Integrand size = 19, antiderivative size = 105 \[ \int (c x)^m \left (a x^q+b x^r\right )^3 \, dx=\frac {a^3 x^{1+3 q} (c x)^m}{1+m+3 q}+\frac {3 a^2 b x^{1+2 q+r} (c x)^m}{1+m+2 q+r}+\frac {3 a b^2 x^{1+q+2 r} (c x)^m}{1+m+q+2 r}+\frac {b^3 x^{1+3 r} (c x)^m}{1+m+3 r} \] Output:
a^3*x^(1+3*q)*(c*x)^m/(1+m+3*q)+3*a^2*b*x^(1+2*q+r)*(c*x)^m/(1+m+2*q+r)+3* a*b^2*x^(1+q+2*r)*(c*x)^m/(1+m+q+2*r)+b^3*x^(1+3*r)*(c*x)^m/(1+m+3*r)
Time = 0.10 (sec) , antiderivative size = 86, normalized size of antiderivative = 0.82 \[ \int (c x)^m \left (a x^q+b x^r\right )^3 \, dx=x (c x)^m \left (\frac {a^3 x^{3 q}}{1+m+3 q}+\frac {b^3 x^{3 r}}{1+m+3 r}+\frac {3 a^2 b x^{2 q+r}}{1+m+2 q+r}+\frac {3 a b^2 x^{q+2 r}}{1+m+q+2 r}\right ) \] Input:
Integrate[(c*x)^m*(a*x^q + b*x^r)^3,x]
Output:
x*(c*x)^m*((a^3*x^(3*q))/(1 + m + 3*q) + (b^3*x^(3*r))/(1 + m + 3*r) + (3* a^2*b*x^(2*q + r))/(1 + m + 2*q + r) + (3*a*b^2*x^(q + 2*r))/(1 + m + q + 2*r))
Time = 0.45 (sec) , antiderivative size = 100, normalized size of antiderivative = 0.95, number of steps used = 5, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.211, Rules used = {1939, 10, 802, 2009}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
\(\displaystyle \int (c x)^m \left (a x^q+b x^r\right )^3 \, dx\) |
\(\Big \downarrow \) 1939 |
\(\displaystyle x^{-m} (c x)^m \int x^m \left (a x^q+b x^r\right )^3dx\) |
\(\Big \downarrow \) 10 |
\(\displaystyle x^{-m} (c x)^m \int x^{m+3 r} \left (a x^{q-r}+b\right )^3dx\) |
\(\Big \downarrow \) 802 |
\(\displaystyle x^{-m} (c x)^m \int \left (a^3 x^{m+3 q}+3 a^2 b x^{m+2 q+r}+3 a b^2 x^{m+q+2 r}+b^3 x^{m+3 r}\right )dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle x^{-m} (c x)^m \left (\frac {a^3 x^{m+3 q+1}}{m+3 q+1}+\frac {3 a^2 b x^{m+2 q+r+1}}{m+2 q+r+1}+\frac {3 a b^2 x^{m+q+2 r+1}}{m+q+2 r+1}+\frac {b^3 x^{m+3 r+1}}{m+3 r+1}\right )\) |
Input:
Int[(c*x)^m*(a*x^q + b*x^r)^3,x]
Output:
((c*x)^m*((a^3*x^(1 + m + 3*q))/(1 + m + 3*q) + (3*a^2*b*x^(1 + m + 2*q + r))/(1 + m + 2*q + r) + (3*a*b^2*x^(1 + m + q + 2*r))/(1 + m + q + 2*r) + (b^3*x^(1 + m + 3*r))/(1 + m + 3*r)))/x^m
Int[(u_.)*((e_.)*(x_))^(m_.)*((a_.)*(x_)^(r_.) + (b_.)*(x_)^(s_.))^(p_.), x _Symbol] :> Simp[1/e^(p*r) Int[u*(e*x)^(m + p*r)*(a + b*x^(s - r))^p, x], x] /; FreeQ[{a, b, e, m, r, s}, x] && IntegerQ[p] && (IntegerQ[p*r] || GtQ [e, 0]) && PosQ[s - r]
