac{42 x^{m + 6} \left (6 d + 5 e\right )}{m + 6} + \frac{42 x^{m + 7} \left (5 d + 6 e\right )}{m + 7} + \frac{30 x^{m + 8} \left (4 d + 7 e\right )}{m + 8} + \frac{15 x^{m + 9} \left (3 d + 8 e\right )}{m + 9} + \frac{5 x^{m + 10} \left (2 d + 9 e\right )}{m + 10} + \frac{x^{m + 11} \left (d + 10 e\right )}{m + 11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**m*(e*x+d)*(x**2+2*x+1)**5,x)
[Out]
d*x**(m + 1)/(m + 1) + e*x**(m + 12)/(m + 12) + x**(m + 2)*(10*d + e)/(m + 2) +
5*x**(m + 3)*(9*d + 2*e)/(m + 3) + 15*x**(m + 4)*(8*d + 3*e)/(m + 4) + 30*x**(m
+ 5)*(7*d + 4*e)/(m + 5) + 42*x**(m + 6)*(6*d + 5*e)/(m + 6) + 42*x**(m + 7)*(5*
d + 6*e)/(m + 7) + 30*x**(m + 8)*(4*d + 7*e)/(m + 8) + 15*x**(m + 9)*(3*d + 8*e)
/(m + 9) + 5*x**(m + 10)*(2*d + 9*e)/(m + 10) + x**(m + 11)*(d + 10*e)/(m + 11)
_______________________________________________________________________________________
Mathematica [B] time = 1.63077, size = 499, normalized size = 2.39 \[ \frac{x^m \left ((m+1) (m+2) (m+3) (m+4) (m+5) (m+6) (m+7) (m+8) (m+9) (m+10) (x+1)^{11} (d (m+12)-2 e (m+6))+m (m+1) (m+2) (m+3) (m+4) (m+5) (m+6) (m+7) (m+8) (m+9) (x+1)^{10} (e (m+1)-d (m+12))+10 m (m+1) (m+2) (m+3) (m+4) (m+5) (m+6) (m+7) (m+8) (x+1)^9 (e (m+1)-d (m+12))+90 m (m+1) (m+2) (m+3) (m+4) (m+5) (m+6) (m+7) (x+1)^8 (e (m+1)-d (m+12))+720 m (m+1) (m+2) (m+3) (m+4) (m+5) (m+6) (x+1)^7 (e (m+1)-d (m+12))+5040 m (m+1) (m+2) (m+3) (m+4) (m+5) (x+1)^6 (e (m+1)-d (m+12))+30240 m (m+1) (m+2) (m+3) (m+4) (x+1)^5 (e (m+1)-d (m+12))+151200 m (m+1) (m+2) (m+3) (x+1)^4 (e (m+1)-d (m+12))+604800 m (m+1) (m+2) (x+1)^3 (e (m+1)-d (m+12))+1814400 m (m+1) (x+1)^2 (e (m+1)-d (m+12))+3628800 m (x+1) (e (m+1)-d (m+12))+3628800 (e (m+1)-d (m+12))+e (m+1) (m+2) (m+3) (m+4) (m+5) (m+6) (m+7) (m+8) (m+9) (m+10) (m+11) (x+1)^{12}\right )}{(m+1) (m+2) (m+3) (m+4) (m+5) (m+6) (m+7) (m+8) (m+9) (m+10) (m+11) (m+12)} \]
Antiderivative was successfully verified.
