3.1474 \(\int (d+e x)^4 \left (a^2+2 a b x+b^2 x^2\right )^3 \, dx\)

Optimal. Leaf size=119 \[ \frac{2 e^3 (a+b x)^{10} (b d-a e)}{5 b^5}+\frac{2 e^2 (a+b x)^9 (b d-a e)^2}{3 b^5}+\frac{e (a+b x)^8 (b d-a e)^3}{2 b^5}+\frac{(a+b x)^7 (b d-a e)^4}{7 b^5}+\frac{e^4 (a+b x)^{11}}{11 b^5} \]

[Out]

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

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Rubi [A]  time = 0.54603, antiderivative size = 119, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{2 e^3 (a+b x)^{10} (b d-a e)}{5 b^5}+\frac{2 e^2 (a+b x)^9 (b d-a e)^2}{3 b^5}+\frac{e (a+b x)^8 (b d-a e)^3}{2 b^5}+\frac{(a+b x)^7 (b d-a e)^4}{7 b^5}+\frac{e^4 (a+b x)^{11}}{11 b^5} \]

Antiderivative was successfully verified.

[In]  Int[(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^3,x]

[Out]

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

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Rubi in Sympy [A]  time = 71.698, size = 105, normalized size = 0.88 \[ \frac{e^{4} \left (a + b x\right )^{11}}{11 b^{5}} - \frac{2 e^{3} \left (a + b x\right )^{10} \left (a e - b d\right )}{5 b^{5}} + \frac{2 e^{2} \left (a + b x\right )^{9} \left (a e - b d\right )^{2}}{3 b^{5}} - \frac{e \left (a + b x\right )^{8} \left (a e - b d\right )^{3}}{2 b^{5}} + \frac{\left (a + b x\right )^{7} \left (a e - b d\right )^{4}}{7 b^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((e*x+d)**4*(b**2*x**2+2*a*b*x+a**2)**3,x)

[Out]

e**4*(a + b*x)**11/(11*b**5) - 2*e**3*(a + b*x)**10*(a*e - b*d)/(5*b**5) + 2*e**
2*(a + b*x)**9*(a*e - b*d)**2/(3*b**5) - e*(a + b*x)**8*(a*e - b*d)**3/(2*b**5)
+ (a + b*x)**7*(a*e - b*d)**4/(7*b**5)

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Mathematica [B]  time = 0.113734, size = 398, normalized size = 3.34 \[ a^6 d^4 x+a^5 d^3 x^2 (2 a e+3 b d)+\frac{1}{3} b^4 e^2 x^9 \left (5 a^2 e^2+8 a b d e+2 b^2 d^2\right )+a^4 d^2 x^3 \left (2 a^2 e^2+8 a b d e+5 b^2 d^2\right )+\frac{1}{2} b^3 e x^8 \left (5 a^3 e^3+15 a^2 b d e^2+9 a b^2 d^2 e+b^3 d^3\right )+a^3 d x^4 \left (a^3 e^3+9 a^2 b d e^2+15 a b^2 d^2 e+5 b^3 d^3\right )+\frac{1}{7} b^2 x^7 \left (15 a^4 e^4+80 a^3 b d e^3+90 a^2 b^2 d^2 e^2+24 a b^3 d^3 e+b^4 d^4\right )+a b x^6 \left (a^4 e^4+10 a^3 b d e^3+20 a^2 b^2 d^2 e^2+10 a b^3 d^3 e+b^4 d^4\right )+\frac{1}{5} a^2 x^5 \left (a^4 e^4+24 a^3 b d e^3+90 a^2 b^2 d^2 e^2+80 a b^3 d^3 e+15 b^4 d^4\right )+\frac{1}{5} b^5 e^3 x^{10} (3 a e+2 b d)+\frac{1}{11} b^6 e^4 x^{11} \]

Antiderivative was successfully verified.

