3.1919 \(\int (a+b x) (d+e x)^3 \left (a^2+2 a b x+b^2 x^2\right )^3 \, dx\)

Optimal. Leaf size=92 \[ \frac{3 e^2 (a+b x)^{10} (b d-a e)}{10 b^4}+\frac{e (a+b x)^9 (b d-a e)^2}{3 b^4}+\frac{(a+b x)^8 (b d-a e)^3}{8 b^4}+\frac{e^3 (a+b x)^{11}}{11 b^4} \]

[Out]

((b*d - a*e)^3*(a + b*x)^8)/(8*b^4) + (e*(b*d - a*e)^2*(a + b*x)^9)/(3*b^4) + (3
*e^2*(b*d - a*e)*(a + b*x)^10)/(10*b^4) + (e^3*(a + b*x)^11)/(11*b^4)

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Rubi [A]  time = 0.424276, antiderivative size = 92, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 31, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.065 \[ \frac{3 e^2 (a+b x)^{10} (b d-a e)}{10 b^4}+\frac{e (a+b x)^9 (b d-a e)^2}{3 b^4}+\frac{(a+b x)^8 (b d-a e)^3}{8 b^4}+\frac{e^3 (a+b x)^{11}}{11 b^4} \]

Antiderivative was successfully verified.

[In]  Int[(a + b*x)*(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^3,x]

[Out]

((b*d - a*e)^3*(a + b*x)^8)/(8*b^4) + (e*(b*d - a*e)^2*(a + b*x)^9)/(3*b^4) + (3
*e^2*(b*d - a*e)*(a + b*x)^10)/(10*b^4) + (e^3*(a + b*x)^11)/(11*b^4)

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Rubi in Sympy [A]  time = 61.1833, size = 80, normalized size = 0.87 \[ \frac{e^{3} \left (a + b x\right )^{11}}{11 b^{4}} - \frac{3 e^{2} \left (a + b x\right )^{10} \left (a e - b d\right )}{10 b^{4}} + \frac{e \left (a + b x\right )^{9} \left (a e - b d\right )^{2}}{3 b^{4}} - \frac{\left (a + b x\right )^{8} \left (a e - b d\right )^{3}}{8 b^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x+a)*(e*x+d)**3*(b**2*x**2+2*a*b*x+a**2)**3,x)

[Out]

e**3*(a + b*x)**11/(11*b**4) - 3*e**2*(a + b*x)**10*(a*e - b*d)/(10*b**4) + e*(a
+ b*x)**9*(a*e - b*d)**2/(3*b**4) - (a + b*x)**8*(a*e - b*d)**3/(8*b**4)

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Mathematica [B]  time = 0.0962704, size = 360, normalized size = 3.91 \[ a^7 d^3 x+\frac{1}{2} a^6 d^2 x^2 (3 a e+7 b d)+\frac{1}{3} b^5 e x^9 \left (7 a^2 e^2+7 a b d e+b^2 d^2\right )+a^5 d x^3 \left (a^2 e^2+7 a b d e+7 b^2 d^2\right )+a b^3 x^7 \left (5 a^3 e^3+15 a^2 b d e^2+9 a b^2 d^2 e+b^3 d^3\right )+\frac{7}{2} a^2 b^2 x^6 \left (a^3 e^3+5 a^2 b d e^2+5 a b^2 d^2 e+b^3 d^3\right )+\frac{7}{5} a^3 b x^5 \left (a^3 e^3+9 a^2 b d e^2+15 a b^2 d^2 e+5 b^3 d^3\right )+\frac{1}{8} b^4 x^8 \left (35 a^3 e^3+63 a^2 b d e^2+21 a b^2 d^2 e+b^3 d^3\right )+\frac{1}{4} a^4 x^4 \left (a^3 e^3+21 a^2 b d e^2+63 a b^2 d^2 e+35 b^3 d^3\right )+\frac{1}{10} b^6 e^2 x^{10} (7 a e+3 b d)+\frac{1}{11} b^7 e^3 x^{11} \]

Antiderivative was successfully verified.

