3.1305 \(\int (a+b x)^6 (c+d x)^{10} \, dx\)
Optimal. Leaf size=170 \[ -\frac{3 b^5 (c+d x)^{16} (b c-a d)}{8 d^7}+\frac{b^4 (c+d x)^{15} (b c-a d)^2}{d^7}-\frac{10 b^3 (c+d x)^{14} (b c-a d)^3}{7 d^7}+\frac{15 b^2 (c+d x)^{13} (b c-a d)^4}{13 d^7}-\frac{b (c+d x)^{12} (b c-a d)^5}{2 d^7}+\frac{(c+d x)^{11} (b c-a d)^6}{11 d^7}+\frac{b^6 (c+d x)^{17}}{17 d^7} \]
[Out]
((b*c - a*d)^6*(c + d*x)^11)/(11*d^7) - (b*(b*c - a*d)^5*(c + d*x)^12)/(2*d^7) +
(15*b^2*(b*c - a*d)^4*(c + d*x)^13)/(13*d^7) - (10*b^3*(b*c - a*d)^3*(c + d*x)^
14)/(7*d^7) + (b^4*(b*c - a*d)^2*(c + d*x)^15)/d^7 - (3*b^5*(b*c - a*d)*(c + d*x
)^16)/(8*d^7) + (b^6*(c + d*x)^17)/(17*d^7)
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Rubi [A] time = 1.46075, antiderivative size = 170, normalized size of antiderivative = 1.,
number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067
\[ -\frac{3 b^5 (c+d x)^{16} (b c-a d)}{8 d^7}+\frac{b^4 (c+d x)^{15} (b c-a d)^2}{d^7}-\frac{10 b^3 (c+d x)^{14} (b c-a d)^3}{7 d^7}+\frac{15 b^2 (c+d x)^{13} (b c-a d)^4}{13 d^7}-\frac{b (c+d x)^{12} (b c-a d)^5}{2 d^7}+\frac{(c+d x)^{11} (b c-a d)^6}{11 d^7}+\frac{b^6 (c+d x)^{17}}{17 d^7} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^6*(c + d*x)^10,x]
[Out]
((b*c - a*d)^6*(c + d*x)^11)/(11*d^7) - (b*(b*c - a*d)^5*(c + d*x)^12)/(2*d^7) +
(15*b^2*(b*c - a*d)^4*(c + d*x)^13)/(13*d^7) - (10*b^3*(b*c - a*d)^3*(c + d*x)^
14)/(7*d^7) + (b^4*(b*c - a*d)^2*(c + d*x)^15)/d^7 - (3*b^5*(b*c - a*d)*(c + d*x
)^16)/(8*d^7) + (b^6*(c + d*x)^17)/(17*d^7)
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Rubi in Sympy [A] time = 119.466, size = 153, normalized size = 0.9 \[ \frac{b^{6} \left (c + d x\right )^{17}}{17 d^{7}} + \frac{3 b^{5} \left (c + d x\right )^{16} \left (a d - b c\right )}{8 d^{7}} + \frac{b^{4} \left (c + d x\right )^{15} \left (a d - b c\right )^{2}}{d^{7}} + \frac{10 b^{3} \left (c + d x\right )^{14} \left (a d - b c\right )^{3}}{7 d^{7}} + \frac{15 b^{2} \left (c + d x\right )^{13} \left (a d - b c\right )^{4}}{13 d^{7}} + \frac{b \left (c + d x\right )^{12} \left (a d - b c\right )^{5}}{2 d^{7}} + \frac{\left (c + d x\right )^{11} \left (a d - b c\right )^{6}}{11 d^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**6*(d*x+c)**10,x)
[Out]