[In] Integrate[x^m*(d + e*x)*(1 + 2*x + x^2)^5,x]
[Out]
(x^m*(3628800*(e*(1 + m) - d*(12 + m)) + 3628800*m*(e*(1 + m) - d*(12 + m))*(1 +
x) + 1814400*m*(1 + m)*(e*(1 + m) - d*(12 + m))*(1 + x)^2 + 604800*m*(1 + m)*(2
+ m)*(e*(1 + m) - d*(12 + m))*(1 + x)^3 + 151200*m*(1 + m)*(2 + m)*(3 + m)*(e*(
1 + m) - d*(12 + m))*(1 + x)^4 + 30240*m*(1 + m)*(2 + m)*(3 + m)*(4 + m)*(e*(1 +
m) - d*(12 + m))*(1 + x)^5 + 5040*m*(1 + m)*(2 + m)*(3 + m)*(4 + m)*(5 + m)*(e*
(1 + m) - d*(12 + m))*(1 + x)^6 + 720*m*(1 + m)*(2 + m)*(3 + m)*(4 + m)*(5 + m)*
(6 + m)*(e*(1 + m) - d*(12 + m))*(1 + x)^7 + 90*m*(1 + m)*(2 + m)*(3 + m)*(4 + m
)*(5 + m)*(6 + m)*(7 + m)*(e*(1 + m) - d*(12 + m))*(1 + x)^8 + 10*m*(1 + m)*(2 +
m)*(3 + m)*(4 + m)*(5 + m)*(6 + m)*(7 + m)*(8 + m)*(e*(1 + m) - d*(12 + m))*(1
+ x)^9 + m*(1 + m)*(2 + m)*(3 + m)*(4 + m)*(5 + m)*(6 + m)*(7 + m)*(8 + m)*(9 +
m)*(e*(1 + m) - d*(12 + m))*(1 + x)^10 + (1 + m)*(2 + m)*(3 + m)*(4 + m)*(5 + m)
*(6 + m)*(7 + m)*(8 + m)*(9 + m)*(10 + m)*(-2*e*(6 + m) + d*(12 + m))*(1 + x)^11
+ e*(1 + m)*(2 + m)*(3 + m)*(4 + m)*(5 + m)*(6 + m)*(7 + m)*(8 + m)*(9 + m)*(10
+ m)*(11 + m)*(1 + x)^12))/((1 + m)*(2 + m)*(3 + m)*(4 + m)*(5 + m)*(6 + m)*(7
+ m)*(8 + m)*(9 + m)*(10 + m)*(11 + m)*(12 + m))
_______________________________________________________________________________________
Maple [B] time = 0.016, size = 2246, normalized size = 10.8 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^m*(e*x+d)*(x^2+2*x+1)^5,x)
[Out]
x^(1+m)*(e*m^11*x^11+d*m^11*x^10+10*e*m^11*x^10+66*e*m^10*x^11+10*d*m^11*x^9+67*
d*m^10*x^10+45*e*m^11*x^9+670*e*m^10*x^10+1925*e*m^9*x^11+45*d*m^11*x^8+680*d*m^
10*x^9+1980*d*m^9*x^10+120*e*m^11*x^8+3060*e*m^10*x^9+19800*e*m^9*x^10+32670*e*m
^8*x^11+120*d*m^11*x^7+3105*d*m^10*x^8+20370*d*m^9*x^9+33990*d*m^8*x^10+210*e*m^
11*x^7+8280*e*m^10*x^8+91665*e*m^9*x^9+339900*e*m^8*x^10+357423*e*m^7*x^11+210*d
*m^11*x^6+8400*d*m^10*x^7+94320*d*m^9*x^8+354000*d*m^8*x^9+375573*d*m^7*x^10+252
*e*m^11*x^6+14700*e*m^10*x^7+251520*e*m^9*x^8+1593000*e*m^8*x^9+3755730*e*m^7*x^
10+2637558*e*m^6*x^11+252*d*m^11*x^5+14910*d*m^10*x^6+258840*d*m^9*x^7+1660770*d
*m^8*x^8+3954630*d*m^7*x^9+2795331*d*m^6*x^10+210*e*m^11*x^5+17892*e*m^10*x^6+45
2970*e*m^9*x^7+4428720*e*m^8*x^8+17795835*e*m^7*x^9+27953310*e*m^6*x^10+13339535
*e*m^5*x^11+210*d*m^11*x^4+18144*d*m^10*x^5+466200*d*m^9*x^6+4621680*d*m^8*x^7+1
8778905*d*m^7*x^8+29720040*d*m^6*x^9+14241590*d*m^5*x^10+120*e*m^11*x^4+15120*e*
m^10*x^5+559440*e*m^9*x^6+8087940*e*m^8*x^7+50077080*e*m^7*x^8+133740180*e*m^6*x
^9+142415900*e*m^5*x^10+45995730*e*m^4*x^11+120*d*m^11*x^3+15330*d*m^10*x^4+5758
20*d*m^9*x^5+8448300*d*m^8*x^6+52962120*d*m^7*x^7+142688385*d*m^6*x^8+152701910*
