1,-1,0,0,0.000000," ","integrate((b*x+a)**3*(D*x**3+C*x**2+B*x+A)/(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2,1,1510,0,157.826774," ","integrate((b*x+a)**2*(D*x**3+C*x**2+B*x+A)/(d*x+c)**(1/2),x)","\begin{cases} \frac{- \frac{2 A a^{2} c}{\sqrt{c + d x}} - 2 A a^{2} \left(- \frac{c}{\sqrt{c + d x}} - \sqrt{c + d x}\right) - \frac{4 A a b c \left(- \frac{c}{\sqrt{c + d x}} - \sqrt{c + d x}\right)}{d} - \frac{4 A a b \left(\frac{c^{2}}{\sqrt{c + d x}} + 2 c \sqrt{c + d x} - \frac{\left(c + d x\right)^{\frac{3}{2}}}{3}\right)}{d} - \frac{2 A b^{2} c \left(\frac{c^{2}}{\sqrt{c + d x}} + 2 c \sqrt{c + d x} - \frac{\left(c + d x\right)^{\frac{3}{2}}}{3}\right)}{d^{2}} - \frac{2 A b^{2} \left(- \frac{c^{3}}{\sqrt{c + d x}} - 3 c^{2} \sqrt{c + d x} + c \left(c + d x\right)^{\frac{3}{2}} - \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d^{2}} - \frac{2 B a^{2} c \left(- \frac{c}{\sqrt{c + d x}} - \sqrt{c + d x}\right)}{d} - \frac{2 B a^{2} \left(\frac{c^{2}}{\sqrt{c + d x}} + 2 c \sqrt{c + d x} - \frac{\left(c + d x\right)^{\frac{3}{2}}}{3}\right)}{d} - \frac{4 B a b c \left(\frac{c^{2}}{\sqrt{c + d x}} + 2 c \sqrt{c + d x} - \frac{\left(c + d x\right)^{\frac{3}{2}}}{3}\right)}{d^{2}} - \frac{4 B a b \left(- \frac{c^{3}}{\sqrt{c + d x}} - 3 c^{2} \sqrt{c + d x} + c \left(c + d x\right)^{\frac{3}{2}} - \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d^{2}} - \frac{2 B b^{2} c \left(- \frac{c^{3}}{\sqrt{c + d x}} - 3 c^{2} \sqrt{c + d x} + c \left(c + d x\right)^{\frac{3}{2}} - \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d^{3}} - \frac{2 B b^{2} \left(\frac{c^{4}}{\sqrt{c + d x}} + 4 c^{3} \sqrt{c + d x} - 2 c^{2} \left(c + d x\right)^{\frac{3}{2}} + \frac{4 c \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{3}} - \frac{2 C a^{2} c \left(\frac{c^{2}}{\sqrt{c + d x}} + 2 c \sqrt{c + d x} - \frac{\left(c + d x\right)^{\frac{3}{2}}}{3}\right)}{d^{2}} - \frac{2 C a^{2} \left(- \frac{c^{3}}{\sqrt{c + d x}} - 3 c^{2} \sqrt{c + d x} + c \left(c + d x\right)^{\frac{3}{2}} - \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d^{2}} - \frac{4 C a b c \left(- \frac{c^{3}}{\sqrt{c + d x}} - 3 c^{2} \sqrt{c + d x} + c \left(c + d x\right)^{\frac{3}{2}} - \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d^{3}} - \frac{4 C a b \left(\frac{c^{4}}{\sqrt{c + d x}} + 4 c^{3} \sqrt{c + d x} - 2 c^{2} \left(c + d x\right)^{\frac{3}{2}} + \frac{4 c \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{3}} - \frac{2 C b^{2} c \left(\frac{c^{4}}{\sqrt{c + d x}} + 4 c^{3} \sqrt{c + d x} - 2 c^{2} \left(c + d x\right)^{\frac{3}{2}} + \frac{4 c \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{4}} - \frac{2 C b^{2} \left(- \frac{c^{5}}{\sqrt{c + d x}} - 5 c^{4} \sqrt{c + d x} + \frac{10 c^{3} \left(c + d x\right)^{\frac{3}{2}}}{3} - 2 c^{2} \left(c + d x\right)^{\frac{5}{2}} + \frac{5 c \left(c + d x\right)^{\frac{7}{2}}}{7} - \frac{\left(c + d x\right)^{\frac{9}{2}}}{9}\right)}{d^{4}} - \frac{2 D a^{2} c \left(- \frac{c^{3}}{\sqrt{c + d x}} - 3 c^{2} \sqrt{c + d x} + c \left(c + d x\right)^{\frac{3}{2}} - \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d^{3}} - \frac{2 D a^{2} \left(\frac{c^{4}}{\sqrt{c + d x}} + 4 c^{3} \sqrt{c + d x} - 2 c^{2} \left(c + d x\right)^{\frac{3}{2}} + \frac{4 c \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{3}} - \frac{4 D a b c \left(\frac{c^{4}}{\sqrt{c + d x}} + 4 c^{3} \sqrt{c + d x} - 2 c^{2} \left(c + d x\right)^{\frac{3}{2}} + \frac{4 c \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{4}} - \frac{4 D a b \left(- \frac{c^{5}}{\sqrt{c + d x}} - 5 c^{4} \sqrt{c + d x} + \frac{10 c^{3} \left(c + d x\right)^{\frac{3}{2}}}{3} - 2 c^{2} \left(c + d x\right)^{\frac{5}{2}} + \frac{5 c \left(c + d x\right)^{\frac{7}{2}}}{7} - \frac{\left(c + d x\right)^{\frac{9}{2}}}{9}\right)}{d^{4}} - \frac{2 D b^{2} c \left(- \frac{c^{5}}{\sqrt{c + d x}} - 5 c^{4} \sqrt{c + d x} + \frac{10 c^{3} \left(c + d x\right)^{\frac{3}{2}}}{3} - 2 c^{2} \left(c + d x\right)^{\frac{5}{2}} + \frac{5 c \left(c + d x\right)^{\frac{7}{2}}}{7} - \frac{\left(c + d x\right)^{\frac{9}{2}}}{9}\right)}{d^{5}} - \frac{2 D b^{2} \left(\frac{c^{6}}{\sqrt{c + d x}} + 6 c^{5} \sqrt{c + d x} - 5 c^{4} \left(c + d x\right)^{\frac{3}{2}} + 4 c^{3} \left(c + d x\right)^{\frac{5}{2}} - \frac{15 c^{2} \left(c + d x\right)^{\frac{7}{2}}}{7} + \frac{2 c \left(c + d x\right)^{\frac{9}{2}}}{3} - \frac{\left(c + d x\right)^{\frac{11}{2}}}{11}\right)}{d^{5}}}{d} & \text{for}\: d \neq 0 \\\frac{A a^{2} x + \frac{D b^{2} x^{6}}{6} + \frac{x^{5} \left(C b^{2} + 2 D a b\right)}{5} + \frac{x^{4} \left(B b^{2} + 2 C a b + D a^{2}\right)}{4} + \frac{x^{3} \left(A b^{2} + 2 B a b + C a^{2}\right)}{3} + \frac{x^{2} \left(2 A a b + B a^{2}\right)}{2}}{\sqrt{c}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*A*a**2*c/sqrt(c + d*x) - 2*A*a**2*(-c/sqrt(c + d*x) - sqrt(c + d*x)) - 4*A*a*b*c*(-c/sqrt(c + d*x) - sqrt(c + d*x))/d - 4*A*a*b*(c**2/sqrt(c + d*x) + 2*c*sqrt(c + d*x) - (c + d*x)**(3/2)/3)/d - 2*A*b**2*c*(c**2/sqrt(c + d*x) + 2*c*sqrt(c + d*x) - (c + d*x)**(3/2)/3)/d**2 - 2*A*b**2*(-c**3/sqrt(c + d*x) - 3*c**2*sqrt(c + d*x) + c*(c + d*x)**(3/2) - (c + d*x)**(5/2)/5)/d**2 - 2*B*a**2*c*(-c/sqrt(c + d*x) - sqrt(c + d*x))/d - 2*B*a**2*(c**2/sqrt(c + d*x) + 2*c*sqrt(c + d*x) - (c + d*x)**(3/2)/3)/d - 4*B*a*b*c*(c**2/sqrt(c + d*x) + 2*c*sqrt(c + d*x) - (c + d*x)**(3/2)/3)/d**2 - 4*B*a*b*(-c**3/sqrt(c + d*x) - 3*c**2*sqrt(c + d*x) + c*(c + d*x)**(3/2) - (c + d*x)**(5/2)/5)/d**2 - 2*B*b**2*c*(-c**3/sqrt(c + d*x) - 3*c**2*sqrt(c + d*x) + c*(c + d*x)**(3/2) - (c + d*x)**(5/2)/5)/d**3 - 2*B*b**2*(c**4/sqrt(c + d*x) + 4*c**3*sqrt(c + d*x) - 2*c**2*(c + d*x)**(3/2) + 4*c*(c + d*x)**(5/2)/5 - (c + d*x)**(7/2)/7)/d**3 - 2*C*a**2*c*(c**2/sqrt(c + d*x) + 2*c*sqrt(c + d*x) - (c + d*x)**(3/2)/3)/d**2 - 2*C*a**2*(-c**3/sqrt(c + d*x) - 3*c**2*sqrt(c + d*x) + c*(c + d*x)**(3/2) - (c + d*x)**(5/2)/5)/d**2 - 4*C*a*b*c*(-c**3/sqrt(c + d*x) - 3*c**2*sqrt(c + d*x) + c*(c + d*x)**(3/2) - (c + d*x)**(5/2)/5)/d**3 - 4*C*a*b*(c**4/sqrt(c + d*x) + 4*c**3*sqrt(c + d*x) - 2*c**2*(c + d*x)**(3/2) + 4*c*(c + d*x)**(5/2)/5 - (c + d*x)**(7/2)/7)/d**3 - 2*C*b**2*c*(c**4/sqrt(c + d*x) + 4*c**3*sqrt(c + d*x) - 2*c**2*(c + d*x)**(3/2) + 4*c*(c + d*x)**(5/2)/5 - (c + d*x)**(7/2)/7)/d**4 - 2*C*b**2*(-c**5/sqrt(c + d*x) - 5*c**4*sqrt(c + d*x) + 10*c**3*(c + d*x)**(3/2)/3 - 2*c**2*(c + d*x)**(5/2) + 5*c*(c + d*x)**(7/2)/7 - (c + d*x)**(9/2)/9)/d**4 - 2*D*a**2*c*(-c**3/sqrt(c + d*x) - 3*c**2*sqrt(c + d*x) + c*(c + d*x)**(3/2) - (c + d*x)**(5/2)/5)/d**3 - 2*D*a**2*(c**4/sqrt(c + d*x) + 4*c**3*sqrt(c + d*x) - 2*c**2*(c + d*x)**(3/2) + 4*c*(c + d*x)**(5/2)/5 - (c + d*x)**(7/2)/7)/d**3 - 4*D*a*b*c*(c**4/sqrt(c + d*x) + 4*c**3*sqrt(c + d*x) - 2*c**2*(c + d*x)**(3/2) + 4*c*(c + d*x)**(5/2)/5 - (c + d*x)**(7/2)/7)/d**4 - 4*D*a*b*(-c**5/sqrt(c + d*x) - 5*c**4*sqrt(c + d*x) + 10*c**3*(c + d*x)**(3/2)/3 - 2*c**2*(c + d*x)**(5/2) + 5*c*(c + d*x)**(7/2)/7 - (c + d*x)**(9/2)/9)/d**4 - 2*D*b**2*c*(-c**5/sqrt(c + d*x) - 5*c**4*sqrt(c + d*x) + 10*c**3*(c + d*x)**(3/2)/3 - 2*c**2*(c + d*x)**(5/2) + 5*c*(c + d*x)**(7/2)/7 - (c + d*x)**(9/2)/9)/d**5 - 2*D*b**2*(c**6/sqrt(c + d*x) + 6*c**5*sqrt(c + d*x) - 5*c**4*(c + d*x)**(3/2) + 4*c**3*(c + d*x)**(5/2) - 15*c**2*(c + d*x)**(7/2)/7 + 2*c*(c + d*x)**(9/2)/3 - (c + d*x)**(11/2)/11)/d**5)/d, Ne(d, 0)), ((A*a**2*x + D*b**2*x**6/6 + x**5*(C*b**2 + 2*D*a*b)/5 + x**4*(B*b**2 + 2*C*a*b + D*a**2)/4 + x**3*(A*b**2 + 2*B*a*b + C*a**2)/3 + x**2*(2*A*a*b + B*a**2)/2)/sqrt(c), True))","A",0
3,1,848,0,87.368208," ","integrate((b*x+a)*(D*x**3+C*x**2+B*x+A)/(d*x+c)**(1/2),x)","\begin{cases} \frac{- \frac{2 A a c}{\sqrt{c + d x}} - 2 A a \left(- \frac{c}{\sqrt{c + d x}} - \sqrt{c + d x}\right) - \frac{2 A b c \left(- \frac{c}{\sqrt{c + d x}} - \sqrt{c + d x}\right)}{d} - \frac{2 A b \left(\frac{c^{2}}{\sqrt{c + d x}} + 2 c \sqrt{c + d x} - \frac{\left(c + d x\right)^{\frac{3}{2}}}{3}\right)}{d} - \frac{2 B a c \left(- \frac{c}{\sqrt{c + d x}} - \sqrt{c + d x}\right)}{d} - \frac{2 B a \left(\frac{c^{2}}{\sqrt{c + d x}} + 2 c \sqrt{c + d x} - \frac{\left(c + d x\right)^{\frac{3}{2}}}{3}\right)}{d} - \frac{2 B b c \left(\frac{c^{2}}{\sqrt{c + d x}} + 2 c \sqrt{c + d x} - \frac{\left(c + d x\right)^{\frac{3}{2}}}{3}\right)}{d^{2}} - \frac{2 B b \left(- \frac{c^{3}}{\sqrt{c + d x}} - 3 c^{2} \sqrt{c + d x} + c \left(c + d x\right)^{\frac{3}{2}} - \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d^{2}} - \frac{2 C a c \left(\frac{c^{2}}{\sqrt{c + d x}} + 2 c \sqrt{c + d x} - \frac{\left(c + d x\right)^{\frac{3}{2}}}{3}\right)}{d^{2}} - \frac{2 C a \left(- \frac{c^{3}}{\sqrt{c + d x}} - 3 c^{2} \sqrt{c + d x} + c \left(c + d x\right)^{\frac{3}{2}} - \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d^{2}} - \frac{2 C b c \left(- \frac{c^{3}}{\sqrt{c + d x}} - 3 c^{2} \sqrt{c + d x} + c \left(c + d x\right)^{\frac{3}{2}} - \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d^{3}} - \frac{2 C b \left(\frac{c^{4}}{\sqrt{c + d x}} + 4 c^{3} \sqrt{c + d x} - 2 c^{2} \left(c + d x\right)^{\frac{3}{2}} + \frac{4 c \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{3}} - \frac{2 D a c \left(- \frac{c^{3}}{\sqrt{c + d x}} - 3 c^{2} \sqrt{c + d x} + c \left(c + d x\right)^{\frac{3}{2}} - \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d^{3}} - \frac{2 D a \left(\frac{c^{4}}{\sqrt{c + d x}} + 4 c^{3} \sqrt{c + d x} - 2 c^{2} \left(c + d x\right)^{\frac{3}{2}} + \frac{4 c \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{3}} - \frac{2 D b c \left(\frac{c^{4}}{\sqrt{c + d x}} + 4 