[In]  Integrate[(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^3,x]

[Out]

a^6*d^4*x + a^5*d^3*(3*b*d + 2*a*e)*x^2 + a^4*d^2*(5*b^2*d^2 + 8*a*b*d*e + 2*a^2
*e^2)*x^3 + a^3*d*(5*b^3*d^3 + 15*a*b^2*d^2*e + 9*a^2*b*d*e^2 + a^3*e^3)*x^4 + (
a^2*(15*b^4*d^4 + 80*a*b^3*d^3*e + 90*a^2*b^2*d^2*e^2 + 24*a^3*b*d*e^3 + a^4*e^4
)*x^5)/5 + a*b*(b^4*d^4 + 10*a*b^3*d^3*e + 20*a^2*b^2*d^2*e^2 + 10*a^3*b*d*e^3 +
a^4*e^4)*x^6 + (b^2*(b^4*d^4 + 24*a*b^3*d^3*e + 90*a^2*b^2*d^2*e^2 + 80*a^3*b*d
*e^3 + 15*a^4*e^4)*x^7)/7 + (b^3*e*(b^3*d^3 + 9*a*b^2*d^2*e + 15*a^2*b*d*e^2 + 5
*a^3*e^3)*x^8)/2 + (b^4*e^2*(2*b^2*d^2 + 8*a*b*d*e + 5*a^2*e^2)*x^9)/3 + (b^5*e^
3*(2*b*d + 3*a*e)*x^10)/5 + (b^6*e^4*x^11)/11

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Maple [B]  time = 0.002, size = 427, normalized size = 3.6 \[{\frac{{e}^{4}{b}^{6}{x}^{11}}{11}}+{\frac{ \left ( 6\,{e}^{4}a{b}^{5}+4\,d{e}^{3}{b}^{6} \right ){x}^{10}}{10}}+{\frac{ \left ( 15\,{e}^{4}{a}^{2}{b}^{4}+24\,d{e}^{3}a{b}^{5}+6\,{d}^{2}{e}^{2}{b}^{6} \right ){x}^{9}}{9}}+{\frac{ \left ( 20\,{e}^{4}{a}^{3}{b}^{3}+60\,d{e}^{3}{a}^{2}{b}^{4}+36\,{d}^{2}{e}^{2}a{b}^{5}+4\,{d}^{3}e{b}^{6} \right ){x}^{8}}{8}}+{\frac{ \left ( 15\,{e}^{4}{b}^{2}{a}^{4}+80\,d{e}^{3}{a}^{3}{b}^{3}+90\,{d}^{2}{e}^{2}{a}^{2}{b}^{4}+24\,{d}^{3}ea{b}^{5}+{d}^{4}{b}^{6} \right ){x}^{7}}{7}}+{\frac{ \left ( 6\,{e}^{4}{a}^{5}b+60\,d{e}^{3}{b}^{2}{a}^{4}+120\,{d}^{2}{e}^{2}{a}^{3}{b}^{3}+60\,{d}^{3}e{a}^{2}{b}^{4}+6\,{d}^{4}a{b}^{5} \right ){x}^{6}}{6}}+{\frac{ \left ({e}^{4}{a}^{6}+24\,d{e}^{3}{a}^{5}b+90\,{d}^{2}{e}^{2}{b}^{2}{a}^{4}+80\,{d}^{3}e{a}^{3}{b}^{3}+15\,{d}^{4}{a}^{2}{b}^{4} \right ){x}^{5}}{5}}+{\frac{ \left ( 4\,d{e}^{3}{a}^{6}+36\,{d}^{2}{e}^{2}{a}^{5}b+60\,{d}^{3}e{b}^{2}{a}^{4}+20\,{d}^{4}{a}^{3}{b}^{3} \right ){x}^{4}}{4}}+{\frac{ \left ( 6\,{d}^{2}{e}^{2}{a}^{6}+24\,{d}^{3}e{a}^{5}b+15\,{d}^{4}{b}^{2}{a}^{4} \right ){x}^{3}}{3}}+{\frac{ \left ( 4\,{d}^{3}e{a}^{6}+6\,{d}^{4}{a}^{5}b \right ){x}^{2}}{2}}+{d}^{4}{a}^{6}x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((e*x+d)^4*(b^2*x^2+2*a*b*x+a^2)^3,x)

[Out]

