1,1,72,0,1.269954," ","integrate(x^4*log(c*(b*x^2+a)^p),x, algorithm=""maxima"")","\frac{1}{5} \, x^{5} \log\left({\left(b x^{2} + a\right)}^{p} c\right) + \frac{2}{75} \, b p {\left(\frac{15 \, a^{3} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{3}} - \frac{3 \, b^{2} x^{5} - 5 \, a b x^{3} + 15 \, a^{2} x}{b^{3}}\right)}"," ",0,"1/5*x^5*log((b*x^2 + a)^p*c) + 2/75*b*p*(15*a^3*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) - (3*b^2*x^5 - 5*a*b*x^3 + 15*a^2*x)/b^3)","A",0
2,1,55,0,0.559596," ","integrate(x^3*log(c*(b*x^2+a)^p),x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \log\left({\left(b x^{2} + a\right)}^{p} c\right) - \frac{1}{8} \, b p {\left(\frac{2 \, a^{2} \log\left(b x^{2} + a\right)}{b^{3}} + \frac{b x^{4} - 2 \, a x^{2}}{b^{2}}\right)}"," ",0,"1/4*x^4*log((b*x^2 + a)^p*c) - 1/8*b*p*(2*a^2*log(b*x^2 + a)/b^3 + (b*x^4 - 2*a*x^2)/b^2)","A",0
3,1,59,0,1.572629," ","integrate(x^2*log(c*(b*x^2+a)^p),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \log\left({\left(b x^{2} + a\right)}^{p} c\right) - \frac{2}{9} \, b p {\left(\frac{3 \, a^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{2}} + \frac{b x^{3} - 3 \, a x}{b^{2}}\right)}"," ",0,"1/3*x^3*log((b*x^2 + a)^p*c) - 2/9*b*p*(3*a^2*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^2) + (b*x^3 - 3*a*x)/b^2)","A",0
4,1,44,0,0.645446," ","integrate(x*log(c*(b*x^2+a)^p),x, algorithm=""maxima"")","-\frac{1}{2} \, b p {\left(\frac{x^{2}}{b} - \frac{a \log\left(b x^{2} + a\right)}{b^{2}}\right)} + \frac{1}{2} \, x^{2} \log\left({\left(b x^{2} + a\right)}^{p} c\right)"," ",0,"-1/2*b*p*(x^2/b - a*log(b*x^2 + a)/b^2) + 1/2*x^2*log((b*x^2 + a)^p*c)","A",0
5,1,45,0,1.417106," ","integrate(log(c*(b*x^2+a)^p),x, algorithm=""maxima"")","2 \, b p {\left(\frac{a \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b} - \frac{x}{b}\right)} + x \log\left({\left(b x^{2} + a\right)}^{p} c\right)"," ",0,"2*b*p*(a*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b) - x/b) + x*log((b*x^2 + a)^p*c)","A",0
6,1,80,0,0.703748," ","integrate(log(c*(b*x^2+a)^p)/x,x, algorithm=""maxima"")","\frac{1}{2} \, b p {\left(\frac{2 \, \log\left(b x^{2} + a\right) \log\left(x\right)}{b} - \frac{2 \, \log\left(\frac{b x^{2}}{a} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{b x^{2}}{a}\right)}{b}\right)} - p \log\left(b x^{2} + a\right) \log\left(x\right) + \log\left({\left(b x^{2} + a\right)}^{p} c\right) \log\left(x\right)"," ",0,"1/2*b*p*(2*log(b*x^2 + a)*log(x)/b - (2*log(b*x^2/a + 1)*log(x) + dilog(-b*x^2/a))/b) - p*log(b*x^2 + a)*log(x) + log((b*x^2 + a)^p*c)*log(x)","B",0
7,1,36,0,1.548429," ","integrate(log(c*(b*x^2+a)^p)/x^2,x, algorithm=""maxima"")","\frac{2 \, b p \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}} - \frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)}{x}"," ",0,"2*b*p*arctan(b*x/sqrt(a*b))/sqrt(a*b) - log((b*x^2 + a)^p*c)/x","A",0
8,1,44,0,0.649012," ","integrate(log(c*(b*x^2+a)^p)/x^3,x, algorithm=""maxima"")","-\frac{1}{2} \, b p {\left(\frac{\log\left(b x^{2} + a\right)}{a} - \frac{\log\left(x^{2}\right)}{a}\right)} - \frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)}{2 \, x^{2}}"," ",0,"-1/2*b*p*(log(b*x^2 + a)/a - log(x^2)/a) - 1/2*log((b*x^2 + a)^p*c)/x^2","A",0
9,1,49,0,1.420866," ","integrate(log(c*(b*x^2+a)^p)/x^4,x, algorithm=""maxima"")","-\frac{2}{3} \, b p {\left(\frac{b \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a} + \frac{1}{a x}\right)} - \frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)}{3 \, x^{3}}"," ",0,"-2/3*b*p*(b*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a) + 1/(a*x)) - 1/3*log((b*x^2 + a)^p*c)/x^3","A",0
10,1,54,0,0.790700," ","integrate(log(c*(b*x^2+a)^p)/x^5,x, algorithm=""maxima"")","\frac{1}{4} \, b p {\left(\frac{b \log\left(b x^{2} + a\right)}{a^{2}} - \frac{b \log\left(x^{2}\right)}{a^{2}} - \frac{1}{a x^{2}}\right)} - \frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)}{4 \, x^{4}}"," ",0,"1/4*b*p*(b*log(b*x^2 + a)/a^2 - b*log(x^2)/a^2 - 1/(a*x^2)) - 1/4*log((b*x^2 + a)^p*c)/x^4","A",0
11,1,62,0,1.530919," ","integrate(log(c*(b*x^2+a)^p)/x^6,x, algorithm=""maxima"")","\frac{2}{15} \, b p {\left(\frac{3 \, b^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} a^{2}} + \frac{3 \, b x^{2} - a}{a^{2} x^{3}}\right)} - \frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)}{5 \, x^{5}}"," ",0,"2/15*b*p*(3*b^2*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2) + (3*b*x^2 - a)/(a^2*x^3)) - 1/5*log((b*x^2 + a)^p*c)/x^5","A",0
12,1,69,0,0.683574," ","integrate(log(c*(b*x^2+a)^p)/x^7,x, algorithm=""maxima"")","-\frac{1}{12} \, b p {\left(\frac{2 \, b^{2} \log\left(b x^{2} + a\right)}{a^{3}} - \frac{2 \, b^{2} \log\left(x^{2}\right)}{a^{3}} - \frac{2 \, b x^{2} - a}{a^{2} x^{4}}\right)} - \frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)}{6 \, x^{6}}"," ",0,"-1/12*b*p*(2*b^2*log(b*x^2 + a)/a^3 - 2*b^2*log(x^2)/a^3 - (2*b*x^2 - a)/(a^2*x^4)) - 1/6*log((b*x^2 + a)^p*c)/x^6","A",0
13,1,55,0,0.624969," ","integrate(x^5*log(c*(b*x^3+a)^p),x, algorithm=""maxima"")","\frac{1}{6} \, x^{6} \log\left({\left(b x^{3} + a\right)}^{p} c\right) - \frac{1}{12} \, b p {\left(\frac{2 \, a^{2} \log\left(b x^{3} + a\right)}{b^{3}} + \frac{b x^{6} - 2 \, a x^{3}}{b^{2}}\right)}"," ",0,"1/6*x^6*log((b*x^3 + a)^p*c) - 1/12*b*p*(2*a^2*log(b*x^3 + a)/b^3 + (b*x^6 - 2*a*x^3)/b^2)","A",0