c^{3} \sqrt{c + d x} - 2 c^{2} \left(c + d x\right)^{\frac{3}{2}} + \frac{4 c \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{4}} - \frac{2 D b \left(- \frac{c^{5}}{\sqrt{c + d x}} - 5 c^{4} \sqrt{c + d x} + \frac{10 c^{3} \left(c + d x\right)^{\frac{3}{2}}}{3} - 2 c^{2} \left(c + d x\right)^{\frac{5}{2}} + \frac{5 c \left(c + d x\right)^{\frac{7}{2}}}{7} - \frac{\left(c + d x\right)^{\frac{9}{2}}}{9}\right)}{d^{4}}}{d} & \text{for}\: d \neq 0 \\\frac{A a x + \frac{D b x^{5}}{5} + \frac{x^{4} \left(C b + D a\right)}{4} + \frac{x^{3} \left(B b + C a\right)}{3} + \frac{x^{2} \left(A b + B a\right)}{2}}{\sqrt{c}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*A*a*c/sqrt(c + d*x) - 2*A*a*(-c/sqrt(c + d*x) - sqrt(c + d*x)) - 2*A*b*c*(-c/sqrt(c + d*x) - sqrt(c + d*x))/d - 2*A*b*(c**2/sqrt(c + d*x) + 2*c*sqrt(c + d*x) - (c + d*x)**(3/2)/3)/d - 2*B*a*c*(-c/sqrt(c + d*x) - sqrt(c + d*x))/d - 2*B*a*(c**2/sqrt(c + d*x) + 2*c*sqrt(c + d*x) - (c + d*x)**(3/2)/3)/d - 2*B*b*c*(c**2/sqrt(c + d*x) + 2*c*sqrt(c + d*x) - (c + d*x)**(3/2)/3)/d**2 - 2*B*b*(-c**3/sqrt(c + d*x) - 3*c**2*sqrt(c + d*x) + c*(c + d*x)**(3/2) - (c + d*x)**(5/2)/5)/d**2 - 2*C*a*c*(c**2/sqrt(c + d*x) + 2*c*sqrt(c + d*x) - (c + d*x)**(3/2)/3)/d**2 - 2*C*a*(-c**3/sqrt(c + d*x) - 3*c**2*sqrt(c + d*x) + c*(c + d*x)**(3/2) - (c + d*x)**(5/2)/5)/d**2 - 2*C*b*c*(-c**3/sqrt(c + d*x) - 3*c**2*sqrt(c + d*x) + c*(c + d*x)**(3/2) - (c + d*x)**(5/2)/5)/d**3 - 2*C*b*(c**4/sqrt(c + d*x) + 4*c**3*sqrt(c + d*x) - 2*c**2*(c + d*x)**(3/2) + 4*c*(c + d*x)**(5/2)/5 - (c + d*x)**(7/2)/7)/d**3 - 2*D*a*c*(-c**3/sqrt(c + d*x) - 3*c**2*sqrt(c + d*x) + c*(c + d*x)**(3/2) - (c + d*x)**(5/2)/5)/d**3 - 2*D*a*(c**4/sqrt(c + d*x) + 4*c**3*sqrt(c + d*x) - 2*c**2*(c + d*x)**(3/2) + 4*c*(c + d*x)**(5/2)/5 - (c + d*x)**(7/2)/7)/d**3 - 2*D*b*c*(c**4/sqrt(c + d*x) + 4*c**3*sqrt(c + d*x) - 2*c**2*(c + d*x)**(3/2) + 4*c*(c + d*x)**(5/2)/5 - (c + d*x)**(7/2)/7)/d**4 - 2*D*b*(-c**5/sqrt(c + d*x) - 5*c**4*sqrt(c + d*x) + 10*c**3*(c + d*x)**(3/2)/3 - 2*c**2*(c + d*x)**(5/2) + 5*c*(c + d*x)**(7/2)/7 - (c + d*x)**(9/2)/9)/d**4)/d, Ne(d, 0)), ((A*a*x + D*b*x**5/5 + x**4*(C*b + D*a)/4 + x**3*(B*b + C*a)/3 + x**2*(A*b + B*a)/2)/sqrt(c), True))","A",0
4,1,354,0,18.093981," ","integrate((D*x**3+C*x**2+B*x+A)/(d*x+c)**(1/2),x)","\begin{cases} \frac{- \frac{2 A c}{\sqrt{c + d x}} - 2 A \left(- \frac{c}{\sqrt{c + d x}} - \sqrt{c + d x}\right) - \frac{2 B c \left(- \frac{c}{\sqrt{c + d x}} - \sqrt{c + d x}\right)}{d} - \frac{2 B \left(\frac{c^{2}}{\sqrt{c + d x}} + 2 c \sqrt{c + d x} - \frac{\left(c + d x\right)^{\frac{3}{2}}}{3}\right)}{d} - \frac{2 C c \left(\frac{c^{2}}{\sqrt{c + d x}} + 2 c \sqrt{c + d x} - \frac{\left(c + d x\right)^{\frac{3}{2}}}{3}\right)}{d^{2}} - \frac{2 C \left(- \frac{c^{3}}{\sqrt{c + d x}} - 3 c^{2} \sqrt{c + d x} + c \left(c + d x\right)^{\frac{3}{2}} - \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d^{2}} - \frac{2 D c \left(- \frac{c^{3}}{\sqrt{c + d x}} - 3 c^{2} \sqrt{c + d x} + c \left(c + d x\right)^{\frac{3}{2}} - \frac{\left(c + d x\right)^{\frac{5}{2}}}{5}\right)}{d^{3}} - \frac{2 D \left(\frac{c^{4}}{\sqrt{c + d x}} + 4 c^{3} \sqrt{c + d x} - 2 c^{2} \left(c + d x\right)^{\frac{3}{2}} + \frac{4 c \left(c + d x\right)^{\frac{5}{2}}}{5} - \frac{\left(c + d x\right)^{\frac{7}{2}}}{7}\right)}{d^{3}}}{d} & \text{for}\: d \neq 0 \\\frac{A x + \frac{B x^{2}}{2} + \frac{C x^{3}}{3} + \frac{D x^{4}}{4}}{\sqrt{c}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2*A*c/sqrt(c + d*x) - 2*A*(-c/sqrt(c + d*x) - sqrt(c + d*x)) - 2*B*c*(-c/sqrt(c + d*x) - sqrt(c + d*x))/d - 2*B*(c**2/sqrt(c + d*x) + 2*c*sqrt(c + d*x) - (c + d*x)**(3/2)/3)/d - 2*C*c*(c**2/sqrt(c + d*x) + 2*c*sqrt(c + d*x) - (c + d*x)**(3/2)/3)/d**2 - 2*C*(-c**3/sqrt(c + d*x) - 3*c**2*sqrt(c + d*x) + c*(c + d*x)**(3/2) - (c + d*x)**(5/2)/5)/d**2 - 2*D*c*(-c**3/sqrt(c + d*x) - 3*c**2*sqrt(c + d*x) + c*(c + d*x)**(3/2) - (c + d*x)**(5/2)/5)/d**3 - 2*D*(c**4/sqrt(c + d*x) + 4*c**3*sqrt(c + d*x) - 2*c**2*(c + d*x)**(3/2) + 4*c*(c + d*x)**(5/2)/5 - (c + d*x)**(7/2)/7)/d**3)/d, Ne(d, 0)), ((A*x + B*x**2/2 + C*x**3/3 + D*x**4/4)/sqrt(c), True))","A",0
5,1,192,0,66.261566," ","integrate((D*x**3+C*x**2+B*x+A)/(b*x+a)/(d*x+c)**(1/2),x)","\frac{2 D \left(c + d x\right)^{\frac{5}{2}}}{5 b d^{3}} - \frac{2 \left(c + d x\right)^{\frac{3}{2}} \left(- C b d + D a d + 2 D b c\right)}{3 b^{2} d^{3}} + \frac{2 \left(- A b^{3} + B a b^{2} - C a^{2} b + D a^{3}\right) \operatorname{atan}{\left(\frac{1}{\sqrt{\frac{b}{a d - b c}} \sqrt{c + d x}} \right)}}{b^{3} \sqrt{\frac{b}{a d - b c}} \left(a d - b c\right)} + \frac{2 \sqrt{c + d x} \left(B b^{2} d^{2} - C a b d^{2} - C b^{2} c d + D a^{2} d^{2} + D a b c d + D b^{2} c^{2}\right)}{b^{3} d^{3}}"," ",0,"2*D*(c + d*x)**(5/2)/(5*b*d**3) - 2*(c + d*x)**(3/2)*(-C*b*d + D*a*d + 2*D*b*c)/(3*b**2*d**3) + 2*(-A*b**3 + B*a*b**2 - C*a**2*b + D*a**3)*atan(1/(sqrt(b/(a*d - b*c))*sqrt(c + d*x)))/(b**3*sqrt(b/(a*d - b*c))*(a*d - b*c)) + 2*sqrt(c + d*x)*(B*b**2*d**2 - C*a*b*d**2 - C*b**2*c*d + D*a**2*d**2 + D*a*b*c*d + D*b**2*c**2)/(b**3*d**3)","A",0
6,-1,0,0,0.000000," ","integrate((D*x**3+C*x**2+B*x+A)/(b*x+a)**2/(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
7,-1,0,0,0.000000," ","integrate((D*x**3+C*x**2+B*x+A)/(b*x+a)**3/(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
8,-1,0,0,0.000000," ","integrate((D*x**3+C*x**2+B*x+A)/(b*x+a)**4/(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
9,-1,0,0,0.000000," ","integrate((D*x**3+C*x**2+B*x+A)/(b*x+a)**5/(d*x+c)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
10,-1,0,0,0.000000," ","integrate((b*x+a)**3*(D*x**3+C*x**2+B*x+A)/(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
11,1,435,0,148.595182," ","integrate((b*x+a)**2*(D*x**3+C*x**2+B*x+A)/(d*x+c)**(3/2),x)","\frac{2 D b^{2} \left(c + d x\right)^{\frac{9}{2}}}{9 d^{6}} + \frac{\left(c + d x\right)^{\frac{7}{2}} \left(2 C b^{2} d + 4 D a b d - 10 D b^{2} c\right)}{7 d^{6}} + \frac{\left(c + d x\right)^{\frac{5}{2}} \left(2 B b^{2} d^{2} + 4 C a b d^{2} - 8 C b^{2} c d + 2 D a^{2} d^{2} - 16 D a b c d + 20 D b^{2} c^{2}\right)}{5 d^{6}} + \frac{\left(c + d x\right)^{\frac{3}{2}} \left(2 A b^{2} d^{3} + 4 B a b d^{3} - 6 B b^{2} c d^{2} + 2 C a^{2} d^{3} - 12 C a b c d^{2} + 12 C b^{2} c^{2} d - 6 D a^{2} c d^{2} + 24 D a b c^{2} d - 20 D b^{2} c^{3}\right)}{3 d^{6}} + \frac{\sqrt{c + d x} \left(4 A a b d^{4} - 4 A b^{2} c d^{3} + 2 B a^{2} d^{4} - 8 B a b c d^{3} + 6 B b^{2} c^{2} d^{2} - 4 C a^{2} c d^{3} + 12 C a b c^{2} d^{2} - 8 C b^{2} c^{3} d + 6 D a^{2} c^{2} d^{2} - 16 D a b c^{3} d + 10 D b^{2} c^{4}\right)}{d^{6}} + \frac{2 \left(a d - b c\right)^{2} \left(- A d^{3} + B c d^{2} - C c^{2} d + D c^{3}\right)}{d^{6} \sqrt{c + d x}}"," ",0,"2*D*b**2*(c + d*x)**(9/2)/(9*d**6) + (c + d*x)**(7/2)*(2*C*b**2*d + 4*D*a*b*d - 10*D*b**2*c)/(7*d**6) + (c + d*x)**(5/2)*(2*B*b**2*d**2 + 4*C*a*b*d**2 - 8*C*b**2*c*d + 2*D*a**2*d**2 - 16*D*a*b*c*d + 20*D*b**2*c**2)/(5*d**6) + (c + d*x)**(3/2)*(2*A*b**2*d**3 + 4*B*a*b*d**3 - 6*B*b**2*c*d**2 + 2*C*a**2*d**3 - 12*C*a*b*c*d**2 + 12*C*b**2*c**2*d - 6*D*a**2*c*d**2 + 24*D*a*b*c**2*d - 20*D*b**2*c**3)/(3*d**6) + sqrt(c + d*x)*(4*A*a*b*d**4 - 4*A*b**2*c*d**3 + 2*B*a**2*d**4 - 8*B*a*b*c*d**3 + 6*B*b**2*c**2*d**2 - 4*C*a**2*c*d**3 + 12*C*a*b*c**2*d**2 - 8*C*b**2*c**3*d + 6*D*a**2*c**2*d**2 - 16*D*a*b*c**3*d + 10*D*b**2*c**4)/d**6 + 2*(a*d - b*c)**2*(-A*d**3 + B*c*d**2 - C*c**2*d + D*c**3)/(d**6*sqrt(c + d*x))","A",0
12,1,230,0,60.709213," ","integrate((b*x+a)*(D*x**3+C*x**2+B*x+A)/(d*x+c)**(3/2),x)","\frac{2 D b \left(c + d x\right)^{\frac{7}{2}}}{7 d^{5}} + \frac{\left(c + d x\right)^{\frac{5}{2}} \left(2 C b d + 2 D a d - 8 D b c\right)}{5 d^{5}} + \frac{\left(c + d x\right)^{\frac{3}{2}} \left(2 B b d^{2} + 2 C a d^{2} - 6 C b c d - 6 D a c d + 12 D b c^{2}\right)}{3 d^{5}} + \frac{\sqrt{c + d x} \left(2 A b d^{3} + 2 B a d^{3} - 4 B b c d^{2} - 4 C a c d^{2} + 6 C b c^{2} d + 6 D a c^{2} d - 8 D b c^{3}\right)}{d^{5}} + \frac{2 \left(a d - b c\right) \left(- A d^{3} + B c d^{2} - C c^{2} d + D c^{3}\right)}{d^{5} \sqrt{c + d x}}"," ",0,"2*D*b*(c + d*x)**(7/2)/(7*d**5) + (c + d*x)**(5/2)*(2*C*b*d + 2*D*a*d - 8*D*b*c)/(5*d**5) + (c + d*x)**(3/2)*(2*B*b*d**2 + 2*C*a*d**2 - 6*C*b*c*d - 6*D*a*c*d + 12*D*b*c**2)/(3*d**5) + sqrt(c + d*x)*(2*A*b*d**3 + 2*B*a*d**3 - 4*B*b*c*d**2 - 4*C*a*c*d**2 + 6*C*b*c**2*d + 6*D*a*c**2*d - 8*D*b*c**3)/d**5 + 2*(a*d - b*c)*(-A*d**3 + B*c*d**2 - C*c**2*d + D*c**3)/(d**5*sqrt(c + d*x))","A",0
13,1,114,0,20.137680," ","integrate((D*x**3+C*x**2+B*x+A)/(d*x+c)**(3/2),x)","\frac{2 D \left(c + d x\right)^{\frac{5}{2}}}{5 d^{4}} + \frac{\left(c + d x\right)^{\frac{3}{2}} \left(2 C d - 6 D c\right)}{3 d^{4}} + \frac{\sqrt{c + d x} \left(2 B d^{2} - 4 C c d + 6 D c^{2}\right)}{d^{4}} + \frac{2 \left(- A d^{3} + B c d^{2} - C c^{2} d + D c^{3}\right)}{d^{4} \sqrt{c + d x}}"," ",0,"2*D*(c + d*x)**(5/2)/(5*d**4) + (c + d*x)**(3/2)*(2*C*d - 6*D*c)/(3*d**4) + sqrt(c + d*x)*(2*B*d**2 - 4*C*c*d + 6*D*c**2)/d**4 + 2*(-A*d**3 + B*c*d**2 - C*c**2*d + D*c**3)/(d**4*sqrt(c + d*x))","A",0
14,1,172,0,85.725215," ","integrate((D*x**3+C*x**2+B*x+A)/(b*x+a)/(d*x+c)**(3/2),x)","\frac{2 D \left(c + d x\right)^{\frac{3}{2}}}{3 b d^{3}} + \frac{2 \left(- A d^{3} + B c d^{2} - C c^{2} d + D c^{3}\right)}{d^{3} \sqrt{c + d x} \left(a d - b c\right)} + \frac{\sqrt{c + d x} \left(2 C b d - 2 D a d - 4 D b c\right)}{b^{2} d^{3}} + \frac{2 \left(- A b^{3} + B a b^{2} - C a^{2} b + D a^{3}\right) \operatorname{atan}{\left(\frac{\sqrt{c + d x}}{\sqrt{\frac{a d - b c}{b}}} \right)}}{b^{3} \sqrt{\frac{a d - b c}{b}} \left(a d - b c\right)}"," ",0,"2*D*(c + d*x)**(3/2)/(3*b*d**3) + 2*(-A*d**3 + B*c*d**2 - C*c**2*d + D*c**3)/(d**3*sqrt(c + d*x)*(a*d - b*c)) + sqrt(c + d*x)*(2*C*b*d - 2*D*a*d - 4*D*b*c)/(b**2*d**3) + 2*(-A*b**3 + B*a*b**2 - C*a**2*b + D*a**3)*atan(sqrt(c + d*x)/sqrt((a*d - b*c)/b))/(b**3*sqrt((a*d - b*c)/b)*(a*d - b*c))","A",0
