3.38 \(\int (d x)^m \left (A+B x+C x^2\right ) \left (a+b x^2+c x^4\right )^2 \, dx\)

Optimal. Leaf size=260 \[ \frac{a^2 A (d x)^{m+1}}{d (m+1)}+\frac{a^2 B (d x)^{m+2}}{d^2 (m+2)}+\frac{(d x)^{m+7} \left (C \left (2 a c+b^2\right )+2 A b c\right )}{d^7 (m+7)}+\frac{(d x)^{m+5} \left (A \left (2 a c+b^2\right )+2 a b C\right )}{d^5 (m+5)}+\frac{a (d x)^{m+3} (a C+2 A b)}{d^3 (m+3)}+\frac{B \left (2 a c+b^2\right ) (d x)^{m+6}}{d^6 (m+6)}+\frac{2 a b B (d x)^{m+4}}{d^4 (m+4)}+\frac{c (d x)^{m+9} (A c+2 b C)}{d^9 (m+9)}+\frac{2 b B c (d x)^{m+8}}{d^8 (m+8)}+\frac{B c^2 (d x)^{m+10}}{d^{10} (m+10)}+\frac{c^2 C (d x)^{m+11}}{d^{11} (m+11)} \]

[Out]

(a^2*A*(d*x)^(1 + m))/(d*(1 + m)) + (a^2*B*(d*x)^(2 + m))/(d^2*(2 + m)) + (a*(2*
A*b + a*C)*(d*x)^(3 + m))/(d^3*(3 + m)) + (2*a*b*B*(d*x)^(4 + m))/(d^4*(4 + m))
+ ((A*(b^2 + 2*a*c) + 2*a*b*C)*(d*x)^(5 + m))/(d^5*(5 + m)) + (B*(b^2 + 2*a*c)*(
d*x)^(6 + m))/(d^6*(6 + m)) + ((2*A*b*c + (b^2 + 2*a*c)*C)*(d*x)^(7 + m))/(d^7*(
7 + m)) + (2*b*B*c*(d*x)^(8 + m))/(d^8*(8 + m)) + (c*(A*c + 2*b*C)*(d*x)^(9 + m)
)/(d^9*(9 + m)) + (B*c^2*(d*x)^(10 + m))/(d^10*(10 + m)) + (c^2*C*(d*x)^(11 + m)
)/(d^11*(11 + m))

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Rubi [A]  time = 0.487742, antiderivative size = 260, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 30, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.033 \[ \frac{a^2 A (d x)^{m+1}}{d (m+1)}+\frac{a^2 B (d x)^{m+2}}{d^2 (m+2)}+\frac{(d x)^{m+7} \left (C \left (2 a c+b^2\right )+2 A b c\right )}{d^7 (m+7)}+\frac{(d x)^{m+5} \left (A \left (2 a c+b^2\right )+2 a b C\right )}{d^5 (m+5)}+\frac{a (d x)^{m+3} (a C+2 A b)}{d^3 (m+3)}+\frac{B \left (2 a c+b^2\right ) (d x)^{m+6}}{d^6 (m+6)}+\frac{2 a b B (d x)^{m+4}}{d^4 (m+4)}+\frac{c (d x)^{m+9} (A c+2 b C)}{d^9 (m+9)}+\frac{2 b B c (d x)^{m+8}}{d^8 (m+8)}+\frac{B c^2 (d x)^{m+10}}{d^{10} (m+10)}+\frac{c^2 C (d x)^{m+11}}{d^{11} (m+11)} \]

Antiderivative was successfully verified.

[In]  Int[(d*x)^m*(A + B*x + C*x^2)*(a + b*x^2 + c*x^4)^2,x]

[Out]

(a^2*A*(d*x)^(1 + m))/(d*(1 + m)) + (a^2*B*(d*x)^(2 + m))/(d^2*(2 + m)) + (a*(2*
A*b + a*C)*(d*x)^(3 + m))/(d^3*(3 + m)) + (2*a*b*B*(d*x)^(4 + m))/(d^4*(4 + m))
+ ((A*(b^2 + 2*a*c) + 2*a*b*C)*(d*x)^(5 + m))/(d^5*(5 + m)) + (B*(b^2 + 2*a*c)*(
d*x)^(6 + m))/(d^6*(6 + m)) + ((2*A*b*c + (b^2 + 2*a*c)*C)*(d*x)^(7 + m))/(d^7*(
7 + m)) + (2*b*B*c*(d*x)^(8 + m))/(d^8*(8 + m)) + (c*(A*c + 2*b*C)*(d*x)^(9 + m)
)/(d^9*(9 + m)) + (B*c^2*(d*x)^(10 + m))/(d^10*(10 + m)) + (c^2*C*(d*x)^(11 + m)
)/(d^11*(11 + m))