14,1,147,0,1.484144," ","integrate(x^4*log(c*(b*x^3+a)^p),x, algorithm=""maxima"")","\frac{1}{5} \, x^{5} \log\left({\left(b x^{3} + a\right)}^{p} c\right) - \frac{1}{50} \, b p {\left(\frac{10 \, \sqrt{3} a^{2} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{b^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{5 \, a^{2} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{b^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{10 \, a^{2} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{b^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{3 \, {\left(2 \, b x^{5} - 5 \, a x^{2}\right)}}{b^{2}}\right)}"," ",0,"1/5*x^5*log((b*x^3 + a)^p*c) - 1/50*b*p*(10*sqrt(3)*a^2*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^3*(a/b)^(1/3)) + 5*a^2*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^3*(a/b)^(1/3)) - 10*a^2*log(x + (a/b)^(1/3))/(b^3*(a/b)^(1/3)) + 3*(2*b*x^5 - 5*a*x^2)/b^2)","A",0
15,1,144,0,1.452074," ","integrate(x^3*log(c*(b*x^3+a)^p),x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \log\left({\left(b x^{3} + a\right)}^{p} c\right) - \frac{1}{16} \, b p {\left(\frac{4 \, \sqrt{3} a^{2} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{2 \, a^{2} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{4 \, a^{2} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{3 \, {\left(b x^{4} - 4 \, a x\right)}}{b^{2}}\right)}"," ",0,"1/4*x^4*log((b*x^3 + a)^p*c) - 1/16*b*p*(4*sqrt(3)*a^2*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^3*(a/b)^(2/3)) - 2*a^2*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^3*(a/b)^(2/3)) + 4*a^2*log(x + (a/b)^(1/3))/(b^3*(a/b)^(2/3)) + 3*(b*x^4 - 4*a*x)/b^2)","A",0
16,1,44,0,0.506217," ","integrate(x^2*log(c*(b*x^3+a)^p),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \log\left({\left(b x^{3} + a\right)}^{p} c\right) - \frac{1}{3} \, {\left(\frac{x^{3}}{b} - \frac{a \log\left(b x^{3} + a\right)}{b^{2}}\right)} b p"," ",0,"1/3*x^3*log((b*x^3 + a)^p*c) - 1/3*(x^3/b - a*log(b*x^3 + a)/b^2)*b*p","A",0
17,1,131,0,1.329388," ","integrate(x*log(c*(b*x^3+a)^p),x, algorithm=""maxima"")","-\frac{1}{4} \, b p {\left(\frac{3 \, x^{2}}{b} - \frac{2 \, \sqrt{3} a \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{a \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{2 \, a \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)} + \frac{1}{2} \, x^{2} \log\left({\left(b x^{3} + a\right)}^{p} c\right)"," ",0,"-1/4*b*p*(3*x^2/b - 2*sqrt(3)*a*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^2*(a/b)^(1/3)) - a*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^2*(a/b)^(1/3)) + 2*a*log(x + (a/b)^(1/3))/(b^2*(a/b)^(1/3))) + 1/2*x^2*log((b*x^3 + a)^p*c)","A",0
18,1,125,0,1.360551," ","integrate(log(c*(b*x^3+a)^p),x, algorithm=""maxima"")","-\frac{1}{2} \, b p {\left(\frac{6 \, x}{b} - \frac{2 \, \sqrt{3} a \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{a \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{2 \, a \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}\right)} + x \log\left({\left(b x^{3} + a\right)}^{p} c\right)"," ",0,"-1/2*b*p*(6*x/b - 2*sqrt(3)*a*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^2*(a/b)^(2/3)) + a*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^2*(a/b)^(2/3)) - 2*a*log(x + (a/b)^(1/3))/(b^2*(a/b)^(2/3))) + x*log((b*x^3 + a)^p*c)","A",0
19,1,80,0,0.658961," ","integrate(log(c*(b*x^3+a)^p)/x,x, algorithm=""maxima"")","\frac{1}{3} \, b p {\left(\frac{3 \, \log\left(b x^{3} + a\right) \log\left(x\right)}{b} - \frac{3 \, \log\left(\frac{b x^{3}}{a} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{b x^{3}}{a}\right)}{b}\right)} - p \log\left(b x^{3} + a\right) \log\left(x\right) + \log\left({\left(b x^{3} + a\right)}^{p} c\right) \log\left(x\right)"," ",0,"1/3*b*p*(3*log(b*x^3 + a)*log(x)/b - (3*log(b*x^3/a + 1)*log(x) + dilog(-b*x^3/a))/b) - p*log(b*x^3 + a)*log(x) + log((b*x^3 + a)^p*c)*log(x)","B",0
20,1,119,0,1.542400," ","integrate(log(c*(b*x^3+a)^p)/x^2,x, algorithm=""maxima"")","\frac{1}{2} \, b p {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{b \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{\log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{b \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{2 \, \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{b \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)} - \frac{\log\left({\left(b x^{3} + a\right)}^{p} c\right)}{x}"," ",0,"1/2*b*p*(2*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b*(a/b)^(1/3)) + log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b*(a/b)^(1/3)) - 2*log(x + (a/b)^(1/3))/(b*(a/b)^(1/3))) - log((b*x^3 + a)^p*c)/x","A",0
21,1,120,0,1.448459," ","integrate(log(c*(b*x^3+a)^p)/x^3,x, algorithm=""maxima"")","\frac{1}{4} \, b p {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{b \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{\log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{b \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{2 \, \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{b \left(\frac{a}{b}\right)^{\frac{2}{3}}}\right)} - \frac{\log\left({\left(b x^{3} + a\right)}^{p} c\right)}{2 \, x^{2}}"," ",0,"1/4*b*p*(2*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b*(a/b)^(2/3)) - log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b*(a/b)^(2/3)) + 2*log(x + (a/b)^(1/3))/(b*(a/b)^(2/3))) - 1/2*log((b*x^3 + a)^p*c)/x^2","A",0