15,-1,0,0,0.000000," ","integrate((D*x**3+C*x**2+B*x+A)/(b*x+a)**2/(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
16,-1,0,0,0.000000," ","integrate((D*x**3+C*x**2+B*x+A)/(b*x+a)**3/(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
17,-1,0,0,0.000000," ","integrate((D*x**3+C*x**2+B*x+A)/(b*x+a)**4/(d*x+c)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
18,-1,0,0,0.000000," ","integrate((b*x+a)**3*(D*x**3+C*x**2+B*x+A)/(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
19,-1,0,0,0.000000," ","integrate((b*x+a)**2*(D*x**3+C*x**2+B*x+A)/(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
20,1,230,0,82.476207," ","integrate((b*x+a)*(D*x**3+C*x**2+B*x+A)/(d*x+c)**(5/2),x)","\frac{2 D b \left(c + d x\right)^{\frac{5}{2}}}{5 d^{5}} + \frac{\left(c + d x\right)^{\frac{3}{2}} \left(2 C b d + 2 D a d - 8 D b c\right)}{3 d^{5}} + \frac{\sqrt{c + d x} \left(2 B b d^{2} + 2 C a d^{2} - 6 C b c d - 6 D a c d + 12 D b c^{2}\right)}{d^{5}} - \frac{2 \left(A b d^{3} + B a d^{3} - 2 B b c d^{2} - 2 C a c d^{2} + 3 C b c^{2} d + 3 D a c^{2} d - 4 D b c^{3}\right)}{d^{5} \sqrt{c + d x}} + \frac{2 \left(a d - b c\right) \left(- A d^{3} + B c d^{2} - C c^{2} d + D c^{3}\right)}{3 d^{5} \left(c + d x\right)^{\frac{3}{2}}}"," ",0,"2*D*b*(c + d*x)**(5/2)/(5*d**5) + (c + d*x)**(3/2)*(2*C*b*d + 2*D*a*d - 8*D*b*c)/(3*d**5) + sqrt(c + d*x)*(2*B*b*d**2 + 2*C*a*d**2 - 6*C*b*c*d - 6*D*a*c*d + 12*D*b*c**2)/d**5 - 2*(A*b*d**3 + B*a*d**3 - 2*B*b*c*d**2 - 2*C*a*c*d**2 + 3*C*b*c**2*d + 3*D*a*c**2*d - 4*D*b*c**3)/(d**5*sqrt(c + d*x)) + 2*(a*d - b*c)*(-A*d**3 + B*c*d**2 - C*c**2*d + D*c**3)/(3*d**5*(c + d*x)**(3/2))","A",0
21,1,425,0,1.418189," ","integrate((D*x**3+C*x**2+B*x+A)/(d*x+c)**(5/2),x)","\begin{cases} - \frac{2 A d^{3}}{3 c d^{4} \sqrt{c + d x} + 3 d^{5} x \sqrt{c + d x}} - \frac{4 B c d^{2}}{3 c d^{4} \sqrt{c + d x} + 3 d^{5} x \sqrt{c + d x}} - \frac{6 B d^{3} x}{3 c d^{4} \sqrt{c + d x} + 3 d^{5} x \sqrt{c + d x}} + \frac{16 C c^{2} d}{3 c d^{4} \sqrt{c + d x} + 3 d^{5} x \sqrt{c + d x}} + \frac{24 C c d^{2} x}{3 c d^{4} \sqrt{c + d x} + 3 d^{5} x \sqrt{c + d x}} + \frac{6 C d^{3} x^{2}}{3 c d^{4} \sqrt{c + d x} + 3 d^{5} x \sqrt{c + d x}} - \frac{32 D c^{3}}{3 c d^{4} \sqrt{c + d x} + 3 d^{5} x \sqrt{c + d x}} - \frac{48 D c^{2} d x}{3 c d^{4} \sqrt{c + d x} + 3 d^{5} x \sqrt{c + d x}} - \frac{12 D c d^{2} x^{2}}{3 c d^{4} \sqrt{c + d x} + 3 d^{5} x \sqrt{c + d x}} + \frac{2 D d^{3} x^{3}}{3 c d^{4} \sqrt{c + d x} + 3 d^{5} x \sqrt{c + d x}} & \text{for}\: d \neq 0 \\\frac{A x + \frac{B x^{2}}{2} + \frac{C x^{3}}{3} + \frac{D x^{4}}{4}}{c^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*A*d**3/(3*c*d**4*sqrt(c + d*x) + 3*d**5*x*sqrt(c + d*x)) - 4*B*c*d**2/(3*c*d**4*sqrt(c + d*x) + 3*d**5*x*sqrt(c + d*x)) - 6*B*d**3*x/(3*c*d**4*sqrt(c + d*x) + 3*d**5*x*sqrt(c + d*x)) + 16*C*c**2*d/(3*c*d**4*sqrt(c + d*x) + 3*d**5*x*sqrt(c + d*x)) + 24*C*c*d**2*x/(3*c*d**4*sqrt(c + d*x) + 3*d**5*x*sqrt(c + d*x)) + 6*C*d**3*x**2/(3*c*d**4*sqrt(c + d*x) + 3*d**5*x*sqrt(c + d*x)) - 32*D*c**3/(3*c*d**4*sqrt(c + d*x) + 3*d**5*x*sqrt(c + d*x)) - 48*D*c**2*d*x/(3*c*d**4*sqrt(c + d*x) + 3*d**5*x*sqrt(c + d*x)) - 12*D*c*d**2*x**2/(3*c*d**4*sqrt(c + d*x) + 3*d**5*x*sqrt(c + d*x)) + 2*D*d**3*x**3/(3*c*d**4*sqrt(c + d*x) + 3*d**5*x*sqrt(c + d*x)), Ne(d, 0)), ((A*x + B*x**2/2 + C*x**3/3 + D*x**4/4)/c**(5/2), True))","A",0
22,1,214,0,153.497337," ","integrate((D*x**3+C*x**2+B*x+A)/(b*x+a)/(d*x+c)**(5/2),x)","\frac{2 D \sqrt{c + d x}}{b d^{3}} - \frac{2 \left(- A b d^{3} + B a d^{3} - 2 C a c d^{2} + C b c^{2} d + 3 D a c^{2} d - 2 D b c^{3}\right)}{d^{3} \sqrt{c + d x} \left(a d - b c\right)^{2}} + \frac{2 \left(- A d^{3} + B c d^{2} - C c^{2} d + D c^{3}\right)}{3 d^{3} \left(c + d x\right)^{\frac{3}{2}} \left(a d - b c\right)} - \frac{2 \left(- A b^{3} + B a b^{2} - C a^{2} b + D a^{3}\right) \operatorname{atan}{\left(\frac{\sqrt{c + d x}}{\sqrt{\frac{a d - b c}{b}}} \right)}}{b^{2} \sqrt{\frac{a d - b c}{b}} \left(a d - b c\right)^{2}}"," ",0,"2*D*sqrt(c + d*x)/(b*d**3) - 2*(-A*b*d**3 + B*a*d**3 - 2*C*a*c*d**2 + C*b*c**2*d + 3*D*a*c**2*d - 2*D*b*c**3)/(d**3*sqrt(c + d*x)*(a*d - b*c)**2) + 2*(-A*d**3 + B*c*d**2 - C*c**2*d + D*c**3)/(3*d**3*(c + d*x)**(3/2)*(a*d - b*c)) - 2*(-A*b**3 + B*a*b**2 - C*a**2*b + D*a**3)*atan(sqrt(c + d*x)/sqrt((a*d - b*c)/b))/(b**2*sqrt((a*d - b*c)/b)*(a*d - b*c)**2)","A",0
23,-1,0,0,0.000000," ","integrate((D*x**3+C*x**2+B*x+A)/(b*x+a)**2/(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
24,-1,0,0,0.000000," ","integrate((D*x**3+C*x**2+B*x+A)/(b*x+a)**3/(d*x+c)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
25,-1,0,0,0.000000," ","integrate((b*x+a)**3*(d*x+c)**n*(D*x**3+C*x**2+B*x+A),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
26,-1,0,0,0.000000," ","integrate((b*x+a)**2*(d*x+c)**n*(D*x**3+C*x**2+B*x+A),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
27,1,13522,0,12.513618," ","integrate((b*x+a)*(d*x+c)**n*(D*x**3+C*x**2+B*x+A),x)","\begin{cases} c^{n} \left(A a x + \frac{A b x^{2}}{2} + \frac{B a x^{2}}{2} + \frac{B b x^{3}}{3} + \frac{C a x^{3}}{3} + \frac{C b x^{4}}{4} + \frac{D a x^{4}}{4} + \frac{D b x^{5}}{5}\right) & \text{for}\: d = 0 \\- \frac{3 A a d^{4}}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} - \frac{A b c d^{3}}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} - \frac{4 A b d^{4} x}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} - \frac{B a c d^{3}}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} - \frac{4 B a d^{4} x}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} - \frac{B b c^{2} d^{2}}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} - \frac{4 B b c d^{3} x}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} - \frac{6 B b d^{4} x^{2}}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} - \frac{C a c^{2} d^{2}}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} - \frac{4 C a c d^{3} x}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} - \frac{6 C a d^{4} x^{2}}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} - \frac{3 C b c^{3} d}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} - \frac{12 C b c^{2} d^{2} x}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} - \frac{18 C b c d^{3} x^{2}}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} - \frac{12 C b d^{4} x^{3}}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} - \frac{3 D a c^{3} d}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} - \frac{12 D a c^{2} d^{2} x}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} - \frac{18 D a c d^{3} x^{2}}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} - \frac{12 D a d^{4} x^{3}}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} + \frac{12 D b c^{4} \log{\left(\frac{c}{d} + x \right)}}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} + \frac{25 D b c^{4}}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} + \frac{48 D b c^{3} d x \log{\left(\frac{c}{d} + x \right)}}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} + \frac{88 D b c^{3} d x}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} + \frac{72 D b c^{2} d^{2} x^{2} \log{\left(\frac{c}{d} + x \right)}}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} + \frac{108 D b c^{2} d^{2} x^{2}}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} + \frac{48 D b c d^{3} x^{3} \log{\left(\frac{c}{d} + x \right)}}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} + \frac{48 D b c d^{3} x^{3}}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} + \frac{12 D b d^{4} x^{4} \log{\left(\frac{c}{d} + x \right)}}{12 c^{4} d^{5} + 48 c^{3} d^{6} x + 72 c^{2} d^{7} x^{2} + 48 c d^{8} x^{3} + 12 d^{9} x^{4}} & \text{for}\: n = -5 \\- \frac{2 A a d^{4}}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} - \frac{A b c d^{3}}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} - \frac{3 A b d^{4} x}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} - \frac{B a c d^{3}}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} - \frac{3 B a d^{4} x}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} - \frac{2 B b c^{2} d^{2}}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} - \frac{6 B b c d^{3} x}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} - \frac{6 B b d^{4} x^{2}}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} - \frac{2 C a c^{2} d^{2}}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} - \frac{6 C a c d^{3} x}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} - \frac{6 C a d^{4} x^{2}}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} + \frac{6 C b c^{3} d \log{\left(\frac{c}{d} + x \right)}}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} + \frac{11 C b c^{3} d}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} + \frac{18 C b c^{2} d^{2} x \log{\left(\frac{c}{d} + x \right)}}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} + \frac{27 C b c^{2} d^{2} x}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} + \frac{18 C b c d^{3} x^{2} \log{\left(\frac{c}{d} + x \right)}}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} + \frac{18 C b c d^{3} x^{2}}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} + \frac{6 C b d^{4} x^{3} \log{\left(\frac{c}{d} + x \right)}}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} + \frac{6 