3.440 \(\int (d+e x)^m \left (b x+c x^2\right )^3 \, dx\)
Optimal. Leaf size=267 \[ \frac{3 d (c d-b e) \left (b^2 e^2-5 b c d e+5 c^2 d^2\right ) (d+e x)^{m+3}}{e^7 (m+3)}-\frac{(2 c d-b e) \left (b^2 e^2-10 b c d e+10 c^2 d^2\right ) (d+e x)^{m+4}}{e^7 (m+4)}+\frac{3 c \left (b^2 e^2-5 b c d e+5 c^2 d^2\right ) (d+e x)^{m+5}}{e^7 (m+5)}-\frac{3 c^2 (2 c d-b e) (d+e x)^{m+6}}{e^7 (m+6)}+\frac{d^3 (c d-b e)^3 (d+e x)^{m+1}}{e^7 (m+1)}-\frac{3 d^2 (c d-b e)^2 (2 c d-b e) (d+e x)^{m+2}}{e^7 (m+2)}+\frac{c^3 (d+e x)^{m+7}}{e^7 (m+7)} \]
[Out]
(d^3*(c*d - b*e)^3*(d + e*x)^(1 + m))/(e^7*(1 + m)) - (3*d^2*(c*d - b*e)^2*(2*c*
d - b*e)*(d + e*x)^(2 + m))/(e^7*(2 + m)) + (3*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*
d*e + b^2*e^2)*(d + e*x)^(3 + m))/(e^7*(3 + m)) - ((2*c*d - b*e)*(10*c^2*d^2 - 1
0*b*c*d*e + b^2*e^2)*(d + e*x)^(4 + m))/(e^7*(4 + m)) + (3*c*(5*c^2*d^2 - 5*b*c*
d*e + b^2*e^2)*(d + e*x)^(5 + m))/(e^7*(5 + m)) - (3*c^2*(2*c*d - b*e)*(d + e*x)
^(6 + m))/(e^7*(6 + m)) + (c^3*(d + e*x)^(7 + m))/(e^7*(7 + m))
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Rubi [A] time = 0.407892, antiderivative size = 267, 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
\[ \frac{3 d (c d-b e) \left (b^2 e^2-5 b c d e+5 c^2 d^2\right ) (d+e x)^{m+3}}{e^7 (m+3)}-\frac{(2 c d-b e) \left (b^2 e^2-10 b c d e+10 c^2 d^2\right ) (d+e x)^{m+4}}{e^7 (m+4)}+\frac{3 c \left (b^2 e^2-5 b c d e+5 c^2 d^2\right ) (d+e x)^{m+5}}{e^7 (m+5)}-\frac{3 c^2 (2 c d-b e) (d+e x)^{m+6}}{e^7 (m+6)}+\frac{d^3 (c d-b e)^3 (d+e x)^{m+1}}{e^7 (m+1)}-\frac{3 d^2 (c d-b e)^2 (2 c d-b e) (d+e x)^{m+2}}{e^7 (m+2)}+\frac{c^3 (d+e x)^{m+7}}{e^7 (m+7)} \]
Antiderivative was successfully verified.
