1,1,841,410,0.009000," ","int((b*x+a)^3*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(1/2),x)","\frac{2 \sqrt{d x +c}\, \left(3465 b^{3} D x^{6} d^{6}+4095 C \,b^{3} d^{6} x^{5}+12285 D a \,b^{2} d^{6} x^{5}-3780 D b^{3} c \,d^{5} x^{5}+5005 B \,b^{3} d^{6} x^{4}+15015 C a \,b^{2} d^{6} x^{4}-4550 C \,b^{3} c \,d^{5} x^{4}+15015 D a^{2} b \,d^{6} x^{4}-13650 D a \,b^{2} c \,d^{5} x^{4}+4200 D b^{3} c^{2} d^{4} x^{4}+6435 A \,b^{3} d^{6} x^{3}+19305 B a \,b^{2} d^{6} x^{3}-5720 B \,b^{3} c \,d^{5} x^{3}+19305 C \,a^{2} b \,d^{6} x^{3}-17160 C a \,b^{2} c \,d^{5} x^{3}+5200 C \,b^{3} c^{2} d^{4} x^{3}+6435 D a^{3} d^{6} x^{3}-17160 D a^{2} b c \,d^{5} x^{3}+15600 D a \,b^{2} c^{2} d^{4} x^{3}-4800 D b^{3} c^{3} d^{3} x^{3}+27027 A a \,b^{2} d^{6} x^{2}-7722 A \,b^{3} c \,d^{5} x^{2}+27027 B \,a^{2} b \,d^{6} x^{2}-23166 B a \,b^{2} c \,d^{5} x^{2}+6864 B \,b^{3} c^{2} d^{4} x^{2}+9009 C \,a^{3} d^{6} x^{2}-23166 C \,a^{2} b c \,d^{5} x^{2}+20592 C a \,b^{2} c^{2} d^{4} x^{2}-6240 C \,b^{3} c^{3} d^{3} x^{2}-7722 D a^{3} c \,d^{5} x^{2}+20592 D a^{2} b \,c^{2} d^{4} x^{2}-18720 D a \,b^{2} c^{3} d^{3} x^{2}+5760 D b^{3} c^{4} d^{2} x^{2}+45045 A \,a^{2} b \,d^{6} x -36036 A a \,b^{2} c \,d^{5} x +10296 A \,b^{3} c^{2} d^{4} x +15015 B \,a^{3} d^{6} x -36036 B \,a^{2} b c \,d^{5} x +30888 B a \,b^{2} c^{2} d^{4} x -9152 B \,b^{3} c^{3} d^{3} x -12012 C \,a^{3} c \,d^{5} x +30888 C \,a^{2} b \,c^{2} d^{4} x -27456 C a \,b^{2} c^{3} d^{3} x +8320 C \,b^{3} c^{4} d^{2} x +10296 D a^{3} c^{2} d^{4} x -27456 D a^{2} b \,c^{3} d^{3} x +24960 D a \,b^{2} c^{4} d^{2} x -7680 D b^{3} c^{5} d x +45045 a^{3} A \,d^{6}-90090 A \,a^{2} b c \,d^{5}+72072 A a \,b^{2} c^{2} d^{4}-20592 A \,b^{3} c^{3} d^{3}-30030 B \,a^{3} c \,d^{5}+72072 B \,a^{2} b \,c^{2} d^{4}-61776 B a \,b^{2} c^{3} d^{3}+18304 B \,b^{3} c^{4} d^{2}+24024 C \,a^{3} c^{2} d^{4}-61776 C \,a^{2} b \,c^{3} d^{3}+54912 C a \,b^{2} c^{4} d^{2}-16640 C \,b^{3} c^{5} d -20592 D a^{3} c^{3} d^{3}+54912 D a^{2} b \,c^{4} d^{2}-49920 D a \,b^{2} c^{5} d +15360 D b^{3} c^{6}\right)}{45045 d^{7}}"," ",0,"2/45045*(d*x+c)^(1/2)*(3465*D*b^3*d^6*x^6+4095*C*b^3*d^6*x^5+12285*D*a*b^2*d^6*x^5-3780*D*b^3*c*d^5*x^5+5005*B*b^3*d^6*x^4+15015*C*a*b^2*d^6*x^4-4550*C*b^3*c*d^5*x^4+15015*D*a^2*b*d^6*x^4-13650*D*a*b^2*c*d^5*x^4+4200*D*b^3*c^2*d^4*x^4+6435*A*b^3*d^6*x^3+19305*B*a*b^2*d^6*x^3-5720*B*b^3*c*d^5*x^3+19305*C*a^2*b*d^6*x^3-17160*C*a*b^2*c*d^5*x^3+5200*C*b^3*c^2*d^4*x^3+6435*D*a^3*d^6*x^3-17160*D*a^2*b*c*d^5*x^3+15600*D*a*b^2*c^2*d^4*x^3-4800*D*b^3*c^3*d^3*x^3+27027*A*a*b^2*d^6*x^2-7722*A*b^3*c*d^5*x^2+27027*B*a^2*b*d^6*x^2-23166*B*a*b^2*c*d^5*x^2+6864*B*b^3*c^2*d^4*x^2+9009*C*a^3*d^6*x^2-23166*C*a^2*b*c*d^5*x^2+20592*C*a*b^2*c^2*d^4*x^2-6240*C*b^3*c^3*d^3*x^2-7722*D*a^3*c*d^5*x^2+20592*D*a^2*b*c^2*d^4*x^2-18720*D*a*b^2*c^3*d^3*x^2+5760*D*b^3*c^4*d^2*x^2+45045*A*a^2*b*d^6*x-36036*A*a*b^2*c*d^5*x+10296*A*b^3*c^2*d^4*x+15015*B*a^3*d^6*x-36036*B*a^2*b*c*d^5*x+30888*B*a*b^2*c^2*d^4*x-9152*B*b^3*c^3*d^3*x-12012*C*a^3*c*d^5*x+30888*C*a^2*b*c^2*d^4*x-27456*C*a*b^2*c^3*d^3*x+8320*C*b^3*c^4*d^2*x+10296*D*a^3*c^2*d^4*x-27456*D*a^2*b*c^3*d^3*x+24960*D*a*b^2*c^4*d^2*x-7680*D*b^3*c^5*d*x+45045*A*a^3*d^6-90090*A*a^2*b*c*d^5+72072*A*a*b^2*c^2*d^4-20592*A*b^3*c^3*d^3-30030*B*a^3*c*d^5+72072*B*a^2*b*c^2*d^4-61776*B*a*b^2*c^3*d^3+18304*B*b^3*c^4*d^2+24024*C*a^3*c^2*d^4-61776*C*a^2*b*c^3*d^3+54912*C*a*b^2*c^4*d^2-16640*C*b^3*c^5*d-20592*D*a^3*c^3*d^3+54912*D*a^2*b*c^4*d^2-49920*D*a*b^2*c^5*d+15360*D*b^3*c^6)/d^7","B"
2,1,505,302,0.007000," ","int((b*x+a)^2*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(1/2),x)","\frac{2 \sqrt{d x +c}\, \left(315 b^{2} D x^{5} d^{5}+385 C \,b^{2} d^{5} x^{4}+770 D a b \,d^{5} x^{4}-350 D b^{2} c \,d^{4} x^{4}+495 B \,b^{2} d^{5} x^{3}+990 C a b \,d^{5} x^{3}-440 C \,b^{2} c \,d^{4} x^{3}+495 D a^{2} d^{5} x^{3}-880 D a b c \,d^{4} x^{3}+400 D b^{2} c^{2} d^{3} x^{3}+693 A \,b^{2} d^{5} x^{2}+1386 B a b \,d^{5} x^{2}-594 B \,b^{2} c \,d^{4} x^{2}+693 C \,a^{2} d^{5} x^{2}-1188 C a b c \,d^{4} x^{2}+528 C \,b^{2} c^{2} d^{3} x^{2}-594 D a^{2} c \,d^{4} x^{2}+1056 D a b \,c^{2} d^{3} x^{2}-480 D b^{2} c^{3} d^{2} x^{2}+2310 A a b \,d^{5} x -924 A \,b^{2} c \,d^{4} x +1155 B \,a^{2} d^{5} x -1848 B a b c \,d^{4} x +792 B \,b^{2} c^{2} d^{3} x -924 C \,a^{2} c \,d^{4} x +1584 C a b \,c^{2} d^{3} x -704 C \,b^{2} c^{3} d^{2} x +792 D a^{2} c^{2} d^{3} x -1408 D a b \,c^{3} d^{2} x +640 D b^{2} c^{4} d x +3465 a^{2} A \,d^{5}-4620 A a b c \,d^{4}+1848 A \,b^{2} c^{2} d^{3}-2310 B \,a^{2} c \,d^{4}+3696 B a b \,c^{2} d^{3}-1584 B \,b^{2} c^{3} d^{2}+1848 C \,a^{2} c^{2} d^{3}-3168 C a b \,c^{3} d^{2}+1408 C \,b^{2} c^{4} d -1584 D a^{2} c^{3} d^{2}+2816 D a b \,c^{4} d -1280 D b^{2} c^{5}\right)}{3465 d^{6}}"," ",0,"2/3465*(d*x+c)^(1/2)*(315*D*b^2*d^5*x^5+385*C*b^2*d^5*x^4+770*D*a*b*d^5*x^4-350*D*b^2*c*d^4*x^4+495*B*b^2*d^5*x^3+990*C*a*b*d^5*x^3-440*C*b^2*c*d^4*x^3+495*D*a^2*d^5*x^3-880*D*a*b*c*d^4*x^3+400*D*b^2*c^2*d^3*x^3+693*A*b^2*d^5*x^2+1386*B*a*b*d^5*x^2-594*B*b^2*c*d^4*x^2+693*C*a^2*d^5*x^2-1188*C*a*b*c*d^4*x^2+528*C*b^2*c^2*d^3*x^2-594*D*a^2*c*d^4*x^2+1056*D*a*b*c^2*d^3*x^2-480*D*b^2*c^3*d^2*x^2+2310*A*a*b*d^5*x-924*A*b^2*c*d^4*x+1155*B*a^2*d^5*x-1848*B*a*b*c*d^4*x+792*B*b^2*c^2*d^3*x-924*C*a^2*c*d^4*x+1584*C*a*b*c^2*d^3*x-704*C*b^2*c^3*d^2*x+792*D*a^2*c^2*d^3*x-1408*D*a*b*c^3*d^2*x+640*D*b^2*c^4*d*x+3465*A*a^2*d^5-4620*A*a*b*c*d^4+1848*A*b^2*c^2*d^3-2310*B*a^2*c*d^4+3696*B*a*b*c^2*d^3-1584*B*b^2*c^3*d^2+1848*C*a^2*c^2*d^3-3168*C*a*b*c^3*d^2+1408*C*b^2*c^4*d-1584*D*a^2*c^3*d^2+2816*D*a*b*c^4*d-1280*D*b^2*c^5)/d^6","A"
3,1,241,194,0.006000," ","int((b*x+a)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(1/2),x)","\frac{2 \sqrt{d x +c}\, \left(35 D b \,x^{4} d^{4}+45 C b \,d^{4} x^{3}+45 D a \,d^{4} x^{3}-40 D b c \,d^{3} x^{3}+63 B b \,d^{4} x^{2}+63 C a \,d^{4} x^{2}-54 C b c \,d^{3} x^{2}-54 D a c \,d^{3} x^{2}+48 D b \,c^{2} d^{2} x^{2}+105 A b \,d^{4} x +105 B a \,d^{4} x -84 B b c \,d^{3} x -84 C a c \,d^{3} x +72 C b \,c^{2} d^{2} x +72 D a \,c^{2} d^{2} x -64 D b \,c^{3} d x +315 A a \,d^{4}-210 A b c \,d^{3}-210 B a c \,d^{3}+168 B b \,c^{2} d^{2}+168 C a \,c^{2} d^{2}-144 C b \,c^{3} d -144 D a \,c^{3} d +128 D b \,c^{4}\right)}{315 d^{5}}"," ",0,"2/315*(d*x+c)^(1/2)*(35*D*b*d^4*x^4+45*C*b*d^4*x^3+45*D*a*d^4*x^3-40*D*b*c*d^3*x^3+63*B*b*d^4*x^2+63*C*a*d^4*x^2-54*C*b*c*d^3*x^2-54*D*a*c*d^3*x^2+48*D*b*c^2*d^2*x^2+105*A*b*d^4*x+105*B*a*d^4*x-84*B*b*c*d^3*x-84*C*a*c*d^3*x+72*C*b*c^2*d^2*x+72*D*a*c^2*d^2*x-64*D*b*c^3*d*x+315*A*a*d^4-210*A*b*c*d^3-210*B*a*c*d^3+168*B*b*c^2*d^2+168*C*a*c^2*d^2-144*C*b*c^3*d-144*D*a*c^3*d+128*D*b*c^4)/d^5","A"
4,1,91,101,0.006000," ","int((D*x^3+C*x^2+B*x+A)/(d*x+c)^(1/2),x)","\frac{2 \sqrt{d x +c}\, \left(15 D x^{3} d^{3}+21 C \,d^{3} x^{2}-18 D c \,d^{2} x^{2}+35 B \,d^{3} x -28 C c \,d^{2} x +24 D c^{2} d x +105 A \,d^{3}-70 B c \,d^{2}+56 C \,c^{2} d -48 D c^{3}\right)}{105 d^{4}}"," ",0,"2/105*(d*x+c)^(1/2)*(15*D*d^3*x^3+21*C*d^3*x^2-18*D*c*d^2*x^2+35*B*d^3*x-28*C*c*d^2*x+24*D*c^2*d*x+105*A*d^3-70*B*c*d^2+56*C*c^2*d-48*D*c^3)/d^4","A"
5,1,338,168,0.015000," ","int((D*x^3+C*x^2+B*x+A)/(b*x+a)/(d*x+c)^(1/2),x)","\frac{2 A \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\sqrt{\left(a d -b c \right) b}}-\frac{2 B a \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\sqrt{\left(a d -b c \right) b}\, b}+\frac{2 C \,a^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\sqrt{\left(a d -b c \right) b}\, b^{2}}-\frac{2 D a^{3} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\sqrt{\left(a d -b c \right) b}\, b^{3}}+\frac{2 \sqrt{d x +c}\, B}{b d}-\frac{2 \sqrt{d x +c}\, C a}{b^{2} d}-\frac{2 \sqrt{d x +c}\, C c}{b \,d^{2}}+\frac{2 \sqrt{d x +c}\, D a^{2}}{b^{3} d}+\frac{2 \sqrt{d x +c}\, D a c}{b^{2} d^{2}}+\frac{2 \sqrt{d x +c}\, D c^{2}}{b \,d^{3}}+\frac{2 \left(d x +c \right)^{\frac{3}{2}} C}{3 b \,d^{2}}-\frac{2 \left(d x +c \right)^{\frac{3}{2}} D a}{3 b^{2} d^{2}}-\frac{4 \left(d x +c \right)^{\frac{3}{2}} D c}{3 b \,d^{3}}+\frac{2 \left(d x +c \right)^{\frac{5}{2}} D}{5 b \,d^{3}}"," ",0,"2/5*D*(d*x+c)^(5/2)/b/d^3+2/3/d^2/b*C*(d*x+c)^(3/2)-2/3/d^2/b^2*D*(d*x+c)^(3/2)*a-4/3/d^3/b*D*(d*x+c)^(3/2)*c+2/d/b*B*(d*x+c)^(1/2)-2/d/b^2*C*a*(d*x+c)^(1/2)-2/d^2/b*C*c*(d*x+c)^(1/2)+2/d/b^3*a^2*D*(d*x+c)^(1/2)+2/d^2/b^2*D*a*c*(d*x+c)^(1/2)+2/d^3/b*D*c^2*(d*x+c)^(1/2)+2/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*A-2/b/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*B*a+2/b^2/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*C*a^2-2/b^3/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*D*a^3","B"
6,1,566,183,0.022000," ","int((D*x^3+C*x^2+B*x+A)/(b*x+a)^2/(d*x+c)^(1/2),x)","\frac{A d \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right) \sqrt{\left(a d -b c \right) b}}+\frac{B a d \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right) \sqrt{\left(a d -b c \right) b}\, b}-\frac{2 B c \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right) \sqrt{\left(a d -b c \right) b}}-\frac{3 C \,a^{2} d \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right) \sqrt{\left(a d -b c \right) b}\, b^{2}}+\frac{4 C a c \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right) \sqrt{\left(a d -b c \right) b}\, b}+\frac{5 D a^{3} d \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right) \sqrt{\left(a d -b c \right) b}\, b^{3}}-\frac{6 D a^{2} c \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right) \sqrt{\left(a d -b c \right) b}\, b^{2}}+\frac{\sqrt{d x +c}\, A d}{\left(a d -b c \right) \left(b d x +a d \right)}-\frac{\sqrt{d x +c}\, B a d}{\left(a d -b c \right) \left(b d x +a d \right) b}+\frac{\sqrt{d x +c}\, C \,a^{2} d}{\left(a d -b c \right) \left(b d x +a d \right) b^{2}}-\frac{\sqrt{d x +c}\, D a^{3} d}{\left(a d -b c \right) \left(b d x +a d \right) b^{3}}+\frac{2 \sqrt{d x +c}\, C}{b^{2} d}-\frac{4 \sqrt{d x +c}\, D a}{b^{3} d}-\frac{2 \sqrt{d x +c}\, D c}{b^{2} d^{2}}+\frac{2 \left(d x +c \right)^{\frac{3}{2}} D}{3 b^{2} d^{2}}"," ",0,"2/3*D*(d*x+c)^(3/2)/b^2/d^2+2/d/b^2*C*(d*x+c)^(1/2)-4/d/b^3*D*a*(d*x+c)^(1/2)-2/d^2/b^2*D*c*(d*x+c)^(1/2)+d/(a*d-b*c)*(d*x+c)^(1/2)/(b*d*x+a*d)*A-d/b/(a*d-b*c)*(d*x+c)^(1/2)/(b*d*x+a*d)*B*a+d/b^2/(a*d-b*c)*(d*x+c)^(1/2)/(b*d*x+a*d)*a^2*C-d/b^3/(a*d-b*c)*(d*x+c)^(1/2)/(b*d*x+a*d)*a^3*D+d/(a*d-b*c)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*A+d/b/(a*d-b*c)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*B*a-2/(a*d-b*c)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*B*c-3*d/b^2/(a*d-b*c)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*C*a^2+4/b/(a*d-b*c)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*C*a*c+5*d/b^3/(a*d-b*c)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*a^3*D-6/b^2/(a*d-b*c)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*D*a^2*c","B"
