3.1320 \(\int \frac{(c+d x)^{10}}{(a+b x)^9} \, dx\)

Optimal. Leaf size=258 \[ \frac{45 d^8 (b c-a d)^2 \log (a+b x)}{b^{11}}-\frac{120 d^7 (b c-a d)^3}{b^{11} (a+b x)}-\frac{105 d^6 (b c-a d)^4}{b^{11} (a+b x)^2}-\frac{84 d^5 (b c-a d)^5}{b^{11} (a+b x)^3}-\frac{105 d^4 (b c-a d)^6}{2 b^{11} (a+b x)^4}-\frac{24 d^3 (b c-a d)^7}{b^{11} (a+b x)^5}-\frac{15 d^2 (b c-a d)^8}{2 b^{11} (a+b x)^6}-\frac{10 d (b c-a d)^9}{7 b^{11} (a+b x)^7}-\frac{(b c-a d)^{10}}{8 b^{11} (a+b x)^8}+\frac{d^9 x (10 b c-9 a d)}{b^{10}}+\frac{d^{10} x^2}{2 b^9} \]

[Out]

(d^9*(10*b*c - 9*a*d)*x)/b^10 + (d^10*x^2)/(2*b^9) - (b*c - a*d)^10/(8*b^11*(a +
b*x)^8) - (10*d*(b*c - a*d)^9)/(7*b^11*(a + b*x)^7) - (15*d^2*(b*c - a*d)^8)/(2
*b^11*(a + b*x)^6) - (24*d^3*(b*c - a*d)^7)/(b^11*(a + b*x)^5) - (105*d^4*(b*c -
a*d)^6)/(2*b^11*(a + b*x)^4) - (84*d^5*(b*c - a*d)^5)/(b^11*(a + b*x)^3) - (105
*d^6*(b*c - a*d)^4)/(b^11*(a + b*x)^2) - (120*d^7*(b*c - a*d)^3)/(b^11*(a + b*x)
) + (45*d^8*(b*c - a*d)^2*Log[a + b*x])/b^11

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Rubi [A]  time = 0.857399, antiderivative size = 258, 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 \[ \frac{45 d^8 (b c-a d)^2 \log (a+b x)}{b^{11}}-\frac{120 d^7 (b c-a d)^3}{b^{11} (a+b x)}-\frac{105 d^6 (b c-a d)^4}{b^{11} (a+b x)^2}-\frac{84 d^5 (b c-a d)^5}{b^{11} (a+b x)^3}-\frac{105 d^4 (b c-a d)^6}{2 b^{11} (a+b x)^4}-\frac{24 d^3 (b c-a d)^7}{b^{11} (a+b x)^5}-\frac{15 d^2 (b c-a d)^8}{2 b^{11} (a+b x)^6}-\frac{10 d (b c-a d)^9}{7 b^{11} (a+b x)^7}-\frac{(b c-a d)^{10}}{8 b^{11} (a+b x)^8}+\frac{d^9 x (10 b c-9 a d)}{b^{10}}+\frac{d^{10} x^2}{2 b^9} \]

Antiderivative was successfully verified.

[In]  Int[(c + d*x)^10/(a + b*x)^9,x]

[Out]

(d^9*(10*b*c - 9*a*d)*x)/b^10 + (d^10*x^2)/(2*b^9) - (b*c - a*d)^10/(8*b^11*(a +
b*x)^8) - (10*d*(b*c - a*d)^9)/(7*b^11*(a + b*x)^7) - (15*d^2*(b*c - a*d)^8)/(2
*b^11*(a + b*x)^6) - (24*d^3*(b*c - a*d)^7)/(b^11*(a + b*x)^5) - (105*d^4*(b*c -
a*d)^6)/(2*b^11*(a + b*x)^4) - (84*d^5*(b*c - a*d)^5)/(b^11*(a + b*x)^3) - (105
*d^6*(b*c - a*d)^4)/(b^11*(a + b*x)^2) - (120*d^7*(b*c - a*d)^3)/(b^11*(a + b*x)
) + (45*d^8*(b*c - a*d)^2*Log[a + b*x])/b^11