[In] Int[(d + e*x)^m*(b*x + c*x^2)^3,x]
[Out]
(d^3*(c*d - b*e)^3*(d + e*x)^(1 + m))/(e^7*(1 + m)) - (3*d^2*(c*d - b*e)^2*(2*c*
d - b*e)*(d + e*x)^(2 + m))/(e^7*(2 + m)) + (3*d*(c*d - b*e)*(5*c^2*d^2 - 5*b*c*
d*e + b^2*e^2)*(d + e*x)^(3 + m))/(e^7*(3 + m)) - ((2*c*d - b*e)*(10*c^2*d^2 - 1
0*b*c*d*e + b^2*e^2)*(d + e*x)^(4 + m))/(e^7*(4 + m)) + (3*c*(5*c^2*d^2 - 5*b*c*
d*e + b^2*e^2)*(d + e*x)^(5 + m))/(e^7*(5 + m)) - (3*c^2*(2*c*d - b*e)*(d + e*x)
^(6 + m))/(e^7*(6 + m)) + (c^3*(d + e*x)^(7 + m))/(e^7*(7 + m))
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Rubi in Sympy [A] time = 81.84, size = 250, normalized size = 0.94 \[ \frac{c^{3} \left (d + e x\right )^{m + 7}}{e^{7} \left (m + 7\right )} + \frac{3 c^{2} \left (d + e x\right )^{m + 6} \left (b e - 2 c d\right )}{e^{7} \left (m + 6\right )} + \frac{3 c \left (d + e x\right )^{m + 5} \left (b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right )}{e^{7} \left (m + 5\right )} - \frac{d^{3} \left (d + e x\right )^{m + 1} \left (b e - c d\right )^{3}}{e^{7} \left (m + 1\right )} + \frac{3 d^{2} \left (d + e x\right )^{m + 2} \left (b e - 2 c d\right ) \left (b e - c d\right )^{2}}{e^{7} \left (m + 2\right )} - \frac{3 d \left (d + e x\right )^{m + 3} \left (b e - c d\right ) \left (b^{2} e^{2} - 5 b c d e + 5 c^{2} d^{2}\right )}{e^{7} \left (m + 3\right )} + \frac{\left (d + e x\right )^{m + 4} \left (b e - 2 c d\right ) \left (b^{2} e^{2} - 10 b c d e + 10 c^{2} d^{2}\right )}{e^{7} \left (m + 4\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((e*x+d)**m*(c*x**2+b*x)**3,x)
[Out]
c**3*(d + e*x)**(m + 7)/(e**7*(m + 7)) + 3*c**2*(d + e*x)**(m + 6)*(b*e - 2*c*d)
/(e**7*(m + 6)) + 3*c*(d + e*x)**(m + 5)*(b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2)/(
e**7*(m + 5)) - d**3*(d + e*x)**(m + 1)*(b*e - c*d)**3/(e**7*(m + 1)) + 3*d**2*(
d + e*x)**(m + 2)*(b*e - 2*c*d)*(b*e - c*d)**2/(e**7*(m + 2)) - 3*d*(d + e*x)**(
m + 3)*(b*e - c*d)*(b**2*e**2 - 5*b*c*d*e + 5*c**2*d**2)/(e**7*(m + 3)) + (d + e
*x)**(m + 4)*(b*e - 2*c*d)*(b**2*e**2 - 10*b*c*d*e + 10*c**2*d**2)/(e**7*(m + 4)
)
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Mathematica [A] time = 0.552354, size = 506, normalized size = 1.9 \[ \frac{(d+e x)^{m+1} \left (b^3 e^3 \left (m^3+18 m^2+107 m+210\right ) \left (-6 d^3+6 d^2 e (m+1) x-3 d e^2 \left (m^2+3 m+2\right ) x^2+e^3 \left (m^3+6 m^2+11 m+6\right ) x^3\right )+3 b^2 c e^2 \left (m^2+13 m+42\right ) \left (24 d^4-24 d^3 e (m+1) x+12 d^2 e^2 \left (m^2+3 m+2\right ) x^2-4 d e^3 \left (m^3+6 m^2+11 m+6\right ) x^3+e^4 \left (m^4+10 m^3+35 m^2+50 m+24\right ) x^4\right )+3 b c^2 e (m+7) \left (-120 d^5+120 d^4 e (m+1) x-60 d^3 e^2 \left (m^2+3 m+2\right ) x^2+20 d^2 e^3 \left (m^3+6 m^2+11 m+6\right ) x^3-5 d e^4 \left (m^4+10 m^3+35 m^2+50 m+24\right ) x^4+e^5 \left (m^5+15 m^4+85 m^3+225 m^2+274 m+120\right ) x^5\right )+c^3 \left (720 d^6-720 d^5 e (m+1) x+360 d^4 e^2 \left (m^2+3 m+2\right ) x^2-120 d^3 e^3 \left (m^3+6 m^2+11 m+6\right ) x^3+30 d^2 e^4 \left (m^4+10 m^3+35 m^2+50 m+24\right ) x^4-6 d e^5 \left (m^5+15 m^4+85 m^3+225 m^2+274 m+120\right ) x^5+e^6 \left (m^6+21 m^5+175 m^4+735 m^3+1624 m^2+1764 m+720\right ) x^6\right )\right )}{e^7 (m+1) (m+2) (m+3) (m+4) (m+5) (m+6) (m+7)} \]
Antiderivative was successfully verified.
