1,1,668,0,1.102634," ","integrate((b*x+a)^3*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3465 \, D b^{3} d^{6} x^{6} + 15360 \, D b^{3} c^{6} + 45045 \, A a^{3} d^{6} + 24024 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} c^{2} d^{4} - 30030 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c d^{5} - 315 \, {\left(12 \, D b^{3} c d^{5} - 13 \, {\left(3 \, D a b^{2} + C b^{3}\right)} d^{6}\right)} x^{5} + 35 \, {\left(120 \, D b^{3} c^{2} d^{4} + 143 \, {\left(3 \, D a^{2} b + 3 \, C a b^{2} + B b^{3}\right)} d^{6} - 130 \, {\left(3 \, D a b^{2} c + C b^{3} c\right)} d^{5}\right)} x^{4} - 20592 \, {\left(D a^{3} c^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c^{3}\right)} d^{3} - 5 \, {\left(960 \, D b^{3} c^{3} d^{3} - 1287 \, {\left(D a^{3} + 3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} d^{6} + 1144 \, {\left(3 \, D a^{2} b c + {\left(3 \, C a b^{2} + B b^{3}\right)} c\right)} d^{5} - 1040 \, {\left(3 \, D a b^{2} c^{2} + C b^{3} c^{2}\right)} d^{4}\right)} x^{3} + 18304 \, {\left(3 \, D a^{2} b c^{4} + {\left(3 \, C a b^{2} + B b^{3}\right)} c^{4}\right)} d^{2} + 3 \, {\left(1920 \, D b^{3} c^{4} d^{2} + 3003 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} d^{6} - 2574 \, {\left(D a^{3} c + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c\right)} d^{5} + 2288 \, {\left(3 \, D a^{2} b c^{2} + {\left(3 \, C a b^{2} + B b^{3}\right)} c^{2}\right)} d^{4} - 2080 \, {\left(3 \, D a b^{2} c^{3} + C b^{3} c^{3}\right)} d^{3}\right)} x^{2} - 16640 \, {\left(3 \, D a b^{2} c^{5} + C b^{3} c^{5}\right)} d - {\left(7680 \, D b^{3} c^{5} d + 12012 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} c d^{5} - 15015 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{6} - 10296 \, {\left(D a^{3} c^{2} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c^{2}\right)} d^{4} + 9152 \, {\left(3 \, D a^{2} b c^{3} + {\left(3 \, C a b^{2} + B b^{3}\right)} c^{3}\right)} d^{3} - 8320 \, {\left(3 \, D a b^{2} c^{4} + C b^{3} c^{4}\right)} d^{2}\right)} x\right)} \sqrt{d x + c}}{45045 \, d^{7}}"," ",0,"2/45045*(3465*D*b^3*d^6*x^6 + 15360*D*b^3*c^6 + 45045*A*a^3*d^6 + 24024*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*c^2*d^4 - 30030*(B*a^3 + 3*A*a^2*b)*c*d^5 - 315*(12*D*b^3*c*d^5 - 13*(3*D*a*b^2 + C*b^3)*d^6)*x^5 + 35*(120*D*b^3*c^2*d^4 + 143*(3*D*a^2*b + 3*C*a*b^2 + B*b^3)*d^6 - 130*(3*D*a*b^2*c + C*b^3*c)*d^5)*x^4 - 20592*(D*a^3*c^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c^3)*d^3 - 5*(960*D*b^3*c^3*d^3 - 1287*(D*a^3 + 3*C*a^2*b + 3*B*a*b^2 + A*b^3)*d^6 + 1144*(3*D*a^2*b*c + (3*C*a*b^2 + B*b^3)*c)*d^5 - 1040*(3*D*a*b^2*c^2 + C*b^3*c^2)*d^4)*x^3 + 18304*(3*D*a^2*b*c^4 + (3*C*a*b^2 + B*b^3)*c^4)*d^2 + 3*(1920*D*b^3*c^4*d^2 + 3003*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*d^6 - 2574*(D*a^3*c + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c)*d^5 + 2288*(3*D*a^2*b*c^2 + (3*C*a*b^2 + B*b^3)*c^2)*d^4 - 2080*(3*D*a*b^2*c^3 + C*b^3*c^3)*d^3)*x^2 - 16640*(3*D*a*b^2*c^5 + C*b^3*c^5)*d - (7680*D*b^3*c^5*d + 12012*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*c*d^5 - 15015*(B*a^3 + 3*A*a^2*b)*d^6 - 10296*(D*a^3*c^2 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c^2)*d^4 + 9152*(3*D*a^2*b*c^3 + (3*C*a*b^2 + B*b^3)*c^3)*d^3 - 8320*(3*D*a*b^2*c^4 + C*b^3*c^4)*d^2)*x)*sqrt(d*x + c)/d^7","A",0
2,1,410,0,0.614261," ","integrate((b*x+a)^2*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, D b^{2} d^{5} x^{5} - 1280 \, D b^{2} c^{5} + 3465 \, A a^{2} d^{5} + 1848 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{2} d^{3} - 2310 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{4} - 35 \, {\left(10 \, D b^{2} c d^{4} - 11 \, {\left(2 \, D a b + C b^{2}\right)} d^{5}\right)} x^{4} + 5 \, {\left(80 \, D b^{2} c^{2} d^{3} + 99 \, {\left(D a^{2} + 2 \, C a b + B b^{2}\right)} d^{5} - 88 \, {\left(2 \, D a b c + C b^{2} c\right)} d^{4}\right)} x^{3} - 1584 \, {\left(D a^{2} c^{3} + {\left(2 \, C a b + B b^{2}\right)} c^{3}\right)} d^{2} - 3 \, {\left(160 \, D b^{2} c^{3} d^{2} - 231 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{5} + 198 \, {\left(D a^{2} c + {\left(2 \, C a b + B b^{2}\right)} c\right)} d^{4} - 176 \, {\left(2 \, D a b c^{2} + C b^{2} c^{2}\right)} d^{3}\right)} x^{2} + 1408 \, {\left(2 \, D a b c^{4} + C b^{2} c^{4}\right)} d + {\left(640 \, D b^{2} c^{4} d - 924 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c d^{4} + 1155 \, {\left(B a^{2} + 2 \, A a b\right)} d^{5} + 792 \, {\left(D a^{2} c^{2} + {\left(2 \, C a b + B b^{2}\right)} c^{2}\right)} d^{3} - 704 \, {\left(2 \, D a b c^{3} + C b^{2} c^{3}\right)} d^{2}\right)} x\right)} \sqrt{d x + c}}{3465 \, d^{6}}"," ",0,"2/3465*(315*D*b^2*d^5*x^5 - 1280*D*b^2*c^5 + 3465*A*a^2*d^5 + 1848*(C*a^2 + 2*B*a*b + A*b^2)*c^2*d^3 - 2310*(B*a^2 + 2*A*a*b)*c*d^4 - 35*(10*D*b^2*c*d^4 - 11*(2*D*a*b + C*b^2)*d^5)*x^4 + 5*(80*D*b^2*c^2*d^3 + 99*(D*a^2 + 2*C*a*b + B*b^2)*d^5 - 88*(2*D*a*b*c + C*b^2*c)*d^4)*x^3 - 1584*(D*a^2*c^3 + (2*C*a*b + B*b^2)*c^3)*d^2 - 3*(160*D*b^2*c^3*d^2 - 231*(C*a^2 + 2*B*a*b + A*b^2)*d^5 + 198*(D*a^2*c + (2*C*a*b + B*b^2)*c)*d^4 - 176*(2*D*a*b*c^2 + C*b^2*c^2)*d^3)*x^2 + 1408*(2*D*a*b*c^4 + C*b^2*c^4)*d + (640*D*b^2*c^4*d - 924*(C*a^2 + 2*B*a*b + A*b^2)*c*d^4 + 1155*(B*a^2 + 2*A*a*b)*d^5 + 792*(D*a^2*c^2 + (2*C*a*b + B*b^2)*c^2)*d^3 - 704*(2*D*a*b*c^3 + C*b^2*c^3)*d^2)*x)*sqrt(d*x + c)/d^6","A",0
3,1,204,0,0.577588," ","integrate((b*x+a)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, D b d^{4} x^{4} + 128 \, D b c^{4} + 315 \, A a d^{4} + 168 \, {\left(C a + B b\right)} c^{2} d^{2} - 210 \, {\left(B a + A b\right)} c d^{3} - 5 \, {\left(8 \, D b c d^{3} - 9 \, {\left(D a + C b\right)} d^{4}\right)} x^{3} + 3 \, {\left(16 \, D b c^{2} d^{2} + 21 \, {\left(C a + B b\right)} d^{4} - 18 \, {\left(D a c + C b c\right)} d^{3}\right)} x^{2} - 144 \, {\left(D a c^{3} + C b c^{3}\right)} d - {\left(64 \, D b c^{3} d + 84 \, {\left(C a + B b\right)} c d^{3} - 105 \, {\left(B a + A b\right)} d^{4} - 72 \, {\left(D a c^{2} + C b c^{2}\right)} d^{2}\right)} x\right)} \sqrt{d x + c}}{315 \, d^{5}}"," ",0,"2/315*(35*D*b*d^4*x^4 + 128*D*b*c^4 + 315*A*a*d^4 + 168*(C*a + B*b)*c^2*d^2 - 210*(B*a + A*b)*c*d^3 - 5*(8*D*b*c*d^3 - 9*(D*a + C*b)*d^4)*x^3 + 3*(16*D*b*c^2*d^2 + 21*(C*a + B*b)*d^4 - 18*(D*a*c + C*b*c)*d^3)*x^2 - 144*(D*a*c^3 + C*b*c^3)*d - (64*D*b*c^3*d + 84*(C*a + B*b)*c*d^3 - 105*(B*a + A*b)*d^4 - 72*(D*a*c^2 + C*b*c^2)*d^2)*x)*sqrt(d*x + c)/d^5","A",0
4,1,90,0,0.978714," ","integrate((D*x^3+C*x^2+B*x+A)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, D d^{3} x^{3} - 48 \, D c^{3} + 56 \, C c^{2} d - 70 \, B c d^{2} + 105 \, A d^{3} - 3 \, {\left(6 \, D c d^{2} - 7 \, C d^{3}\right)} x^{2} + {\left(24 \, D c^{2} d - 28 \, C c d^{2} + 35 \, B d^{3}\right)} x\right)} \sqrt{d x + c}}{105 \, d^{4}}"," ",0,"2/105*(15*D*d^3*x^3 - 48*D*c^3 + 56*C*c^2*d - 70*B*c*d^2 + 105*A*d^3 - 3*(6*D*c*d^2 - 7*C*d^3)*x^2 + (24*D*c^2*d - 28*C*c*d^2 + 35*B*d^3)*x)*sqrt(d*x + c)/d^4","A",0
5,1,565,0,0.800265," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x+a)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(D a^{3} - C a^{2} b + B a b^{2} - A b^{3}\right)} \sqrt{b^{2} c - a b d} d^{3} \log\left(\frac{b d x + 2 \, b c - a d + 2 \, \sqrt{b^{2} c - a b d} \sqrt{d x + c}}{b x + a}\right) + 2 \, {\left(8 \, D b^{4} c^{3} - 15 \, {\left(D a^{3} b - C a^{2} b^{2} + B a b^{3}\right)} d^{3} + 5 \, {\left(D a^{2} b^{2} c - {\left(C a b^{3} - 3 \, B b^{4}\right)} c\right)} d^{2} + 3 \, {\left(D b^{4} c d^{2} - D a b^{3} d^{3}\right)} x^{2} + 2 \, {\left(D a b^{3} c^{2} - 5 \, C b^{4} c^{2}\right)} d - {\left(4 \, D b^{4} c^{2} d - 5 \, {\left(D a^{2} b^{2} - C a b^{3}\right)} d^{3} + {\left(D a b^{3} c - 5 \, C b^{4} c\right)} d^{2}\right)} x\right)} \sqrt{d x + c}}{15 \, {\left(b^{5} c d^{3} - a b^{4} d^{4}\right)}}, -\frac{2 \, {\left(15 \, {\left(D a^{3} - C a^{2} b + B a b^{2} - A b^{3}\right)} \sqrt{-b^{2} c + a b d} d^{3} \arctan\left(\frac{\sqrt{-b^{2} c + a b d} \sqrt{d x + c}}{b d x + b c}\right) - {\left(8 \, D b^{4} c^{3} - 15 \, {\left(D a^{3} b - C a^{2} b^{2} + B a b^{3}\right)} d^{3} + 5 \, {\left(D a^{2} b^{2} c - {\left(C a b^{3} - 3 \, B b^{4}\right)} c\right)} d^{2} + 3 \, {\left(D b^{4} c d^{2} - D a b^{3} d^{3}\right)} x^{2} + 2 \, {\left(D a b^{3} c^{2} - 5 \, C b^{4} c^{2}\right)} d - {\left(4 \, D b^{4} c^{2} d - 5 \, {\left(D a^{2} b^{2} - C a b^{3}\right)} d^{3} + {\left(D a b^{3} c - 5 \, C b^{4} c\right)} d^{2}\right)} x\right)} \sqrt{d x + c}\right)}}{15 \, {\left(b^{5} c d^{3} - a b^{4} d^{4}\right)}}\right]"," ",0,"[1/15*(15*(D*a^3 - C*a^2*b + B*a*b^2 - A*b^3)*sqrt(b^2*c - a*b*d)*d^3*log((b*d*x + 2*b*c - a*d + 2*sqrt(b^2*c - a*b*d)*sqrt(d*x + c))/(b*x + a)) + 2*(8*D*b^4*c^3 - 15*(D*a^3*b - C*a^2*b^2 + B*a*b^3)*d^3 + 5*(D*a^2*b^2*c - (C*a*b^3 - 3*B*b^4)*c)*d^2 + 3*(D*b^4*c*d^2 - D*a*b^3*d^3)*x^2 + 2*(D*a*b^3*c^2 - 5*C*b^4*c^2)*d - (4*D*b^4*c^2*d - 5*(D*a^2*b^2 - C*a*b^3)*d^3 + (D*a*b^3*c - 5*C*b^4*c)*d^2)*x)*sqrt(d*x + c))/(b^5*c*d^3 - a*b^4*d^4), -2/15*(15*(D*a^3 - C*a^2*b + B*a*b^2 - A*b^3)*sqrt(-b^2*c + a*b*d)*d^3*arctan(sqrt(-b^2*c + a*b*d)*sqrt(d*x + c)/(b*d*x + b*c)) - (8*D*b^4*c^3 - 15*(D*a^3*b - C*a^2*b^2 + B*a*b^3)*d^3 + 5*(D*a^2*b^2*c - (C*a*b^3 - 3*B*b^4)*c)*d^2 + 3*(D*b^4*c*d^2 - D*a*b^3*d^3)*x^2 + 2*(D*a*b^3*c^2 - 5*C*b^4*c^2)*d - (4*D*b^4*c^2*d - 5*(D*a^2*b^2 - C*a*b^3)*d^3 + (D*a*b^3*c - 5*C*b^4*c)*d^2)*x)*sqrt(d*x + c))/(b^5*c*d^3 - a*b^4*d^4)]","A",0
6,1,1004,0,0.739142," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x+a)^2/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(5 \, D a^{4} - 3 \, C a^{3} b + B a^{2} b^{2} + A a b^{3}\right)} d^{3} - 2 \, {\left(3 \, D a^{3} b c - {\left(2 \, C a^{2} b^{2} - B a b^{3}\right)} c\right)} d^{2} + {\left({\left(5 \, D a^{3} b - 3 \, C a^{2} b^{2} + B a b^{3} + A b^{4}\right)} d^{3} - 2 \, {\left(3 \, D a^{2} b^{2} c - {\left(2 \, C a b^{3} - B b^{4}\right)} c\right)} d^{2}\right)} x\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, \sqrt{b^{2} c - a b d} \sqrt{d x + c}}{b x + a}\right) + 2 \, {\left(4 \, D a b^{4} c^{3} + 3 \, {\left(5 \, D a^{4} b - 3 \, C a^{3} b^{2} + B a^{2} b^{3} - A a b^{4}\right)} d^{3} - {\left(23 \, D a^{3} b^{2} c - 3 \, {\left(5 \, C a^{2} b^{3} - B a b^{4} + A b^{5}\right)} c\right)} d^{2} - 2 \, {\left(D b^{5} c^{2} d - 2 \, D a b^{4} c d^{2} + D a^{2} b^{3} d^{3}\right)} x^{2} + 2 \, {\left(2 \, D a^{2} b^{3} c^{2} - 3 \, C a b^{4} c^{2}\right)} d + 2 \, {\left(2 \, D b^{5} c^{3} + {\left(5 \, D a^{3} b^{2} - 3 \, C a^{2} b^{3}\right)} d^{3} - 2 \, {\left(4 \, D a^{2} b^{3} c - 3 \, C a b^{4} c\right)} d^{2} + {\left(D a b^{4} c^{2} - 3 \, C b^{5} c^{2}\right)} d\right)} x\right)} \sqrt{d x + c}}{6 \, {\left(a b^{6} c^{2} d^{2} - 2 \, a^{2} b^{5} c d^{3} + a^{3} b^{4} d^{4} + {\left(b^{7} c^{2} d^{2} - 2 \, a b^{6} c d^{3} + a^{2} b^{5} d^{4}\right)} x\right)}}, -\frac{3 \, {\left({\left(5 \, D a^{4} - 3 \, C a^{3} b + B a^{2} b^{2} + A a b^{3}\right)} d^{3} - 2 \, {\left(3 \, D a^{3} b c - {\left(2 \, C a^{2} b^{2} - B a b^{3}\right)} c\right)} d^{2} + {\left({\left(5 \, D a^{3} b - 3 \, C a^{2} b^{2} + B a b^{3} + A b^{4}\right)} d^{3} - 2 \, {\left(3 \, D a^{2} b^{2} c - {\left(2 \, C a b^{3} - B b^{4}\right)} c\right)} d^{2}\right)} x\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{-b^{2} c + a b d} \sqrt{d x + c}}{b d x + b c}\right) + {\left(4 \, D a b^{4} c^{3} + 3 \, {\left(5 \, D a^{4} b - 3 \, C a^{3} b^{2} + B a^{2} b^{3} - A a b^{4}\right)} d^{3} - {\left(23 \, D a^{3} b^{2} c - 3 \, {\left(5 \, C a^{2} b^{3} - B a b^{4} + A b^{5}\right)} c\right)} d^{2} - 2 \, {\left(D b^{5} c^{2} d - 2 \, D a b^{4} c d^{2} + D a^{2} b^{3} d^{3}\right)} x^{2} + 2 \, {\left(2 \, D a^{2} b^{3} c^{2} - 3 \, C a b^{4} c^{2}\right)} d + 2 \, {\left(2 \, D b^{5} c^{3} + {\left(5 \, D a^{3} b^{2} - 3 \, C a^{2} b^{3}\right)} d^{3} - 2 \, {\left(4 \, D a^{2} b^{3} c - 3 \, C a b^{4} c\right)} d^{2} + {\left(D a b^{4} c^{2} - 3 \, C b^{5} c^{2}\right)} d\right)} x\right)} \sqrt{d x + c}}{3 \, {\left(a b^{6} c^{2} d^{2} - 2 \, a^{2} b^{5} c d^{3} + a^{3} b^{4} d^{4} + {\left(b^{7} c^{2} d^{2} - 2 \, a b^{6} c d^{3} + a^{2} b^{5} d^{4}\right)} x\right)}}\right]"," ",0,"[-1/6*(3*((5*D*a^4 - 3*C*a^3*b + B*a^2*b^2 + A*a*b^3)*d^3 - 2*(3*D*a^3*b*c - (2*C*a^2*b^2 - B*a*b^3)*c)*d^2 + ((5*D*a^3*b - 3*C*a^2*b^2 + B*a*b^3 + A*b^4)*d^3 - 2*(3*D*a^2*b^2*c - (2*C*a*b^3 - B*b^4)*c)*d^2)*x)*sqrt(b^2*c - a*b*d)*log((b*d*x + 2*b*c - a*d - 2*sqrt(b^2*c - a*b*d)*sqrt(d*x + c))/(b*x + a)) + 2*(4*D*a*b^4*c^3 + 3*(5*D*a^4*b - 3*C*a^3*b^2 + B*a^2*b^3 - A*a*b^4)*d^3 - (23*D*a^3*b^2*c - 3*(5*C*a^2*b^3 - B*a*b^4 + A*b^5)*c)*d^2 - 2*(D*b^5*c^2*d - 2*D*a*b^4*c*d^2 + D*a^2*b^3*d^3)*x^2 + 2*(2*D*a^2*b^3*c^2 - 3*C*a*b^4*c^2)*d + 2*(2*D*b^5*c^3 + (5*D*a^3*b^2 - 3*C*a^2*b^3)*d^3 - 2*(4*D*a^2*b^3*c - 3*C*a*b^4*c)*d^2 + (D*a*b^4*c^2 - 3*C*b^5*c^2)*d)*x)*sqrt(d*x + c))/(a*b^6*c^2*d^2 - 2*a^2*b^5*c*d^3 + a^3*b^4*d^4 + (b^7*c^2*d^2 - 2*a*b^6*c*d^3 + a^2*b^5*d^4)*x), -1/3*(3*((5*D*a^4 - 3*C*a^3*b + B*a^2*b^2 + A*a*b^3)*d^3 - 2*(3*D*a^3*b*c - (2*C*a^2*b^2 - B*a*b^3)*c)*d^2 + ((5*D*a^3*b - 3*C*a^2*b^2 + B*a*b^3 + A*b^4)*d^3 - 2*(3*D*a^2*b^2*c - (2*C*a*b^3 - B*b^4)*c)*d^2)*x)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(-b^2*c + a*b*d)*sqrt(d*x + c)/(b*d*x + b*c)) + (4*D*a*b^4*c^3 + 3*(5*D*a^4*b - 3*C*a^3*b^2 + B*a^2*b^3 - A*a*b^4)*d^3 - (23*D*a^3*b^2*c - 3*(5*C*a^2*b^3 - B*a*b^4 + A*b^5)*c)*d^2 - 2*(D*b^5*c^2*d - 2*D*a*b^4*c*d^2 + D*a^2*b^3*d^3)*x^2 + 2*(2*D*a^2*b^3*c^2 - 3*C*a*b^4*c^2)*d + 2*(2*D*b^5*c^3 + (5*D*a^3*b^2 - 3*C*a^2*b^3)*d^3 - 2*(4*D*a^2*b^3*c - 3*C*a*b^4*c)*d^2 + (D*a*b^4*c^2 - 3*C*b^5*c^2)*d)*x)*sqrt(d*x + c))/(a*b^6*c^2*d^2 - 2*a^2*b^5*c*d^3 + a^3*b^4*d^4 + (b^7*c^2*d^2 - 2*a*b^6*c*d^3 + a^2*b^5*d^4)*x)]","B",0
7,1,1661,0,0.859361," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x+a)^3/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(15 \, D a^{5} - 3 \, C a^{4} b - B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} d^{3} - 4 \, {\left(9 \, D a^{4} b c - {\left(2 \, C a^{3} b^{2} + B a^{2} b^{3}\right)} c\right)} d^{2} + {\left({\left(15 \, D a^{3} b^{2} - 3 \, C a^{2} b^{3} - B a b^{4} - 3 \, A b^{5}\right)} d^{3} - 4 \, {\left(9 \, D a^{2} b^{3} c - {\left(2 \, C a b^{4} + B b^{5}\right)} c\right)} d^{2} + 8 \, {\left(3 \, D a b^{4} c^{2} - C b^{5} c^{2}\right)} d\right)} x^{2} + 8 \, {\left(3 \, D a^{3} b^{2} c^{2} - C a^{2} b^{3} c^{2}\right)} d + 2 \, {\left({\left(15 \, D a^{4} b - 3 \, C a^{3} b^{2} - B a^{2} b^{3} - 3 \, A a b^{4}\right)} d^{3} - 4 \, {\left(9 \, D a^{3} b^{2} c - {\left(2 \, C a^{2} b^{3} + B a b^{4}\right)} c\right)} d^{2} + 8 \, {\left(3 \, D a^{2} b^{3} c^{2} - C a b^{4} c^{2}\right)} d\right)} x\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x + 2 \, b c - a d + 2 \, \sqrt{b^{2} c - a b d} \sqrt{d x + c}}{b x + a}\right) + 2 \, {\left(8 \, D a^{2} b^{4} c^{3} - {\left(15 \, D a^{5} b - 3 \, C a^{4} b^{2} - B a^{3} b^{3} + 5 \, A a^{2} b^{4}\right)} d^{3} + {\left(41 \, D a^{4} b^{2} c - {\left(9 \, C a^{3} b^{3} - B a^{2} b^{4} - 7 \, A a b^{5}\right)} c\right)} d^{2} + 8 \, {\left(D b^{6} c^{3} - 3 \, D a b^{5} c^{2} d + 3 \, D a^{2} b^{4} c d^{2} - D a^{3} b^{3} d^{3}\right)} x^{2} - 2 \, {\left(17 \, D a^{3} b^{3} c^{2} - {\left(3 \, C a^{2} b^{4} - B a b^{5} - A b^{6}\right)} c^{2}\right)} d + {\left(16 \, D a b^{5} c^{3} - {\left(25 \, D a^{4} b^{2} - 5 \, C a^{3} b^{3} + B a^{2} b^{4} + 3 \, A a b^{5}\right)} d^{3} + {\left(69 \, D a^{3} b^{3} c - {\left(13 \, C a^{2} b^{4} - 5 \, B a b^{5} - 3 \, A b^{6}\right)} c\right)} d^{2} - 4 \, {\left(15 \, D a^{2} b^{4} c^{2} - {\left(2 \, C a b^{5} - B b^{6}\right)} c^{2}\right)} d\right)} x\right)} \sqrt{d x + c}}{8 \, {\left(a^{2} b^{7} c^{3} d - 3 \, a^{3} b^{6} c^{2} d^{2} + 3 \, a^{4} b^{5} c d^{3} - a^{5} b^{4} d^{4} + {\left(b^{9} c^{3} d - 3 \, a b^{8} c^{2} d^{2} + 3 \, a^{2} b^{7} c d^{3} - a^{3} b^{6} d^{4}\right)} x^{2} + 2 \, {\left(a b^{8} c^{3} d - 3 \, a^{2} b^{7} c^{2} d^{2} + 3 \, a^{3} b^{6} c d^{3} - a^{4} b^{5} d^{4}\right)} x\right)}}, -\frac{{\left({\left(15 \, D a^{5} - 3 \, C a^{4} b - B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} d^{3} - 4 \, {\left(9 \, D a^{4} b c - {\left(2 \, C a^{3} b^{2} + B a^{2} b^{3}\right)} c\right)} d^{2} + {\left({\left(15 \, D a^{3} b^{2} - 3 \, C a^{2} b^{3} - B a b^{4} - 3 \, A b^{5}\right)} d^{3} - 4 \, {\left(9 \, D a^{2} b^{3} c - {\left(2 \, C a b^{4} + B b^{5}\right)} c\right)} d^{2} + 8 \, {\left(3 \, D a b^{4} c^{2} - C b^{5} c^{2}\right)} d\right)} x^{2} + 8 \, {\left(3 \, D a^{3} b^{2} c^{2} - C a^{2} b^{3} c^{2}\right)} d + 2 \, {\left({\left(15 \, D a^{4} b - 3 \, C a^{3} b^{2} - B a^{2} b^{3} - 3 \, A a b^{4}\right)} d^{3} - 4 \, {\left(9 \, D a^{3} b^{2} c - {\left(2 \, C a^{2} b^{3} + B a b^{4}\right)} c\right)} d^{2} + 8 \, {\left(3 \, D a^{2} b^{3} c^{2} - C a b^{4} c^{2}\right)} d\right)} x\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{-b^{2} c + a b d} \sqrt{d x + c}}{b d x + b c}\right) - {\left(8 \, D a^{2} b^{4} c^{3} - {\left(15 \, D a^{5} b - 3 \, C a^{4} b^{2} - B a^{3} b^{3} + 5 \, A a^{2} b^{4}\right)} d^{3} + {\left(41 \, D a^{4} b^{2} c - {\left(9 \, C a^{3} b^{3} - B a^{2} b^{4} - 7 \, A a b^{5}\right)} c\right)} d^{2} + 8 \, {\left(D b^{6} c^{3} - 3 \, D a b^{5} c^{2} d + 3 \, D a^{2} b^{4} c d^{2} - D a^{3} b^{3} d^{3}\right)} x^{2} - 2 \, {\left(17 \, D a^{3} b^{3} c^{2} - {\left(3 \, C a^{2} b^{4} - B a b^{5} - A b^{6}\right)} c^{2}\right)} d + {\left(16 \, D a b^{5} c^{3} - {\left(25 \, D a^{4} b^{2} - 5 \, C a^{3} b^{3} + B a^{2} b^{4} + 3 \, A a b^{5}\right)} d^{3} + {\left(69 \, D a^{3} b^{3} c - {\left(13 \, C a^{2} b^{4} - 5 \, B a b^{5} - 3 \, A b^{6}\right)} c\right)} d^{2} - 4 \, {\left(15 \, D a^{2} b^{4} c^{2} - {\left(2 \, C a b^{5} - B b^{6}\right)} c^{2}\right)} d\right)} x\right)} \sqrt{d x + c}}{4 \, {\left(a^{2} b^{7} c^{3} d - 3 \, a^{3} b^{6} c^{2} d^{2} + 3 \, a^{4} b^{5} c d^{3} - a^{5} b^{4} d^{4} + {\left(b^{9} c^{3} d - 3 \, a b^{8} c^{2} d^{2} + 3 \, a^{2} b^{7} c d^{3} - a^{3} b^{6} d^{4}\right)} x^{2} + 2 \, {\left(a b^{8} c^{3} d - 3 \, a^{2} b^{7} c^{2} d^{2} + 3 \, a^{3} b^{6} c d^{3} - a^{4} b^{5} d^{4}\right)} x\right)}}\right]"," ",0,"[1/8*(((15*D*a^5 - 3*C*a^4*b - B*a^3*b^2 - 3*A*a^2*b^3)*d^3 - 4*(9*D*a^4*b*c - (2*C*a^3*b^2 + B*a^2*b^3)*c)*d^2 + ((15*D*a^3*b^2 - 3*C*a^2*b^3 - B*a*b^4 - 3*A*b^5)*d^3 - 4*(9*D*a^2*b^3*c - (2*C*a*b^4 + B*b^5)*c)*d^2 + 8*(3*D*a*b^4*c^2 - C*b^5*c^2)*d)*x^2 + 8*(3*D*a^3*b^2*c^2 - C*a^2*b^3*c^2)*d + 2*((15*D*a^4*b - 3*C*a^3*b^2 - B*a^2*b^3 - 3*A*a*b^4)*d^3 - 4*(9*D*a^3*b^2*c - (2*C*a^2*b^3 + B*a*b^4)*c)*d^2 + 8*(3*D*a^2*b^3*c^2 - C*a*b^4*c^2)*d)*x)*sqrt(b^2*c - a*b*d)*log((b*d*x + 2*b*c - a*d + 2*sqrt(b^2*c - a*b*d)*sqrt(d*x + c))/(b*x + a)) + 2*(8*D*a^2*b^4*c^3 - (15*D*a^5*b - 3*C*a^4*b^2 - B*a^3*b^3 + 5*A*a^2*b^4)*d^3 + (41*D*a^4*b^2*c - (9*C*a^3*b^3 - B*a^2*b^4 - 7*A*a*b^5)*c)*d^2 + 8*(D*b^6*c^3 - 3*D*a*b^5*c^2*d + 3*D*a^2*b^4*c*d^2 - D*a^3*b^3*d^3)*x^2 - 2*(17*D*a^3*b^3*c^2 - (3*C*a^2*b^4 - B*a*b^5 - A*b^6)*c^2)*d + (16*D*a*b^5*c^3 - (25*D*a^4*b^2 - 5*C*a^3*b^3 + B*a^2*b^4 + 3*A*a*b^5)*d^3 + (69*D*a^3*b^3*c - (13*C*a^2*b^4 - 5*B*a*b^5 - 3*A*b^6)*c)*d^2 - 4*(15*D*a^2*b^4*c^2 - (2*C*a*b^5 - B*b^6)*c^2)*d)*x)*sqrt(d*x + c))/(a^2*b^7*c^3*d - 3*a^3*b^6*c^2*d^2 + 3*a^4*b^5*c*d^3 - a^5*b^4*d^4 + (b^9*c^3*d - 3*a*b^8*c^2*d^2 + 3*a^2*b^7*c*d^3 - a^3*b^6*d^4)*x^2 + 2*(a*b^8*c^3*d - 3*a^2*b^7*c^2*d^2 + 3*a^3*b^6*c*d^3 - a^4*b^5*d^4)*x), -1/4*(((15*D*a^5 - 3*C*a^4*b - B*a^3*b^2 - 3*A*a^2*b^3)*d^3 - 4*(9*D*a^4*b*c - (2*C*a^3*b^2 + B*a^2*b^3)*c)*d^2 + ((15*D*a^3*b^2 - 3*C*a^2*b^3 - B*a*b^4 - 3*A*b^5)*d^3 - 4*(9*D*a^2*b^3*c - (2*C*a*b^4 + B*b^5)*c)*d^2 + 8*(3*D*a*b^4*c^2 - C*b^5*c^2)*d)*x^2 + 8*(3*D*a^3*b^2*c^2 - C*a^2*b^3*c^2)*d + 2*((15*D*a^4*b - 3*C*a^3*b^2 - B*a^2*b^3 - 3*A*a*b^4)*d^3 - 4*(9*D*a^3*b^2*c - (2*C*a^2*b^3 + B*a*b^4)*c)*d^2 + 8*(3*D*a^2*b^3*c^2 - C*a*b^4*c^2)*d)*x)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(-b^2*c + a*b*d)*sqrt(d*x + c)/(b*d*x + b*c)) - (8*D*a^2*b^4*c^3 - (15*D*a^5*b - 3*C*a^4*b^2 - B*a^3*b^3 + 5*A*a^2*b^4)*d^3 + (41*D*a^4*b^2*c - (9*C*a^3*b^3 - B*a^2*b^4 - 7*A*a*b^5)*c)*d^2 + 8*(D*b^6*c^3 - 3*D*a*b^5*c^2*d + 3*D*a^2*b^4*c*d^2 - D*a^3*b^3*d^3)*x^2 - 2*(17*D*a^3*b^3*c^2 - (3*C*a^2*b^4 - B*a*b^5 - A*b^6)*c^2)*d + (16*D*a*b^5*c^3 - (25*D*a^4*b^2 - 5*C*a^3*b^3 + B*a^2*b^4 + 3*A*a*b^5)*d^3 + (69*D*a^3*b^3*c - (13*C*a^2*b^4 - 5*B*a*b^5 - 3*A*b^6)*c)*d^2 - 4*(15*D*a^2*b^4*c^2 - (2*C*a*b^5 - B*b^6)*c^2)*d)*x)*sqrt(d*x + c))/(a^2*b^7*c^3*d - 3*a^3*b^6*c^2*d^2 + 3*a^4*b^5*c*d^3 - a^5*b^4*d^4 + (b^9*c^3*d - 3*a*b^8*c^2*d^2 + 3*a^2*b^7*c*d^3 - a^3*b^6*d^4)*x^2 + 2*(a*b^8*c^3*d - 3*a^2*b^7*c^2*d^2 + 3*a^3*b^6*c*d^3 - a^4*b^5*d^4)*x)]","B",0