[In]  Integrate[(a + b*x)*(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^3,x]

[Out]

a^7*d^3*x + (a^6*d^2*(7*b*d + 3*a*e)*x^2)/2 + a^5*d*(7*b^2*d^2 + 7*a*b*d*e + a^2
*e^2)*x^3 + (a^4*(35*b^3*d^3 + 63*a*b^2*d^2*e + 21*a^2*b*d*e^2 + a^3*e^3)*x^4)/4
+ (7*a^3*b*(5*b^3*d^3 + 15*a*b^2*d^2*e + 9*a^2*b*d*e^2 + a^3*e^3)*x^5)/5 + (7*a
^2*b^2*(b^3*d^3 + 5*a*b^2*d^2*e + 5*a^2*b*d*e^2 + a^3*e^3)*x^6)/2 + a*b^3*(b^3*d
^3 + 9*a*b^2*d^2*e + 15*a^2*b*d*e^2 + 5*a^3*e^3)*x^7 + (b^4*(b^3*d^3 + 21*a*b^2*
d^2*e + 63*a^2*b*d*e^2 + 35*a^3*e^3)*x^8)/8 + (b^5*e*(b^2*d^2 + 7*a*b*d*e + 7*a^
2*e^2)*x^9)/3 + (b^6*e^2*(3*b*d + 7*a*e)*x^10)/10 + (b^7*e^3*x^11)/11

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Maple [B]  time = 0.003, size = 616, normalized size = 6.7 \[{\frac{{b}^{7}{e}^{3}{x}^{11}}{11}}+{\frac{ \left ( \left ( a{e}^{3}+3\,bd{e}^{2} \right ){b}^{6}+6\,{b}^{6}{e}^{3}a \right ){x}^{10}}{10}}+{\frac{ \left ( \left ( 3\,ad{e}^{2}+3\,b{d}^{2}e \right ){b}^{6}+6\, \left ( a{e}^{3}+3\,bd{e}^{2} \right ) a{b}^{5}+15\,{b}^{5}{e}^{3}{a}^{2} \right ){x}^{9}}{9}}+{\frac{ \left ( \left ( 3\,a{d}^{2}e+b{d}^{3} \right ){b}^{6}+6\, \left ( 3\,ad{e}^{2}+3\,b{d}^{2}e \right ) a{b}^{5}+15\, \left ( a{e}^{3}+3\,bd{e}^{2} \right ){a}^{2}{b}^{4}+20\,{a}^{3}{b}^{4}{e}^{3} \right ){x}^{8}}{8}}+{\frac{ \left ( a{d}^{3}{b}^{6}+6\, \left ( 3\,a{d}^{2}e+b{d}^{3} \right ) a{b}^{5}+15\, \left ( 3\,ad{e}^{2}+3\,b{d}^{2}e \right ){a}^{2}{b}^{4}+20\, \left ( a{e}^{3}+3\,bd{e}^{2} \right ){a}^{3}{b}^{3}+15\,{b}^{3}{e}^{3}{a}^{4} \right ){x}^{7}}{7}}+{\frac{ \left ( 6\,{a}^{2}{d}^{3}{b}^{5}+15\, \left ( 3\,a{d}^{2}e+b{d}^{3} \right ){a}^{2}{b}^{4}+20\, \left ( 3\,ad{e}^{2}+3\,b{d}^{2}e \right ){a}^{3}{b}^{3}+15\, \left ( a{e}^{3}+3\,bd{e}^{2} \right ){b}^{2}{a}^{4}+6\,{b}^{2}{e}^{3}{a}^{5} \right ){x}^{6}}{6}}+{\frac{ \left ( 15\,{a}^{3}{d}^{3}{b}^{4}+20\, \left ( 3\,a{d}^{2}e+b{d}^{3} \right ){a}^{3}{b}^{3}+15\, \left ( 3\,ad{e}^{2}+3\,b{d}^{2}e \right ){b}^{2}{a}^{4}+6\, \left ( a{e}^{3}+3\,bd{e}^{2} \right ){a}^{5}b+b{e}^{3}{a}^{6} \right ){x}^{5}}{5}}+{\frac{ \left ( 20\,{a}^{4}{d}^{3}{b}^{3}+15\, \left ( 3\,a{d}^{2}e+b{d}^{3} \right ){b}^{2}{a}^{4}+6\, \left ( 3\,ad{e}^{2}+3\,b{d}^{2}e \right ){a}^{5}b+ \left ( a{e}^{3}+3\,bd{e}^{2} \right ){a}^{6} \right ){x}^{4}}{4}}+{\frac{ \left ( 15\,{a}^{5}{d}^{3}{b}^{2}+6\, \left ( 3\,a{d}^{2}e+b{d}^{3} \right ){a}^{5}b+ \left ( 3\,ad{e}^{2}+3\,b{d}^{2}e \right ){a}^{6} \right ){x}^{3}}{3}}+{\frac{ \left ( 6\,{a}^{6}{d}^{3}b+ \left ( 3\,a{d}^{2}e+b{d}^{3} \right ){a}^{6} \right ){x}^{2}}{2}}+{a}^{7}{d}^{3}x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x+a)*(e*x+d)^3*(b^2*x^2+2*a*b*x+a^2)^3,x)