d*m^5*x^9+49412660*d*m^4*x^10+45*e*m^11*x^3+8760*e*m^10*x^4+479850*e*m^9*x^5+101
37960*e*m^8*x^6+92683710*e*m^7*x^7+380502360*e*m^6*x^8+687158595*e*m^5*x^9+49412
6600*e*m^4*x^10+105258076*e*m^3*x^11+45*d*m^11*x^2+8880*d*m^10*x^3+493920*d*m^9*
x^4+10599120*d*m^8*x^5+98249130*d*m^7*x^6+407499120*d*m^6*x^7+740364930*d*m^5*x^
8+533682400*d*m^4*x^9+113667576*d*m^3*x^10+10*e*m^11*x^2+3330*e*m^10*x^3+282240*
e*m^9*x^4+8832600*e*m^8*x^5+117898956*e*m^7*x^6+713123460*e*m^6*x^7+1974306480*e
*m^5*x^8+2401570800*e*m^4*x^9+1136675760*e*m^3*x^10+150917976*e*m^2*x^11+10*d*m^
11*x+3375*d*m^10*x^2+290520*d*m^9*x^3+9242100*d*m^8*x^4+125269956*d*m^7*x^5+7668
49230*d*m^6*x^6+2138834760*d*m^5*x^7+2609872380*d*m^4*x^8+1235244360*d*m^3*x^9+1
63671552*d*m^2*x^10+e*m^11*x+750*e*m^10*x^2+108945*e*m^9*x^3+5281200*e*m^8*x^4+1
04391630*e*m^7*x^5+920219076*e*m^6*x^6+3742960830*e*m^5*x^7+6959659680*e*m^4*x^8
+5558599620*e*m^3*x^9+1636715520*e*m^2*x^10+120543840*e*m*x^11+d*m^11+760*d*m^10
*x+112140*d*m^9*x^2+5530320*d*m^8*x^3+111176730*d*m^7*x^4+993892032*d*m^6*x^5+40
80003900*d*m^5*x^6+7617739920*d*m^4*x^7+6085456200*d*m^3*x^8+1787705280*d*m^2*x^
9+131172480*d*m*x^10+76*e*m^10*x+24920*e*m^9*x^2+2073870*e*m^8*x^3+63529560*e*m^
7*x^4+828243360*e*m^6*x^5+4896004680*e*m^5*x^6+13331044860*e*m^4*x^7+16227883200
*e*m^3*x^8+8044673760*e*m^2*x^9+1311724800*e*m*x^10+39916800*e*x^11+77*d*m^10+25
650*d*m^9*x+2173230*d*m^8*x^2+67814280*d*m^7*x^3+898709490*d*m^6*x^4+5374186020*
d*m^5*x^5+14714704200*d*m^4*x^6+17922900960*d*m^3*x^7+8861564160*d*m^2*x^8+14385
42720*d*m*x^9+43545600*d*x^10+2565*e*m^9*x+482940*e*m^8*x^2+25430355*e*m^7*x^3+5
13548280*e*m^6*x^4+4478488350*e*m^5*x^5+17657645040*e*m^4*x^6+31365076680*e*m^3*
x^7+23630837760*e*m^2*x^8+6473442240*e*m*x^9+435456000*e*x^10+2640*d*m^9+506400*
d*m^8*x+27206145*d*m^7*x^2+559938960*d*m^6*x^3+4954401060*d*m^5*x^4+19684561680*
d*m^4*x^5+35010506160*d*m^3*x^6+26298578880*d*m^2*x^7+7166102400*d*m*x^8+4790016
00*d*x^9+50640*e*m^8*x+6045810*e*m^7*x^2+209977110*e*m^6*x^3+2831086320*e*m^5*x^
4+16403801400*e*m^4*x^5+42012607392*e*m^3*x^6+46022513040*e*m^2*x^7+19109606400*
e*m*x^8+2155507200*e*x^9+53130*d*m^8+6481830*d*m^7*x+230080095*d*m^6*x^2+3159071
880*d*m^5*x^3+18502726200*d*m^4*x^4+47508752592*d*m^3*x^5+51869583360*d*m^2*x^6+
21398515200*d*m*x^7+2395008000*d*x^8+648183*e*m^7*x+51128910*e*m^6*x^2+118465195
5*e*m^5*x^3+10572986400*e*m^4*x^4+39590627160*e*m^3*x^5+62243500032*e*m^2*x^6+37
447401600*e*m*x^7+6386688000*e*x^8+696333*d*m^7+56302680*d*m^6*x+1334320110*d*m^
5*x^2+12092130480*d*m^4*x^3+45499804560*d*m^3*x^4+71279236224*d*m^2*x^5+42540422
400*d*m*x^6+7185024000*d*x^7+5630268*e*m^6*x+296515580*e*m^5*x^2+4534548930*e*m^
4*x^3+25999888320*e*m^3*x^4+59399363520*e*m^2*x^5+51048506880*e*m*x^6+1257379200
