3.1328 \(\int \frac{(A+B x) \left (a+c x^2\right )^3}{(d+e x)^{10}} \, dx\)

Optimal. Leaf size=334 \[ \frac{c \left (4 A c d e \left (3 a e^2+5 c d^2\right )-B \left (3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right )\right )}{6 e^8 (d+e x)^6}-\frac{3 c^2 \left (a B e^2-2 A c d e+7 B c d^2\right )}{4 e^8 (d+e x)^4}+\frac{c^2 \left (-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right )}{5 e^8 (d+e x)^5}-\frac{\left (a e^2+c d^2\right )^2 \left (a B e^2-6 A c d e+7 B c d^2\right )}{8 e^8 (d+e x)^8}+\frac{\left (a e^2+c d^2\right )^3 (B d-A e)}{9 e^8 (d+e x)^9}+\frac{3 c \left (a e^2+c d^2\right ) \left (-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right )}{7 e^8 (d+e x)^7}+\frac{c^3 (7 B d-A e)}{3 e^8 (d+e x)^3}-\frac{B c^3}{2 e^8 (d+e x)^2} \]

[Out]

((B*d - A*e)*(c*d^2 + a*e^2)^3)/(9*e^8*(d + e*x)^9) - ((c*d^2 + a*e^2)^2*(7*B*c*
d^2 - 6*A*c*d*e + a*B*e^2))/(8*e^8*(d + e*x)^8) + (3*c*(c*d^2 + a*e^2)*(7*B*c*d^
3 - 5*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3))/(7*e^8*(d + e*x)^7) + (c*(4*A*c*d*e*(5
*c*d^2 + 3*a*e^2) - B*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4)))/(6*e^8*(d + e*
x)^6) + (c^2*(35*B*c*d^3 - 15*A*c*d^2*e + 15*a*B*d*e^2 - 3*a*A*e^3))/(5*e^8*(d +
e*x)^5) - (3*c^2*(7*B*c*d^2 - 2*A*c*d*e + a*B*e^2))/(4*e^8*(d + e*x)^4) + (c^3*
(7*B*d - A*e))/(3*e^8*(d + e*x)^3) - (B*c^3)/(2*e^8*(d + e*x)^2)

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Rubi [A]  time = 0.958027, antiderivative size = 334, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{c \left (3 a^2 B e^4-12 a A c d e^3+30 a B c d^2 e^2-20 A c^2 d^3 e+35 B c^2 d^4\right )}{6 e^8 (d+e x)^6}-\frac{3 c^2 \left (a B e^2-2 A c d e+7 B c d^2\right )}{4 e^8 (d+e x)^4}+\frac{c^2 \left (-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right )}{5 e^8 (d+e x)^5}-\frac{\left (a e^2+c d^2\right )^2 \left (a B e^2-6 A c d e+7 B c d^2\right )}{8 e^8 (d+e x)^8}+\frac{\left (a e^2+c d^2\right )^3 (B d-A e)}{9 e^8 (d+e x)^9}+\frac{3 c \left (a e^2+c d^2\right ) \left (-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right )}{7 e^8 (d+e x)^7}+\frac{c^3 (7 B d-A e)}{3 e^8 (d+e x)^3}-\frac{B c^3}{2 e^8 (d+e x)^2} \]

Antiderivative was successfully verified.

[In]  Int[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^10,x]

[Out]

((B*d - A*e)*(c*d^2 + a*e^2)^3)/(9*e^8*(d + e*x)^9) - ((c*d^2 + a*e^2)^2*(7*B*c*
d^2 - 6*A*c*d*e + a*B*e^2))/(8*e^8*(d + e*x)^8) + (3*c*(c*d^2 + a*e^2)*(7*B*c*d^
3 - 5*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3))/(7*e^8*(d + e*x)^7) - (c*(35*B*c^2*d^4
- 20*A*c^2*d^3*e + 30*a*B*c*d^2*e^2 - 12*a*A*c*d*e^3 + 3*a^2*B*e^4))/(6*e^8*(d
+ e*x)^6) + (c^2*(35*B*c*d^3 - 15*A*c*d^2*e + 15*a*B*d*e^2 - 3*a*A*e^3))/(5*e^8*
(d + e*x)^5) - (3*c^2*(7*B*c*d^2 - 2*A*c*d*e + a*B*e^2))/(4*e^8*(d + e*x)^4) + (
c^3*(7*B*d - A*e))/(3*e^8*(d + e*x)^3) - (B*c^3)/(2*e^8*(d + e*x)^2)