1/11*e^4*b^6*x^11+1/10*(6*a*b^5*e^4+4*b^6*d*e^3)*x^10+1/9*(15*a^2*b^4*e^4+24*a*b
^5*d*e^3+6*b^6*d^2*e^2)*x^9+1/8*(20*a^3*b^3*e^4+60*a^2*b^4*d*e^3+36*a*b^5*d^2*e^
2+4*b^6*d^3*e)*x^8+1/7*(15*a^4*b^2*e^4+80*a^3*b^3*d*e^3+90*a^2*b^4*d^2*e^2+24*a*
b^5*d^3*e+b^6*d^4)*x^7+1/6*(6*a^5*b*e^4+60*a^4*b^2*d*e^3+120*a^3*b^3*d^2*e^2+60*
a^2*b^4*d^3*e+6*a*b^5*d^4)*x^6+1/5*(a^6*e^4+24*a^5*b*d*e^3+90*a^4*b^2*d^2*e^2+80
*a^3*b^3*d^3*e+15*a^2*b^4*d^4)*x^5+1/4*(4*a^6*d*e^3+36*a^5*b*d^2*e^2+60*a^4*b^2*
d^3*e+20*a^3*b^3*d^4)*x^4+1/3*(6*a^6*d^2*e^2+24*a^5*b*d^3*e+15*a^4*b^2*d^4)*x^3+
1/2*(4*a^6*d^3*e+6*a^5*b*d^4)*x^2+d^4*a^6*x

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Maxima [A]  time = 0.694287, size = 564, normalized size = 4.74 \[ \frac{1}{11} \, b^{6} e^{4} x^{11} + a^{6} d^{4} x + \frac{1}{5} \,{\left (2 \, b^{6} d e^{3} + 3 \, a b^{5} e^{4}\right )} x^{10} + \frac{1}{3} \,{\left (2 \, b^{6} d^{2} e^{2} + 8 \, a b^{5} d e^{3} + 5 \, a^{2} b^{4} e^{4}\right )} x^{9} + \frac{1}{2} \,{\left (b^{6} d^{3} e + 9 \, a b^{5} d^{2} e^{2} + 15 \, a^{2} b^{4} d e^{3} + 5 \, a^{3} b^{3} e^{4}\right )} x^{8} + \frac{1}{7} \,{\left (b^{6} d^{4} + 24 \, a b^{5} d^{3} e + 90 \, a^{2} b^{4} d^{2} e^{2} + 80 \, a^{3} b^{3} d e^{3} + 15 \, a^{4} b^{2} e^{4}\right )} x^{7} +{\left (a b^{5} d^{4} + 10 \, a^{2} b^{4} d^{3} e + 20 \, a^{3} b^{3} d^{2} e^{2} + 10 \, a^{4} b^{2} d e^{3} + a^{5} b e^{4}\right )} x^{6} + \frac{1}{5} \,{\left (15 \, a^{2} b^{4} d^{4} + 80 \, a^{3} b^{3} d^{3} e + 90 \, a^{4} b^{2} d^{2} e^{2} + 24 \, a^{5} b d e^{3} + a^{6} e^{4}\right )} x^{5} +{\left (5 \, a^{3} b^{3} d^{4} + 15 \, a^{4} b^{2} d^{3} e + 9 \, a^{5} b d^{2} e^{2} + a^{6} d e^{3}\right )} x^{4} +{\left (5 \, a^{4} b^{2} d^{4} + 8 \, a^{5} b d^{3} e + 2 \, a^{6} d^{2} e^{2}\right )} x^{3} +{\left (3 \, a^{5} b d^{4} + 2 \, a^{6} d^{3} e\right )} x^{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b^2*x^2 + 2*a*b*x + a^2)^3*(e*x + d)^4,x, algorithm="maxima")

[Out]

1/11*b^6*e^4*x^11 + a^6*d^4*x + 1/5*(2*b^6*d*e^3 + 3*a*b^5*e^4)*x^10 + 1/3*(2*b^
6*d^2*e^2 + 8*a*b^5*d*e^3 + 5*a^2*b^4*e^4)*x^9 + 1/2*(b^6*d^3*e + 9*a*b^5*d^2*e^
2 + 15*a^2*b^4*d*e^3 + 5*a^3*b^3*e^4)*x^8 + 1/7*(b^6*d^4 + 24*a*b^5*d^3*e + 90*a
^2*b^4*d^2*e^2 + 80*a^3*b^3*d*e^3 + 15*a^4*b^2*e^4)*x^7 + (a*b^5*d^4 + 10*a^2*b^
4*d^3*e + 20*a^3*b^3*d^2*e^2 + 10*a^4*b^2*d*e^3 + a^5*b*e^4)*x^6 + 1/5*(15*a^2*b
^4*d^4 + 80*a^3*b^3*d^3*e + 90*a^4*b^2*d^2*e^2 + 24*a^5*b*d*e^3 + a^6*e^4)*x^5 +
(5*a^3*b^3*d^4 + 15*a^4*b^2*d^3*e + 9*a^5*b*d^2*e^2 + a^6*d*e^3)*x^4 + (5*a^4*b
^2*d^4 + 8*a^5*b*d^3*e + 2*a^6*d^2*e^2)*x^3 + (3*a^5*b*d^4 + 2*a^6*d^3*e)*x^2