[Out]

1/11*b^7*e^3*x^11+1/10*((a*e^3+3*b*d*e^2)*b^6+6*b^6*e^3*a)*x^10+1/9*((3*a*d*e^2+
3*b*d^2*e)*b^6+6*(a*e^3+3*b*d*e^2)*a*b^5+15*b^5*e^3*a^2)*x^9+1/8*((3*a*d^2*e+b*d
^3)*b^6+6*(3*a*d*e^2+3*b*d^2*e)*a*b^5+15*(a*e^3+3*b*d*e^2)*a^2*b^4+20*a^3*b^4*e^
3)*x^8+1/7*(a*d^3*b^6+6*(3*a*d^2*e+b*d^3)*a*b^5+15*(3*a*d*e^2+3*b*d^2*e)*a^2*b^4
+20*(a*e^3+3*b*d*e^2)*a^3*b^3+15*b^3*e^3*a^4)*x^7+1/6*(6*a^2*d^3*b^5+15*(3*a*d^2
*e+b*d^3)*a^2*b^4+20*(3*a*d*e^2+3*b*d^2*e)*a^3*b^3+15*(a*e^3+3*b*d*e^2)*b^2*a^4+
6*b^2*e^3*a^5)*x^6+1/5*(15*a^3*d^3*b^4+20*(3*a*d^2*e+b*d^3)*a^3*b^3+15*(3*a*d*e^
2+3*b*d^2*e)*b^2*a^4+6*(a*e^3+3*b*d*e^2)*a^5*b+b*e^3*a^6)*x^5+1/4*(20*a^4*d^3*b^
3+15*(3*a*d^2*e+b*d^3)*b^2*a^4+6*(3*a*d*e^2+3*b*d^2*e)*a^5*b+(a*e^3+3*b*d*e^2)*a
^6)*x^4+1/3*(15*a^5*d^3*b^2+6*(3*a*d^2*e+b*d^3)*a^5*b+(3*a*d*e^2+3*b*d^2*e)*a^6)
*x^3+1/2*(6*a^6*d^3*b+(3*a*d^2*e+b*d^3)*a^6)*x^2+a^7*d^3*x

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Maxima [A]  time = 0.720395, size = 508, normalized size = 5.52 \[ \frac{1}{11} \, b^{7} e^{3} x^{11} + a^{7} d^{3} x + \frac{1}{10} \,{\left (3 \, b^{7} d e^{2} + 7 \, a b^{6} e^{3}\right )} x^{10} + \frac{1}{3} \,{\left (b^{7} d^{2} e + 7 \, a b^{6} d e^{2} + 7 \, a^{2} b^{5} e^{3}\right )} x^{9} + \frac{1}{8} \,{\left (b^{7} d^{3} + 21 \, a b^{6} d^{2} e + 63 \, a^{2} b^{5} d e^{2} + 35 \, a^{3} b^{4} e^{3}\right )} x^{8} +{\left (a b^{6} d^{3} + 9 \, a^{2} b^{5} d^{2} e + 15 \, a^{3} b^{4} d e^{2} + 5 \, a^{4} b^{3} e^{3}\right )} x^{7} + \frac{7}{2} \,{\left (a^{2} b^{5} d^{3} + 5 \, a^{3} b^{4} d^{2} e + 5 \, a^{4} b^{3} d e^{2} + a^{5} b^{2} e^{3}\right )} x^{6} + \frac{7}{5} \,{\left (5 \, a^{3} b^{4} d^{3} + 15 \, a^{4} b^{3} d^{2} e + 9 \, a^{5} b^{2} d e^{2} + a^{6} b e^{3}\right )} x^{5} + \frac{1}{4} \,{\left (35 \, a^{4} b^{3} d^{3} + 63 \, a^{5} b^{2} d^{2} e + 21 \, a^{6} b d e^{2} + a^{7} e^{3}\right )} x^{4} +{\left (7 \, a^{5} b^{2} d^{3} + 7 \, a^{6} b d^{2} e + a^{7} d e^{2}\right )} x^{3} + \frac{1}{2} \,{\left (7 \, a^{6} b d^{3} + 3 \, a^{7} d^{2} e\right )} x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b^2*x^2 + 2*a*b*x + a^2)^3*(b*x + a)*(e*x + d)^3,x, algorithm="maxima")