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Rubi in Sympy [A]  time = 147.274, size = 345, normalized size = 1.03 \[ - \frac{B c^{3}}{2 e^{8} \left (d + e x\right )^{2}} - \frac{c^{3} \left (A e - 7 B d\right )}{3 e^{8} \left (d + e x\right )^{3}} - \frac{3 c^{2} \left (- 2 A c d e + B a e^{2} + 7 B c d^{2}\right )}{4 e^{8} \left (d + e x\right )^{4}} - \frac{c^{2} \left (3 A a e^{3} + 15 A c d^{2} e - 15 B a d e^{2} - 35 B c d^{3}\right )}{5 e^{8} \left (d + e x\right )^{5}} - \frac{c \left (- 12 A a c d e^{3} - 20 A c^{2} d^{3} e + 3 B a^{2} e^{4} + 30 B a c d^{2} e^{2} + 35 B c^{2} d^{4}\right )}{6 e^{8} \left (d + e x\right )^{6}} - \frac{3 c \left (a e^{2} + c d^{2}\right ) \left (A a e^{3} + 5 A c d^{2} e - 3 B a d e^{2} - 7 B c d^{3}\right )}{7 e^{8} \left (d + e x\right )^{7}} - \frac{\left (a e^{2} + c d^{2}\right )^{2} \left (- 6 A c d e + B a e^{2} + 7 B c d^{2}\right )}{8 e^{8} \left (d + e x\right )^{8}} - \frac{\left (A e - B d\right ) \left (a e^{2} + c d^{2}\right )^{3}}{9 e^{8} \left (d + e x\right )^{9}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((B*x+A)*(c*x**2+a)**3/(e*x+d)**10,x)

[Out]

-B*c**3/(2*e**8*(d + e*x)**2) - c**3*(A*e - 7*B*d)/(3*e**8*(d + e*x)**3) - 3*c**
2*(-2*A*c*d*e + B*a*e**2 + 7*B*c*d**2)/(4*e**8*(d + e*x)**4) - c**2*(3*A*a*e**3
+ 15*A*c*d**2*e - 15*B*a*d*e**2 - 35*B*c*d**3)/(5*e**8*(d + e*x)**5) - c*(-12*A*
a*c*d*e**3 - 20*A*c**2*d**3*e + 3*B*a**2*e**4 + 30*B*a*c*d**2*e**2 + 35*B*c**2*d
**4)/(6*e**8*(d + e*x)**6) - 3*c*(a*e**2 + c*d**2)*(A*a*e**3 + 5*A*c*d**2*e - 3*
B*a*d*e**2 - 7*B*c*d**3)/(7*e**8*(d + e*x)**7) - (a*e**2 + c*d**2)**2*(-6*A*c*d*
e + B*a*e**2 + 7*B*c*d**2)/(8*e**8*(d + e*x)**8) - (A*e - B*d)*(a*e**2 + c*d**2)
**3/(9*e**8*(d + e*x)**9)

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Mathematica [A]  time = 0.432885, size = 359, normalized size = 1.07 \[ -\frac{2 A e \left (140 a^3 e^6+15 a^2 c e^4 \left (d^2+9 d e x+36 e^2 x^2\right )+6 a c^2 e^2 \left (d^4+9 d^3 e x+36 d^2 e^2 x^2+84 d e^3 x^3+126 e^4 x^4\right )+5 c^3 \left (d^6+9 d^5 e x+36 d^4 e^2 x^2+84 d^3 e^3 x^3+126 d^2 e^4 x^4+126 d e^5 x^5+84 e^6 x^6\right )\right )+5 B \left (7 a^3 e^6 (d+9 e x)+3 a^2 c e^4 \left (d^3+9 d^2 e x+36 d e^2 x^2+84 e^3 x^3\right )+3 a c^2 e^2 \left (d^5+9 d^4 e x+36 d^3 e^2 x^2+84 d^2 e^3 x^3+126 d e^4 x^4+126 e^5 x^5\right )+7 c^3 \left (d^7+9 d^6 e x+36 d^5 e^2 x^2+84 d^4 e^3 x^3+126 d^3 e^4 x^4+126 d^2 e^5 x^5+84 d e^6 x^6+36 e^7 x^7\right )\right )}{2520 e^8 (d+e x)^9} \]

Antiderivative was successfully verified.