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Rubi in Sympy [A]  time = 75.8458, size = 248, normalized size = 0.95 \[ \frac{A a^{2} \left (d x\right )^{m + 1}}{d \left (m + 1\right )} + \frac{B a^{2} \left (d x\right )^{m + 2}}{d^{2} \left (m + 2\right )} + \frac{2 B a b \left (d x\right )^{m + 4}}{d^{4} \left (m + 4\right )} + \frac{2 B b c \left (d x\right )^{m + 8}}{d^{8} \left (m + 8\right )} + \frac{B c^{2} \left (d x\right )^{m + 10}}{d^{10} \left (m + 10\right )} + \frac{B \left (d x\right )^{m + 6} \left (2 a c + b^{2}\right )}{d^{6} \left (m + 6\right )} + \frac{C c^{2} \left (d x\right )^{m + 11}}{d^{11} \left (m + 11\right )} + \frac{a \left (d x\right )^{m + 3} \left (2 A b + C a\right )}{d^{3} \left (m + 3\right )} + \frac{c \left (d x\right )^{m + 9} \left (A c + 2 C b\right )}{d^{9} \left (m + 9\right )} + \frac{\left (d x\right )^{m + 5} \left (2 A a c + A b^{2} + 2 C a b\right )}{d^{5} \left (m + 5\right )} + \frac{\left (d x\right )^{m + 7} \left (2 A b c + 2 C a c + C b^{2}\right )}{d^{7} \left (m + 7\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((d*x)**m*(C*x**2+B*x+A)*(c*x**4+b*x**2+a)**2,x)

[Out]

A*a**2*(d*x)**(m + 1)/(d*(m + 1)) + B*a**2*(d*x)**(m + 2)/(d**2*(m + 2)) + 2*B*a
*b*(d*x)**(m + 4)/(d**4*(m + 4)) + 2*B*b*c*(d*x)**(m + 8)/(d**8*(m + 8)) + B*c**
2*(d*x)**(m + 10)/(d**10*(m + 10)) + B*(d*x)**(m + 6)*(2*a*c + b**2)/(d**6*(m +
6)) + C*c**2*(d*x)**(m + 11)/(d**11*(m + 11)) + a*(d*x)**(m + 3)*(2*A*b + C*a)/(
d**3*(m + 3)) + c*(d*x)**(m + 9)*(A*c + 2*C*b)/(d**9*(m + 9)) + (d*x)**(m + 5)*(
2*A*a*c + A*b**2 + 2*C*a*b)/(d**5*(m + 5)) + (d*x)**(m + 7)*(2*A*b*c + 2*C*a*c +
C*b**2)/(d**7*(m + 7))

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Mathematica [A]  time = 1.56496, size = 187, normalized size = 0.72 \[ (d x)^m \left (\frac{a^2 A x}{m+1}+\frac{a^2 B x^2}{m+2}+\frac{x^7 \left (2 a c C+2 A b c+b^2 C\right )}{m+7}+\frac{x^5 \left (2 a A c+2 a b C+A b^2\right )}{m+5}+\frac{a x^3 (a C+2 A b)}{m+3}+\frac{B x^6 \left (2 a c+b^2\right )}{m+6}+\frac{2 a b B x^4}{m+4}+\frac{c x^9 (A c+2 b C)}{m+9}+\frac{2 b B c x^8}{m+8}+\frac{B c^2 x^{10}}{m+10}+\frac{c^2 C x^{11}}{m+11}\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[(d*x)^m*(A + B*x + C*x^2)*(a + b*x^2 + c*x^4)^2,x]

[Out]