[Out]

1/11*b^7*e^3*x^11 + a^7*d^3*x + 1/10*(3*b^7*d*e^2 + 7*a*b^6*e^3)*x^10 + 1/3*(b^7
*d^2*e + 7*a*b^6*d*e^2 + 7*a^2*b^5*e^3)*x^9 + 1/8*(b^7*d^3 + 21*a*b^6*d^2*e + 63
*a^2*b^5*d*e^2 + 35*a^3*b^4*e^3)*x^8 + (a*b^6*d^3 + 9*a^2*b^5*d^2*e + 15*a^3*b^4
*d*e^2 + 5*a^4*b^3*e^3)*x^7 + 7/2*(a^2*b^5*d^3 + 5*a^3*b^4*d^2*e + 5*a^4*b^3*d*e
^2 + a^5*b^2*e^3)*x^6 + 7/5*(5*a^3*b^4*d^3 + 15*a^4*b^3*d^2*e + 9*a^5*b^2*d*e^2
+ a^6*b*e^3)*x^5 + 1/4*(35*a^4*b^3*d^3 + 63*a^5*b^2*d^2*e + 21*a^6*b*d*e^2 + a^7
*e^3)*x^4 + (7*a^5*b^2*d^3 + 7*a^6*b*d^2*e + a^7*d*e^2)*x^3 + 1/2*(7*a^6*b*d^3 +
3*a^7*d^2*e)*x^2

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Fricas [A]  time = 0.250577, size = 1, normalized size = 0.01 \[ \frac{1}{11} x^{11} e^{3} b^{7} + \frac{3}{10} x^{10} e^{2} d b^{7} + \frac{7}{10} x^{10} e^{3} b^{6} a + \frac{1}{3} x^{9} e d^{2} b^{7} + \frac{7}{3} x^{9} e^{2} d b^{6} a + \frac{7}{3} x^{9} e^{3} b^{5} a^{2} + \frac{1}{8} x^{8} d^{3} b^{7} + \frac{21}{8} x^{8} e d^{2} b^{6} a + \frac{63}{8} x^{8} e^{2} d b^{5} a^{2} + \frac{35}{8} x^{8} e^{3} b^{4} a^{3} + x^{7} d^{3} b^{6} a + 9 x^{7} e d^{2} b^{5} a^{2} + 15 x^{7} e^{2} d b^{4} a^{3} + 5 x^{7} e^{3} b^{3} a^{4} + \frac{7}{2} x^{6} d^{3} b^{5} a^{2} + \frac{35}{2} x^{6} e d^{2} b^{4} a^{3} + \frac{35}{2} x^{6} e^{2} d b^{3} a^{4} + \frac{7}{2} x^{6} e^{3} b^{2} a^{5} + 7 x^{5} d^{3} b^{4} a^{3} + 21 x^{5} e d^{2} b^{3} a^{4} + \frac{63}{5} x^{5} e^{2} d b^{2} a^{5} + \frac{7}{5} x^{5} e^{3} b a^{6} + \frac{35}{4} x^{4} d^{3} b^{3} a^{4} + \frac{63}{4} x^{4} e d^{2} b^{2} a^{5} + \frac{21}{4} x^{4} e^{2} d b a^{6} + \frac{1}{4} x^{4} e^{3} a^{7} + 7 x^{3} d^{3} b^{2} a^{5} + 7 x^{3} e d^{2} b a^{6} + x^{3} e^{2} d a^{7} + \frac{7}{2} x^{2} d^{3} b a^{6} + \frac{3}{2} x^{2} e d^{2} a^{7} + x d^{3} a^{7} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b^2*x^2 + 2*a*b*x + a^2)^3*(b*x + a)*(e*x + d)^3,x, algorithm="fricas")

[Out]