D a c^{3} d \log{\left(\frac{c}{d} + x \right)}}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} + \frac{11 D a c^{3} d}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} + \frac{18 D a c^{2} d^{2} x \log{\left(\frac{c}{d} + x \right)}}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} + \frac{27 D a c^{2} d^{2} x}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} + \frac{18 D a c d^{3} x^{2} \log{\left(\frac{c}{d} + x \right)}}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} + \frac{18 D a c d^{3} x^{2}}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} + \frac{6 D a d^{4} x^{3} \log{\left(\frac{c}{d} + x \right)}}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} - \frac{24 D b c^{4} \log{\left(\frac{c}{d} + x \right)}}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} - \frac{44 D b c^{4}}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} - \frac{72 D b c^{3} d x \log{\left(\frac{c}{d} + x \right)}}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} - \frac{108 D b c^{3} d x}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} - \frac{72 D b c^{2} d^{2} x^{2} \log{\left(\frac{c}{d} + x \right)}}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} - \frac{72 D b c^{2} d^{2} x^{2}}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} - \frac{24 D b c d^{3} x^{3} \log{\left(\frac{c}{d} + x \right)}}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} + \frac{6 D b d^{4} x^{4}}{6 c^{3} d^{5} + 18 c^{2} d^{6} x + 18 c d^{7} x^{2} + 6 d^{8} x^{3}} & \text{for}\: n = -4 \\- \frac{A a d^{4}}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} - \frac{A b c d^{3}}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} - \frac{2 A b d^{4} x}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} - \frac{B a c d^{3}}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} - \frac{2 B a d^{4} x}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} + \frac{2 B b c^{2} d^{2} \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} + \frac{3 B b c^{2} d^{2}}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} + \frac{4 B b c d^{3} x \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} + \frac{4 B b c d^{3} x}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} + \frac{2 B b d^{4} x^{2} \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} + \frac{2 C a c^{2} d^{2} \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} + \frac{3 C a c^{2} d^{2}}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} + \frac{4 C a c d^{3} x \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} + \frac{4 C a c d^{3} x}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} + \frac{2 C a d^{4} x^{2} \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} - \frac{6 C b c^{3} d \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} - \frac{9 C b c^{3} d}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} - \frac{12 C b c^{2} d^{2} x \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} - \frac{12 C b c^{2} d^{2} x}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} - \frac{6 C b c d^{3} x^{2} \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} + \frac{2 C b d^{4} x^{3}}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} - \frac{6 D a c^{3} d \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} - \frac{9 D a c^{3} d}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} - \frac{12 D a c^{2} d^{2} x \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} - \frac{12 D a c^{2} d^{2} x}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} - \frac{6 D a c d^{3} x^{2} \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} + \frac{2 D a d^{4} x^{3}}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} + \frac{12 D b c^{4} \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} + \frac{18 D b c^{4}}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} + \frac{24 D b c^{3} d x \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} + \frac{24 D b c^{3} d x}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} + \frac{12 D b c^{2} d^{2} x^{2} \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} - \frac{4 D b c d^{3} x^{3}}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} + \frac{D b d^{4} x^{4}}{2 c^{2} d^{5} + 4 c d^{6} x + 2 d^{7} x^{2}} & \text{for}\: n = -3 \\- \frac{6 A a d^{4}}{6 c d^{5} + 6 d^{6} x} + \frac{6 A b c d^{3} \log{\left(\frac{c}{d} + x \right)}}{6 c d^{5} + 6 d^{6} x} + \frac{6 A b c d^{3}}{6 c d^{5} + 6 d^{6} x} + \frac{6 A b d^{4} x \log{\left(\frac{c}{d} + x \right)}}{6 c d^{5} + 6 d^{6} x} + \frac{6 B a c d^{3} \log{\left(\frac{c}{d} + x \right)}}{6 c d^{5} + 6 d^{6} x} + \frac{6 B a c d^{3}}{6 c d^{5} + 6 d^{6} x} + \frac{6 B a d^{4} x \log{\left(\frac{c}{d} + x \right)}}{6 c d^{5} + 6 d^{6} x} - \frac{12 B b c^{2} d^{2} \log{\left(\frac{c}{d} + x \right)}}{6 c d^{5} + 6 d^{6} x} - \frac{12 B b c^{2} d^{2}}{6 c d^{5} + 6 d^{6} x} - \frac{12 B b c d^{3} x \log{\left(\frac{c}{d} + x \right)}}{6 c d^{5} + 6 d^{6} x} + \frac{6 B b d^{4} x^{2}}{6 c d^{5} + 6 d^{6} x} - \frac{12 C a c^{2} d^{2} \log{\left(\frac{c}{d} + x \right)}}{6 c d^{5} + 6 d^{6} x} - \frac{12 C a c^{2} d^{2}}{6 c d^{5} + 6 d^{6} x} - \frac{12 C a c d^{3} x \log{\left(\frac{c}{d} + x \right)}}{6 c d^{5} + 6 d^{6} x} + \frac{6 C a d^{4} x^{2}}{6 c d^{5} + 6 d^{6} x} + \frac{18 C b c^{3} d \log{\left(\frac{c}{d} + x \right)}}{6 c d^{5} + 6 d^{6} x} + \frac{18 C b c^{3} d}{6 c d^{5} + 6 d^{6} x} + \frac{18 C b c^{2} d^{2} x \log{\left(\frac{c}{d} + x \right)}}{6 c d^{5} + 6 d^{6} x} - \frac{9 C b c d^{3} x^{2}}{6 c d^{5} + 6 d^{6} x} + \frac{3 C b d^{4} x^{3}}{6 c d^{5} + 6 d^{6} x} + \frac{18 D a c^{3} d \log{\left(\frac{c}{d} + x \right)}}{6 c d^{5} + 6 d^{6} x} + \frac{18 D a c^{3} d}{6 c d^{5} + 6 d^{6} x} + \frac{18 D a c^{2} d^{2} x \log{\left(\frac{c}{d} + x \right)}}{6 c d^{5} + 6 d^{6} x} - \frac{9 D a c d^{3} x^{2}}{6 c d^{5} + 6 d^{6} x} + \frac{3 D a d^{4} x^{3}}{6 c d^{5} + 6 d^{6} x} - \frac{24 D b c^{4} \log{\left(\frac{c}{d} + x \right)}}{6 c d^{5} + 6 d^{6} x} - \frac{24 D b c^{4}}{6 c d^{5} + 6 d^{6} x} - \frac{24 D b c^{3} d x \log{\left(\frac{c}{d} + x \right)}}{6 c d^{5} + 6 d^{6} x} + \frac{12 D b c^{2} d^{2} x^{2}}{6 c d^{5} + 6 d^{6} x} - \frac{4 D b c d^{3} x^{3}}{6 c d^{5} + 6 d^{6} x} + \frac{2 D b d^{4} x^{4}}{6 c d^{5} + 6 d^{6} x} & \text{for}\: n = -2 \\\frac{A a \log{\left(\frac{c}{d} + x \right)}}{d} - \frac{A b c \log{\left(\frac{c}{d} + x \right)}}{d^{2}} + \frac{A b x}{d} - \frac{B a c \log{\left(\frac{c}{d} + x \right)}}{d^{2}} + \frac{B a x}{d} + \frac{B b c^{2} \log{\left(\frac{c}{d} + x \right)}}{d^{3}} - \frac{B b c x}{d^{2}} + \frac{B b x^{2}}{2 d} + \frac{C a c^{2} \log{\left(\frac{c}{d} + x \right)}}{d^{3}} - \frac{C a c x}{d^{2}} + \frac{C a x^{2}}{2 d} - \frac{C b c^{3} \log{\left(\frac{c}{d} + x \right)}}{d^{4}} + \frac{C b c^{2} x}{d^{3}} - \frac{C b c x^{2}}{2 d^{2}} + \frac{C b x^{3}}{3 d} - \frac{D a c^{3} \log{\left(\frac{c}{d} + x \right)}}{d^{4}} + \frac{D a c^{2} x}{d^{3}} - \frac{D a c x^{2}}{2 d^{2}} + \frac{D a x^{3}}{3 d} + \frac{D b c^{4} \log{\left(\frac{c}{d} + x \right)}}{d^{5}} - \frac{D b c^{3} x}{d^{4}} + \frac{D b c^{2} x^{2}}{2 d^{3}} - \frac{D b c x^{3}}{3 d^{2}} + \frac{D b x^{4}}{4 d} & \text{for}\: n = -1 \\\frac{A a c d^{4} n^{4} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{14 A a c d^{4} n^{3} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{71 A a c d^{4} n^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{154 A a c d^{4} n \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{120 A a c d^{4} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{A a d^{5} n^{4} x \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{14 A a d^{5} n^{3} x \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{71 A a d^{5} n^{2} x \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{154 A a d^{5} n x \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{120 A a d^{5} x \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{A b c^{2} d^{3} n^{3} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{12 A b c^{2} d^{3} n^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{47 A b c^{2} d^{3} n \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{60 A b c^{2} d^{3} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{A b c d^{4} n^{4} x \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{12 A b c d^{4} n^{3} x \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{47 A b c d^{4} n^{2} x \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{60 A b c d^{4} n x \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{A b d^{5} n^{4} x^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{13 A b d^{5} n^{3} x^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{59 A b d^{5} n^{2} x^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{107 A b d^{5} n x^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{60 A b d^{5} x^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{B a c^{2} d^{3} n^{3} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{12 B a c^{2} d^{3} n^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{47 B a c^{2} d^{3} n \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{60 B a c^{2} d^{3} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{B a c d^{4} n^{4} x \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{12 B a c d^{4} n^{3} x \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{47 B a c d^{4} n^{2} x \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{60 B a c d^{4} n x \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{B