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - d^{9} \left (9 a d - 10 b c\right ) \int \frac{1}{b^{10}}\, dx + \frac{d^{10} \int x\, dx}{b^{9}} + \frac{45 d^{8} \left (a d - b c\right )^{2} \log{\left (a + b x \right )}}{b^{11}} + \frac{120 d^{7} \left (a d - b c\right )^{3}}{b^{11} \left (a + b x\right )} - \frac{105 d^{6} \left (a d - b c\right )^{4}}{b^{11} \left (a + b x\right )^{2}} + \frac{84 d^{5} \left (a d - b c\right )^{5}}{b^{11} \left (a + b x\right )^{3}} - \frac{105 d^{4} \left (a d - b c\right )^{6}}{2 b^{11} \left (a + b x\right )^{4}} + \frac{24 d^{3} \left (a d - b c\right )^{7}}{b^{11} \left (a + b x\right )^{5}} - \frac{15 d^{2} \left (a d - b c\right )^{8}}{2 b^{11} \left (a + b x\right )^{6}} + \frac{10 d \left (a d - b c\right )^{9}}{7 b^{11} \left (a + b x\right )^{7}} - \frac{\left (a d - b c\right )^{10}}{8 b^{11} \left (a + b x\right )^{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((d*x+c)**10/(b*x+a)**9,x)

[Out]

-d**9*(9*a*d - 10*b*c)*Integral(b**(-10), x) + d**10*Integral(x, x)/b**9 + 45*d*
*8*(a*d - b*c)**2*log(a + b*x)/b**11 + 120*d**7*(a*d - b*c)**3/(b**11*(a + b*x))
- 105*d**6*(a*d - b*c)**4/(b**11*(a + b*x)**2) + 84*d**5*(a*d - b*c)**5/(b**11*
(a + b*x)**3) - 105*d**4*(a*d - b*c)**6/(2*b**11*(a + b*x)**4) + 24*d**3*(a*d -
b*c)**7/(b**11*(a + b*x)**5) - 15*d**2*(a*d - b*c)**8/(2*b**11*(a + b*x)**6) + 1
0*d*(a*d - b*c)**9/(7*b**11*(a + b*x)**7) - (a*d - b*c)**10/(8*b**11*(a + b*x)**
8)

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Mathematica [B]  time = 0.548969, size = 712, normalized size = 2.76 \[ \frac{3601 a^{10} d^{10}+2 a^9 b d^9 (13144 d x-4609 c)+a^8 b^2 d^8 \left (6849 c^2-68704 c d x+81928 d^2 x^2\right )+8 a^7 b^3 d^7 \left (-105 c^3+6534 c^2 d x-27538 c d^2 x^2+17542 d^3 x^3\right )+14 a^6 b^4 d^6 \left (-15 c^4-480 c^3 d x+12348 c^2 d^2 x^2-28112 c d^3 x^3+10010 d^4 x^4\right )-28 a^5 b^5 d^5 \left (3 c^5+60 c^4 d x+840 c^3 d^2 x^2-11508 c^2 d^3 x^3+15050 c d^4 x^4-2744 d^5 x^5\right )-14 a^4 b^6 d^4 \left (3 c^6+48 c^5 d x+420 c^4 d^2 x^2+3360 c^3 d^3 x^3-26250 c^2 d^4 x^4+19040 c d^5 x^5-1064 d^6 x^6\right )-8 a^3 b^7 d^3 \left (3 c^7+42 c^6 d x+294 c^5 d^2 x^2+1470 c^4 d^3 x^3+7350 c^3 d^4 x^4-32340 c^2 d^5 x^5+10780 c d^6 x^6+728 d^7 x^7\right )-a^2 b^8 d^2 \left (15 c^8+192 c^7 d x+1176 c^6 d^2 x^2+4704 c^5 d^3 x^3+14700 c^4 d^4 x^4+47040 c^3 d^5 x^5-105840 c^2 d^6 x^6+4480 c d^7 x^7+3248 d^8 x^8\right )-2 a b^9 d \left (5 c^9+60 c^8 d x+336 c^7 d^2 x^2+1176 c^6 d^3 x^3+2940 c^5 d^4 x^4+5880 c^4 d^5 x^5+11760 c^3 d^6 x^6-10080 c^2 d^7 x^7-2240 c d^8 x^8+140 d^9 x^9\right )+2520 d^8 (a+b x)^8 (b c-a d)^2 \log (a+b x)+b^{10} \left (-\left (7 c^{10}+80 c^9 d x+420 c^8 d^2 x^2+1344 c^7 d^3 x^3+2940 c^6 d^4 x^4+4704 c^5 d^5 x^5+5880 c^4 d^6 x^6+6720 c^3 d^7 x^7-560 c d^9 x^9-28 d^{10} x^{10}\right )\right )}{56 b^{11} (a+b x)^8} \]

