3.1329 \(\int \frac{(c+d x)^{10}}{(a+b x)^{18}} \, dx\)
Optimal. Leaf size=213 \[ -\frac{d^6 (c+d x)^{11}}{136136 (a+b x)^{11} (b c-a d)^7}+\frac{d^5 (c+d x)^{11}}{12376 (a+b x)^{12} (b c-a d)^6}-\frac{3 d^4 (c+d x)^{11}}{6188 (a+b x)^{13} (b c-a d)^5}+\frac{d^3 (c+d x)^{11}}{476 (a+b x)^{14} (b c-a d)^4}-\frac{d^2 (c+d x)^{11}}{136 (a+b x)^{15} (b c-a d)^3}+\frac{3 d (c+d x)^{11}}{136 (a+b x)^{16} (b c-a d)^2}-\frac{(c+d x)^{11}}{17 (a+b x)^{17} (b c-a d)} \]
[Out]
-(c + d*x)^11/(17*(b*c - a*d)*(a + b*x)^17) + (3*d*(c + d*x)^11)/(136*(b*c - a*d)^2*(a + b*x)^16) - (d^2*(c +
d*x)^11)/(136*(b*c - a*d)^3*(a + b*x)^15) + (d^3*(c + d*x)^11)/(476*(b*c - a*d)^4*(a + b*x)^14) - (3*d^4*(c +
d*x)^11)/(6188*(b*c - a*d)^5*(a + b*x)^13) + (d^5*(c + d*x)^11)/(12376*(b*c - a*d)^6*(a + b*x)^12) - (d^6*(c +
d*x)^11)/(136136*(b*c - a*d)^7*(a + b*x)^11)
________________________________________________________________________________________
Rubi [A] time = 0.0787245, antiderivative size = 213, normalized size of antiderivative = 1.,
number of steps used = 7, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used =
{45, 37} \[ -\frac{d^6 (c+d x)^{11}}{136136 (a+b x)^{11} (b c-a d)^7}+\frac{d^5 (c+d x)^{11}}{12376 (a+b x)^{12} (b c-a d)^6}-\frac{3 d^4 (c+d x)^{11}}{6188 (a+b x)^{13} (b c-a d)^5}+\frac{d^3 (c+d x)^{11}}{476 (a+b x)^{14} (b c-a d)^4}-\frac{d^2 (c+d x)^{11}}{136 (a+b x)^{15} (b c-a d)^3}+\frac{3 d (c+d x)^{11}}{136 (a+b x)^{16} (b c-a d)^2}-\frac{(c+d x)^{11}}{17 (a+b x)^{17} (b c-a d)} \]
Antiderivative was successfully verified.
[In]
Int[(c + d*x)^10/(a + b*x)^18,x]
[Out]
-(c + d*x)^11/(17*(b*c - a*d)*(a + b*x)^17) + (3*d*(c + d*x)^11)/(136*(b*c - a*d)^2*(a + b*x)^16) - (d^2*(c +
d*x)^11)/(136*(b*c - a*d)^3*(a + b*x)^15) + (d^3*(c + d*x)^11)/(476*(b*c - a*d)^4*(a + b*x)^14) - (3*d^4*(c +
d*x)^11)/(6188*(b*c - a*d)^5*(a + b*x)^13) + (d^5*(c + d*x)^11)/(12376*(b*c - a*d)^6*(a + b*x)^12) - (d^6*(c +
d*x)^11)/(136136*(b*c - a*d)^7*(a + b*x)^11)
Rule 45
Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[((a + b*x)^(m + 1)*(c + d*x)^(n + 1