22,1,44,0,0.636914," ","integrate(log(c*(b*x^3+a)^p)/x^4,x, algorithm=""maxima"")","-\frac{1}{3} \, b p {\left(\frac{\log\left(b x^{3} + a\right)}{a} - \frac{\log\left(x^{3}\right)}{a}\right)} - \frac{\log\left({\left(b x^{3} + a\right)}^{p} c\right)}{3 \, x^{3}}"," ",0,"-1/3*b*p*(log(b*x^3 + a)/a - log(x^3)/a) - 1/3*log((b*x^3 + a)^p*c)/x^3","A",0
23,1,127,0,1.465485," ","integrate(log(c*(b*x^3+a)^p)/x^5,x, algorithm=""maxima"")","-\frac{1}{8} \, b p {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{a \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{\log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{a \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{2 \, \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{a \left(\frac{a}{b}\right)^{\frac{1}{3}}} + \frac{6}{a x}\right)} - \frac{\log\left({\left(b x^{3} + a\right)}^{p} c\right)}{4 \, x^{4}}"," ",0,"-1/8*b*p*(2*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*(a/b)^(1/3)) + log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*(a/b)^(1/3)) - 2*log(x + (a/b)^(1/3))/(a*(a/b)^(1/3)) + 6/(a*x)) - 1/4*log((b*x^3 + a)^p*c)/x^4","A",0
24,1,128,0,1.270955," ","integrate(log(c*(b*x^3+a)^p)/x^6,x, algorithm=""maxima"")","-\frac{1}{10} \, b p {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{a \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{\log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{a \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{2 \, \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{a \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{3}{a x^{2}}\right)} - \frac{\log\left({\left(b x^{3} + a\right)}^{p} c\right)}{5 \, x^{5}}"," ",0,"-1/10*b*p*(2*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*(a/b)^(2/3)) - log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(a*(a/b)^(2/3)) + 2*log(x + (a/b)^(1/3))/(a*(a/b)^(2/3)) + 3/(a*x^2)) - 1/5*log((b*x^3 + a)^p*c)/x^5","A",0
25,1,54,0,0.685096," ","integrate(log(c*(b*x^3+a)^p)/x^7,x, algorithm=""maxima"")","\frac{1}{6} \, b p {\left(\frac{b \log\left(b x^{3} + a\right)}{a^{2}} - \frac{b \log\left(x^{3}\right)}{a^{2}} - \frac{1}{a x^{3}}\right)} - \frac{\log\left({\left(b x^{3} + a\right)}^{p} c\right)}{6 \, x^{6}}"," ",0,"1/6*b*p*(b*log(b*x^3 + a)/a^2 - b*log(x^3)/a^2 - 1/(a*x^3)) - 1/6*log((b*x^3 + a)^p*c)/x^6","A",0
26,1,74,0,0.667684," ","integrate(x^4*log(c*(a+b/x)^p),x, algorithm=""maxima"")","\frac{1}{5} \, x^{5} \log\left({\left(a + \frac{b}{x}\right)}^{p} c\right) + \frac{1}{60} \, b p {\left(\frac{12 \, b^{4} \log\left(a x + b\right)}{a^{5}} + \frac{3 \, a^{3} x^{4} - 4 \, a^{2} b x^{3} + 6 \, a b^{2} x^{2} - 12 \, b^{3} x}{a^{4}}\right)}"," ",0,"1/5*x^5*log((a + b/x)^p*c) + 1/60*b*p*(12*b^4*log(a*x + b)/a^5 + (3*a^3*x^4 - 4*a^2*b*x^3 + 6*a*b^2*x^2 - 12*b^3*x)/a^4)","A",0
27,1,64,0,0.658840," ","integrate(x^3*log(c*(a+b/x)^p),x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \log\left({\left(a + \frac{b}{x}\right)}^{p} c\right) - \frac{1}{24} \, b p {\left(\frac{6 \, b^{3} \log\left(a x + b\right)}{a^{4}} - \frac{2 \, a^{2} x^{3} - 3 \, a b x^{2} + 6 \, b^{2} x}{a^{3}}\right)}"," ",0,"1/4*x^4*log((a + b/x)^p*c) - 1/24*b*p*(6*b^3*log(a*x + b)/a^4 - (2*a^2*x^3 - 3*a*b*x^2 + 6*b^2*x)/a^3)","A",0
28,1,51,0,0.714454," ","integrate(x^2*log(c*(a+b/x)^p),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \log\left({\left(a + \frac{b}{x}\right)}^{p} c\right) + \frac{1}{6} \, b p {\left(\frac{2 \, b^{2} \log\left(a x + b\right)}{a^{3}} + \frac{a x^{2} - 2 \, b x}{a^{2}}\right)}"," ",0,"1/3*x^3*log((a + b/x)^p*c) + 1/6*b*p*(2*b^2*log(a*x + b)/a^3 + (a*x^2 - 2*b*x)/a^2)","A",0
29,1,40,0,0.635753," ","integrate(x*log(c*(a+b/x)^p),x, algorithm=""maxima"")","\frac{1}{2} \, b p {\left(\frac{x}{a} - \frac{b \log\left(a x + b\right)}{a^{2}}\right)} + \frac{1}{2} \, x^{2} \log\left({\left(a + \frac{b}{x}\right)}^{p} c\right)"," ",0,"1/2*b*p*(x/a - b*log(a*x + b)/a^2) + 1/2*x^2*log((a + b/x)^p*c)","A",0
30,1,27,0,0.705122," ","integrate(log(c*(a+b/x)^p),x, algorithm=""maxima"")","x \log\left({\left(a + \frac{b}{x}\right)}^{p} c\right) + \frac{b p \log\left(a x + b\right)}{a}"," ",0,"x*log((a + b/x)^p*c) + b*p*log(a*x + b)/a","A",0
31,1,83,0,0.675007," ","integrate(log(c*(a+b/x)^p)/x,x, algorithm=""maxima"")","\frac{1}{2} \, b p {\left(\frac{2 \, \log\left(a + \frac{b}{x}\right) \log\left(x\right)}{b} + \frac{\log\left(x\right)^{2}}{b} - \frac{2 \, {\left(\log\left(\frac{a x}{b} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{a x}{b}\right)\right)}}{b}\right)} - p \log\left(a + \frac{b}{x}\right) \log\left(x\right) + \log\left({\left(a + \frac{b}{x}\right)}^{p} c\right) \log\left(x\right)"," ",0,"1/2*b*p*(2*log(a + b/x)*log(x)/b + log(x)^2/b - 2*(log(a*x/b + 1)*log(x) + dilog(-a*x/b))/b) - p*log(a + b/x)*log(x) + log((a + b/x)^p*c)*log(x)","B",0