Antiderivative was successfully verified.

[In]  Integrate[(c + d*x)^10/(a + b*x)^9,x]

[Out]

(3601*a^10*d^10 + 2*a^9*b*d^9*(-4609*c + 13144*d*x) + a^8*b^2*d^8*(6849*c^2 - 68
704*c*d*x + 81928*d^2*x^2) + 8*a^7*b^3*d^7*(-105*c^3 + 6534*c^2*d*x - 27538*c*d^
2*x^2 + 17542*d^3*x^3) + 14*a^6*b^4*d^6*(-15*c^4 - 480*c^3*d*x + 12348*c^2*d^2*x
^2 - 28112*c*d^3*x^3 + 10010*d^4*x^4) - 28*a^5*b^5*d^5*(3*c^5 + 60*c^4*d*x + 840
*c^3*d^2*x^2 - 11508*c^2*d^3*x^3 + 15050*c*d^4*x^4 - 2744*d^5*x^5) - 14*a^4*b^6*
d^4*(3*c^6 + 48*c^5*d*x + 420*c^4*d^2*x^2 + 3360*c^3*d^3*x^3 - 26250*c^2*d^4*x^4
+ 19040*c*d^5*x^5 - 1064*d^6*x^6) - 8*a^3*b^7*d^3*(3*c^7 + 42*c^6*d*x + 294*c^5
*d^2*x^2 + 1470*c^4*d^3*x^3 + 7350*c^3*d^4*x^4 - 32340*c^2*d^5*x^5 + 10780*c*d^6
*x^6 + 728*d^7*x^7) - a^2*b^8*d^2*(15*c^8 + 192*c^7*d*x + 1176*c^6*d^2*x^2 + 470
4*c^5*d^3*x^3 + 14700*c^4*d^4*x^4 + 47040*c^3*d^5*x^5 - 105840*c^2*d^6*x^6 + 448
0*c*d^7*x^7 + 3248*d^8*x^8) - 2*a*b^9*d*(5*c^9 + 60*c^8*d*x + 336*c^7*d^2*x^2 +
1176*c^6*d^3*x^3 + 2940*c^5*d^4*x^4 + 5880*c^4*d^5*x^5 + 11760*c^3*d^6*x^6 - 100
80*c^2*d^7*x^7 - 2240*c*d^8*x^8 + 140*d^9*x^9) - b^10*(7*c^10 + 80*c^9*d*x + 420
*c^8*d^2*x^2 + 1344*c^7*d^3*x^3 + 2940*c^6*d^4*x^4 + 4704*c^5*d^5*x^5 + 5880*c^4
*d^6*x^6 + 6720*c^3*d^7*x^7 - 560*c*d^9*x^9 - 28*d^10*x^10) + 2520*d^8*(b*c - a*
d)^2*(a + b*x)^8*Log[a + b*x])/(56*b^11*(a + b*x)^8)

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Maple [B]  time = 0.026, size = 1256, normalized size = 4.9 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((d*x+c)^10/(b*x+a)^9,x)

[Out]