))/((b*c - a*d)*(m + 1)), x] - Dist[(d*Simplify[m + n + 2])/((b*c - a*d)*(m + 1)), Int[(a + b*x)^Simplify[m +
1]*(c + d*x)^n, x], x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[b*c - a*d, 0] && ILtQ[Simplify[m + n + 2], 0] &&
NeQ[m, -1] && !(LtQ[m, -1] && LtQ[n, -1] && (EqQ[a, 0] || (NeQ[c, 0] && LtQ[m - n, 0] && IntegerQ[n]))) && (
SumSimplerQ[m, 1] || !SumSimplerQ[n, 1])
Rule 37
Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[((a + b*x)^(m + 1)*(c + d*x)^(n +
1))/((b*c - a*d)*(m + 1)), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[b*c - a*d, 0] && EqQ[m + n + 2, 0] && NeQ
[m, -1]
Rubi steps
\begin{align*} \int \frac{(c+d x)^{10}}{(a+b x)^{18}} \, dx &=-\frac{(c+d x)^{11}}{17 (b c-a d) (a+b x)^{17}}-\frac{(6 d) \int \frac{(c+d x)^{10}}{(a+b x)^{17}} \, dx}{17 (b c-a d)}\\ &=-\frac{(c+d x)^{11}}{17 (b c-a d) (a+b x)^{17}}+\frac{3 d (c+d x)^{11}}{136 (b c-a d)^2 (a+b x)^{16}}+\frac{\left (15 d^2\right ) \int \frac{(c+d x)^{10}}{(a+b x)^{16}} \, dx}{136 (b c-a d)^2}\\ &=-\frac{(c+d x)^{11}}{17 (b c-a d) (a+b x)^{17}}+\frac{3 d (c+d x)^{11}}{136 (b c-a d)^2 (a+b x)^{16}}-\frac{d^2 (c+d x)^{11}}{136 (b c-a d)^3 (a+b x)^{15}}-\frac{d^3 \int \frac{(c+d x)^{10}}{(a+b x)^{15}} \, dx}{34 (b c-a d)^3}\\ &=-\frac{(c+d x)^{11}}{17 (b c-a d) (a+b x)^{17}}+\frac{3 d (c+d x)^{11}}{136 (b c-a d)^2 (a+b x)^{16}}-\frac{d^2 (c+d x)^{11}}{136 (b c-a d)^3 (a+b x)^{15}}+\frac{d^3 (c+d x)^{11}}{476 (b c-a d)^4 (a+b x)^{14}}+\frac{\left (3 d^4\right ) \int \frac{(c+d x)^{10}}{(a+b x)^{14}} \, dx}{476 (b c-a d)^4}\\ &=-\frac{(c+d x)^{11}}{17 (b c-a d) (a+b x)^{17}}+\frac{3 d (c+d x)^{11}}{136 (b c-a d)^2 (a+b x)^{16}}-\frac{d^2 (c+d x)^{11}}{136 (b c-a d)^3 (a+b x)^{15}}+\frac{d^3 (c+d x)^{11}}{476 (b c-a d)^4 (a+b x)^{14}}-\frac{3 d^4 (c+d x)^{11}}{6188 (b c-a d)^5 (a+b x)^{13}}-\frac{\left (3 d^5\right ) \int \frac{(c+d x)^{10}}{(a+b x)^{13}} \, dx}{3094 (b c-a d)^5}\\ &=-\frac{(c+d x)^{11}}{17 (b c-a d) (a+b x)^{17}}+\frac{3 d (c+d x)^{11}}{136 (b c-a d)^2 (a+b x)^{16}}-\frac{d^2 (c+d x)^{11}}{136 (b