a d^{5} n^{4} x^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{13 B a d^{5} n^{3} x^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{59 B a d^{5} n^{2} x^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{107 B a d^{5} n x^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{60 B a d^{5} x^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{2 B b c^{3} d^{2} n^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{18 B b c^{3} d^{2} n \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{40 B b c^{3} d^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{2 B b c^{2} d^{3} n^{3} x \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{18 B b c^{2} d^{3} n^{2} x \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{40 B b c^{2} d^{3} n x \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{B b c d^{4} n^{4} x^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{10 B b c d^{4} n^{3} x^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{29 B b c d^{4} n^{2} x^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{20 B b c d^{4} n x^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{B b d^{5} n^{4} x^{3} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{12 B b d^{5} n^{3} x^{3} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{49 B b d^{5} n^{2} x^{3} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{78 B b d^{5} n x^{3} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{40 B b d^{5} x^{3} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{2 C a c^{3} d^{2} n^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{18 C a c^{3} d^{2} n \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{40 C a c^{3} d^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{2 C a c^{2} d^{3} n^{3} x \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{18 C a c^{2} d^{3} n^{2} x \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{40 C a c^{2} d^{3} n x \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{C a c d^{4} n^{4} x^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{10 C a c d^{4} n^{3} x^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{29 C a c d^{4} n^{2} x^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{20 C a c d^{4} n x^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{C a d^{5} n^{4} x^{3} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{12 C a d^{5} n^{3} x^{3} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{49 C a d^{5} n^{2} x^{3} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{78 C a d^{5} n x^{3} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{40 C a d^{5} x^{3} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{6 C b c^{4} d n \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{30 C b c^{4} d \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{6 C b c^{3} d^{2} n^{2} x \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{30 C b c^{3} d^{2} n x \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{3 C b c^{2} d^{3} n^{3} x^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{18 C b c^{2} d^{3} n^{2} x^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{15 C b c^{2} d^{3} n x^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{C b c d^{4} n^{4} x^{3} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{8 C b c d^{4} n^{3} x^{3} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{17 C b c d^{4} n^{2} x^{3} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{10 C b c d^{4} n x^{3} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{C b d^{5} n^{4} x^{4} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{11 C b d^{5} n^{3} x^{4} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{41 C b d^{5} n^{2} x^{4} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{61 C b d^{5} n x^{4} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{30 C b d^{5} x^{4} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{6 D a c^{4} d n \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{30 D a c^{4} d \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{6 D a c^{3} d^{2} n^{2} x \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{30 D a c^{3} d^{2} n x \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{3 D a c^{2} d^{3} n^{3} x^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{18 D a c^{2} d^{3} n^{2} x^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{15 D a c^{2} d^{3} n x^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{D a c d^{4} n^{4} x^{3} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{8 D a c d^{4} n^{3} x^{3} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{17 D a c d^{4} n^{2} x^{3} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{10 D a c d^{4} n x^{3} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{D a d^{5} n^{4} x^{4} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{11 D a d^{5} n^{3} x^{4} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{41 D a d^{5} n^{2} x^{4} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{61 D a d^{5} n x^{4} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{30 D a d^{5} x^{4} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{24 D b c^{5} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{24 D b c^{4} d n x \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{12 D b c^{3} d^{2} n^{2} x^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{12 D b c^{3} d^{2} n x^{2} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{4 D b c^{2} d^{3} n^{3} x^{3} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{12 D b c^{2} d^{3} n^{2} x^{3} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} - \frac{8 D b c^{2} d^{3} n x^{3} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{D b c d^{4} n^{4} x^{4} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{6 D b c d^{4} n^{3} x^{4} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{11 D b c d^{4} n^{2} x^{4} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{6 D b c d^{4} n x^{4} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{D b d^{5} n^{4} x^{5} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{10 D b d^{5} n^{3} x^{5} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{35 D b d^{5} n^{2} x^{5} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{50 D b d^{5} n x^{5} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} + \frac{24 D b d^{5} x^{5} \left(c + d x\right)^{n}}{d^{5} n^{5} + 15 d^{5} n^{4} + 85 d^{5} n^{3} + 225 d^{5} n^{2} + 274 d^{5} n + 120 d^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**n*(A*a*x + A*b*x**2/2 + B*a*x**2/2 + B*b*x**3/3 + C*a*x**3/3 + C*b*x**4/4 + D*a*x**4/4 + D*b*x**5/5), Eq(d, 0)), (-3*A*a*d**4/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) - A*b*c*d**3/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) - 4*A*b*d**4*x/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) - B*a*c*d**3/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) - 4*B*a*d**4*x/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) - B*b*c**2*d**2/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) - 4*B*b*c*d**3*x/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) - 6*B*b*d**4*x**2/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) - C*a*c**2*d**2/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) - 4*C*a*c*d**3*x/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) - 6*C*a*d**4*x**2/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) - 3*C*b*c**3*d/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) - 12*C*b*c**2*d**2*x/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) - 18*C*b*c*d**3*x**2/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) - 12*C*b*d**4*x**3/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) - 3*D*a*c**3*d/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) - 12*D*a*c**2*d**2*x/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) - 18*D*a*c*d**3*x**2/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) - 12*D*a*d**4*x**3/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) + 12*D*b*c**4*log(c/d + x)/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) + 25*D*b*c**4/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) + 48*D*b*c**3*d*x*log(c/d + x)/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) + 88*D*b*c**3*d*x/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) + 72*D*b*c**2*d**2*x**2*log(c/d + x)/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) + 108*D*b*c**2*d**2*x**2/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) + 48*D*b*c*d**3*x**3*log(c/d + x)/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) + 48*D*b*c*d**3*x**3/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4) + 12*D*b*d**4*x**4*log(c/d + x)/(12*c**4*d**5 + 48*c**3*d**6*x + 72*c**2*d**7*x**2 + 48*c*d**8*x**3 + 12*d**9*x**4), Eq(n, -5)), (-2*A*a*d**4/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) - A*b*c*d**3/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) - 3*A*b*d**4*x/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) - B*a*c*d**3/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) - 3*B*a*d**4*x/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) - 2*B*b*c**2*d**2/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) - 6*B*b*c*d**3*x/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) - 6*B*b*d**4*x**2/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) - 2*C*a*c**2*d**2/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) - 6*C*a*c*d**3*x/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) - 6*C*a*d**4*x**2/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) + 6*C*b*c**3*d*log(c/d + x)/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) + 11*C*b*c**3*d/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) + 18*C*b*c**2*d**2*x*log(c/d + x)/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) + 27*C*b*c**2*d**2*x/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) + 18*C*b*c*d**3*x**2*log(c/d + x)/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) + 18*C*b*c*d**3*x**2/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) + 6*C*b*d**4*x**3*log(c/d + x)/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) + 6*D*a*c**3*d*log(c/d + x)/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) + 11*D*a*c**3*d/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) + 18*D*a*c**2*d**2*x*log(c/d + x)/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) + 27*D*a*c**2*d**2*x/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) + 18*D*a*c*d**3*x**2*log(c/d + x)/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) + 18*D*a*c*d**3*x**2/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) + 6*D*a*d**4*x**3*log(c/d + x)/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) - 24*D*b*c**4*log(c/d + x)/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) - 44*D*b*c**4/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) - 72*D*b*c**3*d*x*log(c/d + x)/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) - 108*D*b*c**3*d*x/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) - 72*D*b*c**2*d**2*x**2*log(c/d + x)/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) - 72*D*b*c**2*d**2*x**2/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) - 24*D*b*c*d**3*x**3*log(c/d + x)/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3) + 6*D*b*d**4*x**4/(6*c**3*d**5 + 18*c**2*d**6*x + 18*c*d**7*x**2 + 6*d**8*x**3), Eq(n, -4)), (-A*a*d**4/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) - A*b*c*d**3/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) - 2*A*b*d**4*x/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) - B*a*c*d**3/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) - 2*B*a*d**4*x/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) + 2*B*b*c**2*d**2*log(c/d + x)/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) + 3*B*b*c**2*d**2/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) + 4*B*b*c*d**3*x*log(c/d + x)/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) + 4*B*b*c*d**3*x/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) + 2*B*b*d**4*x**2*log(c/d + x)/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) + 2*C*a*c**2*d**2*log(c/d + x)/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) + 3*C*a*c**2*d**2/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) + 4*C*a*c*d**3*x*log(c/d + x)/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) + 4*C*a*c*d**3*x/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) + 2*C*a*d**4*x**2*log(c/d + x)/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) - 6*C*b*c**3*d*log(c/d + x)/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) - 9*C*b*c**3*d/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) - 12*C*b*c**2*d**2*x*log(c/d + x)/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) - 12*C*b*c**2*d**2*x/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) - 6*C*b*c*d**3*x**2*log(c/d + x)/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) + 2*C*b*d**4*x**3/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) - 6*D*a*c**3*d*log(c/d + x)/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) - 9*D*a*c**3*d/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) - 12*D*a*c**2*d**2*x*log(c/d + x)/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) - 12*D*a*c**2*d**2*x/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) - 6*D*a*c*d**3*x**2*log(c/d + x)/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) + 2*D*a*d**4*x**3/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) + 12*D*b*c**4*log(c/d + x)/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) + 18*D*b*c**4/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) + 24*D*b*c**3*d*x*log(c/d + x)/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) + 24*D*b*c**3*d*x/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) + 12*D*b*c**2*d**2*x**2*log(c/d + x)/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) - 4*D*b*c*d**3*x**3/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2) + D*b*d**4*x**4/(2*c**2*d**5 + 4*c*d**6*x + 2*d**7*x**2), Eq(n, -3)), (-6*A*a*d**4/(6*c*d**5 + 6*d**6*x) + 6*A*b*c*d**3*log(c/d + x)/(6*c*d**5 + 6*d**6*x) + 6*A*b*c*d**3/(6*c*d**5 + 6*d**6*x) + 6*A*b*d**4*x*log(c/d + x)/(6*c*d**5 + 6*d**6*x) + 6*B*a*c*d**3*log(c/d + x)/(6*c*d**5 + 6*d**6*x) + 6*B*a*c*d**3/(6*c*d**5 + 6*d**6*x) + 6*B*a*d**4*x*log(c/d + x)/(6*c*d**5 + 6*d**6*x) - 12*B*b*c**2*d**2*log(c/d + x)/(6*c*d**5 + 6*d**6*x) - 12*B*b*c**2*d**2/(6*c*d**5 + 6*d**6*x) - 12*B*b*c*d**3*x*log(c/d + x)/(6*c*d**5 + 6*d**6*x) + 6*B*b*d**4*x**2/(6*c*d**5 + 6*d**6*x) - 12*C*a*c**2*d**2*log(c/d + x)/(6*c*d**5 + 6*d**6*x) - 12*C*a*c**2*d**2/(6*c*d**5 + 6*d**6*x) - 12*C*a*c*d**3*x*log(c/d + x)/(6*c*d**5 + 6*d**6*x) + 6*C*a*d**4*x**2/(6*c*d**5 + 6*d**6*x) + 18*C*b*c**3*d*log(c/d + x)/(6*c*d**5 + 6*d**6*x) + 18*C*b*c**3*d/(6*c*d**5 + 6*d**6*x) + 18*C*b*c**2*d**2*x*log(c/d + x)/(6*c*d**5 + 6*d**6*x) - 9*C*b*c*d**3*x**2/(6*c*d**5 + 6*d**6*x) + 3*C*b*d**4*x**3/(6*c*d**5 + 6*d**6*x) + 18*D*a*c**3*d*log(c/d + x)/(6*c*d**5 + 6*d**6*x) + 18*D*a*c**3*d/(6*c*d**5 + 6*d**6*x) + 18*D*a*c**2*d**2*x*log(c/d + x)/(6*c*d**5 + 6*d**6*x) - 9*D*a*c*d**3*x**2/(6*c*d**5 + 6*d**6*x) + 3*D*a*d**4*x**3/(6*c*d**5 + 6*d**6*x) - 24*D*b*c**4*log(c/d + x)/(6*c*d**5 + 6*d**6*x) - 24*D*b*c**4/(6*c*d**5 + 6*d**6*x) - 24*D*b*c**3*d*x*log(c/d + x)/(6*c*d**5 + 6*d**6*x) + 12*D*b*c**2*d**2*x**2/(6*c*d**5 + 6*d**6*x) - 4*D*b*c*d**3*x**3/(6*c*d**5 + 6*d**6*x) + 2*D*b*d**4*x**4/(6*c*d**5 + 6*d**6*x), Eq(n, -2)), (A*a*log(c/d + x)/d - A*b*c*log(c/d + x)/d**2 + A*b*x/d - B*a*c*log(c/d + x)/d**2 + B*a*x/d + B*b*c**2*log(c/d + x)/d**3 - B*b*c*x/d**2 + B*b*x**2/(2*d) + C*a*c**2*log(c/d + x)/d**3 - C*a*c*x/d**2 + C*a*x**2/(2*d) - C*b*c**3*log(c/d + x)/d**4 + C*b*c**2*x/d**3 - C*b*c*x**2/(2*d**2) + C*b*x**3/(3*d) - D*a*c**3*log(c/d + x)/d**4 + D*a*c**2*x/d**3 - D*a*c*x**2/(2*d**2) + D*a*x**3/(3*d) + D*b*c**4*log(c/d + x)/d**5 - D*b*c**3*x/d**4 + D*b*c**2*x**2/(2*d**3) - D*b*c*x**3/(3*d**2) + D*b*x**4/(4*d), Eq(n, -1)), (A*a*c*d**4*n**4*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 14*A*a*c*d**4*n**3*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 71*A*a*c*d**4*n**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 154*A*a*c*d**4*n*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 120*A*a*c*d**4*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + A*a*d**5*n**4*x*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 14*A*a*d**5*n**3*x*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 71*A*a*d**5*n**2*x*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 154*A*a*d**5*n*x*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 120*A*a*d**5*x*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - A*b*c**2*d**3*n**3*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - 12*A*b*c**2*d**3*n**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - 47*A*b*c**2*d**3*n*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - 60*A*b*c**2*d**3*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + A*b*c*d**4*n**4*x*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 12*A*b*c*d**4*n**3*x*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 47*A*b*c*d**4*n**2*x*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 60*A*b*c*d**4*n*x*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + A*b*d**5*n**4*x**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 13*A*b*d**5*n**3*x**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 59*A*b*d**5*n**2*x**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 107*A*b*d**5*n*x**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 60*A*b*d**5*x**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - B*a*c**2*d**3*n**3*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - 12*B*a*c**2*d**3*n**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - 47*B*a*c**2*d**3*n*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - 60*B*a*c**2*d**3*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + B*a*c*d**4*n**4*x*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 12*B*a*c*d**4*n**3*x*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 47*B*a*c*d**4*n**2*x*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 60*B*a*c*d**4*n*x*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + B*a*d**5*n**4*x**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 13*B*a*d**5*n**3*x**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 59*B*a*d**5*n**2*x**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 107*B*a*d**5*n*x**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 60*B*a*d**5*x**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 2*B*b*c**3*d**2*n**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 18*B*b*c**3*d**2*n*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 40*B*b*c**3*d**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - 2*B*b*c**2*d**3*n**3*x*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - 18*B*b*c**2*d**3*n**2*x*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - 40*B*b*c**2*d**3*n*x*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + B*b*c*d**4*n**4*x**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 10*B*b*c*d**4*n**3*x**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 