8,1,2446,0,0.933770," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x+a)^4/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(16 \, D a^{3} b^{3} c^{3} - {\left(5 \, D a^{6} + C a^{5} b + B a^{4} b^{2} + 5 \, A a^{3} b^{3}\right)} d^{3} + {\left(16 \, D b^{6} c^{3} - {\left(5 \, D a^{3} b^{3} + C a^{2} b^{4} + B a b^{5} + 5 \, A b^{6}\right)} d^{3} + 2 \, {\left(9 \, D a^{2} b^{4} c + {\left(2 \, C a b^{5} + 3 \, B b^{6}\right)} c\right)} d^{2} - 8 \, {\left(3 \, D a b^{5} c^{2} + C b^{6} c^{2}\right)} d\right)} x^{3} + 2 \, {\left(9 \, D a^{5} b c + {\left(2 \, C a^{4} b^{2} + 3 \, B a^{3} b^{3}\right)} c\right)} d^{2} + 3 \, {\left(16 \, D a b^{5} c^{3} - {\left(5 \, D a^{4} b^{2} + C a^{3} b^{3} + B a^{2} b^{4} + 5 \, A a b^{5}\right)} d^{3} + 2 \, {\left(9 \, D a^{3} b^{3} c + {\left(2 \, C a^{2} b^{4} + 3 \, B a b^{5}\right)} c\right)} d^{2} - 8 \, {\left(3 \, D a^{2} b^{4} c^{2} + C a b^{5} c^{2}\right)} d\right)} x^{2} - 8 \, {\left(3 \, D a^{4} b^{2} c^{2} + C a^{3} b^{3} c^{2}\right)} d + 3 \, {\left(16 \, D a^{2} b^{4} c^{3} - {\left(5 \, D a^{5} b + C a^{4} b^{2} + B a^{3} b^{3} + 5 \, A a^{2} b^{4}\right)} d^{3} + 2 \, {\left(9 \, D a^{4} b^{2} c + {\left(2 \, C a^{3} b^{3} + 3 \, B a^{2} b^{4}\right)} c\right)} d^{2} - 8 \, {\left(3 \, D a^{3} b^{3} c^{2} + C a^{2} b^{4} c^{2}\right)} d\right)} x\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, \sqrt{b^{2} c - a b d} \sqrt{d x + c}}{b x + a}\right) + 2 \, {\left(44 \, D a^{3} b^{4} c^{3} - 4 \, {\left(2 \, C a^{2} b^{5} + B a b^{6} + 2 \, A b^{7}\right)} c^{3} - 3 \, {\left(5 \, D a^{6} b + C a^{5} b^{2} + B a^{4} b^{3} - 11 \, A a^{3} b^{4}\right)} d^{3} + {\left(59 \, D a^{5} b^{2} c + {\left(13 \, C a^{4} b^{3} - 13 \, B a^{3} b^{4} - 59 \, A a^{2} b^{5}\right)} c\right)} d^{2} + 3 \, {\left(24 \, D a b^{6} c^{3} - 8 \, C b^{7} c^{3} - {\left(11 \, D a^{4} b^{3} - C a^{3} b^{4} - B a^{2} b^{5} - 5 \, A a b^{6}\right)} d^{3} + {\left(41 \, D a^{3} b^{4} c - {\left(5 \, C a^{2} b^{5} + 7 \, B a b^{6} + 5 \, A b^{7}\right)} c\right)} d^{2} - 6 \, {\left(9 \, D a^{2} b^{5} c^{2} - {\left(2 \, C a b^{6} + B b^{7}\right)} c^{2}\right)} d\right)} x^{2} - 2 \, {\left(44 \, D a^{4} b^{3} c^{2} + {\left(C a^{3} b^{4} - 10 \, B a^{2} b^{5} - 17 \, A a b^{6}\right)} c^{2}\right)} d + 2 \, {\left(54 \, D a^{2} b^{5} c^{3} - 6 \, {\left(2 \, C a b^{6} + B b^{7}\right)} c^{3} - 4 \, {\left(5 \, D a^{5} b^{2} + C a^{4} b^{3} - B a^{3} b^{4} - 5 \, A a^{2} b^{5}\right)} d^{3} + {\left(79 \, D a^{4} b^{3} c + {\left(11 \, C a^{3} b^{4} - 29 \, B a^{2} b^{5} - 25 \, A a b^{6}\right)} c\right)} d^{2} - {\left(113 \, D a^{3} b^{4} c^{2} - {\left(5 \, C a^{2} b^{5} + 31 \, B a b^{6} + 5 \, A b^{7}\right)} c^{2}\right)} d\right)} x\right)} \sqrt{d x + c}}{48 \, {\left(a^{3} b^{8} c^{4} - 4 \, a^{4} b^{7} c^{3} d + 6 \, a^{5} b^{6} c^{2} d^{2} - 4 \, a^{6} b^{5} c d^{3} + a^{7} b^{4} d^{4} + {\left(b^{11} c^{4} - 4 \, a b^{10} c^{3} d + 6 \, a^{2} b^{9} c^{2} d^{2} - 4 \, a^{3} b^{8} c d^{3} + a^{4} b^{7} d^{4}\right)} x^{3} + 3 \, {\left(a b^{10} c^{4} - 4 \, a^{2} b^{9} c^{3} d + 6 \, a^{3} b^{8} c^{2} d^{2} - 4 \, a^{4} b^{7} c d^{3} + a^{5} b^{6} d^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{9} c^{4} - 4 \, a^{3} b^{8} c^{3} d + 6 \, a^{4} b^{7} c^{2} d^{2} - 4 \, a^{5} b^{6} c d^{3} + a^{6} b^{5} d^{4}\right)} x\right)}}, \frac{3 \, {\left(16 \, D a^{3} b^{3} c^{3} - {\left(5 \, D a^{6} + C a^{5} b + B a^{4} b^{2} + 5 \, A a^{3} b^{3}\right)} d^{3} + {\left(16 \, D b^{6} c^{3} - {\left(5 \, D a^{3} b^{3} + C a^{2} b^{4} + B a b^{5} + 5 \, A b^{6}\right)} d^{3} + 2 \, {\left(9 \, D a^{2} b^{4} c + {\left(2 \, C a b^{5} + 3 \, B b^{6}\right)} c\right)} d^{2} - 8 \, {\left(3 \, D a b^{5} c^{2} + C b^{6} c^{2}\right)} d\right)} x^{3} + 2 \, {\left(9 \, D a^{5} b c + {\left(2 \, C a^{4} b^{2} + 3 \, B a^{3} b^{3}\right)} c\right)} d^{2} + 3 \, {\left(16 \, D a b^{5} c^{3} - {\left(5 \, D a^{4} b^{2} + C a^{3} b^{3} + B a^{2} b^{4} + 5 \, A a b^{5}\right)} d^{3} + 2 \, {\left(9 \, D a^{3} b^{3} c + {\left(2 \, C a^{2} b^{4} + 3 \, B a b^{5}\right)} c\right)} d^{2} - 8 \, {\left(3 \, D a^{2} b^{4} c^{2} + C a b^{5} c^{2}\right)} d\right)} x^{2} - 8 \, {\left(3 \, D a^{4} b^{2} c^{2} + C a^{3} b^{3} c^{2}\right)} d + 3 \, {\left(16 \, D a^{2} b^{4} c^{3} - {\left(5 \, D a^{5} b + C a^{4} b^{2} + B a^{3} b^{3} + 5 \, A a^{2} b^{4}\right)} d^{3} + 2 \, {\left(9 \, D a^{4} b^{2} c + {\left(2 \, C a^{3} b^{3} + 3 \, B a^{2} b^{4}\right)} c\right)} d^{2} - 8 \, {\left(3 \, D a^{3} b^{3} c^{2} + C a^{2} b^{4} c^{2}\right)} d\right)} x\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{-b^{2} c + a b d} \sqrt{d x + c}}{b d x + b c}\right) + {\left(44 \, D a^{3} b^{4} c^{3} - 4 \, {\left(2 \, C a^{2} b^{5} + B a b^{6} + 2 \, A b^{7}\right)} c^{3} - 3 \, {\left(5 \, D a^{6} b + C a^{5} b^{2} + B a^{4} b^{3} - 11 \, A a^{3} b^{4}\right)} d^{3} + {\left(59 \, D a^{5} b^{2} c + {\left(13 \, C a^{4} b^{3} - 13 \, B a^{3} b^{4} - 59 \, A a^{2} b^{5}\right)} c\right)} d^{2} + 3 \, {\left(24 \, D a b^{6} c^{3} - 8 \, C b^{7} c^{3} - {\left(11 \, D a^{4} b^{3} - C a^{3} b^{4} - B a^{2} b^{5} - 5 \, A a b^{6}\right)} d^{3} + {\left(41 \, D a^{3} b^{4} c - {\left(5 \, C a^{2} b^{5} + 7 \, B a b^{6} + 5 \, A b^{7}\right)} c\right)} d^{2} - 6 \, {\left(9 \, D a^{2} b^{5} c^{2} - {\left(2 \, C a b^{6} + B b^{7}\right)} c^{2}\right)} d\right)} x^{2} - 2 \, {\left(44 \, D a^{4} b^{3} c^{2} + {\left(C a^{3} b^{4} - 10 \, B a^{2} b^{5} - 17 \, A a b^{6}\right)} c^{2}\right)} d + 2 \, {\left(54 \, D a^{2} b^{5} c^{3} - 6 \, {\left(2 \, C a b^{6} + B b^{7}\right)} c^{3} - 4 \, {\left(5 \, D a^{5} b^{2} + C a^{4} b^{3} - B a^{3} b^{4} - 5 \, A a^{2} b^{5}\right)} d^{3} + {\left(79 \, D a^{4} b^{3} c + {\left(11 \, C a^{3} b^{4} - 29 \, B a^{2} b^{5} - 25 \, A a b^{6}\right)} c\right)} d^{2} - {\left(113 \, D a^{3} b^{4} c^{2} - {\left(5 \, C a^{2} b^{5} + 31 \, B a b^{6} + 5 \, A b^{7}\right)} c^{2}\right)} d\right)} x\right)} \sqrt{d x + c}}{24 \, {\left(a^{3} b^{8} c^{4} - 4 \, a^{4} b^{7} c^{3} d + 6 \, a^{5} b^{6} c^{2} d^{2} - 4 \, a^{6} b^{5} c d^{3} + a^{7} b^{4} d^{4} + {\left(b^{11} c^{4} - 4 \, a b^{10} c^{3} d + 6 \, a^{2} b^{9} c^{2} d^{2} - 4 \, a^{3} b^{8} c d^{3} + a^{4} b^{7} d^{4}\right)} x^{3} + 3 \, {\left(a b^{10} c^{4} - 4 \, a^{2} b^{9} c^{3} d + 6 \, a^{3} b^{8} c^{2} d^{2} - 4 \, a^{4} b^{7} c d^{3} + a^{5} b^{6} d^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{9} c^{4} - 4 \, a^{3} b^{8} c^{3} d + 6 \, a^{4} b^{7} c^{2} d^{2} - 4 \, a^{5} b^{6} c d^{3} + a^{6} b^{5} d^{4}\right)} x\right)}}\right]"," ",0,"[1/48*(3*(16*D*a^3*b^3*c^3 - (5*D*a^6 + C*a^5*b + B*a^4*b^2 + 5*A*a^3*b^3)*d^3 + (16*D*b^6*c^3 - (5*D*a^3*b^3 + C*a^2*b^4 + B*a*b^5 + 5*A*b^6)*d^3 + 2*(9*D*a^2*b^4*c + (2*C*a*b^5 + 3*B*b^6)*c)*d^2 - 8*(3*D*a*b^5*c^2 + C*b^6*c^2)*d)*x^3 + 2*(9*D*a^5*b*c + (2*C*a^4*b^2 + 3*B*a^3*b^3)*c)*d^2 + 3*(16*D*a*b^5*c^3 - (5*D*a^4*b^2 + C*a^3*b^3 + B*a^2*b^4 + 5*A*a*b^5)*d^3 + 2*(9*D*a^3*b^3*c + (2*C*a^2*b^4 + 3*B*a*b^5)*c)*d^2 - 8*(3*D*a^2*b^4*c^2 + C*a*b^5*c^2)*d)*x^2 - 8*(3*D*a^4*b^2*c^2 + C*a^3*b^3*c^2)*d + 3*(16*D*a^2*b^4*c^3 - (5*D*a^5*b + C*a^4*b^2 + B*a^3*b^3 + 5*A*a^2*b^4)*d^3 + 2*(9*D*a^4*b^2*c + (2*C*a^3*b^3 + 3*B*a^2*b^4)*c)*d^2 - 8*(3*D*a^3*b^3*c^2 + C*a^2*b^4*c^2)*d)*x)*sqrt(b^2*c - a*b*d)*log((b*d*x + 2*b*c - a*d - 2*sqrt(b^2*c - a*b*d)*sqrt(d*x + c))/(b*x + a)) + 2*(44*D*a^3*b^4*c^3 - 4*(2*C*a^2*b^5 + B*a*b^6 + 2*A*b^7)*c^3 - 3*(5*D*a^6*b + C*a^5*b^2 + B*a^4*b^3 - 11*A*a^3*b^4)*d^3 + (59*D*a^5*b^2*c + (13*C*a^4*b^3 - 13*B*a^3*b^4 - 59*A*a^2*b^5)*c)*d^2 + 3*(24*D*a*b^6*c^3 - 8*C*b^7*c^3 - (11*D*a^4*b^3 - C*a^3*b^4 - B*a^2*b^5 - 5*A*a*b^6)*d^3 + (41*D*a^3*b^4*c - (5*C*a^2*b^5 + 7*B*a*b^6 + 5*A*b^7)*c)*d^2 - 6*(9*D*a^2*b^5*c^2 - (2*C*a*b^6 + B*b^7)*c^2)*d)*x^2 - 2*(44*D*a^4*b^3*c^2 + (C*a^3*b^4 - 10*B*a^2*b^5 - 17*A*a*b^6)*c^2)*d + 2*(54*D*a^2*b^5*c^3 - 6*(2*C*a*b^6 + B*b^7)*c^3 - 4*(5*D*a^5*b^2 + C*a^4*b^3 - B*a^3*b^4 - 5*A*a^2*b^5)*d^3 + (79*D*a^4*b^3*c + (11*C*a^3*b^4 - 29*B*a^2*b^5 - 25*A*a*b^6)*c)*d^2 - (113*D*a^3*b^4*c^2 - (5*C*a^2*b^5 + 31*B*a*b^6 + 5*A*b^7)*c^2)*d)*x)*sqrt(d*x + c))/(a^3*b^8*c^4 - 4*a^4*b^7*c^3*d + 6*a^5*b^6*c^2*d^2 - 4*a^6*b^5*c*d^3 + a^7*b^4*d^4 + (b^11*c^4 - 4*a*b^10*c^3*d + 6*a^2*b^9*c^2*d^2 - 4*a^3*b^8*c*d^3 + a^4*b^7*d^4)*x^3 + 3*(a*b^10*c^4 - 4*a^2*b^9*c^3*d + 6*a^3*b^8*c^2*d^2 - 4*a^4*b^7*c*d^3 + a^5*b^6*d^4)*x^2 + 3*(a^2*b^9*c^4 - 4*a^3*b^8*c^3*d + 6*a^4*b^7*c^2*d^2 - 4*a^5*b^6*c*d^3 + a^6*b^5*d^4)*x), 1/24*(3*(16*D*a^3*b^3*c^3 - (5*D*a^6 + C*a^5*b + B*a^4*b^2 + 5*A*a^3*b^3)*d^3 + (16*D*b^6*c^3 - (5*D*a^3*b^3 + C*a^2*b^4 + B*a*b^5 + 5*A*b^6)*d^3 + 2*(9*D*a^2*b^4*c + (2*C*a*b^5 + 3*B*b^6)*c)*d^2 - 8*(3*D*a*b^5*c^2 + C*b^6*c^2)*d)*x^3 + 2*(9*D*a^5*b*c + (2*C*a^4*b^2 + 3*B*a^3*b^3)*c)*d^2 + 3*(16*D*a*b^5*c^3 - (5*D*a^4*b^2 + C*a^3*b^3 + B*a^2*b^4 + 5*A*a*b^5)*d^3 + 2*(9*D*a^3*b^3*c + (2*C*a^2*b^4 + 3*B*a*b^5)*c)*d^2 - 8*(3*D*a^2*b^4*c^2 + C*a*b^5*c^2)*d)*x^2 - 8*(3*D*a^4*b^2*c^2 + C*a^3*b^3*c^2)*d + 3*(16*D*a^2*b^4*c^3 - (5*D*a^5*b + C*a^4*b^2 + B*a^3*b^3 + 5*A*a^2*b^4)*d^3 + 2*(9*D*a^4*b^2*c + (2*C*a^3*b^3 + 3*B*a^2*b^4)*c)*d^2 - 8*(3*D*a^3*b^3*c^2 + C*a^2*b^4*c^2)*d)*x)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(-b^2*c + a*b*d)*sqrt(d*x + c)/(b*d*x + b*c)) + (44*D*a^3*b^4*c^3 - 4*(2*C*a^2*b^5 + B*a*b^6 + 2*A*b^7)*c^3 - 3*(5*D*a^6*b + C*a^5*b^2 + B*a^4*b^3 - 11*A*a^3*b^4)*d^3 + (59*D*a^5*b^2*c + (13*C*a^4*b^3 - 13*B*a^3*b^4 - 59*A*a^2*b^5)*c)*d^2 + 3*(24*D*a*b^6*c^3 - 8*C*b^7*c^3 - (11*D*a^4*b^3 - C*a^3*b^4 - B*a^2*b^5 - 5*A*a*b^6)*d^3 + (41*D*a^3*b^4*c - (5*C*a^2*b^5 + 7*B*a*b^6 + 5*A*b^7)*c)*d^2 - 6*(9*D*a^2*b^5*c^2 - (2*C*a*b^6 + B*b^7)*c^2)*d)*x^2 - 2*(44*D*a^4*b^3*c^2 + (C*a^3*b^4 - 10*B*a^2*b^5 - 17*A*a*b^6)*c^2)*d + 2*(54*D*a^2*b^5*c^3 - 6*(2*C*a*b^6 + B*b^7)*c^3 - 4*(5*D*a^5*b^2 + C*a^4*b^3 - B*a^3*b^4 - 5*A*a^2*b^5)*d^3 + (79*D*a^4*b^3*c + (11*C*a^3*b^4 - 29*B*a^2*b^5 - 25*A*a*b^6)*c)*d^2 - (113*D*a^3*b^4*c^2 - (5*C*a^2*b^5 + 31*B*a*b^6 + 5*A*b^7)*c^2)*d)*x)*sqrt(d*x + c))/(a^3*b^8*c^4 - 4*a^4*b^7*c^3*d + 6*a^5*b^6*c^2*d^2 - 4*a^6*b^5*c*d^3 + a^7*b^4*d^4 + (b^11*c^4 - 4*a*b^10*c^3*d + 6*a^2*b^9*c^2*d^2 - 4*a^3*b^8*c*d^3 + a^4*b^7*d^4)*x^3 + 3*(a*b^10*c^4 - 4*a^2*b^9*c^3*d + 6*a^3*b^8*c^2*d^2 - 4*a^4*b^7*c*d^3 + a^5*b^6*d^4)*x^2 + 3*(a^2*b^9*c^4 - 4*a^3*b^8*c^3*d + 6*a^4*b^7*c^2*d^2 - 4*a^5*b^6*c*d^3 + a^6*b^5*d^4)*x)]","B",0
9,1,3624,0,0.977446," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x+a)^5/(d*x+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(64 \, D a^{4} b^{3} c^{3} d - {\left(5 \, D a^{7} + 3 \, C a^{6} b + 5 \, B a^{5} b^{2} + 35 \, A a^{4} b^{3}\right)} d^{4} + {\left(64 \, D b^{7} c^{3} d - {\left(5 \, D a^{3} b^{4} + 3 \, C a^{2} b^{5} + 5 \, B a b^{6} + 35 \, A b^{7}\right)} d^{4} + 8 \, {\left(3 \, D a^{2} b^{5} c + {\left(2 \, C a b^{6} + 5 \, B b^{7}\right)} c\right)} d^{3} - 48 \, {\left(D a b^{6} c^{2} + C b^{7} c^{2}\right)} d^{2}\right)} x^{4} + 8 \, {\left(3 \, D a^{6} b c + {\left(2 \, C a^{5} b^{2} + 5 \, B a^{4} b^{3}\right)} c\right)} d^{3} + 4 \, {\left(64 \, D a b^{6} c^{3} d - {\left(5 \, D a^{4} b^{3} + 3 \, C a^{3} b^{4} + 5 \, B a^{2} b^{5} + 35 \, A a b^{6}\right)} d^{4} + 8 \, {\left(3 \, D a^{3} b^{4} c + {\left(2 \, C a^{2} b^{5} + 5 \, B a b^{6}\right)} c\right)} d^{3} - 48 \, {\left(D a^{2} b^{5} c^{2} + C a b^{6} c^{2}\right)} d^{2}\right)} x^{3} - 48 \, {\left(D a^{5} b^{2} c^{2} + C a^{4} b^{3} c^{2}\right)} d^{2} + 6 \, {\left(64 \, D a^{2} b^{5} c^{3} d - {\left(5 \, D a^{5} b^{2} + 3 \, C a^{4} b^{3} + 5 \, B a^{3} b^{4} + 35 \, A a^{2} b^{5}\right)} d^{4} + 8 \, {\left(3 \, D a^{4} b^{3} c + {\left(2 \, C a^{3} b^{4} + 5 \, B a^{2} b^{5}\right)} c\right)} d^{3} - 48 \, {\left(D a^{3} b^{4} c^{2} + C a^{2} b^{5} c^{2}\right)} d^{2}\right)} x^{2} + 4 \, {\left(64 \, D a^{3} b^{4} c^{3} d - {\left(5 \, D a^{6} b + 3 \, C a^{5} b^{2} + 5 \, B a^{4} b^{3} + 35 \, A a^{3} b^{4}\right)} d^{4} + 8 \, {\left(3 \, D a^{5} b^{2} c + {\left(2 \, C a^{4} b^{3} + 5 \, B a^{3} b^{4}\right)} c\right)} d^{3} - 48 \, {\left(D a^{4} b^{3} c^{2} + C a^{3} b^{4} c^{2}\right)} d^{2}\right)} x\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, \sqrt{b^{2} c - a b d} \sqrt{d x + c}}{b x + a}\right) + 2 \, {\left(48 \, D a^{3} b^{5} c^{4} + 16 \, {\left(C a^{2} b^{6} + B a b^{7} + 3 \, A b^{8}\right)} c^{4} - 3 \, {\left(5 \, D a^{7} b + 3 \, C a^{6} b^{2} + 5 \, B a^{5} b^{3} - 93 \, A a^{4} b^{4}\right)} d^{4} + {\left(77 \, D a^{6} b^{2} c + {\left(51 \, C a^{5} b^{3} - 131 \, B a^{4} b^{4} - 605 \, A a^{3} b^{5}\right)} c\right)} d^{3} + 3 \, {\left(64 \, D b^{8} c^{4} + {\left(5 \, D a^{4} b^{4} + 3 \, C a^{3} b^{5} + 5 \, B a^{2} b^{6} + 35 \, A a b^{7}\right)} d^{4} - {\left(29 \, D a^{3} b^{5} c + {\left(19 \, C a^{2} b^{6} + 45 \, B a b^{7} + 35 \, A b^{8}\right)} c\right)} d^{3} + 8 \, {\left(9 \, D a^{2} b^{6} c^{2} + {\left(8 \, C a b^{7} + 5 \, B b^{8}\right)} c^{2}\right)} d^{2} - 16 \, {\left(7 \, D a b^{7} c^{3} + 3 \, C b^{8} c^{3}\right)} d\right)} x^{3} - 2 \, {\left(83 \, D a^{5} b^{3} c^{2} - {\left(23 \, C a^{4} b^{4} + 109 \, B a^{3} b^{5} + 263 \, A a^{2} b^{6}\right)} c^{2}\right)} d^{2} + {\left(288 \, D a b^{7} c^{4} + 96 \, C b^{8} c^{4} - {\left(73 \, D a^{5} b^{3} - 33 \, C a^{4} b^{4} - 55 \, B a^{3} b^{5} - 385 \, A a^{2} b^{6}\right)} d^{4} + {\left(311 \, D a^{4} b^{4} c - 5 \, {\left(43 \, C a^{3} b^{5} + 101 \, B a^{2} b^{6} + 91 \, A a b^{7}\right)} c\right)} d^{3} - 2 \, {\left(215 \, D a^{3} b^{5} c^{2} - {\left(371 \, C a^{2} b^{6} + 265 \, B a b^{7} + 35 \, A b^{8}\right)} c^{2}\right)} d^{2} - 16 \, {\left(6 \, D a^{2} b^{6} c^{3} + {\left(41 \, C a b^{7} + 5 \, B b^{8}\right)} c^{3}\right)} d\right)} x^{2} + 8 \, {\left(7 \, D a^{4} b^{4} c^{3} - {\left(13 \, C a^{3} b^{5} + 11 \, B a^{2} b^{6} + 31 \, A a b^{7}\right)} c^{3}\right)} d + {\left(192 \, D a^{2} b^{6} c^{4} + 64 \, {\left(C a b^{7} + B b^{8}\right)} c^{4} - {\left(55 \, D a^{6} b^{2} + 33 \, C a^{5} b^{3} - 73 \, B a^{4} b^{4} - 511 \, A a^{3} b^{5}\right)} d^{4} + {\left(283 \, D a^{5} b^{3} c + {\left(85 \, C a^{4} b^{4} - 693 \, B a^{3} b^{5} - 763 \, A a^{2} b^{6}\right)} c\right)} d^{3} - 4 \, {\left(131 \, D a^{4} b^{4} c^{2} - {\left(77 \, C a^{3} b^{5} + 229 \, B a^{2} b^{6} + 77 \, A a b^{7}\right)} c^{2}\right)} d^{2} + 8 \, {\left(13 \, D a^{3} b^{5} c^{3} - {\left(53 \, C a^{2} b^{6} + 45 \, B a b^{7} + 7 \, A b^{8}\right)} c^{3}\right)} d\right)} x\right)} \sqrt{d x + c}}{384 \, {\left(a^{4} b^{9} c^{5} - 5 \, a^{5} b^{8} c^{4} d + 10 \, a^{6} b^{7} c^{3} d^{2} - 10 \, a^{7} b^{6} c^{2} d^{3} + 5 \, a^{8} b^{5} c d^{4} - a^{9} b^{4} d^{5} + {\left(b^{13} c^{5} - 5 \, a b^{12} c^{4} d + 10 \, a^{2} b^{11} c^{3} d^{2} - 10 \, a^{3} b^{10} c^{2} d^{3} + 5 \, a^{4} b^{9} c d^{4} - a^{5} b^{8} d^{5}\right)} x^{4} + 4 \, {\left(a b^{12} c^{5} - 5 \, a^{2} b^{11} c^{4} d + 10 \, a^{3} b^{10} c^{3} d^{2} - 10 \, a^{4} b^{9} c^{2} d^{3} + 5 \, a^{5} b^{8} c d^{4} - a^{6} b^{7} d^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{11} c^{5} - 5 \, a^{3} b^{10} c^{4} d + 10 \, a^{4} b^{9} c^{3} d^{2} - 10 \, a^{5} b^{8} c^{2} d^{3} + 5 \, a^{6} b^{7} c d^{4} - a^{7} b^{6} d^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{10} c^{5} - 5 \, a^{4} b^{9} c^{4} d + 10 \, a^{5} b^{8} c^{3} d^{2} - 10 \, a^{6} b^{7} c^{2} d^{3} + 5 \, a^{7} b^{6} c d^{4} - a^{8} b^{5} d^{5}\right)} x\right)}}, -\frac{3 \, {\left(64 \, D a^{4} b^{3} c^{3} d - {\left(5 \, D a^{7} + 3 \, C a^{6} b + 5 \, B a^{5} b^{2} + 35 \, A a^{4} b^{3}\right)} d^{4} + {\left(64 \, D b^{7} c^{3} d - {\left(5 \, D a^{3} b^{4} + 3 \, C a^{2} b^{5} + 5 \, B a b^{6} + 35 \, A b^{7}\right)} d^{4} + 8 \, {\left(3 \, D a^{2} b^{5} c + {\left(2 \, C a b^{6} + 5 \, B b^{7}\right)} c\right)} d^{3} - 48 \, {\left(D a b^{6} c^{2} + C b^{7} c^{2}\right)} d^{2}\right)} x^{4} + 8 \, {\left(3 \, D a^{6} b c + {\left(2 \, C a^{5} b^{2} + 5 \, B a^{4} b^{3}\right)} c\right)} d^{3} + 4 \, {\left(64 \, D a b^{6} c^{3} d - {\left(5 \, D a^{4} b^{3} + 3 \, C a^{3} b^{4} + 5 \, B a^{2} b^{5} + 35 \, A a b^{6}\right)} d^{4} + 8 \, {\left(3 \, D a^{3} b^{4} c + {\left(2 \, C a^{2} b^{5} + 5 \, B a b^{6}\right)} c\right)} d^{3} - 48 \, {\left(D a^{2} b^{5} c^{2} + C a b^{6} c^{2}\right)} d^{2}\right)} x^{3} - 48 \, {\left(D a^{5} b^{2} c^{2} + C a^{4} b^{3} c^{2}\right)} d^{2} + 6 \, {\left(64 \, D a^{2} b^{5} c^{3} d - {\left(5 \, D a^{5} b^{2} + 3 \, C a^{4} b^{3} + 5 \, B a^{3} b^{4} + 35 \, A a^{2} b^{5}\right)} d^{4} + 8 \, {\left(3 \, D a^{4} b^{3} c + {\left(2 \, C a^{3} b^{4} + 5 \, B a^{2} b^{5}\right)} c\right)} d^{3} - 48 \, {\left(D a^{3} b^{4} c^{2} + C a^{2} b^{5} c^{2}\right)} d^{2}\right)} x^{2} + 4 \, {\left(64 \, D a^{3} b^{4} c^{3} d - {\left(5 \, D a^{6} b + 3 \, C a^{5} b^{2} + 5 \, B a^{4} b^{3} + 35 \, A a^{3} b^{4}\right)} d^{4} + 8 \, {\left(3 \, D a^{5} b^{2} c + {\left(2 \, C a^{4} b^{3} + 5 \, B a^{3} b^{4}\right)} c\right)} d^{3} - 48 \, {\left(D a^{4} b^{3} c^{2} + C a^{3} b^{4} c^{2}\right)} d^{2}\right)} x\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{-b^{2} c + a b d} \sqrt{d x + c}}{b d x + b c}\right) + {\left(48 \, D a^{3} b^{5} c^{4} + 16 \, {\left(C a^{2} b^{6} + B a b^{7} + 3 \, A b^{8}\right)} c^{4} - 3 \, {\left(5 \, D a^{7} b + 3 \, C a^{6} b^{2} + 5 \, B a^{5} b^{3} - 93 \, A a^{4} b^{4}\right)} d^{4} + {\left(77 \, D a^{6} b^{2} c + {\left(51 \, C a^{5} b^{3} - 131 \, B a^{4} b^{4} - 605 \, A a^{3} b^{5}\right)} c\right)} d^{3} + 3 \, {\left(64 \, D b^{8} c^{4} + {\left(5 \, D a^{4} b^{4} + 3 \, C a^{3} b^{5} + 5 \, B a^{2} b^{6} + 35 \, A a b^{7}\right)} d^{4} - {\left(29 \, D a^{3} b^{5} c + {\left(19 \, C a^{2} b^{6} + 45 \, B a b^{7} + 35 \, A b^{8}\right)} c\right)} d^{3} + 8 \, {\left(9 \, D a^{2} b^{6} c^{2} + {\left(8 \, C a b^{7} + 5 \, B b^{8}\right)} c^{2}\right)} d^{2} - 16 \, {\left(7 \, D a b^{7} c^{3} + 3 \, C b^{8} c^{3}\right)} d\right)} x^{3} - 2 \, {\left(83 \, D a^{5} b^{3} c^{2} - {\left(23 \, C a^{4} b^{4} + 109 \, B a^{3} b^{5} + 263 \, A a^{2} b^{6}\right)} c^{2}\right)} d^{2} + {\left(288 \, D a b^{7} c^{4} + 96 \, C b^{8} c^{4} - {\left(73 \, D a^{5} b^{3} - 33 \, C a^{4} b^{4} - 55 \, B a^{3} b^{5} - 385 \, A a^{2} b^{6}\right)} d^{4} + {\left(311 \, D a^{4} b^{4} c - 5 \, {\left(43 \, C a^{3} b^{5} + 101 \, B a^{2} b^{6} + 91 \, A a b^{7}\right)} c\right)} d^{3} - 2 \, {\left(215 \, D a^{3} b^{5} c^{2} - {\left(371 \, C a^{2} b^{6} + 265 \, B a b^{7} + 35 \, A b^{8}\right)} c^{2}\right)} d^{2} - 16 \, {\left(6 \, D a^{2} b^{6} c^{3} + {\left(41 \, C a b^{7} + 5 \, B b^{8}\right)} c^{3}\right)} d\right)} x^{2} + 8 \, {\left(7 \, D a^{4} b^{4} c^{3} - {\left(13 \, C a^{3} b^{5} + 11 \, B a^{2} b^{6} + 31 \, A a b^{7}\right)} c^{3}\right)} d + {\left(192 \, D a^{2} b^{6} c^{4} + 64 \, {\left(C a b^{7} + B b^{8}\right)} c^{4} - {\left(55 \, D a^{6} b^{2} + 33 \, C a^{5} b^{3} - 73 \, B a^{4} b^{4} - 511 \, A a^{3} b^{5}\right)} d^{4} + {\left(283 \, D a^{5} b^{3} c + {\left(85 \, C a^{4} b^{4} - 693 \, B a^{3} b^{5} - 763 \, A a^{2} b^{6}\right)} c\right)} d^{3} - 4 \, {\left(131 \, D a^{4} b^{4} c^{2} - {\left(77 \, C a^{3} b^{5} + 229 \, B a^{2} b^{6} + 77 \, A a b^{7}\right)} c^{2}\right)} d^{2} + 8 \, {\left(13 \, D a^{3} b^{5} c^{3} - {\left(53 \, C a^{2} b^{6} + 45 \, B a b^{7} + 7 \, A b^{8}\right)} c^{3}\right)} d\right)} x\right)} \sqrt{d x + c}}{192 \, {\left(a^{4} b^{9} c^{5} - 5 \, a^{5} b^{8} c^{4} d + 10 \, a^{6} b^{7} c^{3} d^{2} - 10 \, a^{7} b^{6} c^{2} d^{3} + 5 \, a^{8} b^{5} c d^{4} - a^{9} b^{4} d^{5} + {\left(b^{13} c^{5} - 5 \, a b^{12} c^{4} d + 10 \, a^{2} b^{11} c^{3} d^{2} - 10 \, a^{3} b^{10} c^{2} d^{3} + 5 \, a^{4} b^{9} c d^{4} - a^{5} b^{8} d^{5}\right)} x^{4} + 4 \, {\left(a b^{12} c^{5} - 5 \, a^{2} b^{11} c^{4} d + 10 \, a^{3} b^{10} c^{3} d^{2} - 10 \, a^{4} b^{9} c^{2} d^{3} + 5 \, a^{5} b^{8} c d^{4} - a^{6} b^{7} d^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{11} c^{5} - 5 \, a^{3} b^{10} c^{4} d + 10 \, a^{4} b^{9} c^{3} d^{2} - 10 \, a^{5} b^{8} c^{2} d^{3} + 5 \, a^{6} b^{7} c d^{4} - a^{7} b^{6} d^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{10} c^{5} - 5 \, a^{4} b^{9} c^{4} d + 10 \, a^{5} b^{8} c^{3} d^{2} - 10 \, a^{6} b^{7} c^{2} d^{3} + 5 \, a^{7} b^{6} c d^{4} - a^{8} b^{5} d^{5}\right)} x\right)}}\right]"," ",0,"[-1/384*(3*(64*D*a^4*b^3*c^3*d - (5*D*a^7 + 3*C*a^6*b + 5*B*a^5*b^2 + 35*A*a^4*b^3)*d^4 + (64*D*b^7*c^3*d - (5*D*a^3*b^4 + 3*C*a^2*b^5 + 5*B*a*b^6 + 35*A*b^7)*d^4 + 8*(3*D*a^2*b^5*c + (2*C*a*b^6 + 5*B*b^7)*c)*d^3 - 48*(D*a*b^6*c^2 + C*b^7*c^2)*d^2)*x^4 + 8*(3*D*a^6*b*c + (2*C*a^5*b^2 + 5*B*a^4*b^3)*c)*d^3 + 4*(64*D*a*b^6*c^3*d - (5*D*a^4*b^3 + 3*C*a^3*b^4 + 5*B*a^2*b^5 + 35*A*a*b^6)*d^4 + 8*(3*D*a^3*b^4*c + (2*C*a^2*b^5 + 5*B*a*b^6)*c)*d^3 - 48*(D*a^2*b^5*c^2 + C*a*b^6*c^2)*d^2)*x^3 - 48*(D*a^5*b^2*c^2 + C*a^4*b^3*c^2)*d^2 + 6*(64*D*a^2*b^5*c^3*d - (5*D*a^5*b^2 + 3*C*a^4*b^3 + 5*B*a^3*b^4 + 35*A*a^2*b^5)*d^4 + 8*(3*D*a^4*b^3*c + (2*C*a^3*b^4 + 5*B*a^2*b^5)*c)*d^3 - 48*(D*a^3*b^4*c^2 + C*a^2*b^5*c^2)*d^2)*x^2 + 4*(64*D*a^3*b^4*c^3*d - (5*D*a^6*b + 3*C*a^5*b^2 + 5*B*a^4*b^3 + 35*A*a^3*b^4)*d^4 + 8*(3*D*a^5*b^2*c + (2*C*a^4*b^3 + 5*B*a^3*b^4)*c)*d^3 - 48*(D*a^4*b^3*c^2 + C*a^3*b^4*c^2)*d^2)*x)*sqrt(b^2*c - a*b*d)*log((b*d*x + 2*b*c - a*d - 2*sqrt(b^2*c - a*b*d)*sqrt(d*x + c))/(b*x + a)) + 2*(48*D*a^3*b^5*c^4 + 16*(C*a^2*b^6 + B*a*b^7 + 3*A*b^8)*c^4 - 3*(5*D*a^7*b + 3*C*a^6*b^2 + 5*B*a^5*b^3 - 93*A*a^4*b^4)*d^4 + (77*D*a^6*b^2*c + (51*C*a^5*b^3 - 131*B*a^4*b^4 - 605*A*a^3*b^5)*c)*d^3 + 3*(64*D*b^8*c^4 + (5*D*a^4*b^4 + 3*C*a^3*b^5 + 5*B*a^2*b^6 + 35*A*a*b^7)*d^4 - (29*D*a^3*b^5*c + (19*C*a^2*b^6 + 45*B*a*b^7 + 35*A*b^8)*c)*d^3 + 8*(9*D*a^2*b^6*c^2 + (8*C*a*b^7 + 5*B*b^8)*c^2)*d^2 - 16*(7*D*a*b^7*c^3 + 3*C*b^8*c^3)*d)*x^3 - 2*(83*D*a^5*b^3*c^2 - (23*C*a^4*b^4 + 109*B*a^3*b^5 + 263*A*a^2*b^6)*c^2)*d^2 + (288*D*a*b^7*c^4 + 96*C*b^8*c^4 - (73*D*a^5*b^3 - 33*C*a^4*b^4 - 55*B*a^3*b^5 - 385*A*a^2*b^6)*d^4 + (311*D*a^4*b^4*c - 5*(43*C*a^3*b^5 + 101*B*a^2*b^6 + 91*A*a*b^7)*c)*d^3 - 2*(215*D*a^3*b^5*c^2 - (371*C*a^2*b^6 + 265*B*a*b^7 + 35*A*b^8)*c^2)*d^2 - 16*(6*D*a^2*b^6*c^3 + (41*C*a*b^7 + 5*B*b^8)*c^3)*d)*x^2 + 8*(7*D*a^4*b^4*c^3 - (13*C*a^3*b^5 + 11*B*a^2*b^6 + 31*A*a*b^7)*c^3)*d + (192*D*a^2*b^6*c^4 + 64*(C*a*b^7 + B*b^8)*c^4 - (55*D*a^6*b^2 + 33*C*a^5*b^3 - 73*B*a^4*b^4 - 511*A*a^3*b^5)*d^4 + (283*D*a^5*b^3*c + (85*C*a^4*b^4 - 693*B*a^3*b^5 - 763*A*a^2*b^6)*c)*d^3 - 4*(131*D*a^4*b^4*c^2 - (77*C*a^3*b^5 + 229*B*a^2*b^6 + 77*A*a*b^7)*c^2)*d^2 + 8*(13*D*a^3*b^5*c^3 - (53*C*a^2*b^6 + 45*B*a*b^7 + 7*A*b^8)*c^3)*d)*x)*sqrt(d*x + c))/(a^4*b^9*c^5 - 5*a^5*b^8*c^4*d + 10*a^6*b^7*c^3*d^2 - 10*a^7*b^6*c^2*d^3 + 5*a^8*b^5*c*d^4 - a^9*b^4*d^5 + (b^13*c^5 - 5*a*b^12*c^4*d + 10*a^2*b^11*c^3*d^2 - 10*a^3*b^10*c^2*d^3 + 5*a^4*b^9*c*d^4 - a^5*b^8*d^5)*x^4 + 4*(a*b^12*c^5 - 5*a^2*b^11*c^4*d + 10*a^3*b^10*c^3*d^2 - 10*a^4*b^9*c^2*d^3 + 5*a^5*b^8*c*d^4 - a^6*b^7*d^5)*x^3 + 6*(a^2*b^11*c^5 - 5*a^3*b^10*c^4*d + 10*a^4*b^9*c^3*d^2 - 10*a^5*b^8*c^2*d^3 + 5*a^6*b^7*c*d^4 - a^7*b^6*d^5)*x^2 + 4*(a^3*b^10*c^5 - 5*a^4*b^9*c^4*d + 10*a^5*b^8*c^3*d^2 - 10*a^6*b^7*c^2*d^3 + 5*a^7*b^6*c*d^4 - a^8*b^5*d^5)*x), -1/192*(3*(64*D*a^4*b^3*c^3*d - (5*D*a^7 + 3*C*a^6*b + 5*B*a^5*b^2 + 35*A*a^4*b^3)*d^4 + (64*D*b^7*c^3*d - (5*D*a^3*b^4 + 3*C*a^2*b^5 + 5*B*a*b^6 + 35*A*b^7)*d^4 + 8*(3*D*a^2*b^5*c + (2*C*a*b^6 + 5*B*b^7)*c)*d^3 - 48*(D*a*b^6*c^2 + C*b^7*c^2)*d^2)*x^4 + 8*(3*D*a^6*b*c + (2*C*a^5*b^2 + 5*B*a^4*b^3)*c)*d^3 + 4*(64*D*a*b^6*c^3*d - (5*D*a^4*b^3 + 3*C*a^3*b^4 + 5*B*a^2*b^5 + 35*A*a*b^6)*d^4 + 8*(3*D*a^3*b^4*c + (2*C*a^2*b^5 + 5*B*a*b^6)*c)*d^3 - 48*(D*a^2*b^5*c^2 + C*a*b^6*c^2)*d^2)*x^3 - 48*(D*a^5*b^2*c^2 + C*a^4*b^3*c^2)*d^2 + 6*(64*D*a^2*b^5*c^3*d - (5*D*a^5*b^2 + 3*C*a^4*b^3 + 5*B*a^3*b^4 + 35*A*a^2*b^5)*d^4 + 8*(3*D*a^4*b^3*c + (2*C*a^3*b^4 + 5*B*a^2*b^5)*c)*d^3 - 48*(D*a^3*b^4*c^2 + C*a^2*b^5*c^2)*d^2)*x^2 + 4*(64*D*a^3*b^4*c^3*d - (5*D*a^6*b + 3*C*a^5*b^2 + 5*B*a^4*b^3 + 35*A*a^3*b^4)*d^4 + 8*(3*D*a^5*b^2*c + (2*C*a^4*b^3 + 5*B*a^3*b^4)*c)*d^3 - 48*(D*a^4*b^3*c^2 + C*a^3*b^4*c^2)*d^2)*x)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(-b^2*c + a*b*d)*sqrt(d*x + c)/(b*d*x + b*c)) + (48*D*a^3*b^5*c^4 + 16*(C*a^2*b^6 + B*a*b^7 + 3*A*b^8)*c^4 - 3*(5*D*a^7*b + 3*C*a^6*b^2 + 5*B*a^5*b^3 - 93*A*a^4*b^4)*d^4 + (77*D*a^6*b^2*c + (51*C*a^5*b^3 - 131*B*a^4*b^4 - 605*A*a^3*b^5)*c)*d^3 + 3*(64*D*b^8*c^4 + (5*D*a^4*b^4 + 3*C*a^3*b^5 + 5*B*a^2*b^6 + 35*A*a*b^7)*d^4 - (29*D*a^3*b^5*c + (19*C*a^2*b^6 + 45*B*a*b^7 + 35*A*b^8)*c)*d^3 + 8*(9*D*a^2*b^6*c^2 + (8*C*a*b^7 + 5*B*b^8)*c^2)*d^2 - 16*(7*D*a*b^7*c^3 + 3*C*b^8*c^3)*d)*x^3 - 2*(83*D*a^5*b^3*c^2 - (23*C*a^4*b^4 + 109*B*a^3*b^5 + 263*A*a^2*b^6)*c^2)*d^2 + (288*D*a*b^7*c^4 + 96*C*b^8*c^4 - (73*D*a^5*b^3 - 33*C*a^4*b^4 - 55*B*a^3*b^5 - 385*A*a^2*b^6)*d^4 + (311*D*a^4*b^4*c - 5*(43*C*a^3*b^5 + 101*B*a^2*b^6 + 91*A*a*b^7)*c)*d^3 - 2*(215*D*a^3*b^5*c^2 - (371*C*a^2*b^6 + 265*B*a*b^7 + 35*A*b^8)*c^2)*d^2 - 16*(6*D*a^2*b^6*c^3 + (41*C*a*b^7 + 5*B*b^8)*c^3)*d)*x^2 + 8*(7*D*a^4*b^4*c^3 - (13*C*a^3*b^5 + 11*B*a^2*b^6 + 31*A*a*b^7)*c^3)*d + (192*D*a^2*b^6*c^4 + 64*(C*a*b^7 + B*b^8)*c^4 - (55*D*a^6*b^2 + 33*C*a^5*b^3 - 73*B*a^4*b^4 - 511*A*a^3*b^5)*d^4 + (283*D*a^5*b^3*c + (85*C*a^4*b^4 - 693*B*a^3*b^5 - 763*A*a^2*b^6)*c)*d^3 - 4*(131*D*a^4*b^4*c^2 - (77*C*a^3*b^5 + 229*B*a^2*b^6 + 77*A*a*b^7)*c^2)*d^2 + 8*(13*D*a^3*b^5*c^3 - (53*C*a^2*b^6 + 45*B*a*b^7 + 7*A*b^8)*c^3)*d)*x)*sqrt(d*x + c))/(a^4*b^9*c^5 - 5*a^5*b^8*c^4*d + 10*a^6*b^7*c^3*d^2 - 10*a^7*b^6*c^2*d^3 + 5*a^8*b^5*c*d^4 - a^9*b^4*d^5 + (b^13*c^5 - 5*a*b^12*c^4*d + 10*a^2*b^11*c^3*d^2 - 10*a^3*b^10*c^2*d^3 + 5*a^4*b^9*c*d^4 - a^5*b^8*d^5)*x^4 + 4*(a*b^12*c^5 - 5*a^2*b^11*c^4*d + 10*a^3*b^10*c^3*d^2 - 10*a^4*b^9*c^2*d^3 + 5*a^5*b^8*c*d^4 - a^6*b^7*d^5)*x^3 + 6*(a^2*b^11*c^5 - 5*a^3*b^10*c^4*d + 10*a^4*b^9*c^3*d^2 - 10*a^5*b^8*c^2*d^3 + 5*a^6*b^7*c*d^4 - a^7*b^6*d^5)*x^2 + 4*(a^3*b^10*c^5 - 5*a^4*b^9*c^4*d + 10*a^5*b^8*c^3*d^2 - 10*a^6*b^7*c^2*d^3 + 5*a^7*b^6*c*d^4 - a^8*b^5*d^5)*x)]","B",0
10,1,677,0,0.626231," ","integrate((b*x+a)^3*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, D b^{3} d^{6} x^{6} - 15360 \, D b^{3} c^{6} - 3465 \, A a^{3} d^{6} - 9240 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} c^{2} d^{4} + 6930 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c d^{5} - 35 \, {\left(12 \, D b^{3} c d^{5} - 11 \, {\left(3 \, D a b^{2} + C b^{3}\right)} d^{6}\right)} x^{5} + 5 \, {\left(120 \, D b^{3} c^{2} d^{4} + 99 \, {\left(3 \, D a^{2} b + 3 \, C a b^{2} + B b^{3}\right)} d^{6} - 110 \, {\left(3 \, D a b^{2} c + C b^{3} c\right)} d^{5}\right)} x^{4} + 11088 \, {\left(D a^{3} c^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c^{3}\right)} d^{3} - {\left(960 \, D b^{3} c^{3} d^{3} - 693 \, {\left(D a^{3} + 3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} d^{6} + 792 \, {\left(3 \, D a^{2} b c + {\left(3 \, C a b^{2} + B b^{3}\right)} c\right)} d^{5} - 880 \, {\left(3 \, D a b^{2} c^{2} + C b^{3} c^{2}\right)} d^{4}\right)} x^{3} - 12672 \, {\left(3 \, D a^{2} b c^{4} + {\left(3 \, C a b^{2} + B b^{3}\right)} c^{4}\right)} d^{2} + {\left(1920 \, D b^{3} c^{4} d^{2} + 1155 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} d^{6} - 1386 \, {\left(D a^{3} c + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c\right)} d^{5} + 1584 \, {\left(3 \, D a^{2} b c^{2} + {\left(3 \, C a b^{2} + B b^{3}\right)} c^{2}\right)} d^{4} - 1760 \, {\left(3 \, D a b^{2} c^{3} + C b^{3} c^{3}\right)} d^{3}\right)} x^{2} + 14080 \, {\left(3 \, D a b^{2} c^{5} + C b^{3} c^{5}\right)} d - {\left(7680 \, D b^{3} c^{5} d + 4620 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} c d^{5} - 3465 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{6} - 5544 \, {\left(D a^{3} c^{2} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c^{2}\right)} d^{4} + 6336 \, {\left(3 \, D a^{2} b c^{3} + {\left(3 \, C a b^{2} + B b^{3}\right)} c^{3}\right)} d^{3} - 7040 \, {\left(3 \, D a b^{2} c^{4} + C b^{3} c^{4}\right)} d^{2}\right)} x\right)} \sqrt{d x + c}}{3465 \, {\left(d^{8} x + c d^{7}\right)}}"," ",0,"2/3465*(315*D*b^3*d^6*x^6 - 15360*D*b^3*c^6 - 3465*A*a^3*d^6 - 9240*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*c^2*d^4 + 6930*(B*a^3 + 3*A*a^2*b)*c*d^5 - 35*(12*D*b^3*c*d^5 - 11*(3*D*a*b^2 + C*b^3)*d^6)*x^5 + 5*(120*D*b^3*c^2*d^4 + 99*(3*D*a^2*b + 3*C*a*b^2 + B*b^3)*d^6 - 110*(3*D*a*b^2*c + C*b^3*c)*d^5)*x^4 + 11088*(D*a^3*c^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c^3)*d^3 - (960*D*b^3*c^3*d^3 - 693*(D*a^3 + 3*C*a^2*b + 3*B*a*b^2 + A*b^3)*d^6 + 792*(3*D*a^2*b*c + (3*C*a*b^2 + B*b^3)*c)*d^5 - 880*(3*D*a*b^2*c^2 + C*b^3*c^2)*d^4)*x^3 - 12672*(3*D*a^2*b*c^4 + (3*C*a*b^2 + B*b^3)*c^4)*d^2 + (1920*D*b^3*c^4*d^2 + 1155*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*d^6 - 1386*(D*a^3*c + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c)*d^5 + 1584*(3*D*a^2*b*c^2 + (3*C*a*b^2 + B*b^3)*c^2)*d^4 - 1760*(3*D*a*b^2*c^3 + C*b^3*c^3)*d^3)*x^2 + 14080*(3*D*a*b^2*c^5 + C*b^3*c^5)*d - (7680*D*b^3*c^5*d + 4620*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*c*d^5 - 3465*(B*a^3 + 3*A*a^2*b)*d^6 - 5544*(D*a^3*c^2 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c^2)*d^4 + 6336*(3*D*a^2*b*c^3 + (3*C*a*b^2 + B*b^3)*c^3)*d^3 - 7040*(3*D*a*b^2*c^4 + C*b^3*c^4)*d^2)*x)*sqrt(d*x + c)/(d^8*x + c*d^7)","A",0
11,1,419,0,0.657049," ","integrate((b*x+a)^2*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, D b^{2} d^{5} x^{5} + 1280 \, D b^{2} c^{5} - 315 \, A a^{2} d^{5} - 840 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{2} d^{3} + 630 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{4} - 5 \, {\left(10 \, D b^{2} c d^{4} - 9 \, {\left(2 \, D a b + C b^{2}\right)} d^{5}\right)} x^{4} + {\left(80 \, D b^{2} c^{2} d^{3} + 63 \, {\left(D a^{2} + 2 \, C a b + B b^{2}\right)} d^{5} - 72 \, {\left(2 \, D a b c + C b^{2} c\right)} d^{4}\right)} x^{3} + 1008 \, {\left(D a^{2} c^{3} + {\left(2 \, C a b + B b^{2}\right)} c^{3}\right)} d^{2} - {\left(160 \, D b^{2} c^{3} d^{2} - 105 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{5} + 126 \, {\left(D a^{2} c + {\left(2 \, C a b + B b^{2}\right)} c\right)} d^{4} - 144 \, {\left(2 \, D a b c^{2} + C b^{2} c^{2}\right)} d^{3}\right)} x^{2} - 1152 \, {\left(2 \, D a b c^{4} + C b^{2} c^{4}\right)} d + {\left(640 \, D b^{2} c^{4} d - 420 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c d^{4} + 315 \, {\left(B a^{2} + 2 \, A a b\right)} d^{5} + 504 \, {\left(D a^{2} c^{2} + {\left(2 \, C a b + B b^{2}\right)} c^{2}\right)} d^{3} - 576 \, {\left(2 \, D a b c^{3} + C b^{2} c^{3}\right)} d^{2}\right)} x\right)} \sqrt{d x + c}}{315 \, {\left(d^{7} x + c d^{6}\right)}}"," ",0,"2/315*(35*D*b^2*d^5*x^5 + 1280*D*b^2*c^5 - 315*A*a^2*d^5 - 840*(C*a^2 + 2*B*a*b + A*b^2)*c^2*d^3 + 630*(B*a^2 + 2*A*a*b)*c*d^4 - 5*(10*D*b^2*c*d^4 - 9*(2*D*a*b + C*b^2)*d^5)*x^4 + (80*D*b^2*c^2*d^3 + 63*(D*a^2 + 2*C*a*b + B*b^2)*d^5 - 72*(2*D*a*b*c + C*b^2*c)*d^4)*x^3 + 1008*(D*a^2*c^3 + (2*C*a*b + B*b^2)*c^3)*d^2 - (160*D*b^2*c^3*d^2 - 105*(C*a^2 + 2*B*a*b + A*b^2)*d^5 + 126*(D*a^2*c + (2*C*a*b + B*b^2)*c)*d^4 - 144*(2*D*a*b*c^2 + C*b^2*c^2)*d^3)*x^2 - 1152*(2*D*a*b*c^4 + C*b^2*c^4)*d + (640*D*b^2*c^4*d - 420*(C*a^2 + 2*B*a*b + A*b^2)*c*d^4 + 315*(B*a^2 + 2*A*a*b)*d^5 + 504*(D*a^2*c^2 + (2*C*a*b + B*b^2)*c^2)*d^3 - 576*(2*D*a*b*c^3 + C*b^2*c^3)*d^2)*x)*sqrt(d*x + c)/(d^7*x + c*d^6)","A",0
12,1,213,0,0.753909," ","integrate((b*x+a)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, D b d^{4} x^{4} - 384 \, D b c^{4} - 105 \, A a d^{4} - 280 \, {\left(C a + B b\right)} c^{2} d^{2} + 210 \, {\left(B a + A b\right)} c d^{3} - 3 \, {\left(8 \, D b c d^{3} - 7 \, {\left(D a + C b\right)} d^{4}\right)} x^{3} + {\left(48 \, D b c^{2} d^{2} + 35 \, {\left(C a + B b\right)} d^{4} - 42 \, {\left(D a c + C b c\right)} d^{3}\right)} x^{2} + 336 \, {\left(D a c^{3} + C b c^{3}\right)} d - {\left(192 \, D b c^{3} d + 140 \, {\left(C a + B b\right)} c d^{3} - 105 \, {\left(B a + A b\right)} d^{4} - 168 \, {\left(D a c^{2} + C b c^{2}\right)} d^{2}\right)} x\right)} \sqrt{d x + c}}{105 \, {\left(d^{6} x + c d^{5}\right)}}"," ",0,"2/105*(15*D*b*d^4*x^4 - 384*D*b*c^4 - 105*A*a*d^4 - 280*(C*a + B*b)*c^2*d^2 + 210*(B*a + A*b)*c*d^3 - 3*(8*D*b*c*d^3 - 7*(D*a + C*b)*d^4)*x^3 + (48*D*b*c^2*d^2 + 35*(C*a + B*b)*d^4 - 42*(D*a*c + C*b*c)*d^3)*x^2 + 336*(D*a*c^3 + C*b*c^3)*d - (192*D*b*c^3*d + 140*(C*a + B*b)*c*d^3 - 105*(B*a + A*b)*d^4 - 168*(D*a*c^2 + C*b*c^2)*d^2)*x)*sqrt(d*x + c)/(d^6*x + c*d^5)","A",0
13,1,100,0,0.849165," ","integrate((D*x^3+C*x^2+B*x+A)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, D d^{3} x^{3} + 48 \, D c^{3} - 40 \, C c^{2} d + 30 \, B c d^{2} - 15 \, A d^{3} - {\left(6 \, D c d^{2} - 5 \, C d^{3}\right)} x^{2} + {\left(24 \, D c^{2} d - 20 \, C c d^{2} + 15 \, B d^{3}\right)} x\right)} \sqrt{d x + c}}{15 \, {\left(d^{5} x + c d^{4}\right)}}"," ",0,"2/15*(3*D*d^3*x^3 + 48*D*c^3 - 40*C*c^2*d + 30*B*c*d^2 - 15*A*d^3 - (6*D*c*d^2 - 5*C*d^3)*x^2 + (24*D*c^2*d - 20*C*c*d^2 + 15*B*d^3)*x)*sqrt(d*x + c)/(d^5*x + c*d^4)","A",0
14,1,866,0,1.038949," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x+a)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(D a^{3} - C a^{2} b + B a b^{2} - A b^{3}\right)} d^{4} x + {\left(D a^{3} c - {\left(C a^{2} b - B a b^{2} + A b^{3}\right)} c\right)} d^{3}\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, \sqrt{b^{2} c - a b d} \sqrt{d x + c}}{b x + a}\right) + 2 \, {\left(8 \, D b^{4} c^{4} + 3 \, A a b^{3} d^{4} + 3 \, {\left(D a^{3} b c - {\left(C a^{2} b^{2} + B a b^{3} + A b^{4}\right)} c\right)} d^{3} - {\left(D a^{2} b^{2} c^{2} - 3 \, {\left(3 \, C a b^{3} + B b^{4}\right)} c^{2}\right)} d^{2} - {\left(D b^{4} c^{2} d^{2} - 2 \, D a b^{3} c d^{3} + D a^{2} b^{2} d^{4}\right)} x^{2} - 2 \, {\left(5 \, D a b^{3} c^{3} + 3 \, C b^{4} c^{3}\right)} d + {\left(4 \, D b^{4} c^{3} d + 3 \, {\left(D a^{3} b - C a^{2} b^{2}\right)} d^{4} - 2 \, {\left(D a^{2} b^{2} c - 3 \, C a b^{3} c\right)} d^{3} - {\left(5 \, D a b^{3} c^{2} + 3 \, C b^{4} c^{2}\right)} d^{2}\right)} x\right)} \sqrt{d x + c}}{3 \, {\left(b^{5} c^{3} d^{3} - 2 \, a b^{4} c^{2} d^{4} + a^{2} b^{3} c d^{5} + {\left(b^{5} c^{2} d^{4} - 2 \, a b^{4} c d^{5} + a^{2} b^{3} d^{6}\right)} x\right)}}, -\frac{2 \, {\left(3 \, {\left({\left(D a^{3} - C a^{2} b + B a b^{2} - A b^{3}\right)} d^{4} x + {\left(D a^{3} c - {\left(C a^{2} b - B a b^{2} + A b^{3}\right)} c\right)} d^{3}\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{-b^{2} c + a b d} \sqrt{d x + c}}{b d x + b c}\right) + {\left(8 \, D b^{4} c^{4} + 3 \, A a b^{3} d^{4} + 3 \, {\left(D a^{3} b c - {\left(C a^{2} b^{2} + B a b^{3} + A b^{4}\right)} c\right)} d^{3} - {\left(D a^{2} b^{2} c^{2} - 3 \, {\left(3 \, C a b^{3} + B b^{4}\right)} c^{2}\right)} d^{2} - {\left(D b^{4} c^{2} d^{2} - 2 \, D a b^{3} c d^{3} + D a^{2} b^{2} d^{4}\right)} x^{2} - 2 \, {\left(5 \, D a b^{3} c^{3} + 3 \, C b^{4} c^{3}\right)} d + {\left(4 \, D b^{4} c^{3} d + 3 \, {\left(D a^{3} b - C a^{2} b^{2}\right)} d^{4} - 2 \, {\left(D a^{2} b^{2} c - 3 \, C a b^{3} c\right)} d^{3} - {\left(5 \, D a b^{3} c^{2} + 3 \, C b^{4} c^{2}\right)} d^{2}\right)} x\right)} \sqrt{d x + c}\right)}}{3 \, {\left(b^{5} c^{3} d^{3} - 2 \, a b^{4} c^{2} d^{4} + a^{2} b^{3} c d^{5} + {\left(b^{5} c^{2} d^{4} - 2 \, a b^{4} c d^{5} + a^{2} b^{3} d^{6}\right)} x\right)}}\right]"," ",0,"[-1/3*(3*((D*a^3 - C*a^2*b + B*a*b^2 - A*b^3)*d^4*x + (D*a^3*c - (C*a^2*b - B*a*b^2 + A*b^3)*c)*d^3)*sqrt(b^2*c - a*b*d)*log((b*d*x + 2*b*c - a*d - 2*sqrt(b^2*c - a*b*d)*sqrt(d*x + c))/(b*x + a)) + 2*(8*D*b^4*c^4 + 3*A*a*b^3*d^4 + 3*(D*a^3*b*c - (C*a^2*b^2 + B*a*b^3 + A*b^4)*c)*d^3 - (D*a^2*b^2*c^2 - 3*(3*C*a*b^3 + B*b^4)*c^2)*d^2 - (D*b^4*c^2*d^2 - 2*D*a*b^3*c*d^3 + D*a^2*b^2*d^4)*x^2 - 2*(5*D*a*b^3*c^3 + 3*C*b^4*c^3)*d + (4*D*b^4*c^3*d + 3*(D*a^3*b - C*a^2*b^2)*d^4 - 2*(D*a^2*b^2*c - 3*C*a*b^3*c)*d^3 - (5*D*a*b^3*c^2 + 3*C*b^4*c^2)*d^2)*x)*sqrt(d*x + c))/(b^5*c^3*d^3 - 2*a*b^4*c^2*d^4 + a^2*b^3*c*d^5 + (b^5*c^2*d^4 - 2*a*b^4*c*d^5 + a^2*b^3*d^6)*x), -2/3*(3*((D*a^3 - C*a^2*b + B*a*b^2 - A*b^3)*d^4*x + (D*a^3*c - (C*a^2*b - B*a*b^2 + A*b^3)*c)*d^3)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(-b^2*c + a*b*d)*sqrt(d*x + c)/(b*d*x + b*c)) + (8*D*b^4*c^4 + 3*A*a*b^3*d^4 + 3*(D*a^3*b*c - (C*a^2*b^2 + B*a*b^3 + A*b^4)*c)*d^3 - (D*a^2*b^2*c^2 - 3*(3*C*a*b^3 + B*b^4)*c^2)*d^2 - (D*b^4*c^2*d^2 - 2*D*a*b^3*c*d^3 + D*a^2*b^2*d^4)*x^2 - 2*(5*D*a*b^3*c^3 + 3*C*b^4*c^3)*d + (4*D*b^4*c^3*d + 3*(D*a^3*b - C*a^2*b^2)*d^4 - 2*(D*a^2*b^2*c - 3*C*a*b^3*c)*d^3 - (5*D*a*b^3*c^2 + 3*C*b^4*c^2)*d^2)*x)*sqrt(d*x + c))/(b^5*c^3*d^3 - 2*a*b^4*c^2*d^4 + a^2*b^3*c*d^5 + (b^5*c^2*d^4 - 2*a*b^4*c*d^5 + a^2*b^3*d^6)*x)]","B",0
15,1,1583,0,1.040918," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x+a)^2/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(3 \, D a^{4} c - {\left(C a^{3} b + B a^{2} b^{2} - 3 \, A a b^{3}\right)} c\right)} d^{3} - 2 \, {\left(3 \, D a^{3} b c^{2} - {\left(2 \, C a^{2} b^{2} - B a b^{3}\right)} c^{2}\right)} d^{2} + {\left({\left(3 \, D a^{3} b - C a^{2} b^{2} - B a b^{3} + 3 \, A b^{4}\right)} d^{4} - 2 \, {\left(3 \, D a^{2} b^{2} c - {\left(2 \, C a b^{3} - B b^{4}\right)} c\right)} d^{3}\right)} x^{2} + {\left({\left(3 \, D a^{4} - C a^{3} b - B a^{2} b^{2} + 3 \, A a b^{3}\right)} d^{4} - 3 \, {\left(D a^{3} b c - {\left(C a^{2} b^{2} - B a b^{3} + A b^{4}\right)} c\right)} d^{3} - 2 \, {\left(3 \, D a^{2} b^{2} c^{2} - {\left(2 \, C a b^{3} - B b^{4}\right)} c^{2}\right)} d^{2}\right)} x\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x + 2 \, b c - a d + 2 \, \sqrt{b^{2} c - a b d} \sqrt{d x + c}}{b x + a}\right) + 2 \, {\left(4 \, D a b^{4} c^{4} + 2 \, A a^{2} b^{3} d^{4} - {\left(3 \, D a^{4} b c - {\left(C a^{3} b^{2} - 3 \, B a^{2} b^{3} - A a b^{4}\right)} c\right)} d^{3} + {\left(7 \, D a^{3} b^{2} c^{2} + {\left(C a^{2} b^{3} + 3 \, B a b^{4} - A b^{5}\right)} c^{2}\right)} d^{2} + 2 \, {\left(D b^{5} c^{3} d - 3 \, D a b^{4} c^{2} d^{2} + 3 \, D a^{2} b^{3} c d^{3} - D a^{3} b^{2} d^{4}\right)} x^{2} - 2 \, {\left(4 \, D a^{2} b^{3} c^{3} + C a b^{4} c^{3}\right)} d + {\left(4 \, D b^{5} c^{4} + 2 \, {\left(C a b^{4} + B b^{5}\right)} c^{2} d^{2} - {\left(3 \, D a^{4} b - C a^{3} b^{2} + B a^{2} b^{3} - 3 \, A a b^{4}\right)} d^{4} + {\left(5 \, D a^{3} b^{2} c - {\left(C a^{2} b^{3} + B a b^{4} + 3 \, A b^{5}\right)} c\right)} d^{3} - 2 \, {\left(3 \, D a b^{4} c^{3} + C b^{5} c^{3}\right)} d\right)} x\right)} \sqrt{d x + c}}{2 \, {\left(a b^{6} c^{4} d^{2} - 3 \, a^{2} b^{5} c^{3} d^{3} + 3 \, a^{3} b^{4} c^{2} d^{4} - a^{4} b^{3} c d^{5} + {\left(b^{7} c^{3} d^{3} - 3 \, a b^{6} c^{2} d^{4} + 3 \, a^{2} b^{5} c d^{5} - a^{3} b^{4} d^{6}\right)} x^{2} + {\left(b^{7} c^{4} d^{2} - 2 \, a b^{6} c^{3} d^{3} + 2 \, a^{3} b^{4} c d^{5} - a^{4} b^{3} d^{6}\right)} x\right)}}, -\frac{{\left({\left(3 \, D a^{4} c - {\left(C a^{3} b + B a^{2} b^{2} - 3 \, A a b^{3}\right)} c\right)} d^{3} - 2 \, {\left(3 \, D a^{3} b c^{2} - {\left(2 \, C a^{2} b^{2} - B a b^{3}\right)} c^{2}\right)} d^{2} + {\left({\left(3 \, D a^{3} b - C a^{2} b^{2} - B a b^{3} + 3 \, A b^{4}\right)} d^{4} - 2 \, {\left(3 \, D a^{2} b^{2} c - {\left(2 \, C a b^{3} - B b^{4}\right)} c\right)} d^{3}\right)} x^{2} + {\left({\left(3 \, D a^{4} - C a^{3} b - B a^{2} b^{2} + 3 \, A a b^{3}\right)} d^{4} - 3 \, {\left(D a^{3} b c - {\left(C a^{2} b^{2} - B a b^{3} + A b^{4}\right)} c\right)} d^{3} - 2 \, {\left(3 \, D a^{2} b^{2} c^{2} - {\left(2 \, C a b^{3} - B b^{4}\right)} c^{2}\right)} d^{2}\right)} x\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{-b^{2} c + a b d} \sqrt{d x + c}}{b d x + b c}\right) - {\left(4 \, D a b^{4} c^{4} + 2 \, A a^{2} b^{3} d^{4} - {\left(3 \, D a^{4} b c - {\left(C a^{3} b^{2} - 3 \, B a^{2} b^{3} - A a b^{4}\right)} c\right)} d^{3} + {\left(7 \, D a^{3} b^{2} c^{2} + {\left(C a^{2} b^{3} + 3 \, B a b^{4} - A b^{5}\right)} c^{2}\right)} d^{2} + 2 \, {\left(D b^{5} c^{3} d - 3 \, D a b^{4} c^{2} d^{2} + 3 \, D a^{2} b^{3} c d^{3} - D a^{3} b^{2} d^{4}\right)} x^{2} - 2 \, {\left(4 \, D a^{2} b^{3} c^{3} + C a b^{4} c^{3}\right)} d + {\left(4 \, D b^{5} c^{4} + 2 \, {\left(C a b^{4} + B b^{5}\right)} c^{2} d^{2} - {\left(3 \, D a^{4} b - C a^{3} b^{2} + B a^{2} b^{3} - 3 \, A a b^{4}\right)} d^{4} + {\left(5 \, D a^{3} b^{2} c - {\left(C a^{2} b^{3} + B a b^{4} + 3 \, A b^{5}\right)} c\right)} d^{3} - 2 \, {\left(3 \, D a b^{4} c^{3} + C b^{5} c^{3}\right)} d\right)} x\right)} \sqrt{d x + c}}{a b^{6} c^{4} d^{2} - 3 \, a^{2} b^{5} c^{3} d^{3} + 3 \, a^{3} b^{4} c^{2} d^{4} - a^{4} b^{3} c d^{5} + {\left(b^{7} c^{3} d^{3} - 3 \, a b^{6} c^{2} d^{4} + 3 \, a^{2} b^{5} c d^{5} - a^{3} b^{4} d^{6}\right)} x^{2} + {\left(b^{7} c^{4} d^{2} - 2 \, a b^{6} c^{3} d^{3} + 2 \, a^{3} b^{4} c d^{5} - a^{4} b^{3} d^{6}\right)} x}\right]"," ",0,"[1/2*(((3*D*a^4*c - (C*a^3*b + B*a^2*b^2 - 3*A*a*b^3)*c)*d^3 - 2*(3*D*a^3*b*c^2 - (2*C*a^2*b^2 - B*a*b^3)*c^2)*d^2 + ((3*D*a^3*b - C*a^2*b^2 - B*a*b^3 + 3*A*b^4)*d^4 - 2*(3*D*a^2*b^2*c - (2*C*a*b^3 - B*b^4)*c)*d^3)*x^2 + ((3*D*a^4 - C*a^3*b - B*a^2*b^2 + 3*A*a*b^3)*d^4 - 3*(D*a^3*b*c - (C*a^2*b^2 - B*a*b^3 + A*b^4)*c)*d^3 - 2*(3*D*a^2*b^2*c^2 - (2*C*a*b^3 - B*b^4)*c^2)*d^2)*x)*sqrt(b^2*c - a*b*d)*log((b*d*x + 2*b*c - a*d + 2*sqrt(b^2*c - a*b*d)*sqrt(d*x + c))/(b*x + a)) + 2*(4*D*a*b^4*c^4 + 2*A*a^2*b^3*d^4 - (3*D*a^4*b*c - (C*a^3*b^2 - 3*B*a^2*b^3 - A*a*b^4)*c)*d^3 + (7*D*a^3*b^2*c^2 + (C*a^2*b^3 + 3*B*a*b^4 - A*b^5)*c^2)*d^2 + 2*(D*b^5*c^3*d - 3*D*a*b^4*c^2*d^2 + 3*D*a^2*b^3*c*d^3 - D*a^3*b^2*d^4)*x^2 - 2*(4*D*a^2*b^3*c^3 + C*a*b^4*c^3)*d + (4*D*b^5*c^4 + 2*(C*a*b^4 + B*b^5)*c^2*d^2 - (3*D*a^4*b - C*a^3*b^2 + B*a^2*b^3 - 3*A*a*b^4)*d^4 + (5*D*a^3*b^2*c - (C*a^2*b^3 + B*a*b^4 + 3*A*b^5)*c)*d^3 - 2*(3*D*a*b^4*c^3 + C*b^5*c^3)*d)*x)*sqrt(d*x + c))/(a*b^6*c^4*d^2 - 3*a^2*b^5*c^3*d^3 + 3*a^3*b^4*c^2*d^4 - a^4*b^3*c*d^5 + (b^7*c^3*d^3 - 3*a*b^6*c^2*d^4 + 3*a^2*b^5*c*d^5 - a^3*b^4*d^6)*x^2 + (b^7*c^4*d^2 - 2*a*b^6*c^3*d^3 + 2*a^3*b^4*c*d^5 - a^4*b^3*d^6)*x), -(((3*D*a^4*c - (C*a^3*b + B*a^2*b^2 - 3*A*a*b^3)*c)*d^3 - 2*(3*D*a^3*b*c^2 - (2*C*a^2*b^2 - B*a*b^3)*c^2)*d^2 + ((3*D*a^3*b - C*a^2*b^2 - B*a*b^3 + 3*A*b^4)*d^4 - 2*(3*D*a^2*b^2*c - (2*C*a*b^3 - B*b^4)*c)*d^3)*x^2 + ((3*D*a^4 - C*a^3*b - B*a^2*b^2 + 3*A*a*b^3)*d^4 - 3*(D*a^3*b*c - (C*a^2*b^2 - B*a*b^3 + A*b^4)*c)*d^3 - 2*(3*D*a^2*b^2*c^2 - (2*C*a*b^3 - B*b^4)*c^2)*d^2)*x)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(-b^2*c + a*b*d)*sqrt(d*x + c)/(b*d*x + b*c)) - (4*D*a*b^4*c^4 + 2*A*a^2*b^3*d^4 - (3*D*a^4*b*c - (C*a^3*b^2 - 3*B*a^2*b^3 - A*a*b^4)*c)*d^3 + (7*D*a^3*b^2*c^2 + (C*a^2*b^3 + 3*B*a*b^4 - A*b^5)*c^2)*d^2 + 2*(D*b^5*c^3*d - 3*D*a*b^4*c^2*d^2 + 3*D*a^2*b^3*c*d^3 - D*a^3*b^2*d^4)*x^2 - 2*(4*D*a^2*b^3*c^3 + C*a*b^4*c^3)*d + (4*D*b^5*c^4 + 2*(C*a*b^4 + B*b^5)*c^2*d^2 - (3*D*a^4*b - C*a^3*b^2 + B*a^2*b^3 - 3*A*a*b^4)*d^4 + (5*D*a^3*b^2*c - (C*a^2*b^3 + B*a*b^4 + 3*A*b^5)*c)*d^3 - 2*(3*D*a*b^4*c^3 + C*b^5*c^3)*d)*x)*sqrt(d*x + c))/(a*b^6*c^4*d^2 - 3*a^2*b^5*c^3*d^3 + 3*a^3*b^4*c^2*d^4 - a^4*b^3*c*d^5 + (b^7*c^3*d^3 - 3*a*b^6*c^2*d^4 + 3*a^2*b^5*c*d^5 - a^3*b^4*d^6)*x^2 + (b^7*c^4*d^2 - 2*a*b^6*c^3*d^3 + 2*a^3*b^4*c*d^5 - a^4*b^3*d^6)*x)]","B",0