c-a d)^3 (a+b x)^{15}}+\frac{d^3 (c+d x)^{11}}{476 (b c-a d)^4 (a+b x)^{14}}-\frac{3 d^4 (c+d x)^{11}}{6188 (b c-a d)^5 (a+b x)^{13}}+\frac{d^5 (c+d x)^{11}}{12376 (b c-a d)^6 (a+b x)^{12}}+\frac{d^6 \int \frac{(c+d x)^{10}}{(a+b x)^{12}} \, dx}{12376 (b c-a d)^6}\\ &=-\frac{(c+d x)^{11}}{17 (b c-a d) (a+b x)^{17}}+\frac{3 d (c+d x)^{11}}{136 (b c-a d)^2 (a+b x)^{16}}-\frac{d^2 (c+d x)^{11}}{136 (b c-a d)^3 (a+b x)^{15}}+\frac{d^3 (c+d x)^{11}}{476 (b c-a d)^4 (a+b x)^{14}}-\frac{3 d^4 (c+d x)^{11}}{6188 (b c-a d)^5 (a+b x)^{13}}+\frac{d^5 (c+d x)^{11}}{12376 (b c-a d)^6 (a+b x)^{12}}-\frac{d^6 (c+d x)^{11}}{136136 (b c-a d)^7 (a+b x)^{11}}\\ \end{align*}
Mathematica [B] time = 0.360073, size = 690, normalized size = 3.24 \[ -\frac{a^2 b^8 d^2 \left (125664 c^6 d^2 x^2+314160 c^5 d^3 x^3+499800 c^4 d^4 x^4+519792 c^3 d^5 x^5+346528 c^2 d^6 x^6+29172 c^7 d x+3003 c^8+136136 c d^7 x^7+24310 d^8 x^8\right )+4 a^3 b^7 d^3 \left (15708 c^5 d^2 x^2+35700 c^4 d^3 x^3+49980 c^3 d^4 x^4+43316 c^2 d^5 x^5+3927 c^6 d x+429 c^7+21658 c d^6 x^6+4862 d^7 x^7\right )+14 a^4 b^6 d^4 \left (2040 c^4 d^2 x^2+4080 c^3 d^3 x^3+4760 c^2 d^4 x^4+561 c^5 d x+66 c^6+3094 c d^5 x^5+884 d^6 x^6\right )+14 a^5 b^5 d^5 \left (816 c^3 d^2 x^2+1360 c^2 d^3 x^3+255 c^4 d x+33 c^5+1190 c d^4 x^4+442 d^5 x^5\right )+14 a^6 b^4 d^6 \left (272 c^2 d^2 x^2+102 c^3 d x+15 c^4+340 c d^3 x^3+170 d^4 x^4\right )+4 a^7 b^3 d^7 \left (119 c^2 d x+21 c^3+238 c d^2 x^2+170 d^3 x^3\right )+a^8 b^2 d^8 \left (28 c^2+119 c d x+136 d^2 x^2\right )+a^9 b d^9 (7 c+17 d x)+a^{10} d^{10}+a b^9 d \left (233376 c^7 d^2 x^2+628320 c^6 d^3 x^3+1099560 c^5 d^4 x^4+1299480 c^4 d^5 x^5+1039584 c^3 d^6 x^6+544544 c^2 d^7 x^7+51051 c^8 d x+5005 c^9+170170 c d^8 x^8+24310 d^9 x^9\right )+b^{10} \left (408408 c^8 d^2 x^2+1166880 c^7 d^3 x^3+2199120 c^6 d^4 x^4+2858856 c^5 d^5 x^5+2598960 c^4 d^6 x^6+1633632 c^3 d^7 x^7+680680 c^2 d^8 x^8+85085 c^9 d x+8008 c^{10}+170170 c d^9 x^9+19448 d^{10} x^{10}\right )}{136136 b^{11} (a+b x)^{17}} \]
Antiderivative was successfully verified.