[In] Integrate[(d + e*x)^m*(b*x + c*x^2)^3,x]
[Out]
((d + e*x)^(1 + m)*(b^3*e^3*(210 + 107*m + 18*m^2 + m^3)*(-6*d^3 + 6*d^2*e*(1 +
m)*x - 3*d*e^2*(2 + 3*m + m^2)*x^2 + e^3*(6 + 11*m + 6*m^2 + m^3)*x^3) + 3*b^2*c
*e^2*(42 + 13*m + m^2)*(24*d^4 - 24*d^3*e*(1 + m)*x + 12*d^2*e^2*(2 + 3*m + m^2)
*x^2 - 4*d*e^3*(6 + 11*m + 6*m^2 + m^3)*x^3 + e^4*(24 + 50*m + 35*m^2 + 10*m^3 +
m^4)*x^4) + 3*b*c^2*e*(7 + m)*(-120*d^5 + 120*d^4*e*(1 + m)*x - 60*d^3*e^2*(2 +
3*m + m^2)*x^2 + 20*d^2*e^3*(6 + 11*m + 6*m^2 + m^3)*x^3 - 5*d*e^4*(24 + 50*m +
35*m^2 + 10*m^3 + m^4)*x^4 + e^5*(120 + 274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5
)*x^5) + c^3*(720*d^6 - 720*d^5*e*(1 + m)*x + 360*d^4*e^2*(2 + 3*m + m^2)*x^2 -
120*d^3*e^3*(6 + 11*m + 6*m^2 + m^3)*x^3 + 30*d^2*e^4*(24 + 50*m + 35*m^2 + 10*m
^3 + m^4)*x^4 - 6*d*e^5*(120 + 274*m + 225*m^2 + 85*m^3 + 15*m^4 + m^5)*x^5 + e^
6*(720 + 1764*m + 1624*m^2 + 735*m^3 + 175*m^4 + 21*m^5 + m^6)*x^6)))/(e^7*(1 +
m)*(2 + m)*(3 + m)*(4 + m)*(5 + m)*(6 + m)*(7 + m))
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Maple [B] time = 0.019, size = 1528, normalized size = 5.7 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((e*x+d)^m*(c*x^2+b*x)^3,x)
[Out]
-(e*x+d)^(1+m)*(-c^3*e^6*m^6*x^6-3*b*c^2*e^6*m^6*x^5-21*c^3*e^6*m^5*x^6-3*b^2*c*
e^6*m^6*x^4-66*b*c^2*e^6*m^5*x^5+6*c^3*d*e^5*m^5*x^5-175*c^3*e^6*m^4*x^6-b^3*e^6
*m^6*x^3-69*b^2*c*e^6*m^5*x^4+15*b*c^2*d*e^5*m^5*x^4-570*b*c^2*e^6*m^4*x^5+90*c^
3*d*e^5*m^4*x^5-735*c^3*e^6*m^3*x^6-24*b^3*e^6*m^5*x^3+12*b^2*c*d*e^5*m^5*x^3-62
1*b^2*c*e^6*m^4*x^4+255*b*c^2*d*e^5*m^4*x^4-2460*b*c^2*e^6*m^3*x^5-30*c^3*d^2*e^
4*m^4*x^4+510*c^3*d*e^5*m^3*x^5-1624*c^3*e^6*m^2*x^6+3*b^3*d*e^5*m^5*x^2-226*b^3
*e^6*m^4*x^3+228*b^2*c*d*e^5*m^4*x^3-2775*b^2*c*e^6*m^3*x^4-60*b*c^2*d^2*e^4*m^4
*x^3+1575*b*c^2*d*e^5*m^3*x^4-5547*b*c^2*e^6*m^2*x^5-300*c^3*d^2*e^4*m^3*x^4+135
0*c^3*d*e^5*m^2*x^5-1764*c^3*e^6*m*x^6+63*b^3*d*e^5*m^4*x^2-1056*b^3*e^6*m^3*x^3
