3.1054 \(\int \frac{(a+b x)^6 (A+B x)}{(d+e x)^{12}} \, dx\)

Optimal. Leaf size=235 \[ \frac{b^3 (a+b x)^7 (-11 a B e+4 A b e+7 b B d)}{9240 e (d+e x)^7 (b d-a e)^5}+\frac{b^2 (a+b x)^7 (-11 a B e+4 A b e+7 b B d)}{1320 e (d+e x)^8 (b d-a e)^4}+\frac{b (a+b x)^7 (-11 a B e+4 A b e+7 b B d)}{330 e (d+e x)^9 (b d-a e)^3}+\frac{(a+b x)^7 (-11 a B e+4 A b e+7 b B d)}{110 e (d+e x)^{10} (b d-a e)^2}-\frac{(a+b x)^7 (B d-A e)}{11 e (d+e x)^{11} (b d-a e)} \]

[Out]

-((B*d - A*e)*(a + b*x)^7)/(11*e*(b*d - a*e)*(d + e*x)^11) + ((7*b*B*d + 4*A*b*e
- 11*a*B*e)*(a + b*x)^7)/(110*e*(b*d - a*e)^2*(d + e*x)^10) + (b*(7*b*B*d + 4*A
*b*e - 11*a*B*e)*(a + b*x)^7)/(330*e*(b*d - a*e)^3*(d + e*x)^9) + (b^2*(7*b*B*d
+ 4*A*b*e - 11*a*B*e)*(a + b*x)^7)/(1320*e*(b*d - a*e)^4*(d + e*x)^8) + (b^3*(7*
b*B*d + 4*A*b*e - 11*a*B*e)*(a + b*x)^7)/(9240*e*(b*d - a*e)^5*(d + e*x)^7)

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Rubi [A]  time = 0.30075, antiderivative size = 235, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 3, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.15 \[ \frac{b^3 (a+b x)^7 (-11 a B e+4 A b e+7 b B d)}{9240 e (d+e x)^7 (b d-a e)^5}+\frac{b^2 (a+b x)^7 (-11 a B e+4 A b e+7 b B d)}{1320 e (d+e x)^8 (b d-a e)^4}+\frac{b (a+b x)^7 (-11 a B e+4 A b e+7 b B d)}{330 e (d+e x)^9 (b d-a e)^3}+\frac{(a+b x)^7 (-11 a B e+4 A b e+7 b B d)}{110 e (d+e x)^{10} (b d-a e)^2}-\frac{(a+b x)^7 (B d-A e)}{11 e (d+e x)^{11} (b d-a e)} \]

Antiderivative was successfully verified.

[In]  Int[((a + b*x)^6*(A + B*x))/(d + e*x)^12,x]

[Out]

-((B*d - A*e)*(a + b*x)^7)/(11*e*(b*d - a*e)*(d + e*x)^11) + ((7*b*B*d + 4*A*b*e
- 11*a*B*e)*(a + b*x)^7)/(110*e*(b*d - a*e)^2*(d + e*x)^10) + (b*(7*b*B*d + 4*A
*b*e - 11*a*B*e)*(a + b*x)^7)/(330*e*(b*d - a*e)^3*(d + e*x)^9) + (b^2*(7*b*B*d
+ 4*A*b*e - 11*a*B*e)*(a + b*x)^7)/(1320*e*(b*d - a*e)^4*(d + e*x)^8) + (b^3*(7*
b*B*d + 4*A*b*e - 11*a*B*e)*(a + b*x)^7)/(9240*e*(b*d - a*e)^5*(d + e*x)^7)