b**6*(c + d*x)**17/(17*d**7) + 3*b**5*(c + d*x)**16*(a*d - b*c)/(8*d**7) + b**4*
(c + d*x)**15*(a*d - b*c)**2/d**7 + 10*b**3*(c + d*x)**14*(a*d - b*c)**3/(7*d**7
) + 15*b**2*(c + d*x)**13*(a*d - b*c)**4/(13*d**7) + b*(c + d*x)**12*(a*d - b*c)
**5/(2*d**7) + (c + d*x)**11*(a*d - b*c)**6/(11*d**7)
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Mathematica [B] time = 0.229511, size = 939, normalized size = 5.52 \[ \frac{1}{17} b^6 d^{10} x^{17}+\frac{1}{8} b^5 d^9 (5 b c+3 a d) x^{16}+b^4 d^8 \left (3 b^2 c^2+4 a b d c+a^2 d^2\right ) x^{15}+\frac{5}{7} b^3 d^7 \left (12 b^3 c^3+27 a b^2 d c^2+15 a^2 b d^2 c+2 a^3 d^3\right ) x^{14}+\frac{5}{13} b^2 d^6 \left (42 b^4 c^4+144 a b^3 d c^3+135 a^2 b^2 d^2 c^2+40 a^3 b d^3 c+3 a^4 d^4\right ) x^{13}+\frac{1}{2} b d^5 \left (42 b^5 c^5+210 a b^4 d c^4+300 a^2 b^3 d^2 c^3+150 a^3 b^2 d^3 c^2+25 a^4 b d^4 c+a^5 d^5\right ) x^{12}+\frac{1}{11} d^4 \left (210 b^6 c^6+1512 a b^5 d c^5+3150 a^2 b^4 d^2 c^4+2400 a^3 b^3 d^3 c^3+675 a^4 b^2 d^4 c^2+60 a^5 b d^5 c+a^6 d^6\right ) x^{11}+c d^3 \left (12 b^6 c^6+126 a b^5 d c^5+378 a^2 b^4 d^2 c^4+420 a^3 b^3 d^3 c^3+180 a^4 b^2 d^4 c^2+27 a^5 b d^5 c+a^6 d^6\right ) x^{10}+5 c^2 d^2 \left (b^6 c^6+16 a b^5 d c^5+70 a^2 b^4 d^2 c^4+112 a^3 b^3 d^3 c^3+70 a^4 b^2 d^4 c^2+16 a^5 b d^5 c+a^6 d^6\right ) x^9+\frac{5}{4} c^3 d \left (b^6 c^6+27 a b^5 d c^5+180 a^2 b^4 d^2 c^4+420 a^3 b^3 d^3 c^3+378 a^4 b^2 d^4 c^2+126 a^5 b d^5 c+12 a^6 d^6\right ) x^8+\frac{1}{7} c^4 \left (b^6 c^6+60 a b^5 d c^5+675 a^2 b^4 d^2 c^4+2400 a^3 b^3 d^3 c^3+3150 a^4 b^2 d^4 c^2+1512 a^5 b d^5 c+210 a^6 d^6\right ) x^7+a c^5 \left (b^5 c^5+25 a b^4 d c^4+150 a^2 b^3 d^2 c^3+300 a^3 b^2 d^3 c^2+210 a^4 b d^4 c+42 a^5 d^5\right ) x^6+a^2 c^6 \left (3 b^4 c^4+40 a b^3 d c^3+135 a^2 b^2 d^2 c^2+144 a^3 b d^3 c+42 a^4 d^4\right ) x^5+\frac{5}{2} a^3 c^7 \left (2 b^3 c^3+15 a b^2 d c^2+27 a^2 b d^2 c+12 a^3 d^3\right ) x^4+5 a^4 c^8 \left (b^2 c^2+4 a b d c+3 a^2 d^2\right ) x^3+a^5 c^9 (3 b c+5 a d) x^2+a^6 c^{10} x \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^6*(c + d*x)^10,x]
[Out]
a^6*c^10*x + a^5*c^9*(3*b*c + 5*a*d)*x^2 + 5*a^4*c^8*(b^2*c^2 + 4*a*b*c*d + 3*a^
2*d^2)*x^3 + (5*a^3*c^7*(2*b^3*c^3 + 15*a*b^2*c^2*d + 27*a^2*b*c*d^2 + 12*a^3*d^
3)*x^4)/2 + a^2*c^6*(3*b^4*c^4 + 40*a*b^3*c^3*d + 135*a^2*b^2*c^2*d^2 + 144*a^3*