1/2*d^10*x^2/b^9+10/7/b^11*d^10/(b*x+a)^7*a^9-10/7/b^2*d/(b*x+a)^7*c^9-105/2/b^1
1*d^10/(b*x+a)^4*a^6-105/2/b^5*d^4/(b*x+a)^4*c^6+84/b^11*d^10/(b*x+a)^3*a^5-84/b
^6*d^5/(b*x+a)^3*c^5-105/b^11*d^10/(b*x+a)^2*a^4-105/b^7*d^6/(b*x+a)^2*c^4-1/8/b
^11/(b*x+a)^8*a^10*d^10+120/b^11*d^10/(b*x+a)*a^3-120/b^8*d^7/(b*x+a)*c^3-15/2/b
^11*d^10/(b*x+a)^6*a^8-15/2/b^3*d^2/(b*x+a)^6*c^8+45/b^11*d^10*ln(b*x+a)*a^2+45/
b^9*d^8*ln(b*x+a)*c^2+10*d^9/b^9*x*c+24/b^11*d^10/(b*x+a)^5*a^7-24/b^4*d^3/(b*x+
a)^5*c^7-9*d^10/b^10*a*x-420/b^10*d^9/(b*x+a)^3*a^4*c+840/b^9*d^8/(b*x+a)^3*a^3*
c^2-210/b^5*d^4/(b*x+a)^6*a^2*c^6+60/b^4*d^3/(b*x+a)^6*a*c^7-90/7/b^10*d^9/(b*x+
a)^7*a^8*c+360/7/b^9*d^8/(b*x+a)^7*a^7*c^2-120/b^8*d^7/(b*x+a)^7*a^6*c^3+180/b^7
*d^6/(b*x+a)^7*a^5*c^4-180/b^6*d^5/(b*x+a)^7*a^4*c^5-525/b^7*d^6/(b*x+a)^6*a^4*c
^4+420/b^6*d^5/(b*x+a)^6*a^3*c^5+5/4/b^10/(b*x+a)^8*a^9*c*d^9-45/8/b^9/(b*x+a)^8
*a^8*c^2*d^8-360/b^10*d^9/(b*x+a)*a^2*c+360/b^9*d^8/(b*x+a)*a*c^2+63/2/b^6/(b*x+
a)^8*a^5*c^5*d^5+420/b^10*d^9/(b*x+a)^2*a^3*c-630/b^9*d^8/(b*x+a)^2*a^2*c^2+420/
b^8*d^7/(b*x+a)^2*a*c^3+120/b^5*d^4/(b*x+a)^7*a^3*c^6-105/4/b^5/(b*x+a)^8*a^4*c^
6*d^4+15/b^4/(b*x+a)^8*a^3*c^7*d^3-45/8/b^3/(b*x+a)^8*a^2*c^8*d^2+5/4/b^2/(b*x+a
)^8*a*c^9*d+15/b^8/(b*x+a)^8*a^7*c^3*d^7-105/4/b^7/(b*x+a)^8*a^6*c^4*d^6-1/8/b/(
b*x+a)^8*c^10+60/b^10*d^9/(b*x+a)^6*a^7*c-210/b^9*d^8/(b*x+a)^6*a^6*c^2+420/b^8*
d^7/(b*x+a)^6*a^5*c^3-504/b^6*d^5/(b*x+a)^5*a^2*c^5+168/b^5*d^4/(b*x+a)^5*a*c^6-
90/b^10*d^9*ln(b*x+a)*a*c+1050/b^8*d^7/(b*x+a)^4*a^3*c^3-1575/2/b^7*d^6/(b*x+a)^
4*a^2*c^4+315/b^6*d^5/(b*x+a)^4*a*c^5-168/b^10*d^9/(b*x+a)^5*a^6*c+504/b^9*d^8/(
b*x+a)^5*a^5*c^2-840/b^8*d^7/(b*x+a)^5*a^4*c^3+840/b^7*d^6/(b*x+a)^5*a^3*c^4-840
/b^8*d^7/(b*x+a)^3*a^2*c^3+420/b^7*d^6/(b*x+a)^3*a*c^4-360/7/b^4*d^3/(b*x+a)^7*a
^2*c^7+90/7/b^3*d^2/(b*x+a)^7*a*c^8+315/b^10*d^9/(b*x+a)^4*a^5*c-1575/2/b^9*d^8/
(b*x+a)^4*a^4*c^2