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Rubi in Sympy [A]  time = 50.5696, size = 221, normalized size = 0.94 \[ - \frac{b^{3} \left (a + b x\right )^{7} \left (4 A b e - 11 B a e + 7 B b d\right )}{9240 e \left (d + e x\right )^{7} \left (a e - b d\right )^{5}} + \frac{b^{2} \left (a + b x\right )^{7} \left (4 A b e - 11 B a e + 7 B b d\right )}{1320 e \left (d + e x\right )^{8} \left (a e - b d\right )^{4}} - \frac{b \left (a + b x\right )^{7} \left (4 A b e - 11 B a e + 7 B b d\right )}{330 e \left (d + e x\right )^{9} \left (a e - b d\right )^{3}} + \frac{\left (a + b x\right )^{7} \left (4 A b e - 11 B a e + 7 B b d\right )}{110 e \left (d + e x\right )^{10} \left (a e - b d\right )^{2}} - \frac{\left (a + b x\right )^{7} \left (A e - B d\right )}{11 e \left (d + e x\right )^{11} \left (a e - b d\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x+a)**6*(B*x+A)/(e*x+d)**12,x)

[Out]

-b**3*(a + b*x)**7*(4*A*b*e - 11*B*a*e + 7*B*b*d)/(9240*e*(d + e*x)**7*(a*e - b*
d)**5) + b**2*(a + b*x)**7*(4*A*b*e - 11*B*a*e + 7*B*b*d)/(1320*e*(d + e*x)**8*(
a*e - b*d)**4) - b*(a + b*x)**7*(4*A*b*e - 11*B*a*e + 7*B*b*d)/(330*e*(d + e*x)*
*9*(a*e - b*d)**3) + (a + b*x)**7*(4*A*b*e - 11*B*a*e + 7*B*b*d)/(110*e*(d + e*x
)**10*(a*e - b*d)**2) - (a + b*x)**7*(A*e - B*d)/(11*e*(d + e*x)**11*(a*e - b*d)
)

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Mathematica [B]  time = 0.964981, size = 605, normalized size = 2.57 \[ -\frac{84 a^6 e^6 (10 A e+B (d+11 e x))+56 a^5 b e^5 \left (9 A e (d+11 e x)+2 B \left (d^2+11 d e x+55 e^2 x^2\right )\right )+35 a^4 b^2 e^4 \left (8 A e \left (d^2+11 d e x+55 e^2 x^2\right )+3 B \left (d^3+11 d^2 e x+55 d e^2 x^2+165 e^3 x^3\right )\right )+20 a^3 b^3 e^3 \left (7 A e \left (d^3+11 d^2 e x+55 d e^2 x^2+165 e^3 x^3\right )+4 B \left (d^4+11 d^3 e x+55 d^2 e^2 x^2+165 d e^3 x^3+330 e^4 x^4\right )\right )+10 a^2 b^4 e^2 \left (6 A e \left (d^4+11 d^3 e x+55 d^2 e^2 x^2+165 d e^3 x^3+330 e^4 x^4\right )+5 B \left (d^5+11 d^4 e x+55 d^3 e^2 x^2+165 d^2 e^3 x^3+330 d e^4 x^4+462 e^5 x^5\right )\right )+4 a b^5 e \left (5 A e \left (d^5+11 d^4 e x+55 d^3 e^2 x^2+165 d^2 e^3 x^3+330 d e^4 x^4+462 e^5 x^5\right )+6 B \left (d^6+11 d^5 e x+55 d^4 e^2 x^2+165 d^3 e^3 x^3+330 d^2 e^4 x^4+462 d e^5 x^5+462 e^6 x^6\right )\right )+b^6 \left (4 A e \left (d^6+11 d^5 e x+55 d^4 e^2 x^2+165 d^3 e^3 x^3+330 d^2 e^4 x^4+462 d e^5 x^5+462 e^6 x^6\right )+7 B \left (d^7+11 d^6 e x+55 d^5 e^2 x^2+165 d^4 e^3 x^3+330 d^3 e^4 x^4+462 d^2 e^5 x^5+462 d e^6 x^6+330 e^7 x^7\right )\right )}{9240 e^8 (d+e x)^{11}} \]

Antiderivative was successfully verified.