-36*b^2*c*d^2*e^4*m^4*x^2+1572*b^2*c*d*e^5*m^3*x^3-6432*b^2*c*e^6*m^2*x^4-780*b*
c^2*d^2*e^4*m^3*x^3+4425*b*c^2*d*e^5*m^2*x^4-6114*b*c^2*e^6*m*x^5+120*c^3*d^3*e^
3*m^3*x^3-1050*c^3*d^2*e^4*m^2*x^4+1644*c^3*d*e^5*m*x^5-720*c^3*e^6*x^6-6*b^3*d^
2*e^4*m^4*x+489*b^3*d*e^5*m^3*x^2-2545*b^3*e^6*m^2*x^3-576*b^2*c*d^2*e^4*m^3*x^2
+4812*b^2*c*d*e^5*m^2*x^3-7236*b^2*c*e^6*m*x^4+180*b*c^2*d^3*e^3*m^3*x^2-3180*b*
c^2*d^2*e^4*m^2*x^3+5610*b*c^2*d*e^5*m*x^4-2520*b*c^2*e^6*x^5+720*c^3*d^3*e^3*m^
2*x^3-1500*c^3*d^2*e^4*m*x^4+720*c^3*d*e^5*x^5-114*b^3*d^2*e^4*m^3*x+1701*b^3*d*
e^5*m^2*x^2-2952*b^3*e^6*m*x^3+72*b^2*c*d^3*e^3*m^3*x-2988*b^2*c*d^2*e^4*m^2*x^2
+6480*b^2*c*d*e^5*m*x^3-3024*b^2*c*e^6*x^4+1800*b*c^2*d^3*e^3*m^2*x^2-4980*b*c^2
*d^2*e^4*m*x^3+2520*b*c^2*d*e^5*x^4-360*c^3*d^4*e^2*m^2*x^2+1320*c^3*d^3*e^3*m*x
^3-720*c^3*d^2*e^4*x^4+6*b^3*d^3*e^3*m^3-750*b^3*d^2*e^4*m^2*x+2532*b^3*d*e^5*m*
x^2-1260*b^3*e^6*x^3+1008*b^2*c*d^3*e^3*m^2*x-5472*b^2*c*d^2*e^4*m*x^2+3024*b^2*
c*d*e^5*x^3-360*b*c^2*d^4*e^2*m^2*x+4140*b*c^2*d^3*e^3*m*x^2-2520*b*c^2*d^2*e^4*
x^3-1080*c^3*d^4*e^2*m*x^2+720*c^3*d^3*e^3*x^3+108*b^3*d^3*e^3*m^2-1902*b^3*d^2*
e^4*m*x+1260*b^3*d*e^5*x^2-72*b^2*c*d^4*e^2*m^2+3960*b^2*c*d^3*e^3*m*x-3024*b^2*
c*d^2*e^4*x^2-2880*b*c^2*d^4*e^2*m*x+2520*b*c^2*d^3*e^3*x^2+720*c^3*d^5*e*m*x-72
0*c^3*d^4*e^2*x^2+642*b^3*d^3*e^3*m-1260*b^3*d^2*e^4*x-936*b^2*c*d^4*e^2*m+3024*
b^2*c*d^3*e^3*x+360*b*c^2*d^5*e*m-2520*b*c^2*d^4*e^2*x+720*c^3*d^5*e*x+1260*b^3*
d^3*e^3-3024*b^2*c*d^4*e^2+2520*b*c^2*d^5*e-720*c^3*d^6)/e^7/(m^7+28*m^6+322*m^5
+1960*m^4+6769*m^3+13132*m^2+13068*m+5040)
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Maxima [A] time = 0.76158, size = 903, normalized size = 3.38 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(e*x + d)^m,x, algorithm="maxima")
[Out]
((m^3 + 6*m^2 + 11*m + 6)*e^4*x^4 + (m^3 + 3*m^2 + 2*m)*d*e^3*x^3 - 3*(m^2 + m)*
d^2*e^2*x^2 + 6*d^3*e*m*x - 6*d^4)*(e*x + d)^m*b^3/((m^4 + 10*m^3 + 35*m^2 + 50*
m + 24)*e^4) + 3*((m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*e^5*x^5 + (m^4 + 6*m^3 + 1