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Maxima [A]  time = 1.50036, size = 1276, normalized size = 4.95 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((d*x + c)^10/(b*x + a)^9,x, algorithm="maxima")

[Out]

-1/56*(7*b^10*c^10 + 10*a*b^9*c^9*d + 15*a^2*b^8*c^8*d^2 + 24*a^3*b^7*c^7*d^3 +
42*a^4*b^6*c^6*d^4 + 84*a^5*b^5*c^5*d^5 + 210*a^6*b^4*c^4*d^6 + 840*a^7*b^3*c^3*
d^7 - 6849*a^8*b^2*c^2*d^8 + 9218*a^9*b*c*d^9 - 3601*a^10*d^10 + 6720*(b^10*c^3*
d^7 - 3*a*b^9*c^2*d^8 + 3*a^2*b^8*c*d^9 - a^3*b^7*d^10)*x^7 + 5880*(b^10*c^4*d^6
+ 4*a*b^9*c^3*d^7 - 18*a^2*b^8*c^2*d^8 + 20*a^3*b^7*c*d^9 - 7*a^4*b^6*d^10)*x^6
+ 2352*(2*b^10*c^5*d^5 + 5*a*b^9*c^4*d^6 + 20*a^2*b^8*c^3*d^7 - 110*a^3*b^7*c^2
*d^8 + 130*a^4*b^6*c*d^9 - 47*a^5*b^5*d^10)*x^5 + 2940*(b^10*c^6*d^4 + 2*a*b^9*c
^5*d^5 + 5*a^2*b^8*c^4*d^6 + 20*a^3*b^7*c^3*d^7 - 125*a^4*b^6*c^2*d^8 + 154*a^5*
b^5*c*d^9 - 57*a^6*b^4*d^10)*x^4 + 336*(4*b^10*c^7*d^3 + 7*a*b^9*c^6*d^4 + 14*a^
2*b^8*c^5*d^5 + 35*a^3*b^7*c^4*d^6 + 140*a^4*b^6*c^3*d^7 - 959*a^5*b^5*c^2*d^8 +
1218*a^6*b^4*c*d^9 - 459*a^7*b^3*d^10)*x^3 + 84*(5*b^10*c^8*d^2 + 8*a*b^9*c^7*d
^3 + 14*a^2*b^8*c^6*d^4 + 28*a^3*b^7*c^5*d^5 + 70*a^4*b^6*c^4*d^6 + 280*a^5*b^5*
c^3*d^7 - 2058*a^6*b^4*c^2*d^8 + 2676*a^7*b^3*c*d^9 - 1023*a^8*b^2*d^10)*x^2 + 8
*(10*b^10*c^9*d + 15*a*b^9*c^8*d^2 + 24*a^2*b^8*c^7*d^3 + 42*a^3*b^7*c^6*d^4 + 8
4*a^4*b^6*c^5*d^5 + 210*a^5*b^5*c^4*d^6 + 840*a^6*b^4*c^3*d^7 - 6534*a^7*b^3*c^2
*d^8 + 8658*a^8*b^2*c*d^9 - 3349*a^9*b*d^10)*x)/(b^19*x^8 + 8*a*b^18*x^7 + 28*a^
2*b^17*x^6 + 56*a^3*b^16*x^5 + 70*a^4*b^15*x^4 + 56*a^5*b^14*x^3 + 28*a^6*b^13*x
^2 + 8*a^7*b^12*x + a^8*b^11) + 1/2*(b*d^10*x^2 + 2*(10*b*c*d^9 - 9*a*d^10)*x)/b
^10 + 45*(b^2*c^2*d^8 - 2*a*b*c*d^9 + a^2*d^10)*log(b*x + a)/b^11

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Fricas [A]  time = 0.231095, size = 1750, normalized size = 6.78 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((d*x + c)^10/(b*x + a)^9,x, algorithm="fricas")

[Out]