[In]  Integrate[((a + b*x)^6*(A + B*x))/(d + e*x)^12,x]

[Out]

-(84*a^6*e^6*(10*A*e + B*(d + 11*e*x)) + 56*a^5*b*e^5*(9*A*e*(d + 11*e*x) + 2*B*
(d^2 + 11*d*e*x + 55*e^2*x^2)) + 35*a^4*b^2*e^4*(8*A*e*(d^2 + 11*d*e*x + 55*e^2*
x^2) + 3*B*(d^3 + 11*d^2*e*x + 55*d*e^2*x^2 + 165*e^3*x^3)) + 20*a^3*b^3*e^3*(7*
A*e*(d^3 + 11*d^2*e*x + 55*d*e^2*x^2 + 165*e^3*x^3) + 4*B*(d^4 + 11*d^3*e*x + 55
*d^2*e^2*x^2 + 165*d*e^3*x^3 + 330*e^4*x^4)) + 10*a^2*b^4*e^2*(6*A*e*(d^4 + 11*d
^3*e*x + 55*d^2*e^2*x^2 + 165*d*e^3*x^3 + 330*e^4*x^4) + 5*B*(d^5 + 11*d^4*e*x +
55*d^3*e^2*x^2 + 165*d^2*e^3*x^3 + 330*d*e^4*x^4 + 462*e^5*x^5)) + 4*a*b^5*e*(5
*A*e*(d^5 + 11*d^4*e*x + 55*d^3*e^2*x^2 + 165*d^2*e^3*x^3 + 330*d*e^4*x^4 + 462*
e^5*x^5) + 6*B*(d^6 + 11*d^5*e*x + 55*d^4*e^2*x^2 + 165*d^3*e^3*x^3 + 330*d^2*e^
4*x^4 + 462*d*e^5*x^5 + 462*e^6*x^6)) + b^6*(4*A*e*(d^6 + 11*d^5*e*x + 55*d^4*e^
2*x^2 + 165*d^3*e^3*x^3 + 330*d^2*e^4*x^4 + 462*d*e^5*x^5 + 462*e^6*x^6) + 7*B*(
d^7 + 11*d^6*e*x + 55*d^5*e^2*x^2 + 165*d^4*e^3*x^3 + 330*d^3*e^4*x^4 + 462*d^2*
e^5*x^5 + 462*d*e^6*x^6 + 330*e^7*x^7)))/(9240*e^8*(d + e*x)^11)

