3.310 \(\int \frac{x^6}{(a+b x)^3 (c+d x)^3} \, dx\)
Optimal. Leaf size=222 \[ \frac{3 a^4 \left (a^2 d^2-4 a b c d+5 b^2 c^2\right ) \log (a+b x)}{b^4 (b c-a d)^5}-\frac{3 c^4 \left (5 a^2 d^2-4 a b c d+b^2 c^2\right ) \log (c+d x)}{d^4 (b c-a d)^5}-\frac{a^6}{2 b^4 (a+b x)^2 (b c-a d)^3}+\frac{3 a^5 (2 b c-a d)}{b^4 (a+b x) (b c-a d)^4}-\frac{3 c^5 (b c-2 a d)}{d^4 (c+d x) (b c-a d)^4}+\frac{c^6}{2 d^4 (c+d x)^2 (b c-a d)^3}+\frac{x}{b^3 d^3} \]
[Out]
x/(b^3*d^3) - a^6/(2*b^4*(b*c - a*d)^3*(a + b*x)^2) + (3*a^5*(2*b*c - a*d))/(b^4*(b*c - a*d)^4*(a + b*x)) + c^
6/(2*d^4*(b*c - a*d)^3*(c + d*x)^2) - (3*c^5*(b*c - 2*a*d))/(d^4*(b*c - a*d)^4*(c + d*x)) + (3*a^4*(5*b^2*c^2
- 4*a*b*c*d + a^2*d^2)*Log[a + b*x])/(b^4*(b*c - a*d)^5) - (3*c^4*(b^2*c^2 - 4*a*b*c*d + 5*a^2*d^2)*Log[c + d*
x])/(d^4*(b*c - a*d)^5)
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Rubi [A] time = 0.284653, antiderivative size = 222, normalized size of antiderivative = 1.,
number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used =
{88} \[ \frac{3 a^4 \left (a^2 d^2-4 a b c d+5 b^2 c^2\right ) \log (a+b x)}{b^4 (b c-a d)^5}-\frac{3 c^4 \left (5 a^2 d^2-4 a b c d+b^2 c^2\right ) \log (c+d x)}{d^4 (b c-a d)^5}-\frac{a^6}{2 b^4 (a+b x)^2 (b c-a d)^3}+\frac{3 a^5 (2 b c-a d)}{b^4 (a+b x) (b c-a d)^4}-\frac{3 c^5 (b c-2 a d)}{d^4 (c+d x) (b c-a d)^4}+\frac{c^6}{2 d^4 (c+d x)^2 (b c-a d)^3}+\frac{x}{b^3 d^3} \]
Antiderivative was successfully verified.
[In]
Int[x^6/((a + b*x)^3*(c + d*x)^3),x]
[Out]
x/(b^3*d^3) - a^6/(2*b^4*(b*c - a*d)^3*(a + b*x)^2) + (3*a^5*(2*b*c - a*d))/(b^4*(b*c - a*d)^4*(a + b*x)) + c^
6/(2*d^4*(b*c - a*d)^3*(c + d*x)^2) - (3*c^5*(b*c - 2*a*d))/(d^4*(b*c - a*d)^4*(c + d*x)) + (3*a^4*(5*b^2*c^2
- 4*a*b*c*d + a^2*d^2)*Log[a + b*x])/(b^4*(b*c - a*d)^5) - (3*c^4*(b^2*c^2 - 4*a*b*c*d + 5*a^2*d^2)*Log[c + d*
x])/(d^4*(b*c - a*d)^5)
Rule 88
Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Int[ExpandI
ntegrand[(a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, p}, x] && IntegersQ[m, n] &&
(IntegerQ[p] || (GtQ[m, 0] && GeQ[n, -1]))
Rubi steps