b*c*d^3 + 42*a^4*d^4)*x^5 + a*c^5*(b^5*c^5 + 25*a*b^4*c^4*d + 150*a^2*b^3*c^3*d^
2 + 300*a^3*b^2*c^2*d^3 + 210*a^4*b*c*d^4 + 42*a^5*d^5)*x^6 + (c^4*(b^6*c^6 + 60
*a*b^5*c^5*d + 675*a^2*b^4*c^4*d^2 + 2400*a^3*b^3*c^3*d^3 + 3150*a^4*b^2*c^2*d^4
+ 1512*a^5*b*c*d^5 + 210*a^6*d^6)*x^7)/7 + (5*c^3*d*(b^6*c^6 + 27*a*b^5*c^5*d +
180*a^2*b^4*c^4*d^2 + 420*a^3*b^3*c^3*d^3 + 378*a^4*b^2*c^2*d^4 + 126*a^5*b*c*d
^5 + 12*a^6*d^6)*x^8)/4 + 5*c^2*d^2*(b^6*c^6 + 16*a*b^5*c^5*d + 70*a^2*b^4*c^4*d
^2 + 112*a^3*b^3*c^3*d^3 + 70*a^4*b^2*c^2*d^4 + 16*a^5*b*c*d^5 + a^6*d^6)*x^9 +
c*d^3*(12*b^6*c^6 + 126*a*b^5*c^5*d + 378*a^2*b^4*c^4*d^2 + 420*a^3*b^3*c^3*d^3
+ 180*a^4*b^2*c^2*d^4 + 27*a^5*b*c*d^5 + a^6*d^6)*x^10 + (d^4*(210*b^6*c^6 + 151
2*a*b^5*c^5*d + 3150*a^2*b^4*c^4*d^2 + 2400*a^3*b^3*c^3*d^3 + 675*a^4*b^2*c^2*d^
4 + 60*a^5*b*c*d^5 + a^6*d^6)*x^11)/11 + (b*d^5*(42*b^5*c^5 + 210*a*b^4*c^4*d +
300*a^2*b^3*c^3*d^2 + 150*a^3*b^2*c^2*d^3 + 25*a^4*b*c*d^4 + a^5*d^5)*x^12)/2 +
(5*b^2*d^6*(42*b^4*c^4 + 144*a*b^3*c^3*d + 135*a^2*b^2*c^2*d^2 + 40*a^3*b*c*d^3
+ 3*a^4*d^4)*x^13)/13 + (5*b^3*d^7*(12*b^3*c^3 + 27*a*b^2*c^2*d + 15*a^2*b*c*d^2
+ 2*a^3*d^3)*x^14)/7 + b^4*d^8*(3*b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^15 + (b^5*d^
9*(5*b*c + 3*a*d)*x^16)/8 + (b^6*d^10*x^17)/17
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Maple [B] time = 0.003, size = 991, normalized size = 5.8 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^6*(d*x+c)^10,x)
[Out]
1/17*b^6*d^10*x^17+1/16*(6*a*b^5*d^10+10*b^6*c*d^9)*x^16+1/15*(15*a^2*b^4*d^10+6
0*a*b^5*c*d^9+45*b^6*c^2*d^8)*x^15+1/14*(20*a^3*b^3*d^10+150*a^2*b^4*c*d^9+270*a
*b^5*c^2*d^8+120*b^6*c^3*d^7)*x^14+1/13*(15*a^4*b^2*d^10+200*a^3*b^3*c*d^9+675*a
^2*b^4*c^2*d^8+720*a*b^5*c^3*d^7+210*b^6*c^4*d^6)*x^13+1/12*(6*a^5*b*d^10+150*a^
4*b^2*c*d^9+900*a^3*b^3*c^2*d^8+1800*a^2*b^4*c^3*d^7+1260*a*b^5*c^4*d^6+252*b^6*
c^5*d^5)*x^12+1/11*(a^6*d^10+60*a^5*b*c*d^9+675*a^4*b^2*c^2*d^8+2400*a^3*b^3*c^3
*d^7+3150*a^2*b^4*c^4*d^6+1512*a*b^5*c^5*d^5+210*b^6*c^6*d^4)*x^11+1/10*(10*a^6*
c*d^9+270*a^5*b*c^2*d^8+1800*a^4*b^2*c^3*d^7+4200*a^3*b^3*c^4*d^6+3780*a^2*b^4*c
^5*d^5+1260*a*b^5*c^6*d^4+120*b^6*c^7*d^3)*x^10+1/9*(45*a^6*c^2*d^8+720*a^5*b*c^
3*d^7+3150*a^4*b^2*c^4*d^6+5040*a^3*b^3*c^5*d^5+3150*a^2*b^4*c^6*d^4+720*a*b^5*c