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Maple [B]  time = 0.013, size = 814, normalized size = 3.5 \[ -{\frac{b \left ( 5\,A{a}^{4}b{e}^{5}-20\,A{a}^{3}{b}^{2}d{e}^{4}+30\,A{a}^{2}{b}^{3}{d}^{2}{e}^{3}-20\,Aa{b}^{4}{d}^{3}{e}^{2}+5\,A{b}^{5}{d}^{4}e+2\,B{a}^{5}{e}^{5}-15\,B{a}^{4}bd{e}^{4}+40\,B{a}^{3}{b}^{2}{d}^{2}{e}^{3}-50\,B{a}^{2}{b}^{3}{d}^{3}{e}^{2}+30\,Ba{b}^{4}{d}^{4}e-7\,B{b}^{5}{d}^{5} \right ) }{3\,{e}^{8} \left ( ex+d \right ) ^{9}}}-{\frac{6\,A{a}^{5}b{e}^{6}-30\,Ad{a}^{4}{b}^{2}{e}^{5}+60\,A{d}^{2}{a}^{3}{b}^{3}{e}^{4}-60\,A{d}^{3}{a}^{2}{b}^{4}{e}^{3}+30\,A{d}^{4}a{b}^{5}{e}^{2}-6\,A{d}^{5}{b}^{6}e+{a}^{6}B{e}^{6}-12\,Bd{a}^{5}b{e}^{5}+45\,B{d}^{2}{a}^{4}{b}^{2}{e}^{4}-80\,B{d}^{3}{a}^{3}{b}^{3}{e}^{3}+75\,B{d}^{4}{a}^{2}{b}^{4}{e}^{2}-36\,B{d}^{5}a{b}^{5}e+7\,{b}^{6}B{d}^{6}}{10\,{e}^{8} \left ( ex+d \right ) ^{10}}}-{\frac{{b}^{4} \left ( 2\,Aab{e}^{2}-2\,Ad{b}^{2}e+5\,B{a}^{2}{e}^{2}-12\,Bdabe+7\,{b}^{2}B{d}^{2} \right ) }{2\,{e}^{8} \left ( ex+d \right ) ^{6}}}-{\frac{5\,{b}^{2} \left ( 4\,A{a}^{3}b{e}^{4}-12\,A{a}^{2}{b}^{2}d{e}^{3}+12\,Aa{b}^{3}{d}^{2}{e}^{2}-4\,A{b}^{4}{d}^{3}e+3\,B{a}^{4}{e}^{4}-16\,B{a}^{3}bd{e}^{3}+30\,B{a}^{2}{b}^{2}{d}^{2}{e}^{2}-24\,Ba{b}^{3}{d}^{3}e+7\,B{b}^{4}{d}^{4} \right ) }{8\,{e}^{8} \left ( ex+d \right ) ^{8}}}-{\frac{5\,{b}^{3} \left ( 3\,A{a}^{2}b{e}^{3}-6\,Ada{b}^{2}{e}^{2}+3\,A{b}^{3}{d}^{2}e+4\,B{a}^{3}{e}^{3}-15\,B{a}^{2}bd{e}^{2}+18\,B{d}^{2}a{b}^{2}e-7\,{b}^{3}B{d}^{3} \right ) }{7\,{e}^{8} \left ( ex+d \right ) ^{7}}}-{\frac{{a}^{6}A{e}^{7}-6\,Ad{a}^{5}b{e}^{6}+15\,A{d}^{2}{a}^{4}{b}^{2}{e}^{5}-20\,A{d}^{3}{a}^{3}{b}^{3}{e}^{4}+15\,A{d}^{4}{a}^{2}{b}^{4}{e}^{3}-6\,A{d}^{5}a{b}^{5}{e}^{2}+A{d}^{6}{b}^{6}e-Bd{a}^{6}{e}^{6}+6\,B{d}^{2}{a}^{5}b{e}^{5}-15\,B{d}^{3}{a}^{4}{b}^{2}{e}^{4}+20\,B{d}^{4}{a}^{3}{b}^{3}{e}^{3}-15\,B{d}^{5}{a}^{2}{b}^{4}{e}^{2}+6\,B{d}^{6}a{b}^{5}e-{b}^{6}B{d}^{7}}{11\,{e}^{8} \left ( ex+d \right ) ^{11}}}-{\frac{B{b}^{6}}{4\,{e}^{8} \left ( ex+d \right ) ^{4}}}-{\frac{{b}^{5} \left ( Abe+6\,Bae-7\,Bbd \right ) }{5\,{e}^{8} \left ( ex+d \right ) ^{5}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x+a)^6*(B*x+A)/(e*x+d)^12,x)

[Out]