1*m^2 + 6*m)*d*e^4*x^4 - 4*(m^3 + 3*m^2 + 2*m)*d^2*e^3*x^3 + 12*(m^2 + m)*d^3*e^
2*x^2 - 24*d^4*e*m*x + 24*d^5)*(e*x + d)^m*b^2*c/((m^5 + 15*m^4 + 85*m^3 + 225*m
^2 + 274*m + 120)*e^5) + 3*((m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120)*e^6*
x^6 + (m^5 + 10*m^4 + 35*m^3 + 50*m^2 + 24*m)*d*e^5*x^5 - 5*(m^4 + 6*m^3 + 11*m^
2 + 6*m)*d^2*e^4*x^4 + 20*(m^3 + 3*m^2 + 2*m)*d^3*e^3*x^3 - 60*(m^2 + m)*d^4*e^2
*x^2 + 120*d^5*e*m*x - 120*d^6)*(e*x + d)^m*b*c^2/((m^6 + 21*m^5 + 175*m^4 + 735
*m^3 + 1624*m^2 + 1764*m + 720)*e^6) + ((m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624
*m^2 + 1764*m + 720)*e^7*x^7 + (m^6 + 15*m^5 + 85*m^4 + 225*m^3 + 274*m^2 + 120*
m)*d*e^6*x^6 - 6*(m^5 + 10*m^4 + 35*m^3 + 50*m^2 + 24*m)*d^2*e^5*x^5 + 30*(m^4 +
6*m^3 + 11*m^2 + 6*m)*d^3*e^4*x^4 - 120*(m^3 + 3*m^2 + 2*m)*d^4*e^3*x^3 + 360*(
m^2 + m)*d^5*e^2*x^2 - 720*d^6*e*m*x + 720*d^7)*(e*x + d)^m*c^3/((m^7 + 28*m^6 +
322*m^5 + 1960*m^4 + 6769*m^3 + 13132*m^2 + 13068*m + 5040)*e^7)
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Fricas [A] time = 0.236711, size = 1956, normalized size = 7.33 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(e*x + d)^m,x, algorithm="fricas")
[Out]
-(6*b^3*d^4*e^3*m^3 - 720*c^3*d^7 + 2520*b*c^2*d^6*e - 3024*b^2*c*d^5*e^2 + 1260
*b^3*d^4*e^3 - (c^3*e^7*m^6 + 21*c^3*e^7*m^5 + 175*c^3*e^7*m^4 + 735*c^3*e^7*m^3
+ 1624*c^3*e^7*m^2 + 1764*c^3*e^7*m + 720*c^3*e^7)*x^7 - (2520*b*c^2*e^7 + (c^3
*d*e^6 + 3*b*c^2*e^7)*m^6 + 3*(5*c^3*d*e^6 + 22*b*c^2*e^7)*m^5 + 5*(17*c^3*d*e^6
+ 114*b*c^2*e^7)*m^4 + 15*(15*c^3*d*e^6 + 164*b*c^2*e^7)*m^3 + (274*c^3*d*e^6 +
5547*b*c^2*e^7)*m^2 + 6*(20*c^3*d*e^6 + 1019*b*c^2*e^7)*m)*x^6 - 3*(1008*b^2*c*
e^7 + (b*c^2*d*e^6 + b^2*c*e^7)*m^6 - (2*c^3*d^2*e^5 - 17*b*c^2*d*e^6 - 23*b^2*c
*e^7)*m^5 - (20*c^3*d^2*e^5 - 105*b*c^2*d*e^6 - 207*b^2*c*e^7)*m^4 - 5*(14*c^3*d
^2*e^5 - 59*b*c^2*d*e^6 - 185*b^2*c*e^7)*m^3 - 2*(50*c^3*d^2*e^5 - 187*b*c^2*d*e