0*e*x^7+6230301*d*m^6+337296950*d*m^5*x+5270196420*d*m^4*x^2+30496298400*d*m^3*x
^3+69444103680*d*m^2*x^4+59077589760*d*m*x^5+14370048000*d*x^6+33729695*e*m^5*x+
1171154760*e*m^4*x^2+11436111900*e*m^3*x^3+39682344960*e*m^2*x^4+49231324800*e*m
*x^5+17244057600*e*x^6+38759930*d*m^5+1386107600*d*m^4*x+13763718360*d*m^3*x^2+4
7696592960*d*m^2*x^3+58406987520*d*m*x^4+20118067200*d*x^5+138610760*e*m^4*x+305
8604080*e*m^3*x^2+17886222360*e*m^2*x^3+33375421440*e*m*x^4+16765056000*e*x^5+16
7310220*d*m^4+3799853160*d*m^3*x+22339514880*d*m^2*x^2+41000774400*d*m*x^3+20118
067200*d*x^4+379985316*e*m^3*x+4964336640*e*m^2*x^2+15375290400*e*m*x^3+11496038
400*e*x^4+489896616*d*m^3+6540442560*d*m^2*x+19901635200*d*m*x^2+14370048000*d*x
^3+654044256*e*m^2*x+4422585600*e*m*x^2+5388768000*e*x^3+924118272*d*m^2+6234710
400*d*m*x+7185024000*d*x^2+623471040*e*m*x+1596672000*e*x^2+1007441280*d*m+23950
08000*d*x+239500800*e*x+479001600*d)/(12+m)/(11+m)/(10+m)/(9+m)/(8+m)/(7+m)/(6+m
)/(5+m)/(4+m)/(3+m)/(2+m)/(1+m)
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 + 2*x + 1)^5*x^m,x, algorithm="maxima")
[Out]
Exception raised: ValueError
_______________________________________________________________________________________
Fricas [A] time = 0.30503, size = 2118, normalized size = 10.13 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 + 2*x + 1)^5*x^m,x, algorithm="fricas")
[Out]
((e*m^11 + 66*e*m^10 + 1925*e*m^9 + 32670*e*m^8 + 357423*e*m^7 + 2637558*e*m^6 +
13339535*e*m^5 + 45995730*e*m^4 + 105258076*e*m^3 + 150917976*e*m^2 + 120543840
*e*m + 39916800*e)*x^12 + ((d + 10*e)*m^11 + 67*(d + 10*e)*m^10 + 1980*(d + 10*e
)*m^9 + 33990*(d + 10*e)*m^8 + 375573*(d + 10*e)*m^7 + 2795331*(d + 10*e)*m^6 +
14241590*(d + 10*e)*m^5 + 49412660*(d + 10*e)*m^4 + 113667576*(d + 10*e)*m^3 + 1
63671552*(d + 10*e)*m^2 + 131172480*(d + 10*e)*m + 43545600*d + 435456000*e)*x^1
1 + 5*((2*d + 9*e)*m^11 + 68*(2*d + 9*e)*m^10 + 2037*(2*d + 9*e)*m^9 + 35400*(2*
d + 9*e)*m^8 + 395463*(2*d + 9*e)*m^7 + 2972004*(2*d + 9*e)*m^6 + 15270191*(2*d
+ 9*e)*m^5 + 53368240*(2*d + 9*e)*m^4 + 123524436*(2*d + 9*e)*m^3 + 178770528*(2
*d + 9*e)*m^2 + 143854272*(2*d + 9*e)*m + 95800320*d + 431101440*e)*x^10 + 15*((
3*d + 8*e)*m^11 + 69*(3*d + 8*e)*m^10 + 2096*(3*d + 8*e)*m^9 + 36906*(3*d + 8*e)
*m^8 + 417309*(3*d + 8*e)*m^7 + 3170853*(3*d + 8*e)*m^6 + 16452554*(3*d + 8*e)*m
^5 + 57997164*(3*d + 8*e)*m^4 + 135232360*(3*d + 8*e)*m^3 + 196923648*(3*d + 8*e
)*m^2 + 159246720*(3*d + 8*e)*m + 159667200*d + 425779200*e)*x^9 + 30*((4*d + 7*
e)*m^11 + 70*(4*d + 7*e)*m^10 + 2157*(4*d + 7*e)*m^9 + 38514*(4*d + 7*e)*m^8 + 4
41351*(4*d + 7*e)*m^7 + 3395826*(4*d + 7*e)*m^6 + 17823623*(4*d + 7*e)*m^5 + 634