^7*d^3+45*b^6*c^8*d^2)*x^9+1/8*(120*a^6*c^3*d^7+1260*a^5*b*c^4*d^6+3780*a^4*b^2*
c^5*d^5+4200*a^3*b^3*c^6*d^4+1800*a^2*b^4*c^7*d^3+270*a*b^5*c^8*d^2+10*b^6*c^9*d
)*x^8+1/7*(210*a^6*c^4*d^6+1512*a^5*b*c^5*d^5+3150*a^4*b^2*c^6*d^4+2400*a^3*b^3*
c^7*d^3+675*a^2*b^4*c^8*d^2+60*a*b^5*c^9*d+b^6*c^10)*x^7+1/6*(252*a^6*c^5*d^5+12
60*a^5*b*c^6*d^4+1800*a^4*b^2*c^7*d^3+900*a^3*b^3*c^8*d^2+150*a^2*b^4*c^9*d+6*a*
b^5*c^10)*x^6+1/5*(210*a^6*c^6*d^4+720*a^5*b*c^7*d^3+675*a^4*b^2*c^8*d^2+200*a^3
*b^3*c^9*d+15*a^2*b^4*c^10)*x^5+1/4*(120*a^6*c^7*d^3+270*a^5*b*c^8*d^2+150*a^4*b
^2*c^9*d+20*a^3*b^3*c^10)*x^4+1/3*(45*a^6*c^8*d^2+60*a^5*b*c^9*d+15*a^4*b^2*c^10
)*x^3+1/2*(10*a^6*c^9*d+6*a^5*b*c^10)*x^2+a^6*c^10*x
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Maxima [A] time = 1.37458, size = 1319, normalized size = 7.76 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^6*(d*x + c)^10,x, algorithm="maxima")
[Out]
1/17*b^6*d^10*x^17 + a^6*c^10*x + 1/8*(5*b^6*c*d^9 + 3*a*b^5*d^10)*x^16 + (3*b^6
*c^2*d^8 + 4*a*b^5*c*d^9 + a^2*b^4*d^10)*x^15 + 5/7*(12*b^6*c^3*d^7 + 27*a*b^5*c
^2*d^8 + 15*a^2*b^4*c*d^9 + 2*a^3*b^3*d^10)*x^14 + 5/13*(42*b^6*c^4*d^6 + 144*a*
b^5*c^3*d^7 + 135*a^2*b^4*c^2*d^8 + 40*a^3*b^3*c*d^9 + 3*a^4*b^2*d^10)*x^13 + 1/
2*(42*b^6*c^5*d^5 + 210*a*b^5*c^4*d^6 + 300*a^2*b^4*c^3*d^7 + 150*a^3*b^3*c^2*d^
8 + 25*a^4*b^2*c*d^9 + a^5*b*d^10)*x^12 + 1/11*(210*b^6*c^6*d^4 + 1512*a*b^5*c^5
*d^5 + 3150*a^2*b^4*c^4*d^6 + 2400*a^3*b^3*c^3*d^7 + 675*a^4*b^2*c^2*d^8 + 60*a^
5*b*c*d^9 + a^6*d^10)*x^11 + (12*b^6*c^7*d^3 + 126*a*b^5*c^6*d^4 + 378*a^2*b^4*c
^5*d^5 + 420*a^3*b^3*c^4*d^6 + 180*a^4*b^2*c^3*d^7 + 27*a^5*b*c^2*d^8 + a^6*c*d^
9)*x^10 + 5*(b^6*c^8*d^2 + 16*a*b^5*c^7*d^3 + 70*a^2*b^4*c^6*d^4 + 112*a^3*b^3*c
^5*d^5 + 70*a^4*b^2*c^4*d^6 + 16*a^5*b*c^3*d^7 + a^6*c^2*d^8)*x^9 + 5/4*(b^6*c^9
*d + 27*a*b^5*c^8*d^2 + 180*a^2*b^4*c^7*d^3 + 420*a^3*b^3*c^6*d^4 + 378*a^4*b^2*
c^5*d^5 + 126*a^5*b*c^4*d^6 + 12*a^6*c^3*d^7)*x^8 + 1/7*(b^6*c^10 + 60*a*b^5*c^9
*d + 675*a^2*b^4*c^8*d^2 + 2400*a^3*b^3*c^7*d^3 + 3150*a^4*b^2*c^6*d^4 + 1512*a^
5*b*c^5*d^5 + 210*a^6*c^4*d^6)*x^7 + (a*b^5*c^10 + 25*a^2*b^4*c^9*d + 150*a^3*b^
3*c^8*d^2 + 300*a^4*b^2*c^7*d^3 + 210*a^5*b*c^6*d^4 + 42*a^6*c^5*d^5)*x^6 + (3*a
^2*b^4*c^10 + 40*a^3*b^3*c^9*d + 135*a^4*b^2*c^8*d^2 + 144*a^5*b*c^7*d^3 + 42*a^