Int[((c_.)*(x_))^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_.), x_Symbol] :> Int[Exp andIntegrand[(c*x)^m*(a + b*x^n)^p, x], x] /; FreeQ[{a, b, c, m, n}, x] && IGtQ[p, 0]
Int[(u_)^(m_.)*((a_.)*(v_)^(j_.) + (b_.)*(v_)^(n_.))^(p_.), x_Symbol] :> Si mp[u^m/(Coefficient[v, x, 1]*v^m) Subst[Int[x^m*(a*x^j + b*x^n)^p, x], x, v], x] /; FreeQ[{a, b, j, m, n, p}, x] && LinearPairQ[u, v, x]
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 1.96 (sec) , antiderivative size = 1162, normalized size of antiderivative = 11.07
method | result | size |
risch | \(\text {Expression too large to display}\) | \(1162\) |
parallelrisch | \(\text {Expression too large to display}\) | \(1559\) |
orering | \(\text {Expression too large to display}\) | \(1618\) |
Input:
int((c*x)^m*(a*x^q+b*x^r)^3,x,method=_RETURNVERBOSE)
Output:
x*(54*a^2*b*m*q*r*(x^q)^2*x^r+12*a*b^2*x^q*(x^r)^2*r+54*a*b^2*q*r*x^q*(x^r )^2+27*a*b^2*q*r^2*x^q*(x^r)^2+9*a^2*b*m*q^2*(x^q)^2*x^r+18*a^2*b*m*r^2*(x ^q)^2*x^r+54*a^2*b*q*r*(x^q)^2*x^r+18*a*b^2*m*q^2*x^q*(x^r)^2+24*a^2*b*m*q *(x^q)^2*x^r+12*a*b^2*m^2*r*x^q*(x^r)^2+54*a*b^2*m*q*r*x^q*(x^r)^2+9*a*b^2 *m*r^2*x^q*(x^r)^2+12*a^2*b*m^2*q*(x^q)^2*x^r+9*a*b^2*r^2*x^q*(x^r)^2+9*m* a^2*b*(x^q)^2*x^r+12*a^2*b*(x^q)^2*x^r*q+15*a^2*b*(x^q)^2*r*x^r+9*m*a*b^2* x^q*(x^r)^2+15*a*b^2*q*x^q*(x^r)^2+b^3*m^3*(x^r)^3+3*(x^r)^2*x^q*a*b^2+15* a^3*q*r^2*(x^q)^3+6*b^3*m^2*q*(x^r)^3+3*b^3*m^2*r*(x^r)^3+11*b^3*m*q^2*(x^ r)^3+2*b^3*m*r^2*(x^r)^3+15*b^3*q^2*r*(x^r)^3+6*b^3*q*r^2*(x^r)^3+6*a^3*m* q*(x^q)^3+12*a^3*m*r*(x^q)^3+14*a^3*q*r*(x^q)^3+12*b^3*m*q*(x^r)^3+6*b^3*m *r*(x^r)^3+14*b^3*q*r*(x^r)^3+3*a^3*m^2*q*(x^q)^3+6*a^3*m^2*r*(x^q)^3+30*a *b^2*m*q*x^q*(x^r)^2+54*a*b^2*q^2*r*x^q*(x^r)^2+2*b^3*r^2*(x^r)^3+15*a*b^2 *m^2*q*x^q*(x^r)^2+24*a*b^2*m*r*x^q*(x^r)^2+30*a^2*b*m*r*(x^q)^2*x^r+54*a^ 2*b*q*r^2*(x^q)^2*x^r+27*a^2*b*q^2*r*(x^q)^2*x^r+15*a^2*b*m^2*r*(x^q)^2*x^ r+2*a^3*m*q^2*(x^q)^3+11*a^3*m*r^2*(x^q)^3+6*a^3*q^2*r*(x^q)^3+3*m*a^3*(x^ q)^3+3*a^3*(x^q)^3*q+3*a^2*b*m^3*(x^q)^2*x^r+3*a*b^2*m^3*x^q*(x^r)^2+14*b^ 3*m*q*r*(x^r)^3+9*a^2*b*m^2*(x^q)^2*x^r+9*a^2*b*q^2*(x^q)^2*x^r+18*a^2*b*r ^2*(x^q)^2*x^r+9*a*b^2*m^2*x^q*(x^r)^2+18*a*b^2*q^2*x^q*(x^r)^2+14*a^3*m*q *r*(x^q)^3+3*a^3*m^2*(x^q)^3+2*a^3*q^2*(x^q)^3+11*a^3*r^2*(x^q)^3+3*b^3*m^ 2*(x^r)^3+(x^q)^3*a^3+3*x^r*(x^q)^2*a^2*b+(x^r)^3*b^3+6*a^3*r*(x^q)^3+1...