[In]  Integrate[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^10,x]

[Out]

-(2*A*e*(140*a^3*e^6 + 15*a^2*c*e^4*(d^2 + 9*d*e*x + 36*e^2*x^2) + 6*a*c^2*e^2*(
d^4 + 9*d^3*e*x + 36*d^2*e^2*x^2 + 84*d*e^3*x^3 + 126*e^4*x^4) + 5*c^3*(d^6 + 9*
d^5*e*x + 36*d^4*e^2*x^2 + 84*d^3*e^3*x^3 + 126*d^2*e^4*x^4 + 126*d*e^5*x^5 + 84
*e^6*x^6)) + 5*B*(7*a^3*e^6*(d + 9*e*x) + 3*a^2*c*e^4*(d^3 + 9*d^2*e*x + 36*d*e^
2*x^2 + 84*e^3*x^3) + 3*a*c^2*e^2*(d^5 + 9*d^4*e*x + 36*d^3*e^2*x^2 + 84*d^2*e^3
*x^3 + 126*d*e^4*x^4 + 126*e^5*x^5) + 7*c^3*(d^7 + 9*d^6*e*x + 36*d^5*e^2*x^2 +
84*d^4*e^3*x^3 + 126*d^3*e^4*x^4 + 126*d^2*e^5*x^5 + 84*d*e^6*x^6 + 36*e^7*x^7))
)/(2520*e^8*(d + e*x)^9)

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Maple [A]  time = 0.012, size = 449, normalized size = 1.3 \[{\frac{c \left ( 12\,Aacd{e}^{3}+20\,A{c}^{2}{d}^{3}e-3\,B{e}^{4}{a}^{2}-30\,Bac{d}^{2}{e}^{2}-35\,B{c}^{2}{d}^{4} \right ) }{6\,{e}^{8} \left ( ex+d \right ) ^{6}}}+{\frac{3\,{c}^{2} \left ( 2\,Acde-aB{e}^{2}-7\,Bc{d}^{2} \right ) }{4\,{e}^{8} \left ( ex+d \right ) ^{4}}}-{\frac{{c}^{3} \left ( Ae-7\,Bd \right ) }{3\,{e}^{8} \left ( ex+d \right ) ^{3}}}-{\frac{B{c}^{3}}{2\,{e}^{8} \left ( ex+d \right ) ^{2}}}-{\frac{{c}^{2} \left ( 3\,aA{e}^{3}+15\,Ac{d}^{2}e-15\,aBd{e}^{2}-35\,Bc{d}^{3} \right ) }{5\,{e}^{8} \left ( ex+d \right ) ^{5}}}-{\frac{A{a}^{3}{e}^{7}+3\,A{d}^{2}{a}^{2}c{e}^{5}+3\,A{d}^{4}a{c}^{2}{e}^{3}+A{d}^{6}{c}^{3}e-B{a}^{3}d{e}^{6}-3\,B{a}^{2}c{d}^{3}{e}^{4}-3\,Ba{c}^{2}{d}^{5}{e}^{2}-B{c}^{3}{d}^{7}}{9\,{e}^{8} \left ( ex+d \right ) ^{9}}}-{\frac{-6\,Ad{a}^{2}c{e}^{5}-12\,A{d}^{3}a{c}^{2}{e}^{3}-6\,A{d}^{5}{c}^{3}e+B{a}^{3}{e}^{6}+9\,B{a}^{2}c{d}^{2}{e}^{4}+15\,Ba{c}^{2}{d}^{4}{e}^{2}+7\,B{c}^{3}{d}^{6}}{8\,{e}^{8} \left ( ex+d \right ) ^{8}}}-{\frac{3\,c \left ( A{a}^{2}{e}^{5}+6\,A{d}^{2}ac{e}^{3}+5\,A{d}^{4}{c}^{2}e-3\,Bd{a}^{2}{e}^{4}-10\,aBc{d}^{3}{e}^{2}-7\,B{c}^{2}{d}^{5} \right ) }{7\,{e}^{8} \left ( ex+d \right ) ^{7}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((B*x+A)*(c*x^2+a)^3/(e*x+d)^10,x)