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Fricas [A]  time = 0.18011, size = 1, normalized size = 0.01 \[ \frac{1}{11} x^{11} e^{4} b^{6} + \frac{2}{5} x^{10} e^{3} d b^{6} + \frac{3}{5} x^{10} e^{4} b^{5} a + \frac{2}{3} x^{9} e^{2} d^{2} b^{6} + \frac{8}{3} x^{9} e^{3} d b^{5} a + \frac{5}{3} x^{9} e^{4} b^{4} a^{2} + \frac{1}{2} x^{8} e d^{3} b^{6} + \frac{9}{2} x^{8} e^{2} d^{2} b^{5} a + \frac{15}{2} x^{8} e^{3} d b^{4} a^{2} + \frac{5}{2} x^{8} e^{4} b^{3} a^{3} + \frac{1}{7} x^{7} d^{4} b^{6} + \frac{24}{7} x^{7} e d^{3} b^{5} a + \frac{90}{7} x^{7} e^{2} d^{2} b^{4} a^{2} + \frac{80}{7} x^{7} e^{3} d b^{3} a^{3} + \frac{15}{7} x^{7} e^{4} b^{2} a^{4} + x^{6} d^{4} b^{5} a + 10 x^{6} e d^{3} b^{4} a^{2} + 20 x^{6} e^{2} d^{2} b^{3} a^{3} + 10 x^{6} e^{3} d b^{2} a^{4} + x^{6} e^{4} b a^{5} + 3 x^{5} d^{4} b^{4} a^{2} + 16 x^{5} e d^{3} b^{3} a^{3} + 18 x^{5} e^{2} d^{2} b^{2} a^{4} + \frac{24}{5} x^{5} e^{3} d b a^{5} + \frac{1}{5} x^{5} e^{4} a^{6} + 5 x^{4} d^{4} b^{3} a^{3} + 15 x^{4} e d^{3} b^{2} a^{4} + 9 x^{4} e^{2} d^{2} b a^{5} + x^{4} e^{3} d a^{6} + 5 x^{3} d^{4} b^{2} a^{4} + 8 x^{3} e d^{3} b a^{5} + 2 x^{3} e^{2} d^{2} a^{6} + 3 x^{2} d^{4} b a^{5} + 2 x^{2} e d^{3} a^{6} + x d^{4} a^{6} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b^2*x^2 + 2*a*b*x + a^2)^3*(e*x + d)^4,x, algorithm="fricas")

[Out]

1/11*x^11*e^4*b^6 + 2/5*x^10*e^3*d*b^6 + 3/5*x^10*e^4*b^5*a + 2/3*x^9*e^2*d^2*b^
6 + 8/3*x^9*e^3*d*b^5*a + 5/3*x^9*e^4*b^4*a^2 + 1/2*x^8*e*d^3*b^6 + 9/2*x^8*e^2*
d^2*b^5*a + 15/2*x^8*e^3*d*b^4*a^2 + 5/2*x^8*e^4*b^3*a^3 + 1/7*x^7*d^4*b^6 + 24/
7*x^7*e*d^3*b^5*a + 90/7*x^7*e^2*d^2*b^4*a^2 + 80/7*x^7*e^3*d*b^3*a^3 + 15/7*x^7
*e^4*b^2*a^4 + x^6*d^4*b^5*a + 10*x^6*e*d^3*b^4*a^2 + 20*x^6*e^2*d^2*b^3*a^3 + 1
0*x^6*e^3*d*b^2*a^4 + x^6*e^4*b*a^5 + 3*x^5*d^4*b^4*a^2 + 16*x^5*e*d^3*b^3*a^3 +
18*x^5*e^2*d^2*b^2*a^4 + 24/5*x^5*e^3*d*b*a^5 + 1/5*x^5*e^4*a^6 + 5*x^4*d^4*b^3
*a^3 + 15*x^4*e*d^3*b^2*a^4 + 9*x^4*e^2*d^2*b*a^5 + x^4*e^3*d*a^6 + 5*x^3*d^4*b^
2*a^4 + 8*x^3*e*d^3*b*a^5 + 2*x^3*e^2*d^2*a^6 + 3*x^2*d^4*b*a^5 + 2*x^2*e*d^3*a^
6 + x*d^4*a^6