Leaf count of result is larger than twice the leaf count of optimal. 763 vs. \(2 (105) = 210\).
Time = 0.11 (sec) , antiderivative size = 763, normalized size of antiderivative = 7.27 \[ \int (c x)^m \left (a x^q+b x^r\right )^3 \, dx =\text {Too large to display} \] Input:
integrate((c*x)^m*(a*x^q+b*x^r)^3,x, algorithm="fricas")
Output:
(3*(a*b^2*m^3 + 3*a*b^2*m^2 + 3*a*b^2*m + a*b^2 + 6*(a*b^2*m + a*b^2)*q^2 + 3*(a*b^2*m + 3*a*b^2*q + a*b^2)*r^2 + 5*(a*b^2*m^2 + 2*a*b^2*m + a*b^2)* q + 2*(2*a*b^2*m^2 + 9*a*b^2*q^2 + 4*a*b^2*m + 2*a*b^2 + 9*(a*b^2*m + a*b^ 2)*q)*r)*x*x^q*x^(2*r)*e^(m*log(c) + m*log(x)) + 3*(a^2*b*m^3 + 3*a^2*b*m^ 2 + 3*a^2*b*m + a^2*b + 3*(a^2*b*m + a^2*b)*q^2 + 6*(a^2*b*m + 3*a^2*b*q + a^2*b)*r^2 + 4*(a^2*b*m^2 + 2*a^2*b*m + a^2*b)*q + (5*a^2*b*m^2 + 9*a^2*b *q^2 + 10*a^2*b*m + 5*a^2*b + 18*(a^2*b*m + a^2*b)*q)*r)*x*x^(2*q)*x^r*e^( m*log(c) + m*log(x)) + (a^3*m^3 + 6*a^3*r^3 + 3*a^3*m^2 + 3*a^3*m + a^3 + 2*(a^3*m + a^3)*q^2 + (11*a^3*m + 15*a^3*q + 11*a^3)*r^2 + 3*(a^3*m^2 + 2* a^3*m + a^3)*q + 2*(3*a^3*m^2 + 3*a^3*q^2 + 6*a^3*m + 3*a^3 + 7*(a^3*m + a ^3)*q)*r)*x*x^(3*q)*e^(m*log(c) + m*log(x)) + (b^3*m^3 + 6*b^3*q^3 + 3*b^3 *m^2 + 3*b^3*m + b^3 + 11*(b^3*m + b^3)*q^2 + 2*(b^3*m + 3*b^3*q + b^3)*r^ 2 + 6*(b^3*m^2 + 2*b^3*m + b^3)*q + (3*b^3*m^2 + 15*b^3*q^2 + 6*b^3*m + 3* b^3 + 14*(b^3*m + b^3)*q)*r)*x*x^(3*r)*e^(m*log(c) + m*log(x)))/(m^4 + 6*( m + 1)*q^3 + 6*(m + 3*q + 1)*r^3 + 4*m^3 + 11*(m^2 + 2*m + 1)*q^2 + (11*m^ 2 + 48*(m + 1)*q + 45*q^2 + 22*m + 11)*r^2 + 6*m^2 + 6*(m^3 + 3*m^2 + 3*m + 1)*q + 2*(3*m^3 + 24*(m + 1)*q^2 + 9*q^3 + 9*m^2 + 16*(m^2 + 2*m + 1)*q + 9*m + 3)*r + 4*m + 1)
Leaf count of result is larger than twice the leaf count of optimal. 17454 vs. \(2 (100) = 200\).