7,1,1207,257,0.030000," ","int((D*x^3+C*x^2+B*x+A)/(b*x+a)^3/(d*x+c)^(1/2),x)","\frac{3 \left(d x +c \right)^{\frac{3}{2}} A b \,d^{2}}{4 \left(b d x +a d \right)^{2} \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right)}+\frac{3 A \,d^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{4 \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \sqrt{\left(a d -b c \right) b}}+\frac{B a \,d^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{4 \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \sqrt{\left(a d -b c \right) b}\, b}+\frac{\left(d x +c \right)^{\frac{3}{2}} B a \,d^{2}}{4 \left(b d x +a d \right)^{2} \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right)}-\frac{\left(d x +c \right)^{\frac{3}{2}} B b c d}{\left(b d x +a d \right)^{2} \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right)}-\frac{B c d \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \sqrt{\left(a d -b c \right) b}}-\frac{5 \left(d x +c \right)^{\frac{3}{2}} C \,a^{2} d^{2}}{4 \left(b d x +a d \right)^{2} \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) b}+\frac{3 C \,a^{2} d^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{4 \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \sqrt{\left(a d -b c \right) b}\, b^{2}}-\frac{2 C a c d \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \sqrt{\left(a d -b c \right) b}\, b}+\frac{2 \left(d x +c \right)^{\frac{3}{2}} C a c d}{\left(b d x +a d \right)^{2} \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right)}+\frac{2 C \,c^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \sqrt{\left(a d -b c \right) b}}+\frac{9 \left(d x +c \right)^{\frac{3}{2}} D a^{3} d^{2}}{4 \left(b d x +a d \right)^{2} \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) b^{2}}-\frac{15 D a^{3} d^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{4 \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \sqrt{\left(a d -b c \right) b}\, b^{3}}-\frac{3 \left(d x +c \right)^{\frac{3}{2}} D a^{2} c d}{\left(b d x +a d \right)^{2} \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) b}+\frac{9 D a^{2} c d \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \sqrt{\left(a d -b c \right) b}\, b^{2}}-\frac{6 D a \,c^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \sqrt{\left(a d -b c \right) b}\, b}+\frac{5 \sqrt{d x +c}\, A \,d^{2}}{4 \left(b d x +a d \right)^{2} \left(a d -b c \right)}-\frac{\sqrt{d x +c}\, B a \,d^{2}}{4 \left(b d x +a d \right)^{2} \left(a d -b c \right) b}-\frac{\sqrt{d x +c}\, B c d}{\left(b d x +a d \right)^{2} \left(a d -b c \right)}-\frac{3 \sqrt{d x +c}\, C \,a^{2} d^{2}}{4 \left(b d x +a d \right)^{2} \left(a d -b c \right) b^{2}}+\frac{2 \sqrt{d x +c}\, C a c d}{\left(b d x +a d \right)^{2} \left(a d -b c \right) b}+\frac{7 \sqrt{d x +c}\, D a^{3} d^{2}}{4 \left(b d x +a d \right)^{2} \left(a d -b c \right) b^{3}}-\frac{3 \sqrt{d x +c}\, D a^{2} c d}{\left(b d x +a d \right)^{2} \left(a d -b c \right) b^{2}}+\frac{2 \sqrt{d x +c}\, D}{b^{3} d}"," ",0,"2*D*(d*x+c)^(1/2)/b^3/d+3/4*d^2*b/(b*d*x+a*d)^2/(a^2*d^2-2*a*b*c*d+b^2*c^2)*(d*x+c)^(3/2)*A+1/4*d^2/(b*d*x+a*d)^2/(a^2*d^2-2*a*b*c*d+b^2*c^2)*(d*x+c)^(3/2)*B*a-d*b/(b*d*x+a*d)^2/(a^2*d^2-2*a*b*c*d+b^2*c^2)*(d*x+c)^(3/2)*c*B-5/4*d^2/b/(b*d*x+a*d)^2/(a^2*d^2-2*a*b*c*d+b^2*c^2)*(d*x+c)^(3/2)*C*a^2+2*d/(b*d*x+a*d)^2/(a^2*d^2-2*a*b*c*d+b^2*c^2)*(d*x+c)^(3/2)*C*a*c+9/4*d^2/b^2/(b*d*x+a*d)^2/(a^2*d^2-2*a*b*c*d+b^2*c^2)*(d*x+c)^(3/2)*a^3*D-3*d/b/(b*d*x+a*d)^2/(a^2*d^2-2*a*b*c*d+b^2*c^2)*(d*x+c)^(3/2)*D*a^2*c+5/4*d^2/(b*d*x+a*d)^2/(a*d-b*c)*(d*x+c)^(1/2)*A-1/4*d^2/b/(b*d*x+a*d)^2/(a*d-b*c)*(d*x+c)^(1/2)*B*a-d/(b*d*x+a*d)^2/(a*d-b*c)*(d*x+c)^(1/2)*c*B-3/4*d^2/b^2/(b*d*x+a*d)^2/(a*d-b*c)*(d*x+c)^(1/2)*C*a^2+2*d/b/(b*d*x+a*d)^2/(a*d-b*c)*(d*x+c)^(1/2)*C*a*c+7/4*d^2/b^3/(b*d*x+a*d)^2/(a*d-b*c)*(d*x+c)^(1/2)*a^3*D-3*d/b^2/(b*d*x+a*d)^2/(a*d-b*c)*(d*x+c)^(1/2)*D*a^2*c+3/4*d^2/(a^2*d^2-2*a*b*c*d+b^2*c^2)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*A+1/4*d^2/b/(a^2*d^2-2*a*b*c*d+b^2*c^2)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*B*a-d/(a^2*d^2-2*a*b*c*d+b^2*c^2)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*B*c+3/4*d^2/b^2/(a^2*d^2-2*a*b*c*d+b^2*c^2)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*a^2*C-2*d/b/(a^2*d^2-2*a*b*c*d+b^2*c^2)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*C*a*c+2/(a^2*d^2-2*a*b*c*d+b^2*c^2)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*C*c^2-15/4*d^2/b^3/(a^2*d^2-2*a*b*c*d+b^2*c^2)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*a^3*D+9*d/b^2/(a^2*d^2-2*a*b*c*d+b^2*c^2)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*D*a^2*c-6/b/(a^2*d^2-2*a*b*c*d+b^2*c^2)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*D*a*c^2","B"
8,1,1186,351,0.029000," ","int((D*x^3+C*x^2+B*x+A)/(b*x+a)^4/(d*x+c)^(1/2),x)","\frac{5 A \,d^{3} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{8 \left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) \sqrt{\left(a d -b c \right) b}}+\frac{B a \,d^{3} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{8 \left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) \sqrt{\left(a d -b c \right) b}\, b}-\frac{3 B c \,d^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{4 \left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) \sqrt{\left(a d -b c \right) b}}+\frac{C \,a^{2} d^{3} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{8 \left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) \sqrt{\left(a d -b c \right) b}\, b^{2}}-\frac{C a c \,d^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{2 \left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) \sqrt{\left(a d -b c \right) b}\, b}+\frac{C \,c^{2} d \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) \sqrt{\left(a d -b c \right) b}}+\frac{5 D a^{3} d^{3} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{8 \left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) \sqrt{\left(a d -b c \right) b}\, b^{3}}-\frac{9 D a^{2} c \,d^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{4 \left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) \sqrt{\left(a d -b c \right) b}\, b^{2}}+\frac{3 D a \,c^{2} d \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) \sqrt{\left(a d -b c \right) b}\, b}-\frac{2 D c^{3} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) \sqrt{\left(a d -b c \right) b}}+\frac{\frac{\left(5 A \,b^{3} d^{2}+B a \,b^{2} d^{2}-6 B \,b^{3} c d +a^{2} b C \,d^{2}-4 C a \,b^{2} c d +8 C \,b^{3} c^{2}-11 a^{3} d^{2} D+30 D a^{2} b c d -24 D a \,b^{2} c^{2}\right) \left(d x +c \right)^{\frac{5}{2}} d}{8 \left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) b}+\frac{\left(5 A \,b^{3} d^{2}+B a \,b^{2} d^{2}-6 B \,b^{3} c d -a^{2} b C \,d^{2}+6 C \,b^{3} c^{2}-5 a^{3} d^{2} D+18 D a^{2} b c d -18 D a \,b^{2} c^{2}\right) \left(d x +c \right)^{\frac{3}{2}} d}{3 \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) b^{2}}+\frac{\left(11 A \,b^{3} d^{2}-B a \,b^{2} d^{2}-10 B \,b^{3} c d -a^{2} b C \,d^{2}+4 C a \,b^{2} c d +8 C \,b^{3} c^{2}-5 a^{3} d^{2} D+18 D a^{2} b c d -24 D a \,b^{2} c^{2}\right) \sqrt{d x +c}\, d}{8 \left(a d -b c \right) b^{3}}}{\left(a d -b c +\left(d x +c \right) b \right)^{3}}"," ",0,"2*(1/16*d*(5*A*b^3*d^2+B*a*b^2*d^2-6*B*b^3*c*d+C*a^2*b*d^2-4*C*a*b^2*c*d+8*C*b^3*c^2-11*D*a^3*d^2+30*D*a^2*b*c*d-24*D*a*b^2*c^2)/b/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)*(d*x+c)^(5/2)+1/6*(5*A*b^3*d^2+B*a*b^2*d^2-6*B*b^3*c*d-C*a^2*b*d^2+6*C*b^3*c^2-5*D*a^3*d^2+18*D*a^2*b*c*d-18*D*a*b^2*c^2)/b^2*d/(a^2*d^2-2*a*b*c*d+b^2*c^2)*(d*x+c)^(3/2)+1/16*(11*A*b^3*d^2-B*a*b^2*d^2-10*B*b^3*c*d-C*a^2*b*d^2+4*C*a*b^2*c*d+8*C*b^3*c^2-5*D*a^3*d^2+18*D*a^2*b*c*d-24*D*a*b^2*c^2)/b^3*d/(a*d-b*c)*(d*x+c)^(1/2))/(b*(d*x+c)+a*d-b*c)^3+5/8/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*A*d^3+1/8/b/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*a*B*d^3-3/4/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*B*c*d^2+1/8/b^2/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*a^2*C*d^3-1/2/b/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*C*a*c*d^2+1/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*C*c^2*d+5/8/b^3/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*a^3*d^3*D-9/4/b^2/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*D*a^2*c*d^2+3/b/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*D*a*c^2*d-2/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*D*c^3","B"