[In]
Integrate[(c + d*x)^10/(a + b*x)^18,x]
[Out]
-(a^10*d^10 + a^9*b*d^9*(7*c + 17*d*x) + a^8*b^2*d^8*(28*c^2 + 119*c*d*x + 136*d^2*x^2) + 4*a^7*b^3*d^7*(21*c^
3 + 119*c^2*d*x + 238*c*d^2*x^2 + 170*d^3*x^3) + 14*a^6*b^4*d^6*(15*c^4 + 102*c^3*d*x + 272*c^2*d^2*x^2 + 340*
c*d^3*x^3 + 170*d^4*x^4) + 14*a^5*b^5*d^5*(33*c^5 + 255*c^4*d*x + 816*c^3*d^2*x^2 + 1360*c^2*d^3*x^3 + 1190*c*
d^4*x^4 + 442*d^5*x^5) + 14*a^4*b^6*d^4*(66*c^6 + 561*c^5*d*x + 2040*c^4*d^2*x^2 + 4080*c^3*d^3*x^3 + 4760*c^2
*d^4*x^4 + 3094*c*d^5*x^5 + 884*d^6*x^6) + 4*a^3*b^7*d^3*(429*c^7 + 3927*c^6*d*x + 15708*c^5*d^2*x^2 + 35700*c
^4*d^3*x^3 + 49980*c^3*d^4*x^4 + 43316*c^2*d^5*x^5 + 21658*c*d^6*x^6 + 4862*d^7*x^7) + a^2*b^8*d^2*(3003*c^8 +
29172*c^7*d*x + 125664*c^6*d^2*x^2 + 314160*c^5*d^3*x^3 + 499800*c^4*d^4*x^4 + 519792*c^3*d^5*x^5 + 346528*c^
2*d^6*x^6 + 136136*c*d^7*x^7 + 24310*d^8*x^8) + a*b^9*d*(5005*c^9 + 51051*c^8*d*x + 233376*c^7*d^2*x^2 + 62832
0*c^6*d^3*x^3 + 1099560*c^5*d^4*x^4 + 1299480*c^4*d^5*x^5 + 1039584*c^3*d^6*x^6 + 544544*c^2*d^7*x^7 + 170170*
c*d^8*x^8 + 24310*d^9*x^9) + b^10*(8008*c^10 + 85085*c^9*d*x + 408408*c^8*d^2*x^2 + 1166880*c^7*d^3*x^3 + 2199
120*c^6*d^4*x^4 + 2858856*c^5*d^5*x^5 + 2598960*c^4*d^6*x^6 + 1633632*c^3*d^7*x^7 + 680680*c^2*d^8*x^8 + 17017
0*c*d^9*x^9 + 19448*d^10*x^10))/(136136*b^11*(a + b*x)^17)
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Maple [B] time = 0.01, size = 867, normalized size = 4.1 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((d*x+c)^10/(b*x+a)^18,x)
[Out]
12*d^7*(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)/b^11/(b*x+a)^10+5/4*d^9*(a*d-b*c)/b^11/(b*x+a)^8+60/7*d^3
*(a^7*d^7-7*a^6*b*c*d^6+21*a^5*b^2*c^2*d^5-35*a^4*b^3*c^3*d^4+35*a^3*b^4*c^4*d^3-21*a^2*b^5*c^5*d^2+7*a*b^6*c^
6*d-b^7*c^7)/b^11/(b*x+a)^14+5/8*d*(a^9*d^9-9*a^8*b*c*d^8+36*a^7*b^2*c^2*d^7-84*a^6*b^3*c^3*d^6+126*a^5*b^4*c^
4*d^5-126*a^4*b^5*c^5*d^4+84*a^3*b^6*c^6*d^3-36*a^2*b^7*c^7*d^2+9*a*b^8*c^8*d-b^9*c^9)/b^11/(b*x+a)^16-210/11*
d^6*(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)/b^11/(b*x+a)^11-1/17*(a^10*d^10-10*a^9*b*c
*d^9+45*a^8*b^2*c^2*d^8-120*a^7*b^3*c^3*d^7+210*a^6*b^4*c^4*d^6-252*a^5*b^5*c^5*d^5+210*a^4*b^6*c^6*d^4-120*a^