\begin{align*} \int \frac{x^6}{(a+b x)^3 (c+d x)^3} \, dx &=\int \left (\frac{1}{b^3 d^3}+\frac{a^6}{b^3 (b c-a d)^3 (a+b x)^3}+\frac{3 a^5 (-2 b c+a d)}{b^3 (b c-a d)^4 (a+b x)^2}+\frac{3 a^4 \left (5 b^2 c^2-4 a b c d+a^2 d^2\right )}{b^3 (b c-a d)^5 (a+b x)}+\frac{c^6}{d^3 (-b c+a d)^3 (c+d x)^3}+\frac{3 c^5 (b c-2 a d)}{d^3 (-b c+a d)^4 (c+d x)^2}+\frac{3 c^4 \left (b^2 c^2-4 a b c d+5 a^2 d^2\right )}{d^3 (-b c+a d)^5 (c+d x)}\right ) \, dx\\ &=\frac{x}{b^3 d^3}-\frac{a^6}{2 b^4 (b c-a d)^3 (a+b x)^2}+\frac{3 a^5 (2 b c-a d)}{b^4 (b c-a d)^4 (a+b x)}+\frac{c^6}{2 d^4 (b c-a d)^3 (c+d x)^2}-\frac{3 c^5 (b c-2 a d)}{d^4 (b c-a d)^4 (c+d x)}+\frac{3 a^4 \left (5 b^2 c^2-4 a b c d+a^2 d^2\right ) \log (a+b x)}{b^4 (b c-a d)^5}-\frac{3 c^4 \left (b^2 c^2-4 a b c d+5 a^2 d^2\right ) \log (c+d x)}{d^4 (b c-a d)^5}\\ \end{align*}
Mathematica [A] time = 0.329298, size = 221, normalized size = 1. \[ \frac{3 a^4 \left (a^2 d^2-4 a b c d+5 b^2 c^2\right ) \log (a+b x)}{b^4 (b c-a d)^5}+\frac{3 c^4 \left (5 a^2 d^2-4 a b c d+b^2 c^2\right ) \log (c+d x)}{d^4 (a d-b c)^5}-\frac{a^6}{2 b^4 (a+b x)^2 (b c-a d)^3}-\frac{3 a^5 (a d-2 b c)}{b^4 (a+b x) (b c-a d)^4}-\frac{3 c^5 (b c-2 a d)}{d^4 (c+d x) (b c-a d)^4}-\frac{c^6}{2 d^4 (c+d x)^2 (a d-b c)^3}+\frac{x}{b^3 d^3} \]
Antiderivative was successfully verified.
[In]
Integrate[x^6/((a + b*x)^3*(c + d*x)^3),x]
[Out]
x/(b^3*d^3) - a^6/(2*b^4*(b*c - a*d)^3*(a + b*x)^2) - (3*a^5*(-2*b*c + a*d))/(b^4*(b*c - a*d)^4*(a + b*x)) - c
^6/(2*d^4*(-(b*c) + a*d)^3*(c + d*x)^2) - (3*c^5*(b*c - 2*a*d))/(d^4*(b*c - a*d)^4*(c + d*x)) + (3*a^4*(5*b^2*
c^2 - 4*a*b*c*d + a^2*d^2)*Log[a + b*x])/(b^4*(b*c - a*d)^5) + (3*c^4*(b^2*c^2 - 4*a*b*c*d + 5*a^2*d^2)*Log[c
+ d*x])/(d^4*(-(b*c) + a*d)^5)
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Maple [A] time = 0.017, size = 324, normalized size = 1.5 \begin{align*}{\frac{x}{{b}^{3}{d}^{3}}}-{\frac{{c}^{6}}{2\,{d}^{4} \left ( ad-bc \right ) ^{3} \left ( dx+c \right ) ^{2}}}+15\,{\frac{{c}^{4}\ln \left ( dx+c \right ){a}^{2}}{{d}^{2} \left ( ad-bc \right ) ^{5}}}-12\,{\frac{{c}^{5}\ln \left ( dx+c \right ) ab}{{d}^{3} \left ( ad-bc \right ) ^{5}}}+3\,{\frac{{c}^{6}\ln \left ( dx+c \right ){b}^{2}}{{d}^{4} \left ( ad-bc \right ) ^{5}}}+6\,{\frac{{c}^{5}a}{{d}^{3} \left ( ad-bc \right ) ^{4} \left ( dx+c \right ) }}-3\,{\frac{{c}^{6}b}{ \left ( ad-bc \right ) ^{4}{d}^{4} \left ( dx+c \right ) }}+{\frac{{a}^{6}}{2\,{b}^{4} \left ( ad-bc \right ) ^{3} \left ( bx+a \right ) ^{2}}}-3\,{\frac{{a}^{6}\ln \left ( bx+a \right ){d}^{2}}{{b}^{4} \left ( ad-bc \right ) ^{5}}}+12\,{\frac{{a}^{5}\ln \left ( bx+a \right ) cd}{{b}^{3} \left ( ad-bc \right ) ^{5}}}-15\,{\frac{{a}^{4}\ln \left ( bx+a \right ){c}^{2}}{{b}^{2} \left ( ad-bc \right ) ^{5}}}-3\,{\frac{{a}^{6}d}{ \left ( ad-bc \right ) ^{4}{b}^{4} \left ( bx+a \right ) }}+6\,{\frac{{a}^{5}c}{{b}^{3} \left ( ad-bc \right ) ^{4} \left ( bx+a \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(x^6/(b*x+a)^3/(d*x+c)^3,x)
[Out]
x/b^3/d^3-1/2/d^4*c^6/(a*d-b*c)^3/(d*x+c)^2+15/d^2*c^4/(a*d-b*c)^5*ln(d*x+c)*a^2-12/d^3*c^5/(a*d-b*c)^5*ln(d*x
+c)*a*b+3/d^4*c^6/(a*d-b*c)^5*ln(d*x+c)*b^2+6/d^3*c^5/(a*d-b*c)^4/(d*x+c)*a-3/d^4*c^6/(a*d-b*c)^4/(d*x+c)*b+1/
2/b^4*a^6/(a*d-b*c)^3/(b*x+a)^2-3/b^4*a^6/(a*d-b*c)^5*ln(b*x+a)*d^2+12/b^3*a^5/(a*d-b*c)^5*ln(b*x+a)*c*d-15/b^
2*a^4/(a*d-b*c)^5*ln(b*x+a)*c^2-3/b^4*a^6/(a*d-b*c)^4/(b*x+a)*d+6/b^3*a^5/(a*d-b*c)^4/(b*x+a)*c
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Maxima [B] time = 1.16051, size = 1104, normalized size = 4.97 \begin{align*} \frac{3 \,{\left (5 \, a^{4} b^{2} c^{2} - 4 \, a^{5} b c d + a^{6} d^{2}\right )} \log \left (b x + a\right )}{b^{9} c^{5} - 5 \, a b^{8} c^{4} d + 10 \, a^{2} b^{7} c^{3} d^{2} - 10 \, a^{3} b^{6} c^{2} d^{3} + 5 \, a^{4} b^{5} c d^{4} - a^{5} b^{4} d^{5}} - \frac{3 \,{\left (b^{2} c^{6} - 4 \, a b c^{5} d + 5 \, a^{2} c^{4} d^{2}\right )} \log \left (d x + c\right )}{b^{5} c^{5} d^{4} - 5 \, a b^{4} c^{4} d^{5} + 10 \, a^{2} b^{3} c^{3} d^{6} - 10 \, a^{3} b^{2} c^{2} d^{7} + 5 \, a^{4} b c d^{8} - a^{5} d^{9}} - \frac{5 \, a^{2} b^{5} c^{7} - 11 \, a^{3} b^{4} c^{6} d - 11 \, a^{6} b c^{3} d^{4} + 5 \, a^{7} c^{2} d^{5} + 6 \,{\left (b^{7} c^{6} d - 2 \, a b^{6} c^{5} d^{2} - 2 \, a^{5} b^{2} c d^{6} + a^{6} b d^{7}\right )} x^{3} +{\left (5 \, b^{7} c^{7} + a b^{6} c^{6} d - 24 \, a^{2} b^{5} c^{5} d^{2} - 24 \, a^{5} b^{2} c^{2} d^{5} + a^{6} b c d^{6} + 5 \, a^{7} d^{7}\right )} x^{2} + 2 \,{\left (5 \, a b^{6} c^{7} - 8 \, a^{2} b^{5} c^{6} d - 6 \, a^{3} b^{4} c^{5} d^{2} - 6 \, a^{5} b^{2} c^{3} d^{4} - 8 \, a^{6} b c^{2} d^{5} + 5 \, a^{7} c d^{6}\right )} x}{2 \,{\left (a^{2} b^{8} c^{6} d^{4} - 4 \, a^{3} b^{7} c^{5} d^{5} + 6 \, a^{4} b^{6} c^{4} d^{6} - 4 \, a^{5} b^{5} c^{3} d^{7} + a^{6} b^{4} c^{2} d^{8} +{\left (b^{10} c^{4} d^{6} - 4 \, a b^{9} c^{3} d^{7} + 6 \, a^{2} b^{8} c^{2} d^{8} - 4 \, a^{3} b^{7} c d^{9} + a^{4} b^{6} d^{10}\right )} x^{4} + 2 \,{\left (b^{10} c^{5} d^{5} - 3 \, a b^{9} c^{4} d^{6} + 2 \, a^{2} b^{8} c^{3} d^{7} + 2 \, a^{3} b^{7} c^{2} d^{8} - 3 \, a^{4} b^{6} c d^{9} + a^{5} b^{5} d^{10}\right )} x^{3} +{\left (b^{10} c^{6} d^{4} - 9 \, a^{2} b^{8} c^{4} d^{6} + 16 \, a^{3} b^{7} c^{3} d^{7} - 9 \, a^{4} b^{6} c^{2} d^{8} + a^{6} b^{4} d^{10}\right )} x^{2} + 2 \,{\left (a b^{9} c^{6} d^{4} - 3 \, a^{2} b^{8} c^{5} d^{5} + 2 \, a^{3} b^{7} c^{4} d^{6} + 2 \, a^{4} b^{6} c^{3} d^{7} - 3 \, a^{5} b^{5} c^{2} d^{8} + a^{6} b^{4} c d^{9}\right )} x\right )}} + \frac{x}{b^{3} d^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(x^6/(b*x+a)^3/(d*x+c)^3,x, algorithm="maxima")
[Out]
3*(5*a^4*b^2*c^2 - 4*a^5*b*c*d + a^6*d^2)*log(b*x + a)/(b^9*c^5 - 5*a*b^8*c^4*d + 10*a^2*b^7*c^3*d^2 - 10*a^3*
b^6*c^2*d^3 + 5*a^4*b^5*c*d^4 - a^5*b^4*d^5) - 3*(b^2*c^6 - 4*a*b*c^5*d + 5*a^2*c^4*d^2)*log(d*x + c)/(b^5*c^5
*d^4 - 5*a*b^4*c^4*d^5 + 10*a^2*b^3*c^3*d^6 - 10*a^3*b^2*c^2*d^7 + 5*a^4*b*c*d^8 - a^5*d^9) - 1/2*(5*a^2*b^5*c
^7 - 11*a^3*b^4*c^6*d - 11*a^6*b*c^3*d^4 + 5*a^7*c^2*d^5 + 6*(b^7*c^6*d - 2*a*b^6*c^5*d^2 - 2*a^5*b^2*c*d^6 +
a^6*b*d^7)*x^3 + (5*b^7*c^7 + a*b^6*c^6*d - 24*a^2*b^5*c^5*d^2 - 24*a^5*b^2*c^2*d^5 + a^6*b*c*d^6 + 5*a^7*d^7)
*x^2 + 2*(5*a*b^6*c^7 - 8*a^2*b^5*c^6*d - 6*a^3*b^4*c^5*d^2 - 6*a^5*b^2*c^3*d^4 - 8*a^6*b*c^2*d^5 + 5*a^7*c*d^