Time = 15.87 (sec) , antiderivative size = 17454, normalized size of antiderivative = 166.23 \[ \int (c x)^m \left (a x^q+b x^r\right )^3 \, dx=\text {Too large to display} \] Input:
integrate((c*x)**m*(a*x**q+b*x**r)**3,x)
Output:
Piecewise((a**3*x*x**(3*r)*(c*x)**(-3*r - 1)*log(x) + 3*a**2*b*x*x**(3*r)* (c*x)**(-3*r - 1)*log(x) + 3*a*b**2*x*x**(3*r)*(c*x)**(-3*r - 1)*log(x) + b**3*x*x**(3*r)*(c*x)**(-3*r - 1)*log(x), Eq(q, r) & Eq(m, -3*r - 1)), (a* *3*x*x**(3*q)*(c*x)**(-3*q - 1)*log(x) + 3*a**2*b*Piecewise((x*x**(2*q)*x* *r*(c*x)**(-3*q - 1)/(-q + r), Ne(q - r, 0)), (x*x**(2*q)*x**r*(c*x)**(-3* q - 1)*log(x), True)) + 3*a*b**2*Piecewise((x*x**q*x**(2*r)*(c*x)**(-3*q - 1)/(-2*q + 2*r), Ne(2*q - 2*r, 0)), (x*x**q*x**(2*r)*(c*x)**(-3*q - 1)*lo g(x), True)) + b**3*Piecewise((x*x**(3*r)*(c*x)**(-3*q - 1)/(-3*q + 3*r), Ne(3*q - 3*r, 0)), (x*x**(3*r)*(c*x)**(-3*q - 1)*log(x), True)), Eq(m, -3* q - 1)), (a**3*Piecewise((x*x**(3*q)*(c*x)**(-3*r - 1)/(3*q - 3*r), Ne(3*q - 3*r, 0)), (x*x**(3*q)*(c*x)**(-3*r - 1)*log(x), True)) + 3*a**2*b*Piece wise((x*x**(2*q)*x**r*(c*x)**(-3*r - 1)/(2*q - 2*r), Ne(2*q - 2*r, 0)), (x *x**(2*q)*x**r*(c*x)**(-3*r - 1)*log(x), True)) + 3*a*b**2*Piecewise((x*x* *q*x**(2*r)*(c*x)**(-3*r - 1)/(q - r), Ne(q - r, 0)), (x*x**q*x**(2*r)*(c* x)**(-3*r - 1)*log(x), True)) + b**3*x*x**(3*r)*(c*x)**(-3*r - 1)*log(x), Eq(m, -3*r - 1)), (a**3*Piecewise((x*x**(3*q)*(c*x)**(-2*q - r - 1)/(q - r ), Ne(q - r, 0)), (x*x**(3*q)*(c*x)**(-2*q - r - 1)*log(x), True)) + 3*a** 2*b*x*x**(2*q)*x**r*(c*x)**(-2*q - r - 1)*log(x) + 3*a*b**2*Piecewise((x*x **q*x**(2*r)*(c*x)**(-2*q - r - 1)/(-q + r), Ne(q - r, 0)), (x*x**q*x**(2* r)*(c*x)**(-2*q - r - 1)*log(x), True)) + b**3*Piecewise((x*x**(3*r)*(c...
Time = 0.05 (sec) , antiderivative size = 123, normalized size of antiderivative = 1.17 \[ \int (c x)^m \left (a x^q+b x^r\right )^3 \, dx=\frac {a^{3} c^{m} x e^{\left (m \log \left (x\right ) + 3 \, q \log \left (x\right )\right )}}{m + 3 \, q + 1} + \frac {3 \, a^{2} b c^{m} x e^{\left (m \log \left (x\right ) + 2 \, q \log \left (x\right ) + r \log \left (x\right )\right )}}{m + 2 \, q + r + 1} + \frac {3 \, a b^{2} c^{m} x e^{\left (m \log \left (x\right ) + q \log \left (x\right ) + 2 \, r \log \left (x\right )\right )}}{m + q + 2 \, r + 1} + \frac {b^{3} c^{m} x e^{\left (m \log \left (x\right ) + 3 \, r \log \left (x\right )\right )}}{m + 3 \, r + 1} \] Input:
integrate((c*x)^m*(a*x^q+b*x^r)^3,x, algorithm="maxima")
Output:
a^3*c^m*x*e^(m*log(x) + 3*q*log(x))/(m + 3*q + 1) + 3*a^2*b*c^m*x*e^(m*log (x) + 2*q*log(x) + r*log(x))/(m + 2*q + r + 1) + 3*a*b^2*c^m*x*e^(m*log(x) + q*log(x) + 2*r*log(x))/(m + q + 2*r + 1) + b^3*c^m*x*e^(m*log(x) + 3*r* log(x))/(m + 3*r + 1)
Leaf count of result is larger than twice the leaf count of optimal. 4599 vs. \(2 (105) = 210\).