[Out]

1/6*c*(12*A*a*c*d*e^3+20*A*c^2*d^3*e-3*B*a^2*e^4-30*B*a*c*d^2*e^2-35*B*c^2*d^4)/
e^8/(e*x+d)^6+3/4*c^2*(2*A*c*d*e-B*a*e^2-7*B*c*d^2)/e^8/(e*x+d)^4-1/3*c^3*(A*e-7
*B*d)/e^8/(e*x+d)^3-1/2*B*c^3/e^8/(e*x+d)^2-1/5*c^2*(3*A*a*e^3+15*A*c*d^2*e-15*B
*a*d*e^2-35*B*c*d^3)/e^8/(e*x+d)^5-1/9*(A*a^3*e^7+3*A*a^2*c*d^2*e^5+3*A*a*c^2*d^
4*e^3+A*c^3*d^6*e-B*a^3*d*e^6-3*B*a^2*c*d^3*e^4-3*B*a*c^2*d^5*e^2-B*c^3*d^7)/e^8
/(e*x+d)^9-1/8*(-6*A*a^2*c*d*e^5-12*A*a*c^2*d^3*e^3-6*A*c^3*d^5*e+B*a^3*e^6+9*B*
a^2*c*d^2*e^4+15*B*a*c^2*d^4*e^2+7*B*c^3*d^6)/e^8/(e*x+d)^8-3/7*c*(A*a^2*e^5+6*A
*a*c*d^2*e^3+5*A*c^2*d^4*e-3*B*a^2*d*e^4-10*B*a*c*d^3*e^2-7*B*c^2*d^5)/e^8/(e*x+
d)^7

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Maxima [A]  time = 0.725827, size = 737, normalized size = 2.21 \[ -\frac{1260 \, B c^{3} e^{7} x^{7} + 35 \, B c^{3} d^{7} + 10 \, A c^{3} d^{6} e + 15 \, B a c^{2} d^{5} e^{2} + 12 \, A a c^{2} d^{4} e^{3} + 15 \, B a^{2} c d^{3} e^{4} + 30 \, A a^{2} c d^{2} e^{5} + 35 \, B a^{3} d e^{6} + 280 \, A a^{3} e^{7} + 420 \,{\left (7 \, B c^{3} d e^{6} + 2 \, A c^{3} e^{7}\right )} x^{6} + 630 \,{\left (7 \, B c^{3} d^{2} e^{5} + 2 \, A c^{3} d e^{6} + 3 \, B a c^{2} e^{7}\right )} x^{5} + 126 \,{\left (35 \, B c^{3} d^{3} e^{4} + 10 \, A c^{3} d^{2} e^{5} + 15 \, B a c^{2} d e^{6} + 12 \, A a c^{2} e^{7}\right )} x^{4} + 84 \,{\left (35 \, B c^{3} d^{4} e^{3} + 10 \, A c^{3} d^{3} e^{4} + 15 \, B a c^{2} d^{2} e^{5} + 12 \, A a c^{2} d e^{6} + 15 \, B a^{2} c e^{7}\right )} x^{3} + 36 \,{\left (35 \, B c^{3} d^{5} e^{2} + 10 \, A c^{3} d^{4} e^{3} + 15 \, B a c^{2} d^{3} e^{4} + 12 \, A a c^{2} d^{2} e^{5} + 15 \, B a^{2} c d e^{6} + 30 \, A a^{2} c e^{7}\right )} x^{2} + 9 \,{\left (35 \, B c^{3} d^{6} e + 10 \, A c^{3} d^{5} e^{2} + 15 \, B a c^{2} d^{4} e^{3} + 12 \, A a c^{2} d^{3} e^{4} + 15 \, B a^{2} c d^{2} e^{5} + 30 \, A a^{2} c d e^{6} + 35 \, B a^{3} e^{7}\right )} x}{2520 \,{\left (e^{17} x^{9} + 9 \, d e^{16} x^{8} + 36 \, d^{2} e^{15} x^{7} + 84 \, d^{3} e^{14} x^{6} + 126 \, d^{4} e^{13} x^{5} + 126 \, d^{5} e^{12} x^{4} + 84 \, d^{6} e^{11} x^{3} + 36 \, d^{7} e^{10} x^{2} + 9 \, d^{8} e^{9} x + d^{9} e^{8}\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^2 + a)^3*(B*x + A)/(e*x + d)^10,x, algorithm="maxima")