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Sympy [A]  time = 0.316312, size = 462, normalized size = 3.88 \[ a^{6} d^{4} x + \frac{b^{6} e^{4} x^{11}}{11} + x^{10} \left (\frac{3 a b^{5} e^{4}}{5} + \frac{2 b^{6} d e^{3}}{5}\right ) + x^{9} \left (\frac{5 a^{2} b^{4} e^{4}}{3} + \frac{8 a b^{5} d e^{3}}{3} + \frac{2 b^{6} d^{2} e^{2}}{3}\right ) + x^{8} \left (\frac{5 a^{3} b^{3} e^{4}}{2} + \frac{15 a^{2} b^{4} d e^{3}}{2} + \frac{9 a b^{5} d^{2} e^{2}}{2} + \frac{b^{6} d^{3} e}{2}\right ) + x^{7} \left (\frac{15 a^{4} b^{2} e^{4}}{7} + \frac{80 a^{3} b^{3} d e^{3}}{7} + \frac{90 a^{2} b^{4} d^{2} e^{2}}{7} + \frac{24 a b^{5} d^{3} e}{7} + \frac{b^{6} d^{4}}{7}\right ) + x^{6} \left (a^{5} b e^{4} + 10 a^{4} b^{2} d e^{3} + 20 a^{3} b^{3} d^{2} e^{2} + 10 a^{2} b^{4} d^{3} e + a b^{5} d^{4}\right ) + x^{5} \left (\frac{a^{6} e^{4}}{5} + \frac{24 a^{5} b d e^{3}}{5} + 18 a^{4} b^{2} d^{2} e^{2} + 16 a^{3} b^{3} d^{3} e + 3 a^{2} b^{4} d^{4}\right ) + x^{4} \left (a^{6} d e^{3} + 9 a^{5} b d^{2} e^{2} + 15 a^{4} b^{2} d^{3} e + 5 a^{3} b^{3} d^{4}\right ) + x^{3} \left (2 a^{6} d^{2} e^{2} + 8 a^{5} b d^{3} e + 5 a^{4} b^{2} d^{4}\right ) + x^{2} \left (2 a^{6} d^{3} e + 3 a^{5} b d^{4}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((e*x+d)**4*(b**2*x**2+2*a*b*x+a**2)**3,x)

[Out]

a**6*d**4*x + b**6*e**4*x**11/11 + x**10*(3*a*b**5*e**4/5 + 2*b**6*d*e**3/5) + x
**9*(5*a**2*b**4*e**4/3 + 8*a*b**5*d*e**3/3 + 2*b**6*d**2*e**2/3) + x**8*(5*a**3
*b**3*e**4/2 + 15*a**2*b**4*d*e**3/2 + 9*a*b**5*d**2*e**2/2 + b**6*d**3*e/2) + x
**7*(15*a**4*b**2*e**4/7 + 80*a**3*b**3*d*e**3/7 + 90*a**2*b**4*d**2*e**2/7 + 24
*a*b**5*d**3*e/7 + b**6*d**4/7) + x**6*(a**5*b*e**4 + 10*a**4*b**2*d*e**3 + 20*a
**3*b**3*d**2*e**2 + 10*a**2*b**4*d**3*e + a*b**5*d**4) + x**5*(a**6*e**4/5 + 24
*a**5*b*d*e**3/5 + 18*a**4*b**2*d**2*e**2 + 16*a**3*b**3*d**3*e + 3*a**2*b**4*d*
*4) + x**4*(a**6*d*e**3 + 9*a**5*b*d**2*e**2 + 15*a**4*b**2*d**3*e + 5*a**3*b**3
*d**4) + x**3*(2*a**6*d**2*e**2 + 8*a**5*b*d**3*e + 5*a**4*b**2*d**4) + x**2*(2*
a**6*d**3*e + 3*a**5*b*d**4)