32,1,50,0,0.647326," ","integrate(log(c*(a+b/x)^p)/x^2,x, algorithm=""maxima"")","-b p {\left(\frac{a \log\left(a x + b\right)}{b^{2}} - \frac{a \log\left(x\right)}{b^{2}} - \frac{1}{b x}\right)} - \frac{\log\left({\left(a + \frac{b}{x}\right)}^{p} c\right)}{x}"," ",0,"-b*p*(a*log(a*x + b)/b^2 - a*log(x)/b^2 - 1/(b*x)) - log((a + b/x)^p*c)/x","A",0
33,1,63,0,0.648633," ","integrate(log(c*(a+b/x)^p)/x^3,x, algorithm=""maxima"")","\frac{1}{4} \, b p {\left(\frac{2 \, a^{2} \log\left(a x + b\right)}{b^{3}} - \frac{2 \, a^{2} \log\left(x\right)}{b^{3}} - \frac{2 \, a x - b}{b^{2} x^{2}}\right)} - \frac{\log\left({\left(a + \frac{b}{x}\right)}^{p} c\right)}{2 \, x^{2}}"," ",0,"1/4*b*p*(2*a^2*log(a*x + b)/b^3 - 2*a^2*log(x)/b^3 - (2*a*x - b)/(b^2*x^2)) - 1/2*log((a + b/x)^p*c)/x^2","A",0
34,1,74,0,0.645687," ","integrate(log(c*(a+b/x)^p)/x^4,x, algorithm=""maxima"")","-\frac{1}{18} \, b p {\left(\frac{6 \, a^{3} \log\left(a x + b\right)}{b^{4}} - \frac{6 \, a^{3} \log\left(x\right)}{b^{4}} - \frac{6 \, a^{2} x^{2} - 3 \, a b x + 2 \, b^{2}}{b^{3} x^{3}}\right)} - \frac{\log\left({\left(a + \frac{b}{x}\right)}^{p} c\right)}{3 \, x^{3}}"," ",0,"-1/18*b*p*(6*a^3*log(a*x + b)/b^4 - 6*a^3*log(x)/b^4 - (6*a^2*x^2 - 3*a*b*x + 2*b^2)/(b^3*x^3)) - 1/3*log((a + b/x)^p*c)/x^3","A",0
35,1,85,0,0.695992," ","integrate(log(c*(a+b/x)^p)/x^5,x, algorithm=""maxima"")","\frac{1}{48} \, b p {\left(\frac{12 \, a^{4} \log\left(a x + b\right)}{b^{5}} - \frac{12 \, a^{4} \log\left(x\right)}{b^{5}} - \frac{12 \, a^{3} x^{3} - 6 \, a^{2} b x^{2} + 4 \, a b^{2} x - 3 \, b^{3}}{b^{4} x^{4}}\right)} - \frac{\log\left({\left(a + \frac{b}{x}\right)}^{p} c\right)}{4 \, x^{4}}"," ",0,"1/48*b*p*(12*a^4*log(a*x + b)/b^5 - 12*a^4*log(x)/b^5 - (12*a^3*x^3 - 6*a^2*b*x^2 + 4*a*b^2*x - 3*b^3)/(b^4*x^4)) - 1/4*log((a + b/x)^p*c)/x^4","A",0
36,1,59,0,1.465313," ","integrate(x^4*log(c*(a+b/x^2)^p),x, algorithm=""maxima"")","\frac{1}{5} \, x^{5} \log\left({\left(a + \frac{b}{x^{2}}\right)}^{p} c\right) + \frac{2}{15} \, b p {\left(\frac{3 \, b^{2} \arctan\left(\frac{a x}{\sqrt{a b}}\right)}{\sqrt{a b} a^{2}} + \frac{a x^{3} - 3 \, b x}{a^{2}}\right)}"," ",0,"1/5*x^5*log((a + b/x^2)^p*c) + 2/15*b*p*(3*b^2*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*a^2) + (a*x^3 - 3*b*x)/a^2)","A",0
37,1,44,0,0.516767," ","integrate(x^3*log(c*(a+b/x^2)^p),x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \log\left({\left(a + \frac{b}{x^{2}}\right)}^{p} c\right) + \frac{1}{4} \, b p {\left(\frac{x^{2}}{a} - \frac{b \log\left(a x^{2} + b\right)}{a^{2}}\right)}"," ",0,"1/4*x^4*log((a + b/x^2)^p*c) + 1/4*b*p*(x^2/a - b*log(a*x^2 + b)/a^2)","A",0
38,1,48,0,1.500343," ","integrate(x^2*log(c*(a+b/x^2)^p),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \log\left({\left(a + \frac{b}{x^{2}}\right)}^{p} c\right) - \frac{2}{3} \, b p {\left(\frac{b \arctan\left(\frac{a x}{\sqrt{a b}}\right)}{\sqrt{a b} a} - \frac{x}{a}\right)}"," ",0,"1/3*x^3*log((a + b/x^2)^p*c) - 2/3*b*p*(b*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*a) - x/a)","A",0
39,1,33,0,0.588204," ","integrate(x*log(c*(a+b/x^2)^p),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \log\left({\left(a + \frac{b}{x^{2}}\right)}^{p} c\right) + \frac{b p \log\left(a x^{2} + b\right)}{2 \, a}"," ",0,"1/2*x^2*log((a + b/x^2)^p*c) + 1/2*b*p*log(a*x^2 + b)/a","A",0
40,1,33,0,1.847653," ","integrate(log(c*(a+b/x^2)^p),x, algorithm=""maxima"")","\frac{2 \, b p \arctan\left(\frac{a x}{\sqrt{a b}}\right)}{\sqrt{a b}} + x \log\left({\left(a + \frac{b}{x^{2}}\right)}^{p} c\right)"," ",0,"2*b*p*arctan(a*x/sqrt(a*b))/sqrt(a*b) + x*log((a + b/x^2)^p*c)","A",0
41,1,89,0,0.631989," ","integrate(log(c*(a+b/x^2)^p)/x,x, algorithm=""maxima"")","\frac{1}{2} \, b p {\left(\frac{2 \, \log\left(a + \frac{b}{x^{2}}\right) \log\left(x\right)}{b} + \frac{2 \, \log\left(x\right)^{2}}{b} - \frac{2 \, \log\left(\frac{a x^{2}}{b} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{a x^{2}}{b}\right)}{b}\right)} - p \log\left(a + \frac{b}{x^{2}}\right) \log\left(x\right) + \log\left({\left(a + \frac{b}{x^{2}}\right)}^{p} c\right) \log\left(x\right)"," ",0,"1/2*b*p*(2*log(a + b/x^2)*log(x)/b + 2*log(x)^2/b - (2*log(a*x^2/b + 1)*log(x) + dilog(-a*x^2/b))/b) - p*log(a + b/x^2)*log(x) + log((a + b/x^2)^p*c)*log(x)","B",0
42,1,49,0,1.411115," ","integrate(log(c*(a+b/x^2)^p)/x^2,x, algorithm=""maxima"")","2 \, b p {\left(\frac{a \arctan\left(\frac{a x}{\sqrt{a b}}\right)}{\sqrt{a b} b} + \frac{1}{b x}\right)} - \frac{\log\left({\left(a + \frac{b}{x^{2}}\right)}^{p} c\right)}{x}"," ",0,"2*b*p*(a*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*b) + 1/(b*x)) - log((a + b/x^2)^p*c)/x","A",0
43,1,54,0,0.646864," ","integrate(log(c*(a+b/x^2)^p)/x^3,x, algorithm=""maxima"")","-\frac{1}{2} \, b p {\left(\frac{a \log\left(a x^{2} + b\right)}{b^{2}} - \frac{a \log\left(x^{2}\right)}{b^{2}} - \frac{1}{b x^{2}}\right)} - \frac{\log\left({\left(a + \frac{b}{x^{2}}\right)}^{p} c\right)}{2 \, x^{2}}"," ",0,"-1/2*b*p*(a*log(a*x^2 + b)/b^2 - a*log(x^2)/b^2 - 1/(b*x^2)) - 1/2*log((a + b/x^2)^p*c)/x^2","A",0
44,1,62,0,1.578851," ","integrate(log(c*(a+b/x^2)^p)/x^4,x, algorithm=""maxima"")","-\frac{2}{9} \, b p {\left(\frac{3 \, a^{2} \arctan\left(\frac{a x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{2}} + \frac{3 \, a x^{2} - b}{b^{2} x^{3}}\right)} - \frac{\log\left({\left(a + \frac{b}{x^{2}}\right)}^{p} c\right)}{3 \, x^{3}}"," ",0,"-2/9*b*p*(3*a^2*arctan(a*x/sqrt(a*b))/(sqrt(a*b)*b^2) + (3*a*x^2 - b)/(b^2*x^3)) - 1/3*log((a + b/x^2)^p*c)/x^3","A",0