[Out]

-1/2520*(1260*B*c^3*e^7*x^7 + 35*B*c^3*d^7 + 10*A*c^3*d^6*e + 15*B*a*c^2*d^5*e^2
+ 12*A*a*c^2*d^4*e^3 + 15*B*a^2*c*d^3*e^4 + 30*A*a^2*c*d^2*e^5 + 35*B*a^3*d*e^6
+ 280*A*a^3*e^7 + 420*(7*B*c^3*d*e^6 + 2*A*c^3*e^7)*x^6 + 630*(7*B*c^3*d^2*e^5
+ 2*A*c^3*d*e^6 + 3*B*a*c^2*e^7)*x^5 + 126*(35*B*c^3*d^3*e^4 + 10*A*c^3*d^2*e^5
+ 15*B*a*c^2*d*e^6 + 12*A*a*c^2*e^7)*x^4 + 84*(35*B*c^3*d^4*e^3 + 10*A*c^3*d^3*e
^4 + 15*B*a*c^2*d^2*e^5 + 12*A*a*c^2*d*e^6 + 15*B*a^2*c*e^7)*x^3 + 36*(35*B*c^3*
d^5*e^2 + 10*A*c^3*d^4*e^3 + 15*B*a*c^2*d^3*e^4 + 12*A*a*c^2*d^2*e^5 + 15*B*a^2*
c*d*e^6 + 30*A*a^2*c*e^7)*x^2 + 9*(35*B*c^3*d^6*e + 10*A*c^3*d^5*e^2 + 15*B*a*c^
2*d^4*e^3 + 12*A*a*c^2*d^3*e^4 + 15*B*a^2*c*d^2*e^5 + 30*A*a^2*c*d*e^6 + 35*B*a^
3*e^7)*x)/(e^17*x^9 + 9*d*e^16*x^8 + 36*d^2*e^15*x^7 + 84*d^3*e^14*x^6 + 126*d^4
*e^13*x^5 + 126*d^5*e^12*x^4 + 84*d^6*e^11*x^3 + 36*d^7*e^10*x^2 + 9*d^8*e^9*x +
d^9*e^8)