-1/3*b*(5*A*a^4*b*e^5-20*A*a^3*b^2*d*e^4+30*A*a^2*b^3*d^2*e^3-20*A*a*b^4*d^3*e^2
+5*A*b^5*d^4*e+2*B*a^5*e^5-15*B*a^4*b*d*e^4+40*B*a^3*b^2*d^2*e^3-50*B*a^2*b^3*d^
3*e^2+30*B*a*b^4*d^4*e-7*B*b^5*d^5)/e^8/(e*x+d)^9-1/10*(6*A*a^5*b*e^6-30*A*a^4*b
^2*d*e^5+60*A*a^3*b^3*d^2*e^4-60*A*a^2*b^4*d^3*e^3+30*A*a*b^5*d^4*e^2-6*A*b^6*d^
5*e+B*a^6*e^6-12*B*a^5*b*d*e^5+45*B*a^4*b^2*d^2*e^4-80*B*a^3*b^3*d^3*e^3+75*B*a^
2*b^4*d^4*e^2-36*B*a*b^5*d^5*e+7*B*b^6*d^6)/e^8/(e*x+d)^10-1/2*b^4*(2*A*a*b*e^2-
2*A*b^2*d*e+5*B*a^2*e^2-12*B*a*b*d*e+7*B*b^2*d^2)/e^8/(e*x+d)^6-5/8*b^2*(4*A*a^3
*b*e^4-12*A*a^2*b^2*d*e^3+12*A*a*b^3*d^2*e^2-4*A*b^4*d^3*e+3*B*a^4*e^4-16*B*a^3*
b*d*e^3+30*B*a^2*b^2*d^2*e^2-24*B*a*b^3*d^3*e+7*B*b^4*d^4)/e^8/(e*x+d)^8-5/7*b^3
*(3*A*a^2*b*e^3-6*A*a*b^2*d*e^2+3*A*b^3*d^2*e+4*B*a^3*e^3-15*B*a^2*b*d*e^2+18*B*
a*b^2*d^2*e-7*B*b^3*d^3)/e^8/(e*x+d)^7-1/11*(A*a^6*e^7-6*A*a^5*b*d*e^6+15*A*a^4*
b^2*d^2*e^5-20*A*a^3*b^3*d^3*e^4+15*A*a^2*b^4*d^4*e^3-6*A*a*b^5*d^5*e^2+A*b^6*d^
6*e-B*a^6*d*e^6+6*B*a^5*b*d^2*e^5-15*B*a^4*b^2*d^3*e^4+20*B*a^3*b^3*d^4*e^3-15*B
*a^2*b^4*d^5*e^2+6*B*a*b^5*d^6*e-B*b^6*d^7)/e^8/(e*x+d)^11-1/4*B*b^6/e^8/(e*x+d)
^4-1/5*b^5*(A*b*e+6*B*a*e-7*B*b*d)/e^8/(e*x+d)^5

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Maxima [A]  time = 1.42132, size = 1192, normalized size = 5.07 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((B*x + A)*(b*x + a)^6/(e*x + d)^12,x, algorithm="maxima")

[Out]

-1/9240*(2310*B*b^6*e^7*x^7 + 7*B*b^6*d^7 + 840*A*a^6*e^7 + 4*(6*B*a*b^5 + A*b^6
)*d^6*e + 10*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^2 + 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*
d^4*e^3 + 35*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 + 56*(2*B*a^5*b + 5*A*a^4*b^2)*
d^2*e^5 + 84*(B*a^6 + 6*A*a^5*b)*d*e^6 + 462*(7*B*b^6*d*e^6 + 4*(6*B*a*b^5 + A*b
^6)*e^7)*x^6 + 462*(7*B*b^6*d^2*e^5 + 4*(6*B*a*b^5 + A*b^6)*d*e^6 + 10*(5*B*a^2*
b^4 + 2*A*a*b^5)*e^7)*x^5 + 330*(7*B*b^6*d^3*e^4 + 4*(6*B*a*b^5 + A*b^6)*d^2*e^5
+ 10*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6 + 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^7)*x^4
+ 165*(7*B*b^6*d^4*e^3 + 4*(6*B*a*b^5 + A*b^6)*d^3*e^4 + 10*(5*B*a^2*b^4 + 2*A*a
*b^5)*d^2*e^5 + 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^6 + 35*(3*B*a^4*b^2 + 4*A*a^3
*b^3)*e^7)*x^3 + 55*(7*B*b^6*d^5*e^2 + 4*(6*B*a*b^5 + A*b^6)*d^4*e^3 + 10*(5*B*a
^2*b^4 + 2*A*a*b^5)*d^3*e^4 + 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 + 35*(3*B*a
^4*b^2 + 4*A*a^3*b^3)*d*e^6 + 56*(2*B*a^5*b + 5*A*a^4*b^2)*e^7)*x^2 + 11*(7*B*b^
6*d^6*e + 4*(6*B*a*b^5 + A*b^6)*d^5*e^2 + 10*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 +
20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 + 35*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^5
+ 56*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^6 + 84*(B*a^6 + 6*A*a^5*b)*e^7)*x)/(e^19*x^1
1 + 11*d*e^18*x^10 + 55*d^2*e^17*x^9 + 165*d^3*e^16*x^8 + 330*d^4*e^15*x^7 + 462
*d^5*e^14*x^6 + 462*d^6*e^13*x^5 + 330*d^7*e^12*x^4 + 165*d^8*e^11*x^3 + 55*d^9*
e^10*x^2 + 11*d^10*e^9*x + d^11*e^8)