9,1,3252,467,0.030000," ","int((D*x^3+C*x^2+B*x+A)/(b*x+a)^5/(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"3/4/b/(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*D*a*c^2*d^2+73/192/(b*d*x+a*d)^4/(a^2*d^2-2*a*b*c*d+b^2*c^2)*(d*x+c)^(3/2)*a*B*d^4+11/64/(b*d*x+a*d)^4/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)*(d*x+c)^(5/2)*a^2*C*d^4-d/(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*D*c^3+3/4/(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*C*c^2*d^2-d/(b*d*x+a*d)^4/(a*d-b*c)*(d*x+c)^(1/2)*D*c^3+5/64/(b*d*x+a*d)^4/(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)*(d*x+c)^(7/2)*a^3*d^4*D+385/192/(b*d*x+a*d)^4*b^2/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)*(d*x+c)^(5/2)*A*d^4-1/4/(b*d*x+a*d)^4/(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)*(d*x+c)^(7/2)*C*a*b^2*c*d^3-11/12/(b*d*x+a*d)^4*b/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)*(d*x+c)^(5/2)*C*a*c*d^3-5/8/(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*B*c*d^3+511/192/(b*d*x+a*d)^4*b/(a^2*d^2-2*a*b*c*d+b^2*c^2)*(d*x+c)^(3/2)*A*d^4+5/4/(b*d*x+a*d)^4/(a*d-b*c)*(d*x+c)^(1/2)*C*c^2*d^2-11/8/(b*d*x+a*d)^4/(a*d-b*c)*(d*x+c)^(1/2)*B*c*d^3+35/64/(b*d*x+a*d)^4/(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)*(d*x+c)^(7/2)*A*b^3*d^4+35/64/(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*A*d^4+93/64/(b*d*x+a*d)^4/(a*d-b*c)*(d*x+c)^(1/2)*A*d^4-3/8/(b*d*x+a*d)^4/(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)*(d*x+c)^(7/2)*D*a^2*b*c*d^3+11/8/(b*d*x+a*d)^4/b/(a^2*d^2-2*a*b*c*d+b^2*c^2)*(d*x+c)^(3/2)*D*a^2*c*d^3+3/4/(b*d*x+a*d)^4/(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)*(d*x+c)^(7/2)*D*a*b^2*c^2*d^2+1/4/(b*d*x+a*d)^4/(a*d-b*c)/b*(d*x+c)^(1/2)*C*a*c*d^3+3/8/(b*d*x+a*d)^4/(a*d-b*c)/b^2*(d*x+c)^(1/2)*D*a^2*c*d^3-3/4/(b*d*x+a*d)^4/(a*d-b*c)/b*(d*x+c)^(1/2)*D*a*c^2*d^2-1/4/b/(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*C*a*c*d^3-3/8/b^2/(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*D*a^2*c*d^3+3/4/(b*d*x+a*d)^4*b/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)*(d*x+c)^(5/2)*D*a*c^2*d^2-55/192/(b*d*x+a*d)^4/b^2/(a^2*d^2-2*a*b*c*d+b^2*c^2)*(d*x+c)^(3/2)*a^3*d^4*D+5/8/(b*d*x+a*d)^4/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)*(d*x+c)^(5/2)*D*a^2*c*d^3-5/64/(b*d*x+a*d)^4/(a*d-b*c)/b*(d*x+c)^(1/2)*a*B*d^4-d/(b*d*x+a*d)^4/(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)*(d*x+c)^(7/2)*D*b^3*c^3-5/64/(b*d*x+a*d)^4/(a*d-b*c)/b^3*(d*x+c)^(1/2)*a^3*d^4*D-73/192/(b*d*x+a*d)^4/b/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)*(d*x+c)^(5/2)*a^3*d^4*D+3/4/(b*d*x+a*d)^4/(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)*(d*x+c)^(7/2)*C*b^3*c^2*d^2+55/192/(b*d*x+a*d)^4*b/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)*(d*x+c)^(5/2)*a*B*d^4-55/24/(b*d*x+a*d)^4*b^2/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)*(d*x+c)^(5/2)*B*c*d^3-5/8/(b*d*x+a*d)^4/(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)*(d*x+c)^(7/2)*B*b^3*c*d^3+5/64/b/(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*a*B*d^4+5/64/b^3/(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*a^3*d^4*D-3/4/(b*d*x+a*d)^4/(a^2*d^2-2*a*b*c*d+b^2*c^2)*(d*x+c)^(3/2)*D*a*c^2*d^2-3*d/(b*d*x+a*d)^4*b^2/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)*(d*x+c)^(5/2)*D*c^3+3/64/b^2/(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*a^2*C*d^4-3/64/(b*d*x+a*d)^4/(a*d-b*c)/b^2*(d*x+c)^(1/2)*a^2*C*d^4-5/12/(b*d*x+a*d)^4/(a^2*d^2-2*a*b*c*d+b^2*c^2)*(d*x+c)^(3/2)*C*a*c*d^3+3/64/(b*d*x+a*d)^4/(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)*(d*x+c)^(7/2)*a^2*b*C*d^4+5/64/(b*d*x+a*d)^4/(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)*(d*x+c)^(7/2)*a*b^2*B*d^4-73/24/(b*d*x+a*d)^4*b/(a^2*d^2-2*a*b*c*d+b^2*c^2)*(d*x+c)^(3/2)*B*c*d^3-11/64/(b*d*x+a*d)^4/b/(a^2*d^2-2*a*b*c*d+b^2*c^2)*(d*x+c)^(3/2)*a^2*C*d^4+13/4/(b*d*x+a*d)^4*b/(a^2*d^2-2*a*b*c*d+b^2*c^2)*(d*x+c)^(3/2)*C*c^2*d^2+11/4/(b*d*x+a*d)^4*b^2/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)*(d*x+c)^(5/2)*C*c^2*d^2-3*d/(b*d*x+a*d)^4*b/(a^2*d^2-2*a*b*c*d+b^2*c^2)*(d*x+c)^(3/2)*D*c^3","B"
10,1,841,410,0.010000," ","int((b*x+a)^3*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(3/2),x)","-\frac{2 \left(-315 b^{3} D x^{6} d^{6}-385 C \,b^{3} d^{6} x^{5}-1155 D a \,b^{2} d^{6} x^{5}+420 D b^{3} c \,d^{5} x^{5}-495 B \,b^{3} d^{6} x^{4}-1485 C a \,b^{2} d^{6} x^{4}+550 C \,b^{3} c \,d^{5} x^{4}-1485 D a^{2} b \,d^{6} x^{4}+1650 D a \,b^{2} c \,d^{5} x^{4}-600 D b^{3} c^{2} d^{4} x^{4}-693 A \,b^{3} d^{6} x^{3}-2079 B a \,b^{2} d^{6} x^{3}+792 B \,b^{3} c \,d^{5} x^{3}-2079 C \,a^{2} b \,d^{6} x^{3}+2376 C a \,b^{2} c \,d^{5} x^{3}-880 C \,b^{3} c^{2} d^{4} x^{3}-693 D a^{3} d^{6} x^{3}+2376 D a^{2} b c \,d^{5} x^{3}-2640 D a \,b^{2} c^{2} d^{4} x^{3}+960 D b^{3} c^{3} d^{3} x^{3}-3465 A a \,b^{2} d^{6} x^{2}+1386 A \,b^{3} c \,d^{5} x^{2}-3465 B \,a^{2} b \,d^{6} x^{2}+4158 B a \,b^{2} c \,d^{5} x^{2}-1584 B \,b^{3} c^{2} d^{4} x^{2}-1155 C \,a^{3} d^{6} x^{2}+4158 C \,a^{2} b c \,d^{5} x^{2}-4752 C a \,b^{2} c^{2} d^{4} x^{2}+1760 C \,b^{3} c^{3} d^{3} x^{2}+1386 D a^{3} c \,d^{5} x^{2}-4752 D a^{2} b \,c^{2} d^{4} x^{2}+5280 D a \,b^{2} c^{3} d^{3} x^{2}-1920 D b^{3} c^{4} d^{2} x^{2}-10395 A \,a^{2} b \,d^{6} x +13860 A a \,b^{2} c \,d^{5} x -5544 A \,b^{3} c^{2} d^{4} x -3465 B \,a^{3} d^{6} x +13860 B \,a^{2} b c \,d^{5} x -16632 B a \,b^{2} c^{2} d^{4} x +6336 B \,b^{3} c^{3} d^{3} x +4620 C \,a^{3} c \,d^{5} x -16632 C \,a^{2} b \,c^{2} d^{4} x +19008 C a \,b^{2} c^{3} d^{3} x -7040 C \,b^{3} c^{4} d^{2} x -5544 D a^{3} c^{2} d^{4} x +19008 D a^{2} b \,c^{3} d^{3} x -21120 D a \,b^{2} c^{4} d^{2} x +7680 D b^{3} c^{5} d x +3465 a^{3} A \,d^{6}-20790 A \,a^{2} b c \,d^{5}+27720 A a \,b^{2} c^{2} d^{4}-11088 A \,b^{3} c^{3} d^{3}-6930 B \,a^{3} c \,d^{5}+27720 B \,a^{2} b \,c^{2} d^{4}-33264 B a \,b^{2} c^{3} d^{3}+12672 B \,b^{3} c^{4} d^{2}+9240 C \,a^{3} c^{2} d^{4}-33264 C \,a^{2} b \,c^{3} d^{3}+38016 C a \,b^{2} c^{4} d^{2}-14080 C \,b^{3} c^{5} d -11088 D a^{3} c^{3} d^{3}+38016 D a^{2} b \,c^{4} d^{2}-42240 D a \,b^{2} c^{5} d +15360 D b^{3} c^{6}\right)}{3465 \sqrt{d x +c}\, d^{7}}"," ",0,"-2/3465/(d*x+c)^(1/2)*(-315*D*b^3*d^6*x^6-385*C*b^3*d^6*x^5-1155*D*a*b^2*d^6*x^5+420*D*b^3*c*d^5*x^5-495*B*b^3*d^6*x^4-1485*C*a*b^2*d^6*x^4+550*C*b^3*c*d^5*x^4-1485*D*a^2*b*d^6*x^4+1650*D*a*b^2*c*d^5*x^4-600*D*b^3*c^2*d^4*x^4-693*A*b^3*d^6*x^3-2079*B*a*b^2*d^6*x^3+792*B*b^3*c*d^5*x^3-2079*C*a^2*b*d^6*x^3+2376*C*a*b^2*c*d^5*x^3-880*C*b^3*c^2*d^4*x^3-693*D*a^3*d^6*x^3+2376*D*a^2*b*c*d^5*x^3-2640*D*a*b^2*c^2*d^4*x^3+960*D*b^3*c^3*d^3*x^3-3465*A*a*b^2*d^6*x^2+1386*A*b^3*c*d^5*x^2-3465*B*a^2*b*d^6*x^2+4158*B*a*b^2*c*d^5*x^2-1584*B*b^3*c^2*d^4*x^2-1155*C*a^3*d^6*x^2+4158*C*a^2*b*c*d^5*x^2-4752*C*a*b^2*c^2*d^4*x^2+1760*C*b^3*c^3*d^3*x^2+1386*D*a^3*c*d^5*x^2-4752*D*a^2*b*c^2*d^4*x^2+5280*D*a*b^2*c^3*d^3*x^2-1920*D*b^3*c^4*d^2*x^2-10395*A*a^2*b*d^6*x+13860*A*a*b^2*c*d^5*x-5544*A*b^3*c^2*d^4*x-3465*B*a^3*d^6*x+13860*B*a^2*b*c*d^5*x-16632*B*a*b^2*c^2*d^4*x+6336*B*b^3*c^3*d^3*x+4620*C*a^3*c*d^5*x-16632*C*a^2*b*c^2*d^4*x+19008*C*a*b^2*c^3*d^3*x-7040*C*b^3*c^4*d^2*x-5544*D*a^3*c^2*d^4*x+19008*D*a^2*b*c^3*d^3*x-21120*D*a*b^2*c^4*d^2*x+7680*D*b^3*c^5*d*x+3465*A*a^3*d^6-20790*A*a^2*b*c*d^5+27720*A*a*b^2*c^2*d^4-11088*A*b^3*c^3*d^3-6930*B*a^3*c*d^5+27720*B*a^2*b*c^2*d^4-33264*B*a*b^2*c^3*d^3+12672*B*b^3*c^4*d^2+9240*C*a^3*c^2*d^4-33264*C*a^2*b*c^3*d^3+38016*C*a*b^2*c^4*d^2-14080*C*b^3*c^5*d-11088*D*a^3*c^3*d^3+38016*D*a^2*b*c^4*d^2-42240*D*a*b^2*c^5*d+15360*D*b^3*c^6)/d^7","B"
11,1,505,302,0.009000," ","int((b*x+a)^2*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(3/2),x)","-\frac{2 \left(-35 b^{2} D x^{5} d^{5}-45 C \,b^{2} d^{5} x^{4}-90 D a b \,d^{5} x^{4}+50 D b^{2} c \,d^{4} x^{4}-63 B \,b^{2} d^{5} x^{3}-126 C a b \,d^{5} x^{3}+72 C \,b^{2} c \,d^{4} x^{3}-63 D a^{2} d^{5} x^{3}+144 D a b c \,d^{4} x^{3}-80 D b^{2} c^{2} d^{3} x^{3}-105 A \,b^{2} d^{5} x^{2}-210 B a b \,d^{5} x^{2}+126 B \,b^{2} c \,d^{4} x^{2}-105 C \,a^{2} d^{5} x^{2}+252 C a b c \,d^{4} x^{2}-144 C \,b^{2} c^{2} d^{3} x^{2}+126 D a^{2} c \,d^{4} x^{2}-288 D a b \,c^{2} d^{3} x^{2}+160 D b^{2} c^{3} d^{2} x^{2}-630 A a b \,d^{5} x +420 A \,b^{2} c \,d^{4} x -315 B \,a^{2} d^{5} x +840 B a b c \,d^{4} x -504 B \,b^{2} c^{2} d^{3} x +420 C \,a^{2} c \,d^{4} x -1008 C a b \,c^{2} d^{3} x +576 C \,b^{2} c^{3} d^{2} x -504 D a^{2} c^{2} d^{3} x +1152 D a b \,c^{3} d^{2} x -640 D b^{2} c^{4} d x +315 a^{2} A \,d^{5}-1260 A a b c \,d^{4}+840 A \,b^{2} c^{2} d^{3}-630 B \,a^{2} c \,d^{4}+1680 B a b \,c^{2} d^{3}-1008 B \,b^{2} c^{3} d^{2}+840 C \,a^{2} c^{2} d^{3}-2016 C a b \,c^{3} d^{2}+1152 C \,b^{2} c^{4} d -1008 D a^{2} c^{3} d^{2}+2304 D a b \,c^{4} d -1280 D b^{2} c^{5}\right)}{315 \sqrt{d x +c}\, d^{6}}"," ",0,"-2/315/(d*x+c)^(1/2)*(-35*D*b^2*d^5*x^5-45*C*b^2*d^5*x^4-90*D*a*b*d^5*x^4+50*D*b^2*c*d^4*x^4-63*B*b^2*d^5*x^3-126*C*a*b*d^5*x^3+72*C*b^2*c*d^4*x^3-63*D*a^2*d^5*x^3+144*D*a*b*c*d^4*x^3-80*D*b^2*c^2*d^3*x^3-105*A*b^2*d^5*x^2-210*B*a*b*d^5*x^2+126*B*b^2*c*d^4*x^2-105*C*a^2*d^5*x^2+252*C*a*b*c*d^4*x^2-144*C*b^2*c^2*d^3*x^2+126*D*a^2*c*d^4*x^2-288*D*a*b*c^2*d^3*x^2+160*D*b^2*c^3*d^2*x^2-630*A*a*b*d^5*x+420*A*b^2*c*d^4*x-315*B*a^2*d^5*x+840*B*a*b*c*d^4*x-504*B*b^2*c^2*d^3*x+420*C*a^2*c*d^4*x-1008*C*a*b*c^2*d^3*x+576*C*b^2*c^3*d^2*x-504*D*a^2*c^2*d^3*x+1152*D*a*b*c^3*d^2*x-640*D*b^2*c^4*d*x+315*A*a^2*d^5-1260*A*a*b*c*d^4+840*A*b^2*c^2*d^3-630*B*a^2*c*d^4+1680*B*a*b*c^2*d^3-1008*B*b^2*c^3*d^2+840*C*a^2*c^2*d^3-2016*C*a*b*c^3*d^2+1152*C*b^2*c^4*d-1008*D*a^2*c^3*d^2+2304*D*a*b*c^4*d-1280*D*b^2*c^5)/d^6","A"
12,1,241,194,0.007000," ","int((b*x+a)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(3/2),x)","-\frac{2 \left(-15 D b \,x^{4} d^{4}-21 C b \,d^{4} x^{3}-21 D a \,d^{4} x^{3}+24 D b c \,d^{3} x^{3}-35 B b \,d^{4} x^{2}-35 C a \,d^{4} x^{2}+42 C b c \,d^{3} x^{2}+42 D a c \,d^{3} x^{2}-48 D b \,c^{2} d^{2} x^{2}-105 A b \,d^{4} x -105 B a \,d^{4} x +140 B b c \,d^{3} x +140 C a c \,d^{3} x -168 C b \,c^{2} d^{2} x -168 D a \,c^{2} d^{2} x +192 D b \,c^{3} d x +105 A a \,d^{4}-210 A b c \,d^{3}-210 B a c \,d^{3}+280 B b \,c^{2} d^{2}+280 C a \,c^{2} d^{2}-336 C b \,c^{3} d -336 D a \,c^{3} d +384 D b \,c^{4}\right)}{105 \sqrt{d x +c}\, d^{5}}"," ",0,"-2/105/(d*x+c)^(1/2)*(-15*D*b*d^4*x^4-21*C*b*d^4*x^3-21*D*a*d^4*x^3+24*D*b*c*d^3*x^3-35*B*b*d^4*x^2-35*C*a*d^4*x^2+42*C*b*c*d^3*x^2+42*D*a*c*d^3*x^2-48*D*b*c^2*d^2*x^2-105*A*b*d^4*x-105*B*a*d^4*x+140*B*b*c*d^3*x+140*C*a*c*d^3*x-168*C*b*c^2*d^2*x-168*D*a*c^2*d^2*x+192*D*b*c^3*d*x+105*A*a*d^4-210*A*b*c*d^3-210*B*a*c*d^3+280*B*b*c^2*d^2+280*C*a*c^2*d^2-336*C*b*c^3*d-336*D*a*c^3*d+384*D*b*c^4)/d^5","A"
13,1,91,101,0.005000," ","int((D*x^3+C*x^2+B*x+A)/(d*x+c)^(3/2),x)","-\frac{2 \left(-3 D x^{3} d^{3}-5 C \,d^{3} x^{2}+6 D c \,d^{2} x^{2}-15 B \,d^{3} x +20 C c \,d^{2} x -24 D c^{2} d x +15 A \,d^{3}-30 B c \,d^{2}+40 C \,c^{2} d -48 D c^{3}\right)}{15 \sqrt{d x +c}\, d^{4}}"," ",0,"-2/15/(d*x+c)^(1/2)*(-3*D*d^3*x^3-5*C*d^3*x^2+6*D*c*d^2*x^2-15*B*d^3*x+20*C*c*d^2*x-24*D*c^2*d*x+15*A*d^3-30*B*c*d^2+40*C*c^2*d-48*D*c^3)/d^4","A"