6*c^6*d^4)*x^5 + 5/2*(2*a^3*b^3*c^10 + 15*a^4*b^2*c^9*d + 27*a^5*b*c^8*d^2 + 12*
a^6*c^7*d^3)*x^4 + 5*(a^4*b^2*c^10 + 4*a^5*b*c^9*d + 3*a^6*c^8*d^2)*x^3 + (3*a^5
*b*c^10 + 5*a^6*c^9*d)*x^2
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Fricas [A] time = 0.212921, size = 1, normalized size = 0.01 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^6*(d*x + c)^10,x, algorithm="fricas")
[Out]
1/17*x^17*d^10*b^6 + 5/8*x^16*d^9*c*b^6 + 3/8*x^16*d^10*b^5*a + 3*x^15*d^8*c^2*b
^6 + 4*x^15*d^9*c*b^5*a + x^15*d^10*b^4*a^2 + 60/7*x^14*d^7*c^3*b^6 + 135/7*x^14
*d^8*c^2*b^5*a + 75/7*x^14*d^9*c*b^4*a^2 + 10/7*x^14*d^10*b^3*a^3 + 210/13*x^13*
d^6*c^4*b^6 + 720/13*x^13*d^7*c^3*b^5*a + 675/13*x^13*d^8*c^2*b^4*a^2 + 200/13*x
^13*d^9*c*b^3*a^3 + 15/13*x^13*d^10*b^2*a^4 + 21*x^12*d^5*c^5*b^6 + 105*x^12*d^6
*c^4*b^5*a + 150*x^12*d^7*c^3*b^4*a^2 + 75*x^12*d^8*c^2*b^3*a^3 + 25/2*x^12*d^9*
c*b^2*a^4 + 1/2*x^12*d^10*b*a^5 + 210/11*x^11*d^4*c^6*b^6 + 1512/11*x^11*d^5*c^5
*b^5*a + 3150/11*x^11*d^6*c^4*b^4*a^2 + 2400/11*x^11*d^7*c^3*b^3*a^3 + 675/11*x^
11*d^8*c^2*b^2*a^4 + 60/11*x^11*d^9*c*b*a^5 + 1/11*x^11*d^10*a^6 + 12*x^10*d^3*c
^7*b^6 + 126*x^10*d^4*c^6*b^5*a + 378*x^10*d^5*c^5*b^4*a^2 + 420*x^10*d^6*c^4*b^
3*a^3 + 180*x^10*d^7*c^3*b^2*a^4 + 27*x^10*d^8*c^2*b*a^5 + x^10*d^9*c*a^6 + 5*x^
9*d^2*c^8*b^6 + 80*x^9*d^3*c^7*b^5*a + 350*x^9*d^4*c^6*b^4*a^2 + 560*x^9*d^5*c^5
*b^3*a^3 + 350*x^9*d^6*c^4*b^2*a^4 + 80*x^9*d^7*c^3*b*a^5 + 5*x^9*d^8*c^2*a^6 +
5/4*x^8*d*c^9*b^6 + 135/4*x^8*d^2*c^8*b^5*a + 225*x^8*d^3*c^7*b^4*a^2 + 525*x^8*
d^4*c^6*b^3*a^3 + 945/2*x^8*d^5*c^5*b^2*a^4 + 315/2*x^8*d^6*c^4*b*a^5 + 15*x^8*d
^7*c^3*a^6 + 1/7*x^7*c^10*b^6 + 60/7*x^7*d*c^9*b^5*a + 675/7*x^7*d^2*c^8*b^4*a^2
+ 2400/7*x^7*d^3*c^7*b^3*a^3 + 450*x^7*d^4*c^6*b^2*a^4 + 216*x^7*d^5*c^5*b*a^5
+ 30*x^7*d^6*c^4*a^6 + x^6*c^10*b^5*a + 25*x^6*d*c^9*b^4*a^2 + 150*x^6*d^2*c^8*b
^3*a^3 + 300*x^6*d^3*c^7*b^2*a^4 + 210*x^6*d^4*c^6*b*a^5 + 42*x^6*d^5*c^5*a^6 +
3*x^5*c^10*b^4*a^2 + 40*x^5*d*c^9*b^3*a^3 + 135*x^5*d^2*c^8*b^2*a^4 + 144*x^5*d^
3*c^7*b*a^5 + 42*x^5*d^4*c^6*a^6 + 5*x^4*c^10*b^3*a^3 + 75/2*x^4*d*c^9*b^2*a^4 +
135/2*x^4*d^2*c^8*b*a^5 + 30*x^4*d^3*c^7*a^6 + 5*x^3*c^10*b^2*a^4 + 20*x^3*d*c^
9*b*a^5 + 15*x^3*d^2*c^8*a^6 + 3*x^2*c^10*b*a^5 + 5*x^2*d*c^9*a^6 + x*c^10*a^6