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Fricas [A]  time = 0.209802, size = 1192, normalized size = 5.07 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((B*x + A)*(b*x + a)^6/(e*x + d)^12,x, algorithm="fricas")

[Out]

-1/9240*(2310*B*b^6*e^7*x^7 + 7*B*b^6*d^7 + 840*A*a^6*e^7 + 4*(6*B*a*b^5 + A*b^6
)*d^6*e + 10*(5*B*a^2*b^4 + 2*A*a*b^5)*d^5*e^2 + 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*
d^4*e^3 + 35*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^3*e^4 + 56*(2*B*a^5*b + 5*A*a^4*b^2)*
d^2*e^5 + 84*(B*a^6 + 6*A*a^5*b)*d*e^6 + 462*(7*B*b^6*d*e^6 + 4*(6*B*a*b^5 + A*b
^6)*e^7)*x^6 + 462*(7*B*b^6*d^2*e^5 + 4*(6*B*a*b^5 + A*b^6)*d*e^6 + 10*(5*B*a^2*
b^4 + 2*A*a*b^5)*e^7)*x^5 + 330*(7*B*b^6*d^3*e^4 + 4*(6*B*a*b^5 + A*b^6)*d^2*e^5
+ 10*(5*B*a^2*b^4 + 2*A*a*b^5)*d*e^6 + 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*e^7)*x^4
+ 165*(7*B*b^6*d^4*e^3 + 4*(6*B*a*b^5 + A*b^6)*d^3*e^4 + 10*(5*B*a^2*b^4 + 2*A*a
*b^5)*d^2*e^5 + 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d*e^6 + 35*(3*B*a^4*b^2 + 4*A*a^3
*b^3)*e^7)*x^3 + 55*(7*B*b^6*d^5*e^2 + 4*(6*B*a*b^5 + A*b^6)*d^4*e^3 + 10*(5*B*a
^2*b^4 + 2*A*a*b^5)*d^3*e^4 + 20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^2*e^5 + 35*(3*B*a
^4*b^2 + 4*A*a^3*b^3)*d*e^6 + 56*(2*B*a^5*b + 5*A*a^4*b^2)*e^7)*x^2 + 11*(7*B*b^
6*d^6*e + 4*(6*B*a*b^5 + A*b^6)*d^5*e^2 + 10*(5*B*a^2*b^4 + 2*A*a*b^5)*d^4*e^3 +
20*(4*B*a^3*b^3 + 3*A*a^2*b^4)*d^3*e^4 + 35*(3*B*a^4*b^2 + 4*A*a^3*b^3)*d^2*e^5
+ 56*(2*B*a^5*b + 5*A*a^4*b^2)*d*e^6 + 84*(B*a^6 + 6*A*a^5*b)*e^7)*x)/(e^19*x^1
1 + 11*d*e^18*x^10 + 55*d^2*e^17*x^9 + 165*d^3*e^16*x^8 + 330*d^4*e^15*x^7 + 462
*d^5*e^14*x^6 + 462*d^6*e^13*x^5 + 330*d^7*e^12*x^4 + 165*d^8*e^11*x^3 + 55*d^9*
e^10*x^2 + 11*d^10*e^9*x + d^11*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)**6*(B*x+A)/(e*x+d)**12,x)

[Out]

Timed out

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GIAC/XCAS [A]  time = 0.230363, size = 1, normalized size = 0. \[ \mathit{Done} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((B*x + A)*(b*x + a)^6/(e*x + d)^12,x, algorithm="giac")

[Out]

Done