16,1,2594,0,1.099539," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x+a)^3/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(3 \, D a^{5} c + {\left(C a^{4} b + 3 \, B a^{3} b^{2} - 15 \, A a^{2} b^{3}\right)} c\right)} d^{3} + {\left({\left(3 \, D a^{3} b^{2} + C a^{2} b^{3} + 3 \, B a b^{4} - 15 \, A b^{5}\right)} d^{4} - 4 \, {\left(3 \, D a^{2} b^{3} c + {\left(2 \, C a b^{4} - 3 \, B b^{5}\right)} c\right)} d^{3} + 8 \, {\left(3 \, D a b^{4} c^{2} - C b^{5} c^{2}\right)} d^{2}\right)} x^{3} - 4 \, {\left(3 \, D a^{4} b c^{2} + {\left(2 \, C a^{3} b^{2} - 3 \, B a^{2} b^{3}\right)} c^{2}\right)} d^{2} + {\left(2 \, {\left(3 \, D a^{4} b + C a^{3} b^{2} + 3 \, B a^{2} b^{3} - 15 \, A a b^{4}\right)} d^{4} - 3 \, {\left(7 \, D a^{3} b^{2} c + {\left(5 \, C a^{2} b^{3} - 9 \, B a b^{4} + 5 \, A b^{5}\right)} c\right)} d^{3} + 12 \, {\left(3 \, D a^{2} b^{3} c^{2} - {\left(2 \, C a b^{4} - B b^{5}\right)} c^{2}\right)} d^{2} + 8 \, {\left(3 \, D a b^{4} c^{3} - C b^{5} c^{3}\right)} d\right)} x^{2} + 8 \, {\left(3 \, D a^{3} b^{2} c^{3} - C a^{2} b^{3} c^{3}\right)} d - {\left(24 \, {\left(C a^{2} b^{3} - B a b^{4}\right)} c^{2} d^{2} - {\left(3 \, D a^{5} + C a^{4} b + 3 \, B a^{3} b^{2} - 15 \, A a^{2} b^{3}\right)} d^{4} + 6 \, {\left(D a^{4} b c + {\left(C a^{3} b^{2} - 3 \, B a^{2} b^{3} + 5 \, A a b^{4}\right)} c\right)} d^{3} - 16 \, {\left(3 \, D a^{2} b^{3} c^{3} - C a b^{4} c^{3}\right)} d\right)} x\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, \sqrt{b^{2} c - a b d} \sqrt{d x + c}}{b x + a}\right) + 2 \, {\left(8 \, D a^{2} b^{4} c^{4} + 8 \, A a^{3} b^{3} d^{4} + {\left(3 \, D a^{5} b c + {\left(C a^{4} b^{2} - 13 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} c\right)} d^{3} - {\left(13 \, D a^{4} b^{2} c^{2} - {\left(13 \, C a^{3} b^{3} + 11 \, B a^{2} b^{4} - 11 \, A a b^{5}\right)} c^{2}\right)} d^{2} + {\left(8 \, D b^{6} c^{4} + {\left(5 \, D a^{4} b^{2} - C a^{3} b^{3} - 3 \, B a^{2} b^{4} + 15 \, A a b^{5}\right)} d^{4} - {\left(17 \, D a^{3} b^{3} c - 3 \, {\left(3 \, C a^{2} b^{4} - 3 \, B a b^{5} - 5 \, A b^{6}\right)} c\right)} d^{3} + 12 \, {\left(D a^{2} b^{4} c^{2} + B b^{6} c^{2}\right)} d^{2} - 8 \, {\left(D a b^{5} c^{3} + C b^{6} c^{3}\right)} d\right)} x^{2} + 2 \, {\left(D a^{3} b^{3} c^{3} - {\left(7 \, C a^{2} b^{4} - B a b^{5} - A b^{6}\right)} c^{3}\right)} d + {\left(16 \, D a b^{5} c^{4} + {\left(3 \, D a^{5} b + C a^{4} b^{2} - 5 \, B a^{3} b^{3} + 25 \, A a^{2} b^{4}\right)} d^{4} - 4 \, {\left(2 \, D a^{4} b^{2} c - {\left(C a^{3} b^{3} - 4 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} c\right)} d^{3} - {\left(7 \, D a^{3} b^{3} c^{2} - {\left(19 \, C a^{2} b^{4} + 17 \, B a b^{5} - 5 \, A b^{6}\right)} c^{2}\right)} d^{2} - 4 \, {\left(D a^{2} b^{4} c^{3} + {\left(6 \, C a b^{5} - B b^{6}\right)} c^{3}\right)} d\right)} x\right)} \sqrt{d x + c}}{8 \, {\left(a^{2} b^{7} c^{5} d - 4 \, a^{3} b^{6} c^{4} d^{2} + 6 \, a^{4} b^{5} c^{3} d^{3} - 4 \, a^{5} b^{4} c^{2} d^{4} + a^{6} b^{3} c d^{5} + {\left(b^{9} c^{4} d^{2} - 4 \, a b^{8} c^{3} d^{3} + 6 \, a^{2} b^{7} c^{2} d^{4} - 4 \, a^{3} b^{6} c d^{5} + a^{4} b^{5} d^{6}\right)} x^{3} + {\left(b^{9} c^{5} d - 2 \, a b^{8} c^{4} d^{2} - 2 \, a^{2} b^{7} c^{3} d^{3} + 8 \, a^{3} b^{6} c^{2} d^{4} - 7 \, a^{4} b^{5} c d^{5} + 2 \, a^{5} b^{4} d^{6}\right)} x^{2} + {\left(2 \, a b^{8} c^{5} d - 7 \, a^{2} b^{7} c^{4} d^{2} + 8 \, a^{3} b^{6} c^{3} d^{3} - 2 \, a^{4} b^{5} c^{2} d^{4} - 2 \, a^{5} b^{4} c d^{5} + a^{6} b^{3} d^{6}\right)} x\right)}}, -\frac{{\left({\left(3 \, D a^{5} c + {\left(C a^{4} b + 3 \, B a^{3} b^{2} - 15 \, A a^{2} b^{3}\right)} c\right)} d^{3} + {\left({\left(3 \, D a^{3} b^{2} + C a^{2} b^{3} + 3 \, B a b^{4} - 15 \, A b^{5}\right)} d^{4} - 4 \, {\left(3 \, D a^{2} b^{3} c + {\left(2 \, C a b^{4} - 3 \, B b^{5}\right)} c\right)} d^{3} + 8 \, {\left(3 \, D a b^{4} c^{2} - C b^{5} c^{2}\right)} d^{2}\right)} x^{3} - 4 \, {\left(3 \, D a^{4} b c^{2} + {\left(2 \, C a^{3} b^{2} - 3 \, B a^{2} b^{3}\right)} c^{2}\right)} d^{2} + {\left(2 \, {\left(3 \, D a^{4} b + C a^{3} b^{2} + 3 \, B a^{2} b^{3} - 15 \, A a b^{4}\right)} d^{4} - 3 \, {\left(7 \, D a^{3} b^{2} c + {\left(5 \, C a^{2} b^{3} - 9 \, B a b^{4} + 5 \, A b^{5}\right)} c\right)} d^{3} + 12 \, {\left(3 \, D a^{2} b^{3} c^{2} - {\left(2 \, C a b^{4} - B b^{5}\right)} c^{2}\right)} d^{2} + 8 \, {\left(3 \, D a b^{4} c^{3} - C b^{5} c^{3}\right)} d\right)} x^{2} + 8 \, {\left(3 \, D a^{3} b^{2} c^{3} - C a^{2} b^{3} c^{3}\right)} d - {\left(24 \, {\left(C a^{2} b^{3} - B a b^{4}\right)} c^{2} d^{2} - {\left(3 \, D a^{5} + C a^{4} b + 3 \, B a^{3} b^{2} - 15 \, A a^{2} b^{3}\right)} d^{4} + 6 \, {\left(D a^{4} b c + {\left(C a^{3} b^{2} - 3 \, B a^{2} b^{3} + 5 \, A a b^{4}\right)} c\right)} d^{3} - 16 \, {\left(3 \, D a^{2} b^{3} c^{3} - C a b^{4} c^{3}\right)} d\right)} x\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{-b^{2} c + a b d} \sqrt{d x + c}}{b d x + b c}\right) + {\left(8 \, D a^{2} b^{4} c^{4} + 8 \, A a^{3} b^{3} d^{4} + {\left(3 \, D a^{5} b c + {\left(C a^{4} b^{2} - 13 \, B a^{3} b^{3} + A a^{2} b^{4}\right)} c\right)} d^{3} - {\left(13 \, D a^{4} b^{2} c^{2} - {\left(13 \, C a^{3} b^{3} + 11 \, B a^{2} b^{4} - 11 \, A a b^{5}\right)} c^{2}\right)} d^{2} + {\left(8 \, D b^{6} c^{4} + {\left(5 \, D a^{4} b^{2} - C a^{3} b^{3} - 3 \, B a^{2} b^{4} + 15 \, A a b^{5}\right)} d^{4} - {\left(17 \, D a^{3} b^{3} c - 3 \, {\left(3 \, C a^{2} b^{4} - 3 \, B a b^{5} - 5 \, A b^{6}\right)} c\right)} d^{3} + 12 \, {\left(D a^{2} b^{4} c^{2} + B b^{6} c^{2}\right)} d^{2} - 8 \, {\left(D a b^{5} c^{3} + C b^{6} c^{3}\right)} d\right)} x^{2} + 2 \, {\left(D a^{3} b^{3} c^{3} - {\left(7 \, C a^{2} b^{4} - B a b^{5} - A b^{6}\right)} c^{3}\right)} d + {\left(16 \, D a b^{5} c^{4} + {\left(3 \, D a^{5} b + C a^{4} b^{2} - 5 \, B a^{3} b^{3} + 25 \, A a^{2} b^{4}\right)} d^{4} - 4 \, {\left(2 \, D a^{4} b^{2} c - {\left(C a^{3} b^{3} - 4 \, B a^{2} b^{4} - 5 \, A a b^{5}\right)} c\right)} d^{3} - {\left(7 \, D a^{3} b^{3} c^{2} - {\left(19 \, C a^{2} b^{4} + 17 \, B a b^{5} - 5 \, A b^{6}\right)} c^{2}\right)} d^{2} - 4 \, {\left(D a^{2} b^{4} c^{3} + {\left(6 \, C a b^{5} - B b^{6}\right)} c^{3}\right)} d\right)} x\right)} \sqrt{d x + c}}{4 \, {\left(a^{2} b^{7} c^{5} d - 4 \, a^{3} b^{6} c^{4} d^{2} + 6 \, a^{4} b^{5} c^{3} d^{3} - 4 \, a^{5} b^{4} c^{2} d^{4} + a^{6} b^{3} c d^{5} + {\left(b^{9} c^{4} d^{2} - 4 \, a b^{8} c^{3} d^{3} + 6 \, a^{2} b^{7} c^{2} d^{4} - 4 \, a^{3} b^{6} c d^{5} + a^{4} b^{5} d^{6}\right)} x^{3} + {\left(b^{9} c^{5} d - 2 \, a b^{8} c^{4} d^{2} - 2 \, a^{2} b^{7} c^{3} d^{3} + 8 \, a^{3} b^{6} c^{2} d^{4} - 7 \, a^{4} b^{5} c d^{5} + 2 \, a^{5} b^{4} d^{6}\right)} x^{2} + {\left(2 \, a b^{8} c^{5} d - 7 \, a^{2} b^{7} c^{4} d^{2} + 8 \, a^{3} b^{6} c^{3} d^{3} - 2 \, a^{4} b^{5} c^{2} d^{4} - 2 \, a^{5} b^{4} c d^{5} + a^{6} b^{3} d^{6}\right)} x\right)}}\right]"," ",0,"[-1/8*(((3*D*a^5*c + (C*a^4*b + 3*B*a^3*b^2 - 15*A*a^2*b^3)*c)*d^3 + ((3*D*a^3*b^2 + C*a^2*b^3 + 3*B*a*b^4 - 15*A*b^5)*d^4 - 4*(3*D*a^2*b^3*c + (2*C*a*b^4 - 3*B*b^5)*c)*d^3 + 8*(3*D*a*b^4*c^2 - C*b^5*c^2)*d^2)*x^3 - 4*(3*D*a^4*b*c^2 + (2*C*a^3*b^2 - 3*B*a^2*b^3)*c^2)*d^2 + (2*(3*D*a^4*b + C*a^3*b^2 + 3*B*a^2*b^3 - 15*A*a*b^4)*d^4 - 3*(7*D*a^3*b^2*c + (5*C*a^2*b^3 - 9*B*a*b^4 + 5*A*b^5)*c)*d^3 + 12*(3*D*a^2*b^3*c^2 - (2*C*a*b^4 - B*b^5)*c^2)*d^2 + 8*(3*D*a*b^4*c^3 - C*b^5*c^3)*d)*x^2 + 8*(3*D*a^3*b^2*c^3 - C*a^2*b^3*c^3)*d - (24*(C*a^2*b^3 - B*a*b^4)*c^2*d^2 - (3*D*a^5 + C*a^4*b + 3*B*a^3*b^2 - 15*A*a^2*b^3)*d^4 + 6*(D*a^4*b*c + (C*a^3*b^2 - 3*B*a^2*b^3 + 5*A*a*b^4)*c)*d^3 - 16*(3*D*a^2*b^3*c^3 - C*a*b^4*c^3)*d)*x)*sqrt(b^2*c - a*b*d)*log((b*d*x + 2*b*c - a*d - 2*sqrt(b^2*c - a*b*d)*sqrt(d*x + c))/(b*x + a)) + 2*(8*D*a^2*b^4*c^4 + 8*A*a^3*b^3*d^4 + (3*D*a^5*b*c + (C*a^4*b^2 - 13*B*a^3*b^3 + A*a^2*b^4)*c)*d^3 - (13*D*a^4*b^2*c^2 - (13*C*a^3*b^3 + 11*B*a^2*b^4 - 11*A*a*b^5)*c^2)*d^2 + (8*D*b^6*c^4 + (5*D*a^4*b^2 - C*a^3*b^3 - 3*B*a^2*b^4 + 15*A*a*b^5)*d^4 - (17*D*a^3*b^3*c - 3*(3*C*a^2*b^4 - 3*B*a*b^5 - 5*A*b^6)*c)*d^3 + 12*(D*a^2*b^4*c^2 + B*b^6*c^2)*d^2 - 8*(D*a*b^5*c^3 + C*b^6*c^3)*d)*x^2 + 2*(D*a^3*b^3*c^3 - (7*C*a^2*b^4 - B*a*b^5 - A*b^6)*c^3)*d + (16*D*a*b^5*c^4 + (3*D*a^5*b + C*a^4*b^2 - 5*B*a^3*b^3 + 25*A*a^2*b^4)*d^4 - 4*(2*D*a^4*b^2*c - (C*a^3*b^3 - 4*B*a^2*b^4 - 5*A*a*b^5)*c)*d^3 - (7*D*a^3*b^3*c^2 - (19*C*a^2*b^4 + 17*B*a*b^5 - 5*A*b^6)*c^2)*d^2 - 4*(D*a^2*b^4*c^3 + (6*C*a*b^5 - B*b^6)*c^3)*d)*x)*sqrt(d*x + c))/(a^2*b^7*c^5*d - 4*a^3*b^6*c^4*d^2 + 6*a^4*b^5*c^3*d^3 - 4*a^5*b^4*c^2*d^4 + a^6*b^3*c*d^5 + (b^9*c^4*d^2 - 4*a*b^8*c^3*d^3 + 6*a^2*b^7*c^2*d^4 - 4*a^3*b^6*c*d^5 + a^4*b^5*d^6)*x^3 + (b^9*c^5*d - 2*a*b^8*c^4*d^2 - 2*a^2*b^7*c^3*d^3 + 8*a^3*b^6*c^2*d^4 - 7*a^4*b^5*c*d^5 + 2*a^5*b^4*d^6)*x^2 + (2*a*b^8*c^5*d - 7*a^2*b^7*c^4*d^2 + 8*a^3*b^6*c^3*d^3 - 2*a^4*b^5*c^2*d^4 - 2*a^5*b^4*c*d^5 + a^6*b^3*d^6)*x), -1/4*(((3*D*a^5*c + (C*a^4*b + 3*B*a^3*b^2 - 15*A*a^2*b^3)*c)*d^3 + ((3*D*a^3*b^2 + C*a^2*b^3 + 3*B*a*b^4 - 15*A*b^5)*d^4 - 4*(3*D*a^2*b^3*c + (2*C*a*b^4 - 3*B*b^5)*c)*d^3 + 8*(3*D*a*b^4*c^2 - C*b^5*c^2)*d^2)*x^3 - 4*(3*D*a^4*b*c^2 + (2*C*a^3*b^2 - 3*B*a^2*b^3)*c^2)*d^2 + (2*(3*D*a^4*b + C*a^3*b^2 + 3*B*a^2*b^3 - 15*A*a*b^4)*d^4 - 3*(7*D*a^3*b^2*c + (5*C*a^2*b^3 - 9*B*a*b^4 + 5*A*b^5)*c)*d^3 + 12*(3*D*a^2*b^3*c^2 - (2*C*a*b^4 - B*b^5)*c^2)*d^2 + 8*(3*D*a*b^4*c^3 - C*b^5*c^3)*d)*x^2 + 8*(3*D*a^3*b^2*c^3 - C*a^2*b^3*c^3)*d - (24*(C*a^2*b^3 - B*a*b^4)*c^2*d^2 - (3*D*a^5 + C*a^4*b + 3*B*a^3*b^2 - 15*A*a^2*b^3)*d^4 + 6*(D*a^4*b*c + (C*a^3*b^2 - 3*B*a^2*b^3 + 5*A*a*b^4)*c)*d^3 - 16*(3*D*a^2*b^3*c^3 - C*a*b^4*c^3)*d)*x)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(-b^2*c + a*b*d)*sqrt(d*x + c)/(b*d*x + b*c)) + (8*D*a^2*b^4*c^4 + 8*A*a^3*b^3*d^4 + (3*D*a^5*b*c + (C*a^4*b^2 - 13*B*a^3*b^3 + A*a^2*b^4)*c)*d^3 - (13*D*a^4*b^2*c^2 - (13*C*a^3*b^3 + 11*B*a^2*b^4 - 11*A*a*b^5)*c^2)*d^2 + (8*D*b^6*c^4 + (5*D*a^4*b^2 - C*a^3*b^3 - 3*B*a^2*b^4 + 15*A*a*b^5)*d^4 - (17*D*a^3*b^3*c - 3*(3*C*a^2*b^4 - 3*B*a*b^5 - 5*A*b^6)*c)*d^3 + 12*(D*a^2*b^4*c^2 + B*b^6*c^2)*d^2 - 8*(D*a*b^5*c^3 + C*b^6*c^3)*d)*x^2 + 2*(D*a^3*b^3*c^3 - (7*C*a^2*b^4 - B*a*b^5 - A*b^6)*c^3)*d + (16*D*a*b^5*c^4 + (3*D*a^5*b + C*a^4*b^2 - 5*B*a^3*b^3 + 25*A*a^2*b^4)*d^4 - 4*(2*D*a^4*b^2*c - (C*a^3*b^3 - 4*B*a^2*b^4 - 5*A*a*b^5)*c)*d^3 - (7*D*a^3*b^3*c^2 - (19*C*a^2*b^4 + 17*B*a*b^5 - 5*A*b^6)*c^2)*d^2 - 4*(D*a^2*b^4*c^3 + (6*C*a*b^5 - B*b^6)*c^3)*d)*x)*sqrt(d*x + c))/(a^2*b^7*c^5*d - 4*a^3*b^6*c^4*d^2 + 6*a^4*b^5*c^3*d^3 - 4*a^5*b^4*c^2*d^4 + a^6*b^3*c*d^5 + (b^9*c^4*d^2 - 4*a*b^8*c^3*d^3 + 6*a^2*b^7*c^2*d^4 - 4*a^3*b^6*c*d^5 + a^4*b^5*d^6)*x^3 + (b^9*c^5*d - 2*a*b^8*c^4*d^2 - 2*a^2*b^7*c^3*d^3 + 8*a^3*b^6*c^2*d^4 - 7*a^4*b^5*c*d^5 + 2*a^5*b^4*d^6)*x^2 + (2*a*b^8*c^5*d - 7*a^2*b^7*c^4*d^2 + 8*a^3*b^6*c^3*d^3 - 2*a^4*b^5*c^2*d^4 - 2*a^5*b^4*c*d^5 + a^6*b^3*d^6)*x)]","B",0
17,1,3834,0,1.277297," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x+a)^4/(d*x+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(16 \, D a^{3} b^{3} c^{4} + {\left(16 \, D b^{6} c^{3} d + {\left(D a^{3} b^{3} + C a^{2} b^{4} + 5 \, B a b^{5} - 35 \, A b^{6}\right)} d^{4} - 6 \, {\left(D a^{2} b^{4} c + {\left(2 \, C a b^{5} - 5 \, B b^{6}\right)} c\right)} d^{3} + 24 \, {\left(D a b^{5} c^{2} - C b^{6} c^{2}\right)} d^{2}\right)} x^{4} + {\left(D a^{6} c + {\left(C a^{5} b + 5 \, B a^{4} b^{2} - 35 \, A a^{3} b^{3}\right)} c\right)} d^{3} + {\left(16 \, D b^{6} c^{4} + 3 \, {\left(D a^{4} b^{2} + C a^{3} b^{3} + 5 \, B a^{2} b^{4} - 35 \, A a b^{5}\right)} d^{4} - {\left(17 \, D a^{3} b^{3} c + 5 \, {\left(7 \, C a^{2} b^{4} - 19 \, B a b^{5} + 7 \, A b^{6}\right)} c\right)} d^{3} + 6 \, {\left(11 \, D a^{2} b^{4} c^{2} - {\left(14 \, C a b^{5} - 5 \, B b^{6}\right)} c^{2}\right)} d^{2} + 24 \, {\left(3 \, D a b^{5} c^{3} - C b^{6} c^{3}\right)} d\right)} x^{3} - 6 \, {\left(D a^{5} b c^{2} + {\left(2 \, C a^{4} b^{2} - 5 \, B a^{3} b^{3}\right)} c^{2}\right)} d^{2} + 3 \, {\left(16 \, D a b^{5} c^{4} + {\left(D a^{5} b + C a^{4} b^{2} + 5 \, B a^{3} b^{3} - 35 \, A a^{2} b^{4}\right)} d^{4} - {\left(5 \, D a^{4} b^{2} c + {\left(11 \, C a^{3} b^{3} - 35 \, B a^{2} b^{4} + 35 \, A a b^{5}\right)} c\right)} d^{3} + 6 \, {\left(3 \, D a^{3} b^{3} c^{2} - {\left(6 \, C a^{2} b^{4} - 5 \, B a b^{5}\right)} c^{2}\right)} d^{2} + 8 \, {\left(5 \, D a^{2} b^{4} c^{3} - 3 \, C a b^{5} c^{3}\right)} d\right)} x^{2} + 24 \, {\left(D a^{4} b^{2} c^{3} - C a^{3} b^{3} c^{3}\right)} d + {\left(48 \, D a^{2} b^{4} c^{4} + {\left(D a^{6} + C a^{5} b + 5 \, B a^{4} b^{2} - 35 \, A a^{3} b^{3}\right)} d^{4} - 3 \, {\left(D a^{5} b c + {\left(3 \, C a^{4} b^{2} - 15 \, B a^{3} b^{3} + 35 \, A a^{2} b^{4}\right)} c\right)} d^{3} + 6 \, {\left(D a^{4} b^{2} c^{2} - 5 \, {\left(2 \, C a^{3} b^{3} - 3 \, B a^{2} b^{4}\right)} c^{2}\right)} d^{2} + 8 \, {\left(11 \, D a^{3} b^{3} c^{3} - 9 \, C a^{2} b^{4} c^{3}\right)} d\right)} x\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, \sqrt{b^{2} c - a b d} \sqrt{d x + c}}{b x + a}\right) + 2 \, {\left(92 \, D a^{3} b^{4} c^{4} + 48 \, A a^{4} b^{3} d^{4} - 4 \, {\left(2 \, C a^{2} b^{5} + B a b^{6} + 2 \, A b^{7}\right)} c^{4} + 3 \, {\left(D a^{6} b c + {\left(C a^{5} b^{2} - 27 \, B a^{4} b^{3} + 13 \, A a^{3} b^{4}\right)} c\right)} d^{3} + 3 \, {\left(16 \, D b^{7} c^{4} - {\left(D a^{4} b^{3} + C a^{3} b^{4} + 5 \, B a^{2} b^{5} - 35 \, A a b^{6}\right)} d^{4} + {\left(7 \, D a^{3} b^{4} c + {\left(13 \, C a^{2} b^{5} - 25 \, B a b^{6} - 35 \, A b^{7}\right)} c\right)} d^{3} - 6 \, {\left(5 \, D a^{2} b^{5} c^{2} - {\left(2 \, C a b^{6} + 5 \, B b^{7}\right)} c^{2}\right)} d^{2} + 8 \, {\left(D a b^{6} c^{3} - 3 \, C b^{7} c^{3}\right)} d\right)} x^{3} - {\left(19 \, D a^{5} b^{2} c^{2} - {\left(91 \, C a^{4} b^{3} + 53 \, B a^{3} b^{4} - 125 \, A a^{2} b^{5}\right)} c^{2}\right)} d^{2} + {\left(216 \, D a b^{6} c^{4} - 24 \, C b^{7} c^{4} + 8 \, {\left(D a^{5} b^{2} - C a^{4} b^{3} - 5 \, B a^{3} b^{4} + 35 \, A a^{2} b^{5}\right)} d^{4} - {\left(25 \, D a^{4} b^{3} c - {\left(103 \, C a^{3} b^{4} - 205 \, B a^{2} b^{5} - 245 \, A a b^{6}\right)} c\right)} d^{3} - {\left(73 \, D a^{3} b^{4} c^{2} - {\left(109 \, C a^{2} b^{5} + 215 \, B a b^{6} - 35 \, A b^{7}\right)} c^{2}\right)} d^{2} - 6 \, {\left(21 \, D a^{2} b^{5} c^{3} + 5 \, {\left(6 \, C a b^{6} - B b^{7}\right)} c^{3}\right)} d\right)} x^{2} - 2 \, {\left(38 \, D a^{4} b^{3} c^{3} + {\left(43 \, C a^{3} b^{4} - 16 \, B a^{2} b^{5} - 23 \, A a b^{6}\right)} c^{3}\right)} d + {\left(252 \, D a^{2} b^{5} c^{4} - 12 \, {\left(2 \, C a b^{6} + B b^{7}\right)} c^{4} + 3 \, {\left(D a^{6} b + C a^{5} b^{2} - 11 \, B a^{4} b^{3} + 77 \, A a^{3} b^{4}\right)} d^{4} - {\left(11 \, D a^{5} b^{2} c - {\left(35 \, C a^{4} b^{3} - 179 \, B a^{3} b^{4} - 133 \, A a^{2} b^{5}\right)} c\right)} d^{3} - 2 \, {\left(25 \, D a^{4} b^{3} c^{2} - {\left(106 \, C a^{3} b^{4} + 65 \, B a^{2} b^{5} - 56 \, A a b^{6}\right)} c^{2}\right)} d^{2} - 2 \, {\left(97 \, D a^{3} b^{4} c^{3} + {\left(113 \, C a^{2} b^{5} - 47 \, B a b^{6} - 7 \, A b^{7}\right)} c^{3}\right)} d\right)} x\right)} \sqrt{d x + c}}{48 \, {\left(a^{3} b^{8} c^{6} - 5 \, a^{4} b^{7} c^{5} d + 10 \, a^{5} b^{6} c^{4} d^{2} - 10 \, a^{6} b^{5} c^{3} d^{3} + 5 \, a^{7} b^{4} c^{2} d^{4} - a^{8} b^{3} c d^{5} + {\left(b^{11} c^{5} d - 5 \, a b^{10} c^{4} d^{2} + 10 \, a^{2} b^{9} c^{3} d^{3} - 10 \, a^{3} b^{8} c^{2} d^{4} + 5 \, a^{4} b^{7} c d^{5} - a^{5} b^{6} d^{6}\right)} x^{4} + {\left(b^{11} c^{6} - 2 \, a b^{10} c^{5} d - 5 \, a^{2} b^{9} c^{4} d^{2} + 20 \, a^{3} b^{8} c^{3} d^{3} - 25 \, a^{4} b^{7} c^{2} d^{4} + 14 \, a^{5} b^{6} c d^{5} - 3 \, a^{6} b^{5} d^{6}\right)} x^{3} + 3 \, {\left(a b^{10} c^{6} - 4 \, a^{2} b^{9} c^{5} d + 5 \, a^{3} b^{8} c^{4} d^{2} - 5 \, a^{5} b^{6} c^{2} d^{4} + 4 \, a^{6} b^{5} c d^{5} - a^{7} b^{4} d^{6}\right)} x^{2} + {\left(3 \, a^{2} b^{9} c^{6} - 14 \, a^{3} b^{8} c^{5} d + 25 \, a^{4} b^{7} c^{4} d^{2} - 20 \, a^{5} b^{6} c^{3} d^{3} + 5 \, a^{6} b^{5} c^{2} d^{4} + 2 \, a^{7} b^{4} c d^{5} - a^{8} b^{3} d^{6}\right)} x\right)}}, \frac{3 \, {\left(16 \, D a^{3} b^{3} c^{4} + {\left(16 \, D b^{6} c^{3} d + {\left(D a^{3} b^{3} + C a^{2} b^{4} + 5 \, B a b^{5} - 35 \, A b^{6}\right)} d^{4} - 6 \, {\left(D a^{2} b^{4} c + {\left(2 \, C a b^{5} - 5 \, B b^{6}\right)} c\right)} d^{3} + 24 \, {\left(D a b^{5} c^{2} - C b^{6} c^{2}\right)} d^{2}\right)} x^{4} + {\left(D a^{6} c + {\left(C a^{5} b + 5 \, B a^{4} b^{2} - 35 \, A a^{3} b^{3}\right)} c\right)} d^{3} + {\left(16 \, D b^{6} c^{4} + 3 \, {\left(D a^{4} b^{2} + C a^{3} b^{3} + 5 \, B a^{2} b^{4} - 35 \, A a b^{5}\right)} d^{4} - {\left(17 \, D a^{3} b^{3} c + 5 \, {\left(7 \, C a^{2} b^{4} - 19 \, B a b^{5} + 7 \, A b^{6}\right)} c\right)} d^{3} + 6 \, {\left(11 \, D a^{2} b^{4} c^{2} - {\left(14 \, C a b^{5} - 5 \, B b^{6}\right)} c^{2}\right)} d^{2} + 24 \, {\left(3 \, D a b^{5} c^{3} - C b^{6} c^{3}\right)} d\right)} x^{3} - 6 \, {\left(D a^{5} b c^{2} + {\left(2 \, C a^{4} b^{2} - 5 \, B a^{3} b^{3}\right)} c^{2}\right)} d^{2} + 3 \, {\left(16 \, D a b^{5} c^{4} + {\left(D a^{5} b + C a^{4} b^{2} + 5 \, B a^{3} b^{3} - 35 \, A a^{2} b^{4}\right)} d^{4} - {\left(5 \, D a^{4} b^{2} c + {\left(11 \, C a^{3} b^{3} - 35 \, B a^{2} b^{4} + 35 \, A a b^{5}\right)} c\right)} d^{3} + 6 \, {\left(3 \, D a^{3} b^{3} c^{2} - {\left(6 \, C a^{2} b^{4} - 5 \, B a b^{5}\right)} c^{2}\right)} d^{2} + 8 \, {\left(5 \, D a^{2} b^{4} c^{3} - 3 \, C a b^{5} c^{3}\right)} d\right)} x^{2} + 24 \, {\left(D a^{4} b^{2} c^{3} - C a^{3} b^{3} c^{3}\right)} d + {\left(48 \, D a^{2} b^{4} c^{4} + {\left(D a^{6} + C a^{5} b + 5 \, B a^{4} b^{2} - 35 \, A a^{3} b^{3}\right)} d^{4} - 3 \, {\left(D a^{5} b c + {\left(3 \, C a^{4} b^{2} - 15 \, B a^{3} b^{3} + 35 \, A a^{2} b^{4}\right)} c\right)} d^{3} + 6 \, {\left(D a^{4} b^{2} c^{2} - 5 \, {\left(2 \, C a^{3} b^{3} - 3 \, B a^{2} b^{4}\right)} c^{2}\right)} d^{2} + 8 \, {\left(11 \, D a^{3} b^{3} c^{3} - 9 \, C a^{2} b^{4} c^{3}\right)} d\right)} x\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{-b^{2} c + a b d} \sqrt{d x + c}}{b d x + b c}\right) + {\left(92 \, D a^{3} b^{4} c^{4} + 48 \, A a^{4} b^{3} d^{4} - 4 \, {\left(2 \, C a^{2} b^{5} + B a b^{6} + 2 \, A b^{7}\right)} c^{4} + 3 \, {\left(D a^{6} b c + {\left(C a^{5} b^{2} - 27 \, B a^{4} b^{3} + 13 \, A a^{3} b^{4}\right)} c\right)} d^{3} + 3 \, {\left(16 \, D b^{7} c^{4} - {\left(D a^{4} b^{3} + C a^{3} b^{4} + 5 \, B a^{2} b^{5} - 35 \, A a b^{6}\right)} d^{4} + {\left(7 \, D a^{3} b^{4} c + {\left(13 \, C a^{2} b^{5} - 25 \, B a b^{6} - 35 \, A b^{7}\right)} c\right)} d^{3} - 6 \, {\left(5 \, D a^{2} b^{5} c^{2} - {\left(2 \, C a b^{6} + 5 \, B b^{7}\right)} c^{2}\right)} d^{2} + 8 \, {\left(D a b^{6} c^{3} - 3 \, C b^{7} c^{3}\right)} d\right)} x^{3} - {\left(19 \, D a^{5} b^{2} c^{2} - {\left(91 \, C a^{4} b^{3} + 53 \, B a^{3} b^{4} - 125 \, A a^{2} b^{5}\right)} c^{2}\right)} d^{2} + {\left(216 \, D a b^{6} c^{4} - 24 \, C b^{7} c^{4} + 8 \, {\left(D a^{5} b^{2} - C a^{4} b^{3} - 5 \, B a^{3} b^{4} + 35 \, A a^{2} b^{5}\right)} d^{4} - {\left(25 \, D a^{4} b^{3} c - {\left(103 \, C a^{3} b^{4} - 205 \, B a^{2} b^{5} - 245 \, A a b^{6}\right)} c\right)} d^{3} - {\left(73 \, D a^{3} b^{4} c^{2} - {\left(109 \, C a^{2} b^{5} + 215 \, B a b^{6} - 35 \, A b^{7}\right)} c^{2}\right)} d^{2} - 6 \, {\left(21 \, D a^{2} b^{5} c^{3} + 5 \, {\left(6 \, C a b^{6} - B b^{7}\right)} c^{3}\right)} d\right)} x^{2} - 2 \, {\left(38 \, D a^{4} b^{3} c^{3} + {\left(43 \, C a^{3} b^{4} - 16 \, B a^{2} b^{5} - 23 \, A a b^{6}\right)} c^{3}\right)} d + {\left(252 \, D a^{2} b^{5} c^{4} - 12 \, {\left(2 \, C a b^{6} + B b^{7}\right)} c^{4} + 3 \, {\left(D a^{6} b + C a^{5} b^{2} - 11 \, B a^{4} b^{3} + 77 \, A a^{3} b^{4}\right)} d^{4} - {\left(11 \, D a^{5} b^{2} c - {\left(35 \, C a^{4} b^{3} - 179 \, B a^{3} b^{4} - 133 \, A a^{2} b^{5}\right)} c\right)} d^{3} - 2 \, {\left(25 \, D a^{4} b^{3} c^{2} - {\left(106 \, C a^{3} b^{4} + 65 \, B a^{2} b^{5} - 56 \, A a b^{6}\right)} c^{2}\right)} d^{2} - 2 \, {\left(97 \, D a^{3} b^{4} c^{3} + {\left(113 \, C a^{2} b^{5} - 47 \, B a b^{6} - 7 \, A b^{7}\right)} c^{3}\right)} d\right)} x\right)} \sqrt{d x + c}}{24 \, {\left(a^{3} b^{8} c^{6} - 5 \, a^{4} b^{7} c^{5} d + 10 \, a^{5} b^{6} c^{4} d^{2} - 10 \, a^{6} b^{5} c^{3} d^{3} + 5 \, a^{7} b^{4} c^{2} d^{4} - a^{8} b^{3} c