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GIAC/XCAS [A]  time = 0.209041, size = 616, normalized size = 5.18 \[ \frac{1}{11} \, b^{6} x^{11} e^{4} + \frac{2}{5} \, b^{6} d x^{10} e^{3} + \frac{2}{3} \, b^{6} d^{2} x^{9} e^{2} + \frac{1}{2} \, b^{6} d^{3} x^{8} e + \frac{1}{7} \, b^{6} d^{4} x^{7} + \frac{3}{5} \, a b^{5} x^{10} e^{4} + \frac{8}{3} \, a b^{5} d x^{9} e^{3} + \frac{9}{2} \, a b^{5} d^{2} x^{8} e^{2} + \frac{24}{7} \, a b^{5} d^{3} x^{7} e + a b^{5} d^{4} x^{6} + \frac{5}{3} \, a^{2} b^{4} x^{9} e^{4} + \frac{15}{2} \, a^{2} b^{4} d x^{8} e^{3} + \frac{90}{7} \, a^{2} b^{4} d^{2} x^{7} e^{2} + 10 \, a^{2} b^{4} d^{3} x^{6} e + 3 \, a^{2} b^{4} d^{4} x^{5} + \frac{5}{2} \, a^{3} b^{3} x^{8} e^{4} + \frac{80}{7} \, a^{3} b^{3} d x^{7} e^{3} + 20 \, a^{3} b^{3} d^{2} x^{6} e^{2} + 16 \, a^{3} b^{3} d^{3} x^{5} e + 5 \, a^{3} b^{3} d^{4} x^{4} + \frac{15}{7} \, a^{4} b^{2} x^{7} e^{4} + 10 \, a^{4} b^{2} d x^{6} e^{3} + 18 \, a^{4} b^{2} d^{2} x^{5} e^{2} + 15 \, a^{4} b^{2} d^{3} x^{4} e + 5 \, a^{4} b^{2} d^{4} x^{3} + a^{5} b x^{6} e^{4} + \frac{24}{5} \, a^{5} b d x^{5} e^{3} + 9 \, a^{5} b d^{2} x^{4} e^{2} + 8 \, a^{5} b d^{3} x^{3} e + 3 \, a^{5} b d^{4} x^{2} + \frac{1}{5} \, a^{6} x^{5} e^{4} + a^{6} d x^{4} e^{3} + 2 \, a^{6} d^{2} x^{3} e^{2} + 2 \, a^{6} d^{3} x^{2} e + a^{6} d^{4} x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b^2*x^2 + 2*a*b*x + a^2)^3*(e*x + d)^4,x, algorithm="giac")

[Out]

1/11*b^6*x^11*e^4 + 2/5*b^6*d*x^10*e^3 + 2/3*b^6*d^2*x^9*e^2 + 1/2*b^6*d^3*x^8*e
+ 1/7*b^6*d^4*x^7 + 3/5*a*b^5*x^10*e^4 + 8/3*a*b^5*d*x^9*e^3 + 9/2*a*b^5*d^2*x^
8*e^2 + 24/7*a*b^5*d^3*x^7*e + a*b^5*d^4*x^6 + 5/3*a^2*b^4*x^9*e^4 + 15/2*a^2*b^
4*d*x^8*e^3 + 90/7*a^2*b^4*d^2*x^7*e^2 + 10*a^2*b^4*d^3*x^6*e + 3*a^2*b^4*d^4*x^
5 + 5/2*a^3*b^3*x^8*e^4 + 80/7*a^3*b^3*d*x^7*e^3 + 20*a^3*b^3*d^2*x^6*e^2 + 16*a
^3*b^3*d^3*x^5*e + 5*a^3*b^3*d^4*x^4 + 15/7*a^4*b^2*x^7*e^4 + 10*a^4*b^2*d*x^6*e
^3 + 18*a^4*b^2*d^2*x^5*e^2 + 15*a^4*b^2*d^3*x^4*e + 5*a^4*b^2*d^4*x^3 + a^5*b*x
^6*e^4 + 24/5*a^5*b*d*x^5*e^3 + 9*a^5*b*d^2*x^4*e^2 + 8*a^5*b*d^3*x^3*e + 3*a^5*
b*d^4*x^2 + 1/5*a^6*x^5*e^4 + a^6*d*x^4*e^3 + 2*a^6*d^2*x^3*e^2 + 2*a^6*d^3*x^2*
e + a^6*d^4*x