14,1,366,173,0.017000," ","int((D*x^3+C*x^2+B*x+A)/(b*x+a)/(d*x+c)^(3/2),x)","-\frac{2 A b \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right) \sqrt{\left(a d -b c \right) b}}+\frac{2 B a \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right) \sqrt{\left(a d -b c \right) b}}-\frac{2 C \,a^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right) \sqrt{\left(a d -b c \right) b}\, b}+\frac{2 D a^{3} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right) \sqrt{\left(a d -b c \right) b}\, b^{2}}-\frac{2 A}{\left(a d -b c \right) \sqrt{d x +c}}+\frac{2 B c}{\left(a d -b c \right) \sqrt{d x +c}\, d}-\frac{2 C \,c^{2}}{\left(a d -b c \right) \sqrt{d x +c}\, d^{2}}+\frac{2 D c^{3}}{\left(a d -b c \right) \sqrt{d x +c}\, d^{3}}+\frac{2 \sqrt{d x +c}\, C}{b \,d^{2}}-\frac{2 \sqrt{d x +c}\, D a}{b^{2} d^{2}}-\frac{4 \sqrt{d x +c}\, D c}{b \,d^{3}}+\frac{2 \left(d x +c \right)^{\frac{3}{2}} D}{3 b \,d^{3}}"," ",0,"2/3*D*(d*x+c)^(3/2)/b/d^3+2/d^2/b*C*(d*x+c)^(1/2)-2/d^2/b^2*D*a*(d*x+c)^(1/2)-4*c*D*(d*x+c)^(1/2)/b/d^3-2/(a*d-b*c)*b/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*A+2/(a*d-b*c)/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*B*a-2/(a*d-b*c)/b/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*C*a^2+2/(a*d-b*c)/b^2/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*D*a^3-2/(a*d-b*c)/(d*x+c)^(1/2)*A+2/d/(a*d-b*c)/(d*x+c)^(1/2)*B*c-2/d^2/(a*d-b*c)/(d*x+c)^(1/2)*C*c^2+2/d^3/(a*d-b*c)/(d*x+c)^(1/2)*D*c^3","B"
15,1,604,237,0.028000," ","int((D*x^3+C*x^2+B*x+A)/(b*x+a)^2/(d*x+c)^(3/2),x)","-\frac{3 A b d \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{2} \sqrt{\left(a d -b c \right) b}}+\frac{B a d \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{2} \sqrt{\left(a d -b c \right) b}}+\frac{2 B b c \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{2} \sqrt{\left(a d -b c \right) b}}+\frac{C \,a^{2} d \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{2} \sqrt{\left(a d -b c \right) b}\, b}-\frac{4 C a c \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{2} \sqrt{\left(a d -b c \right) b}}-\frac{3 D a^{3} d \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{2} \sqrt{\left(a d -b c \right) b}\, b^{2}}+\frac{6 D a^{2} c \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{2} \sqrt{\left(a d -b c \right) b}\, b}-\frac{\sqrt{d x +c}\, A b d}{\left(a d -b c \right)^{2} \left(b d x +a d \right)}+\frac{\sqrt{d x +c}\, B a d}{\left(a d -b c \right)^{2} \left(b d x +a d \right)}-\frac{\sqrt{d x +c}\, C \,a^{2} d}{\left(a d -b c \right)^{2} \left(b d x +a d \right) b}+\frac{\sqrt{d x +c}\, D a^{3} d}{\left(a d -b c \right)^{2} \left(b d x +a d \right) b^{2}}-\frac{2 A d}{\left(a d -b c \right)^{2} \sqrt{d x +c}}+\frac{2 B c}{\left(a d -b c \right)^{2} \sqrt{d x +c}}-\frac{2 C \,c^{2}}{\left(a d -b c \right)^{2} \sqrt{d x +c}\, d}+\frac{2 D c^{3}}{\left(a d -b c \right)^{2} \sqrt{d x +c}\, d^{2}}+\frac{2 \sqrt{d x +c}\, D}{b^{2} d^{2}}"," ",0,"2*D*(d*x+c)^(1/2)/b^2/d^2-d/(a*d-b*c)^2*b*(d*x+c)^(1/2)/(b*d*x+a*d)*A+d/(a*d-b*c)^2*(d*x+c)^(1/2)/(b*d*x+a*d)*B*a-d/(a*d-b*c)^2/b*(d*x+c)^(1/2)/(b*d*x+a*d)*C*a^2+d/(a*d-b*c)^2/b^2*(d*x+c)^(1/2)/(b*d*x+a*d)*a^3*D-3*d/(a*d-b*c)^2*b/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*A+d/(a*d-b*c)^2/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*B*a+2/(a*d-b*c)^2*b/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*B*c+d/(a*d-b*c)^2/b/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*C*a^2-4/(a*d-b*c)^2/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*C*a*c-3*d/(a*d-b*c)^2/b^2/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*a^3*D+6/(a*d-b*c)^2/b/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*D*a^2*c-2*d/(a*d-b*c)^2/(d*x+c)^(1/2)*A+2/(a*d-b*c)^2/(d*x+c)^(1/2)*B*c-2/d/(a*d-b*c)^2/(d*x+c)^(1/2)*C*c^2+2/d^2/(a*d-b*c)^2/(d*x+c)^(1/2)*D*c^3","B"
16,1,1225,326,0.033000," ","int((D*x^3+C*x^2+B*x+A)/(b*x+a)^3/(d*x+c)^(3/2),x)","-\frac{9 \sqrt{d x +c}\, A a b \,d^{3}}{4 \left(a d -b c \right)^{3} \left(b d x +a d \right)^{2}}+\frac{9 \sqrt{d x +c}\, A \,b^{2} c \,d^{2}}{4 \left(a d -b c \right)^{3} \left(b d x +a d \right)^{2}}+\frac{5 \sqrt{d x +c}\, B \,a^{2} d^{3}}{4 \left(a d -b c \right)^{3} \left(b d x +a d \right)^{2}}-\frac{\sqrt{d x +c}\, B a b c \,d^{2}}{4 \left(a d -b c \right)^{3} \left(b d x +a d \right)^{2}}-\frac{\sqrt{d x +c}\, B \,b^{2} c^{2} d}{\left(a d -b c \right)^{3} \left(b d x +a d \right)^{2}}-\frac{\sqrt{d x +c}\, C \,a^{3} d^{3}}{4 \left(a d -b c \right)^{3} \left(b d x +a d \right)^{2} b}-\frac{7 \sqrt{d x +c}\, C \,a^{2} c \,d^{2}}{4 \left(a d -b c \right)^{3} \left(b d x +a d \right)^{2}}+\frac{2 \sqrt{d x +c}\, C a b \,c^{2} d}{\left(a d -b c \right)^{3} \left(b d x +a d \right)^{2}}-\frac{3 \sqrt{d x +c}\, D a^{4} d^{3}}{4 \left(a d -b c \right)^{3} \left(b d x +a d \right)^{2} b^{2}}+\frac{15 \sqrt{d x +c}\, D a^{3} c \,d^{2}}{4 \left(a d -b c \right)^{3} \left(b d x +a d \right)^{2} b}-\frac{3 \sqrt{d x +c}\, D a^{2} c^{2} d}{\left(a d -b c \right)^{3} \left(b d x +a d \right)^{2}}-\frac{7 \left(d x +c \right)^{\frac{3}{2}} A \,b^{2} d^{2}}{4 \left(a d -b c \right)^{3} \left(b d x +a d \right)^{2}}-\frac{15 A b \,d^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{\left(a d -b c \right) b}}+\frac{3 \left(d x +c \right)^{\frac{3}{2}} B a b \,d^{2}}{4 \left(a d -b c \right)^{3} \left(b d x +a d \right)^{2}}+\frac{3 B a \,d^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{\left(a d -b c \right) b}}+\frac{\left(d x +c \right)^{\frac{3}{2}} B \,b^{2} c d}{\left(a d -b c \right)^{3} \left(b d x +a d \right)^{2}}+\frac{3 B b c d \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{3} \sqrt{\left(a d -b c \right) b}}+\frac{C \,a^{2} d^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{\left(a d -b c \right) b}\, b}+\frac{\left(d x +c \right)^{\frac{3}{2}} C \,a^{2} d^{2}}{4 \left(a d -b c \right)^{3} \left(b d x +a d \right)^{2}}-\frac{2 \left(d x +c \right)^{\frac{3}{2}} C a b c d}{\left(a d -b c \right)^{3} \left(b d x +a d \right)^{2}}-\frac{2 C a c d \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{3} \sqrt{\left(a d -b c \right) b}}-\frac{2 C b \,c^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{3} \sqrt{\left(a d -b c \right) b}}-\frac{5 \left(d x +c \right)^{\frac{3}{2}} D a^{3} d^{2}}{4 \left(a d -b c \right)^{3} \left(b d x +a d \right)^{2} b}+\frac{3 D a^{3} d^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{\left(a d -b c \right) b}\, b^{2}}-\frac{3 D a^{2} c d \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{3} \sqrt{\left(a d -b c \right) b}\, b}+\frac{3 \left(d x +c \right)^{\frac{3}{2}} D a^{2} c d}{\left(a d -b c \right)^{3} \left(b d x +a d \right)^{2}}+\frac{6 D a \,c^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{3} \sqrt{\left(a d -b c \right) b}}-\frac{2 A \,d^{2}}{\left(a d -b c \right)^{3} \sqrt{d x +c}}+\frac{2 B c d}{\left(a d -b c \right)^{3} \sqrt{d x +c}}-\frac{2 C \,c^{2}}{\left(a d -b c \right)^{3} \sqrt{d x +c}}+\frac{2 D c^{3}}{\left(a d -b c \right)^{3} \sqrt{d x +c}\, d}"," ",0,"-2*d^2/(a*d-b*c)^3/(d*x+c)^(1/2)*A-2/(a*d-b*c)^3/(d*x+c)^(1/2)*C*c^2-1/4*d^3/(a*d-b*c)^3/(b*d*x+a*d)^2/b*(d*x+c)^(1/2)*C*a^3+3/4*d^2/(a*d-b*c)^3/(b*d*x+a*d)^2*b*(d*x+c)^(3/2)*B*a+d/(a*d-b*c)^3/(b*d*x+a*d)^2*b^2*(d*x+c)^(3/2)*B*c+2/d/(a*d-b*c)^3/(d*x+c)^(1/2)*D*c^3-1/4*d^2/(a*d-b*c)^3/(b*d*x+a*d)^2*b*(d*x+c)^(1/2)*B*a*c+2*d/(a*d-b*c)^3/(b*d*x+a*d)^2*b*(d*x+c)^(1/2)*C*a*c^2-5/4*d^2/(a*d-b*c)^3/(b*d*x+a*d)^2/b*(d*x+c)^(3/2)*a^3*D+3*d/(a*d-b*c)^3/(b*d*x+a*d)^2*(d*x+c)^(3/2)*D*a^2*c+3*d/(a*d-b*c)^3*b/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*B*c+1/4*d^2/(a*d-b*c)^3/b/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*a^2*C-2*d/(a*d-b*c)^3/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*C*a*c-7/4*d^2/(a*d-b*c)^3/(b*d*x+a*d)^2*(d*x+c)^(1/2)*C*a^2*c-3/4*d^3/(a*d-b*c)^3/(b*d*x+a*d)^2/b^2*(d*x+c)^(1/2)*D*a^4-3*d/(a*d-b*c)^3/(b*d*x+a*d)^2*(d*x+c)^(1/2)*D*a^2*c^2+3/4*d^2/(a*d-b*c)^3/b^2/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*a^3*D-9/4*d^3/(a*d-b*c)^3/(b*d*x+a*d)^2*b*(d*x+c)^(1/2)*A*a+9/4*d^2/(a*d-b*c)^3/(b*d*x+a*d)^2*b^2*(d*x+c)^(1/2)*A*c-d/(a*d-b*c)^3/(b*d*x+a*d)^2*b^2*(d*x+c)^(1/2)*B*c^2-3*d/(a*d-b*c)^3/b/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*D*a^2*c-2*d/(a*d-b*c)^3/(b*d*x+a*d)^2*b*(d*x+c)^(3/2)*C*a*c+15/4*d^2/(a*d-b*c)^3/(b*d*x+a*d)^2/b*(d*x+c)^(1/2)*D*a^3*c+2*d/(a*d-b*c)^3/(d*x+c)^(1/2)*B*c+3/4*d^2/(a*d-b*c)^3/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*B*a-15/4*d^2/(a*d-b*c)^3*b/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*A-7/4*d^2/(a*d-b*c)^3/(b*d*x+a*d)^2*b^2*(d*x+c)^(3/2)*A+1/4*d^2/(a*d-b*c)^3/(b*d*x+a*d)^2*(d*x+c)^(3/2)*C*a^2+5/4*d^3/(a*d-b*c)^3/(b*d*x+a*d)^2*(d*x+c)^(1/2)*B*a^2-2/(a*d-b*c)^3*b/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*C*c^2+6/(a*d-b*c)^3/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*D*a*c^2","B"
17,1,2108,435,0.041000," ","int((D*x^3+C*x^2+B*x+A)/(b*x+a)^4/(d*x+c)^(3/2),x)","-\frac{29 \sqrt{d x +c}\, A \,a^{2} b \,d^{5}}{8 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}+\frac{29 \sqrt{d x +c}\, A a \,b^{2} c \,d^{4}}{4 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}-\frac{29 \sqrt{d x +c}\, A \,b^{3} c^{2} d^{3}}{8 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}+\frac{11 \sqrt{d x +c}\, B \,a^{3} d^{5}}{8 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}-\frac{\sqrt{d x +c}\, B \,a^{2} b c \,d^{4}}{2 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}-\frac{25 \sqrt{d x +c}\, B a \,b^{2} c^{2} d^{3}}{8 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}+\frac{9 \sqrt{d x +c}\, B \,b^{3} c^{3} d^{2}}{4 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}-\frac{\sqrt{d x +c}\, C \,a^{4} d^{5}}{8 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3} b}-\frac{9 \sqrt{d x +c}\, C \,a^{3} c \,d^{4}}{4 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}+\frac{31 \sqrt{d x +c}\, C \,a^{2} b \,c^{2} d^{3}}{8 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}-\frac{\sqrt{d x +c}\, C a \,b^{2} c^{3} d^{2}}{2 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}-\frac{\sqrt{d x +c}\, C \,b^{3} c^{4} d}{\left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}-\frac{\sqrt{d x +c}\, D a^{5} d^{5}}{8 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3} b^{2}}+\frac{\sqrt{d x +c}\, D a^{4} c \,d^{4}}{\left(a d -b c \right)^{4} \left(b d x +a d \right)^{3} b}+\frac{11 \sqrt{d x +c}\, D a^{3} c^{2} d^{3}}{8 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}-\frac{21 \sqrt{d x +c}\, D a^{2} b \,c^{3} d^{2}}{4 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}+\frac{3 \sqrt{d x +c}\, D a \,b^{2} c^{4} d}{\left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}-\frac{17 \left(d x +c \right)^{\frac{3}{2}} A a \,b^{2} d^{4}}{3 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}+\frac{17 \left(d x +c \right)^{\frac{3}{2}} A \,b^{3} c \,d^{3}}{3 