45,1,35,0,0.707249," ","integrate(log(1+b/x)/x,x, algorithm=""maxima"")","\log\left(b + x\right) \log\left(x\right) - \frac{1}{2} \, \log\left(x\right)^{2} - \log\left(x\right) \log\left(\frac{x}{b} + 1\right) - {\rm Li}_2\left(-\frac{x}{b}\right)"," ",0,"log(b + x)*log(x) - 1/2*log(x)^2 - log(x)*log(x/b + 1) - dilog(-x/b)","B",0
46,1,120,0,0.625375," ","integrate(x^3*log(c*(a+b*x^(1/2))^p),x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \log\left({\left(b \sqrt{x} + a\right)}^{p} c\right) - \frac{1}{3360} \, b p {\left(\frac{840 \, a^{8} \log\left(b \sqrt{x} + a\right)}{b^{9}} + \frac{105 \, b^{7} x^{4} - 120 \, a b^{6} x^{\frac{7}{2}} + 140 \, a^{2} b^{5} x^{3} - 168 \, a^{3} b^{4} x^{\frac{5}{2}} + 210 \, a^{4} b^{3} x^{2} - 280 \, a^{5} b^{2} x^{\frac{3}{2}} + 420 \, a^{6} b x - 840 \, a^{7} \sqrt{x}}{b^{8}}\right)}"," ",0,"1/4*x^4*log((b*sqrt(x) + a)^p*c) - 1/3360*b*p*(840*a^8*log(b*sqrt(x) + a)/b^9 + (105*b^7*x^4 - 120*a*b^6*x^(7/2) + 140*a^2*b^5*x^3 - 168*a^3*b^4*x^(5/2) + 210*a^4*b^3*x^2 - 280*a^5*b^2*x^(3/2) + 420*a^6*b*x - 840*a^7*sqrt(x))/b^8)","A",0
47,1,98,0,0.680004," ","integrate(x^2*log(c*(a+b*x^(1/2))^p),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \log\left({\left(b \sqrt{x} + a\right)}^{p} c\right) - \frac{1}{180} \, b p {\left(\frac{60 \, a^{6} \log\left(b \sqrt{x} + a\right)}{b^{7}} + \frac{10 \, b^{5} x^{3} - 12 \, a b^{4} x^{\frac{5}{2}} + 15 \, a^{2} b^{3} x^{2} - 20 \, a^{3} b^{2} x^{\frac{3}{2}} + 30 \, a^{4} b x - 60 \, a^{5} \sqrt{x}}{b^{6}}\right)}"," ",0,"1/3*x^3*log((b*sqrt(x) + a)^p*c) - 1/180*b*p*(60*a^6*log(b*sqrt(x) + a)/b^7 + (10*b^5*x^3 - 12*a*b^4*x^(5/2) + 15*a^2*b^3*x^2 - 20*a^3*b^2*x^(3/2) + 30*a^4*b*x - 60*a^5*sqrt(x))/b^6)","A",0
48,1,76,0,0.647005," ","integrate(x*log(c*(a+b*x^(1/2))^p),x, algorithm=""maxima"")","-\frac{1}{24} \, b p {\left(\frac{12 \, a^{4} \log\left(b \sqrt{x} + a\right)}{b^{5}} + \frac{3 \, b^{3} x^{2} - 4 \, a b^{2} x^{\frac{3}{2}} + 6 \, a^{2} b x - 12 \, a^{3} \sqrt{x}}{b^{4}}\right)} + \frac{1}{2} \, x^{2} \log\left({\left(b \sqrt{x} + a\right)}^{p} c\right)"," ",0,"-1/24*b*p*(12*a^4*log(b*sqrt(x) + a)/b^5 + (3*b^3*x^2 - 4*a*b^2*x^(3/2) + 6*a^2*b*x - 12*a^3*sqrt(x))/b^4) + 1/2*x^2*log((b*sqrt(x) + a)^p*c)","A",0
49,1,50,0,0.585436," ","integrate(log(c*(a+b*x^(1/2))^p),x, algorithm=""maxima"")","-\frac{1}{2} \, b p {\left(\frac{2 \, a^{2} \log\left(b \sqrt{x} + a\right)}{b^{3}} + \frac{b x - 2 \, a \sqrt{x}}{b^{2}}\right)} + x \log\left({\left(b \sqrt{x} + a\right)}^{p} c\right)"," ",0,"-1/2*b*p*(2*a^2*log(b*sqrt(x) + a)/b^3 + (b*x - 2*a*sqrt(x))/b^2) + x*log((b*sqrt(x) + a)^p*c)","A",0
50,1,79,0,0.637640," ","integrate(log(c*(a+b*x^(1/2))^p)/x,x, algorithm=""maxima"")","b p {\left(\frac{\log\left(b \sqrt{x} + a\right) \log\left(x\right)}{b} - \frac{\log\left(x\right) \log\left(\frac{b \sqrt{x}}{a} + 1\right) + 2 \, {\rm Li}_2\left(-\frac{b \sqrt{x}}{a}\right)}{b}\right)} - p \log\left(b \sqrt{x} + a\right) \log\left(x\right) + \log\left({\left(b \sqrt{x} + a\right)}^{p} c\right) \log\left(x\right)"," ",0,"b*p*(log(b*sqrt(x) + a)*log(x)/b - (log(x)*log(b*sqrt(x)/a + 1) + 2*dilog(-b*sqrt(x)/a))/b) - p*log(b*sqrt(x) + a)*log(x) + log((b*sqrt(x) + a)^p*c)*log(x)","B",0
51,1,53,0,0.618084," ","integrate(log(c*(a+b*x^(1/2))^p)/x^2,x, algorithm=""maxima"")","\frac{1}{2} \, b p {\left(\frac{2 \, b \log\left(b \sqrt{x} + a\right)}{a^{2}} - \frac{b \log\left(x\right)}{a^{2}} - \frac{2}{a \sqrt{x}}\right)} - \frac{\log\left({\left(b \sqrt{x} + a\right)}^{p} c\right)}{x}"," ",0,"1/2*b*p*(2*b*log(b*sqrt(x) + a)/a^2 - b*log(x)/a^2 - 2/(a*sqrt(x))) - log((b*sqrt(x) + a)^p*c)/x","A",0
52,1,76,0,0.653541," ","integrate(log(c*(a+b*x^(1/2))^p)/x^3,x, algorithm=""maxima"")","\frac{1}{12} \, b p {\left(\frac{6 \, b^{3} \log\left(b \sqrt{x} + a\right)}{a^{4}} - \frac{3 \, b^{3} \log\left(x\right)}{a^{4}} - \frac{6 \, b^{2} x - 3 \, a b \sqrt{x} + 2 \, a^{2}}{a^{3} x^{\frac{3}{2}}}\right)} - \frac{\log\left({\left(b \sqrt{x} + a\right)}^{p} c\right)}{2 \, x^{2}}"," ",0,"1/12*b*p*(6*b^3*log(b*sqrt(x) + a)/a^4 - 3*b^3*log(x)/a^4 - (6*b^2*x - 3*a*b*sqrt(x) + 2*a^2)/(a^3*x^(3/2))) - 1/2*log((b*sqrt(x) + a)^p*c)/x^2","A",0
53,1,98,0,0.583853," ","integrate(log(c*(a+b*x^(1/2))^p)/x^4,x, algorithm=""maxima"")","\frac{1}{180} \, b p {\left(\frac{60 \, b^{5} \log\left(b \sqrt{x} + a\right)}{a^{6}} - \frac{30 \, b^{5} \log\left(x\right)}{a^{6}} - \frac{60 \, b^{4} x^{2} - 30 \, a b^{3} x^{\frac{3}{2}} + 20 \, a^{2} b^{2} x - 15 \, a^{3} b \sqrt{x} + 12 \, a^{4}}{a^{5} x^{\frac{5}{2}}}\right)} - \frac{\log\left({\left(b \sqrt{x} + a\right)}^{p} c\right)}{3 \, x^{3}}"," ",0,"1/180*b*p*(60*b^5*log(b*sqrt(x) + a)/a^6 - 30*b^5*log(x)/a^6 - (60*b^4*x^2 - 30*a*b^3*x^(3/2) + 20*a^2*b^2*x - 15*a^3*b*sqrt(x) + 12*a^4)/(a^5*x^(5/2))) - 1/3*log((b*sqrt(x) + a)^p*c)/x^3","A",0
54,1,31,0,0.580957," ","integrate(log(a+b*x^(1/2))/x^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left({\left(b \sqrt{x} + a\right)} \log\left(b \sqrt{x} + a\right) - b \sqrt{x} - a\right)}}{b}"," ",0,"2*((b*sqrt(x) + a)*log(b*sqrt(x) + a) - b*sqrt(x) - a)/b","A",0