1/56*(28*b^10*d^10*x^10 - 7*b^10*c^10 - 10*a*b^9*c^9*d - 15*a^2*b^8*c^8*d^2 - 24
*a^3*b^7*c^7*d^3 - 42*a^4*b^6*c^6*d^4 - 84*a^5*b^5*c^5*d^5 - 210*a^6*b^4*c^4*d^6
- 840*a^7*b^3*c^3*d^7 + 6849*a^8*b^2*c^2*d^8 - 9218*a^9*b*c*d^9 + 3601*a^10*d^1
0 + 280*(2*b^10*c*d^9 - a*b^9*d^10)*x^9 + 112*(40*a*b^9*c*d^9 - 29*a^2*b^8*d^10)
*x^8 - 448*(15*b^10*c^3*d^7 - 45*a*b^9*c^2*d^8 + 10*a^2*b^8*c*d^9 + 13*a^3*b^7*d
^10)*x^7 - 392*(15*b^10*c^4*d^6 + 60*a*b^9*c^3*d^7 - 270*a^2*b^8*c^2*d^8 + 220*a
^3*b^7*c*d^9 - 38*a^4*b^6*d^10)*x^6 - 784*(6*b^10*c^5*d^5 + 15*a*b^9*c^4*d^6 + 6
0*a^2*b^8*c^3*d^7 - 330*a^3*b^7*c^2*d^8 + 340*a^4*b^6*c*d^9 - 98*a^5*b^5*d^10)*x
^5 - 980*(3*b^10*c^6*d^4 + 6*a*b^9*c^5*d^5 + 15*a^2*b^8*c^4*d^6 + 60*a^3*b^7*c^3
*d^7 - 375*a^4*b^6*c^2*d^8 + 430*a^5*b^5*c*d^9 - 143*a^6*b^4*d^10)*x^4 - 112*(12
*b^10*c^7*d^3 + 21*a*b^9*c^6*d^4 + 42*a^2*b^8*c^5*d^5 + 105*a^3*b^7*c^4*d^6 + 42
0*a^4*b^6*c^3*d^7 - 2877*a^5*b^5*c^2*d^8 + 3514*a^6*b^4*c*d^9 - 1253*a^7*b^3*d^1
0)*x^3 - 28*(15*b^10*c^8*d^2 + 24*a*b^9*c^7*d^3 + 42*a^2*b^8*c^6*d^4 + 84*a^3*b^
7*c^5*d^5 + 210*a^4*b^6*c^4*d^6 + 840*a^5*b^5*c^3*d^7 - 6174*a^6*b^4*c^2*d^8 + 7
868*a^7*b^3*c*d^9 - 2926*a^8*b^2*d^10)*x^2 - 8*(10*b^10*c^9*d + 15*a*b^9*c^8*d^2
+ 24*a^2*b^8*c^7*d^3 + 42*a^3*b^7*c^6*d^4 + 84*a^4*b^6*c^5*d^5 + 210*a^5*b^5*c^
4*d^6 + 840*a^6*b^4*c^3*d^7 - 6534*a^7*b^3*c^2*d^8 + 8588*a^8*b^2*c*d^9 - 3286*a
^9*b*d^10)*x + 2520*(a^8*b^2*c^2*d^8 - 2*a^9*b*c*d^9 + a^10*d^10 + (b^10*c^2*d^8
- 2*a*b^9*c*d^9 + a^2*b^8*d^10)*x^8 + 8*(a*b^9*c^2*d^8 - 2*a^2*b^8*c*d^9 + a^3*
b^7*d^10)*x^7 + 28*(a^2*b^8*c^2*d^8 - 2*a^3*b^7*c*d^9 + a^4*b^6*d^10)*x^6 + 56*(
a^3*b^7*c^2*d^8 - 2*a^4*b^6*c*d^9 + a^5*b^5*d^10)*x^5 + 70*(a^4*b^6*c^2*d^8 - 2*
a^5*b^5*c*d^9 + a^6*b^4*d^10)*x^4 + 56*(a^5*b^5*c^2*d^8 - 2*a^6*b^4*c*d^9 + a^7*
b^3*d^10)*x^3 + 28*(a^6*b^4*c^2*d^8 - 2*a^7*b^3*c*d^9 + a^8*b^2*d^10)*x^2 + 8*(a
^7*b^3*c^2*d^8 - 2*a^8*b^2*c*d^9 + a^9*b*d^10)*x)*log(b*x + a))/(b^19*x^8 + 8*a*
b^18*x^7 + 28*a^2*b^17*x^6 + 56*a^3*b^16*x^5 + 70*a^4*b^15*x^4 + 56*a^5*b^14*x^3
+ 28*a^6*b^13*x^2 + 8*a^7*b^12*x + a^8*b^11)