3*b^7*c^7*d^3+45*a^2*b^8*c^8*d^2-10*a*b^9*c^9*d+b^10*c^10)/b^11/(b*x+a)^17-210/13*d^4*(a^6*d^6-6*a^5*b*c*d^5+1
5*a^4*b^2*c^2*d^4-20*a^3*b^3*c^3*d^3+15*a^2*b^4*c^4*d^2-6*a*b^5*c^5*d+b^6*c^6)/b^11/(b*x+a)^13-3*d^2*(a^8*d^8-
8*a^7*b*c*d^7+28*a^6*b^2*c^2*d^6-56*a^5*b^3*c^3*d^5+70*a^4*b^4*c^4*d^4-56*a^3*b^5*c^5*d^3+28*a^2*b^6*c^6*d^2-8
*a*b^7*c^7*d+b^8*c^8)/b^11/(b*x+a)^15+21*d^5*(a^5*d^5-5*a^4*b*c*d^4+10*a^3*b^2*c^2*d^3-10*a^2*b^3*c^3*d^2+5*a*
b^4*c^4*d-b^5*c^5)/b^11/(b*x+a)^12-5*d^8*(a^2*d^2-2*a*b*c*d+b^2*c^2)/b^11/(b*x+a)^9-1/7*d^10/b^11/(b*x+a)^7
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Maxima [B] time = 1.30187, size = 1405, normalized size = 6.6 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((d*x+c)^10/(b*x+a)^18,x, algorithm="maxima")
[Out]
-1/136136*(19448*b^10*d^10*x^10 + 8008*b^10*c^10 + 5005*a*b^9*c^9*d + 3003*a^2*b^8*c^8*d^2 + 1716*a^3*b^7*c^7*
d^3 + 924*a^4*b^6*c^6*d^4 + 462*a^5*b^5*c^5*d^5 + 210*a^6*b^4*c^4*d^6 + 84*a^7*b^3*c^3*d^7 + 28*a^8*b^2*c^2*d^
8 + 7*a^9*b*c*d^9 + a^10*d^10 + 24310*(7*b^10*c*d^9 + a*b^9*d^10)*x^9 + 24310*(28*b^10*c^2*d^8 + 7*a*b^9*c*d^9
+ a^2*b^8*d^10)*x^8 + 19448*(84*b^10*c^3*d^7 + 28*a*b^9*c^2*d^8 + 7*a^2*b^8*c*d^9 + a^3*b^7*d^10)*x^7 + 12376
*(210*b^10*c^4*d^6 + 84*a*b^9*c^3*d^7 + 28*a^2*b^8*c^2*d^8 + 7*a^3*b^7*c*d^9 + a^4*b^6*d^10)*x^6 + 6188*(462*b
^10*c^5*d^5 + 210*a*b^9*c^4*d^6 + 84*a^2*b^8*c^3*d^7 + 28*a^3*b^7*c^2*d^8 + 7*a^4*b^6*c*d^9 + a^5*b^5*d^10)*x^
5 + 2380*(924*b^10*c^6*d^4 + 462*a*b^9*c^5*d^5 + 210*a^2*b^8*c^4*d^6 + 84*a^3*b^7*c^3*d^7 + 28*a^4*b^6*c^2*d^8
+ 7*a^5*b^5*c*d^9 + a^6*b^4*d^10)*x^4 + 680*(1716*b^10*c^7*d^3 + 924*a*b^9*c^6*d^4 + 462*a^2*b^8*c^5*d^5 + 21
0*a^3*b^7*c^4*d^6 + 84*a^4*b^6*c^3*d^7 + 28*a^5*b^5*c^2*d^8 + 7*a^6*b^4*c*d^9 + a^7*b^3*d^10)*x^3 + 136*(3003*
b^10*c^8*d^2 + 1716*a*b^9*c^7*d^3 + 924*a^2*b^8*c^6*d^4 + 462*a^3*b^7*c^5*d^5 + 210*a^4*b^6*c^4*d^6 + 84*a^5*b
^5*c^3*d^7 + 28*a^6*b^4*c^2*d^8 + 7*a^7*b^3*c*d^9 + a^8*b^2*d^10)*x^2 + 17*(5005*b^10*c^9*d + 3003*a*b^9*c^8*d
^2 + 1716*a^2*b^8*c^7*d^3 + 924*a^3*b^7*c^6*d^4 + 462*a^4*b^6*c^5*d^5 + 210*a^5*b^5*c^4*d^6 + 84*a^6*b^4*c^3*d
^7 + 28*a^7*b^3*c^2*d^8 + 7*a^8*b^2*c*d^9 + a^9*b*d^10)*x)/(b^28*x^17 + 17*a*b^27*x^16 + 136*a^2*b^26*x^15 + 6