55,0,0,0,0.000000," ","integrate((f*x)^m*log(c*(e*x^3+d)^p),x, algorithm=""maxima"")","\frac{f^{m} x x^{m} \log\left({\left(e x^{3} + d\right)}^{p}\right)}{m + 1} + \int \frac{{\left({\left(e f^{m} {\left(m + 1\right)} \log\left(c\right) - 3 \, e f^{m} p\right)} x^{3} + d f^{m} {\left(m + 1\right)} \log\left(c\right)\right)} x^{m}}{e {\left(m + 1\right)} x^{3} + d {\left(m + 1\right)}}\,{d x}"," ",0,"f^m*x*x^m*log((e*x^3 + d)^p)/(m + 1) + integrate(((e*f^m*(m + 1)*log(c) - 3*e*f^m*p)*x^3 + d*f^m*(m + 1)*log(c))*x^m/(e*(m + 1)*x^3 + d*(m + 1)), x)","F",0
56,0,0,0,0.000000," ","integrate((f*x)^m*log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","\frac{f^{m} p x x^{m} \log\left(e x^{2} + d\right)}{m + 1} + \int \frac{{\left(d f^{m} {\left(m + 1\right)} \log\left(c\right) + {\left(e f^{m} {\left(m + 1\right)} \log\left(c\right) - 2 \, e f^{m} p\right)} x^{2}\right)} x^{m}}{e {\left(m + 1\right)} x^{2} + d {\left(m + 1\right)}}\,{d x}"," ",0,"f^m*p*x*x^m*log(e*x^2 + d)/(m + 1) + integrate((d*f^m*(m + 1)*log(c) + (e*f^m*(m + 1)*log(c) - 2*e*f^m*p)*x^2)*x^m/(e*(m + 1)*x^2 + d*(m + 1)), x)","F",0
57,0,0,0,0.000000," ","integrate((f*x)^m*log(c*(e*x+d)^p),x, algorithm=""maxima"")","\frac{f^{m} x x^{m} \log\left({\left(e x + d\right)}^{p}\right)}{m + 1} + \int \frac{{\left(d f^{m} {\left(m + 1\right)} \log\left(c\right) + {\left(e f^{m} {\left(m + 1\right)} \log\left(c\right) - e f^{m} p\right)} x\right)} x^{m}}{e {\left(m + 1\right)} x + d {\left(m + 1\right)}}\,{d x}"," ",0,"f^m*x*x^m*log((e*x + d)^p)/(m + 1) + integrate((d*f^m*(m + 1)*log(c) + (e*f^m*(m + 1)*log(c) - e*f^m*p)*x)*x^m/(e*(m + 1)*x + d*(m + 1)), x)","F",0
58,0,0,0,0.000000," ","integrate((f*x)^m*log(c*(d+e/x)^p),x, algorithm=""maxima"")","\frac{f^{m} x x^{m} \log\left({\left(d x + e\right)}^{p}\right) - f^{m} x x^{m} \log\left(x^{p}\right)}{m + 1} + \int \frac{{\left(d f^{m} {\left(m + 1\right)} x \log\left(c\right) + e f^{m} {\left(m + 1\right)} \log\left(c\right) + e f^{m} p\right)} x^{m}}{d {\left(m + 1\right)} x + e {\left(m + 1\right)}}\,{d x}"," ",0,"(f^m*x*x^m*log((d*x + e)^p) - f^m*x*x^m*log(x^p))/(m + 1) + integrate((d*f^m*(m + 1)*x*log(c) + e*f^m*(m + 1)*log(c) + e*f^m*p)*x^m/(d*(m + 1)*x + e*(m + 1)), x)","F",0
59,0,0,0,0.000000," ","integrate((f*x)^m*log(c*(d+e/x^2)^p),x, algorithm=""maxima"")","\frac{f^{m} p x x^{m} \log\left(d x^{2} + e\right) - 2 \, f^{m} x x^{m} \log\left(x^{p}\right)}{m + 1} + \int \frac{{\left(d f^{m} {\left(m + 1\right)} x^{2} \log\left(c\right) + e f^{m} {\left(m + 1\right)} \log\left(c\right) + 2 \, e f^{m} p\right)} x^{m}}{d {\left(m + 1\right)} x^{2} + e {\left(m + 1\right)}}\,{d x}"," ",0,"(f^m*p*x*x^m*log(d*x^2 + e) - 2*f^m*x*x^m*log(x^p))/(m + 1) + integrate((d*f^m*(m + 1)*x^2*log(c) + e*f^m*(m + 1)*log(c) + 2*e*f^m*p)*x^m/(d*(m + 1)*x^2 + e*(m + 1)), x)","F",0
60,0,0,0,0.000000," ","integrate((f*x)^m*log(c*(d+e/x^3)^p),x, algorithm=""maxima"")","\frac{f^{m} x x^{m} \log\left({\left(d x^{3} + e\right)}^{p}\right) - 3 \, f^{m} x x^{m} \log\left(x^{p}\right)}{m + 1} + \int \frac{{\left(d f^{m} {\left(m + 1\right)} x^{3} \log\left(c\right) + e f^{m} {\left(m + 1\right)} \log\left(c\right) + 3 \, e f^{m} p\right)} x^{m}}{d {\left(m + 1\right)} x^{3} + e {\left(m + 1\right)}}\,{d x}"," ",0,"(f^m*x*x^m*log((d*x^3 + e)^p) - 3*f^m*x*x^m*log(x^p))/(m + 1) + integrate((d*f^m*(m + 1)*x^3*log(c) + e*f^m*(m + 1)*log(c) + 3*e*f^m*p)*x^m/(d*(m + 1)*x^3 + e*(m + 1)), x)","F",0
61,0,0,0,0.000000," ","integrate((f*x)^m*log(c*(d+e*x^(1/2))^p),x, algorithm=""maxima"")","e^{2} f^{m} p \int \frac{x x^{m}}{2 \, {\left(d e {\left(m + 1\right)} \sqrt{x} + d^{2} {\left(m + 1\right)}\right)}}\,{d x} + \frac{d f^{m} {\left(2 \, m + 3\right)} p x x^{m} \log\left(e \sqrt{x} + d\right) + d f^{m} {\left(2 \, m + 3\right)} x x^{m} \log\left(c\right) - e f^{m} p x^{\frac{3}{2}} x^{m}}{{\left(2 \, m^{2} + 5 \, m + 3\right)} d}"," ",0,"e^2*f^m*p*integrate(1/2*x*x^m/(d*e*(m + 1)*sqrt(x) + d^2*(m + 1)), x) + (d*f^m*(2*m + 3)*p*x*x^m*log(e*sqrt(x) + d) + d*f^m*(2*m + 3)*x*x^m*log(c) - e*f^m*p*x^(3/2)*x^m)/((2*m^2 + 5*m + 3)*d)","F",0
62,0,0,0,0.000000," ","integrate((f*x)^m*log(c*(d+e/x^(1/2))^p),x, algorithm=""maxima"")","d^{2} f^{m} p \int \frac{x x^{m}}{2 \, {\left(d e {\left(m + 1\right)} \sqrt{x} + e^{2} {\left(m + 1\right)}\right)}}\,{d x} + \frac{2 \, {\left(2 \, m^{2} + 5 \, m + 3\right)} e f^{m} p x x^{m} \log\left(d \sqrt{x} + e\right) - 2 \, {\left(2 \, m^{2} + 5 \, m + 3\right)} e f^{m} x x^{m} \log\left(x^{\frac{1}{2} \, p}\right) - 2 \, {\left(m p + p\right)} d f^{m} x^{\frac{3}{2}} x^{m} + {\left(2 \, {\left(2 \, m^{2} + 5 \, m + 3\right)} e f^{m} \log\left(c\right) + {\left(2 \, m p + 3 \, p\right)} e f^{m}\right)} x x^{m}}{2 \, {\left(2 \, m^{3} + 7 \, m^{2} + 8 \, m + 3\right)} e}"," ",0,"d^2*f^m*p*integrate(1/2*x*x^m/(d*e*(m + 1)*sqrt(x) + e^2*(m + 1)), x) + 1/2*(2*(2*m^2 + 5*m + 3)*e*f^m*p*x*x^m*log(d*sqrt(x) + e) - 2*(2*m^2 + 5*m + 3)*e*f^m*x*x^m*log(x^(1/2*p)) - 2*(m*p + p)*d*f^m*x^(3/2)*x^m + (2*(2*m^2 + 5*m + 3)*e*f^m*log(c) + (2*m*p + 3*p)*e*f^m)*x*x^m)/((2*m^3 + 7*m^2 + 8*m + 3)*e)","F",0