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Fricas [A]  time = 0.27663, size = 737, normalized size = 2.21 \[ -\frac{1260 \, B c^{3} e^{7} x^{7} + 35 \, B c^{3} d^{7} + 10 \, A c^{3} d^{6} e + 15 \, B a c^{2} d^{5} e^{2} + 12 \, A a c^{2} d^{4} e^{3} + 15 \, B a^{2} c d^{3} e^{4} + 30 \, A a^{2} c d^{2} e^{5} + 35 \, B a^{3} d e^{6} + 280 \, A a^{3} e^{7} + 420 \,{\left (7 \, B c^{3} d e^{6} + 2 \, A c^{3} e^{7}\right )} x^{6} + 630 \,{\left (7 \, B c^{3} d^{2} e^{5} + 2 \, A c^{3} d e^{6} + 3 \, B a c^{2} e^{7}\right )} x^{5} + 126 \,{\left (35 \, B c^{3} d^{3} e^{4} + 10 \, A c^{3} d^{2} e^{5} + 15 \, B a c^{2} d e^{6} + 12 \, A a c^{2} e^{7}\right )} x^{4} + 84 \,{\left (35 \, B c^{3} d^{4} e^{3} + 10 \, A c^{3} d^{3} e^{4} + 15 \, B a c^{2} d^{2} e^{5} + 12 \, A a c^{2} d e^{6} + 15 \, B a^{2} c e^{7}\right )} x^{3} + 36 \,{\left (35 \, B c^{3} d^{5} e^{2} + 10 \, A c^{3} d^{4} e^{3} + 15 \, B a c^{2} d^{3} e^{4} + 12 \, A a c^{2} d^{2} e^{5} + 15 \, B a^{2} c d e^{6} + 30 \, A a^{2} c e^{7}\right )} x^{2} + 9 \,{\left (35 \, B c^{3} d^{6} e + 10 \, A c^{3} d^{5} e^{2} + 15 \, B a c^{2} d^{4} e^{3} + 12 \, A a c^{2} d^{3} e^{4} + 15 \, B a^{2} c d^{2} e^{5} + 30 \, A a^{2} c d e^{6} + 35 \, B a^{3} e^{7}\right )} x}{2520 \,{\left (e^{17} x^{9} + 9 \, d e^{16} x^{8} + 36 \, d^{2} e^{15} x^{7} + 84 \, d^{3} e^{14} x^{6} + 126 \, d^{4} e^{13} x^{5} + 126 \, d^{5} e^{12} x^{4} + 84 \, d^{6} e^{11} x^{3} + 36 \, d^{7} e^{10} x^{2} + 9 \, d^{8} e^{9} x + d^{9} e^{8}\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^2 + a)^3*(B*x + A)/(e*x + d)^10,x, algorithm="fricas")

[Out]

-1/2520*(1260*B*c^3*e^7*x^7 + 35*B*c^3*d^7 + 10*A*c^3*d^6*e + 15*B*a*c^2*d^5*e^2
+ 12*A*a*c^2*d^4*e^3 + 15*B*a^2*c*d^3*e^4 + 30*A*a^2*c*d^2*e^5 + 35*B*a^3*d*e^6
+ 280*A*a^3*e^7 + 420*(7*B*c^3*d*e^6 + 2*A*c^3*e^7)*x^6 + 630*(7*B*c^3*d^2*e^5
+ 2*A*c^3*d*e^6 + 3*B*a*c^2*e^7)*x^5 + 126*(35*B*c^3*d^3*e^4 + 10*A*c^3*d^2*e^5
+ 15*B*a*c^2*d*e^6 + 12*A*a*c^2*e^7)*x^4 + 84*(35*B*c^3*d^4*e^3 + 10*A*c^3*d^3*e
^4 + 15*B*a*c^2*d^2*e^5 + 12*A*a*c^2*d*e^6 + 15*B*a^2*c*e^7)*x^3 + 36*(35*B*c^3*
d^5*e^2 + 10*A*c^3*d^4*e^3 + 15*B*a*c^2*d^3*e^4 + 12*A*a*c^2*d^2*e^5 + 15*B*a^2*
c*d*e^6 + 30*A*a^2*c*e^7)*x^2 + 9*(35*B*c^3*d^6*e + 10*A*c^3*d^5*e^2 + 15*B*a*c^
2*d^4*e^3 + 12*A*a*c^2*d^3*e^4 + 15*B*a^2*c*d^2*e^5 + 30*A*a^2*c*d*e^6 + 35*B*a^
3*e^7)*x)/(e^17*x^9 + 9*d*e^16*x^8 + 36*d^2*e^15*x^7 + 84*d^3*e^14*x^6 + 126*d^4
*e^13*x^5 + 126*d^5*e^12*x^4 + 84*d^6*e^11*x^3 + 36*d^7*e^10*x^2 + 9*d^8*e^9*x +
d^9*e^8)

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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((B*x+A)*(c*x**2+a)**3/(e*x+d)**10,x)

[Out]