1/11*x^11*e^3*b^7 + 3/10*x^10*e^2*d*b^7 + 7/10*x^10*e^3*b^6*a + 1/3*x^9*e*d^2*b^
7 + 7/3*x^9*e^2*d*b^6*a + 7/3*x^9*e^3*b^5*a^2 + 1/8*x^8*d^3*b^7 + 21/8*x^8*e*d^2
*b^6*a + 63/8*x^8*e^2*d*b^5*a^2 + 35/8*x^8*e^3*b^4*a^3 + x^7*d^3*b^6*a + 9*x^7*e
*d^2*b^5*a^2 + 15*x^7*e^2*d*b^4*a^3 + 5*x^7*e^3*b^3*a^4 + 7/2*x^6*d^3*b^5*a^2 +
35/2*x^6*e*d^2*b^4*a^3 + 35/2*x^6*e^2*d*b^3*a^4 + 7/2*x^6*e^3*b^2*a^5 + 7*x^5*d^
3*b^4*a^3 + 21*x^5*e*d^2*b^3*a^4 + 63/5*x^5*e^2*d*b^2*a^5 + 7/5*x^5*e^3*b*a^6 +
35/4*x^4*d^3*b^3*a^4 + 63/4*x^4*e*d^2*b^2*a^5 + 21/4*x^4*e^2*d*b*a^6 + 1/4*x^4*e
^3*a^7 + 7*x^3*d^3*b^2*a^5 + 7*x^3*e*d^2*b*a^6 + x^3*e^2*d*a^7 + 7/2*x^2*d^3*b*a
^6 + 3/2*x^2*e*d^2*a^7 + x*d^3*a^7

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Sympy [A]  time = 0.321918, size = 427, normalized size = 4.64 \[ a^{7} d^{3} x + \frac{b^{7} e^{3} x^{11}}{11} + x^{10} \left (\frac{7 a b^{6} e^{3}}{10} + \frac{3 b^{7} d e^{2}}{10}\right ) + x^{9} \left (\frac{7 a^{2} b^{5} e^{3}}{3} + \frac{7 a b^{6} d e^{2}}{3} + \frac{b^{7} d^{2} e}{3}\right ) + x^{8} \left (\frac{35 a^{3} b^{4} e^{3}}{8} + \frac{63 a^{2} b^{5} d e^{2}}{8} + \frac{21 a b^{6} d^{2} e}{8} + \frac{b^{7} d^{3}}{8}\right ) + x^{7} \left (5 a^{4} b^{3} e^{3} + 15 a^{3} b^{4} d e^{2} + 9 a^{2} b^{5} d^{2} e + a b^{6} d^{3}\right ) + x^{6} \left (\frac{7 a^{5} b^{2} e^{3}}{2} + \frac{35 a^{4} b^{3} d e^{2}}{2} + \frac{35 a^{3} b^{4} d^{2} e}{2} + \frac{7 a^{2} b^{5} d^{3}}{2}\right ) + x^{5} \left (\frac{7 a^{6} b e^{3}}{5} + \frac{63 a^{5} b^{2} d e^{2}}{5} + 21 a^{4} b^{3} d^{2} e + 7 a^{3} b^{4} d^{3}\right ) + x^{4} \left (\frac{a^{7} e^{3}}{4} + \frac{21 a^{6} b d e^{2}}{4} + \frac{63 a^{5} b^{2} d^{2} e}{4} + \frac{35 a^{4} b^{3} d^{3}}{4}\right ) + x^{3} \left (a^{7} d e^{2} + 7 a^{6} b d^{2} e + 7 a^{5} b^{2} d^{3}\right ) + x^{2} \left (\frac{3 a^{7} d^{2} e}{2} + \frac{7 a^{6} b d^{3}}{2}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x+a)*(e*x+d)**3*(b**2*x**2+2*a*b*x+a**2)**3,x)

[Out]

a**7*d**3*x + b**7*e**3*x**11/11 + x**10*(7*a*b**6*e**3/10 + 3*b**7*d*e**2/10) +
x**9*(7*a**2*b**5*e**3/3 + 7*a*b**6*d*e**2/3 + b**7*d**2*e/3) + x**8*(35*a**3*b
**4*e**3/8 + 63*a**2*b**5*d*e**2/8 + 21*a*b**6*d**2*e/8 + b**7*d**3/8) + x**7*(5
*a**4*b**3*e**3 + 15*a**3*b**4*d*e**2 + 9*a**2*b**5*d**2*e + a*b**6*d**3) + x**6
*(7*a**5*b**2*e**3/2 + 35*a**4*b**3*d*e**2/2 + 35*a**3*b**4*d**2*e/2 + 7*a**2*b*
*5*d**3/2) + x**5*(7*a**6*b*e**3/5 + 63*a**5*b**2*d*e**2/5 + 21*a**4*b**3*d**2*e
+ 7*a**3*b**4*d**3) + x**4*(a**7*e**3/4 + 21*a**6*b*d*e**2/4 + 63*a**5*b**2*d**
2*e/4 + 35*a**4*b**3*d**3/4) + x**3*(a**7*d*e**2 + 7*a**6*b*d**2*e + 7*a**5*b**2
*d**3) + x**2*(3*a**7*d**2*e/2 + 7*a**6*b*d**3/2)