80*a^3*b^25*x^14 + 2380*a^4*b^24*x^13 + 6188*a^5*b^23*x^12 + 12376*a^6*b^22*x^11 + 19448*a^7*b^21*x^10 + 24310
*a^8*b^20*x^9 + 24310*a^9*b^19*x^8 + 19448*a^10*b^18*x^7 + 12376*a^11*b^17*x^6 + 6188*a^12*b^16*x^5 + 2380*a^1
3*b^15*x^4 + 680*a^14*b^14*x^3 + 136*a^15*b^13*x^2 + 17*a^16*b^12*x + a^17*b^11)
________________________________________________________________________________________
Fricas [B] time = 1.93375, size = 2338, normalized size = 10.98 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((d*x+c)^10/(b*x+a)^18,x, algorithm="fricas")
[Out]
-1/136136*(19448*b^10*d^10*x^10 + 8008*b^10*c^10 + 5005*a*b^9*c^9*d + 3003*a^2*b^8*c^8*d^2 + 1716*a^3*b^7*c^7*
d^3 + 924*a^4*b^6*c^6*d^4 + 462*a^5*b^5*c^5*d^5 + 210*a^6*b^4*c^4*d^6 + 84*a^7*b^3*c^3*d^7 + 28*a^8*b^2*c^2*d^
8 + 7*a^9*b*c*d^9 + a^10*d^10 + 24310*(7*b^10*c*d^9 + a*b^9*d^10)*x^9 + 24310*(28*b^10*c^2*d^8 + 7*a*b^9*c*d^9
+ a^2*b^8*d^10)*x^8 + 19448*(84*b^10*c^3*d^7 + 28*a*b^9*c^2*d^8 + 7*a^2*b^8*c*d^9 + a^3*b^7*d^10)*x^7 + 12376
*(210*b^10*c^4*d^6 + 84*a*b^9*c^3*d^7 + 28*a^2*b^8*c^2*d^8 + 7*a^3*b^7*c*d^9 + a^4*b^6*d^10)*x^6 + 6188*(462*b
^10*c^5*d^5 + 210*a*b^9*c^4*d^6 + 84*a^2*b^8*c^3*d^7 + 28*a^3*b^7*c^2*d^8 + 7*a^4*b^6*c*d^9 + a^5*b^5*d^10)*x^
5 + 2380*(924*b^10*c^6*d^4 + 462*a*b^9*c^5*d^5 + 210*a^2*b^8*c^4*d^6 + 84*a^3*b^7*c^3*d^7 + 28*a^4*b^6*c^2*d^8
+ 7*a^5*b^5*c*d^9 + a^6*b^4*d^10)*x^4 + 680*(1716*b^10*c^7*d^3 + 924*a*b^9*c^6*d^4 + 462*a^2*b^8*c^5*d^5 + 21
0*a^3*b^7*c^4*d^6 + 84*a^4*b^6*c^3*d^7 + 28*a^5*b^5*c^2*d^8 + 7*a^6*b^4*c*d^9 + a^7*b^3*d^10)*x^3 + 136*(3003*
b^10*c^8*d^2 + 1716*a*b^9*c^7*d^3 + 924*a^2*b^8*c^6*d^4 + 462*a^3*b^7*c^5*d^5 + 210*a^4*b^6*c^4*d^6 + 84*a^5*b
^5*c^3*d^7 + 28*a^6*b^4*c^2*d^8 + 7*a^7*b^3*c*d^9 + a^8*b^2*d^10)*x^2 + 17*(5005*b^10*c^9*d + 3003*a*b^9*c^8*d
^2 + 1716*a^2*b^8*c^7*d^3 + 924*a^3*b^7*c^6*d^4 + 462*a^4*b^6*c^5*d^5 + 210*a^5*b^5*c^4*d^6 + 84*a^6*b^4*c^3*d
^7 + 28*a^7*b^3*c^2*d^8 + 7*a^8*b^2*c*d^9 + a^9*b*d^10)*x)/(b^28*x^17 + 17*a*b^27*x^16 + 136*a^2*b^26*x^15 + 6
80*a^3*b^25*x^14 + 2380*a^4*b^24*x^13 + 6188*a^5*b^23*x^12 + 12376*a^6*b^22*x^11 + 19448*a^7*b^21*x^10 + 24310
*a^8*b^20*x^9 + 24310*a^9*b^19*x^8 + 19448*a^10*b^18*x^7 + 12376*a^11*b^17*x^6 + 6188*a^12*b^16*x^5 + 2380*a^1