(d*x)^m*((a^2*A*x)/(1 + m) + (a^2*B*x^2)/(2 + m) + (a*(2*A*b + a*C)*x^3)/(3 + m)
+ (2*a*b*B*x^4)/(4 + m) + ((A*b^2 + 2*a*A*c + 2*a*b*C)*x^5)/(5 + m) + (B*(b^2 +
2*a*c)*x^6)/(6 + m) + ((2*A*b*c + b^2*C + 2*a*c*C)*x^7)/(7 + m) + (2*b*B*c*x^8)
/(8 + m) + (c*(A*c + 2*b*C)*x^9)/(9 + m) + (B*c^2*x^10)/(10 + m) + (c^2*C*x^11)/
(11 + m))

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Maple [B]  time = 0.013, size = 2187, normalized size = 8.4 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((d*x)^m*(C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2,x)

[Out]

x*(C*c^2*m^10*x^10+B*c^2*m^10*x^9+55*C*c^2*m^9*x^10+A*c^2*m^10*x^8+56*B*c^2*m^9*
x^9+2*C*b*c*m^10*x^8+1320*C*c^2*m^8*x^10+57*A*c^2*m^9*x^8+2*B*b*c*m^10*x^7+1365*
B*c^2*m^8*x^9+114*C*b*c*m^9*x^8+18150*C*c^2*m^7*x^10+2*A*b*c*m^10*x^6+1412*A*c^2
*m^8*x^8+116*B*b*c*m^9*x^7+19020*B*c^2*m^7*x^9+2*C*a*c*m^10*x^6+C*b^2*m^10*x^6+2
824*C*b*c*m^8*x^8+157773*C*c^2*m^6*x^10+118*A*b*c*m^9*x^6+19962*A*c^2*m^7*x^8+2*
B*a*c*m^10*x^5+B*b^2*m^10*x^5+2922*B*b*c*m^8*x^7+167223*B*c^2*m^6*x^9+118*C*a*c*
m^9*x^6+59*C*b^2*m^9*x^6+39924*C*b*c*m^7*x^8+902055*C*c^2*m^5*x^10+2*A*a*c*m^10*
x^4+A*b^2*m^10*x^4+3024*A*b*c*m^8*x^6+177765*A*c^2*m^6*x^8+120*B*a*c*m^9*x^5+60*
B*b^2*m^9*x^5+41964*B*b*c*m^7*x^7+965328*B*c^2*m^5*x^9+2*C*a*b*m^10*x^4+3024*C*a
*c*m^8*x^6+1512*C*b^2*m^8*x^6+355530*C*b*c*m^6*x^8+3416930*C*c^2*m^4*x^10+122*A*
a*c*m^9*x^4+61*A*b^2*m^9*x^4+44172*A*b*c*m^7*x^6+1037673*A*c^2*m^5*x^8+2*B*a*b*m
^10*x^3+3130*B*a*c*m^8*x^5+1565*B*b^2*m^8*x^5+379134*B*b*c*m^6*x^7+3686255*B*c^2
*m^4*x^9+122*C*a*b*m^9*x^4+44172*C*a*c*m^7*x^6+22086*C*b^2*m^7*x^6+2075346*C*b*c
*m^5*x^8+8409500*C*c^2*m^3*x^10+2*A*a*b*m^10*x^2+3240*A*a*c*m^8*x^4+1620*A*b^2*m
^8*x^4+405642*A*b*c*m^6*x^6+4000478*A*c^2*m^4*x^8+124*B*a*b*m^9*x^3+46560*B*a*c*
m^7*x^5+23280*B*b^2*m^7*x^5+2242044*B*b*c*m^5*x^7+9133180*B*c^2*m^3*x^9+C*a^2*m^
10*x^2+3240*C*a*b*m^8*x^4+405642*C*a*c*m^6*x^6+202821*C*b^2*m^6*x^6+8000956*C*b*
c*m^4*x^8+12753576*C*c^2*m^2*x^10+126*A*a*b*m^9*x^2+49140*A*a*c*m^7*x^4+24570*A*
b^2*m^7*x^4+2435622*A*b*c*m^5*x^6+9991428*A*c^2*m^3*x^8+B*a^2*m^10*x+3354*B*a*b*
m^8*x^3+435486*B*a*c*m^6*x^5+217743*B*b^2*m^6*x^5+8742718*B*b*c*m^4*x^7+13926276
*B*c^2*m^2*x^9+63*C*a^2*m^9*x^2+49140*C*a*b*m^7*x^4+2435622*C*a*c*m^5*x^6+121781
1*C*b^2*m^5*x^6+19982856*C*b*c*m^3*x^8+10628640*C*c^2*m*x^10+A*a^2*m^10+3472*A*a