29*B*b*c*d**4*n**2*x**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 20*B*b*c*d**4*n*x**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + B*b*d**5*n**4*x**3*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 12*B*b*d**5*n**3*x**3*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 49*B*b*d**5*n**2*x**3*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 78*B*b*d**5*n*x**3*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 40*B*b*d**5*x**3*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 2*C*a*c**3*d**2*n**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 18*C*a*c**3*d**2*n*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 40*C*a*c**3*d**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - 2*C*a*c**2*d**3*n**3*x*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - 18*C*a*c**2*d**3*n**2*x*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - 40*C*a*c**2*d**3*n*x*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + C*a*c*d**4*n**4*x**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 10*C*a*c*d**4*n**3*x**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 29*C*a*c*d**4*n**2*x**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 20*C*a*c*d**4*n*x**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + C*a*d**5*n**4*x**3*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 12*C*a*d**5*n**3*x**3*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 49*C*a*d**5*n**2*x**3*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 78*C*a*d**5*n*x**3*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 40*C*a*d**5*x**3*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - 6*C*b*c**4*d*n*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - 30*C*b*c**4*d*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 6*C*b*c**3*d**2*n**2*x*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 30*C*b*c**3*d**2*n*x*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - 3*C*b*c**2*d**3*n**3*x**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - 18*C*b*c**2*d**3*n**2*x**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - 15*C*b*c**2*d**3*n*x**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + C*b*c*d**4*n**4*x**3*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 8*C*b*c*d**4*n**3*x**3*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 17*C*b*c*d**4*n**2*x**3*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 10*C*b*c*d**4*n*x**3*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + C*b*d**5*n**4*x**4*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 11*C*b*d**5*n**3*x**4*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 41*C*b*d**5*n**2*x**4*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 61*C*b*d**5*n*x**4*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 30*C*b*d**5*x**4*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - 6*D*a*c**4*d*n*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - 30*D*a*c**4*d*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 6*D*a*c**3*d**2*n**2*x*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 30*D*a*c**3*d**2*n*x*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - 3*D*a*c**2*d**3*n**3*x**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - 18*D*a*c**2*d**3*n**2*x**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - 15*D*a*c**2*d**3*n*x**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + D*a*c*d**4*n**4*x**3*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 8*D*a*c*d**4*n**3*x**3*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 17*D*a*c*d**4*n**2*x**3*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 10*D*a*c*d**4*n*x**3*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + D*a*d**5*n**4*x**4*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 11*D*a*d**5*n**3*x**4*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 41*D*a*d**5*n**2*x**4*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 61*D*a*d**5*n*x**4*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 30*D*a*d**5*x**4*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 24*D*b*c**5*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - 24*D*b*c**4*d*n*x*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 12*D*b*c**3*d**2*n**2*x**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 12*D*b*c**3*d**2*n*x**2*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - 4*D*b*c**2*d**3*n**3*x**3*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - 12*D*b*c**2*d**3*n**2*x**3*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) - 8*D*b*c**2*d**3*n*x**3*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + D*b*c*d**4*n**4*x**4*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 6*D*b*c*d**4*n**3*x**4*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 11*D*b*c*d**4*n**2*x**4*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 6*D*b*c*d**4*n*x**4*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + D*b*d**5*n**4*x**5*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 10*D*b*d**5*n**3*x**5*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 35*D*b*d**5*n**2*x**5*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 50*D*b*d**5*n*x**5*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5) + 24*D*b*d**5*x**5*(c + d*x)**n/(d**5*n**5 + 15*d**5*n**4 + 85*d**5*n**3 + 225*d**5*n**2 + 274*d**5*n + 120*d**5), True))","A",0
28,1,3798,0,4.321714," ","integrate((d*x+c)**n*(D*x**3+C*x**2+B*x+A),x)","\begin{cases} c^{n} \left(A x + \frac{B x^{2}}{2} + \frac{C x^{3}}{3} + \frac{D x^{4}}{4}\right) & \text{for}\: d = 0 \\- \frac{2 A d^{3}}{6 c^{3} d^{4} + 18 c^{2} d^{5} x + 18 c d^{6} x^{2} + 6 d^{7} x^{3}} - \frac{B c d^{2}}{6 c^{3} d^{4} + 18 c^{2} d^{5} x + 18 c d^{6} x^{2} + 6 d^{7} x^{3}} - \frac{3 B d^{3} x}{6 c^{3} d^{4} + 18 c^{2} d^{5} x + 18 c d^{6} x^{2} + 6 d^{7} x^{3}} - \frac{2 C c^{2} d}{6 c^{3} d^{4} + 18 c^{2} d^{5} x + 18 c d^{6} x^{2} + 6 d^{7} x^{3}} - \frac{6 C c d^{2} x}{6 c^{3} d^{4} + 18 c^{2} d^{5} x + 18 c d^{6} x^{2} + 6 d^{7} x^{3}} - \frac{6 C d^{3} x^{2}}{6 c^{3} d^{4} + 18 c^{2} d^{5} x + 18 c d^{6} x^{2} + 6 d^{7} x^{3}} + \frac{6 D c^{3} \log{\left(\frac{c}{d} + x \right)}}{6 c^{3} d^{4} + 18 c^{2} d^{5} x + 18 c d^{6} x^{2} + 6 d^{7} x^{3}} + \frac{11 D c^{3}}{6 c^{3} d^{4} + 18 c^{2} d^{5} x + 18 c d^{6} x^{2} + 6 d^{7} x^{3}} + \frac{18 D c^{2} d x \log{\left(\frac{c}{d} + x \right)}}{6 c^{3} d^{4} + 18 c^{2} d^{5} x + 18 c d^{6} x^{2} + 6 d^{7} x^{3}} + \frac{27 D c^{2} d x}{6 c^{3} d^{4} + 18 c^{2} d^{5} x + 18 c d^{6} x^{2} + 6 d^{7} x^{3}} + \frac{18 D c d^{2} x^{2} \log{\left(\frac{c}{d} + x \right)}}{6 c^{3} d^{4} + 18 c^{2} d^{5} x + 18 c d^{6} x^{2} + 6 d^{7} x^{3}} + \frac{18 D c d^{2} x^{2}}{6 c^{3} d^{4} + 18 c^{2} d^{5} x + 18 c d^{6} x^{2} + 6 d^{7} x^{3}} + \frac{6 D d^{3} x^{3} \log{\left(\frac{c}{d} + x \right)}}{6 c^{3} d^{4} + 18 c^{2} d^{5} x + 18 c d^{6} x^{2} + 6 d^{7} x^{3}} & \text{for}\: n = -4 \\- \frac{A d^{3}}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} - \frac{B c d^{2}}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} - \frac{2 B d^{3} x}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} + \frac{2 C c^{2} d \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} + \frac{3 C c^{2} d}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} + \frac{4 C c d^{2} x \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} + \frac{4 C c d^{2} x}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} + \frac{2 C d^{3} x^{2} \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} - \frac{6 D c^{3} \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} - \frac{9 D c^{3}}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} - \frac{12 D c^{2} d x \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} - \frac{12 D c^{2} d x}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} - \frac{6 D c d^{2} x^{2} \log{\left(\frac{c}{d} + x \right)}}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} + \frac{2 D d^{3} x^{3}}{2 c^{2} d^{4} + 4 c d^{5} x + 2 d^{6} x^{2}} & \text{for}\: n = -3 \\- \frac{2 A d^{3}}{2 c d^{4} + 2 d^{5} x} + \frac{2 B c d^{2} \log{\left(\frac{c}{d} + x \right)}}{2 c d^{4} + 2 d^{5} x} + \frac{2 B c d^{2}}{2 c d^{4} + 2 d^{5} x} + \frac{2 B d^{3} x \log{\left(\frac{c}{d} + x \right)}}{2 c d^{4} + 2 d^{5} x} - \frac{4 C c^{2} d \log{\left(\frac{c}{d} + x \right)}}{2 c d^{4} + 2 d^{5} x} - \frac{4 C c^{2} d}{2 c d^{4} + 2 d^{5} x} - \frac{4 C c d^{2} x \log{\left(\frac{c}{d} + x \right)}}{2 c d^{4} + 2 d^{5} x} + \frac{2 C d^{3} x^{2}}{2 c d^{4} + 2 d^{5} x} + \frac{6 D c^{3} \log{\left(\frac{c}{d} + x \right)}}{2 c d^{4} + 2 d^{5} x} + \frac{6 D c^{3}}{2 c d^{4} + 2 d^{5} x} + \frac{6 D c^{2} d x \log{\left(\frac{c}{d} + x \right)}}{2 c d^{4} + 2 d^{5} x} - \frac{3 D c d^{2} x^{2}}{2 c d^{4} + 2 d^{5} x} + \frac{D d^{3} x^{3}}{2 c d^{4} + 2 d^{5} x} & \text{for}\: n = -2 \\\frac{A \log{\left(\frac{c}{d} + x \right)}}{d} - \frac{B c \log{\left(\frac{c}{d} + x \right)}}{d^{2}} + \frac{B x}{d} + \frac{C c^{2} \log{\left(\frac{c}{d} + x \right)}}{d^{3}} - \frac{C c x}{d^{2}} + \frac{C x^{2}}{2 d} - \frac{D c^{3} \log{\left(\frac{c}{d} + x \right)}}{d^{4}} + \frac{D c^{2} x}{d^{3}} - \frac{D c x^{2}}{2 d^{2}} + \frac{D x^{3}}{3 d} & \text{for}\: n = -1 \\\frac{A c d^{3} n^{3} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{9 A c d^{3} n^{2} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{26 A c d^{3} n \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{24 A c d^{3} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{A d^{4} n^{3} x \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{9 A