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}+\frac{5 \left(d x +c \right)^{\frac{3}{2}} B \,a^{2} b \,d^{4}}{3 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}+\frac{7 \left(d x +c \right)^{\frac{3}{2}} B a \,b^{2} c \,d^{3}}{3 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}-\frac{4 \left(d x +c \right)^{\frac{3}{2}} B \,b^{3} c^{2} d^{2}}{\left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}+\frac{\left(d x +c \right)^{\frac{3}{2}} C \,a^{3} d^{4}}{3 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}-\frac{13 \left(d x +c \right)^{\frac{3}{2}} C \,a^{2} b c \,d^{3}}{3 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}+\frac{2 \left(d x +c \right)^{\frac{3}{2}} C a \,b^{2} c^{2} d^{2}}{\left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}+\frac{2 \left(d x +c \right)^{\frac{3}{2}} C \,b^{3} c^{3} d}{\left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}-\frac{\left(d x +c \right)^{\frac{3}{2}} D a^{4} d^{4}}{3 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3} b}+\frac{\left(d x +c \right)^{\frac{3}{2}} D a^{3} c \,d^{3}}{3 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}+\frac{6 \left(d x +c \right)^{\frac{3}{2}} D a^{2} b \,c^{2} d^{2}}{\left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}-\frac{6 \left(d x +c \right)^{\frac{3}{2}} D a \,b^{2} c^{3} d}{\left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}-\frac{19 \left(d x +c \right)^{\frac{5}{2}} A \,b^{3} d^{3}}{8 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}+\frac{5 \left(d x +c \right)^{\frac{5}{2}} B a \,b^{2} d^{3}}{8 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}+\frac{7 \left(d x +c \right)^{\frac{5}{2}} B \,b^{3} c \,d^{2}}{4 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}+\frac{\left(d x +c \right)^{\frac{5}{2}} C \,a^{2} b \,d^{3}}{8 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}-\frac{3 \left(d x +c \right)^{\frac{5}{2}} C a \,b^{2} c \,d^{2}}{2 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}-\frac{\left(d x +c \right)^{\frac{5}{2}} C \,b^{3} c^{2} d}{\left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}+\frac{\left(d x +c \right)^{\frac{5}{2}} D a^{3} d^{3}}{8 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}-\frac{3 \left(d x +c \right)^{\frac{5}{2}} D a^{2} b c \,d^{2}}{4 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}+\frac{3 \left(d x +c \right)^{\frac{5}{2}} D a \,b^{2} c^{2} d}{\left(a d -b c \right)^{4} \left(b d x +a d \right)^{3}}-\frac{35 A b \,d^{3} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{8 \left(a d -b c \right)^{4} \sqrt{\left(a d -b c \right) b}}+\frac{5 B a \,d^{3} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{8 \left(a d -b c \right)^{4} \sqrt{\left(a d -b c \right) b}}+\frac{15 B b c \,d^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{4 \left(a d -b c \right)^{4} \sqrt{\left(a d -b c \right) b}}+\frac{C \,a^{2} d^{3} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{8 \left(a d -b c \right)^{4} \sqrt{\left(a d -b c \right) b}\, b}-\frac{3 C a c \,d^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{2 \left(a d -b c \right)^{4} \sqrt{\left(a d -b c \right) b}}-\frac{3 C b \,c^{2} d \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{4} \sqrt{\left(a d -b c \right) b}}+\frac{D a^{3} d^{3} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{8 \left(a d -b c \right)^{4} \sqrt{\left(a d -b c \right) b}\, b^{2}}-\frac{3 D a^{2} c \,d^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{4 \left(a d -b c \right)^{4} \sqrt{\left(a d -b c \right) b}\, b}+\frac{3 D a \,c^{2} d \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{4} \sqrt{\left(a d -b c \right) b}}+\frac{2 D b \,c^{3} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{4} \sqrt{\left(a d -b c \right) b}}-\frac{2 A \,d^{3}}{\left(a d -b c \right)^{4} \sqrt{d x +c}}+\frac{2 B c \,d^{2}}{\left(a d -b c \right)^{4} \sqrt{d x +c}}-\frac{2 C \,c^{2} d}{\left(a d -b c \right)^{4} \sqrt{d x +c}}+\frac{2 D c^{3}}{\left(a d -b c \right)^{4} \sqrt{d x +c}}"," ",0,"-13/3/(a*d-b*c)^4/(b*d*x+a*d)^3*b*d^3*(d*x+c)^(3/2)*C*a^2*c+1/(a*d-b*c)^4/(b*d*x+a*d)^3*d^4/b*(d*x+c)^(1/2)*D*a^4*c-21/4/(a*d-b*c)^4/(b*d*x+a*d)^3*d^2*b*(d*x+c)^(1/2)*D*a^2*c^3+6/(a*d-b*c)^4/(b*d*x+a*d)^3*b*d^2*(d*x+c)^(3/2)*D*a^2*c^2-1/2/(a*d-b*c)^4/(b*d*x+a*d)^3*d^2*b^2*(d*x+c)^(1/2)*C*a*c^3-3/2/(a*d-b*c)^4/(b*d*x+a*d)^3*(d*x+c)^(5/2)*C*a*b^2*c*d^2-3/4/(a*d-b*c)^4/(b*d*x+a*d)^3*(d*x+c)^(5/2)*D*a^2*b*c*d^2-2/(a*d-b*c)^4/(d*x+c)^(1/2)*A*d^3+2/(a*d-b*c)^4/(d*x+c)^(1/2)*D*c^3+2/(a*d-b*c)^4/(b*d*x+a*d)^3*b^2*d^2*(d*x+c)^(3/2)*C*a*c^2-3/4/(a*d-b*c)^4/b/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*D*a^2*c*d^2-6/(a*d-b*c)^4/(b*d*x+a*d)^3*b^2*d*(d*x+c)^(3/2)*D*a*c^3+29/4/(a*d-b*c)^4/(b*d*x+a*d)^3*d^4*b^2*(d*x+c)^(1/2)*A*a*c-1/2/(a*d-b*c)^4/(b*d*x+a*d)^3*d^4*b*(d*x+c)^(1/2)*B*a^2*c-25/8/(a*d-b*c)^4/(b*d*x+a*d)^3*d^3*b^2*(d*x+c)^(1/2)*B*a*c^2+31/8/(a*d-b*c)^4/(b*d*x+a*d)^3*d^3*b*(d*x+c)^(1/2)*C*a^2*c^2+3/(a*d-b*c)^4/(b*d*x+a*d)^3*d*b^2*(d*x+c)^(1/2)*D*a*c^4+3/(a*d-b*c)^4/(b*d*x+a*d)^3*(d*x+c)^(5/2)*D*a*b^2*c^2*d+7/3/(a*d-b*c)^4/(b*d*x+a*d)^3*b^2*d^3*(d*x+c)^(3/2)*B*a*c-19/8/(a*d-b*c)^4/(b*d*x+a*d)^3*(d*x+c)^(5/2)*A*b^3*d^3+1/8/(a*d-b*c)^4/(b*d*x+a*d)^3*(d*x+c)^(5/2)*a^3*d^3*D+1/3/(a*d-b*c)^4/(b*d*x+a*d)^3*d^4*(d*x+c)^(3/2)*C*a^3+11/8/(a*d-b*c)^4/(b*d*x+a*d)^3*d^5*(d*x+c)^(1/2)*B*a^3+2/(a*d-b*c)^4*b/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*D*c^3-35/8/(a*d-b*c)^4*b/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*A*d^3+5/8/(a*d-b*c)^4/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*a*B*d^3+2/(a*d-b*c)^4/(d*x+c)^(1/2)*B*c*d^2+17/3/(a*d-b*c)^4/(b*d*x+a*d)^3*b^3*d^3*(d*x+c)^(3/2)*A*c+1/3/(a*d-b*c)^4/(b*d*x+a*d)^3*d^3*(d*x+c)^(3/2)*D*a^3*c-9/4/(a*d-b*c)^4/(b*d*x+a*d)^3*d^4*(d*x+c)^(1/2)*C*a^3*c+5/3/(a*d-b*c)^4/(b*d*x+a*d)^3*b*d^4*(d*x+c)^(3/2)*B*a^2-4/(a*d-b*c)^4/(b*d*x+a*d)^3*b^3*d^2*(d*x+c)^(3/2)*B*c^2+2/(a*d-b*c)^4/(b*d*x+a*d)^3*b^3*d*(d*x+c)^(3/2)*c^3*C-1/3/(a*d-b*c)^4/(b*d*x+a*d)^3/b*d^4*(d*x+c)^(3/2)*D*a^4-29/8/(a*d-b*c)^4/(b*d*x+a*d)^3*d^5*b*(d*x+c)^(1/2)*A*a^2+11/8/(a*d-b*c)^4/(b*d*x+a*d)^3*d^3*(d*x+c)^(1/2)*D*a^3*c^2-3/2/(a*d-b*c)^4/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*C*a*c*d^2+3/(a*d-b*c)^4/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*D*a*c^2*d+15/4/(a*d-b*c)^4*b/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*B*c*d^2+1/8/(a*d-b*c)^4/b/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*a^2*C*d^3-3/(a*d-b*c)^4*b/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*C*c^2*d+1/8/(a*d-b*c)^4/b^2/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*a^3*d^3*D-29/8/(a*d-b*c)^4/(b*d*x+a*d)^3*d^3*b^3*(d*x+c)^(1/2)*A*c^2+9/4/(a*d-b*c)^4/(b*d*x+a*d)^3*d^2*b^3*(d*x+c)^(1/2)*B*c^3-1/8/(a*d-b*c)^4/(b*d*x+a*d)^3*d^5/b*(d*x+c)^(1/2)*C*a^4-1/(a*d-b*c)^4/(b*d*x+a*d)^3*d*b^3*(d*x+c)^(1/2)*C*c^4-1/8/(a*d-b*c)^4/(b*d*x+a*d)^3*d^5/b^2*(d*x+c)^(1/2)*D*a^5+7/4/(a*d-b*c)^4/(b*d*x+a*d)^3*(d*x+c)^(5/2)*B*b^3*c*d^2-1/(a*d-b*c)^4/(b*d*x+a*d)^3*(d*x+c)^(5/2)*C*b^3*c^2*d+5/8/(a*d-b*c)^4/(b*d*x+a*d)^3*(d*x+c)^(5/2)*a*b^2*B*d^3+1/8/(a*d-b*c)^4/(b*d*x+a*d)^3*(d*x+c)^(5/2)*a^2*b*C*d^3-17/3/(a*d-b*c)^4/(b*d*x+a*d)^3*b^2*d^4*(d*x+c)^(3/2)*A*a-2/(a*d-b*c)^4/(d*x+c)^(1/2)*C*c^2*d","B"
18,1,841,410,0.010000," ","int((b*x+a)^3*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(5/2),x)","-\frac{2 \left(-35 b^{3} D x^{6} d^{6}-45 C \,b^{3} d^{6} x^{5}-135 D a \,b^{2} d^{6} x^{5}+60 D b^{3} c \,d^{5} x^{5}-63 B \,b^{3} d^{6} x^{4}-189 C a \,b^{2} d^{6} x^{4}+90 C \,b^{3} c \,d^{5} x^{4}-189 D a^{2} b \,d^{6} x^{4}+270 D a \,b^{2} c \,d^{5} x^{4}-120 D b^{3} c^{2} d^{4} x^{4}-105 A \,b^{3} d^{6} x^{3}-315 B a \,b^{2} d^{6} x^{3}+168 B \,b^{3} c \,d^{5} x^{3}-315 C \,a^{2} b \,d^{6} x^{3}+504 C a \,b^{2} c \,d^{5} x^{3}-240 C \,b^{3} c^{2} d^{4} x^{3}-105 D a^{3} d^{6} x^{3}+504 D a^{2} b c \,d^{5} x^{3}-720 D a \,b^{2} c^{2} d^{4} x^{3}+320 D b^{3} c^{3} d^{3} x^{3}-945 A a \,b^{2} d^{6} x^{2}+630 A \,b^{3} c \,d^{5} x^{2}-945 B \,a^{2} b \,d^{6} x^{2}+1890 B a \,b^{2} c \,d^{5} x^{2}-1008 B \,b^{3} c^{2} d^{4} x^{2}-315 C \,a^{3} d^{6} x^{2}+1890 C \,a^{2} b c \,d^{5} x^{2}-3024 C a \,b^{2} c^{2} d^{4} x^{2}+1440 C \,b^{3} c^{3} d^{3} x^{2}+630 D a^{3} c \,d^{5} x^{2}-3024 D a^{2} b \,c^{2} d^{4} x^{2}+4320 D a \,b^{2} c^{3} d^{3} x^{2}-1920 D b^{3} c^{4} d^{2} x^{2}+945 A \,a^{2} b \,d^{6} x -3780 A a \,b^{2} c \,d^{5} x +2520 A \,b^{3} c^{2} d^{4} x +315 B \,a^{3} d^{6} x -3780 B \,a^{2} b c \,d^{5} x +7560 B a \,b^{2} c^{2} d^{4} x -4032 B \,b^{3} c^{3} d^{3} x -1260 C \,a^{3} c \,d^{5} x +7560 C \,a^{2} b \,c^{2} d^{4} x -12096 C a \,b^{2} c^{3} d^{3} x +5760 C \,b^{3} c^{4} d^{2} x +2520 D a^{3} c^{2} d^{4} x -12096 D a^{2} b \,c^{3} d^{3} x +17280 D a \,b^{2} c^{4} d^{2} x -7680 D b^{3} c^{5} d x +105 a^{3} A \,d^{6}+630 A \,a^{2} b c \,d^{5}-2520 A a \,b^{2} c^{2} d^{4}+1680 A \,b^{3} c^{3} d^{3}+210 B \,a^{3} c \,d^{5}-2520 B \,a^{2} b \,c^{2} d^{4}+5040 B a \,b^{2} c^{3} d^{3}-2688 B \,b^{3} c^{4} d^{2}-840 C \,a^{3} c^{2} d^{4}+5040 C \,a^{2} b \,c^{3} d^{3}-8064 C a \,b^{2} c^{4} d^{2}+3840 C \,b^{3} c^{5} d +1680 D a^{3} c^{3} d^{3}-8064 D a^{2} b \,c^{4} d^{2}+11520 D a \,b^{2} c^{5} d -5120 D b^{3} c^{6}\right)}{315 \left(d x +c \right)^{\frac{3}{2}} d^{7}}"," ",0,"-2/315/(d*x+c)^(3/2)*(-35*D*b^3*d^6*x^6-45*C*b^3*d^6*x^5-135*D*a*b^2*d^6*x^5+60*D*b^3*c*d^5*x^5-63*B*b^3*d^6*x^4-189*C*a*b^2*d^6*x^4+90*C*b^3*c*d^5*x^4-189*D*a^2*b*d^6*x^4+270*D*a*b^2*c*d^5*x^4-120*D*b^3*c^2*d^4*x^4-105*A*b^3*d^6*x^3-315*B*a*b^2*d^6*x^3+168*B*b^3*c*d^5*x^3-315*C*a^2*b*d^6*x^3+504*C*a*b^2*c*d^5*x^3-240*C*b^3*c^2*d^4*x^3-105*D*a^3*d^6*x^3+504*D*a^2*b*c*d^5*x^3-720*D*a*b^2*c^2*d^4*x^3+320*D*b^3*c^3*d^3*x^3-945*A*a*b^2*d^6*x^2+630*A*b^3*c*d^5*x^2-945*B*a^2*b*d^6*x^2+1890*B*a*b^2*c*d^5*x^2-1008*B*b^3*c^2*d^4*x^2-315*C*a^3*d^6*x^2+1890*C*a^2*b*c*d^5*x^2-3024*C*a*b^2*c^2*d^4*x^2+1440*C*b^3*c^3*d^3*x^2+630*D*a^3*c*d^5*x^2-3024*D*a^2*b*c^2*d^4*x^2+4320*D*a*b^2*c^3*d^3*x^2-1920*D*b^3*c^4*d^2*x^2+945*A*a^2*b*d^6*x-3780*A*a*b^2*c*d^5*x+2520*A*b^3*c^2*d^4*x+315*B*a^3*d^6*x-3780*B*a^2*b*c*d^5*x+7560*B*a*b^2*c^2*d^4*x-4032*B*b^3*c^3*d^3*x-1260*C*a^3*c*d^5*x+7560*C*a^2*b*c^2*d^4*x-12096*C*a*b^2*c^3*d^3*x+5760*C*b^3*c^4*d^2*x+2520*D*a^3*c^2*d^4*x-12096*D*a^2*b*c^3*d^3*x+17280*D*a*b^2*c^4*d^2*x-7680*D*b^3*c^5*d*x+105*A*a^3*d^6+630*A*a^2*b*c*d^5-2520*A*a*b^2*c^2*d^4+1680*A*b^3*c^3*d^3+210*B*a^3*c*d^5-2520*B*a^2*b*c^2*d^4+5040*B*a*b^2*c^3*d^3-2688*B*b^3*c^4*d^2-840*C*a^3*c^2*d^4+5040*C*a^2*b*c^3*d^3-8064*C*a*b^2*c^4*d^2+3840*C*b^3*c^5*d+1680*D*a^3*c^3*d^3-8064*D*a^2*b*c^4*d^2+11520*D*a*b^2*c^5*d-5120*D*b^3*c^6)/d^7","B"