*b*m^8*x^2+469146*A*a*c*m^6*x^4+234573*A*b^2*m^6*x^4+9629716*A*b*c*m^4*x^6+15335
224*A*c^2*m^2*x^8+64*B*a^2*m^9*x+51924*B*a*b*m^7*x^3+2662200*B*a*c*m^5*x^5+13311
00*B*b^2*m^5*x^5+22049716*B*b*c*m^3*x^7+11655216*B*c^2*m*x^9+1736*C*a^2*m^8*x^2+
469146*C*a*b*m^6*x^4+9629716*C*a*c*m^4*x^6+4814858*C*b^2*m^4*x^6+30670448*C*b*c*
m^2*x^8+3628800*C*c^2*x^10+65*A*a^2*m^9+54924*A*a*b*m^7*x^2+2929386*A*a*c*m^5*x^
4+1464693*A*b^2*m^5*x^4+24583448*A*b*c*m^3*x^6+12900960*A*c^2*m*x^8+1797*B*a^2*m
^8*x+507150*B*a*b*m^6*x^3+10705870*B*a*c*m^4*x^5+5352935*B*b^2*m^4*x^5+34118424*
B*b*c*m^2*x^7+3991680*B*c^2*x^9+27462*C*a^2*m^7*x^2+2929386*C*a*b*m^5*x^4+245834
48*C*a*c*m^3*x^6+12291724*C*b^2*m^3*x^6+25801920*C*b*c*m*x^8+1860*A*a^2*m^8+5500
74*A*a*b*m^6*x^2+12032140*A*a*c*m^4*x^4+6016070*A*b^2*m^4*x^4+38432016*A*b*c*m^2
*x^6+4435200*A*c^2*x^8+29076*B*a^2*m^7*x+3246516*B*a*b*m^5*x^3+27756240*B*a*c*m^
3*x^5+13878120*B*b^2*m^3*x^5+28888560*B*b*c*m*x^7+275037*C*a^2*m^6*x^2+12032140*
C*a*b*m^4*x^4+38432016*C*a*c*m^2*x^6+19216008*C*b^2*m^2*x^6+8870400*C*b*c*x^8+30
810*A*a^2*m^7+3624894*A*a*b*m^5*x^2+31830760*A*a*c*m^3*x^4+15915380*A*b^2*m^3*x^
4+32811840*A*b*c*m*x^6+299271*B*a^2*m^6*x+13693006*B*a*b*m^4*x^3+43978712*B*a*c*
m^2*x^5+21989356*B*b^2*m^2*x^5+9979200*B*b*c*x^7+1812447*C*a^2*m^5*x^2+31830760*
C*a*b*m^3*x^4+32811840*C*a*c*m*x^6+16405920*C*b^2*m*x^6+326613*A*a^2*m^6+1580438
8*A*a*b*m^4*x^2+51362352*A*a*c*m^2*x^4+25681176*A*b^2*m^2*x^4+11404800*A*b*c*x^6
+2039016*B*a^2*m^5*x+37219436*B*a*b*m^3*x^3+37963680*B*a*c*m*x^5+18981840*B*b^2*
m*x^5+7902194*C*a^2*m^4*x^2+51362352*C*a*b*m^2*x^4+11404800*C*a*c*x^6+5702400*C*
b^2*x^6+2310945*A*a^2*m^5+44578296*A*a*b*m^3*x^2+45024192*A*a*c*m*x^4+22512096*A
*b^2*m*x^4+9261503*B*a^2*m^4*x+61638408*B*a*b*m^2*x^3+13305600*B*a*c*x^5+6652800
*B*b^2*x^5+22289148*C*a^2*m^3*x^2+45024192*C*a*b*m*x^4+11028590*A*a^2*m^4+767812
64*A*a*b*m^2*x^2+15966720*A*a*c*x^4+7983360*A*b^2*x^4+27472724*B*a^2*m^3*x+55282
320*B*a*b*m*x^3+38390632*C*a^2*m^2*x^2+15966720*C*a*b*x^4+34967140*A*a^2*m^3+714
92160*A*a*b*m*x^2+50312628*B*a^2*m^2*x+19958400*B*a*b*x^3+35746080*C*a^2*m*x^2+7
0290936*A*a^2*m^2+26611200*A*a*b*x^2+50292720*B*a^2*m*x+13305600*C*a^2*x^2+80627
040*A*a^2*m+19958400*B*a^2*x+39916800*A*a^2)*(d*x)^m/(11+m)/(10+m)/(9+m)/(8+m)/(
7+m)/(6+m)/(5+m)/(4+m)/(3+m)/(2+m)/(1+m)