d^{5} + {\left(b^{11} c^{5} d - 5 \, a b^{10} c^{4} d^{2} + 10 \, a^{2} b^{9} c^{3} d^{3} - 10 \, a^{3} b^{8} c^{2} d^{4} + 5 \, a^{4} b^{7} c d^{5} - a^{5} b^{6} d^{6}\right)} x^{4} + {\left(b^{11} c^{6} - 2 \, a b^{10} c^{5} d - 5 \, a^{2} b^{9} c^{4} d^{2} + 20 \, a^{3} b^{8} c^{3} d^{3} - 25 \, a^{4} b^{7} c^{2} d^{4} + 14 \, a^{5} b^{6} c d^{5} - 3 \, a^{6} b^{5} d^{6}\right)} x^{3} + 3 \, {\left(a b^{10} c^{6} - 4 \, a^{2} b^{9} c^{5} d + 5 \, a^{3} b^{8} c^{4} d^{2} - 5 \, a^{5} b^{6} c^{2} d^{4} + 4 \, a^{6} b^{5} c d^{5} - a^{7} b^{4} d^{6}\right)} x^{2} + {\left(3 \, a^{2} b^{9} c^{6} - 14 \, a^{3} b^{8} c^{5} d + 25 \, a^{4} b^{7} c^{4} d^{2} - 20 \, a^{5} b^{6} c^{3} d^{3} + 5 \, a^{6} b^{5} c^{2} d^{4} + 2 \, a^{7} b^{4} c d^{5} - a^{8} b^{3} d^{6}\right)} x\right)}}\right]"," ",0,"[1/48*(3*(16*D*a^3*b^3*c^4 + (16*D*b^6*c^3*d + (D*a^3*b^3 + C*a^2*b^4 + 5*B*a*b^5 - 35*A*b^6)*d^4 - 6*(D*a^2*b^4*c + (2*C*a*b^5 - 5*B*b^6)*c)*d^3 + 24*(D*a*b^5*c^2 - C*b^6*c^2)*d^2)*x^4 + (D*a^6*c + (C*a^5*b + 5*B*a^4*b^2 - 35*A*a^3*b^3)*c)*d^3 + (16*D*b^6*c^4 + 3*(D*a^4*b^2 + C*a^3*b^3 + 5*B*a^2*b^4 - 35*A*a*b^5)*d^4 - (17*D*a^3*b^3*c + 5*(7*C*a^2*b^4 - 19*B*a*b^5 + 7*A*b^6)*c)*d^3 + 6*(11*D*a^2*b^4*c^2 - (14*C*a*b^5 - 5*B*b^6)*c^2)*d^2 + 24*(3*D*a*b^5*c^3 - C*b^6*c^3)*d)*x^3 - 6*(D*a^5*b*c^2 + (2*C*a^4*b^2 - 5*B*a^3*b^3)*c^2)*d^2 + 3*(16*D*a*b^5*c^4 + (D*a^5*b + C*a^4*b^2 + 5*B*a^3*b^3 - 35*A*a^2*b^4)*d^4 - (5*D*a^4*b^2*c + (11*C*a^3*b^3 - 35*B*a^2*b^4 + 35*A*a*b^5)*c)*d^3 + 6*(3*D*a^3*b^3*c^2 - (6*C*a^2*b^4 - 5*B*a*b^5)*c^2)*d^2 + 8*(5*D*a^2*b^4*c^3 - 3*C*a*b^5*c^3)*d)*x^2 + 24*(D*a^4*b^2*c^3 - C*a^3*b^3*c^3)*d + (48*D*a^2*b^4*c^4 + (D*a^6 + C*a^5*b + 5*B*a^4*b^2 - 35*A*a^3*b^3)*d^4 - 3*(D*a^5*b*c + (3*C*a^4*b^2 - 15*B*a^3*b^3 + 35*A*a^2*b^4)*c)*d^3 + 6*(D*a^4*b^2*c^2 - 5*(2*C*a^3*b^3 - 3*B*a^2*b^4)*c^2)*d^2 + 8*(11*D*a^3*b^3*c^3 - 9*C*a^2*b^4*c^3)*d)*x)*sqrt(b^2*c - a*b*d)*log((b*d*x + 2*b*c - a*d - 2*sqrt(b^2*c - a*b*d)*sqrt(d*x + c))/(b*x + a)) + 2*(92*D*a^3*b^4*c^4 + 48*A*a^4*b^3*d^4 - 4*(2*C*a^2*b^5 + B*a*b^6 + 2*A*b^7)*c^4 + 3*(D*a^6*b*c + (C*a^5*b^2 - 27*B*a^4*b^3 + 13*A*a^3*b^4)*c)*d^3 + 3*(16*D*b^7*c^4 - (D*a^4*b^3 + C*a^3*b^4 + 5*B*a^2*b^5 - 35*A*a*b^6)*d^4 + (7*D*a^3*b^4*c + (13*C*a^2*b^5 - 25*B*a*b^6 - 35*A*b^7)*c)*d^3 - 6*(5*D*a^2*b^5*c^2 - (2*C*a*b^6 + 5*B*b^7)*c^2)*d^2 + 8*(D*a*b^6*c^3 - 3*C*b^7*c^3)*d)*x^3 - (19*D*a^5*b^2*c^2 - (91*C*a^4*b^3 + 53*B*a^3*b^4 - 125*A*a^2*b^5)*c^2)*d^2 + (216*D*a*b^6*c^4 - 24*C*b^7*c^4 + 8*(D*a^5*b^2 - C*a^4*b^3 - 5*B*a^3*b^4 + 35*A*a^2*b^5)*d^4 - (25*D*a^4*b^3*c - (103*C*a^3*b^4 - 205*B*a^2*b^5 - 245*A*a*b^6)*c)*d^3 - (73*D*a^3*b^4*c^2 - (109*C*a^2*b^5 + 215*B*a*b^6 - 35*A*b^7)*c^2)*d^2 - 6*(21*D*a^2*b^5*c^3 + 5*(6*C*a*b^6 - B*b^7)*c^3)*d)*x^2 - 2*(38*D*a^4*b^3*c^3 + (43*C*a^3*b^4 - 16*B*a^2*b^5 - 23*A*a*b^6)*c^3)*d + (252*D*a^2*b^5*c^4 - 12*(2*C*a*b^6 + B*b^7)*c^4 + 3*(D*a^6*b + C*a^5*b^2 - 11*B*a^4*b^3 + 77*A*a^3*b^4)*d^4 - (11*D*a^5*b^2*c - (35*C*a^4*b^3 - 179*B*a^3*b^4 - 133*A*a^2*b^5)*c)*d^3 - 2*(25*D*a^4*b^3*c^2 - (106*C*a^3*b^4 + 65*B*a^2*b^5 - 56*A*a*b^6)*c^2)*d^2 - 2*(97*D*a^3*b^4*c^3 + (113*C*a^2*b^5 - 47*B*a*b^6 - 7*A*b^7)*c^3)*d)*x)*sqrt(d*x + c))/(a^3*b^8*c^6 - 5*a^4*b^7*c^5*d + 10*a^5*b^6*c^4*d^2 - 10*a^6*b^5*c^3*d^3 + 5*a^7*b^4*c^2*d^4 - a^8*b^3*c*d^5 + (b^11*c^5*d - 5*a*b^10*c^4*d^2 + 10*a^2*b^9*c^3*d^3 - 10*a^3*b^8*c^2*d^4 + 5*a^4*b^7*c*d^5 - a^5*b^6*d^6)*x^4 + (b^11*c^6 - 2*a*b^10*c^5*d - 5*a^2*b^9*c^4*d^2 + 20*a^3*b^8*c^3*d^3 - 25*a^4*b^7*c^2*d^4 + 14*a^5*b^6*c*d^5 - 3*a^6*b^5*d^6)*x^3 + 3*(a*b^10*c^6 - 4*a^2*b^9*c^5*d + 5*a^3*b^8*c^4*d^2 - 5*a^5*b^6*c^2*d^4 + 4*a^6*b^5*c*d^5 - a^7*b^4*d^6)*x^2 + (3*a^2*b^9*c^6 - 14*a^3*b^8*c^5*d + 25*a^4*b^7*c^4*d^2 - 20*a^5*b^6*c^3*d^3 + 5*a^6*b^5*c^2*d^4 + 2*a^7*b^4*c*d^5 - a^8*b^3*d^6)*x), 1/24*(3*(16*D*a^3*b^3*c^4 + (16*D*b^6*c^3*d + (D*a^3*b^3 + C*a^2*b^4 + 5*B*a*b^5 - 35*A*b^6)*d^4 - 6*(D*a^2*b^4*c + (2*C*a*b^5 - 5*B*b^6)*c)*d^3 + 24*(D*a*b^5*c^2 - C*b^6*c^2)*d^2)*x^4 + (D*a^6*c + (C*a^5*b + 5*B*a^4*b^2 - 35*A*a^3*b^3)*c)*d^3 + (16*D*b^6*c^4 + 3*(D*a^4*b^2 + C*a^3*b^3 + 5*B*a^2*b^4 - 35*A*a*b^5)*d^4 - (17*D*a^3*b^3*c + 5*(7*C*a^2*b^4 - 19*B*a*b^5 + 7*A*b^6)*c)*d^3 + 6*(11*D*a^2*b^4*c^2 - (14*C*a*b^5 - 5*B*b^6)*c^2)*d^2 + 24*(3*D*a*b^5*c^3 - C*b^6*c^3)*d)*x^3 - 6*(D*a^5*b*c^2 + (2*C*a^4*b^2 - 5*B*a^3*b^3)*c^2)*d^2 + 3*(16*D*a*b^5*c^4 + (D*a^5*b + C*a^4*b^2 + 5*B*a^3*b^3 - 35*A*a^2*b^4)*d^4 - (5*D*a^4*b^2*c + (11*C*a^3*b^3 - 35*B*a^2*b^4 + 35*A*a*b^5)*c)*d^3 + 6*(3*D*a^3*b^3*c^2 - (6*C*a^2*b^4 - 5*B*a*b^5)*c^2)*d^2 + 8*(5*D*a^2*b^4*c^3 - 3*C*a*b^5*c^3)*d)*x^2 + 24*(D*a^4*b^2*c^3 - C*a^3*b^3*c^3)*d + (48*D*a^2*b^4*c^4 + (D*a^6 + C*a^5*b + 5*B*a^4*b^2 - 35*A*a^3*b^3)*d^4 - 3*(D*a^5*b*c + (3*C*a^4*b^2 - 15*B*a^3*b^3 + 35*A*a^2*b^4)*c)*d^3 + 6*(D*a^4*b^2*c^2 - 5*(2*C*a^3*b^3 - 3*B*a^2*b^4)*c^2)*d^2 + 8*(11*D*a^3*b^3*c^3 - 9*C*a^2*b^4*c^3)*d)*x)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(-b^2*c + a*b*d)*sqrt(d*x + c)/(b*d*x + b*c)) + (92*D*a^3*b^4*c^4 + 48*A*a^4*b^3*d^4 - 4*(2*C*a^2*b^5 + B*a*b^6 + 2*A*b^7)*c^4 + 3*(D*a^6*b*c + (C*a^5*b^2 - 27*B*a^4*b^3 + 13*A*a^3*b^4)*c)*d^3 + 3*(16*D*b^7*c^4 - (D*a^4*b^3 + C*a^3*b^4 + 5*B*a^2*b^5 - 35*A*a*b^6)*d^4 + (7*D*a^3*b^4*c + (13*C*a^2*b^5 - 25*B*a*b^6 - 35*A*b^7)*c)*d^3 - 6*(5*D*a^2*b^5*c^2 - (2*C*a*b^6 + 5*B*b^7)*c^2)*d^2 + 8*(D*a*b^6*c^3 - 3*C*b^7*c^3)*d)*x^3 - (19*D*a^5*b^2*c^2 - (91*C*a^4*b^3 + 53*B*a^3*b^4 - 125*A*a^2*b^5)*c^2)*d^2 + (216*D*a*b^6*c^4 - 24*C*b^7*c^4 + 8*(D*a^5*b^2 - C*a^4*b^3 - 5*B*a^3*b^4 + 35*A*a^2*b^5)*d^4 - (25*D*a^4*b^3*c - (103*C*a^3*b^4 - 205*B*a^2*b^5 - 245*A*a*b^6)*c)*d^3 - (73*D*a^3*b^4*c^2 - (109*C*a^2*b^5 + 215*B*a*b^6 - 35*A*b^7)*c^2)*d^2 - 6*(21*D*a^2*b^5*c^3 + 5*(6*C*a*b^6 - B*b^7)*c^3)*d)*x^2 - 2*(38*D*a^4*b^3*c^3 + (43*C*a^3*b^4 - 16*B*a^2*b^5 - 23*A*a*b^6)*c^3)*d + (252*D*a^2*b^5*c^4 - 12*(2*C*a*b^6 + B*b^7)*c^4 + 3*(D*a^6*b + C*a^5*b^2 - 11*B*a^4*b^3 + 77*A*a^3*b^4)*d^4 - (11*D*a^5*b^2*c - (35*C*a^4*b^3 - 179*B*a^3*b^4 - 133*A*a^2*b^5)*c)*d^3 - 2*(25*D*a^4*b^3*c^2 - (106*C*a^3*b^4 + 65*B*a^2*b^5 - 56*A*a*b^6)*c^2)*d^2 - 2*(97*D*a^3*b^4*c^3 + (113*C*a^2*b^5 - 47*B*a*b^6 - 7*A*b^7)*c^3)*d)*x)*sqrt(d*x + c))/(a^3*b^8*c^6 - 5*a^4*b^7*c^5*d + 10*a^5*b^6*c^4*d^2 - 10*a^6*b^5*c^3*d^3 + 5*a^7*b^4*c^2*d^4 - a^8*b^3*c*d^5 + (b^11*c^5*d - 5*a*b^10*c^4*d^2 + 10*a^2*b^9*c^3*d^3 - 10*a^3*b^8*c^2*d^4 + 5*a^4*b^7*c*d^5 - a^5*b^6*d^6)*x^4 + (b^11*c^6 - 2*a*b^10*c^5*d - 5*a^2*b^9*c^4*d^2 + 20*a^3*b^8*c^3*d^3 - 25*a^4*b^7*c^2*d^4 + 14*a^5*b^6*c*d^5 - 3*a^6*b^5*d^6)*x^3 + 3*(a*b^10*c^6 - 4*a^2*b^9*c^5*d + 5*a^3*b^8*c^4*d^2 - 5*a^5*b^6*c^2*d^4 + 4*a^6*b^5*c*d^5 - a^7*b^4*d^6)*x^2 + (3*a^2*b^9*c^6 - 14*a^3*b^8*c^5*d + 25*a^4*b^7*c^4*d^2 - 20*a^5*b^6*c^3*d^3 + 5*a^6*b^5*c^2*d^4 + 2*a^7*b^4*c*d^5 - a^8*b^3*d^6)*x)]","B",0
18,1,689,0,0.957676," ","integrate((b*x+a)^3*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, D b^{3} d^{6} x^{6} + 5120 \, D b^{3} c^{6} - 105 \, A a^{3} d^{6} + 840 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} c^{2} d^{4} - 210 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c d^{5} - 15 \, {\left(4 \, D b^{3} c d^{5} - 3 \, {\left(3 \, D a b^{2} + C b^{3}\right)} d^{6}\right)} x^{5} + 3 \, {\left(40 \, D b^{3} c^{2} d^{4} + 21 \, {\left(3 \, D a^{2} b + 3 \, C a b^{2} + B b^{3}\right)} d^{6} - 30 \, {\left(3 \, D a b^{2} c + C b^{3} c\right)} d^{5}\right)} x^{4} - 1680 \, {\left(D a^{3} c^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c^{3}\right)} d^{3} - {\left(320 \, D b^{3} c^{3} d^{3} - 105 \, {\left(D a^{3} + 3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} d^{6} + 168 \, {\left(3 \, D a^{2} b c + {\left(3 \, C a b^{2} + B b^{3}\right)} c\right)} d^{5} - 240 \, {\left(3 \, D a b^{2} c^{2} + C b^{3} c^{2}\right)} d^{4}\right)} x^{3} + 2688 \, {\left(3 \, D a^{2} b c^{4} + {\left(3 \, C a b^{2} + B b^{3}\right)} c^{4}\right)} d^{2} + 3 \, {\left(640 \, D b^{3} c^{4} d^{2} + 105 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} d^{6} - 210 \, {\left(D a^{3} c + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c\right)} d^{5} + 336 \, {\left(3 \, D a^{2} b c^{2} + {\left(3 \, C a b^{2} + B b^{3}\right)} c^{2}\right)} d^{4} - 480 \, {\left(3 \, D a b^{2} c^{3} + C b^{3} c^{3}\right)} d^{3}\right)} x^{2} - 3840 \, {\left(3 \, D a b^{2} c^{5} + C b^{3} c^{5}\right)} d + 3 \, {\left(2560 \, D b^{3} c^{5} d + 420 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} c d^{5} - 105 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{6} - 840 \, {\left(D a^{3} c^{2} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c^{2}\right)} d^{4} + 1344 \, {\left(3 \, D a^{2} b c^{3} + {\left(3 \, C a b^{2} + B b^{3}\right)} c^{3}\right)} d^{3} - 1920 \, {\left(3 \, D a b^{2} c^{4} + C b^{3} c^{4}\right)} d^{2}\right)} x\right)} \sqrt{d x + c}}{315 \, {\left(d^{9} x^{2} + 2 \, c d^{8} x + c^{2} d^{7}\right)}}"," ",0,"2/315*(35*D*b^3*d^6*x^6 + 5120*D*b^3*c^6 - 105*A*a^3*d^6 + 840*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*c^2*d^4 - 210*(B*a^3 + 3*A*a^2*b)*c*d^5 - 15*(4*D*b^3*c*d^5 - 3*(3*D*a*b^2 + C*b^3)*d^6)*x^5 + 3*(40*D*b^3*c^2*d^4 + 21*(3*D*a^2*b + 3*C*a*b^2 + B*b^3)*d^6 - 30*(3*D*a*b^2*c + C*b^3*c)*d^5)*x^4 - 1680*(D*a^3*c^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c^3)*d^3 - (320*D*b^3*c^3*d^3 - 105*(D*a^3 + 3*C*a^2*b + 3*B*a*b^2 + A*b^3)*d^6 + 168*(3*D*a^2*b*c + (3*C*a*b^2 + B*b^3)*c)*d^5 - 240*(3*D*a*b^2*c^2 + C*b^3*c^2)*d^4)*x^3 + 2688*(3*D*a^2*b*c^4 + (3*C*a*b^2 + B*b^3)*c^4)*d^2 + 3*(640*D*b^3*c^4*d^2 + 105*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*d^6 - 210*(D*a^3*c + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c)*d^5 + 336*(3*D*a^2*b*c^2 + (3*C*a*b^2 + B*b^3)*c^2)*d^4 - 480*(3*D*a*b^2*c^3 + C*b^3*c^3)*d^3)*x^2 - 3840*(3*D*a*b^2*c^5 + C*b^3*c^5)*d + 3*(2560*D*b^3*c^5*d + 420*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*c*d^5 - 105*(B*a^3 + 3*A*a^2*b)*d^6 - 840*(D*a^3*c^2 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c^2)*d^4 + 1344*(3*D*a^2*b*c^3 + (3*C*a*b^2 + B*b^3)*c^3)*d^3 - 1920*(3*D*a*b^2*c^4 + C*b^3*c^4)*d^2)*x)*sqrt(d*x + c)/(d^9*x^2 + 2*c*d^8*x + c^2*d^7)","A",0
19,1,431,0,0.688361," ","integrate((b*x+a)^2*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, D b^{2} d^{5} x^{5} - 1280 \, D b^{2} c^{5} - 35 \, A a^{2} d^{5} + 280 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{2} d^{3} - 70 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{4} - 3 \, {\left(10 \, D b^{2} c d^{4} - 7 \, {\left(2 \, D a b + C b^{2}\right)} d^{5}\right)} x^{4} + {\left(80 \, D b^{2} c^{2} d^{3} + 35 \, {\left(D a^{2} + 2 \, C a b + B b^{2}\right)} d^{5} - 56 \, {\left(2 \, D a b c + C b^{2} c\right)} d^{4}\right)} x^{3} - 560 \, {\left(D a^{2} c^{3} + {\left(2 \, C a b + B b^{2}\right)} c^{3}\right)} d^{2} - 3 \, {\left(160 \, D b^{2} c^{3} d^{2} - 35 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{5} + 70 \, {\left(D a^{2} c + {\left(2 \, C a b + B b^{2}\right)} c\right)} d^{4} - 112 \, {\left(2 \, D a b c^{2} + C b^{2} c^{2}\right)} d^{3}\right)} x^{2} + 896 \, {\left(2 \, D a b c^{4} + C b^{2} c^{4}\right)} d - 3 \, {\left(640 \, D b^{2} c^{4} d - 140 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c d^{4} + 35 \, {\left(B a^{2} + 2 \, A a b\right)} d^{5} + 280 \, {\left(D a^{2} c^{2} + {\left(2 \, C a b + B b^{2}\right)} c^{2}\right)} d^{3} - 448 \, {\left(2 \, D a b c^{3} + C b^{2} c^{3}\right)} d^{2}\right)} x\right)} \sqrt{d x + c}}{105 \, {\left(d^{8} x^{2} + 2 \, c d^{7} x + c^{2} d^{6}\right)}}"," ",0,"2/105*(15*D*b^2*d^5*x^5 - 1280*D*b^2*c^5 - 35*A*a^2*d^5 + 280*(C*a^2 + 2*B*a*b + A*b^2)*c^2*d^3 - 70*(B*a^2 + 2*A*a*b)*c*d^4 - 3*(10*D*b^2*c*d^4 - 7*(2*D*a*b + C*b^2)*d^5)*x^4 + (80*D*b^2*c^2*d^3 + 35*(D*a^2 + 2*C*a*b + B*b^2)*d^5 - 56*(2*D*a*b*c + C*b^2*c)*d^4)*x^3 - 560*(D*a^2*c^3 + (2*C*a*b + B*b^2)*c^3)*d^2 - 3*(160*D*b^2*c^3*d^2 - 35*(C*a^2 + 2*B*a*b + A*b^2)*d^5 + 70*(D*a^2*c + (2*C*a*b + B*b^2)*c)*d^4 - 112*(2*D*a*b*c^2 + C*b^2*c^2)*d^3)*x^2 + 896*(2*D*a*b*c^4 + C*b^2*c^4)*d - 3*(640*D*b^2*c^4*d - 140*(C*a^2 + 2*B*a*b + A*b^2)*c*d^4 + 35*(B*a^2 + 2*A*a*b)*d^5 + 280*(D*a^2*c^2 + (2*C*a*b + B*b^2)*c^2)*d^3 - 448*(2*D*a*b*c^3 + C*b^2*c^3)*d^2)*x)*sqrt(d*x + c)/(d^8*x^2 + 2*c*d^7*x + c^2*d^6)","A",0
20,1,225,0,0.820794," ","integrate((b*x+a)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, D b d^{4} x^{4} + 128 \, D b c^{4} - 5 \, A a d^{4} + 40 \, {\left(C a + B b\right)} c^{2} d^{2} - 10 \, {\left(B a + A b\right)} c d^{3} - {\left(8 \, D b c d^{3} - 5 \, {\left(D a + C b\right)} d^{4}\right)} x^{3} + 3 \, {\left(16 \, D b c^{2} d^{2} + 5 \, {\left(C a + B b\right)} d^{4} - 10 \, {\left(D a c + C b c\right)} d^{3}\right)} x^{2} - 80 \, {\left(D a c^{3} + C b c^{3}\right)} d + 3 \, {\left(64 \, D b c^{3} d + 20 \, {\left(C a + B b\right)} c d^{3} - 5 \, {\left(B a + A b\right)} d^{4} - 40 \, {\left(D a c^{2} + C b c^{2}\right)} d^{2}\right)} x\right)} \sqrt{d x + c}}{15 \, {\left(d^{7} x^{2} + 2 \, c d^{6} x + c^{2} d^{5}\right)}}"," ",0,"2/15*(3*D*b*d^4*x^4 + 128*D*b*c^4 - 5*A*a*d^4 + 40*(C*a + B*b)*c^2*d^2 - 10*(B*a + A*b)*c*d^3 - (8*D*b*c*d^3 - 5*(D*a + C*b)*d^4)*x^3 + 3*(16*D*b*c^2*d^2 + 5*(C*a + B*b)*d^4 - 10*(D*a*c + C*b*c)*d^3)*x^2 - 80*(D*a*c^3 + C*b*c^3)*d + 3*(64*D*b*c^3*d + 20*(C*a + B*b)*c*d^3 - 5*(B*a + A*b)*d^4 - 40*(D*a*c^2 + C*b*c^2)*d^2)*x)*sqrt(d*x + c)/(d^7*x^2 + 2*c*d^6*x + c^2*d^5)","A",0
21,1,110,0,0.880436," ","integrate((D*x^3+C*x^2+B*x+A)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(D d^{3} x^{3} - 16 \, D c^{3} + 8 \, C c^{2} d - 2 \, B c d^{2} - A d^{3} - 3 \, {\left(2 \, D c d^{2} - C d^{3}\right)} x^{2} - 3 \, {\left(8 \, D c^{2} d - 4 \, C c d^{2} + B d^{3}\right)} x\right)} \sqrt{d x + c}}{3 \, {\left(d^{6} x^{2} + 2 \, c d^{5} x + c^{2} d^{4}\right)}}"," ",0,"2/3*(D*d^3*x^3 - 16*D*c^3 + 8*C*c^2*d - 2*B*c*d^2 - A*d^3 - 3*(2*D*c*d^2 - C*d^3)*x^2 - 3*(8*D*c^2*d - 4*C*c*d^2 + B*d^3)*x)*sqrt(d*x + c)/(d^6*x^2 + 2*c*d^5*x + c^2*d^4)","A",0
22,1,1287,0,0.831016," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x+a)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(D a^{3} - C a^{2} b + B a b^{2} - A b^{3}\right)} d^{5} x^{2} + 2 \, {\left(D a^{3} c - {\left(C a^{2} b - B a b^{2} + A b^{3}\right)} c\right)} d^{4} x + {\left(D a^{3} c^{2} - {\left(C a^{2} b - B a b^{2} + A b^{3}\right)} c^{2}\right)} d^{3}\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x + 2 \, b c - a d + 2 \, \sqrt{b^{2} c - a b d} \sqrt{d x + c}}{b x + a}\right) + 2 \, {\left(8 \, D b^{4} c^{5} + A a^{2} b^{2} d^{5} + {\left(2 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} c d^{4} - {\left(3 \, D a^{3} b c^{2} + {\left(5 \, C a^{2} b^{2} + B a b^{3} - 4 \, A b^{4}\right)} c^{2}\right)} d^{3} + {\left(17 \, D a^{2} b^{2} c^{3} + {\left(7 \, C a b^{3} - B b^{4}\right)} c^{3}\right)} d^{2} + 3 \, {\left(D b^{4} c^{3} d^{2} - 3 \, D a b^{3} c^{2} d^{3} + 3 \, D a^{2} b^{2} c d^{4} - D a^{3} b d^{5}\right)} x^{2} - 2 \, {\left(11 \, D a b^{3} c^{4} + C b^{4} c^{4}\right)} d + 3 \, {\left(4 \, D b^{4} c^{4} d + {\left(B a^{2} b^{2} - A a b^{3}\right)} d^{5} - {\left(2 \, D a^{3} b c + {\left(2 \, C a^{2} b^{2} + B a b^{3} - A b^{4}\right)} c\right)} d^{4} + 3 \, {\left(3 \, D a^{2} b^{2} c^{2} + C a b^{3} c^{2}\right)} d^{3} - {\left(11 \, D a b^{3} c^{3} + C b^{4} c^{3}\right)} d^{2}\right)} x\right)} \sqrt{d x + c}}{3 \, {\left(b^{5} c^{5} d^{3} - 3 \, a b^{4} c^{4} d^{4} + 3 \, a^{2} b^{3} c^{3} d^{5} - a^{3} b^{2} c^{2} d^{6} + {\left(b^{5} c^{3} d^{5} - 3 \, a b^{4} c^{2} d^{6} + 3 \, a^{2} b^{3} c d^{7} - a^{3} b^{2} d^{8}\right)} x^{2} + 2 \, {\left(b^{5} c^{4} d^{4} - 3 \, a b^{4} c^{3} d^{5} + 3 \, a^{2} b^{3} c^{2} d^{6} - a^{3} b^{2} c d^{7}\right)} x\right)}}, -\frac{2 \, {\left(3 \, {\left({\left(D a^{3} - C a^{2} b + B a b^{2} - A b^{3}\right)} d^{5} x^{2} + 2 \, {\left(D a^{3} c - {\left(C a^{2} b - B a b^{2} + A b^{3}\right)} c\right)} d^{4} x + {\left(D a^{3} c^{2} - {\left(C a^{2} b - B a b^{2} + A b^{3}\right)} c^{2}\right)} d^{3}\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{-b^{2} c + a b d} \sqrt{d x + c}}{b d x + b c}\right) - {\left(8 \, D b^{4} c^{5} + A a^{2} b^{2} d^{5} + {\left(2 \, B a^{2} b^{2} - 5 \, A a b^{3}\right)} c d^{4} - {\left(3 \, D a^{3} b c^{2} + {\left(5 \, C a^{2} b^{2} + B a b^{3} - 4 \, A b^{4}\right)} c^{2}\right)} d^{3} + {\left(17 \, D a^{2} b^{2} c^{3} + {\left(7 \, C a b^{3} - B b^{4}\right)} c^{3}\right)} d^{2} + 3 \, {\left(D b^{4} c^{3} d^{2} - 3 \, D a b^{3} c^{2} d^{3} + 3 \, D a^{2} b^{2} c d^{4} - D a^{3} b d^{5}\right)} x^{2} - 2 \, {\left(11 \, D a b^{3} c^{4} + C b^{4} c^{4}\right)} d + 3 \, {\left(4 \, D b^{4} c^{4} d + {\left(B a^{2} b^{2} - A a b^{3}\right)} d^{5} - {\left(2 \, D a^{3} b c + {\left(2 \, C a^{2} b^{2} + B a b^{3} - A b^{4}\right)} c\right)} d^{4} + 3 \, {\left(3 \, D a^{2} b^{2} c^{2} + C a b^{3} c^{2}\right)} d^{3} - {\left(11 \, D a b^{3} c^{3} + C b^{4} c^{3}\right)} d^{2}\right)} x\right)} \sqrt{d x + c}\right)}}{3 \, {\left(b^{5} c^{5} d^{3} - 3 \, a b^{4} c^{4} d^{4} + 3 \, a^{2} b^{3} c^{3} d^{5} - a^{3} b^{2} c^{2} d^{6} + {\left(b^{5} c^{3} d^{5} - 3 \, a b^{4} c^{2} d^{6} + 3 \, a^{2} b^{3} c d^{7} - a^{3} b^{2} d^{8}\right)} x^{2} + 2 \, {\left(b^{5} c^{4} d^{4} - 3 \, a b^{4} c^{3} d^{5} + 3 \, a^{2} b^{3} c^{2} d^{6} - a^{3} b^{2} c d^{7}\right)} x\right)}}\right]"," ",0,"[1/3*(3*((D*a^3 - C*a^2*b + B*a*b^2 - A*b^3)*d^5*x^2 + 2*(D*a^3*c - (C*a^2*b - B*a*b^2 + A*b^3)*c)*d^4*x + (D*a^3*c^2 - (C*a^2*b - B*a*b^2 + A*b^3)*c^2)*d^3)*sqrt(b^2*c - a*b*d)*log((b*d*x + 2*b*c - a*d + 2*sqrt(b^2*c - a*b*d)*sqrt(d*x + c))/(b*x + a)) + 2*(8*D*b^4*c^5 + A*a^2*b^2*d^5 + (2*B*a^2*b^2 - 5*A*a*b^3)*c*d^4 - (3*D*a^3*b*c^2 + (5*C*a^2*b^2 + B*a*b^3 - 4*A*b^4)*c^2)*d^3 + (17*D*a^2*b^2*c^3 + (7*C*a*b^3 - B*b^4)*c^3)*d^2 + 3*(D*b^4*c^3*d^2 - 3*D*a*b^3*c^2*d^3 + 3*D*a^2*b^2*c*d^4 - D*a^3*b*d^5)*x^2 - 2*(11*D*a*b^3*c^4 + C*b^4*c^4)*d + 3*(4*D*b^4*c^4*d + (B*a^2*b^2 - A*a*b^3)*d^5 - (2*D*a^3*b*c + (2*C*a^2*b^2 + B*a*b^3 - A*b^4)*c)*d^4 + 3*(3*D*a^2*b^2*c^2 + C*a*b^3*c^2)*d^3 - (11*D*a*b^3*c^3 + C*b^4*c^3)*d^2)*x)*sqrt(d*x + c))/(b^5*c^5*d^3 - 3*a*b^4*c^4*d^4 + 3*a^2*b^3*c^3*d^5 - a^3*b^2*c^2*d^6 + (b^5*c^3*d^5 - 3*a*b^4*c^2*d^6 + 3*a^2*b^3*c*d^7 - a^3*b^2*d^8)*x^2 + 2*(b^5*c^4*d^4 - 3*a*b^4*c^3*d^5 + 3*a^2*b^3*c^2*d^6 - a^3*b^2*c*d^7)*x), -2/3*(3*((D*a^3 - C*a^2*b + B*a*b^2 - A*b^3)*d^5*x^2 + 2*(D*a^3*c - (C*a^2*b - B*a*b^2 + A*b^3)*c)*d^4*x + (D*a^3*c^2 - (C*a^2*b - B*a*b^2 + A*b^3)*c^2)*d^3)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(-b^2*c + a*b*d)*sqrt(d*x + c)/(b*d*x + b*c)) - (8*D*b^4*c^5 + A*a^2*b^2*d^5 + (2*B*a^2*b^2 - 5*A*a*b^3)*c*d^4 - (3*D*a^3*b*c^2 + (5*C*a^2*b^2 + B*a*b^3 - 4*A*b^4)*c^2)*d^3 + (17*D*a^2*b^2*c^3 + (7*C*a*b^3 - B*b^4)*c^3)*d^2 + 3*(D*b^4*c^3*d^2 - 3*D*a*b^3*c^2*d^3 + 3*D*a^2*b^2*c*d^4 - D*a^3*b*d^5)*x^2 - 2*(11*D*a*b^3*c^4 + C*b^4*c^4)*d + 3*(4*D*b^4*c^4*d + (B*a^2*b^2 - A*a*b^3)*d^5 - (2*D*a^3*b*c + (2*C*a^2*b^2 + B*a*b^3 - A*b^4)*c)*d^4 + 3*(3*D*a^2*b^2*c^2 + C*a*b^3*c^2)*d^3 - (11*D*a*b^3*c^3 + C*b^4*c^3)*d^2)*x)*sqrt(d*x + c))/(b^5*c^5*d^3 - 3*a*b^4*c^4*d^4 + 3*a^2*b^3*c^3*d^5 - a^3*b^2*c^2*d^6 + (b^5*c^3*d^5 - 3*a*b^4*c^2*d^6 + 3*a^2*b^3*c*d^7 - a^3*b^2*d^8)*x^2 + 2*(b^5*c^4*d^4 - 3*a*b^4*c^3*d^5 + 3*a^2*b^3*c^2*d^6 - a^3*b^2*c*d^7)*x)]","B",0