19,1,505,302,0.009000," ","int((b*x+a)^2*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(5/2),x)","-\frac{2 \left(-15 b^{2} D x^{5} d^{5}-21 C \,b^{2} d^{5} x^{4}-42 D a b \,d^{5} x^{4}+30 D b^{2} c \,d^{4} x^{4}-35 B \,b^{2} d^{5} x^{3}-70 C a b \,d^{5} x^{3}+56 C \,b^{2} c \,d^{4} x^{3}-35 D a^{2} d^{5} x^{3}+112 D a b c \,d^{4} x^{3}-80 D b^{2} c^{2} d^{3} x^{3}-105 A \,b^{2} d^{5} x^{2}-210 B a b \,d^{5} x^{2}+210 B \,b^{2} c \,d^{4} x^{2}-105 C \,a^{2} d^{5} x^{2}+420 C a b c \,d^{4} x^{2}-336 C \,b^{2} c^{2} d^{3} x^{2}+210 D a^{2} c \,d^{4} x^{2}-672 D a b \,c^{2} d^{3} x^{2}+480 D b^{2} c^{3} d^{2} x^{2}+210 A a b \,d^{5} x -420 A \,b^{2} c \,d^{4} x +105 B \,a^{2} d^{5} x -840 B a b c \,d^{4} x +840 B \,b^{2} c^{2} d^{3} x -420 C \,a^{2} c \,d^{4} x +1680 C a b \,c^{2} d^{3} x -1344 C \,b^{2} c^{3} d^{2} x +840 D a^{2} c^{2} d^{3} x -2688 D a b \,c^{3} d^{2} x +1920 D b^{2} c^{4} d x +35 a^{2} A \,d^{5}+140 A a b c \,d^{4}-280 A \,b^{2} c^{2} d^{3}+70 B \,a^{2} c \,d^{4}-560 B a b \,c^{2} d^{3}+560 B \,b^{2} c^{3} d^{2}-280 C \,a^{2} c^{2} d^{3}+1120 C a b \,c^{3} d^{2}-896 C \,b^{2} c^{4} d +560 D a^{2} c^{3} d^{2}-1792 D a b \,c^{4} d +1280 D b^{2} c^{5}\right)}{105 \left(d x +c \right)^{\frac{3}{2}} d^{6}}"," ",0,"-2/105/(d*x+c)^(3/2)*(-15*D*b^2*d^5*x^5-21*C*b^2*d^5*x^4-42*D*a*b*d^5*x^4+30*D*b^2*c*d^4*x^4-35*B*b^2*d^5*x^3-70*C*a*b*d^5*x^3+56*C*b^2*c*d^4*x^3-35*D*a^2*d^5*x^3+112*D*a*b*c*d^4*x^3-80*D*b^2*c^2*d^3*x^3-105*A*b^2*d^5*x^2-210*B*a*b*d^5*x^2+210*B*b^2*c*d^4*x^2-105*C*a^2*d^5*x^2+420*C*a*b*c*d^4*x^2-336*C*b^2*c^2*d^3*x^2+210*D*a^2*c*d^4*x^2-672*D*a*b*c^2*d^3*x^2+480*D*b^2*c^3*d^2*x^2+210*A*a*b*d^5*x-420*A*b^2*c*d^4*x+105*B*a^2*d^5*x-840*B*a*b*c*d^4*x+840*B*b^2*c^2*d^3*x-420*C*a^2*c*d^4*x+1680*C*a*b*c^2*d^3*x-1344*C*b^2*c^3*d^2*x+840*D*a^2*c^2*d^3*x-2688*D*a*b*c^3*d^2*x+1920*D*b^2*c^4*d*x+35*A*a^2*d^5+140*A*a*b*c*d^4-280*A*b^2*c^2*d^3+70*B*a^2*c*d^4-560*B*a*b*c^2*d^3+560*B*b^2*c^3*d^2-280*C*a^2*c^2*d^3+1120*C*a*b*c^3*d^2-896*C*b^2*c^4*d+560*D*a^2*c^3*d^2-1792*D*a*b*c^4*d+1280*D*b^2*c^5)/d^6","A"
20,1,241,194,0.007000," ","int((b*x+a)*(D*x^3+C*x^2+B*x+A)/(d*x+c)^(5/2),x)","-\frac{2 \left(-3 D b \,x^{4} d^{4}-5 C b \,d^{4} x^{3}-5 D a \,d^{4} x^{3}+8 D b c \,d^{3} x^{3}-15 B b \,d^{4} x^{2}-15 C a \,d^{4} x^{2}+30 C b c \,d^{3} x^{2}+30 D a c \,d^{3} x^{2}-48 D b \,c^{2} d^{2} x^{2}+15 A b \,d^{4} x +15 B a \,d^{4} x -60 B b c \,d^{3} x -60 C a c \,d^{3} x +120 C b \,c^{2} d^{2} x +120 D a \,c^{2} d^{2} x -192 D b \,c^{3} d x +5 A a \,d^{4}+10 A b c \,d^{3}+10 B a c \,d^{3}-40 B b \,c^{2} d^{2}-40 C a \,c^{2} d^{2}+80 C b \,c^{3} d +80 D a \,c^{3} d -128 D b \,c^{4}\right)}{15 \left(d x +c \right)^{\frac{3}{2}} d^{5}}"," ",0,"-2/15/(d*x+c)^(3/2)*(-3*D*b*d^4*x^4-5*C*b*d^4*x^3-5*D*a*d^4*x^3+8*D*b*c*d^3*x^3-15*B*b*d^4*x^2-15*C*a*d^4*x^2+30*C*b*c*d^3*x^2+30*D*a*c*d^3*x^2-48*D*b*c^2*d^2*x^2+15*A*b*d^4*x+15*B*a*d^4*x-60*B*b*c*d^3*x-60*C*a*c*d^3*x+120*C*b*c^2*d^2*x+120*D*a*c^2*d^2*x-192*D*b*c^3*d*x+5*A*a*d^4+10*A*b*c*d^3+10*B*a*c*d^3-40*B*b*c^2*d^2-40*C*a*c^2*d^2+80*C*b*c^3*d+80*D*a*c^3*d-128*D*b*c^4)/d^5","A"
21,1,90,101,0.005000," ","int((D*x^3+C*x^2+B*x+A)/(d*x+c)^(5/2),x)","-\frac{2 \left(-D x^{3} d^{3}-3 C \,d^{3} x^{2}+6 D c \,d^{2} x^{2}+3 B \,d^{3} x -12 C c \,d^{2} x +24 D c^{2} d x +A \,d^{3}+2 B c \,d^{2}-8 C \,c^{2} d +16 D c^{3}\right)}{3 \left(d x +c \right)^{\frac{3}{2}} d^{4}}"," ",0,"-2/3/(d*x+c)^(3/2)*(-D*d^3*x^3-3*C*d^3*x^2+6*D*c*d^2*x^2+3*B*d^3*x-12*C*c*d^2*x+24*D*c^2*d*x+A*d^3+2*B*c*d^2-8*C*c^2*d+16*D*c^3)/d^4","A"
22,1,464,192,0.019000," ","int((D*x^3+C*x^2+B*x+A)/(b*x+a)/(d*x+c)^(5/2),x)","\frac{2 A \,b^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{2} \sqrt{\left(a d -b c \right) b}}-\frac{2 B a b \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{2} \sqrt{\left(a d -b c \right) b}}+\frac{2 C \,a^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{2} \sqrt{\left(a d -b c \right) b}}-\frac{2 D a^{3} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{2} \sqrt{\left(a d -b c \right) b}\, b}+\frac{2 A b}{\left(a d -b c \right)^{2} \sqrt{d x +c}}-\frac{2 B a}{\left(a d -b c \right)^{2} \sqrt{d x +c}}+\frac{4 C a c}{\left(a d -b c \right)^{2} \sqrt{d x +c}\, d}-\frac{2 C b \,c^{2}}{\left(a d -b c \right)^{2} \sqrt{d x +c}\, d^{2}}-\frac{6 D a \,c^{2}}{\left(a d -b c \right)^{2} \sqrt{d x +c}\, d^{2}}+\frac{4 D b \,c^{3}}{\left(a d -b c \right)^{2} \sqrt{d x +c}\, d^{3}}-\frac{2 A}{3 \left(a d -b c \right) \left(d x +c \right)^{\frac{3}{2}}}+\frac{2 B c}{3 \left(a d -b c \right) \left(d x +c \right)^{\frac{3}{2}} d}-\frac{2 C \,c^{2}}{3 \left(a d -b c \right) \left(d x +c \right)^{\frac{3}{2}} d^{2}}+\frac{2 D c^{3}}{3 \left(a d -b c \right) \left(d x +c \right)^{\frac{3}{2}} d^{3}}+\frac{2 \sqrt{d x +c}\, D}{b \,d^{3}}"," ",0,"2*D*(d*x+c)^(1/2)/b/d^3+2*b^2/(a*d-b*c)^2/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*A-2*b/(a*d-b*c)^2/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*B*a+2/(a*d-b*c)^2/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*C*a^2-2/b/(a*d-b*c)^2/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*D*a^3-2/3/(a*d-b*c)/(d*x+c)^(3/2)*A+2/3/d/(a*d-b*c)/(d*x+c)^(3/2)*B*c-2/3/d^2/(a*d-b*c)/(d*x+c)^(3/2)*C*c^2+2/3/d^3/(a*d-b*c)/(d*x+c)^(3/2)*D*c^3+2/(a*d-b*c)^2/(d*x+c)^(1/2)*A*b-2/(a*d-b*c)^2/(d*x+c)^(1/2)*B*a+4/d/(a*d-b*c)^2/(d*x+c)^(1/2)*C*a*c-2/d^2/(a*d-b*c)^2/(d*x+c)^(1/2)*C*b*c^2-6/d^2/(a*d-b*c)^2/(d*x+c)^(1/2)*D*a*c^2+4/d^3/(a*d-b*c)^2/(d*x+c)^(1/2)*D*b*c^3","B"
23,1,730,317,0.028000," ","int((D*x^3+C*x^2+B*x+A)/(b*x+a)^2/(d*x+c)^(5/2),x)","\frac{5 A \,b^{2} d \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{3} \sqrt{\left(a d -b c \right) b}}-\frac{3 B a b d \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{3} \sqrt{\left(a d -b c \right) b}}-\frac{2 B \,b^{2} c \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{3} \sqrt{\left(a d -b c \right) b}}+\frac{C \,a^{2} d \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{3} \sqrt{\left(a d -b c \right) b}}+\frac{4 C a b c \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{3} \sqrt{\left(a d -b c \right) b}}+\frac{D a^{3} d \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{3} \sqrt{\left(a d -b c \right) b}\, b}-\frac{6 D a^{2} c \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{3} \sqrt{\left(a d -b c \right) b}}+\frac{\sqrt{d x +c}\, A \,b^{2} d}{\left(a d -b c \right)^{3} \left(b d x +a d \right)}-\frac{\sqrt{d x +c}\, B a b d}{\left(a d -b c \right)^{3} \left(b d x +a d \right)}+\frac{\sqrt{d x +c}\, C \,a^{2} d}{\left(a d -b c \right)^{3} \left(b d x +a d \right)}-\frac{\sqrt{d x +c}\, D a^{3} d}{\left(a d -b c \right)^{3} \left(b d x +a d \right) b}+\frac{4 A b d}{\left(a d -b c \right)^{3} \sqrt{d x +c}}-\frac{2 B a d}{\left(a d -b c \right)^{3} \sqrt{d x +c}}-\frac{2 B b c}{\left(a d -b c \right)^{3} \sqrt{d x +c}}+\frac{4 C a c}{\left(a d -b c \right)^{3} \sqrt{d x +c}}-\frac{6 D a \,c^{2}}{\left(a d -b c \right)^{3} \sqrt{d x +c}\, d}+\frac{2 D b \,c^{3}}{\left(a d -b c \right)^{3} \sqrt{d x +c}\, d^{2}}-\frac{2 A d}{3 \left(a d -b c \right)^{2} \left(d x +c \right)^{\frac{3}{2}}}+\frac{2 B c}{3 \left(a d -b c \right)^{2} \left(d x +c \right)^{\frac{3}{2}}}-\frac{2 C \,c^{2}}{3 \left(a d -b c \right)^{2} \left(d x +c \right)^{\frac{3}{2}} d}+\frac{2 D c^{3}}{3 \left(a d -b c \right)^{2} \left(d x +c \right)^{\frac{3}{2}} d^{2}}"," ",0,"d/(a*d-b*c)^3*b^2*(d*x+c)^(1/2)/(b*d*x+a*d)*A-d/(a*d-b*c)^3*b*(d*x+c)^(1/2)/(b*d*x+a*d)*a*B+d/(a*d-b*c)^3*(d*x+c)^(1/2)/(b*d*x+a*d)*C*a^2-d/(a*d-b*c)^3/b*(d*x+c)^(1/2)/(b*d*x+a*d)*a^3*D+5*d/(a*d-b*c)^3*b^2/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*A-3*d/(a*d-b*c)^3*b/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*B*a-2/(a*d-b*c)^3*b^2/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*B*c+d/(a*d-b*c)^3/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*C*a^2+4/(a*d-b*c)^3*b/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*C*a*c+d/(a*d-b*c)^3/b/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*a^3*D-6/(a*d-b*c)^3/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*D*a^2*c-2/3*d/(a*d-b*c)^2/(d*x+c)^(3/2)*A+2/3/(a*d-b*c)^2/(d*x+c)^(3/2)*B*c-2/3/d/(a*d-b*c)^2/(d*x+c)^(3/2)*C*c^2+2/3/d^2/(a*d-b*c)^2/(d*x+c)^(3/2)*D*c^3+4*d/(a*d-b*c)^3/(d*x+c)^(1/2)*A*b-2*d/(a*d-b*c)^3/(d*x+c)^(1/2)*B*a-2/(a*d-b*c)^3/(d*x+c)^(1/2)*B*b*c+4/(a*d-b*c)^3/(d*x+c)^(1/2)*C*a*c-6/d/(a*d-b*c)^3/(d*x+c)^(1/2)*D*a*c^2+2/d^2/(a*d-b*c)^3/(d*x+c)^(1/2)*D*b*c^3","B"
24,1,1376,411,0.037000," ","int((D*x^3+C*x^2+B*x+A)/(b*x+a)^3/(d*x+c)^(5/2),x)","\frac{13 \sqrt{d x +c}\, A a \,b^{2} d^{3}}{4 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{2}}-\frac{13 \sqrt{d x +c}\, A \,b^{3} c \,d^{2}}{4 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{2}}-\frac{9 \sqrt{d x +c}\, B \,a^{2} b \,d^{3}}{4 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{2}}+\frac{5 \sqrt{d x +c}\, B a \,b^{2} c \,d^{2}}{4 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{2}}+\frac{\sqrt{d x +c}\, B \,b^{3} c^{2} d}{\left(a d -b c \right)^{4} \left(b d x +a d \right)^{2}}+\frac{5 \sqrt{d x +c}\, C \,a^{3} d^{3}}{4 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{2}}+\frac{3 \sqrt{d x +c}\, C \,a^{2} b c \,d^{2}}{4 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{2}}-\frac{2 \sqrt{d x +c}\, C a \,b^{2} c^{2} d}{\left(a d -b c \right)^{4} \left(b d x +a d \right)^{2}}-\frac{\sqrt{d x +c}\, D a^{4} d^{3}}{4 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{2} b}-\frac{11 \sqrt{d x +c}\, D a^{3} c \,d^{2}}{4 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{2}}+\frac{3 \sqrt{d x +c}\, D a^{2} b \,c^{2} d}{\left(a d -b c \right)^{4} \left(b d x +a d \right)^{2}}+\frac{11 \left(d x +c \right)^{\frac{3}{2}} A \,b^{3} d^{2}}{4 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{2}}+\frac{35 A \,b^{2} d^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{4 \left(a d -b c \right)^{4} \sqrt{\left(a d -b c \right) b}}-\frac{7 \left(d x +c \right)^{\frac{3}{2}} B a \,b^{2} d^{2}}{4 