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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((d*x+c)**10/(b*x+a)**9,x)

[Out]

Timed out

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GIAC/XCAS [A]  time = 0.226643, size = 1176, normalized size = 4.56 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((d*x + c)^10/(b*x + a)^9,x, algorithm="giac")

[Out]

45*(b^2*c^2*d^8 - 2*a*b*c*d^9 + a^2*d^10)*ln(abs(b*x + a))/b^11 + 1/2*(b^9*d^10*
x^2 + 20*b^9*c*d^9*x - 18*a*b^8*d^10*x)/b^18 - 1/56*(7*b^10*c^10 + 10*a*b^9*c^9*
d + 15*a^2*b^8*c^8*d^2 + 24*a^3*b^7*c^7*d^3 + 42*a^4*b^6*c^6*d^4 + 84*a^5*b^5*c^
5*d^5 + 210*a^6*b^4*c^4*d^6 + 840*a^7*b^3*c^3*d^7 - 6849*a^8*b^2*c^2*d^8 + 9218*
a^9*b*c*d^9 - 3601*a^10*d^10 + 6720*(b^10*c^3*d^7 - 3*a*b^9*c^2*d^8 + 3*a^2*b^8*
c*d^9 - a^3*b^7*d^10)*x^7 + 5880*(b^10*c^4*d^6 + 4*a*b^9*c^3*d^7 - 18*a^2*b^8*c^
2*d^8 + 20*a^3*b^7*c*d^9 - 7*a^4*b^6*d^10)*x^6 + 2352*(2*b^10*c^5*d^5 + 5*a*b^9*
c^4*d^6 + 20*a^2*b^8*c^3*d^7 - 110*a^3*b^7*c^2*d^8 + 130*a^4*b^6*c*d^9 - 47*a^5*
b^5*d^10)*x^5 + 2940*(b^10*c^6*d^4 + 2*a*b^9*c^5*d^5 + 5*a^2*b^8*c^4*d^6 + 20*a^
3*b^7*c^3*d^7 - 125*a^4*b^6*c^2*d^8 + 154*a^5*b^5*c*d^9 - 57*a^6*b^4*d^10)*x^4 +
336*(4*b^10*c^7*d^3 + 7*a*b^9*c^6*d^4 + 14*a^2*b^8*c^5*d^5 + 35*a^3*b^7*c^4*d^6
+ 140*a^4*b^6*c^3*d^7 - 959*a^5*b^5*c^2*d^8 + 1218*a^6*b^4*c*d^9 - 459*a^7*b^3*
d^10)*x^3 + 84*(5*b^10*c^8*d^2 + 8*a*b^9*c^7*d^3 + 14*a^2*b^8*c^6*d^4 + 28*a^3*b
^7*c^5*d^5 + 70*a^4*b^6*c^4*d^6 + 280*a^5*b^5*c^3*d^7 - 2058*a^6*b^4*c^2*d^8 + 2
676*a^7*b^3*c*d^9 - 1023*a^8*b^2*d^10)*x^2 + 8*(10*b^10*c^9*d + 15*a*b^9*c^8*d^2
+ 24*a^2*b^8*c^7*d^3 + 42*a^3*b^7*c^6*d^4 + 84*a^4*b^6*c^5*d^5 + 210*a^5*b^5*c^
4*d^6 + 840*a^6*b^4*c^3*d^7 - 6534*a^7*b^3*c^2*d^8 + 8658*a^8*b^2*c*d^9 - 3349*a
^9*b*d^10)*x)/((b*x + a)^8*b^11)