23,1,2444,0,0.872538," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x+a)^2/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(D a^{4} c^{2} + {\left(C a^{3} b - 3 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} c^{2}\right)} d^{3} + {\left({\left(D a^{3} b + C a^{2} b^{2} - 3 \, B a b^{3} + 5 \, A b^{4}\right)} d^{5} - 2 \, {\left(3 \, D a^{2} b^{2} c - {\left(2 \, C a b^{3} - B b^{4}\right)} c\right)} d^{4}\right)} x^{3} - 2 \, {\left(3 \, D a^{3} b c^{3} - {\left(2 \, C a^{2} b^{2} - B a b^{3}\right)} c^{3}\right)} d^{2} + {\left({\left(D a^{4} + C a^{3} b - 3 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} d^{5} - 2 \, {\left(2 \, D a^{3} b c - {\left(3 \, C a^{2} b^{2} - 4 \, B a b^{3} + 5 \, A b^{4}\right)} c\right)} d^{4} - 4 \, {\left(3 \, D a^{2} b^{2} c^{2} - {\left(2 \, C a b^{3} - B b^{4}\right)} c^{2}\right)} d^{3}\right)} x^{2} + {\left(2 \, {\left(D a^{4} c + {\left(C a^{3} b - 3 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} c\right)} d^{4} - {\left(11 \, D a^{3} b c^{2} - {\left(9 \, C a^{2} b^{2} - 7 \, B a b^{3} + 5 \, A b^{4}\right)} c^{2}\right)} d^{3} - 2 \, {\left(3 \, D a^{2} b^{2} c^{3} - {\left(2 \, C a b^{3} - B b^{4}\right)} c^{3}\right)} d^{2}\right)} x\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, \sqrt{b^{2} c - a b d} \sqrt{d x + c}}{b x + a}\right) + 2 \, {\left(4 \, D a b^{4} c^{5} + 2 \, A a^{3} b^{2} d^{5} + 4 \, {\left(B a^{3} b^{2} - 4 \, A a^{2} b^{3}\right)} c d^{4} + {\left(3 \, D a^{4} b c^{2} - {\left(13 \, C a^{3} b^{2} - 7 \, B a^{2} b^{3} - 11 \, A a b^{4}\right)} c^{2}\right)} d^{3} + {\left(13 \, D a^{3} b^{2} c^{3} + {\left(11 \, C a^{2} b^{3} - 11 \, B a b^{4} + 3 \, A b^{5}\right)} c^{3}\right)} d^{2} + 3 \, {\left(2 \, D b^{5} c^{4} d - 8 \, D a b^{4} c^{3} d^{2} + {\left(D a^{4} b - C a^{3} b^{2} + 3 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} d^{5} - {\left(D a^{3} b^{2} c + {\left(3 \, C a^{2} b^{3} + B a b^{4} - 5 \, A b^{5}\right)} c\right)} d^{4} + 2 \, {\left(3 \, D a^{2} b^{3} c^{2} + {\left(2 \, C a b^{4} - B b^{5}\right)} c^{2}\right)} d^{3}\right)} x^{2} - 2 \, {\left(10 \, D a^{2} b^{3} c^{4} - C a b^{4} c^{4}\right)} d + 2 \, {\left(2 \, D b^{5} c^{5} + {\left(3 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} d^{5} + {\left(3 \, D a^{4} b c - {\left(9 \, C a^{3} b^{2} - 5 \, B a^{2} b^{3} + 5 \, A a b^{4}\right)} c\right)} d^{4} + 2 \, {\left(3 \, D a^{3} b^{2} c^{2} + {\left(2 \, C a^{2} b^{3} - 2 \, B a b^{4} + 5 \, A b^{5}\right)} c^{2}\right)} d^{3} - 4 \, {\left(D a^{2} b^{3} c^{3} - {\left(C a b^{4} - B b^{5}\right)} c^{3}\right)} d^{2} - {\left(7 \, D a b^{4} c^{4} - C b^{5} c^{4}\right)} d\right)} x\right)} \sqrt{d x + c}}{6 \, {\left(a b^{6} c^{6} d^{2} - 4 \, a^{2} b^{5} c^{5} d^{3} + 6 \, a^{3} b^{4} c^{4} d^{4} - 4 \, a^{4} b^{3} c^{3} d^{5} + a^{5} b^{2} c^{2} d^{6} + {\left(b^{7} c^{4} d^{4} - 4 \, a b^{6} c^{3} d^{5} + 6 \, a^{2} b^{5} c^{2} d^{6} - 4 \, a^{3} b^{4} c d^{7} + a^{4} b^{3} d^{8}\right)} x^{3} + {\left(2 \, b^{7} c^{5} d^{3} - 7 \, a b^{6} c^{4} d^{4} + 8 \, a^{2} b^{5} c^{3} d^{5} - 2 \, a^{3} b^{4} c^{2} d^{6} - 2 \, a^{4} b^{3} c d^{7} + a^{5} b^{2} d^{8}\right)} x^{2} + {\left(b^{7} c^{6} d^{2} - 2 \, a b^{6} c^{5} d^{3} - 2 \, a^{2} b^{5} c^{4} d^{4} + 8 \, a^{3} b^{4} c^{3} d^{5} - 7 \, a^{4} b^{3} c^{2} d^{6} + 2 \, a^{5} b^{2} c d^{7}\right)} x\right)}}, -\frac{3 \, {\left({\left(D a^{4} c^{2} + {\left(C a^{3} b - 3 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} c^{2}\right)} d^{3} + {\left({\left(D a^{3} b + C a^{2} b^{2} - 3 \, B a b^{3} + 5 \, A b^{4}\right)} d^{5} - 2 \, {\left(3 \, D a^{2} b^{2} c - {\left(2 \, C a b^{3} - B b^{4}\right)} c\right)} d^{4}\right)} x^{3} - 2 \, {\left(3 \, D a^{3} b c^{3} - {\left(2 \, C a^{2} b^{2} - B a b^{3}\right)} c^{3}\right)} d^{2} + {\left({\left(D a^{4} + C a^{3} b - 3 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} d^{5} - 2 \, {\left(2 \, D a^{3} b c - {\left(3 \, C a^{2} b^{2} - 4 \, B a b^{3} + 5 \, A b^{4}\right)} c\right)} d^{4} - 4 \, {\left(3 \, D a^{2} b^{2} c^{2} - {\left(2 \, C a b^{3} - B b^{4}\right)} c^{2}\right)} d^{3}\right)} x^{2} + {\left(2 \, {\left(D a^{4} c + {\left(C a^{3} b - 3 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} c\right)} d^{4} - {\left(11 \, D a^{3} b c^{2} - {\left(9 \, C a^{2} b^{2} - 7 \, B a b^{3} + 5 \, A b^{4}\right)} c^{2}\right)} d^{3} - 2 \, {\left(3 \, D a^{2} b^{2} c^{3} - {\left(2 \, C a b^{3} - B b^{4}\right)} c^{3}\right)} d^{2}\right)} x\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{-b^{2} c + a b d} \sqrt{d x + c}}{b d x + b c}\right) + {\left(4 \, D a b^{4} c^{5} + 2 \, A a^{3} b^{2} d^{5} + 4 \, {\left(B a^{3} b^{2} - 4 \, A a^{2} b^{3}\right)} c d^{4} + {\left(3 \, D a^{4} b c^{2} - {\left(13 \, C a^{3} b^{2} - 7 \, B a^{2} b^{3} - 11 \, A a b^{4}\right)} c^{2}\right)} d^{3} + {\left(13 \, D a^{3} b^{2} c^{3} + {\left(11 \, C a^{2} b^{3} - 11 \, B a b^{4} + 3 \, A b^{5}\right)} c^{3}\right)} d^{2} + 3 \, {\left(2 \, D b^{5} c^{4} d - 8 \, D a b^{4} c^{3} d^{2} + {\left(D a^{4} b - C a^{3} b^{2} + 3 \, B a^{2} b^{3} - 5 \, A a b^{4}\right)} d^{5} - {\left(D a^{3} b^{2} c + {\left(3 \, C a^{2} b^{3} + B a b^{4} - 5 \, A b^{5}\right)} c\right)} d^{4} + 2 \, {\left(3 \, D a^{2} b^{3} c^{2} + {\left(2 \, C a b^{4} - B b^{5}\right)} c^{2}\right)} d^{3}\right)} x^{2} - 2 \, {\left(10 \, D a^{2} b^{3} c^{4} - C a b^{4} c^{4}\right)} d + 2 \, {\left(2 \, D b^{5} c^{5} + {\left(3 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} d^{5} + {\left(3 \, D a^{4} b c - {\left(9 \, C a^{3} b^{2} - 5 \, B a^{2} b^{3} + 5 \, A a b^{4}\right)} c\right)} d^{4} + 2 \, {\left(3 \, D a^{3} b^{2} c^{2} + {\left(2 \, C a^{2} b^{3} - 2 \, B a b^{4} + 5 \, A b^{5}\right)} c^{2}\right)} d^{3} - 4 \, {\left(D a^{2} b^{3} c^{3} - {\left(C a b^{4} - B b^{5}\right)} c^{3}\right)} d^{2} - {\left(7 \, D a b^{4} c^{4} - C b^{5} c^{4}\right)} d\right)} x\right)} \sqrt{d x + c}}{3 \, {\left(a b^{6} c^{6} d^{2} - 4 \, a^{2} b^{5} c^{5} d^{3} + 6 \, a^{3} b^{4} c^{4} d^{4} - 4 \, a^{4} b^{3} c^{3} d^{5} + a^{5} b^{2} c^{2} d^{6} + {\left(b^{7} c^{4} d^{4} - 4 \, a b^{6} c^{3} d^{5} + 6 \, a^{2} b^{5} c^{2} d^{6} - 4 \, a^{3} b^{4} c d^{7} + a^{4} b^{3} d^{8}\right)} x^{3} + {\left(2 \, b^{7} c^{5} d^{3} - 7 \, a b^{6} c^{4} d^{4} + 8 \, a^{2} b^{5} c^{3} d^{5} - 2 \, a^{3} b^{4} c^{2} d^{6} - 2 \, a^{4} b^{3} c d^{7} + a^{5} b^{2} d^{8}\right)} x^{2} + {\left(b^{7} c^{6} d^{2} - 2 \, a b^{6} c^{5} d^{3} - 2 \, a^{2} b^{5} c^{4} d^{4} + 8 \, a^{3} b^{4} c^{3} d^{5} - 7 \, a^{4} b^{3} c^{2} d^{6} + 2 \, a^{5} b^{2} c d^{7}\right)} x\right)}}\right]"," ",0,"[-1/6*(3*((D*a^4*c^2 + (C*a^3*b - 3*B*a^2*b^2 + 5*A*a*b^3)*c^2)*d^3 + ((D*a^3*b + C*a^2*b^2 - 3*B*a*b^3 + 5*A*b^4)*d^5 - 2*(3*D*a^2*b^2*c - (2*C*a*b^3 - B*b^4)*c)*d^4)*x^3 - 2*(3*D*a^3*b*c^3 - (2*C*a^2*b^2 - B*a*b^3)*c^3)*d^2 + ((D*a^4 + C*a^3*b - 3*B*a^2*b^2 + 5*A*a*b^3)*d^5 - 2*(2*D*a^3*b*c - (3*C*a^2*b^2 - 4*B*a*b^3 + 5*A*b^4)*c)*d^4 - 4*(3*D*a^2*b^2*c^2 - (2*C*a*b^3 - B*b^4)*c^2)*d^3)*x^2 + (2*(D*a^4*c + (C*a^3*b - 3*B*a^2*b^2 + 5*A*a*b^3)*c)*d^4 - (11*D*a^3*b*c^2 - (9*C*a^2*b^2 - 7*B*a*b^3 + 5*A*b^4)*c^2)*d^3 - 2*(3*D*a^2*b^2*c^3 - (2*C*a*b^3 - B*b^4)*c^3)*d^2)*x)*sqrt(b^2*c - a*b*d)*log((b*d*x + 2*b*c - a*d - 2*sqrt(b^2*c - a*b*d)*sqrt(d*x + c))/(b*x + a)) + 2*(4*D*a*b^4*c^5 + 2*A*a^3*b^2*d^5 + 4*(B*a^3*b^2 - 4*A*a^2*b^3)*c*d^4 + (3*D*a^4*b*c^2 - (13*C*a^3*b^2 - 7*B*a^2*b^3 - 11*A*a*b^4)*c^2)*d^3 + (13*D*a^3*b^2*c^3 + (11*C*a^2*b^3 - 11*B*a*b^4 + 3*A*b^5)*c^3)*d^2 + 3*(2*D*b^5*c^4*d - 8*D*a*b^4*c^3*d^2 + (D*a^4*b - C*a^3*b^2 + 3*B*a^2*b^3 - 5*A*a*b^4)*d^5 - (D*a^3*b^2*c + (3*C*a^2*b^3 + B*a*b^4 - 5*A*b^5)*c)*d^4 + 2*(3*D*a^2*b^3*c^2 + (2*C*a*b^4 - B*b^5)*c^2)*d^3)*x^2 - 2*(10*D*a^2*b^3*c^4 - C*a*b^4*c^4)*d + 2*(2*D*b^5*c^5 + (3*B*a^3*b^2 - 5*A*a^2*b^3)*d^5 + (3*D*a^4*b*c - (9*C*a^3*b^2 - 5*B*a^2*b^3 + 5*A*a*b^4)*c)*d^4 + 2*(3*D*a^3*b^2*c^2 + (2*C*a^2*b^3 - 2*B*a*b^4 + 5*A*b^5)*c^2)*d^3 - 4*(D*a^2*b^3*c^3 - (C*a*b^4 - B*b^5)*c^3)*d^2 - (7*D*a*b^4*c^4 - C*b^5*c^4)*d)*x)*sqrt(d*x + c))/(a*b^6*c^6*d^2 - 4*a^2*b^5*c^5*d^3 + 6*a^3*b^4*c^4*d^4 - 4*a^4*b^3*c^3*d^5 + a^5*b^2*c^2*d^6 + (b^7*c^4*d^4 - 4*a*b^6*c^3*d^5 + 6*a^2*b^5*c^2*d^6 - 4*a^3*b^4*c*d^7 + a^4*b^3*d^8)*x^3 + (2*b^7*c^5*d^3 - 7*a*b^6*c^4*d^4 + 8*a^2*b^5*c^3*d^5 - 2*a^3*b^4*c^2*d^6 - 2*a^4*b^3*c*d^7 + a^5*b^2*d^8)*x^2 + (b^7*c^6*d^2 - 2*a*b^6*c^5*d^3 - 2*a^2*b^5*c^4*d^4 + 8*a^3*b^4*c^3*d^5 - 7*a^4*b^3*c^2*d^6 + 2*a^5*b^2*c*d^7)*x), -1/3*(3*((D*a^4*c^2 + (C*a^3*b - 3*B*a^2*b^2 + 5*A*a*b^3)*c^2)*d^3 + ((D*a^3*b + C*a^2*b^2 - 3*B*a*b^3 + 5*A*b^4)*d^5 - 2*(3*D*a^2*b^2*c - (2*C*a*b^3 - B*b^4)*c)*d^4)*x^3 - 2*(3*D*a^3*b*c^3 - (2*C*a^2*b^2 - B*a*b^3)*c^3)*d^2 + ((D*a^4 + C*a^3*b - 3*B*a^2*b^2 + 5*A*a*b^3)*d^5 - 2*(2*D*a^3*b*c - (3*C*a^2*b^2 - 4*B*a*b^3 + 5*A*b^4)*c)*d^4 - 4*(3*D*a^2*b^2*c^2 - (2*C*a*b^3 - B*b^4)*c^2)*d^3)*x^2 + (2*(D*a^4*c + (C*a^3*b - 3*B*a^2*b^2 + 5*A*a*b^3)*c)*d^4 - (11*D*a^3*b*c^2 - (9*C*a^2*b^2 - 7*B*a*b^3 + 5*A*b^4)*c^2)*d^3 - 2*(3*D*a^2*b^2*c^3 - (2*C*a*b^3 - B*b^4)*c^3)*d^2)*x)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(-b^2*c + a*b*d)*sqrt(d*x + c)/(b*d*x + b*c)) + (4*D*a*b^4*c^5 + 2*A*a^3*b^2*d^5 + 4*(B*a^3*b^2 - 4*A*a^2*b^3)*c*d^4 + (3*D*a^4*b*c^2 - (13*C*a^3*b^2 - 7*B*a^2*b^3 - 11*A*a*b^4)*c^2)*d^3 + (13*D*a^3*b^2*c^3 + (11*C*a^2*b^3 - 11*B*a*b^4 + 3*A*b^5)*c^3)*d^2 + 3*(2*D*b^5*c^4*d - 8*D*a*b^4*c^3*d^2 + (D*a^4*b - C*a^3*b^2 + 3*B*a^2*b^3 - 5*A*a*b^4)*d^5 - (D*a^3*b^2*c + (3*C*a^2*b^3 + B*a*b^4 - 5*A*b^5)*c)*d^4 + 2*(3*D*a^2*b^3*c^2 + (2*C*a*b^4 - B*b^5)*c^2)*d^3)*x^2 - 2*(10*D*a^2*b^3*c^4 - C*a*b^4*c^4)*d + 2*(2*D*b^5*c^5 + (3*B*a^3*b^2 - 5*A*a^2*b^3)*d^5 + (3*D*a^4*b*c - (9*C*a^3*b^2 - 5*B*a^2*b^3 + 5*A*a*b^4)*c)*d^4 + 2*(3*D*a^3*b^2*c^2 + (2*C*a^2*b^3 - 2*B*a*b^4 + 5*A*b^5)*c^2)*d^3 - 4*(D*a^2*b^3*c^3 - (C*a*b^4 - B*b^5)*c^3)*d^2 - (7*D*a*b^4*c^4 - C*b^5*c^4)*d)*x)*sqrt(d*x + c))/(a*b^6*c^6*d^2 - 4*a^2*b^5*c^5*d^3 + 6*a^3*b^4*c^4*d^4 - 4*a^4*b^3*c^3*d^5 + a^5*b^2*c^2*d^6 + (b^7*c^4*d^4 - 4*a*b^6*c^3*d^5 + 6*a^2*b^5*c^2*d^6 - 4*a^3*b^4*c*d^7 + a^4*b^3*d^8)*x^3 + (2*b^7*c^5*d^3 - 7*a*b^6*c^4*d^4 + 8*a^2*b^5*c^3*d^5 - 2*a^3*b^4*c^2*d^6 - 2*a^4*b^3*c*d^7 + a^5*b^2*d^8)*x^2 + (b^7*c^6*d^2 - 2*a*b^6*c^5*d^3 - 2*a^2*b^5*c^4*d^4 + 8*a^3*b^4*c^3*d^5 - 7*a^4*b^3*c^2*d^6 + 2*a^5*b^2*c*d^7)*x)]","B",0
24,1,3889,0,1.247740," ","integrate((D*x^3+C*x^2+B*x+A)/(b*x+a)^3/(d*x+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left({\left(D a^{3} b^{2} + 3 \, C a^{2} b^{3} - 15 \, B a b^{4} + 35 \, A b^{5}\right)} d^{5} - 4 \, {\left(3 \, D a^{2} b^{3} c - {\left(6 \, C a b^{4} - 5 \, B b^{5}\right)} c\right)} d^{4} - 8 \, {\left(3 \, D a b^{4} c^{2} - C b^{5} c^{2}\right)} d^{3}\right)} x^{4} + {\left(D a^{5} c^{2} + {\left(3 \, C a^{4} b - 15 \, B a^{3} b^{2} + 35 \, A a^{2} b^{3}\right)} c^{2}\right)} d^{3} + 2 \, {\left({\left(D a^{4} b + 3 \, C a^{3} b^{2} - 15 \, B a^{2} b^{3} + 35 \, A a b^{4}\right)} d^{5} - {\left(11 \, D a^{3} b^{2} c - {\left(27 \, C a^{2} b^{3} - 35 \, B a b^{4} + 35 \, A b^{5}\right)} c\right)} d^{4} - 4 \, {\left(9 \, D a^{2} b^{3} c^{2} - {\left(8 \, C a b^{4} - 5 \, B b^{5}\right)} c^{2}\right)} d^{3} - 8 \, {\left(3 \, D a b^{4} c^{3} - C b^{5} c^{3}\right)} d^{2}\right)} x^{3} - 4 \, {\left(3 \, D a^{4} b c^{3} - {\left(6 \, C a^{3} b^{2} - 5 \, B a^{2} b^{3}\right)} c^{3}\right)} d^{2} + {\left({\left(D a^{5} + 3 \, C a^{4} b - 15 \, B a^{3} b^{2} + 35 \, A a^{2} b^{3}\right)} d^{5} - 4 \, {\left(2 \, D a^{4} b c - {\left(9 \, C a^{3} b^{2} - 20 \, B a^{2} b^{3} + 35 \, A a b^{4}\right)} c\right)} d^{4} - {\left(71 \, D a^{3} b^{2} c^{2} - {\left(107 \, C a^{2} b^{3} - 95 \, B a b^{4} + 35 \, A b^{5}\right)} c^{2}\right)} d^{3} - 4 \, {\left(27 \, D a^{2} b^{3} c^{3} - {\left(14 \, C a b^{4} - 5 \, B b^{5}\right)} c^{3}\right)} d^{2} - 8 \, {\left(3 \, D a b^{4} c^{4} - C b^{5} c^{4}\right)} d\right)} x^{2} - 8 \, {\left(3 \, D a^{3} b^{2} c^{4} - C a^{2} b^{3} c^{4}\right)} d + 2 \, {\left({\left(D a^{5} c + {\left(3 \, C a^{4} b - 15 \, B a^{3} b^{2} + 35 \, A a^{2} b^{3}\right)} c\right)} d^{4} - {\left(11 \, D a^{4} b c^{2} - {\left(27 \, C a^{3} b^{2} - 35 \, B a^{2} b^{3} + 35 \, A a b^{4}\right)} c^{2}\right)} d^{3} - 4 \, {\left(9 \, D a^{3} b^{2} c^{3} - {\left(8 \, C a^{2} b^{3} - 5 \, B a b^{4}\right)} c^{3}\right)} d^{2} - 8 \, {\left(3 \, D a^{2} b^{3} c^{4} - C a b^{4} c^{4}\right)} d\right)} x\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, \sqrt{b^{2} c - a b d} \sqrt{d x + c}}{b x + a}\right) - 2 \, {\left(8 \, D a^{2} b^{4} c^{5} - 8 \, A a^{4} b^{2} d^{5} - 8 \, {\left(2 \, B a^{4} b^{2} - 11 \, A a^{3} b^{3}\right)} c d^{4} - {\left(3 \, D a^{5} b c^{2} - {\left(55 \, C a^{4} b^{2} - 67 \, B a^{3} b^{3} - 41 \, A a^{2} b^{4}\right)} c^{2}\right)} d^{3} + 3 \, {\left({\left(D a^{4} b^{2} + 3 \, C a^{3} b^{3} - 15 \, B a^{2} b^{4} + 35 \, A a b^{5}\right)} d^{5} - {\left(13 \, D a^{3} b^{3} c - {\left(21 \, C a^{2} b^{4} - 5 \, B a b^{5} - 35 \, A b^{6}\right)} c\right)} d^{4} - 4 \, {\left(3 \, D a^{2} b^{4} c^{2} + {\left(4 \, C a b^{5} - 5 \, B b^{6}\right)} c^{2}\right)} d^{3} + 8 \, {\left(3 \, D a b^{5} c^{3} - C b^{6} c^{3}\right)} d^{2}\right)} x^{3} - {\left(91 \, D a^{4} b^{2} c^{3} + {\left(5 \, C a^{3} b^{3} - 77 \, B a^{2} b^{4} + 45 \, A a b^{5}\right)} c^{3}\right)} d^{2} + {\left(8 \, D b^{6} c^{5} - {\left(3 \, D a^{5} b - 15 \, C a^{4} b^{2} + 75 \, B a^{3} b^{3} - 175 \, A a^{2} b^{4}\right)} d^{5} - {\left(21 \, D a^{4} b^{2} c - {\left(117 \, C a^{3} b^{3} - 85 \, B a^{2} b^{4} - 35 \, A a b^{5}\right)} c\right)} d^{4} - 4 \, {\left(48 \, D a^{3} b^{3} c^{2} - {\left(C a^{2} b^{4} + 20 \, B a b^{5} - 35 \, A b^{6}\right)} c^{2}\right)} d^{3} + 8 \, {\left(19 \, D a^{2} b^{4} c^{3} - {\left(13 \, C a b^{5} - 10 \, B b^{6}\right)} c^{3}\right)} d^{2} + 8 \, {\left(7 \, D a b^{5} c^{4} - 4 \, C b^{6} c^{4}\right)} d\right)} x^{2} + 2 \, {\left(43 \, D a^{3} b^{3} c^{4} - {\left(25 \, C a^{2} b^{4} - 3 \, B a b^{5} - 3 \, A b^{6}\right)} c^{4}\right)} d + {\left(16 \, D a b^{5} c^{5} - 8 \, {\left(3 \, B a^{4} b^{2} - 7 \, A a^{3} b^{3}\right)} d^{5} - 2 \, {\left(3 \, D a^{5} b c - {\left(39 \, C a^{4} b^{2} - 55 \, B a^{3} b^{3} + 91 \, A a^{2} b^{4}\right)} c\right)} d^{4} - {\left(123 \, D a^{4} b^{2} c^{2} - {\left(71 \, C a^{3} b^{3} - 11 \, B a^{2} b^{4} - 217 \, A a b^{5}\right)} c^{2}\right)} d^{3} - {\left(35 \, D a^{3} b^{3} c^{3} + {\left(61 \, C a^{2} b^{4} - 133 \, B a b^{5} + 21 \, A b^{6}\right)} c^{3}\right)} d^{2} + 4 \, {\left(37 \, D a^{2} b^{4} c^{4} - {\left(22 \, C a b^{5} - 3 \, B b^{6}\right)} c^{4}\right)} d\right)} x\right)} \sqrt{d x + c}}{24 \, {\left(a^{2} b^{7} c^{7} d - 5 \, a^{3} b^{6} c^{6} d^{2} + 10 \, a^{4} b^{5} c^{5} d^{3} - 10 \, a^{5} b^{4} c^{4} d^{4} + 5 \, a^{6} b^{3} c^{3} d^{5} - a^{7} b^{2} c^{2} d^{6} + {\left(b^{9} c^{5} d^{3} - 5 \, a b^{8} c^{4} d^{4} + 10 \, a^{2} b^{7} c^{3} d^{5} - 10 \, a^{3} b^{6} c^{2} d^{6} + 5 \, a^{4} b^{5} c d^{7} - a^{5} b^{4} d^{8}\right)} x^{4} + 2 \, {\left(b^{9} c^{6} d^{2} - 4 \, a b^{8} c^{5} d^{3} + 5 \, a^{2} b^{7} c^{4} d^{4} - 5 \, a^{4} b^{5} c^{2} d^{6} + 4 \, a^{5} b^{4} c d^{7} - a^{6} b^{3} d^{8}\right)} x^{3} + {\left(b^{9} c^{7} d - a b^{8} c^{6} d^{2} - 9 \, a^{2} b^{7} c^{5} d^{3} + 25 \, a^{3} b^{6} c^{4} d^{4} - 25 \, a^{4} b^{5} c^{3} d^{5} + 9 \, a^{5} b^{4} c^{2} d^{6} + a^{6} b^{3} c d^{7} - a^{7} b^{2} d^{8}\right)} x^{2} + 2 \, {\left(a b^{8} c^{7} d - 4 \, a^{2} b^{7} c^{6} d^{2} + 5 \, a^{3} b^{6} c^{5} d^{3} - 5 \, a^{5} b^{4} c^{3} d^{5} + 4 \, a^{6} b^{3} c^{2} d^{6} - a^{7} b^{2} c d^{7}\right)} x\right)}}, \frac{3 \, {\left({\left({\left(D a^{3} b^{2} + 3 \, C a^{2} b^{3} - 15 \, B a b^{4} + 35 \, A b^{5}\right)} d^{5} - 4 \, {\left(3 \, D a^{2} b^{3} c - {\left(6 \, C a b^{4} - 5 \, B b^{5}\right)} c\right)} d^{4} - 8 \, {\left(3 \, D a b^{4} c^{2} - C b^{5} c^{2}\right)} d^{3}\right)} x^{4} + {\left(D a^{5} c^{2} + {\left(3 \, C a^{4} b - 15 \, B a^{3} b^{2} + 35 \, A a^{2} b^{3}\right)} c^{2}\right)} d^{3} + 2 \, {\left({\left(D a^{4} b + 3 \, C a^{3} b^{2} - 15 \, B a^{2} b^{3} + 35 \, A a b^{4}\right)} d^{5} - {\left(11 \, D a^{3} b^{2} c - {\left(27 \, C a^{2} b^{3} - 35 \, B a b^{4} + 35 \, A b^{5}\right)} c\right)} d^{4} - 4 \, {\left(9 \, D a^{2} b^{3} c^{2} - {\left(8 \, C a b^{4} - 5 \, B b^{5}\right)} c^{2}\right)} d^{3} - 8 \, {\left(3 \, D a b^{4} c^{3} - C b^{5} c^{3}\right)} d^{2}\right)} x^{3} - 4 \, {\left(3 \, D a^{4} b c^{3} - {\left(6 \, C a^{3} b^{2} - 5 \, B a^{2} b^{3}\right)} c^{3}\right)} d^{2} + {\left({\left(D a^{5} + 3 \, C a^{4} b - 15 \, B a^{3} b^{2} + 35 \, A a^{2} b^{3}\right)} d^{5} - 4 \, {\left(2 \, D a^{4} b c - {\left(9 \, C a^{3} b^{2} - 20 \, B a^{2} b^{3} + 35 \, A a b^{4}\right)} c\right)} d^{4} - {\left(71 \, D a^{3} b^{2} c^{2} - {\left(107 \, C a^{2} b^{3} - 95 \, B a b^{4} + 35 \, A b^{5}\right)} c^{2}\right)} d^{3} - 4 \, {\left(27 \, D a^{2} b^{3} c^{3} - {\left(14 \, C a b^{4} - 5 \, B b^{5}\right)} c^{3}\right)} d^{2} - 8 \, {\left(3 \, D a b^{4} c^{4} - C b^{5} c^{4}\right)} d\right)} x^{2} - 8 \, {\left(3 \, D a^{3} b^{2} c^{4} - C a^{2} b^{3} c^{4}\right)} d + 2 \, {\left({\left(D a^{5} c + {\left(3 \, C a^{4} b - 15 \, B a^{3} b^{2} + 35 \, A a^{2} b^{3}\right)} c\right)} d^{4} - {\left(11 \, D a^{4} b c^{2} - {\left(27 \, C a^{3} b^{2} - 35 \, B a^{2} b^{3} + 35 \, A a b^{4}\right)} c^{2}\right)} d^{3} - 4 \, {\left(9 \, D a^{3} b^{2} c^{3} - {\left(8 \, C a^{2} b^{3} - 5 \, B a b^{4}\right)} c^{3}\right)} d^{2} - 8 \, {\left(3 \, D a^{2} b^{3} c^{4} - C a b^{4} c^{4}\right)} d\right)} x\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{-b^{2} c + a b d} \sqrt{d x + c}}{b d x + b c}\right) - {\left(8 \, D a^{2} b^{4} c^{5} - 8 \, A a^{4} b^{2} d^{5} - 8 \, {\left(2 \, B a^{4} b^{2} - 11 \, A a^{3} b^{3}\right)} c d^{4} - {\left(3 \, D a^{5} b c^{2} - {\left(55 \, C a^{4} b^{2} - 67 \, B a^{3} b^{3} - 41 \, A a^{2} b^{4}\right)} c^{2}\right)} d^{3} + 3 \, {\left({\left(D a^{4} b^{2} + 3 \, C a^{3} b^{3} - 15 \, B a^{2} b^{4} + 35 \, A a b^{5}\right)} d^{5} - {\left(13 \, D a^{3} b^{3} c - {\left(21 \, C a^{2} b^{4} - 5 \, B a b^{5} - 35 \, A b^{6}\right)} c\right)} d^{4} - 4 \, {\left(3 \, D a^{2} b^{4} c^{2} + {\left(4 \, C a b^{5} - 5 \, B b^{6}\right)} c^{2}\right)} d^{3} + 8 \, {\left(3 \, D a b^{5} c^{3} - C b^{6} c^{3}\right)} d^{2}\right)} x^{3} - {\left(91 \, D a^{4} b^{2} c^{3} + {\left(5 \, C a^{3} b^{3} - 77 \, B a^{2} b^{4} + 45 \, A a b^{5}\right)} c^{3}\right)} d^{2} + {\left(8 \, D b^{6} c^{5} - {\left(3 \, D a^{5} b - 15 \, C a^{4} b^{2} + 75 \, B a^{3} b^{3} - 175 \, A a^{2} b^{4}\right)} d^{5} - {\left(21 \, D a^{4} b^{2} c - {\left(117 \, C a^{3} b^{3} - 85 \, B a^{2} b^{4} - 35 \, A a b^{5}\right)} c\right)} d^{4} - 4 \, {\left(48 \, D a^{3} b^{3} c^{2} - {\left(C a^{2} b^{4} + 20 \, B a b^{5} - 35 \, A b^{6}\right)} c^{2}\right)} d^{3} + 8 \, {\left(19 \, D a^{2} b^{4} c^{3} - {\left(13 \, C a b^{5} - 10 \, B b^{6}\right)} c^{3}\right)} d^{2} + 8 \, {\left(7 \, D a b^{5} c^{4} - 4 \, C b^{6} c^{4}\right)} d\right)} x^{2} + 2 \, {\left(43 \, D a^{3} b^{3} c^{4} - {\left(25 \, C a^{2} b^{4} - 3 \, B a b^{5} - 3 \, A b^{6}\right)} c^{4}\right)} d + {\left(16 \, D a b^{5} c^{5} - 8 \, {\left(3 \, B a^{4} b^{2} - 7 \, A a^{3} b^{3}\right)} d^{5} - 2 \, {\left(3 \, D a^{5} b c - {\left(39 \, C a^{4} b^{2} - 55 \, B a^{3} b^{3} + 91 \, A a^{2} b^{4}\right)} c\right)} d^{4} - {\left(123 \, D a^{4} b^{2} c^{2} - {\left(71 \, C a^{3} b^{3} - 11 \, B a^{2} b^{4} - 217 \, A a b^{5}\right)} c^{2}\right)} d^{3} - {\left(35 \, D a^{3} b^{3} c^{3} + {\left(61 \, C a^{2} b^{4} - 133 \, B a b^{5} + 21 \, A b^{6}\right)} c^{3}\right)} d^{2} + 4 \, {\left(37 \, D a^{2} b^{4} c^{4} - {\left(22 \, C a b^{5} - 3 \, B b^{6}\right)} c^{4}\right)} d\right)} x\right)} \sqrt{d x + c}}{12 \, {\left(a^{2} b^{7} c^{7} d - 5 \, a^{3} b^{6} c^{6} d^{2} + 10 \, a^{4} b^{5} c^{5} d^{3} - 10 \, a^{5} b^{4} c^{4} d^{4} + 5 \, a^{6} b^{3} c^{3} d^{5} - a^{7} b^{2} c^{2} d^{6} + {\left(b^{9} c^{5} d^{3} - 5 \, a b^{8} c^{4} d^{4} + 10 \, a^{2} b^{7} c^{3} d^{5} - 10 \, a^{3} b^{6} c^{2} d^{6} + 5 \, a^{4} b^{5} c d^{7} - a^{5} b^{4} d^{8}\right)} x^{4} + 2 \, {\left(b^{9} c^{6} d^{2} - 4 \, a b^{8} c^{5} d^{3} + 5 \, a^{2} b^{7} c^{4} d^{4} - 5 \, a^{4} b^{5} c^{2} d^{6} + 4 \, a^{5} b^{4} c d^{7} - a^{6} b^{3} d^{8}\right)} x^{3} + {\left(b^{9} c^{7} d - a b^{8} c^{6} d^{2} - 9 \, a^{2} b^{7} c^{5} d^{3} + 25 \, a^{3} b^{6} c^{4} d^{4} - 25 \, a^{4} b^{5} c^{3} d^{5} + 9 \, a^{5} b^{4} c^{2} d^{6} + a^{6} b^{3} c d^{7} - a^{7} b^{2} d^{8}\right)} x^{2} + 2 \, {\left(a b^{8} c^{7} d - 4 \, a^{2} b^{7} c^{6} d^{2} + 5 \, a^{3} b^{6} c^{5} d^{3} - 5 \, a^{5} b^{4} c^{3} d^{5} + 4 \, a^{6} b^{3} c^{2} d^{6} - a^{7} b^{2} c d^{7}\right)} x\right)}}\right]"," ",0,"[1/24*(3*(((D*a^3*b^2 + 3*C*a^2*b^3 - 15*B*a*b^4 + 35*A*b^5)*d^5 - 4*(3*D*a^2*b^3*c - (6*C*a*b^4 - 5*B*b^5)*c)*d^4 - 8*(3*D*a*b^4*c^2 - C*b^5*c^2)*d^3)*x^4 + (D*a^5*c^2 + (3*C*a^4*b - 15*B*a^3*b^2 + 35*A*a^2*b^3)*c^2)*d^3 + 2*((D*a^4*b + 3*C*a^3*b^2 - 15*B*a^2*b^3 + 35*A*a*b^4)*d^5 - (11*D*a^3*b^2*c - (27*C*a^2*b^3 - 35*B*a*b^4 + 35*A*b^5)*c)*d^4 - 4*(9*D*a^2*b^3*c^2 - (8*C*a*b^4 - 5*B*b^5)*c^2)*d^3 - 8*(3*D*a*b^4*c^3 - C*b^5*c^3)*d^2)*x^3 - 4*(3*D*a^4*b*c^3 - (6*C*a^3*b^2 - 5*B*a^2*b^3)*c^3)*d^2 + ((D*a^5 + 3*C*a^4*b - 15*B*a^3*b^2 + 35*A*a^2*b^3)*d^5 - 4*(2*D*a^4*b*c - (9*C*a^3*b^2 - 20*B*a^2*b^3 + 35*A*a*b^4)*c)*d^4 - (71*D*a^3*b^2*c^2 - (107*C*a^2*b^3 - 95*B*a*b^4 + 35*A*b^5)*c^2)*d^3 - 4*(27*D*a^2*b^3*c^3 - (14*C*a*b^4 - 5*B*b^5)*c^3)*d^2 - 8*(3*D*a*b^4*c^4 - C*b^5*c^4)*d)*x^2 - 8*(3*D*a^3*b^2*c^4 - C*a^2*b^3*c^4)*d + 2*((D*a^5*c + (3*C*a^4*b - 15*B*a^3*b^2 + 35*A*a^2*b^3)*c)*d^4 - (11*D*a^4*b*c^2 - (27*C*a^3*b^2 - 35*B*a^2*b^3 + 35*A*a*b^4)*c^2)*d^3 - 4*(9*D*a^3*b^2*c^3 - (8*C*a^2*b^3 - 5*B*a*b^4)*c^3)*d^2 - 8*(3*D*a^2*b^3*c^4 - C*a*b^4*c^4)*d)*x)*sqrt(b^2*c - a*b*d)*log((b*d*x + 2*b*c - a*d - 2*sqrt(b^2*c - a*b*d)*sqrt(d*x + c))/(b*x + a)) - 2*(8*D*a^2*b^4*c^5 - 8*A*a^4*b^2*d^5 - 8*(2*B*a^4*b^2 - 11*A*a^3*b^3)*c*d^4 - (3*D*a^5*b*c^2 - (55*C*a^4*b^2 - 67*B*a^3*b^3 - 41*A*a^2*b^4)*c^2)*d^3 + 3*((D*a^4*b^2 + 3*C*a^3*b^3 - 15*B*a^2*b^4 + 35*A*a*b^5)*d^5 - (13*D*a^3*b^3*c - (21*C*a^2*b^4 - 5*B*a*b^5 - 35*A*b^6)*c)*d^4 - 4*(3*D*a^2*b^4*c^2 + (4*C*a*b^5 - 5*B*b^6)*c^2)*d^3 + 8*(3*D*a*b^5*c^3 - C*b^6*c^3)*d^2)*x^3 - (91*D*a^4*b^2*c^3 + (5*C*a^3*b^3 - 77*B*a^2*b^4 + 45*A*a*b^5)*c^3)*d^2 + (8*D*b^6*c^5 - (3*D*a^5*b - 15*C*a^4*b^2 + 75*B*a^3*b^3 - 175*A*a^2*b^4)*d^5 - (21*D*a^4*b^2*c - (117*C*a^3*b^3 - 85*B*a^2*b^4 - 35*A*a*b^5)*c)*d^4 - 4*(48*D*a^3*b^3*c^2 - (C*a^2*b^4 + 20*B*a*b^5 - 35*A*b^6)*c^2)*d^3 + 8*(19*D*a^2*b^4*c^3 - (13*C*a*b^5 - 10*B*b^6)*c^3)*d^2 + 8*(7*D*a*b^5*c^4 - 4*C*b^6*c^4)*d)*x^2 + 2*(43*D*a^3*b^3*c^4 - (25*C*a^2*b^4 - 3*B*a*b^5 - 3*A*b^6)*c^4)*d + (16*D*a*b^5*c^5 - 8*(3*B*a^4*b^2 - 7*A*a^3*b^3)*d^5 - 2*(3*D*a^5*b*c - (39*C*a^4*b^2 - 55*B*a^3*b^3 + 91*A*a^2*b^4)*c)*d^4 - (123*D*a^4*b^2*c^2 - (71*C*a^3*b^3 - 11*B*a^2*b^4 - 217*A*a*b^5)*c^2)*d^3 - (35*D*a^3*b^3*c^3 + (61*C*a^2*b^4 - 133*B*a*b^5 + 21*A*b^6)*c^3)*d^2 + 4*(37*D*a^2*b^4*c^4 - (22*C*a*b^5 - 3*B*b^6)*c^4)*d)*x)*sqrt(d*x + c))/(a^2*b^7*c^7*d - 5*a^3*b^6*c^6*d^2 + 10*a^4*b^5*c^5*d^3 - 10*a^5*b^4*c^4*d^4 + 5*a^6*b^3*c^3*d^5 - a^7*b^2*c^2*d^6 + (b^9*c^5*d^3 - 5*a*b^8*c^4*d^4 + 10*a^2*b^7*c^3*d^5 - 10*a^3*b^6*c^2*d^6 + 5*a^4*b^5*c*d^7 - a^5*b^4*d^8)*x^4 + 2*(b^9*c^6*d^2 - 4*a*b^8*c^5*d^3 + 5*a^2*b^7*c^4*d^4 - 5*a^4*b^5*c^2*d^6 + 4*a^5*b^4*c*d^7 - a^6*b^3*d^8)*x^3 + (b^9*c^7*d - a*b^8*c^6*d^2 - 9*a^2*b^7*c^5*d^3 + 25*a^3*b^6*c^4*d^4 - 25*a^4*b^5*c^3*d^5 + 9*a^5*b^4*c^2*d^6 + a^6*b^3*c*d^7 - a^7*b^2*d^8)*x^2 + 2*(a*b^8*c^7*d - 4*a^2*b^7*c^6*d^2 + 5*a^3*b^6*c^5*d^3 - 5*a^5*b^4*c^3*d^5 + 4*a^6*b^3*c^2*d^6 - a^7*b^2*c*d^7)*x), 1/12*(3*(((D*a^3*b^2 + 3*C*a^2*b^3 - 15*B*a*b^4 + 35*A*b^5)*d^5 - 4*(3*D*a^2*b^3*c - (6*C*a*b^4 - 5*B*b^5)*c)*d^4 - 8*(3*D*a*b^4*c^2 - C*b^5*c^2)*d^3)*x^4 + (D*a^5*c^2 + (3*C*a^4*b - 15*B*a^3*b^2 + 35*A*a^2*b^3)*c^2)*d^3 + 2*((D*a^4*b + 3*C*a^3*b^2 - 15*B*a^2*b^3 + 35*A*a*b^4)*d^5 - (11*D*a^3*b^2*c - (27*C*a^2*b^3 - 35*B*a*b^4 + 35*A*b^5)*c)*d^4 - 4*(9*D*a^2*b^3*c^2 - (8*C*a*b^4 - 5*B*b^5)*c^2)*d^3 - 8*(3*D*a*b^4*c^3 - C*b^5*c^3)*d^2)*x^3 - 4*(3*D*a^4*b*c^3 - (6*C*a^3*b^2 - 5*B*a^2*b^3)*c^3)*d^2 + ((D*a^5 + 3*C*a^4*b - 15*B*a^3*b^2 + 35*A*a^2*b^3)*d^5 - 4*(2*D*a^4*b*c - (9*C*a^3*b^2 - 20*B*a^2*b^3 + 35*A*a*b^4)*c)*d^4 - (71*D*a^3*b^2*c^2 - (107*C*a^2*b^3 - 95*B*a*b^4 + 35*A*b^5)*c^2)*d^3 - 4*(27*D*a^2*b^3*c^3 - (14*C*a*b^4 - 5*B*b^5)*c^3)*d^2 - 8*(3*D*a*b^4*c^4 - C*b^5*c^4)*d)*x^2 - 8*(3*D*a^3*b^2*c^4 - C*a^2*b^3*c^4)*d + 2*((D*a^5*c + (3*C*a^4*b - 15*B*a^3*b^2 + 35*A*a^2*b^3)*c)*d^4 - (11*D*a^4*b*c^2 - (27*C*a^3*b^2 - 35*B*a^2*b^3 + 35*A*a*b^4)*c^2)*d^3 - 4*(9*D*a^3*b^2*c^3 - (8*C*a^2*b^3 - 5*B*a*b^4)*c^3)*d^2 - 8*(3*D*a^2*b^3*c^4 - C*a*b^4*c^4)*d)*x)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(-b^2*c + a*b*d)*sqrt(d*x + c)/(b*d*x + b*c)) - (8*D*a^2*b^4*c^5 - 8*A*a^4*b^2*d^5 - 8*(2*B*a^4*b^2 - 11*A*a^3*b^3)*c*d^4 - (3*D*a^5*b*c^2 - (55*C*a^4*b^2 - 67*B*a^3*b^3 - 41*A*a^2*b^4)*c^2)*d^3 + 3*((D*a^4*b^2 + 3*C*a^3*b^3 - 15*B*a^2*b^4 + 35*A*a*b^5)*d^5 - (13*D*a^3*b^3*c - (21*C*a^2*b^4 - 5*B*a*b^5 - 35*A*b^6)*c)*d^4 - 4*(3*D*a^2*b^4*c^2 + (4*C*a*b^5 - 5*B*b^6)*c^2)*d^3 + 8*(3*D*a*b^5*c^3 - C*b^6*c^3)*d^2)*x^3 - (91*D*a^4*b^2*c^3 + (5*C*a^3*b^3 - 77*B*a^2*b^4 + 45*A*a*b^5)*c^3)*d^2 + (8*D*b^6*c^5 - (3*D*a^5*b - 15*C*a^4*b^2 + 75*B*a^3*b^3 - 175*A*a^2*b^4)*d^5 - (21*D*a^4*b^2*c - (117*C*a^3*b^3 - 85*B*a^2*b^4 - 35*A*a*b^5)*c)*d^4 - 4*(48*D*a^3*b^3*c^2 - (C*a^2*b^4 + 20*B*a*b^5 - 35*A*b^6)*c^2)*d^3 + 8*(19*D*a^2*b^4*c^3 - (13*C*a*b^5 - 10*B*b^6)*c^3)*d^2 + 8*(7*D*a*b^5*c^4 - 4*C*b^6*c^4)*d)*x^2 + 2*(43*D*a^3*b^3*c^4 - (25*C*a^2*b^4 - 3*B*a*b^5 - 3*A*b^6)*c^4)*d + (16*D*a*b^5*c^5 - 8*(3*B*a^4*b^2 - 7*A*a^3*b^3)*d^5 - 2*(3*D*a^5*b*c - (39*C*a^4*b^2 - 55*B*a^3*b^3 + 91*A*a^2*b^4)*c)*d^4 - (123*D*a^4*b^2*c^2 - (71*C*a^3*b^3 - 11*B*a^2*b^4 - 217*A*a*b^5)*c^2)*d^3 - (35*D*a^3*b^3*c^3 + (61*C*a^2*b^4 - 133*B*a*b^5 + 21*A*b^6)*c^3)*d^2 + 4*(37*D*a^2*b^4*c^4 - (22*C*a*b^5 - 3*B*b^6)*c^4)*d)*x)*sqrt(d*x + c))/(a^2*b^7*c^7*d - 5*a^3*b^6*c^6*d^2 + 10*a^4*b^5*c^5*d^3 - 10*a^5*b^4*c^4*d^4 + 5*a^6*b^3*c^3*d^5 - a^7*b^2*c^2*d^6 + (b^9*c^5*d^3 - 5*a*b^8*c^4*d^4 + 10*a^2*b^7*c^3*d^5 - 10*a^3*b^6*c^2*d^6 + 5*a^4*b^5*c*d^7 - a^5*b^4*d^8)*x^4 + 2*(b^9*c^6*d^2 - 4*a*b^8*c^5*d^3 + 5*a^2*b^7*c^4*d^4 - 5*a^4*b^5*c^2*d^6 + 4*a^5*b^4*c*d^7 - a^6*b^3*d^8)*x^3 + (b^9*c^7*d - a*b^8*c^6*d^2 - 9*a^2*b^7*c^5*d^3 + 25*a^3*b^6*c^4*d^4 - 25*a^4*b^5*c^3*d^5 + 9*a^5*b^4*c^2*d^6 + a^6*b^3*c*d^7 - a^7*b^2*d^8)*x^2 + 2*(a*b^8*c^7*d - 4*a^2*b^7*c^6*d^2 + 5*a^3*b^6*c^5*d^3 - 5*a^5*b^4*c^3*d^5 + 4*a^6*b^3*c^2*d^6 - a^7*b^2*c*d^7)*x)]","B",0
25,1,4115,0,1.070870," ","integrate((b*x+a)^3*(d*x+c)^n*(D*x^3+C*x^2+B*x+A),x, algorithm=""fricas"")","\frac{{\left(A a^{3} c d^{6} n^{6} + 720 \, D b^{3} c^{7} + 5040 \, A a^{3} c d^{6} + 1680 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} c^{3} d^{4} - 2520 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{2} d^{5} + {\left(D b^{3} d^{7} n^{6} + 21 \, D b^{3} d^{7} n^{5} + 175 \, D b^{3} d^{7} n^{4} + 735 \, D b^{3} d^{7} n^{3} + 1624 \, D b^{3} d^{7} n^{2} + 1764 \, D b^{3} d^{7} n + 720 \, D b^{3} d^{7}\right)} x^{7} + {\left(840 \, {\left(3 \, D a b^{2} + C b^{3}\right)} d^{7} + {\left(D b^{3} c d^{6} + {\left(3 \, D a b^{2} + C b^{3}\right)} d^{7}\right)} n^{6} + {\left(15 \, D b^{3} c d^{6} + 22 \, {\left(3 \, D a b^{2} + C b^{3}\right)} d^{7}\right)} n^{5} + 5 \, {\left(17 \, D b^{3} c d^{6} + 38 \, {\left(3 \, D a b^{2} + C b^{3}\right)} d^{7}\right)} n^{4} + 5 \, {\left(45 \, D b^{3} c d^{6} + 164 \, {\left(3 \, D a b^{2} + C b^{3}\right)} d^{7}\right)} n^{3} + {\left(274 \, D b^{3} c d^{6} + 1849 \, {\left(3 \, D a b^{2} + C b^{3}\right)} d^{7}\right)} n^{2} + 2 \, {\left(60 \, D b^{3} c d^{6} + 1019 \, {\left(3 \, D a b^{2} + C b^{3}\right)} d^{7}\right)} n\right)} x^{6} + {\left(27 \, A a^{3} c d^{6} - {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{2} d^{5}\right)} n^{5} + {\left(1008 \, {\left(3 \, D a^{2} b + 3 \, C a b^{2} + B b^{3}\right)} d^{7} + {\left({\left(3 \, D a^{2} b + 3 \, C a b^{2} + B b^{3}\right)} d^{7} + {\left(3 \, D a b^{2} c + C b^{3} c\right)} d^{6}\right)} n^{6} - {\left(6 \, D b^{3} c^{2} d^{5} - 23 \, {\left(3 \, D a^{2} b + 3 \, C a b^{2} + B b^{3}\right)} d^{7} - 17 \, {\left(3 \, D a b^{2} c + C b^{3} c\right)} d^{6}\right)} n^{5} - 3 \, {\left(20 \, D b^{3} c^{2} d^{5} - 69 \, {\left(3 \, D a^{2} b + 3 \, C a b^{2} + B b^{3}\right)} d^{7} - 35 \, {\left(3 \, D a b^{2} c + C b^{3} c\right)} d^{6}\right)} n^{4} - 5 \, {\left(42 \, D b^{3} c^{2} d^{5} - 185 \, {\left(3 \, D a^{2} b + 3 \, C a b^{2} + B b^{3}\right)} d^{7} - 59 \, {\left(3 \, D a b^{2} c + C b^{3} c\right)} d^{6}\right)} n^{3} - 2 \, {\left(150 \, D b^{3} c^{2} d^{5} - 1072 \, {\left(3 \, D a^{2} b + 3 \, C a b^{2} + B b^{3}\right)} d^{7} - 187 \, {\left(3 \, D a b^{2} c + C b^{3} c\right)} d^{6}\right)} n^{2} - 12 \, {\left(12 \, D b^{3} c^{2} d^{5} - 201 \, {\left(3 \, D a^{2} b + 3 \, C a b^{2} + B b^{3}\right)} d^{7} - 14 \, {\left(3 \, D a b^{2} c + C b^{3} c\right)} d^{6}\right)} n\right)} x^{5} + {\left(295 \, A a^{3} c d^{6} + 2 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} c^{3} d^{4} - 25 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{2} d^{5}\right)} n^{4} + {\left(1260 \, {\left(D a^{3} + 3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} d^{7} + {\left({\left(D a^{3} + 3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} d^{7} + {\left(3 \, D a^{2} b c + {\left(3 \, C a b^{2} + B b^{3}\right)} c\right)} d^{6}\right)} n^{6} + {\left(24 \, {\left(D a^{3} + 3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} d^{7} + 19 \, {\left(3 \, D a^{2} b c + {\left(3 \, C a b^{2} + B b^{3}\right)} c\right)} d^{6} - 5 \, {\left(3 \, D a b^{2} c^{2} + C b^{3} c^{2}\right)} d^{5}\right)} n^{5} + {\left(30 \, D b^{3} c^{3} d^{4} + 226 \, {\left(D a^{3} + 3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} d^{7} + 131 \, {\left(3 \, D a^{2} b c + {\left(3 \, C a b^{2} + B b^{3}\right)} c\right)} d^{6} - 65 \, {\left(3 \, D a b^{2} c^{2} + C b^{3} c^{2}\right)} d^{5}\right)} n^{4} + {\left(180 \, D b^{3} c^{3} d^{4} + 1056 \, {\left(D a^{3} + 3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} d^{7} + 401 \, {\left(3 \, D a^{2} b c + {\left(3 \, C a b^{2} + B b^{3}\right)} c\right)} d^{6} - 265 \, {\left(3 \, D a b^{2} c^{2} + C b^{3} c^{2}\right)} d^{5}\right)} n^{3} + 5 \, {\left(66 \, D b^{3} c^{3} d^{4} + 509 \, {\left(D a^{3} + 3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} d^{7} + 108 \, {\left(3 \, D a^{2} b c + {\left(3 \, C a b^{2} + B b^{3}\right)} c\right)} d^{6} - 83 \, {\left(3 \, D a b^{2} c^{2} + C b^{3} c^{2}\right)} d^{5}\right)} n^{2} + 6 \, {\left(30 \, D b^{3} c^{3} d^{4} + 492 \, {\left(D a^{3} + 3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} d^{7} + 42 \, {\left(3 \, D a^{2} b c + {\left(3 \, C a b^{2} + B b^{3}\right)} c\right)} d^{6} - 35 \, {\left(3 \, D a b^{2} c^{2} + C b^{3} c^{2}\right)} d^{5}\right)} n\right)} x^{4} - 1260 \, {\left(D a^{3} c^{4} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c^{4}\right)} d^{3} + {\left(1665 \, A a^{3} c d^{6} + 44 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} c^{3} d^{4} - 245 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{2} d^{5} - 6 \, {\left(D a^{3} c^{4} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c^{4}\right)} d^{3}\right)} n^{3} + {\left(1680 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} d^{7} + {\left({\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} d^{7} + {\left(D a^{3} c + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c\right)} d^{6}\right)} n^{6} + {\left(25 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} d^{7} + 21 \, {\left(D a^{3} c + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c\right)} d^{6} - 4 \, {\left(3 \, D a^{2} b c^{2} + {\left(3 \, C a b^{2} + B b^{3}\right)} c^{2}\right)} d^{5}\right)} n^{5} + {\left(247 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} d^{7} + 163 \, {\left(D a^{3} c + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c\right)} d^{6} - 64 \, {\left(3 \, D a^{2} b c^{2} + {\left(3 \, C a b^{2} + B b^{3}\right)} c^{2}\right)} d^{5} + 20 \, {\left(3 \, D a b^{2} c^{3} + C b^{3} c^{3}\right)} d^{4}\right)} n^{4} - {\left(120 \, D b^{3} c^{4} d^{3} - 1219 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} d^{7} - 567 \, {\left(D a^{3} c + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c\right)} d^{6} + 332 \, {\left(3 \, D a^{2} b c^{2} + {\left(3 \, C a b^{2} + B b^{3}\right)} c^{2}\right)} d^{5} - 200 \, {\left(3 \, D a b^{2} c^{3} + C b^{3} c^{3}\right)} d^{4}\right)} n^{3} - 4 \, {\left(90 \, D b^{3} c^{4} d^{3} - 778 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} d^{7} - 211 \, {\left(D a^{3} c + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c\right)} d^{6} + 152 \, {\left(3 \, D a^{2} b c^{2} + {\left(3 \, C a b^{2} + B b^{3}\right)} c^{2}\right)} d^{5} - 115 \, {\left(3 \, D a b^{2} c^{3} + C b^{3} c^{3}\right)} d^{4}\right)} n^{2} - 4 \, {\left(60 \, D b^{3} c^{4} d^{3} - 949 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} d^{7} - 105 \, {\left(D a^{3} c + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c\right)} d^{6} + 84 \, {\left(3 \, D a^{2} b c^{2} + {\left(3 \, C a b^{2} + B b^{3}\right)} c^{2}\right)} d^{5} - 70 \, {\left(3 \, D a b^{2} c^{3} + C b^{3} c^{3}\right)} d^{4}\right)} n\right)} x^{3} + 1008 \, {\left(3 \, D a^{2} b c^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} c^{5}\right)} d^{2} + {\left(5104 \, A a^{3} c d^{6} + 358 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} c^{3} d^{4} - 1175 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{2} d^{5} - 108 \, {\left(D a^{3} c^{4} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c^{4}\right)} d^{3} + 24 \, {\left(3 \, D a^{2} b c^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} c^{5}\right)} d^{2}\right)} n^{2} + {\left(2520 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{7} + {\left({\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} c d^{6} + {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{7}\right)} n^{6} + {\left(23 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} c d^{6} + 26 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{7} - 3 \, {\left(D a^{3} c^{2} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c^{2}\right)} d^{5}\right)} n^{5} + 3 \, {\left(67 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} c d^{6} + 90 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{7} - 19 \, {\left(D a^{3} c^{2} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c^{2}\right)} d^{5} + 4 \, {\left(3 \, D a^{2} b c^{3} + {\left(3 \, C a b^{2} + B b^{3}\right)} c^{3}\right)} d^{4}\right)} n^{4} + {\left(817 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} c d^{6} + 1420 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{7} - 375 \, {\left(D a^{3} c^{2} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c^{2}\right)} d^{5} + 168 \, {\left(3 \, D a^{2} b c^{3} + {\left(3 \, C a b^{2} + B b^{3}\right)} c^{3}\right)} d^{4} - 60 \, {\left(3 \, D a b^{2} c^{4} + C b^{3} c^{4}\right)} d^{3}\right)} n^{3} + {\left(360 \, D b^{3} c^{5} d^{2} + 1478 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} c d^{6} + 3929 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{7} - 951 \, {\left(D a^{3} c^{2} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c^{2}\right)} d^{5} + 660 \, {\left(3 \, D a^{2} b c^{3} + {\left(3 \, C a b^{2} + B b^{3}\right)} c^{3}\right)} d^{4} - 480 \, {\left(3 \, D a b^{2} c^{4} + C b^{3} c^{4}\right)} d^{3}\right)} n^{2} + 6 \, {\left(60 \, D b^{3} c^{5} d^{2} + 140 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} c d^{6} + 879 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} d^{7} - 105 \, {\left(D a^{3} c^{2} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c^{2}\right)} d^{5} + 84 \, {\left(3 \, D a^{2} b c^{3} + {\left(3 \, C a b^{2} + B b^{3}\right)} c^{3}\right)} d^{4} - 70 \, {\left(3 \, D a b^{2} c^{4} + C b^{3} c^{4}\right)} d^{3}\right)} n\right)} x^{2} - 840 \, {\left(3 \, D a b^{2} c^{6} + C b^{3} c^{6}\right)} d + 2 \, {\left(4014 \, A a^{3} c d^{6} + 638 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} c^{3} d^{4} - 1377 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c^{2} d^{5} - 321 \, {\left(D a^{3} c^{4} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c^{4}\right)} d^{3} + 156 \, {\left(3 \, D a^{2} b c^{5} + {\left(3 \, C a b^{2} + B b^{3}\right)} c^{5}\right)} d^{2} - 60 \, {\left(3 \, D a b^{2} c^{6} + C b^{3} c^{6}\right)} d\right)} n + {\left(5040 \, A a^{3} d^{7} + {\left(A a^{3} d^{7} + {\left(B a^{3} + 3 \, A a^{2} b\right)} c d^{6}\right)} n^{6} + {\left(27 \, A a^{3} d^{7} - 2 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} c^{2} d^{5} + 25 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c d^{6}\right)} n^{5} + {\left(295 \, A a^{3} d^{7} - 44 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} c^{2} d^{5} + 245 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c d^{6} + 6 \, {\left(D a^{3} c^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c^{3}\right)} d^{4}\right)} n^{4} + {\left(1665 \, A a^{3} d^{7} - 358 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} c^{2} d^{5} + 1175 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c d^{6} + 108 \, {\left(D a^{3} c^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c^{3}\right)} d^{4} - 24 \, {\left(3 \, D a^{2} b c^{4} + {\left(3 \, C a b^{2} + B b^{3}\right)} c^{4}\right)} d^{3}\right)} n^{3} + 2 \, {\left(2552 \, A a^{3} d^{7} - 638 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} c^{2} d^{5} + 1377 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c d^{6} + 321 \, {\left(D a^{3} c^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c^{3}\right)} d^{4} - 156 \, {\left(3 \, D a^{2} b c^{4} + {\left(3 \, C a b^{2} + B b^{3}\right)} c^{4}\right)} d^{3} + 60 \, {\left(3 \, D a b^{2} c^{5} + C b^{3} c^{5}\right)} d^{2}\right)} n^{2} - 12 \, {\left(60 \, D b^{3} c^{6} d - 669 \, A a^{3} d^{7} + 140 \, {\left(C a^{3} + 3 \, B a^{2} b + 3 \, A a b^{2}\right)} c^{2} d^{5} - 210 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} c d^{6} - 105 \, {\left(D a^{3} c^{3} + {\left(3 \, C a^{2} b + 3 \, B a b^{2} + A b^{3}\right)} c^{3}\right)} d^{4} + 84 \, {\left(3 \, D a^{2} b c^{4} + {\left(3 \, C a b^{2} + B b^{3}\right)} c^{4}\right)} d^{3} - 70 \, {\left(3 \, D a b^{2} c^{5} + C b^{3} c^{5}\right)} d^{2}\right)} n\right)} x\right)} {\left(d x + c\right)}^{n}}{d^{7} n^{7} + 28 \, d^{7} n^{6} + 322 \, d^{7} n^{5} + 1960 \, d^{7} n^{4} + 6769 \, d^{7} n^{3} + 13132 \, d^{7} n^{2} + 13068 \, d^{7} n + 5040 \, d^{7}}"," ",0,"(A*a^3*c*d^6*n^6 + 720*D*b^3*c^7 + 5040*A*a^3*c*d^6 + 1680*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*c^3*d^4 - 2520*(B*a^3 + 3*A*a^2*b)*c^2*d^5 + (D*b^3*d^7*n^6 + 21*D*b^3*d^7*n^5 + 175*D*b^3*d^7*n^4 + 735*D*b^3*d^7*n^3 + 1624*D*b^3*d^7*n^2 + 1764*D*b^3*d^7*n + 720*D*b^3*d^7)*x^7 + (840*(3*D*a*b^2 + C*b^3)*d^7 + (D*b^3*c*d^6 + (3*D*a*b^2 + C*b^3)*d^7)*n^6 + (15*D*b^3*c*d^6 + 22*(3*D*a*b^2 + C*b^3)*d^7)*n^5 + 5*(17*D*b^3*c*d^6 + 38*(3*D*a*b^2 + C*b^3)*d^7)*n^4 + 5*(45*D*b^3*c*d^6 + 164*(3*D*a*b^2 + C*b^3)*d^7)*n^3 + (274*D*b^3*c*d^6 + 1849*(3*D*a*b^2 + C*b^3)*d^7)*n^2 + 2*(60*D*b^3*c*d^6 + 1019*(3*D*a*b^2 + C*b^3)*d^7)*n)*x^6 + (27*A*a^3*c*d^6 - (B*a^3 + 3*A*a^2*b)*c^2*d^5)*n^5 + (1008*(3*D*a^2*b + 3*C*a*b^2 + B*b^3)*d^7 + ((3*D*a^2*b + 3*C*a*b^2 + B*b^3)*d^7 + (3*D*a*b^2*c + C*b^3*c)*d^6)*n^6 - (6*D*b^3*c^2*d^5 - 23*(3*D*a^2*b + 3*C*a*b^2 + B*b^3)*d^7 - 17*(3*D*a*b^2*c + C*b^3*c)*d^6)*n^5 - 3*(20*D*b^3*c^2*d^5 - 69*(3*D*a^2*b + 3*C*a*b^2 + B*b^3)*d^7 - 35*(3*D*a*b^2*c + C*b^3*c)*d^6)*n^4 - 5*(42*D*b^3*c^2*d^5 - 185*(3*D*a^2*b + 3*C*a*b^2 + B*b^3)*d^7 - 59*(3*D*a*b^2*c + C*b^3*c)*d^6)*n^3 - 2*(150*D*b^3*c^2*d^5 - 1072*(3*D*a^2*b + 3*C*a*b^2 + B*b^3)*d^7 - 187*(3*D*a*b^2*c + C*b^3*c)*d^6)*n^2 - 12*(12*D*b^3*c^2*d^5 - 201*(3*D*a^2*b + 3*C*a*b^2 + B*b^3)*d^7 - 14*(3*D*a*b^2*c + C*b^3*c)*d^6)*n)*x^5 + (295*A*a^3*c*d^6 + 2*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*c^3*d^4 - 25*(B*a^3 + 3*A*a^2*b)*c^2*d^5)*n^4 + (1260*(D*a^3 + 3*C*a^2*b + 3*B*a*b^2 + A*b^3)*d^7 + ((D*a^3 + 3*C*a^2*b + 3*B*a*b^2 + A*b^3)*d^7 + (3*D*a^2*b*c + (3*C*a*b^2 + B*b^3)*c)*d^6)*n^6 + (24*(D*a^3 + 3*C*a^2*b + 3*B*a*b^2 + A*b^3)*d^7 + 19*(3*D*a^2*b*c + (3*C*a*b^2 + B*b^3)*c)*d^6 - 5*(3*D*a*b^2*c^2 + C*b^3*c^2)*d^5)*n^5 + (30*D*b^3*c^3*d^4 + 226*(D*a^3 + 3*C*a^2*b + 3*B*a*b^2 + A*b^3)*d^7 + 131*(3*D*a^2*b*c + (3*C*a*b^2 + B*b^3)*c)*d^6 - 65*(3*D*a*b^2*c^2 + C*b^3*c^2)*d^5)*n^4 + (180*D*b^3*c^3*d^4 + 1056*(D*a^3 + 3*C*a^2*b + 3*B*a*b^2 + A*b^3)*d^7 + 401*(3*D*a^2*b*c + (3*C*a*b^2 + B*b^3)*c)*d^6 - 265*(3*D*a*b^2*c^2 + C*b^3*c^2)*d^5)*n^3 + 5*(66*D*b^3*c^3*d^4 + 509*(D*a^3 + 3*C*a^2*b + 3*B*a*b^2 + A*b^3)*d^7 + 108*(3*D*a^2*b*c + (3*C*a*b^2 + B*b^3)*c)*d^6 - 83*(3*D*a*b^2*c^2 + C*b^3*c^2)*d^5)*n^2 + 6*(30*D*b^3*c^3*d^4 + 492*(D*a^3 + 3*C*a^2*b + 3*B*a*b^2 + A*b^3)*d^7 + 42*(3*D*a^2*b*c + (3*C*a*b^2 + B*b^3)*c)*d^6 - 35*(3*D*a*b^2*c^2 + C*b^3*c^2)*d^5)*n)*x^4 - 1260*(D*a^3*c^4 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c^4)*d^3 + (1665*A*a^3*c*d^6 + 44*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*c^3*d^4 - 245*(B*a^3 + 3*A*a^2*b)*c^2*d^5 - 6*(D*a^3*c^4 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c^4)*d^3)*n^3 + (1680*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*d^7 + ((C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*d^7 + (D*a^3*c + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c)*d^6)*n^6 + (25*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*d^7 + 21*(D*a^3*c + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c)*d^6 - 4*(3*D*a^2*b*c^2 + (3*C*a*b^2 + B*b^3)*c^2)*d^5)*n^5 + (247*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*d^7 + 163*(D*a^3*c + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c)*d^6 - 64*(3*D*a^2*b*c^2 + (3*C*a*b^2 + B*b^3)*c^2)*d^5 + 20*(3*D*a*b^2*c^3 + C*b^3*c^3)*d^4)*n^4 - (120*D*b^3*c^4*d^3 - 1219*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*d^7 - 567*(D*a^3*c + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c)*d^6 + 332*(3*D*a^2*b*c^2 + (3*C*a*b^2 + B*b^3)*c^2)*d^5 - 200*(3*D*a*b^2*c^3 + C*b^3*c^3)*d^4)*n^3 - 4*(90*D*b^3*c^4*d^3 - 778*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*d^7 - 211*(D*a^3*c + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c)*d^6 + 152*(3*D*a^2*b*c^2 + (3*C*a*b^2 + B*b^3)*c^2)*d^5 - 115*(3*D*a*b^2*c^3 + C*b^3*c^3)*d^4)*n^2 - 4*(60*D*b^3*c^4*d^3 - 949*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*d^7 - 105*(D*a^3*c + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c)*d^6 + 84*(3*D*a^2*b*c^2 + (3*C*a*b^2 + B*b^3)*c^2)*d^5 - 70*(3*D*a*b^2*c^3 + C*b^3*c^3)*d^4)*n)*x^3 + 1008*(3*D*a^2*b*c^5 + (3*C*a*b^2 + B*b^3)*c^5)*d^2 + (5104*A*a^3*c*d^6 + 358*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*c^3*d^4 - 1175*(B*a^3 + 3*A*a^2*b)*c^2*d^5 - 108*(D*a^3*c^4 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c^4)*d^3 + 24*(3*D*a^2*b*c^5 + (3*C*a*b^2 + B*b^3)*c^5)*d^2)*n^2 + (2520*(B*a^3 + 3*A*a^2*b)*d^7 + ((C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*c*d^6 + (B*a^3 + 3*A*a^2*b)*d^7)*n^6 + (23*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*c*d^6 + 26*(B*a^3 + 3*A*a^2*b)*d^7 - 3*(D*a^3*c^2 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c^2)*d^5)*n^5 + 3*(67*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*c*d^6 + 90*(B*a^3 + 3*A*a^2*b)*d^7 - 19*(D*a^3*c^2 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c^2)*d^5 + 4*(3*D*a^2*b*c^3 + (3*C*a*b^2 + B*b^3)*c^3)*d^4)*n^4 + (817*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*c*d^6 + 1420*(B*a^3 + 3*A*a^2*b)*d^7 - 375*(D*a^3*c^2 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c^2)*d^5 + 168*(3*D*a^2*b*c^3 + (3*C*a*b^2 + B*b^3)*c^3)*d^4 - 60*(3*D*a*b^2*c^4 + C*b^3*c^4)*d^3)*n^3 + (360*D*b^3*c^5*d^2 + 1478*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*c*d^6 + 3929*(B*a^3 + 3*A*a^2*b)*d^7 - 951*(D*a^3*c^2 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c^2)*d^5 + 660*(3*D*a^2*b*c^3 + (3*C*a*b^2 + B*b^3)*c^3)*d^4 - 480*(3*D*a*b^2*c^4 + C*b^3*c^4)*d^3)*n^2 + 6*(60*D*b^3*c^5*d^2 + 140*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*c*d^6 + 879*(B*a^3 + 3*A*a^2*b)*d^7 - 105*(D*a^3*c^2 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c^2)*d^5 + 84*(3*D*a^2*b*c^3 + (3*C*a*b^2 + B*b^3)*c^3)*d^4 - 70*(3*D*a*b^2*c^4 + C*b^3*c^4)*d^3)*n)*x^2 - 840*(3*D*a*b^2*c^6 + C*b^3*c^6)*d + 2*(4014*A*a^3*c*d^6 + 638*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*c^3*d^4 - 1377*(B*a^3 + 3*A*a^2*b)*c^2*d^5 - 321*(D*a^3*c^4 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c^4)*d^3 + 156*(3*D*a^2*b*c^5 + (3*C*a*b^2 + B*b^3)*c^5)*d^2 - 60*(3*D*a*b^2*c^6 + C*b^3*c^6)*d)*n + (5040*A*a^3*d^7 + (A*a^3*d^7 + (B*a^3 + 3*A*a^2*b)*c*d^6)*n^6 + (27*A*a^3*d^7 - 2*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*c^2*d^5 + 25*(B*a^3 + 3*A*a^2*b)*c*d^6)*n^5 + (295*A*a^3*d^7 - 44*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*c^2*d^5 + 245*(B*a^3 + 3*A*a^2*b)*c*d^6 + 6*(D*a^3*c^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c^3)*d^4)*n^4 + (1665*A*a^3*d^7 - 358*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*c^2*d^5 + 1175*(B*a^3 + 3*A*a^2*b)*c*d^6 + 108*(D*a^3*c^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c^3)*d^4 - 24*(3*D*a^2*b*c^4 + (3*C*a*b^2 + B*b^3)*c^4)*d^3)*n^3 + 2*(2552*A*a^3*d^7 - 638*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*c^2*d^5 + 1377*(B*a^3 + 3*A*a^2*b)*c*d^6 + 321*(D*a^3*c^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c^3)*d^4 - 156*(3*D*a^2*b*c^4 + (3*C*a*b^2 + B*b^3)*c^4)*d^3 + 60*(3*D*a*b^2*c^5 + C*b^3*c^5)*d^2)*n^2 - 12*(60*D*b^3*c^6*d - 669*A*a^3*d^7 + 140*(C*a^3 + 3*B*a^2*b + 3*A*a*b^2)*c^2*d^5 - 210*(B*a^3 + 3*A*a^2*b)*c*d^6 - 105*(D*a^3*c^3 + (3*C*a^2*b + 3*B*a*b^2 + A*b^3)*c^3)*d^4 + 84*(3*D*a^2*b*c^4 + (3*C*a*b^2 + B*b^3)*c^4)*d^3 - 70*(3*D*a*b^2*c^5 + C*b^3*c^5)*d^2)*n)*x)*(d*x + c)^n/(d^7*n^7 + 28*d^7*n^6 + 322*d^7*n^5 + 1960*d^7*n^4 + 6769*d^7*n^3 + 13132*d^7*n^2 + 13068*d^7*n + 5040*d^7)","B",0