3*b^15*x^4 + 680*a^14*b^14*x^3 + 136*a^15*b^13*x^2 + 17*a^16*b^12*x + a^17*b^11)
________________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((d*x+c)**10/(b*x+a)**18,x)
[Out]
Timed out
________________________________________________________________________________________
Giac [B] time = 1.06845, size = 1297, normalized size = 6.09 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((d*x+c)^10/(b*x+a)^18,x, algorithm="giac")
[Out]
-1/136136*(19448*b^10*d^10*x^10 + 170170*b^10*c*d^9*x^9 + 24310*a*b^9*d^10*x^9 + 680680*b^10*c^2*d^8*x^8 + 170
170*a*b^9*c*d^9*x^8 + 24310*a^2*b^8*d^10*x^8 + 1633632*b^10*c^3*d^7*x^7 + 544544*a*b^9*c^2*d^8*x^7 + 136136*a^
2*b^8*c*d^9*x^7 + 19448*a^3*b^7*d^10*x^7 + 2598960*b^10*c^4*d^6*x^6 + 1039584*a*b^9*c^3*d^7*x^6 + 346528*a^2*b
^8*c^2*d^8*x^6 + 86632*a^3*b^7*c*d^9*x^6 + 12376*a^4*b^6*d^10*x^6 + 2858856*b^10*c^5*d^5*x^5 + 1299480*a*b^9*c
^4*d^6*x^5 + 519792*a^2*b^8*c^3*d^7*x^5 + 173264*a^3*b^7*c^2*d^8*x^5 + 43316*a^4*b^6*c*d^9*x^5 + 6188*a^5*b^5*
d^10*x^5 + 2199120*b^10*c^6*d^4*x^4 + 1099560*a*b^9*c^5*d^5*x^4 + 499800*a^2*b^8*c^4*d^6*x^4 + 199920*a^3*b^7*
c^3*d^7*x^4 + 66640*a^4*b^6*c^2*d^8*x^4 + 16660*a^5*b^5*c*d^9*x^4 + 2380*a^6*b^4*d^10*x^4 + 1166880*b^10*c^7*d
^3*x^3 + 628320*a*b^9*c^6*d^4*x^3 + 314160*a^2*b^8*c^5*d^5*x^3 + 142800*a^3*b^7*c^4*d^6*x^3 + 57120*a^4*b^6*c^
3*d^7*x^3 + 19040*a^5*b^5*c^2*d^8*x^3 + 4760*a^6*b^4*c*d^9*x^3 + 680*a^7*b^3*d^10*x^3 + 408408*b^10*c^8*d^2*x^
2 + 233376*a*b^9*c^7*d^3*x^2 + 125664*a^2*b^8*c^6*d^4*x^2 + 62832*a^3*b^7*c^5*d^5*x^2 + 28560*a^4*b^6*c^4*d^6*
x^2 + 11424*a^5*b^5*c^3*d^7*x^2 + 3808*a^6*b^4*c^2*d^8*x^2 + 952*a^7*b^3*c*d^9*x^2 + 136*a^8*b^2*d^10*x^2 + 85
085*b^10*c^9*d*x + 51051*a*b^9*c^8*d^2*x + 29172*a^2*b^8*c^7*d^3*x + 15708*a^3*b^7*c^6*d^4*x + 7854*a^4*b^6*c^
5*d^5*x + 3570*a^5*b^5*c^4*d^6*x + 1428*a^6*b^4*c^3*d^7*x + 476*a^7*b^3*c^2*d^8*x + 119*a^8*b^2*c*d^9*x + 17*a
^9*b*d^10*x + 8008*b^10*c^10 + 5005*a*b^9*c^9*d + 3003*a^2*b^8*c^8*d^2 + 1716*a^3*b^7*c^7*d^3 + 924*a^4*b^6*c^
6*d^4 + 462*a^5*b^5*c^5*d^5 + 210*a^6*b^4*c^4*d^6 + 84*a^7*b^3*c^3*d^7 + 28*a^8*b^2*c^2*d^8 + 7*a^9*b*c*d^9 +
a^10*d^10)/((b*x + a)^17*b^11)