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{2}}-\frac{15 B a b \,d^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{4 \left(a d -b c \right)^{4} \sqrt{\left(a d -b c \right) b}}-\frac{\left(d x +c \right)^{\frac{3}{2}} B \,b^{3} c d}{\left(a d -b c \right)^{4} \left(b d x +a d \right)^{2}}-\frac{5 B \,b^{2} c d \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{4} \sqrt{\left(a d -b c \right) b}}+\frac{3 \left(d x +c \right)^{\frac{3}{2}} C \,a^{2} b \,d^{2}}{4 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{2}}+\frac{3 C \,a^{2} d^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{4 \left(a d -b c \right)^{4} \sqrt{\left(a d -b c \right) b}}+\frac{2 \left(d x +c \right)^{\frac{3}{2}} C a \,b^{2} c d}{\left(a d -b c \right)^{4} \left(b d x +a d \right)^{2}}+\frac{6 C a b c d \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{4} \sqrt{\left(a d -b c \right) b}}+\frac{2 C \,b^{2} c^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{4} \sqrt{\left(a d -b c \right) b}}+\frac{D a^{3} d^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{4 \left(a d -b c \right)^{4} \sqrt{\left(a d -b c \right) b}\, b}+\frac{\left(d x +c \right)^{\frac{3}{2}} D a^{3} d^{2}}{4 \left(a d -b c \right)^{4} \left(b d x +a d \right)^{2}}-\frac{3 \left(d x +c \right)^{\frac{3}{2}} D a^{2} b c d}{\left(a d -b c \right)^{4} \left(b d x +a d \right)^{2}}-\frac{3 D a^{2} c d \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{4} \sqrt{\left(a d -b c \right) b}}-\frac{6 D a b \,c^{2} \arctan \left(\frac{\sqrt{d x +c}\, b}{\sqrt{\left(a d -b c \right) b}}\right)}{\left(a d -b c \right)^{4} \sqrt{\left(a d -b c \right) b}}+\frac{6 A b \,d^{2}}{\left(a d -b c \right)^{4} \sqrt{d x +c}}-\frac{2 B a \,d^{2}}{\left(a d -b c \right)^{4} \sqrt{d x +c}}-\frac{4 B b c d}{\left(a d -b c \right)^{4} \sqrt{d x +c}}+\frac{4 C a c d}{\left(a d -b c \right)^{4} \sqrt{d x +c}}+\frac{2 C b \,c^{2}}{\left(a d -b c \right)^{4} \sqrt{d x +c}}-\frac{6 D a \,c^{2}}{\left(a d -b c \right)^{4} \sqrt{d x +c}}-\frac{2 A \,d^{2}}{3 \left(a d -b c \right)^{3} \left(d x +c \right)^{\frac{3}{2}}}+\frac{2 B c d}{3 \left(a d -b c \right)^{3} \left(d x +c \right)^{\frac{3}{2}}}-\frac{2 C \,c^{2}}{3 \left(a d -b c \right)^{3} \left(d x +c \right)^{\frac{3}{2}}}+\frac{2 D c^{3}}{3 \left(a d -b c \right)^{3} \left(d x +c \right)^{\frac{3}{2}} d}"," ",0,"-2/3*d^2/(a*d-b*c)^3/(d*x+c)^(3/2)*A-2/3/(a*d-b*c)^3/(d*x+c)^(3/2)*C*c^2+2/3/d/(a*d-b*c)^3/(d*x+c)^(3/2)*D*c^3+35/4*d^2/(a*d-b*c)^4*b^2/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*A+11/4*d^2/(a*d-b*c)^4/(b*d*x+a*d)^2*(d*x+c)^(3/2)*A*b^3+1/4*d^2/(a*d-b*c)^4/(b*d*x+a*d)^2*(d*x+c)^(3/2)*a^3*D+5/4*d^3/(a*d-b*c)^4/(b*d*x+a*d)^2*(d*x+c)^(1/2)*C*a^3+2/(a*d-b*c)^4*b^2/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*C*c^2-4*d/(a*d-b*c)^4/(d*x+c)^(1/2)*B*b*c+4*d/(a*d-b*c)^4/(d*x+c)^(1/2)*C*a*c+3/4*d^2/(a*d-b*c)^4/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*a^2*C-2*d^2/(a*d-b*c)^4/(d*x+c)^(1/2)*B*a+2/3*d/(a*d-b*c)^3/(d*x+c)^(3/2)*B*c+6*d^2/(a*d-b*c)^4/(d*x+c)^(1/2)*A*b+2/(a*d-b*c)^4/(d*x+c)^(1/2)*c^2*b*C-6/(a*d-b*c)^4/(d*x+c)^(1/2)*a*c^2*D+2*d/(a*d-b*c)^4/(b*d*x+a*d)^2*(d*x+c)^(3/2)*C*a*b^2*c-3*d/(a*d-b*c)^4/(b*d*x+a*d)^2*(d*x+c)^(3/2)*D*a^2*b*c+3*d/(a*d-b*c)^4/(b*d*x+a*d)^2*b*(d*x+c)^(1/2)*a^2*c^2*D+5/4*d^2/(a*d-b*c)^4/(b*d*x+a*d)^2*b^2*(d*x+c)^(1/2)*B*a*c+3/4*d^2/(a*d-b*c)^4/(b*d*x+a*d)^2*b*(d*x+c)^(1/2)*C*a^2*c-2*d/(a*d-b*c)^4/(b*d*x+a*d)^2*b^2*(d*x+c)^(1/2)*a*c^2*C+6*d/(a*d-b*c)^4*b/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*C*a*c+13/4*d^3/(a*d-b*c)^4/(b*d*x+a*d)^2*b^2*(d*x+c)^(1/2)*A*a-13/4*d^2/(a*d-b*c)^4/(b*d*x+a*d)^2*b^3*(d*x+c)^(1/2)*A*c-9/4*d^3/(a*d-b*c)^4/(b*d*x+a*d)^2*b*(d*x+c)^(1/2)*B*a^2-6/(a*d-b*c)^4*b/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*D*a*c^2+d/(a*d-b*c)^4/(b*d*x+a*d)^2*b^3*(d*x+c)^(1/2)*c^2*B-1/4*d^3/(a*d-b*c)^4/(b*d*x+a*d)^2/b*(d*x+c)^(1/2)*D*a^4-11/4*d^2/(a*d-b*c)^4/(b*d*x+a*d)^2*(d*x+c)^(1/2)*D*a^3*c+1/4*d^2/(a*d-b*c)^4/b/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*a^3*D-3*d/(a*d-b*c)^4/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*D*a^2*c-5*d/(a*d-b*c)^4*b^2/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*B*c-15/4*d^2/(a*d-b*c)^4*b/((a*d-b*c)*b)^(1/2)*arctan((d*x+c)^(1/2)/((a*d-b*c)*b)^(1/2)*b)*B*a-7/4*d^2/(a*d-b*c)^4/(b*d*x+a*d)^2*(d*x+c)^(3/2)*B*a*b^2-d/(a*d-b*c)^4/(b*d*x+a*d)^2*(d*x+c)^(3/2)*B*b^3*c+3/4*d^2/(a*d-b*c)^4/(b*d*x+a*d)^2*(d*x+c)^(3/2)*a^2*b*C","B"
25,1,5003,455,0.035000," ","int((b*x+a)^3*(d*x+c)^n*(D*x^3+C*x^2+B*x+A),x)","\text{output too large to display}"," ",0,"result too large to display","B"
26,1,2588,338,0.021000," ","int((b*x+a)^2*(d*x+c)^n*(D*x^3+C*x^2+B*x+A),x)","\frac{\left(D b^{2} d^{5} n^{5} x^{5}+C \,b^{2} d^{5} n^{5} x^{4}+2 D a b \,d^{5} n^{5} x^{4}+15 D b^{2} d^{5} n^{4} x^{5}+B \,b^{2} d^{5} n^{5} x^{3}+2 C a b \,d^{5} n^{5} x^{3}+16 C \,b^{2} d^{5} n^{4} x^{4}+D a^{2} d^{5} n^{5} x^{3}+32 D a b \,d^{5} n^{4} x^{4}-5 D b^{2} c \,d^{4} n^{4} x^{4}+85 D b^{2} d^{5} n^{3} x^{5}+A \,b^{2} d^{5} n^{5} x^{2}+2 B a b \,d^{5} n^{5} x^{2}+17 B \,b^{2} d^{5} n^{4} x^{3}+C \,a^{2} d^{5} n^{5} x^{2}+34 C a b \,d^{5} n^{4} x^{3}-4 C \,b^{2} c \,d^{4} n^{4} x^{3}+95 C \,b^{2} d^{5} n^{3} x^{4}+17 D a^{2} d^{5} n^{4} x^{3}-8 D a b c \,d^{4} n^{4} x^{3}+190 D a b \,d^{5} n^{3} x^{4}-50 D b^{2} c \,d^{4} n^{3} x^{4}+225 D b^{2} d^{5} n^{2} x^{5}+2 A a b \,d^{5} n^{5} x +18 A \,b^{2} d^{5} n^{4} x^{2}+B \,a^{2} d^{5} n^{5} x +36 B a b \,d^{5} n^{4} x^{2}-3 B \,b^{2} c \,d^{4} n^{4} x^{2}+107 B \,b^{2} d^{5} n^{3} x^{3}+18 C \,a^{2} d^{5} n^{4} x^{2}-6 C a b c \,d^{4} n^{4} x^{2}+214 C a b \,d^{5} n^{3} x^{3}-48 C \,b^{2} c \,d^{4} n^{3} x^{3}+260 C \,b^{2} d^{5} n^{2} x^{4}-3 D a^{2} c \,d^{4} n^{4} x^{2}+107 D a^{2} d^{5} n^{3} x^{3}-96 D a b c \,d^{4} n^{3} x^{3}+520 D a b \,d^{5} n^{2} x^{4}+20 D b^{2} c^{2} d^{3} n^{3} x^{3}-175 D b^{2} c \,d^{4} n^{2} x^{4}+274 D b^{2} d^{5} n \,x^{5}+A \,a^{2} d^{5} n^{5}+38 A a b \,d^{5} n^{4} x -2 A \,b^{2} c \,d^{4} n^{4} x +121 A \,b^{2} d^{5} n^{3} x^{2}+19 B \,a^{2} d^{5} n^{4} x -4 B a b c \,d^{4} n^{4} x +242 B a b \,d^{5} n^{3} x^{2}-42 B \,b^{2} c \,d^{4} n^{3} x^{2}+307 B \,b^{2} d^{5} n^{2} x^{3}-2 C \,a^{2} c \,d^{4} n^{4} x +121 C \,a^{2} d^{5} n^{3} x^{2}-84 C a b c \,d^{4} n^{3} x^{2}+614 C a b \,d^{5} n^{2} x^{3}+12 C \,b^{2} c^{2} d^{3} n^{3} x^{2}-188 C \,b^{2} c \,d^{4} n^{2} x^{3}+324 C \,b^{2} d^{5} n \,x^{4}-42 D a^{2} c \,d^{4} n^{3} x^{2}+307 D a^{2} d^{5} n^{2} x^{3}+24 D a b \,c^{2} d^{3} n^{3} x^{2}-376 D a b c \,d^{4} n^{2} x^{3}+648 D a b \,d^{5} n \,x^{4}+120 D b^{2} c^{2} d^{3} n^{2} x^{3}-250 D b^{2} c \,d^{4} n \,x^{4}+120 b^{2} D x^{5} d^{5}+20 A \,a^{2} d^{5} n^{4}-2 A a b c \,d^{4} n^{4}+274 A a b \,d^{5} n^{3} x -32 A \,b^{2} c \,d^{4} n^{3} x +372 A \,b^{2} d^{5} n^{2} x^{2}-B \,a^{2} c \,d^{4} n^{4}+137 B \,a^{2} d^{5} n^{3} x -64 B a b c \,d^{4} n^{3} x +744 B a b \,d^{5} n^{2} x^{2}+6 B \,b^{2} c^{2} d^{3} n^{3} x -195 B \,b^{2} c \,d^{4} n^{2} x^{2}+396 B \,b^{2} d^{5} n \,x^{3}-32 C \,a^{2} c \,d^{4} n^{3} x +372 C \,a^{2} d^{5} n^{2} x^{2}+12 C a b \,c^{2} d^{3} n^{3} x -390 C a b c \,d^{4} n^{2} x^{2}+792 C a b \,d^{5} n \,x^{3}+108 C \,b^{2} c^{2} d^{3} n^{2} x^{2}-288 C \,b^{2} c \,d^{4} n \,x^{3}+144 C \,b^{2} d^{5} x^{4}+6 D a^{2} c^{2} d^{3} n^{3} x -195 D a^{2} c \,d^{4} n^{2} x^{2}+396 D a^{2} d^{5} n \,x^{3}+216 D a b \,c^{2} d^{3} n^{2} x^{2}-576 D a b c \,d^{4} n \,x^{3}+288 D a b \,d^{5} x^{4}-60 D b^{2} c^{3} d^{2} n^{2} x^{2}+220 D b^{2} c^{2} d^{3} n \,x^{3}-120 D b^{2} c \,d^{4} x^{4}+155 A \,a^{2} d^{5} n^{3}-36 A a b c \,d^{4} n^{3}+922 A a b \,d^{5} n^{2} x +2 A \,b^{2} c^{2} d^{3} n^{3}-178 A \,b^{2} c \,d^{4} n^{2} x +508 A \,b^{2} d^{5} n \,x^{2}-18 B \,a^{2} c \,d^{4} n^{3}+461 B \,a^{2} d^{5} n^{2} x +4 B a b \,c^{2} d^{3} n^{3}-356 B a b c \,d^{4} n^{2} x +1016 B a b \,d^{5} n \,x^{2}+72 B \,b^{2} c^{2} d^{3} n^{2} x -336 B \,b^{2} c \,d^{4} n \,x^{2}+180 B \,b^{2} d^{5} x^{3}+2 C \,a^{2} c^{2} d^{3} n^{3}-178 C \,a^{2} c \,d^{4} n^{2} x +508 C \,a^{2} d^{5} n \,x^{2}+144 C a b \,c^{2} d^{3} n^{2} x -672 C a b c \,d^{4} n \,x^{2}+360 C a b \,d^{5} x^{3}-24 C \,b^{2} c^{3} d^{2} n^{2} x +240 C \,b^{2} c^{2} d^{3} n \,x^{2}-144 C \,b^{2} c \,d^{4} x^{3}+72 D a^{2} c^{2} d^{3} n^{2} x -336 D a^{2} c \,d^{4} n \,x^{2}+180 D a^{2} d^{5} x^{3}-48 D a b \,c^{3} d^{2} n^{2} x +480 D a b \,c^{2} d^{3} n \,x^{2}-288 D a b c \,d^{4} x^{3}-180 D b^{2} c^{3} d^{2} n \,x^{2}+120 D b^{2} c^{2} d^{3} x^{3}+580 A \,a^{2} d^{5} n^{2}-238 A a b c \,d^{4} n^{2}+1404 A a b \,d^{5} n x +30 A \,b^{2} c^{2} d^{3} n^{2}-388 A \,b^{2} c \,d^{4} n x +240 A \,b^{2} d^{5} x^{2}-119 B \,a^{2} c \,d^{4} n^{2}+702 B \,a^{2} d^{5} n x +60 B a b \,c^{2} d^{3} n^{2}-776 B a b c \,d^{4} n x +480 B a b \,d^{5} x^{2}-6 B \,b^{2} c^{3} d^{2} n^{2}+246 B \,b^{2} c^{2} d^{3} n x -180 B \,b^{2} c \,d^{4} x^{2}+30 C \,a^{2} c^{2} d^{3} n^{2}-388 C \,a^{2} c \,d^{4} n x +240 C \,a^{2} d^{5} x^{2}-12 C a b \,c^{3} d^{2} n^{2}+492 C a b \,c^{2} d^{3} n x -360 C a b c \,d^{4} x^{2}-168 C \,b^{2} c^{3} d^{2} n x +144 C \,b^{2} c^{2} d^{3} x^{2}-6 D a^{2} c^{3} d^{2} n^{2}+246 D a^{2} c^{2} d^{3} n x -180 D a^{2} c \,d^{4} x^{2}-336 D a b \,c^{3} d^{2} n x +288 D a b \,c^{2} d^{3} x^{2}+120 D b^{2} c^{4} d n x -120 D b^{2} c^{3} d^{2} x^{2}+1044 A \,a^{2} d^{5} n -684 A a b c \,d^{4} n +720 A a b \,d^{5} x +148 A \,b^{2} c^{2} d^{3} n -240 A \,b^{2} c \,d^{4} x -342 B \,a^{2} c \,d^{4} n +360 B \,a^{2} d^{5} x +296 B a b \,c^{2} d^{3} n -480 B a b c \,d^{4} x -66 B \,b^{2} c^{3} d^{2} n +180 B \,b^{2} c^{2} d^{3} x +148 C \,a^{2} c^{2} d^{3} n -240 C \,a^{2} c \,d^{4} x -132 C a b \,c^{3} d^{2} n +360 C a b \,c^{2} d^{3} x +24 C \,b^{2} c^{4} d n -144 C \,b^{2} c^{3} d^{2} x -66 D a^{2} c^{3} d^{2} n +180 D a^{2} c^{2} d^{3} x +48 D a b \,c^{4} d n -288 D a b \,c^{3} d^{2} x +120 D b^{2} c^{4} d x +720 a^{2} A \,d^{5}-720 A a b c \,d^{4}+240 A \,b^{2} c^{2} d^{3}-360 B \,a^{2} c \,d^{4}+480 B a b \,c^{2} d^{3}-180 B \,b^{2} c^{3} d^{2}+240 C \,a^{2} c^{2} d^{3}-360 C a b \,c^{3} d^{2}+144 C \,b^{2} c^{4} d -180 D a^{2} c^{3} d^{2}+288 D a b \,c^{4} d -120 D b^{2} c^{5}\right) \left(d x +c \right)^{n +1}}{\left(n^{6}+21 n^{5}+175 n^{4}+735 n^{3}+1624 n^{2}+1764 n +720\right) d^{6}}"," ",0,"(d*x+c)^(n+1)*(D*b^2*d^5*n^5*x^5+C*b^2*d^5*n^5*x^4+2*D*a*b*d^5*n^5*x^4+15*D*b^2*d^5*n^4*x^5+B*b^2*d^5*n^5*x^3+2*C*a*b*d^5*n^5*x^3+16*C*b^2*d^5*n^4*x^4+D*a^2*d^5*n^5*x^3+32*D*a*b*d^5*n^4*x^4-5*D*b^2*c*d^4*n^4*x^4+85*D*b^2*d^5*n^3*x^5+A*b^2*d^5*n^5*x^2+2*B*a*b*d^5*n^5*x^2+17*B*b^2*d^5*n^4*x^3+C*a^2*d^5*n^5*x^2+34*C*a*b*d^5*n^4*x^3-4*C*b^2*c*d^4*n^4*x^3+95*C*b^2*d^5*n^3*x^4+17*D*a^2*d^5*n^4*x^3-8*D*a*b*c*d^4*n^4*x^3+190*D*a*b*d^5*n^3*x^4-50*D*b^2*c*d^4*n^3*x^4+225*D*b^2*d^5*n^2*x^5+2*A*a*b*d^5*n^5*x+18*A*b^2*d^5*n^4*x^2+B*a^2*d^5*n^5*x+36*B*a*b*d^5*n^4*x^2-3*B*b^2*c*d^4*n^4*x^2+107*B*b^2*d^5*n^3*x^3+18*C*a^2*d^5*n^4*x^2-6*C*a*b*c*d^4*n^4*x^2+214*C*a*b*d^5*n^3*x^3-48*C*b^2*c*d^4*n^3*x^3+260*C*b^2*d^5*n^2*x^4-3*D*a^2*c*d^4*n^4*x^2+107*D*a^2*d^5*n^3*x^3-96*D*a*b*c*d^4*n^3*x^3+520*D*a*b*d^5*n^2*x^4+20*D*b^2*c^2*d^3*n^3*x^3-175*D*b^2*c*d^4*n^2*x^4+274*D*b^2*d^5*n*x^5+A*a^2*d^5*n^5+38*A*a*b*d^5*n^4*x-2*A*b^2*c*d^4*n^4*x+121*A*b^2*d^5*n^3*x^2+19*B*a^2*d^5*n^4*x-4*B*a*b*c*d^4*n^4*x+242*B*a*b*d^5*n^3*x^2-42*B*b^2*c*d^4*n^3*x^2+307*B*b^2*d^5*n^2*x^3-2*C*a^2*c*d^4*n^4*x+121*C*a^2*d^5*n^3*x^2-84*C*a*b*c*d^4*n^3*x^2+614*C*a*b*d^5*n^2*x^3+12*C*b^2*c^2*d^3*n^3*x^2-188*C*b^2*c*d^4*n^2*x^3+324*C*b^2*d^5*n*x^4-42*D*a^2*c*d^4*n^3*x^2+307*D*a^2*d^5*n^2*x^3+24*D*a*b*c^2*d^3*n^3*x^2-376*D*a*b*c*d^4*n^2*x^3+648*D*a*b*d^5*n*x^4+120*D*b^2*c^2*d^3*n^2*x^3-250*D*b^2*c*d^4*n*x^4+120*D*b^2*d^5*x^5+20*A*a^2*d^5*n^4-2*A*a*b*c*d^4*n^4+274*A*a*b*d^5*n^3*x-32*A*b^2*c*d^4*n^3*x+372*A*b^2*d^5*n^2*x^2-B*a^2*c*d^4*n^4+137*B*a^2*d^5*n^3*x-64*B*a*b*c*d^4*n^3*x+744*B*a*b*d^5*n^2*x^2+6*B*b^2*c^2*d^3*n^3*x-195*B*b^2*c*d^4*n^2*x^2+396*B*b^2*d^5*n*x^3-32*C*a^2*c*d^4*n^3*x+372*C*a^2*d^5*n^2*x^2+12*C*a*b*c^2*d^3*n^3*x-390*C*a*b*c*d^4*n^2*x^2+792*C*a*b*d^5*n*x^3+108*C*b^2*c^2*d^3*n^2*x^2-288*C*b^2*c*d^4*n*x^3+144*C*b^2*d^5*x^4+6*D*a^2*c^2*d^3*n^3*x-195*D*a^2*c*d^4*n^2*x^2+396*D*a^2*d^5*n*x^3+216*D*a*b*c^2*d^3*n^2*x^2-576*D*a*b*c*d^4*n*x^3+288*D*a*b*d^5*x^4-60*D*b^2*c^3*d^2*n^2*x^2+220*D*b^2*c^2*d^3*n*x^3-120*D*b^2*c*d^4*x^4+155*A*a^2*d^5*n^3-36*A*a*b*c*d^4*n^3+922*A*a*b*d^5*n^2*x+2*A*b^2*c^2*d^3*n^3-178*A*b^2*c*d^4*n^2*x+508*A*b^2*d^5*n*x^2-18*B*a^2*c*d^4*n^3+461*B*a^2*d^5*n^2*x+4*B*a*b*c^2*d^3*n^3-356*B*a*b*c*d^4*n^2*x+1016*B*a*b*d^5*n*x^2+72*B*b^2*c^2*d^3*n^2*x-336*B*b^2*c*d^4*n*x^2+180*B*b^2*d^5*x^3+2*C*a^2*c^2*d^3*n^3-178*C*a^2*c*d^4*n^2*x+508*C*a^2*d^5*n*x^2+144*C*a*b*c^2*d^3*n^2*x-672*C*a*b*c*d^4*n*x^2+360*C*a*b*d^5*x^3-24*C*b^2*c^3*d^2*n^2*x+240*C*b^2*c^2*d^3*n*x^2-144*C*b^2*c*d^4*x^3+72*D*a^2*c^2*d^3*n^2*x-336*D*a^2*c*d^4*n*x^2+180*D*a^2*d^5*x^3-48*D*a*b*c^3*d^2*n^2*x+480*D*a*b*c^2*d^3*n*x^2-288*D*a*b*c*d^4*x^3-180*D*b^2*c^3*d^2*n*x^2+120*D*b^2*c^2*d^3*x^3+580*A*a^2*d^5*n^2-238*A*a*b*c*d^4*n^2+1404*A*a*b*d^5*n*x+30*A*b^2*c^2*d^3*n^2-388*A*b^2*c*d^4*n*x+240*A*b^2*d^5*x^2-119*B*a^2*c*d^4*n^2+702*B*a^2*d^5*n*x+60*B*a*b*c^2*d^3*n^2-776*B*a*b*c*d^4*n*x+480*B*a*b*d^5*x^2-6*B*b^2*c^3*d^2*n^2+246*B*b^2*c^2*d^3*n*x-180*B*b^2*c*d^4*x^2+30*C*a^2*c^2*d^3*n^2-388*C*a^2*c*d^4*n*x+240*C*a^2*d^5*x^2-12*C*a*b*c^3*d^2*n^2+492*C*a*b*c^2*d^3*n*x-360*C*a*b*c*d^4*x^2-168*C*b^2*c^3*d^2*n*x+144*C*b^2*c^2*d^3*x^2-6*D*a^2*c^3*d^2*n^2+246*D*a^2*c^2*d^3*n*x-180*D*a^2*c*d^4*x^2-336*D*a*b*c^3*d^2*n*x+288*D*a*b*c^2*d^3*x^2+120*D*b^2*c^4*d*n*x-120*D*b^2*c^3*d^2*x^2+1044*A*a^2*d^5*n-684*A*a*b*c*d^4*n+720*A*a*b*d^5*x+148*A*b^2*c^2*d^3*n-240*A*b^2*c*d^4*x-342*B*a^2*c*d^4*n+360*B*a^2*d^5*x+296*B*a*b*c^2*d^3*n-480*B*a*b*c*d^4*x-66*B*b^2*c^3*d^2*n+180*B*b^2*c^2*d^3*x+148*C*a^2*c^2*d^3*n-240*C*a^2*c*d^4*x-132*C*a*b*c^3*d^2*n+360*C*a*b*c^2*d^3*x+24*C*b^2*c^4*d*n-144*C*b^2*c^3*d^2*x-66*D*a^2*c^3*d^2*n+180*D*a^2*c^2*d^3*x+48*D*a*b*c^4*d*n-288*D*a*b*c^3*d^2*x+120*D*b^2*c^4*d*x+720*A*a^2*d^5-720*A*a*b*c*d^4+240*A*b^2*c^2*d^3-360*B*a^2*c*d^4+480*B*a*b*c^2*d^3-180*B*b^2*c^3*d^2+240*C*a^2*c^2*d^3-360*C*a*b*c^3*d^2+144*C*b^2*c^4*d-180*D*a^2*c^3*d^2+288*D*a*b*c^4*d-120*D*b^2*c^5)/d^6/(n^6+21*n^5+175*n^4+735*n^3+1624*n^2+1764*n+720)","B"
27,1,1039,226,0.012000," ","int((b*x+a)*(d*x+c)^n*(D*x^3+C*x^2+B*x+A),x)","\frac{\left(D b \,d^{4} n^{4} x^{4}+C b \,d^{4} n^{4} x^{3}+D a \,d^{4} n^{4} x^{3}+10 D b \,d^{4} n^{3} x^{4}+B b \,d^{4} n^{4} x^{2}+C a \,d^{4} n^{4} x^{2}+11 C b \,d^{4} n^{3} x^{3}+11 D a \,d^{4} n^{3} x^{3}-4 D b c \,d^{3} n^{3} x^{3}+35 D b \,d^{4} n^{2} x^{4}+A b \,d^{4} n^{4} x +B a \,d^{4} n^{4} x +12 B b \,d^{4} n^{3} x^{2}+12 C a \,d^{4} n^{3} x^{2}-3 C b c \,d^{3} n^{3} x^{2}+41 C b \,d^{4} n^{2} x^{3}-3 D a c \,d^{3} n^{3} x^{2}+41 D a \,d^{4} n^{2} x^{3}-24 D b c \,d^{3} n^{2} x^{3}+50 D b \,d^{4} n \,x^{4}+A a \,d^{4} n^{4}+13 A b \,d^{4} n^{3} x +13 B a \,d^{4} n^{3} x -2 B b c \,d^{3} n^{3} x +49 B b \,d^{4} n^{2} x^{2}-2 C a c \,d^{3} n^{3} x +49 C a \,d^{4} n^{2} x^{2}-24 C b c \,d^{3} n^{2} x^{2}+61 C b \,d^{4} n \,x^{3}-24 D a c \,d^{3} n^{2} x^{2}+61 D a \,d^{4} n \,x^{3}+12 D b \,c^{2} d^{2} n^{2} x^{2}-44 D b c \,d^{3} n \,x^{3}+24 D b \,x^{4} d^{4}+14 A a \,d^{4} n^{3}-A b c \,d^{3} n^{3}+59 A b \,d^{4} n^{2} x -B a c \,d^{3} n^{3}+59 B a \,d^{4} n^{2} x -20 B b c \,d^{3} n^{2} x +78 B b \,d^{4} n \,x^{2}-20 C a c \,d^{3} n^{2} x +78 C a \,d^{4} n \,x^{2}+6 C b \,c^{2} d^{2} n^{2} x -51 C b c \,d^{3} n \,x^{2}+30 C b \,d^{4} x^{3}+6 D a \,c^{2} d^{2} n^{2} x -51 D a c \,d^{3} n \,x^{2}+30 D a \,d^{4} x^{3}+36 D b \,c^{2} d^{2} n \,x^{2}-24 D b c \,d^{3} x^{3}+71 A a \,d^{4} n^{2}-12 A b c \,d^{3} n^{2}+107 A b \,d^{4} n x -12 B a c \,d^{3} n^{2}+107 B a \,d^{4} n x +2 B b \,c^{2} d^{2} n^{2}-58 B b c \,d^{3} n x +40 B b \,d^{4} x^{2}+2 C a \,c^{2} d^{2} n^{2}-58 C a c \,d^{3} n x +40 C a \,d^{4} x^{2}+36 C b \,c^{2} d^{2} n x -30 C b c \,d^{3} x^{2}+36 D a \,c^{2} d^{2} n x -30 D a c \,d^{3} x^{2}-24 D b \,c^{3} d n x +24 D b \,c^{2} d^{2} x^{2}+154 A a \,d^{4} n -47 A b c \,d^{3} n +60 A b \,d^{4} x -47 B a c \,d^{3} n +60 B a \,d^{4} x +18 B b \,c^{2} d^{2} n -40 B b c \,d^{3} x +18 C a \,c^{2} d^{2} n -40 C a c \,d^{3} x -6 C b \,c^{3} d n +30 C b \,c^{2} d^{2} x -6 D a \,c^{3} d n +30 D a \,c^{2} d^{2} x -24 D b \,c^{3} d x +120 A a \,d^{4}-60 A b c \,d^{3}-60 B a c \,d^{3}+40 B b \,c^{2} d^{2}+40 C a \,c^{2} d^{2}-30 C b \,c^{3} d -30 D a \,c^{3} d +24 D b \,c^{4}\right) \left(d x +c \right)^{n +1}}{\left(n^{5}+15 n^{4}+85 n^{3}+225 n^{2}+274 n +120\right) d^{5}}"," ",0,"(d*x+c)^(n+1)*(D*b*d^4*n^4*x^4+C*b*d^4*n^4*x^3+D*a*d^4*n^4*x^3+10*D*b*d^4*n^3*x^4+B*b*d^4*n^4*x^2+C*a*d^4*n^4*x^2+11*C*b*d^4*n^3*x^3+11*D*a*d^4*n^3*x^3-4*D*b*c*d^3*n^3*x^3+35*D*b*d^4*n^2*x^4+A*b*d^4*n^4*x+B*a*d^4*n^4*x+12*B*b*d^4*n^3*x^2+12*C*a*d^4*n^3*x^2-3*C*b*c*d^3*n^3*x^2+41*C*b*d^4*n^2*x^3-3*D*a*c*d^3*n^3*x^2+41*D*a*d^4*n^2*x^3-24*D*b*c*d^3*n^2*x^3+50*D*b*d^4*n*x^4+A*a*d^4*n^4+13*A*b*d^4*n^3*x+13*B*a*d^4*n^3*x-2*B*b*c*d^3*n^3*x+49*B*b*d^4*n^2*x^2-2*C*a*c*d^3*n^3*x+49*C*a*d^4*n^2*x^2-24*C*b*c*d^3*n^2*x^2+61*C*b*d^4*n*x^3-24*D*a*c*d^3*n^2*x^2+61*D*a*d^4*n*x^3+12*D*b*c^2*d^2*n^2*x^2-44*D*b*c*d^3*n*x^3+24*D*b*d^4*x^4+14*A*a*d^4*n^3-A*b*c*d^3*n^3+59*A*b*d^4*n^2*x-B*a*c*d^3*n^3+59*B*a*d^4*n^2*x-20*B*b*c*d^3*n^2*x+78*B*b*d^4*n*x^2-20*C*a*c*d^3*n^2*x+78*C*a*d^4*n*x^2+6*C*b*c^2*d^2*n^2*x-51*C*b*c*d^3*n*x^2+30*C*b*d^4*x^3+6*D*a*c^2*d^2*n^2*x-51*D*a*c*d^3*n*x^2+30*D*a*d^4*x^3+36*D*b*c^2*d^2*n*x^2-24*D*b*c*d^3*x^3+71*A*a*d^4*n^2-12*A*b*c*d^3*n^2+107*A*b*d^4*n*x-12*B*a*c*d^3*n^2+107*B*a*d^4*n*x+2*B*b*c^2*d^2*n^2-58*B*b*c*d^3*n*x+40*B*b*d^4*x^2+2*C*a*c^2*d^2*n^2-58*C*a*c*d^3*n*x+40*C*a*d^4*x^2+36*C*b*c^2*d^2*n*x-30*C*b*c*d^3*x^2+36*D*a*c^2*d^2*n*x-30*D*a*c*d^3*x^2-24*D*b*c^3*d*n*x+24*D*b*c^2*d^2*x^2+154*A*a*d^4*n-47*A*b*c*d^3*n+60*A*b*d^4*x-47*B*a*c*d^3*n+60*B*a*d^4*x+18*B*b*c^2*d^2*n-40*B*b*c*d^3*x+18*C*a*c^2*d^2*n-40*C*a*c*d^3*x-6*C*b*c^3*d*n+30*C*b*c^2*d^2*x-6*D*a*c^3*d*n+30*D*a*c^2*d^2*x-24*D*b*c^3*d*x+120*A*a*d^4-60*A*b*c*d^3-60*B*a*c*d^3+40*B*b*c^2*d^2+40*C*a*c^2*d^2-30*C*b*c^3*d-30*D*a*c^3*d+24*D*b*c^4)/d^5/(n^5+15*n^4+85*n^3+225*n^2+274*n+120)","B"
28,1,308,126,0.008000," ","int((d*x+c)^n*(D*x^3+C*x^2+B*x+A),x)","\frac{\left(D d^{3} n^{3} x^{3}+C \,d^{3} n^{3} x^{2}+6 D d^{3} n^{2} x^{3}+B \,d^{3} n^{3} x +7 C \,d^{3} n^{2} x^{2}-3 D c \,d^{2} n^{2} x^{2}+11 D d^{3} n \,x^{3}+A \,d^{3} n^{3}+8 B \,d^{3} n^{2} x -2 C c \,d^{2} n^{2} x +14 C \,d^{3} n \,x^{2}-9 D c \,d^{2} n \,x^{2}+6 D x^{3} d^{3}+9 A \,d^{3} n^{2}-B c \,d^{2} n^{2}+19 B \,d^{3} n x -10 C c \,d^{2} n x +8 C \,d^{3} x^{2}+6 D c^{2} d n x -6 D c \,d^{2} x^{2}+26 A \,d^{3} n -7 B c \,d^{2} n +12 B \,d^{3} x +2 C \,c^{2} d n -8 C c \,d^{2} x +6 D c^{2} d x +24 A \,d^{3}-12 B c \,d^{2}+8 C \,c^{2} d -6 D c^{3}\right) \left(d x +c \right)^{n +1}}{\left(n^{4}+10 n^{3}+35 n^{2}+50 n +24\right) d^{4}}"," ",0,"(d*x+c)^(n+1)*(D*d^3*n^3*x^3+C*d^3*n^3*x^2+6*D*d^3*n^2*x^3+B*d^3*n^3*x+7*C*d^3*n^2*x^2-3*D*c*d^2*n^2*x^2+11*D*d^3*n*x^3+A*d^3*n^3+8*B*d^3*n^2*x-2*C*c*d^2*n^2*x+14*C*d^3*n*x^2-9*D*c*d^2*n*x^2+6*D*d^3*x^3+9*A*d^3*n^2-B*c*d^2*n^2+19*B*d^3*n*x-10*C*c*d^2*n*x+8*C*d^3*x^2+6*D*c^2*d*n*x-6*D*c*d^2*x^2+26*A*d^3*n-7*B*c*d^2*n+12*B*d^3*x+2*C*c^2*d*n-8*C*c*d^2*x+6*D*c^2*d*x+24*A*d^3-12*B*c*d^2+8*C*c^2*d-6*D*c^3)/d^4/(n^4+10*n^3+35*n^2+50*n+24)","B"
29,0,0,205,0.244000," ","int((d*x+c)^n*(D*x^3+C*x^2+B*x+A)/(b*x+a),x)","\int \frac{\left(D x^{3}+C \,x^{2}+B x +A \right) \left(d x +c \right)^{n}}{b x +a}\, dx"," ",0,"int((d*x+c)^n*(D*x^3+C*x^2+B*x+A)/(b*x+a),x)","F"
30,0,0,222,0.242000," ","int((d*x+c)^n*(D*x^3+C*x^2+B*x+A)/(b*x+a)^2,x)","\int \frac{\left(D x^{3}+C \,x^{2}+B x +A \right) \left(d x +c \right)^{n}}{\left(b x +a \right)^{2}}\, dx"," ",0,"int((d*x+c)^n*(D*x^3+C*x^2+B*x+A)/(b*x+a)^2,x)","F"
31,0,0,325,0.243000," ","int((d*x+c)^n*(D*x^3+C*x^2+B*x+A)/(b*x+a)^3,x)","\int \frac{\left(D x^{3}+C \,x^{2}+B x +A \right) \left(d x +c \right)^{n}}{\left(b x +a \right)^{3}}\, dx"," ",0,"int((d*x+c)^n*(D*x^3+C*x^2+B*x+A)/(b*x+a)^3,x)","F"
32,0,0,143,0.243000," ","int((b*x+a)^m*(B*x+A)*(d*x+c)^n,x)","\int \left(B x +A \right) \left(b x +a \right)^{m} \left(d x +c \right)^{n}\, dx"," ",0,"int((b*x+a)^m*(B*x+A)*(d*x+c)^n,x)","F"
33,0,0,270,0.245000," ","int((b*x+a)^m*(d*x+c)^n*(C*x^2+B*x+A),x)","\int \left(C \,x^{2}+B x +A \right) \left(b x +a \right)^{m} \left(d x +c \right)^{n}\, dx"," ",0,"int((b*x+a)^m*(d*x+c)^n*(C*x^2+B*x+A),x)","F"
34,0,0,608,0.256000," ","int((b*x+a)^m*(d*x+c)^n*(D*x^3+C*x^2+B*x+A),x)","\int \left(D x^{3}+C \,x^{2}+B x +A \right) \left(b x +a \right)^{m} \left(d x +c \right)^{n}\, dx"," ",0,"int((b*x+a)^m*(d*x+c)^n*(D*x^3+C*x^2+B*x+A),x)","F"