6)*x)/(a^2*b^8*c^6*d^4 - 4*a^3*b^7*c^5*d^5 + 6*a^4*b^6*c^4*d^6 - 4*a^5*b^5*c^3*d^7 + a^6*b^4*c^2*d^8 + (b^10*c
^4*d^6 - 4*a*b^9*c^3*d^7 + 6*a^2*b^8*c^2*d^8 - 4*a^3*b^7*c*d^9 + a^4*b^6*d^10)*x^4 + 2*(b^10*c^5*d^5 - 3*a*b^9
*c^4*d^6 + 2*a^2*b^8*c^3*d^7 + 2*a^3*b^7*c^2*d^8 - 3*a^4*b^6*c*d^9 + a^5*b^5*d^10)*x^3 + (b^10*c^6*d^4 - 9*a^2
*b^8*c^4*d^6 + 16*a^3*b^7*c^3*d^7 - 9*a^4*b^6*c^2*d^8 + a^6*b^4*d^10)*x^2 + 2*(a*b^9*c^6*d^4 - 3*a^2*b^8*c^5*d
^5 + 2*a^3*b^7*c^4*d^6 + 2*a^4*b^6*c^3*d^7 - 3*a^5*b^5*c^2*d^8 + a^6*b^4*c*d^9)*x) + x/(b^3*d^3)
________________________________________________________________________________________
Fricas [B] time = 4.01565, size = 2870, normalized size = 12.93 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(x^6/(b*x+a)^3/(d*x+c)^3,x, algorithm="fricas")
[Out]
-1/2*(5*a^2*b^6*c^8 - 16*a^3*b^5*c^7*d + 11*a^4*b^4*c^6*d^2 - 11*a^6*b^2*c^4*d^4 + 16*a^7*b*c^3*d^5 - 5*a^8*c^
2*d^6 - 2*(b^8*c^5*d^3 - 5*a*b^7*c^4*d^4 + 10*a^2*b^6*c^3*d^5 - 10*a^3*b^5*c^2*d^6 + 5*a^4*b^4*c*d^7 - a^5*b^3
*d^8)*x^5 - 4*(b^8*c^6*d^2 - 4*a*b^7*c^5*d^3 + 5*a^2*b^6*c^4*d^4 - 5*a^4*b^4*c^2*d^6 + 4*a^5*b^3*c*d^7 - a^6*b
^2*d^8)*x^4 + 2*(2*b^8*c^7*d - 8*a*b^7*c^6*d^2 + 15*a^2*b^6*c^5*d^3 - 25*a^3*b^5*c^4*d^4 + 25*a^4*b^4*c^3*d^5
- 15*a^5*b^3*c^2*d^6 + 8*a^6*b^2*c*d^7 - 2*a^7*b*d^8)*x^3 + (5*b^8*c^8 - 8*a*b^7*c^7*d - 9*a^2*b^6*c^6*d^2 + 4
*a^3*b^5*c^5*d^3 - 4*a^5*b^3*c^3*d^5 + 9*a^6*b^2*c^2*d^6 + 8*a^7*b*c*d^7 - 5*a^8*d^8)*x^2 + 2*(5*a*b^7*c^8 - 1
4*a^2*b^6*c^7*d + 7*a^3*b^5*c^6*d^2 - 4*a^4*b^4*c^5*d^3 + 4*a^5*b^3*c^4*d^4 - 7*a^6*b^2*c^3*d^5 + 14*a^7*b*c^2
*d^6 - 5*a^8*c*d^7)*x - 6*(5*a^6*b^2*c^4*d^4 - 4*a^7*b*c^3*d^5 + a^8*c^2*d^6 + (5*a^4*b^4*c^2*d^6 - 4*a^5*b^3*
c*d^7 + a^6*b^2*d^8)*x^4 + 2*(5*a^4*b^4*c^3*d^5 + a^5*b^3*c^2*d^6 - 3*a^6*b^2*c*d^7 + a^7*b*d^8)*x^3 + (5*a^4*
b^4*c^4*d^4 + 16*a^5*b^3*c^3*d^5 - 10*a^6*b^2*c^2*d^6 + a^8*d^8)*x^2 + 2*(5*a^5*b^3*c^4*d^4 + a^6*b^2*c^3*d^5
- 3*a^7*b*c^2*d^6 + a^8*c*d^7)*x)*log(b*x + a) + 6*(a^2*b^6*c^8 - 4*a^3*b^5*c^7*d + 5*a^4*b^4*c^6*d^2 + (b^8*c
^6*d^2 - 4*a*b^7*c^5*d^3 + 5*a^2*b^6*c^4*d^4)*x^4 + 2*(b^8*c^7*d - 3*a*b^7*c^6*d^2 + a^2*b^6*c^5*d^3 + 5*a^3*b