26,1,2258,0,0.920330," ","integrate((b*x+a)^2*(d*x+c)^n*(D*x^3+C*x^2+B*x+A),x, algorithm=""fricas"")","\frac{{\left(A a^{2} c d^{5} n^{5} - 120 \, D b^{2} c^{6} + 720 \, A a^{2} c d^{5} + 240 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{3} d^{3} - 360 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} d^{4} + {\left(D b^{2} d^{6} n^{5} + 15 \, D b^{2} d^{6} n^{4} + 85 \, D b^{2} d^{6} n^{3} + 225 \, D b^{2} d^{6} n^{2} + 274 \, D b^{2} d^{6} n + 120 \, D b^{2} d^{6}\right)} x^{6} + {\left(144 \, {\left(2 \, D a b + C b^{2}\right)} d^{6} + {\left(D b^{2} c d^{5} + {\left(2 \, D a b + C b^{2}\right)} d^{6}\right)} n^{5} + 2 \, {\left(5 \, D b^{2} c d^{5} + 8 \, {\left(2 \, D a b + C b^{2}\right)} d^{6}\right)} n^{4} + 5 \, {\left(7 \, D b^{2} c d^{5} + 19 \, {\left(2 \, D a b + C b^{2}\right)} d^{6}\right)} n^{3} + 10 \, {\left(5 \, D b^{2} c d^{5} + 26 \, {\left(2 \, D a b + C b^{2}\right)} d^{6}\right)} n^{2} + 12 \, {\left(2 \, D b^{2} c d^{5} + 27 \, {\left(2 \, D a b + C b^{2}\right)} d^{6}\right)} n\right)} x^{5} + {\left(20 \, A a^{2} c d^{5} - {\left(B a^{2} + 2 \, A a b\right)} c^{2} d^{4}\right)} n^{4} + {\left(180 \, {\left(D a^{2} + 2 \, C a b + B b^{2}\right)} d^{6} + {\left({\left(D a^{2} + 2 \, C a b + B b^{2}\right)} d^{6} + {\left(2 \, D a b c + C b^{2} c\right)} d^{5}\right)} n^{5} - {\left(5 \, D b^{2} c^{2} d^{4} - 17 \, {\left(D a^{2} + 2 \, C a b + B b^{2}\right)} d^{6} - 12 \, {\left(2 \, D a b c + C b^{2} c\right)} d^{5}\right)} n^{4} - {\left(30 \, D b^{2} c^{2} d^{4} - 107 \, {\left(D a^{2} + 2 \, C a b + B b^{2}\right)} d^{6} - 47 \, {\left(2 \, D a b c + C b^{2} c\right)} d^{5}\right)} n^{3} - {\left(55 \, D b^{2} c^{2} d^{4} - 307 \, {\left(D a^{2} + 2 \, C a b + B b^{2}\right)} d^{6} - 72 \, {\left(2 \, D a b c + C b^{2} c\right)} d^{5}\right)} n^{2} - 6 \, {\left(5 \, D b^{2} c^{2} d^{4} - 66 \, {\left(D a^{2} + 2 \, C a b + B b^{2}\right)} d^{6} - 6 \, {\left(2 \, D a b c + C b^{2} c\right)} d^{5}\right)} n\right)} x^{4} + {\left(155 \, A a^{2} c d^{5} + 2 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{3} d^{3} - 18 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} d^{4}\right)} n^{3} + {\left(240 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{6} + {\left({\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{6} + {\left(D a^{2} c + {\left(2 \, C a b + B b^{2}\right)} c\right)} d^{5}\right)} n^{5} + 2 \, {\left(9 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{6} + 7 \, {\left(D a^{2} c + {\left(2 \, C a b + B b^{2}\right)} c\right)} d^{5} - 2 \, {\left(2 \, D a b c^{2} + C b^{2} c^{2}\right)} d^{4}\right)} n^{4} + {\left(20 \, D b^{2} c^{3} d^{3} + 121 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{6} + 65 \, {\left(D a^{2} c + {\left(2 \, C a b + B b^{2}\right)} c\right)} d^{5} - 36 \, {\left(2 \, D a b c^{2} + C b^{2} c^{2}\right)} d^{4}\right)} n^{3} + 4 \, {\left(15 \, D b^{2} c^{3} d^{3} + 93 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{6} + 28 \, {\left(D a^{2} c + {\left(2 \, C a b + B b^{2}\right)} c\right)} d^{5} - 20 \, {\left(2 \, D a b c^{2} + C b^{2} c^{2}\right)} d^{4}\right)} n^{2} + 4 \, {\left(10 \, D b^{2} c^{3} d^{3} + 127 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} d^{6} + 15 \, {\left(D a^{2} c + {\left(2 \, C a b + B b^{2}\right)} c\right)} d^{5} - 12 \, {\left(2 \, D a b c^{2} + C b^{2} c^{2}\right)} d^{4}\right)} n\right)} x^{3} - 180 \, {\left(D a^{2} c^{4} + {\left(2 \, C a b + B b^{2}\right)} c^{4}\right)} d^{2} + {\left(580 \, A a^{2} c d^{5} + 30 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{3} d^{3} - 119 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} d^{4} - 6 \, {\left(D a^{2} c^{4} + {\left(2 \, C a b + B b^{2}\right)} c^{4}\right)} d^{2}\right)} n^{2} + {\left(360 \, {\left(B a^{2} + 2 \, A a b\right)} d^{6} + {\left({\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c d^{5} + {\left(B a^{2} + 2 \, A a b\right)} d^{6}\right)} n^{5} + {\left(16 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c d^{5} + 19 \, {\left(B a^{2} + 2 \, A a b\right)} d^{6} - 3 \, {\left(D a^{2} c^{2} + {\left(2 \, C a b + B b^{2}\right)} c^{2}\right)} d^{4}\right)} n^{4} + {\left(89 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c d^{5} + 137 \, {\left(B a^{2} + 2 \, A a b\right)} d^{6} - 36 \, {\left(D a^{2} c^{2} + {\left(2 \, C a b + B b^{2}\right)} c^{2}\right)} d^{4} + 12 \, {\left(2 \, D a b c^{3} + C b^{2} c^{3}\right)} d^{3}\right)} n^{3} - {\left(60 \, D b^{2} c^{4} d^{2} - 194 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c d^{5} - 461 \, {\left(B a^{2} + 2 \, A a b\right)} d^{6} + 123 \, {\left(D a^{2} c^{2} + {\left(2 \, C a b + B b^{2}\right)} c^{2}\right)} d^{4} - 84 \, {\left(2 \, D a b c^{3} + C b^{2} c^{3}\right)} d^{3}\right)} n^{2} - 6 \, {\left(10 \, D b^{2} c^{4} d^{2} - 20 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c d^{5} - 117 \, {\left(B a^{2} + 2 \, A a b\right)} d^{6} + 15 \, {\left(D a^{2} c^{2} + {\left(2 \, C a b + B b^{2}\right)} c^{2}\right)} d^{4} - 12 \, {\left(2 \, D a b c^{3} + C b^{2} c^{3}\right)} d^{3}\right)} n\right)} x^{2} + 144 \, {\left(2 \, D a b c^{5} + C b^{2} c^{5}\right)} d + 2 \, {\left(522 \, A a^{2} c d^{5} + 74 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{3} d^{3} - 171 \, {\left(B a^{2} + 2 \, A a b\right)} c^{2} d^{4} - 33 \, {\left(D a^{2} c^{4} + {\left(2 \, C a b + B b^{2}\right)} c^{4}\right)} d^{2} + 12 \, {\left(2 \, D a b c^{5} + C b^{2} c^{5}\right)} d\right)} n + {\left(720 \, A a^{2} d^{6} + {\left(A a^{2} d^{6} + {\left(B a^{2} + 2 \, A a b\right)} c d^{5}\right)} n^{5} + 2 \, {\left(10 \, A a^{2} d^{6} - {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{2} d^{4} + 9 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{5}\right)} n^{4} + {\left(155 \, A a^{2} d^{6} - 30 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{2} d^{4} + 119 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{5} + 6 \, {\left(D a^{2} c^{3} + {\left(2 \, C a b + B b^{2}\right)} c^{3}\right)} d^{3}\right)} n^{3} + 2 \, {\left(290 \, A a^{2} d^{6} - 74 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{2} d^{4} + 171 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{5} + 33 \, {\left(D a^{2} c^{3} + {\left(2 \, C a b + B b^{2}\right)} c^{3}\right)} d^{3} - 12 \, {\left(2 \, D a b c^{4} + C b^{2} c^{4}\right)} d^{2}\right)} n^{2} + 12 \, {\left(10 \, D b^{2} c^{5} d + 87 \, A a^{2} d^{6} - 20 \, {\left(C a^{2} + 2 \, B a b + A b^{2}\right)} c^{2} d^{4} + 30 \, {\left(B a^{2} + 2 \, A a b\right)} c d^{5} + 15 \, {\left(D a^{2} c^{3} + {\left(2 \, C a b + B b^{2}\right)} c^{3}\right)} d^{3} - 12 \, {\left(2 \, D a b c^{4} + C b^{2} c^{4}\right)} d^{2}\right)} n\right)} x\right)} {\left(d x + c\right)}^{n}}{d^{6} n^{6} + 21 \, d^{6} n^{5} + 175 \, d^{6} n^{4} + 735 \, d^{6} n^{3} + 1624 \, d^{6} n^{2} + 1764 \, d^{6} n + 720 \, d^{6}}"," ",0,"(A*a^2*c*d^5*n^5 - 120*D*b^2*c^6 + 720*A*a^2*c*d^5 + 240*(C*a^2 + 2*B*a*b + A*b^2)*c^3*d^3 - 360*(B*a^2 + 2*A*a*b)*c^2*d^4 + (D*b^2*d^6*n^5 + 15*D*b^2*d^6*n^4 + 85*D*b^2*d^6*n^3 + 225*D*b^2*d^6*n^2 + 274*D*b^2*d^6*n + 120*D*b^2*d^6)*x^6 + (144*(2*D*a*b + C*b^2)*d^6 + (D*b^2*c*d^5 + (2*D*a*b + C*b^2)*d^6)*n^5 + 2*(5*D*b^2*c*d^5 + 8*(2*D*a*b + C*b^2)*d^6)*n^4 + 5*(7*D*b^2*c*d^5 + 19*(2*D*a*b + C*b^2)*d^6)*n^3 + 10*(5*D*b^2*c*d^5 + 26*(2*D*a*b + C*b^2)*d^6)*n^2 + 12*(2*D*b^2*c*d^5 + 27*(2*D*a*b + C*b^2)*d^6)*n)*x^5 + (20*A*a^2*c*d^5 - (B*a^2 + 2*A*a*b)*c^2*d^4)*n^4 + (180*(D*a^2 + 2*C*a*b + B*b^2)*d^6 + ((D*a^2 + 2*C*a*b + B*b^2)*d^6 + (2*D*a*b*c + C*b^2*c)*d^5)*n^5 - (5*D*b^2*c^2*d^4 - 17*(D*a^2 + 2*C*a*b + B*b^2)*d^6 - 12*(2*D*a*b*c + C*b^2*c)*d^5)*n^4 - (30*D*b^2*c^2*d^4 - 107*(D*a^2 + 2*C*a*b + B*b^2)*d^6 - 47*(2*D*a*b*c + C*b^2*c)*d^5)*n^3 - (55*D*b^2*c^2*d^4 - 307*(D*a^2 + 2*C*a*b + B*b^2)*d^6 - 72*(2*D*a*b*c + C*b^2*c)*d^5)*n^2 - 6*(5*D*b^2*c^2*d^4 - 66*(D*a^2 + 2*C*a*b + B*b^2)*d^6 - 6*(2*D*a*b*c + C*b^2*c)*d^5)*n)*x^4 + (155*A*a^2*c*d^5 + 2*(C*a^2 + 2*B*a*b + A*b^2)*c^3*d^3 - 18*(B*a^2 + 2*A*a*b)*c^2*d^4)*n^3 + (240*(C*a^2 + 2*B*a*b + A*b^2)*d^6 + ((C*a^2 + 2*B*a*b + A*b^2)*d^6 + (D*a^2*c + (2*C*a*b + B*b^2)*c)*d^5)*n^5 + 2*(9*(C*a^2 + 2*B*a*b + A*b^2)*d^6 + 7*(D*a^2*c + (2*C*a*b + B*b^2)*c)*d^5 - 2*(2*D*a*b*c^2 + C*b^2*c^2)*d^4)*n^4 + (20*D*b^2*c^3*d^3 + 121*(C*a^2 + 2*B*a*b + A*b^2)*d^6 + 65*(D*a^2*c + (2*C*a*b + B*b^2)*c)*d^5 - 36*(2*D*a*b*c^2 + C*b^2*c^2)*d^4)*n^3 + 4*(15*D*b^2*c^3*d^3 + 93*(C*a^2 + 2*B*a*b + A*b^2)*d^6 + 28*(D*a^2*c + (2*C*a*b + B*b^2)*c)*d^5 - 20*(2*D*a*b*c^2 + C*b^2*c^2)*d^4)*n^2 + 4*(10*D*b^2*c^3*d^3 + 127*(C*a^2 + 2*B*a*b + A*b^2)*d^6 + 15*(D*a^2*c + (2*C*a*b + B*b^2)*c)*d^5 - 12*(2*D*a*b*c^2 + C*b^2*c^2)*d^4)*n)*x^3 - 180*(D*a^2*c^4 + (2*C*a*b + B*b^2)*c^4)*d^2 + (580*A*a^2*c*d^5 + 30*(C*a^2 + 2*B*a*b + A*b^2)*c^3*d^3 - 119*(B*a^2 + 2*A*a*b)*c^2*d^4 - 6*(D*a^2*c^4 + (2*C*a*b + B*b^2)*c^4)*d^2)*n^2 + (360*(B*a^2 + 2*A*a*b)*d^6 + ((C*a^2 + 2*B*a*b + A*b^2)*c*d^5 + (B*a^2 + 2*A*a*b)*d^6)*n^5 + (16*(C*a^2 + 2*B*a*b + A*b^2)*c*d^5 + 19*(B*a^2 + 2*A*a*b)*d^6 - 3*(D*a^2*c^2 + (2*C*a*b + B*b^2)*c^2)*d^4)*n^4 + (89*(C*a^2 + 2*B*a*b + A*b^2)*c*d^5 + 137*(B*a^2 + 2*A*a*b)*d^6 - 36*(D*a^2*c^2 + (2*C*a*b + B*b^2)*c^2)*d^4 + 12*(2*D*a*b*c^3 + C*b^2*c^3)*d^3)*n^3 - (60*D*b^2*c^4*d^2 - 194*(C*a^2 + 2*B*a*b + A*b^2)*c*d^5 - 461*(B*a^2 + 2*A*a*b)*d^6 + 123*(D*a^2*c^2 + (2*C*a*b + B*b^2)*c^2)*d^4 - 84*(2*D*a*b*c^3 + C*b^2*c^3)*d^3)*n^2 - 6*(10*D*b^2*c^4*d^2 - 20*(C*a^2 + 2*B*a*b + A*b^2)*c*d^5 - 117*(B*a^2 + 2*A*a*b)*d^6 + 15*(D*a^2*c^2 + (2*C*a*b + B*b^2)*c^2)*d^4 - 12*(2*D*a*b*c^3 + C*b^2*c^3)*d^3)*n)*x^2 + 144*(2*D*a*b*c^5 + C*b^2*c^5)*d + 2*(522*A*a^2*c*d^5 + 74*(C*a^2 + 2*B*a*b + A*b^2)*c^3*d^3 - 171*(B*a^2 + 2*A*a*b)*c^2*d^4 - 33*(D*a^2*c^4 + (2*C*a*b + B*b^2)*c^4)*d^2 + 12*(2*D*a*b*c^5 + C*b^2*c^5)*d)*n + (720*A*a^2*d^6 + (A*a^2*d^6 + (B*a^2 + 2*A*a*b)*c*d^5)*n^5 + 2*(10*A*a^2*d^6 - (C*a^2 + 2*B*a*b + A*b^2)*c^2*d^4 + 9*(B*a^2 + 2*A*a*b)*c*d^5)*n^4 + (155*A*a^2*d^6 - 30*(C*a^2 + 2*B*a*b + A*b^2)*c^2*d^4 + 119*(B*a^2 + 2*A*a*b)*c*d^5 + 6*(D*a^2*c^3 + (2*C*a*b + B*b^2)*c^3)*d^3)*n^3 + 2*(290*A*a^2*d^6 - 74*(C*a^2 + 2*B*a*b + A*b^2)*c^2*d^4 + 171*(B*a^2 + 2*A*a*b)*c*d^5 + 33*(D*a^2*c^3 + (2*C*a*b + B*b^2)*c^3)*d^3 - 12*(2*D*a*b*c^4 + C*b^2*c^4)*d^2)*n^2 + 12*(10*D*b^2*c^5*d + 87*A*a^2*d^6 - 20*(C*a^2 + 2*B*a*b + A*b^2)*c^2*d^4 + 30*(B*a^2 + 2*A*a*b)*c*d^5 + 15*(D*a^2*c^3 + (2*C*a*b + B*b^2)*c^3)*d^3 - 12*(2*D*a*b*c^4 + C*b^2*c^4)*d^2)*n)*x)*(d*x + c)^n/(d^6*n^6 + 21*d^6*n^5 + 175*d^6*n^4 + 735*d^6*n^3 + 1624*d^6*n^2 + 1764*d^6*n + 720*d^6)","B",0
27,1,988,0,1.046569," ","integrate((b*x+a)*(d*x+c)^n*(D*x^3+C*x^2+B*x+A),x, algorithm=""fricas"")","\frac{{\left(A a c d^{4} n^{4} + 24 \, D b c^{5} + 120 \, A a c d^{4} + 40 \, {\left(C a + B b\right)} c^{3} d^{2} - 60 \, {\left(B a + A b\right)} c^{2} d^{3} + {\left(D b d^{5} n^{4} + 10 \, D b d^{5} n^{3} + 35 \, D b d^{5} n^{2} + 50 \, D b d^{5} n + 24 \, D b d^{5}\right)} x^{5} + {\left(30 \, {\left(D a + C b\right)} d^{5} + {\left(D b c d^{4} + {\left(D a + C b\right)} d^{5}\right)} n^{4} + {\left(6 \, D b c d^{4} + 11 \, {\left(D a + C b\right)} d^{5}\right)} n^{3} + {\left(11 \, D b c d^{4} + 41 \, {\left(D a + C b\right)} d^{5}\right)} n^{2} + {\left(6 \, D b c d^{4} + 61 \, {\left(D a + C b\right)} d^{5}\right)} n\right)} x^{4} + {\left(14 \, A a c d^{4} - {\left(B a + A b\right)} c^{2} d^{3}\right)} n^{3} + {\left(40 \, {\left(C a + B b\right)} d^{5} + {\left({\left(C a + B b\right)} d^{5} + {\left(D a c + C b c\right)} d^{4}\right)} n^{4} - 4 \, {\left(D b c^{2} d^{3} - 3 \, {\left(C a + B b\right)} d^{5} - 2 \, {\left(D a c + C b c\right)} d^{4}\right)} n^{3} - {\left(12 \, D b c^{2} d^{3} - 49 \, {\left(C a + B b\right)} d^{5} - 17 \, {\left(D a c + C b c\right)} d^{4}\right)} n^{2} - 2 \, {\left(4 \, D b c^{2} d^{3} - 39 \, {\left(C a + B b\right)} d^{5} - 5 \, {\left(D a c + C b c\right)} d^{4}\right)} n\right)} x^{3} + {\left(71 \, A a c d^{4} + 2 \, {\left(C a + B b\right)} c^{3} d^{2} - 12 \, {\left(B a + A b\right)} c^{2} d^{3}\right)} n^{2} + {\left(60 \, {\left(B a + A b\right)} d^{5} + {\left({\left(C a + B b\right)} c d^{4} + {\left(B a + A b\right)} d^{5}\right)} n^{4} + {\left(10 \, {\left(C a + B b\right)} c d^{4} + 13 \, {\left(B a + A b\right)} d^{5} - 3 \, {\left(D a c^{2} + C b c^{2}\right)} d^{3}\right)} n^{3} + {\left(12 \, D b c^{3} d^{2} + 29 \, {\left(C a + B b\right)} c d^{4} + 59 \, {\left(B a + A b\right)} d^{5} - 18 \, {\left(D a c^{2} + C b c^{2}\right)} d^{3}\right)} n^{2} + {\left(12 \, D b c^{3} d^{2} + 20 \, {\left(C a + B b\right)} c d^{4} + 107 \, {\left(B a + A b\right)} d^{5} - 15 \, {\left(D a c^{2} + C b c^{2}\right)} d^{3}\right)} n\right)} x^{2} - 30 \, {\left(D a c^{4} + C b c^{4}\right)} d + {\left(154 \, A a c d^{4} + 18 \, {\left(C a + B b\right)} c^{3} d^{2} - 47 \, {\left(B a + A b\right)} c^{2} d^{3} - 6 \, {\left(D a c^{4} + C b c^{4}\right)} d\right)} n + {\left(120 \, A a d^{5} + {\left(A a d^{5} + {\left(B a + A b\right)} c d^{4}\right)} n^{4} + 2 \, {\left(7 \, A a d^{5} - {\left(C a + B b\right)} c^{2} d^{3} + 6 \, {\left(B a + A b\right)} c d^{4}\right)} n^{3} + {\left(71 \, A a d^{5} - 18 \, {\left(C a + B b\right)} c^{2} d^{3} + 47 \, {\left(B a + A b\right)} c d^{4} + 6 \, {\left(D a c^{3} + C b c^{3}\right)} d^{2}\right)} n^{2} - 2 \, {\left(12 \, D b c^{4} d - 77 \, A a d^{5} + 20 \, {\left(C a + B b\right)} c^{2} d^{3} - 30 \, {\left(B a + A b\right)} c d^{4} - 15 \, {\left(D a c^{3} + C b c^{3}\right)} d^{2}\right)} n\right)} x\right)} {\left(d x + c\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}}"," ",0,"(A*a*c*d^4*n^4 + 24*D*b*c^5 + 120*A*a*c*d^4 + 40*(C*a + B*b)*c^3*d^2 - 60*(B*a + A*b)*c^2*d^3 + (D*b*d^5*n^4 + 10*D*b*d^5*n^3 + 35*D*b*d^5*n^2 + 50*D*b*d^5*n + 24*D*b*d^5)*x^5 + (30*(D*a + C*b)*d^5 + (D*b*c*d^4 + (D*a + C*b)*d^5)*n^4 + (6*D*b*c*d^4 + 11*(D*a + C*b)*d^5)*n^3 + (11*D*b*c*d^4 + 41*(D*a + C*b)*d^5)*n^2 + (6*D*b*c*d^4 + 61*(D*a + C*b)*d^5)*n)*x^4 + (14*A*a*c*d^4 - (B*a + A*b)*c^2*d^3)*n^3 + (40*(C*a + B*b)*d^5 + ((C*a + B*b)*d^5 + (D*a*c + C*b*c)*d^4)*n^4 - 4*(D*b*c^2*d^3 - 3*(C*a + B*b)*d^5 - 2*(D*a*c + C*b*c)*d^4)*n^3 - (12*D*b*c^2*d^3 - 49*(C*a + B*b)*d^5 - 17*(D*a*c + C*b*c)*d^4)*n^2 - 2*(4*D*b*c^2*d^3 - 39*(C*a + B*b)*d^5 - 5*(D*a*c + C*b*c)*d^4)*n)*x^3 + (71*A*a*c*d^4 + 2*(C*a + B*b)*c^3*d^2 - 12*(B*a + A*b)*c^2*d^3)*n^2 + (60*(B*a + A*b)*d^5 + ((C*a + B*b)*c*d^4 + (B*a + A*b)*d^5)*n^4 + (10*(C*a + B*b)*c*d^4 + 13*(B*a + A*b)*d^5 - 3*(D*a*c^2 + C*b*c^2)*d^3)*n^3 + (12*D*b*c^3*d^2 + 29*(C*a + B*b)*c*d^4 + 59*(B*a + A*b)*d^5 - 18*(D*a*c^2 + C*b*c^2)*d^3)*n^2 + (12*D*b*c^3*d^2 + 20*(C*a + B*b)*c*d^4 + 107*(B*a + A*b)*d^5 - 15*(D*a*c^2 + C*b*c^2)*d^3)*n)*x^2 - 30*(D*a*c^4 + C*b*c^4)*d + (154*A*a*c*d^4 + 18*(C*a + B*b)*c^3*d^2 - 47*(B*a + A*b)*c^2*d^3 - 6*(D*a*c^4 + C*b*c^4)*d)*n + (120*A*a*d^5 + (A*a*d^5 + (B*a + A*b)*c*d^4)*n^4 + 2*(7*A*a*d^5 - (C*a + B*b)*c^2*d^3 + 6*(B*a + A*b)*c*d^4)*n^3 + (71*A*a*d^5 - 18*(C*a + B*b)*c^2*d^3 + 47*(B*a + A*b)*c*d^4 + 6*(D*a*c^3 + C*b*c^3)*d^2)*n^2 - 2*(12*D*b*c^4*d - 77*A*a*d^5 + 20*(C*a + B*b)*c^2*d^3 - 30*(B*a + A*b)*c*d^4 - 15*(D*a*c^3 + C*b*c^3)*d^2)*n)*x)*(d*x + c)^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",0
28,1,394,0,0.872868," ","integrate((d*x+c)^n*(D*x^3+C*x^2+B*x+A),x, algorithm=""fricas"")","\frac{{\left(A c d^{3} n^{3} - 6 \, D c^{4} + 8 \, C c^{3} d - 12 \, B c^{2} d^{2} + 24 \, A c d^{3} + {\left(D d^{4} n^{3} + 6 \, D d^{4} n^{2} + 11 \, D d^{4} n + 6 \, D d^{4}\right)} x^{4} + {\left(8 \, C d^{4} + {\left(D c d^{3} + C d^{4}\right)} n^{3} + {\left(3 \, D c d^{3} + 7 \, C d^{4}\right)} n^{2} + 2 \, {\left(D c d^{3} + 7 \, C d^{4}\right)} n\right)} x^{3} - {\left(B c^{2} d^{2} - 9 \, A c d^{3}\right)} n^{2} + {\left(12 \, B d^{4} + {\left(C c d^{3} + B d^{4}\right)} n^{3} - {\left(3 \, D c^{2} d^{2} - 5 \, C c d^{3} - 8 \, B d^{4}\right)} n^{2} - {\left(3 \, D c^{2} d^{2} - 4 \, C c d^{3} - 19 \, B d^{4}\right)} n\right)} x^{2} + {\left(2 \, C c^{3} d - 7 \, B c^{2} d^{2} + 26 \, A c d^{3}\right)} n + {\left(24 \, A d^{4} + {\left(B c d^{3} + A d^{4}\right)} n^{3} - {\left(2 \, C c^{2} d^{2} - 7 \, B c d^{3} - 9 \, A d^{4}\right)} n^{2} + 2 \, {\left(3 \, D c^{3} d - 4 \, C c^{2} d^{2} + 6 \, B c d^{3} + 13 \, A d^{4}\right)} n\right)} x\right)} {\left(d x + c\right)}^{n}}{d^{4} n^{4} + 10 \, d^{4} n^{3} + 35 \, d^{4} n^{2} + 50 \, d^{4} n + 24 \, d^{4}}"," ",0,"(A*c*d^3*n^3 - 6*D*c^4 + 8*C*c^3*d - 12*B*c^2*d^2 + 24*A*c*d^3 + (D*d^4*n^3 + 6*D*d^4*n^2 + 11*D*d^4*n + 6*D*d^4)*x^4 + (8*C*d^4 + (D*c*d^3 + C*d^4)*n^3 + (3*D*c*d^3 + 7*C*d^4)*n^2 + 2*(D*c*d^3 + 7*C*d^4)*n)*x^3 - (B*c^2*d^2 - 9*A*c*d^3)*n^2 + (12*B*d^4 + (C*c*d^3 + B*d^4)*n^3 - (3*D*c^2*d^2 - 5*C*c*d^3 - 8*B*d^4)*n^2 - (3*D*c^2*d^2 - 4*C*c*d^3 - 19*B*d^4)*n)*x^2 + (2*C*c^3*d - 7*B*c^2*d^2 + 26*A*c*d^3)*n + (24*A*d^4 + (B*c*d^3 + A*d^4)*n^3 - (2*C*c^2*d^2 - 7*B*c*d^3 - 9*A*d^4)*n^2 + 2*(3*D*c^3*d - 4*C*c^2*d^2 + 6*B*c*d^3 + 13*A*d^4)*n)*x)*(d*x + c)^n/(d^4*n^4 + 10*d^4*n^3 + 35*d^4*n^2 + 50*d^4*n + 24*d^4)","B",0
29,0,0,0,0.875409," ","integrate((d*x+c)^n*(D*x^3+C*x^2+B*x+A)/(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(D x^{3} + C x^{2} + B x + A\right)} {\left(d x + c\right)}^{n}}{b x + a}, x\right)"," ",0,"integral((D*x^3 + C*x^2 + B*x + A)*(d*x + c)^n/(b*x + a), x)","F",0
30,0,0,0,0.852773," ","integrate((d*x+c)^n*(D*x^3+C*x^2+B*x+A)/(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(D x^{3} + C x^{2} + B x + A\right)} {\left(d x + c\right)}^{n}}{b^{2} x^{2} + 2 \, a b x + a^{2}}, x\right)"," ",0,"integral((D*x^3 + C*x^2 + B*x + A)*(d*x + c)^n/(b^2*x^2 + 2*a*b*x + a^2), x)","F",0
31,0,0,0,0.971823," ","integrate((d*x+c)^n*(D*x^3+C*x^2+B*x+A)/(b*x+a)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(D x^{3} + C x^{2} + B x + A\right)} {\left(d x + c\right)}^{n}}{b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}}, x\right)"," ",0,"integral((D*x^3 + C*x^2 + B*x + A)*(d*x + c)^n/(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3), x)","F",0
32,0,0,0,1.225854," ","integrate((b*x+a)^m*(B*x+A)*(d*x+c)^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(B x + A\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n}, x\right)"," ",0,"integral((B*x + A)*(b*x + a)^m*(d*x + c)^n, x)","F",0
33,0,0,0,0.860979," ","integrate((b*x+a)^m*(d*x+c)^n*(C*x^2+B*x+A),x, algorithm=""fricas"")","{\rm integral}\left({\left(C x^{2} + B x + A\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n}, x\right)"," ",0,"integral((C*x^2 + B*x + A)*(b*x + a)^m*(d*x + c)^n, x)","F",0
34,0,0,0,1.176035," ","integrate((b*x+a)^m*(d*x+c)^n*(D*x^3+C*x^2+B*x+A),x, algorithm=""fricas"")","{\rm integral}\left({\left(D x^{3} + C x^{2} + B x + A\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n}, x\right)"," ",0,"integral((D*x^3 + C*x^2 + B*x + A)*(b*x + a)^m*(d*x + c)^n, x)","F",0