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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((c*x^4 + b*x^2 + a)^2*(C*x^2 + B*x + A)*(d*x)^m,x, algorithm="maxima")

[Out]

Exception raised: ValueError

_______________________________________________________________________________________

Fricas [A]  time = 0.345777, size = 2164, normalized size = 8.32 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^4 + b*x^2 + a)^2*(C*x^2 + B*x + A)*(d*x)^m,x, algorithm="fricas")

[Out]

((C*c^2*m^10 + 55*C*c^2*m^9 + 1320*C*c^2*m^8 + 18150*C*c^2*m^7 + 157773*C*c^2*m^
6 + 902055*C*c^2*m^5 + 3416930*C*c^2*m^4 + 8409500*C*c^2*m^3 + 12753576*C*c^2*m^
2 + 10628640*C*c^2*m + 3628800*C*c^2)*x^11 + (B*c^2*m^10 + 56*B*c^2*m^9 + 1365*B
*c^2*m^8 + 19020*B*c^2*m^7 + 167223*B*c^2*m^6 + 965328*B*c^2*m^5 + 3686255*B*c^2
*m^4 + 9133180*B*c^2*m^3 + 13926276*B*c^2*m^2 + 11655216*B*c^2*m + 3991680*B*c^2
)*x^10 + ((2*C*b*c + A*c^2)*m^10 + 57*(2*C*b*c + A*c^2)*m^9 + 1412*(2*C*b*c + A*
c^2)*m^8 + 19962*(2*C*b*c + A*c^2)*m^7 + 177765*(2*C*b*c + A*c^2)*m^6 + 1037673*
(2*C*b*c + A*c^2)*m^5 + 4000478*(2*C*b*c + A*c^2)*m^4 + 9991428*(2*C*b*c + A*c^2
)*m^3 + 8870400*C*b*c + 4435200*A*c^2 + 15335224*(2*C*b*c + A*c^2)*m^2 + 1290096
0*(2*C*b*c + A*c^2)*m)*x^9 + 2*(B*b*c*m^10 + 58*B*b*c*m^9 + 1461*B*b*c*m^8 + 209
82*B*b*c*m^7 + 189567*B*b*c*m^6 + 1121022*B*b*c*m^5 + 4371359*B*b*c*m^4 + 110248
58*B*b*c*m^3 + 17059212*B*b*c*m^2 + 14444280*B*b*c*m + 4989600*B*b*c)*x^8 + ((C*
b^2 + 2*(C*a + A*b)*c)*m^10 + 59*(C*b^2 + 2*(C*a + A*b)*c)*m^9 + 1512*(C*b^2 + 2
*(C*a + A*b)*c)*m^8 + 22086*(C*b^2 + 2*(C*a + A*b)*c)*m^7 + 202821*(C*b^2 + 2*(C
*a + A*b)*c)*m^6 + 1217811*(C*b^2 + 2*(C*a + A*b)*c)*m^5 + 4814858*(C*b^2 + 2*(C
*a + A*b)*c)*m^4 + 12291724*(C*b^2 + 2*(C*a + A*b)*c)*m^3 + 5702400*C*b^2 + 1921
6008*(C*b^2 + 2*(C*a + A*b)*c)*m^2 + 11404800*(C*a + A*b)*c + 16405920*(C*b^2 +
2*(C*a + A*b)*c)*m)*x^7 + ((B*b^2 + 2*B*a*c)*m^10 + 60*(B*b^2 + 2*B*a*c)*m^9 + 1
565*(B*b^2 + 2*B*a*c)*m^8 + 23280*(B*b^2 + 2*B*a*c)*m^7 + 217743*(B*b^2 + 2*B*a*
c)*m^6 + 1331100*(B*b^2 + 2*B*a*c)*m^5 + 5352935*(B*b^2 + 2*B*a*c)*m^4 + 1387812