81166*(4*d + 7*e)*m^4 + 149357508*(4*d + 7*e)*m^3 + 219154824*(4*d + 7*e)*m^2 +
178320960*(4*d + 7*e)*m + 239500800*d + 419126400*e)*x^8 + 42*((5*d + 6*e)*m^11
+ 71*(5*d + 6*e)*m^10 + 2220*(5*d + 6*e)*m^9 + 40230*(5*d + 6*e)*m^8 + 467853*(5
*d + 6*e)*m^7 + 3651663*(5*d + 6*e)*m^6 + 19428590*(5*d + 6*e)*m^5 + 70070020*(5
*d + 6*e)*m^4 + 166716696*(5*d + 6*e)*m^3 + 246998016*(5*d + 6*e)*m^2 + 20257344
0*(5*d + 6*e)*m + 342144000*d + 410572800*e)*x^7 + 42*((6*d + 5*e)*m^11 + 72*(6*
d + 5*e)*m^10 + 2285*(6*d + 5*e)*m^9 + 42060*(6*d + 5*e)*m^8 + 497103*(6*d + 5*e
)*m^7 + 3944016*(6*d + 5*e)*m^6 + 21326135*(6*d + 5*e)*m^5 + 78113340*(6*d + 5*e
)*m^4 + 188526796*(6*d + 5*e)*m^3 + 282854112*(6*d + 5*e)*m^2 + 234434880*(6*d +
5*e)*m + 479001600*d + 399168000*e)*x^6 + 30*((7*d + 4*e)*m^11 + 73*(7*d + 4*e)
*m^10 + 2352*(7*d + 4*e)*m^9 + 44010*(7*d + 4*e)*m^8 + 529413*(7*d + 4*e)*m^7 +
4279569*(7*d + 4*e)*m^6 + 23592386*(7*d + 4*e)*m^5 + 88108220*(7*d + 4*e)*m^4 +
216665736*(7*d + 4*e)*m^3 + 330686208*(7*d + 4*e)*m^2 + 278128512*(7*d + 4*e)*m
+ 670602240*d + 383201280*e)*x^5 + 15*((8*d + 3*e)*m^11 + 74*(8*d + 3*e)*m^10 +
2421*(8*d + 3*e)*m^9 + 46086*(8*d + 3*e)*m^8 + 565119*(8*d + 3*e)*m^7 + 4666158*
(8*d + 3*e)*m^6 + 26325599*(8*d + 3*e)*m^5 + 100767754*(8*d + 3*e)*m^4 + 2541358
20*(8*d + 3*e)*m^3 + 397471608*(8*d + 3*e)*m^2 + 341673120*(8*d + 3*e)*m + 95800
3200*d + 359251200*e)*x^4 + 5*((9*d + 2*e)*m^11 + 75*(9*d + 2*e)*m^10 + 2492*(9*
d + 2*e)*m^9 + 48294*(9*d + 2*e)*m^8 + 604581*(9*d + 2*e)*m^7 + 5112891*(9*d + 2
*e)*m^6 + 29651558*(9*d + 2*e)*m^5 + 117115476*(9*d + 2*e)*m^4 + 305860408*(9*d
+ 2*e)*m^3 + 496433664*(9*d + 2*e)*m^2 + 442258560*(9*d + 2*e)*m + 1437004800*d
+ 319334400*e)*x^3 + ((10*d + e)*m^11 + 76*(10*d + e)*m^10 + 2565*(10*d + e)*m^9
+ 50640*(10*d + e)*m^8 + 648183*(10*d + e)*m^7 + 5630268*(10*d + e)*m^6 + 33729
695*(10*d + e)*m^5 + 138610760*(10*d + e)*m^4 + 379985316*(10*d + e)*m^3 + 65404
4256*(10*d + e)*m^2 + 623471040*(10*d + e)*m + 2395008000*d + 239500800*e)*x^2 +
(d*m^11 + 77*d*m^10 + 2640*d*m^9 + 53130*d*m^8 + 696333*d*m^7 + 6230301*d*m^6 +
38759930*d*m^5 + 167310220*d*m^4 + 489896616*d*m^3 + 924118272*d*m^2 + 10074412
80*d*m + 479001600*d)*x)*x^m/(m^12 + 78*m^11 + 2717*m^10 + 55770*m^9 + 749463*m^
8 + 6926634*m^7 + 44990231*m^6 + 206070150*m^5 + 657206836*m^4 + 1414014888*m^3
+ 1931559552*m^2 + 1486442880*m + 479001600)
_______________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**m*(e*x+d)*(x**2+2*x+1)**5,x)
[Out]
Timed out
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.285388, size = 1, normalized size = 0. \[ \mathit{Done} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((e*x + d)*(x^2 + 2*x + 1)^5*x^m,x, algorithm="giac")
[Out]
Done