Time = 0.30 (sec) , antiderivative size = 4599, normalized size of antiderivative = 43.80 \[ \int (c x)^m \left (a x^q+b x^r\right )^3 \, dx=\text {Too large to display} \] Input:
integrate((c*x)^m*(a*x^q+b*x^r)^3,x, algorithm="giac")
Output:
(3*a*b^2*m^3*x*x^q*x^(2*r)*e^(m*log(c) + m*log(x)) + 15*a*b^2*m^2*q*x*x^q* x^(2*r)*e^(m*log(c) + m*log(x)) + 18*a*b^2*m*q^2*x*x^q*x^(2*r)*e^(m*log(c) + m*log(x)) + 12*a*b^2*m^2*r*x*x^q*x^(2*r)*e^(m*log(c) + m*log(x)) + 54*a *b^2*m*q*r*x*x^q*x^(2*r)*e^(m*log(c) + m*log(x)) + 54*a*b^2*q^2*r*x*x^q*x^ (2*r)*e^(m*log(c) + m*log(x)) + 9*a*b^2*m*r^2*x*x^q*x^(2*r)*e^(m*log(c) + m*log(x)) + 27*a*b^2*q*r^2*x*x^q*x^(2*r)*e^(m*log(c) + m*log(x)) + 3*a^2*b *m^3*x*x^(2*q)*x^r*e^(m*log(c) + m*log(x)) + 12*a^2*b*m^2*q*x*x^(2*q)*x^r* e^(m*log(c) + m*log(x)) + 9*a^2*b*m*q^2*x*x^(2*q)*x^r*e^(m*log(c) + m*log( x)) + 15*a^2*b*m^2*r*x*x^(2*q)*x^r*e^(m*log(c) + m*log(x)) + 54*a^2*b*m*q* r*x*x^(2*q)*x^r*e^(m*log(c) + m*log(x)) + 27*a^2*b*q^2*r*x*x^(2*q)*x^r*e^( m*log(c) + m*log(x)) + 18*a^2*b*m*r^2*x*x^(2*q)*x^r*e^(m*log(c) + m*log(x) ) + 54*a^2*b*q*r^2*x*x^(2*q)*x^r*e^(m*log(c) + m*log(x)) + 3*a*b^2*m^3*x*x ^q*x^r*e^(m*log(c) + m*log(x)) + 15*a*b^2*m^2*q*x*x^q*x^r*e^(m*log(c) + m* log(x)) + 18*a*b^2*m*q^2*x*x^q*x^r*e^(m*log(c) + m*log(x)) + 12*a*b^2*m^2* r*x*x^q*x^r*e^(m*log(c) + m*log(x)) + 54*a*b^2*m*q*r*x*x^q*x^r*e^(m*log(c) + m*log(x)) + 54*a*b^2*q^2*r*x*x^q*x^r*e^(m*log(c) + m*log(x)) + 9*a*b^2* m*r^2*x*x^q*x^r*e^(m*log(c) + m*log(x)) + 27*a*b^2*q*r^2*x*x^q*x^r*e^(m*lo g(c) + m*log(x)) + a^3*m^3*x*x^(3*q)*e^(m*log(c) + m*log(x)) + 3*a^3*m^2*q *x*x^(3*q)*e^(m*log(c) + m*log(x)) + 2*a^3*m*q^2*x*x^(3*q)*e^(m*log(c) + m *log(x)) + 6*a^3*m^2*r*x*x^(3*q)*e^(m*log(c) + m*log(x)) + 14*a^3*m*q*r...