Timed out

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GIAC/XCAS [A]  time = 0.302719, size = 617, normalized size = 1.85 \[ -\frac{{\left (1260 \, B c^{3} x^{7} e^{7} + 2940 \, B c^{3} d x^{6} e^{6} + 4410 \, B c^{3} d^{2} x^{5} e^{5} + 4410 \, B c^{3} d^{3} x^{4} e^{4} + 2940 \, B c^{3} d^{4} x^{3} e^{3} + 1260 \, B c^{3} d^{5} x^{2} e^{2} + 315 \, B c^{3} d^{6} x e + 35 \, B c^{3} d^{7} + 840 \, A c^{3} x^{6} e^{7} + 1260 \, A c^{3} d x^{5} e^{6} + 1260 \, A c^{3} d^{2} x^{4} e^{5} + 840 \, A c^{3} d^{3} x^{3} e^{4} + 360 \, A c^{3} d^{4} x^{2} e^{3} + 90 \, A c^{3} d^{5} x e^{2} + 10 \, A c^{3} d^{6} e + 1890 \, B a c^{2} x^{5} e^{7} + 1890 \, B a c^{2} d x^{4} e^{6} + 1260 \, B a c^{2} d^{2} x^{3} e^{5} + 540 \, B a c^{2} d^{3} x^{2} e^{4} + 135 \, B a c^{2} d^{4} x e^{3} + 15 \, B a c^{2} d^{5} e^{2} + 1512 \, A a c^{2} x^{4} e^{7} + 1008 \, A a c^{2} d x^{3} e^{6} + 432 \, A a c^{2} d^{2} x^{2} e^{5} + 108 \, A a c^{2} d^{3} x e^{4} + 12 \, A a c^{2} d^{4} e^{3} + 1260 \, B a^{2} c x^{3} e^{7} + 540 \, B a^{2} c d x^{2} e^{6} + 135 \, B a^{2} c d^{2} x e^{5} + 15 \, B a^{2} c d^{3} e^{4} + 1080 \, A a^{2} c x^{2} e^{7} + 270 \, A a^{2} c d x e^{6} + 30 \, A a^{2} c d^{2} e^{5} + 315 \, B a^{3} x e^{7} + 35 \, B a^{3} d e^{6} + 280 \, A a^{3} e^{7}\right )} e^{\left (-8\right )}}{2520 \,{\left (x e + d\right )}^{9}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((c*x^2 + a)^3*(B*x + A)/(e*x + d)^10,x, algorithm="giac")

[Out]

-1/2520*(1260*B*c^3*x^7*e^7 + 2940*B*c^3*d*x^6*e^6 + 4410*B*c^3*d^2*x^5*e^5 + 44
10*B*c^3*d^3*x^4*e^4 + 2940*B*c^3*d^4*x^3*e^3 + 1260*B*c^3*d^5*x^2*e^2 + 315*B*c
^3*d^6*x*e + 35*B*c^3*d^7 + 840*A*c^3*x^6*e^7 + 1260*A*c^3*d*x^5*e^6 + 1260*A*c^
3*d^2*x^4*e^5 + 840*A*c^3*d^3*x^3*e^4 + 360*A*c^3*d^4*x^2*e^3 + 90*A*c^3*d^5*x*e
^2 + 10*A*c^3*d^6*e + 1890*B*a*c^2*x^5*e^7 + 1890*B*a*c^2*d*x^4*e^6 + 1260*B*a*c
^2*d^2*x^3*e^5 + 540*B*a*c^2*d^3*x^2*e^4 + 135*B*a*c^2*d^4*x*e^3 + 15*B*a*c^2*d^
5*e^2 + 1512*A*a*c^2*x^4*e^7 + 1008*A*a*c^2*d*x^3*e^6 + 432*A*a*c^2*d^2*x^2*e^5
+ 108*A*a*c^2*d^3*x*e^4 + 12*A*a*c^2*d^4*e^3 + 1260*B*a^2*c*x^3*e^7 + 540*B*a^2*
c*d*x^2*e^6 + 135*B*a^2*c*d^2*x*e^5 + 15*B*a^2*c*d^3*e^4 + 1080*A*a^2*c*x^2*e^7
+ 270*A*a^2*c*d*x*e^6 + 30*A*a^2*c*d^2*e^5 + 315*B*a^3*x*e^7 + 35*B*a^3*d*e^6 +
280*A*a^3*e^7)*e^(-8)/(x*e + d)^9