^5*c^4*d^4)*x^3 + (b^8*c^8 - 10*a^2*b^6*c^6*d^2 + 16*a^3*b^5*c^5*d^3 + 5*a^4*b^4*c^4*d^4)*x^2 + 2*(a*b^7*c^8 -
3*a^2*b^6*c^7*d + a^3*b^5*c^6*d^2 + 5*a^4*b^4*c^5*d^3)*x)*log(d*x + c))/(a^2*b^9*c^7*d^4 - 5*a^3*b^8*c^6*d^5
+ 10*a^4*b^7*c^5*d^6 - 10*a^5*b^6*c^4*d^7 + 5*a^6*b^5*c^3*d^8 - a^7*b^4*c^2*d^9 + (b^11*c^5*d^6 - 5*a*b^10*c^4
*d^7 + 10*a^2*b^9*c^3*d^8 - 10*a^3*b^8*c^2*d^9 + 5*a^4*b^7*c*d^10 - a^5*b^6*d^11)*x^4 + 2*(b^11*c^6*d^5 - 4*a*
b^10*c^5*d^6 + 5*a^2*b^9*c^4*d^7 - 5*a^4*b^7*c^2*d^9 + 4*a^5*b^6*c*d^10 - a^6*b^5*d^11)*x^3 + (b^11*c^7*d^4 -
a*b^10*c^6*d^5 - 9*a^2*b^9*c^5*d^6 + 25*a^3*b^8*c^4*d^7 - 25*a^4*b^7*c^3*d^8 + 9*a^5*b^6*c^2*d^9 + a^6*b^5*c*d
^10 - a^7*b^4*d^11)*x^2 + 2*(a*b^10*c^7*d^4 - 4*a^2*b^9*c^6*d^5 + 5*a^3*b^8*c^5*d^6 - 5*a^5*b^6*c^3*d^8 + 4*a^
6*b^5*c^2*d^9 - a^7*b^4*c*d^10)*x)
________________________________________________________________________________________
Sympy [B] time = 17.9774, size = 1685, normalized size = 7.59 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(x**6/(b*x+a)**3/(d*x+c)**3,x)
[Out]
-3*a**4*(a**2*d**2 - 4*a*b*c*d + 5*b**2*c**2)*log(x + (3*a**10*d**9*(a**2*d**2 - 4*a*b*c*d + 5*b**2*c**2)/(b*(
a*d - b*c)**5) - 18*a**9*c*d**8*(a**2*d**2 - 4*a*b*c*d + 5*b**2*c**2)/(a*d - b*c)**5 + 45*a**8*b*c**2*d**7*(a*
*2*d**2 - 4*a*b*c*d + 5*b**2*c**2)/(a*d - b*c)**5 - 60*a**7*b**2*c**3*d**6*(a**2*d**2 - 4*a*b*c*d + 5*b**2*c**
2)/(a*d - b*c)**5 + 45*a**6*b**3*c**4*d**5*(a**2*d**2 - 4*a*b*c*d + 5*b**2*c**2)/(a*d - b*c)**5 + 3*a**6*c*d**
5 - 18*a**5*b**4*c**5*d**4*(a**2*d**2 - 4*a*b*c*d + 5*b**2*c**2)/(a*d - b*c)**5 - 12*a**5*b*c**2*d**4 + 3*a**4
*b**5*c**6*d**3*(a**2*d**2 - 4*a*b*c*d + 5*b**2*c**2)/(a*d - b*c)**5 + 15*a**4*b**2*c**3*d**3 + 15*a**3*b**3*c
**4*d**2 - 12*a**2*b**4*c**5*d + 3*a*b**5*c**6)/(3*a**6*d**6 - 12*a**5*b*c*d**5 + 15*a**4*b**2*c**2*d**4 + 15*
a**2*b**4*c**4*d**2 - 12*a*b**5*c**5*d + 3*b**6*c**6))/(b**4*(a*d - b*c)**5) + 3*c**4*(5*a**2*d**2 - 4*a*b*c*d
+ b**2*c**2)*log(x + (-3*a**6*b**3*c**4*d**5*(5*a**2*d**2 - 4*a*b*c*d + b**2*c**2)/(a*d - b*c)**5 + 3*a**6*c*