^6 - 1072*b^2*c*e^7)*m^2 - 12*(4*c^3*d^2*e^5 - 14*b*c^2*d*e^6 - 201*b^2*c*e^7)*m
)*x^5 - (1260*b^3*e^7 + (3*b^2*c*d*e^6 + b^3*e^7)*m^6 - 3*(5*b*c^2*d^2*e^5 - 19*
b^2*c*d*e^6 - 8*b^3*e^7)*m^5 + (30*c^3*d^3*e^4 - 195*b*c^2*d^2*e^5 + 393*b^2*c*d
*e^6 + 226*b^3*e^7)*m^4 + 3*(60*c^3*d^3*e^4 - 265*b*c^2*d^2*e^5 + 401*b^2*c*d*e^
6 + 352*b^3*e^7)*m^3 + 5*(66*c^3*d^3*e^4 - 249*b*c^2*d^2*e^5 + 324*b^2*c*d*e^6 +
509*b^3*e^7)*m^2 + 18*(10*c^3*d^3*e^4 - 35*b*c^2*d^2*e^5 + 42*b^2*c*d*e^6 + 164
*b^3*e^7)*m)*x^4 - (b^3*d*e^6*m^6 - 3*(4*b^2*c*d^2*e^5 - 7*b^3*d*e^6)*m^5 + (60*
b*c^2*d^3*e^4 - 192*b^2*c*d^2*e^5 + 163*b^3*d*e^6)*m^4 - 3*(40*c^3*d^4*e^3 - 200
*b*c^2*d^3*e^4 + 332*b^2*c*d^2*e^5 - 189*b^3*d*e^6)*m^3 - 4*(90*c^3*d^4*e^3 - 34
5*b*c^2*d^3*e^4 + 456*b^2*c*d^2*e^5 - 211*b^3*d*e^6)*m^2 - 12*(20*c^3*d^4*e^3 -
70*b*c^2*d^3*e^4 + 84*b^2*c*d^2*e^5 - 35*b^3*d*e^6)*m)*x^3 - 36*(2*b^2*c*d^5*e^2
- 3*b^3*d^4*e^3)*m^2 + 3*(b^3*d^2*e^5*m^5 - (12*b^2*c*d^3*e^4 - 19*b^3*d^2*e^5)
*m^4 + (60*b*c^2*d^4*e^3 - 168*b^2*c*d^3*e^4 + 125*b^3*d^2*e^5)*m^3 - (120*c^3*d
^5*e^2 - 480*b*c^2*d^4*e^3 + 660*b^2*c*d^3*e^4 - 317*b^3*d^2*e^5)*m^2 - 6*(20*c^
3*d^5*e^2 - 70*b*c^2*d^4*e^3 + 84*b^2*c*d^3*e^4 - 35*b^3*d^2*e^5)*m)*x^2 + 6*(60
*b*c^2*d^6*e - 156*b^2*c*d^5*e^2 + 107*b^3*d^4*e^3)*m - 6*(b^3*d^3*e^4*m^4 - 6*(
2*b^2*c*d^4*e^3 - 3*b^3*d^3*e^4)*m^3 + (60*b*c^2*d^5*e^2 - 156*b^2*c*d^4*e^3 + 1
07*b^3*d^3*e^4)*m^2 - 6*(20*c^3*d^6*e - 70*b*c^2*d^5*e^2 + 84*b^2*c*d^4*e^3 - 35
*b^3*d^3*e^4)*m)*x)*(e*x + d)^m/(e^7*m^7 + 28*e^7*m^6 + 322*e^7*m^5 + 1960*e^7*m
^4 + 6769*e^7*m^3 + 13132*e^7*m^2 + 13068*e^7*m + 5040*e^7)
_______________________________________________________________________________________
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((e*x+d)**m*(c*x**2+b*x)**3,x)
[Out]
Timed out
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.21196, size = 1, normalized size = 0. \[ \mathit{Done} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^3*(e*x + d)^m,x, algorithm="giac")
[Out]
Done