63,0,0,0,0.000000," ","integrate((f*x)^m*log(c*(d+e*x^n)^p),x, algorithm=""maxima"")","d f^{m} n p \int \frac{x^{m}}{e {\left(m + 1\right)} x^{n} + d {\left(m + 1\right)}}\,{d x} + \frac{f^{m} {\left(m + 1\right)} x x^{m} \log\left({\left(e x^{n} + d\right)}^{p}\right) - {\left(f^{m} n p - f^{m} {\left(m + 1\right)} \log\left(c\right)\right)} x x^{m}}{m^{2} + 2 \, m + 1}"," ",0,"d*f^m*n*p*integrate(x^m/(e*(m + 1)*x^n + d*(m + 1)), x) + (f^m*(m + 1)*x*x^m*log((e*x^n + d)^p) - (f^m*n*p - f^m*(m + 1)*log(c))*x*x^m)/(m^2 + 2*m + 1)","F",0
64,1,115,0,0.767449," ","integrate((f*x)^(-1+3*n)*log(c*(d+e*x^n)^p),x, algorithm=""maxima"")","\frac{e p {\left(\frac{6 \, d^{3} f^{3 \, n} \log\left(\frac{e x^{n} + d}{e}\right)}{e^{4} n} - \frac{2 \, e^{2} f^{3 \, n} x^{3 \, n} - 3 \, d e f^{3 \, n} x^{2 \, n} + 6 \, d^{2} f^{3 \, n} x^{n}}{e^{3} n}\right)}}{18 \, f} + \frac{\left(f x\right)^{3 \, n} \log\left({\left(e x^{n} + d\right)}^{p} c\right)}{3 \, f n}"," ",0,"1/18*e*p*(6*d^3*f^(3*n)*log((e*x^n + d)/e)/(e^4*n) - (2*e^2*f^(3*n)*x^(3*n) - 3*d*e*f^(3*n)*x^(2*n) + 6*d^2*f^(3*n)*x^n)/(e^3*n))/f + 1/3*(f*x)^(3*n)*log((e*x^n + d)^p*c)/(f*n)","A",0
65,1,95,0,0.694598," ","integrate((f*x)^(-1+2*n)*log(c*(d+e*x^n)^p),x, algorithm=""maxima"")","-\frac{e p {\left(\frac{2 \, d^{2} f^{2 \, n} \log\left(\frac{e x^{n} + d}{e}\right)}{e^{3} n} + \frac{e f^{2 \, n} x^{2 \, n} - 2 \, d f^{2 \, n} x^{n}}{e^{2} n}\right)}}{4 \, f} + \frac{\left(f x\right)^{2 \, n} \log\left({\left(e x^{n} + d\right)}^{p} c\right)}{2 \, f n}"," ",0,"-1/4*e*p*(2*d^2*f^(2*n)*log((e*x^n + d)/e)/(e^3*n) + (e*f^(2*n)*x^(2*n) - 2*d*f^(2*n)*x^n)/(e^2*n))/f + 1/2*(f*x)^(2*n)*log((e*x^n + d)^p*c)/(f*n)","A",0
66,1,70,0,0.752537," ","integrate((f*x)^(-1+n)*log(c*(d+e*x^n)^p),x, algorithm=""maxima"")","-\frac{e p {\left(\frac{f^{n} x^{n}}{e n} - \frac{d f^{n} \log\left(\frac{e x^{n} + d}{e}\right)}{e^{2} n}\right)}}{f} + \frac{\left(f x\right)^{n} \log\left({\left(e x^{n} + d\right)}^{p} c\right)}{f n}"," ",0,"-e*p*(f^n*x^n/(e*n) - d*f^n*log((e*x^n + d)/e)/(e^2*n))/f + (f*x)^n*log((e*x^n + d)^p*c)/(f*n)","A",0
67,0,0,0,0.000000," ","integrate(log(c*(d+e*x^n)^p)/f/x,x, algorithm=""maxima"")","\frac{2 \, d n p \int \frac{\log\left(x\right)}{e x x^{n} + d x}\,{d x} - n p \log\left(x\right)^{2} + 2 \, \log\left({\left(e x^{n} + d\right)}^{p}\right) \log\left(x\right) + 2 \, \log\left(c\right) \log\left(x\right)}{2 \, f}"," ",0,"1/2*(2*d*n*p*integrate(log(x)/(e*x*x^n + d*x), x) - n*p*log(x)^2 + 2*log((e*x^n + d)^p)*log(x) + 2*log(c)*log(x))/f","F",0
68,1,71,0,0.725124," ","integrate((f*x)^(-1-n)*log(c*(d+e*x^n)^p),x, algorithm=""maxima"")","\frac{e p {\left(\frac{\log\left(x\right)}{d f^{n}} - \frac{\log\left(\frac{e x^{n} + d}{e}\right)}{d f^{n} n}\right)}}{f} - \frac{\log\left({\left(e x^{n} + d\right)}^{p} c\right)}{\left(f x\right)^{n} f n}"," ",0,"e*p*(log(x)/(d*f^n) - log((e*x^n + d)/e)/(d*f^n*n))/f - log((e*x^n + d)^p*c)/((f*x)^n*f*n)","A",0
69,1,99,0,0.737631," ","integrate((f*x)^(-1-2*n)*log(c*(d+e*x^n)^p),x, algorithm=""maxima"")","-\frac{e p {\left(\frac{e \log\left(x\right)}{d^{2} f^{2 \, n}} - \frac{e \log\left(\frac{e x^{n} + d}{e}\right)}{d^{2} f^{2 \, n} n} + \frac{1}{d f^{2 \, n} n x^{n}}\right)}}{2 \, f} - \frac{\log\left({\left(e x^{n} + d\right)}^{p} c\right)}{2 \, \left(f x\right)^{2 \, n} f n}"," ",0,"-1/2*e*p*(e*log(x)/(d^2*f^(2*n)) - e*log((e*x^n + d)/e)/(d^2*f^(2*n)*n) + 1/(d*f^(2*n)*n*x^n))/f - 1/2*log((e*x^n + d)^p*c)/((f*x)^(2*n)*f*n)","A",0
70,0,0,0,0.000000," ","integrate(x^2*log(c*(d+e*x^n)^p),x, algorithm=""maxima"")","-\frac{1}{9} \, {\left(n p - 3 \, \log\left(c\right)\right)} x^{3} + d n p \int \frac{x^{2}}{3 \, {\left(e x^{n} + d\right)}}\,{d x} + \frac{1}{3} \, x^{3} \log\left({\left(e x^{n} + d\right)}^{p}\right)"," ",0,"-1/9*(n*p - 3*log(c))*x^3 + d*n*p*integrate(1/3*x^2/(e*x^n + d), x) + 1/3*x^3*log((e*x^n + d)^p)","F",0
71,0,0,0,0.000000," ","integrate(x*log(c*(d+e*x^n)^p),x, algorithm=""maxima"")","d n p \int \frac{x}{2 \, {\left(e x^{n} + d\right)}}\,{d x} - \frac{1}{4} \, {\left(n p - 2 \, \log\left(c\right)\right)} x^{2} + \frac{1}{2} \, x^{2} \log\left({\left(e x^{n} + d\right)}^{p}\right)"," ",0,"d*n*p*integrate(1/2*x/(e*x^n + d), x) - 1/4*(n*p - 2*log(c))*x^2 + 1/2*x^2*log((e*x^n + d)^p)","F",0
72,0,0,0,0.000000," ","integrate(log(c*(d+e*x^n)^p),x, algorithm=""maxima"")","d n p \int \frac{1}{e x^{n} + d}\,{d x} - {\left(n p - \log\left(c\right)\right)} x + x \log\left({\left(e x^{n} + d\right)}^{p}\right)"," ",0,"d*n*p*integrate(1/(e*x^n + d), x) - (n*p - log(c))*x + x*log((e*x^n + d)^p)","F",0
73,0,0,0,0.000000," ","integrate(log(c*(d+e*x^n)^p)/x,x, algorithm=""maxima"")","d n p \int \frac{\log\left(x\right)}{e x x^{n} + d x}\,{d x} - \frac{1}{2} \, n p \log\left(x\right)^{2} + \log\left({\left(e x^{n} + d\right)}^{p}\right) \log\left(x\right) + \log\left(c\right) \log\left(x\right)"," ",0,"d*n*p*integrate(log(x)/(e*x*x^n + d*x), x) - 1/2*n*p*log(x)^2 + log((e*x^n + d)^p)*log(x) + log(c)*log(x)","F",0
74,0,0,0,0.000000," ","integrate(log(c*(d+e*x^n)^p)/x^2,x, algorithm=""maxima"")","-d n p \int \frac{1}{e x^{2} x^{n} + d x^{2}}\,{d x} - \frac{n p + \log\left({\left(e x^{n} + d\right)}^{p}\right) + \log\left(c\right)}{x}"," ",0,"-d*n*p*integrate(1/(e*x^2*x^n + d*x^2), x) - (n*p + log((e*x^n + d)^p) + log(c))/x","F",0