d**5 + 18*a**5*b**4*c**5*d**4*(5*a**2*d**2 - 4*a*b*c*d + b**2*c**2)/(a*d - b*c)**5 - 12*a**5*b*c**2*d**4 - 45*
a**4*b**5*c**6*d**3*(5*a**2*d**2 - 4*a*b*c*d + b**2*c**2)/(a*d - b*c)**5 + 15*a**4*b**2*c**3*d**3 + 60*a**3*b*
*6*c**7*d**2*(5*a**2*d**2 - 4*a*b*c*d + b**2*c**2)/(a*d - b*c)**5 + 15*a**3*b**3*c**4*d**2 - 45*a**2*b**7*c**8
*d*(5*a**2*d**2 - 4*a*b*c*d + b**2*c**2)/(a*d - b*c)**5 - 12*a**2*b**4*c**5*d + 18*a*b**8*c**9*(5*a**2*d**2 -
4*a*b*c*d + b**2*c**2)/(a*d - b*c)**5 + 3*a*b**5*c**6 - 3*b**9*c**10*(5*a**2*d**2 - 4*a*b*c*d + b**2*c**2)/(d*
(a*d - b*c)**5))/(3*a**6*d**6 - 12*a**5*b*c*d**5 + 15*a**4*b**2*c**2*d**4 + 15*a**2*b**4*c**4*d**2 - 12*a*b**5
*c**5*d + 3*b**6*c**6))/(d**4*(a*d - b*c)**5) - (5*a**7*c**2*d**5 - 11*a**6*b*c**3*d**4 - 11*a**3*b**4*c**6*d
+ 5*a**2*b**5*c**7 + x**3*(6*a**6*b*d**7 - 12*a**5*b**2*c*d**6 - 12*a*b**6*c**5*d**2 + 6*b**7*c**6*d) + x**2*(
5*a**7*d**7 + a**6*b*c*d**6 - 24*a**5*b**2*c**2*d**5 - 24*a**2*b**5*c**5*d**2 + a*b**6*c**6*d + 5*b**7*c**7) +
x*(10*a**7*c*d**6 - 16*a**6*b*c**2*d**5 - 12*a**5*b**2*c**3*d**4 - 12*a**3*b**4*c**5*d**2 - 16*a**2*b**5*c**6
*d + 10*a*b**6*c**7))/(2*a**6*b**4*c**2*d**8 - 8*a**5*b**5*c**3*d**7 + 12*a**4*b**6*c**4*d**6 - 8*a**3*b**7*c*
*5*d**5 + 2*a**2*b**8*c**6*d**4 + x**4*(2*a**4*b**6*d**10 - 8*a**3*b**7*c*d**9 + 12*a**2*b**8*c**2*d**8 - 8*a*
b**9*c**3*d**7 + 2*b**10*c**4*d**6) + x**3*(4*a**5*b**5*d**10 - 12*a**4*b**6*c*d**9 + 8*a**3*b**7*c**2*d**8 +
8*a**2*b**8*c**3*d**7 - 12*a*b**9*c**4*d**6 + 4*b**10*c**5*d**5) + x**2*(2*a**6*b**4*d**10 - 18*a**4*b**6*c**2
*d**8 + 32*a**3*b**7*c**3*d**7 - 18*a**2*b**8*c**4*d**6 + 2*b**10*c**6*d**4) + x*(4*a**6*b**4*c*d**9 - 12*a**5
*b**5*c**2*d**8 + 8*a**4*b**6*c**3*d**7 + 8*a**3*b**7*c**4*d**6 - 12*a**2*b**8*c**5*d**5 + 4*a*b**9*c**6*d**4)
) + x/(b**3*d**3)
________________________________________________________________________________________
Giac [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: NotImplementedError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate(x^6/(b*x+a)^3/(d*x+c)^3,x, algorithm="giac")
[Out]
Exception raised: NotImplementedError