_______________________________________________________________________________________
Sympy [A] time = 0.523504, size = 1088, normalized size = 6.4 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**6*(d*x+c)**10,x)
[Out]
a**6*c**10*x + b**6*d**10*x**17/17 + x**16*(3*a*b**5*d**10/8 + 5*b**6*c*d**9/8)
+ x**15*(a**2*b**4*d**10 + 4*a*b**5*c*d**9 + 3*b**6*c**2*d**8) + x**14*(10*a**3*
b**3*d**10/7 + 75*a**2*b**4*c*d**9/7 + 135*a*b**5*c**2*d**8/7 + 60*b**6*c**3*d**
7/7) + x**13*(15*a**4*b**2*d**10/13 + 200*a**3*b**3*c*d**9/13 + 675*a**2*b**4*c*
*2*d**8/13 + 720*a*b**5*c**3*d**7/13 + 210*b**6*c**4*d**6/13) + x**12*(a**5*b*d*
*10/2 + 25*a**4*b**2*c*d**9/2 + 75*a**3*b**3*c**2*d**8 + 150*a**2*b**4*c**3*d**7
+ 105*a*b**5*c**4*d**6 + 21*b**6*c**5*d**5) + x**11*(a**6*d**10/11 + 60*a**5*b*
c*d**9/11 + 675*a**4*b**2*c**2*d**8/11 + 2400*a**3*b**3*c**3*d**7/11 + 3150*a**2
*b**4*c**4*d**6/11 + 1512*a*b**5*c**5*d**5/11 + 210*b**6*c**6*d**4/11) + x**10*(
a**6*c*d**9 + 27*a**5*b*c**2*d**8 + 180*a**4*b**2*c**3*d**7 + 420*a**3*b**3*c**4
*d**6 + 378*a**2*b**4*c**5*d**5 + 126*a*b**5*c**6*d**4 + 12*b**6*c**7*d**3) + x*
*9*(5*a**6*c**2*d**8 + 80*a**5*b*c**3*d**7 + 350*a**4*b**2*c**4*d**6 + 560*a**3*
b**3*c**5*d**5 + 350*a**2*b**4*c**6*d**4 + 80*a*b**5*c**7*d**3 + 5*b**6*c**8*d**
2) + x**8*(15*a**6*c**3*d**7 + 315*a**5*b*c**4*d**6/2 + 945*a**4*b**2*c**5*d**5/
2 + 525*a**3*b**3*c**6*d**4 + 225*a**2*b**4*c**7*d**3 + 135*a*b**5*c**8*d**2/4 +
5*b**6*c**9*d/4) + x**7*(30*a**6*c**4*d**6 + 216*a**5*b*c**5*d**5 + 450*a**4*b*
*2*c**6*d**4 + 2400*a**3*b**3*c**7*d**3/7 + 675*a**2*b**4*c**8*d**2/7 + 60*a*b**
5*c**9*d/7 + b**6*c**10/7) + x**6*(42*a**6*c**5*d**5 + 210*a**5*b*c**6*d**4 + 30
0*a**4*b**2*c**7*d**3 + 150*a**3*b**3*c**8*d**2 + 25*a**2*b**4*c**9*d + a*b**5*c
**10) + x**5*(42*a**6*c**6*d**4 + 144*a**5*b*c**7*d**3 + 135*a**4*b**2*c**8*d**2
+ 40*a**3*b**3*c**9*d + 3*a**2*b**4*c**10) + x**4*(30*a**6*c**7*d**3 + 135*a**5
*b*c**8*d**2/2 + 75*a**4*b**2*c**9*d/2 + 5*a**3*b**3*c**10) + x**3*(15*a**6*c**8
*d**2 + 20*a**5*b*c**9*d + 5*a**4*b**2*c**10) + x**2*(5*a**6*c**9*d + 3*a**5*b*c
**10)
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.215667, size = 1, normalized size = 0.01 \[ \mathit{Done} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^6*(d*x + c)^10,x, algorithm="giac")
[Out]
Done