d^{4} n^{2} x \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{26 A d^{4} n x \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{24 A d^{4} x \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} - \frac{B c^{2} d^{2} n^{2} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} - \frac{7 B c^{2} d^{2} n \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} - \frac{12 B c^{2} d^{2} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{B c d^{3} n^{3} x \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{7 B c d^{3} n^{2} x \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{12 B c d^{3} n x \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{B d^{4} n^{3} x^{2} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{8 B d^{4} n^{2} x^{2} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{19 B d^{4} n x^{2} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{12 B d^{4} x^{2} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{2 C c^{3} d n \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{8 C c^{3} d \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} - \frac{2 C c^{2} d^{2} n^{2} x \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} - \frac{8 C c^{2} d^{2} n x \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{C c d^{3} n^{3} x^{2} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{5 C c d^{3} n^{2} x^{2} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{4 C c d^{3} n x^{2} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{C d^{4} n^{3} x^{3} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{7 C d^{4} n^{2} x^{3} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{14 C d^{4} n x^{3} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{8 C d^{4} x^{3} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} - \frac{6 D c^{4} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{6 D c^{3} d n x \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} - \frac{3 D c^{2} d^{2} n^{2} x^{2} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} - \frac{3 D c^{2} d^{2} n x^{2} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{D c d^{3} n^{3} x^{3} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{3 D c d^{3} n^{2} x^{3} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{2 D c d^{3} n x^{3} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{D d^{4} n^{3} x^{4} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{6 D d^{4} n^{2} x^{4} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{11 D d^{4} n x^{4} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} + \frac{6 D d^{4} x^{4} \left(c + d x\right)^{n}}{d^{4} n^{4} + 10 d^{4} n^{3} + 35 d^{4} n^{2} + 50 d^{4} n + 24 d^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**n*(A*x + B*x**2/2 + C*x**3/3 + D*x**4/4), Eq(d, 0)), (-2*A*d**3/(6*c**3*d**4 + 18*c**2*d**5*x + 18*c*d**6*x**2 + 6*d**7*x**3) - B*c*d**2/(6*c**3*d**4 + 18*c**2*d**5*x + 18*c*d**6*x**2 + 6*d**7*x**3) - 3*B*d**3*x/(6*c**3*d**4 + 18*c**2*d**5*x + 18*c*d**6*x**2 + 6*d**7*x**3) - 2*C*c**2*d/(6*c**3*d**4 + 18*c**2*d**5*x + 18*c*d**6*x**2 + 6*d**7*x**3) - 6*C*c*d**2*x/(6*c**3*d**4 + 18*c**2*d**5*x + 18*c*d**6*x**2 + 6*d**7*x**3) - 6*C*d**3*x**2/(6*c**3*d**4 + 18*c**2*d**5*x + 18*c*d**6*x**2 + 6*d**7*x**3) + 6*D*c**3*log(c/d + x)/(6*c**3*d**4 + 18*c**2*d**5*x + 18*c*d**6*x**2 + 6*d**7*x**3) + 11*D*c**3/(6*c**3*d**4 + 18*c**2*d**5*x + 18*c*d**6*x**2 + 6*d**7*x**3) + 18*D*c**2*d*x*log(c/d + x)/(6*c**3*d**4 + 18*c**2*d**5*x + 18*c*d**6*x**2 + 6*d**7*x**3) + 27*D*c**2*d*x/(6*c**3*d**4 + 18*c**2*d**5*x + 18*c*d**6*x**2 + 6*d**7*x**3) + 18*D*c*d**2*x**2*log(c/d + x)/(6*c**3*d**4 + 18*c**2*d**5*x + 18*c*d**6*x**2 + 6*d**7*x**3) + 18*D*c*d**2*x**2/(6*c**3*d**4 + 18*c**2*d**5*x + 18*c*d**6*x**2 + 6*d**7*x**3) + 6*D*d**3*x**3*log(c/d + x)/(6*c**3*d**4 + 18*c**2*d**5*x + 18*c*d**6*x**2 + 6*d**7*x**3), Eq(n, -4)), (-A*d**3/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2) - B*c*d**2/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2) - 2*B*d**3*x/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2) + 2*C*c**2*d*log(c/d + x)/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2) + 3*C*c**2*d/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2) + 4*C*c*d**2*x*log(c/d + x)/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2) + 4*C*c*d**2*x/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2) + 2*C*d**3*x**2*log(c/d + x)/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2) - 6*D*c**3*log(c/d + x)/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2) - 9*D*c**3/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2) - 12*D*c**2*d*x*log(c/d + x)/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2) - 12*D*c**2*d*x/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2) - 6*D*c*d**2*x**2*log(c/d + x)/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2) + 2*D*d**3*x**3/(2*c**2*d**4 + 4*c*d**5*x + 2*d**6*x**2), Eq(n, -3)), (-2*A*d**3/(2*c*d**4 + 2*d**5*x) + 2*B*c*d**2*log(c/d + x)/(2*c*d**4 + 2*d**5*x) + 2*B*c*d**2/(2*c*d**4 + 2*d**5*x) + 2*B*d**3*x*log(c/d + x)/(2*c*d**4 + 2*d**5*x) - 4*C*c**2*d*log(c/d + x)/(2*c*d**4 + 2*d**5*x) - 4*C*c**2*d/(2*c*d**4 + 2*d**5*x) - 4*C*c*d**2*x*log(c/d + x)/(2*c*d**4 + 2*d**5*x) + 2*C*d**3*x**2/(2*c*d**4 + 2*d**5*x) + 6*D*c**3*log(c/d + x)/(2*c*d**4 + 2*d**5*x) + 6*D*c**3/(2*c*d**4 + 2*d**5*x) + 6*D*c**2*d*x*log(c/d + x)/(2*c*d**4 + 2*d**5*x) - 3*D*c*d**2*x**2/(2*c*d**4 + 2*d**5*x) + D*d**3*x**3/(2*c*d**4 + 2*d**5*x), Eq(n, -2)), (A*log(c/d + x)/d - B*c*log(c/d + x)/d**2 + B*x/d + C*c**2*log(c/d + x)/d**3 - C*c*x/d**2 + C*x**2/(2*d) - D*c**3*log(c/d + x)/d**4 + D*c**2*x/d**3 - D*c*x**2/(2*d**2) + D*x**3/(3*d), Eq(n, -1)), (A*c*d**3*n**3*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 9*A*c*d**3*n**2*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 26*A*c*d**3*n*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 24*A*c*d**3*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + A*d**4*n**3*x*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 9*A*d**4*n**2*x*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 26*A*d**4*n*x*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 24*A*d**4*x*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) - B*c**2*d**2*n**2*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) - 7*B*c**2*d**2*n*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) - 12*B*c**2*d**2*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + B*c*d**3*n**3*x*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 7*B*c*d**3*n**2*x*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 12*B*c*d**3*n*x*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + B*d**4*n**3*x**2*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 8*B*d**4*n**2*x**2*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 19*B*d**4*n*x**2*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 12*B*d**4*x**2*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 2*C*c**3*d*n*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 8*C*c**3*d*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) - 2*C*c**2*d**2*n**2*x*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) - 8*C*c**2*d**2*n*x*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + C*c*d**3*n**3*x**2*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 5*C*c*d**3*n**2*x**2*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 4*C*c*d**3*n*x**2*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + C*d**4*n**3*x**3*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 7*C*d**4*n**2*x**3*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 14*C*d**4*n*x**3*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 8*C*d**4*x**3*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) - 6*D*c**4*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 6*D*c**3*d*n*x*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) - 3*D*c**2*d**2*n**2*x**2*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) - 3*D*c**2*d**2*n*x**2*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + D*c*d**3*n**3*x**3*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 3*D*c*d**3*n**2*x**3*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 2*D*c*d**3*n*x**3*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + D*d**4*n**3*x**4*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 6*D*d**4*n**2*x**4*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 11*D*d**4*n*x**4*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4) + 6*D*d**4*x**4*(c + d*x)**n/(d**4*n**4 + 10*d**4*n**3 + 35*d**4*n**2 + 50*d**4*n + 24*d**4), True))","A",0
29,0,0,0,0.000000," ","integrate((d*x+c)**n*(D*x**3+C*x**2+B*x+A)/(b*x+a),x)","\int \frac{\left(c + d x\right)^{n} \left(A + B x + C x^{2} + D x^{3}\right)}{a + b x}\, dx"," ",0,"Integral((c + d*x)**n*(A + B*x + C*x**2 + D*x**3)/(a + b*x), x)","F",0
30,-2,0,0,0.000000," ","integrate((d*x+c)**n*(D*x**3+C*x**2+B*x+A)/(b*x+a)**2,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
31,0,0,0,0.000000," ","integrate((d*x+c)**n*(D*x**3+C*x**2+B*x+A)/(b*x+a)**3,x)","\int \frac{\left(c + d x\right)^{n} \left(A + B x + C x^{2} + D x^{3}\right)}{\left(a + b x\right)^{3}}\, dx"," ",0,"Integral((c + d*x)**n*(A + B*x + C*x**2 + D*x**3)/(a + b*x)**3, x)","F",0
32,-2,0,0,0.000000," ","integrate((b*x+a)**m*(B*x+A)*(d*x+c)**n,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
33,-2,0,0,0.000000," ","integrate((b*x+a)**m*(d*x+c)**n*(C*x**2+B*x+A),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
34,-2,0,0,0.000000," ","integrate((b*x+a)**m*(d*x+c)**n*(D*x**3+C*x**2+B*x+A),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