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GIAC/XCAS [A]  time = 0.28116, size = 556, normalized size = 6.04 \[ \frac{1}{11} \, b^{7} x^{11} e^{3} + \frac{3}{10} \, b^{7} d x^{10} e^{2} + \frac{1}{3} \, b^{7} d^{2} x^{9} e + \frac{1}{8} \, b^{7} d^{3} x^{8} + \frac{7}{10} \, a b^{6} x^{10} e^{3} + \frac{7}{3} \, a b^{6} d x^{9} e^{2} + \frac{21}{8} \, a b^{6} d^{2} x^{8} e + a b^{6} d^{3} x^{7} + \frac{7}{3} \, a^{2} b^{5} x^{9} e^{3} + \frac{63}{8} \, a^{2} b^{5} d x^{8} e^{2} + 9 \, a^{2} b^{5} d^{2} x^{7} e + \frac{7}{2} \, a^{2} b^{5} d^{3} x^{6} + \frac{35}{8} \, a^{3} b^{4} x^{8} e^{3} + 15 \, a^{3} b^{4} d x^{7} e^{2} + \frac{35}{2} \, a^{3} b^{4} d^{2} x^{6} e + 7 \, a^{3} b^{4} d^{3} x^{5} + 5 \, a^{4} b^{3} x^{7} e^{3} + \frac{35}{2} \, a^{4} b^{3} d x^{6} e^{2} + 21 \, a^{4} b^{3} d^{2} x^{5} e + \frac{35}{4} \, a^{4} b^{3} d^{3} x^{4} + \frac{7}{2} \, a^{5} b^{2} x^{6} e^{3} + \frac{63}{5} \, a^{5} b^{2} d x^{5} e^{2} + \frac{63}{4} \, a^{5} b^{2} d^{2} x^{4} e + 7 \, a^{5} b^{2} d^{3} x^{3} + \frac{7}{5} \, a^{6} b x^{5} e^{3} + \frac{21}{4} \, a^{6} b d x^{4} e^{2} + 7 \, a^{6} b d^{2} x^{3} e + \frac{7}{2} \, a^{6} b d^{3} x^{2} + \frac{1}{4} \, a^{7} x^{4} e^{3} + a^{7} d x^{3} e^{2} + \frac{3}{2} \, a^{7} d^{2} x^{2} e + a^{7} d^{3} x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b^2*x^2 + 2*a*b*x + a^2)^3*(b*x + a)*(e*x + d)^3,x, algorithm="giac")

[Out]

1/11*b^7*x^11*e^3 + 3/10*b^7*d*x^10*e^2 + 1/3*b^7*d^2*x^9*e + 1/8*b^7*d^3*x^8 +
7/10*a*b^6*x^10*e^3 + 7/3*a*b^6*d*x^9*e^2 + 21/8*a*b^6*d^2*x^8*e + a*b^6*d^3*x^7
+ 7/3*a^2*b^5*x^9*e^3 + 63/8*a^2*b^5*d*x^8*e^2 + 9*a^2*b^5*d^2*x^7*e + 7/2*a^2*
b^5*d^3*x^6 + 35/8*a^3*b^4*x^8*e^3 + 15*a^3*b^4*d*x^7*e^2 + 35/2*a^3*b^4*d^2*x^6
*e + 7*a^3*b^4*d^3*x^5 + 5*a^4*b^3*x^7*e^3 + 35/2*a^4*b^3*d*x^6*e^2 + 21*a^4*b^3
*d^2*x^5*e + 35/4*a^4*b^3*d^3*x^4 + 7/2*a^5*b^2*x^6*e^3 + 63/5*a^5*b^2*d*x^5*e^2
+ 63/4*a^5*b^2*d^2*x^4*e + 7*a^5*b^2*d^3*x^3 + 7/5*a^6*b*x^5*e^3 + 21/4*a^6*b*d
*x^4*e^2 + 7*a^6*b*d^2*x^3*e + 7/2*a^6*b*d^3*x^2 + 1/4*a^7*x^4*e^3 + a^7*d*x^3*e
^2 + 3/2*a^7*d^2*x^2*e + a^7*d^3*x