0*(B*b^2 + 2*B*a*c)*m^3 + 6652800*B*b^2 + 13305600*B*a*c + 21989356*(B*b^2 + 2*B
*a*c)*m^2 + 18981840*(B*b^2 + 2*B*a*c)*m)*x^6 + ((2*C*a*b + A*b^2 + 2*A*a*c)*m^1
0 + 61*(2*C*a*b + A*b^2 + 2*A*a*c)*m^9 + 1620*(2*C*a*b + A*b^2 + 2*A*a*c)*m^8 +
24570*(2*C*a*b + A*b^2 + 2*A*a*c)*m^7 + 234573*(2*C*a*b + A*b^2 + 2*A*a*c)*m^6 +
1464693*(2*C*a*b + A*b^2 + 2*A*a*c)*m^5 + 6016070*(2*C*a*b + A*b^2 + 2*A*a*c)*m
^4 + 15915380*(2*C*a*b + A*b^2 + 2*A*a*c)*m^3 + 15966720*C*a*b + 7983360*A*b^2 +
15966720*A*a*c + 25681176*(2*C*a*b + A*b^2 + 2*A*a*c)*m^2 + 22512096*(2*C*a*b +
A*b^2 + 2*A*a*c)*m)*x^5 + 2*(B*a*b*m^10 + 62*B*a*b*m^9 + 1677*B*a*b*m^8 + 25962
*B*a*b*m^7 + 253575*B*a*b*m^6 + 1623258*B*a*b*m^5 + 6846503*B*a*b*m^4 + 18609718
*B*a*b*m^3 + 30819204*B*a*b*m^2 + 27641160*B*a*b*m + 9979200*B*a*b)*x^4 + ((C*a^
2 + 2*A*a*b)*m^10 + 63*(C*a^2 + 2*A*a*b)*m^9 + 1736*(C*a^2 + 2*A*a*b)*m^8 + 2746
2*(C*a^2 + 2*A*a*b)*m^7 + 275037*(C*a^2 + 2*A*a*b)*m^6 + 1812447*(C*a^2 + 2*A*a*
b)*m^5 + 7902194*(C*a^2 + 2*A*a*b)*m^4 + 22289148*(C*a^2 + 2*A*a*b)*m^3 + 133056
00*C*a^2 + 26611200*A*a*b + 38390632*(C*a^2 + 2*A*a*b)*m^2 + 35746080*(C*a^2 + 2
*A*a*b)*m)*x^3 + (B*a^2*m^10 + 64*B*a^2*m^9 + 1797*B*a^2*m^8 + 29076*B*a^2*m^7 +
299271*B*a^2*m^6 + 2039016*B*a^2*m^5 + 9261503*B*a^2*m^4 + 27472724*B*a^2*m^3 +
50312628*B*a^2*m^2 + 50292720*B*a^2*m + 19958400*B*a^2)*x^2 + (A*a^2*m^10 + 65*
A*a^2*m^9 + 1860*A*a^2*m^8 + 30810*A*a^2*m^7 + 326613*A*a^2*m^6 + 2310945*A*a^2*
m^5 + 11028590*A*a^2*m^4 + 34967140*A*a^2*m^3 + 70290936*A*a^2*m^2 + 80627040*A*
a^2*m + 39916800*A*a^2)*x)*(d*x)^m/(m^11 + 66*m^10 + 1925*m^9 + 32670*m^8 + 3574
23*m^7 + 2637558*m^6 + 13339535*m^5 + 45995730*m^4 + 105258076*m^3 + 150917976*m
^2 + 120543840*m + 39916800)

_______________________________________________________________________________________

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((d*x)**m*(C*x**2+B*x+A)*(c*x**4+b*x**2+a)**2,x)

[Out]

Timed out

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.302109, size = 1, normalized size = 0. \[ \mathit{Done} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^4 + b*x^2 + a)^2*(C*x^2 + B*x + A)*(d*x)^m,x, algorithm="giac")

[Out]

Done