Time = 9.18 (sec) , antiderivative size = 163, normalized size of antiderivative = 1.55 \[ \int (c x)^m \left (a x^q+b x^r\right )^3 \, dx={\left (c\,x\right )}^m\,\left (\frac {a^3\,x^{3\,q+1}}{m+3\,q+1}+\frac {b^3\,x^{3\,r+1}}{m+3\,r+1}+\frac {3\,a\,b^2\,x^{q+2\,r+1}\,\left (m+2\,q+r+1\right )}{m^2+3\,m\,q+3\,m\,r+2\,m+2\,q^2+5\,q\,r+3\,q+2\,r^2+3\,r+1}+\frac {3\,a^2\,b\,x^{2\,q+r+1}\,\left (m+q+2\,r+1\right )}{m^2+3\,m\,q+3\,m\,r+2\,m+2\,q^2+5\,q\,r+3\,q+2\,r^2+3\,r+1}\right ) \] Input:
int((c*x)^m*(a*x^q + b*x^r)^3,x)
Output:
(c*x)^m*((a^3*x^(3*q + 1))/(m + 3*q + 1) + (b^3*x^(3*r + 1))/(m + 3*r + 1) + (3*a*b^2*x^(q + 2*r + 1)*(m + 2*q + r + 1))/(2*m + 3*q + 3*r + 3*m*q + 3*m*r + 5*q*r + m^2 + 2*q^2 + 2*r^2 + 1) + (3*a^2*b*x^(2*q + r + 1)*(m + q + 2*r + 1))/(2*m + 3*q + 3*r + 3*m*q + 3*m*r + 5*q*r + m^2 + 2*q^2 + 2*r^ 2 + 1))
Time = 0.22 (sec) , antiderivative size = 1231, normalized size of antiderivative = 11.72 \[ \int (c x)^m \left (a x^q+b x^r\right )^3 \, dx =\text {Too large to display} \] Input:
int((c*x)^m*(a*x^q+b*x^r)^3,x)
Output:
(x**m*c**m*x*(x**(3*q)*a**3*m**3 + 3*x**(3*q)*a**3*m**2*q + 6*x**(3*q)*a** 3*m**2*r + 3*x**(3*q)*a**3*m**2 + 2*x**(3*q)*a**3*m*q**2 + 14*x**(3*q)*a** 3*m*q*r + 6*x**(3*q)*a**3*m*q + 11*x**(3*q)*a**3*m*r**2 + 12*x**(3*q)*a**3 *m*r + 3*x**(3*q)*a**3*m + 6*x**(3*q)*a**3*q**2*r + 2*x**(3*q)*a**3*q**2 + 15*x**(3*q)*a**3*q*r**2 + 14*x**(3*q)*a**3*q*r + 3*x**(3*q)*a**3*q + 6*x* *(3*q)*a**3*r**3 + 11*x**(3*q)*a**3*r**2 + 6*x**(3*q)*a**3*r + x**(3*q)*a* *3 + 3*x**(2*q + r)*a**2*b*m**3 + 12*x**(2*q + r)*a**2*b*m**2*q + 15*x**(2 *q + r)*a**2*b*m**2*r + 9*x**(2*q + r)*a**2*b*m**2 + 9*x**(2*q + r)*a**2*b *m*q**2 + 54*x**(2*q + r)*a**2*b*m*q*r + 24*x**(2*q + r)*a**2*b*m*q + 18*x **(2*q + r)*a**2*b*m*r**2 + 30*x**(2*q + r)*a**2*b*m*r + 9*x**(2*q + r)*a* *2*b*m + 27*x**(2*q + r)*a**2*b*q**2*r + 9*x**(2*q + r)*a**2*b*q**2 + 54*x **(2*q + r)*a**2*b*q*r**2 + 54*x**(2*q + r)*a**2*b*q*r + 12*x**(2*q + r)*a **2*b*q + 18*x**(2*q + r)*a**2*b*r**2 + 15*x**(2*q + r)*a**2*b*r + 3*x**(2 *q + r)*a**2*b + 3*x**(q + 2*r)*a*b**2*m**3 + 15*x**(q + 2*r)*a*b**2*m**2* q + 12*x**(q + 2*r)*a*b**2*m**2*r + 9*x**(q + 2*r)*a*b**2*m**2 + 18*x**(q + 2*r)*a*b**2*m*q**2 + 54*x**(q + 2*r)*a*b**2*m*q*r + 30*x**(q + 2*r)*a*b* *2*m*q + 9*x**(q + 2*r)*a*b**2*m*r**2 + 24*x**(q + 2*r)*a*b**2*m*r + 9*x** (q + 2*r)*a*b**2*m + 54*x**(q + 2*r)*a*b**2*q**2*r + 18*x**(q + 2*r)*a*b** 2*q**2 + 27*x**(q + 2*r)*a*b**2*q*r**2 + 54*x**(q + 2*r)*a*b**2*q*r + 15*x **(q + 2*r)*a*b**2*q + 9*x**(q + 2*r)*a*b**2*r**2 + 12*x**(q + 2*r)*a*b...