75,0,0,0,0.000000," ","integrate(log(c*(d+e*x^n)^p)/x^3,x, algorithm=""maxima"")","-d n p \int \frac{1}{2 \, {\left(e x^{3} x^{n} + d x^{3}\right)}}\,{d x} - \frac{n p + 2 \, \log\left({\left(e x^{n} + d\right)}^{p}\right) + 2 \, \log\left(c\right)}{4 \, x^{2}}"," ",0,"-d*n*p*integrate(1/2/(e*x^3*x^n + d*x^3), x) - 1/4*(n*p + 2*log((e*x^n + d)^p) + 2*log(c))/x^2","F",0
76,0,0,0,0.000000," ","integrate(log(c*(d+e*x^n)^p)/x^4,x, algorithm=""maxima"")","-d n p \int \frac{1}{3 \, {\left(e x^{4} x^{n} + d x^{4}\right)}}\,{d x} - \frac{n p + 3 \, \log\left({\left(e x^{n} + d\right)}^{p}\right) + 3 \, \log\left(c\right)}{9 \, x^{3}}"," ",0,"-d*n*p*integrate(1/3/(e*x^4*x^n + d*x^4), x) - 1/9*(n*p + 3*log((e*x^n + d)^p) + 3*log(c))/x^3","F",0
77,1,145,0,0.696221," ","integrate(x^5*log(c*(b*x^2+a)^p)^2,x, algorithm=""maxima"")","\frac{1}{6} \, x^{6} \log\left({\left(b x^{2} + a\right)}^{p} c\right)^{2} + \frac{1}{18} \, b p {\left(\frac{6 \, a^{3} \log\left(b x^{2} + a\right)}{b^{4}} - \frac{2 \, b^{2} x^{6} - 3 \, a b x^{4} + 6 \, a^{2} x^{2}}{b^{3}}\right)} \log\left({\left(b x^{2} + a\right)}^{p} c\right) + \frac{{\left(4 \, b^{3} x^{6} - 15 \, a b^{2} x^{4} + 66 \, a^{2} b x^{2} - 18 \, a^{3} \log\left(b x^{2} + a\right)^{2} - 66 \, a^{3} \log\left(b x^{2} + a\right)\right)} p^{2}}{108 \, b^{3}}"," ",0,"1/6*x^6*log((b*x^2 + a)^p*c)^2 + 1/18*b*p*(6*a^3*log(b*x^2 + a)/b^4 - (2*b^2*x^6 - 3*a*b*x^4 + 6*a^2*x^2)/b^3)*log((b*x^2 + a)^p*c) + 1/108*(4*b^3*x^6 - 15*a*b^2*x^4 + 66*a^2*b*x^2 - 18*a^3*log(b*x^2 + a)^2 - 66*a^3*log(b*x^2 + a))*p^2/b^3","A",0
78,1,120,0,0.771580," ","integrate(x^3*log(c*(b*x^2+a)^p)^2,x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \log\left({\left(b x^{2} + a\right)}^{p} c\right)^{2} - \frac{1}{4} \, b p {\left(\frac{2 \, a^{2} \log\left(b x^{2} + a\right)}{b^{3}} + \frac{b x^{4} - 2 \, a x^{2}}{b^{2}}\right)} \log\left({\left(b x^{2} + a\right)}^{p} c\right) + \frac{{\left(b^{2} x^{4} - 6 \, a b x^{2} + 2 \, a^{2} \log\left(b x^{2} + a\right)^{2} + 6 \, a^{2} \log\left(b x^{2} + a\right)\right)} p^{2}}{8 \, b^{2}}"," ",0,"1/4*x^4*log((b*x^2 + a)^p*c)^2 - 1/4*b*p*(2*a^2*log(b*x^2 + a)/b^3 + (b*x^4 - 2*a*x^2)/b^2)*log((b*x^2 + a)^p*c) + 1/8*(b^2*x^4 - 6*a*b*x^2 + 2*a^2*log(b*x^2 + a)^2 + 6*a^2*log(b*x^2 + a))*p^2/b^2","A",0
79,1,97,0,0.726530," ","integrate(x*log(c*(b*x^2+a)^p)^2,x, algorithm=""maxima"")","-b p {\left(\frac{x^{2}}{b} - \frac{a \log\left(b x^{2} + a\right)}{b^{2}}\right)} \log\left({\left(b x^{2} + a\right)}^{p} c\right) + \frac{1}{2} \, x^{2} \log\left({\left(b x^{2} + a\right)}^{p} c\right)^{2} + \frac{{\left(2 \, b x^{2} - a \log\left(b x^{2} + a\right)^{2} - 2 \, a \log\left(b x^{2} + a\right)\right)} p^{2}}{2 \, b}"," ",0,"-b*p*(x^2/b - a*log(b*x^2 + a)/b^2)*log((b*x^2 + a)^p*c) + 1/2*x^2*log((b*x^2 + a)^p*c)^2 + 1/2*(2*b*x^2 - a*log(b*x^2 + a)^2 - 2*a*log(b*x^2 + a))*p^2/b","A",0
80,1,118,0,0.752097," ","integrate(log(c*(b*x^2+a)^p)^2/x,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\log\left(b x^{2} + a\right)^{2} \log\left(-\frac{b x^{2} + a}{a} + 1\right) + 2 \, {\rm Li}_2\left(\frac{b x^{2} + a}{a}\right) \log\left(b x^{2} + a\right) - 2 \, {\rm Li}_{3}(\frac{b x^{2} + a}{a})\right)} p^{2} + {\left(\log\left(b x^{2} + a\right) \log\left(-\frac{b x^{2} + a}{a} + 1\right) + {\rm Li}_2\left(\frac{b x^{2} + a}{a}\right)\right)} p \log\left(c\right) + \log\left(c\right)^{2} \log\left(x\right)"," ",0,"1/2*(log(b*x^2 + a)^2*log(-(b*x^2 + a)/a + 1) + 2*dilog((b*x^2 + a)/a)*log(b*x^2 + a) - 2*polylog(3, (b*x^2 + a)/a))*p^2 + (log(b*x^2 + a)*log(-(b*x^2 + a)/a + 1) + dilog((b*x^2 + a)/a))*p*log(c) + log(c)^2*log(x)","A",0
81,1,118,0,0.688867," ","integrate(log(c*(b*x^2+a)^p)^2/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, b^{2} p^{2} {\left(\frac{\log\left(b x^{2} + a\right)^{2}}{a b} - \frac{2 \, {\left(2 \, \log\left(\frac{b x^{2}}{a} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{b x^{2}}{a}\right)\right)}}{a b}\right)} - b p {\left(\frac{\log\left(b x^{2} + a\right)}{a} - \frac{\log\left(x^{2}\right)}{a}\right)} \log\left({\left(b x^{2} + a\right)}^{p} c\right) - \frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)^{2}}{2 \, x^{2}}"," ",0,"1/2*b^2*p^2*(log(b*x^2 + a)^2/(a*b) - 2*(2*log(b*x^2/a + 1)*log(x) + dilog(-b*x^2/a))/(a*b)) - b*p*(log(b*x^2 + a)/a - log(x^2)/a)*log((b*x^2 + a)^p*c) - 1/2*log((b*x^2 + a)^p*c)^2/x^2","A",0
82,1,142,0,0.976769," ","integrate(log(c*(b*x^2+a)^p)^2/x^5,x, algorithm=""maxima"")","-\frac{1}{4} \, b^{2} p^{2} {\left(\frac{\log\left(b x^{2} + a\right)^{2}}{a^{2}} - \frac{2 \, {\left(2 \, \log\left(\frac{b x^{2}}{a} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{b x^{2}}{a}\right)\right)}}{a^{2}} + \frac{2 \, \log\left(b x^{2} + a\right)}{a^{2}} - \frac{4 \, \log\left(x\right)}{a^{2}}\right)} + \frac{1}{2} \, b p {\left(\frac{b \log\left(b x^{2} + a\right)}{a^{2}} - \frac{b \log\left(x^{2}\right)}{a^{2}} - \frac{1}{a x^{2}}\right)} \log\left({\left(b x^{2} + a\right)}^{p} c\right) - \frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)^{2}}{4 \, x^{4}}"," ",0,"-1/4*b^2*p^2*(log(b*x^2 + a)^2/a^2 - 2*(2*log(b*x^2/a + 1)*log(x) + dilog(-b*x^2/a))/a^2 + 2*log(b*x^2 + a)/a^2 - 4*log(x)/a^2) + 1/2*b*p*(b*log(b*x^2 + a)/a^2 - b*log(x^2)/a^2 - 1/(a*x^2))*log((b*x^2 + a)^p*c) - 1/4*log((b*x^2 + a)^p*c)^2/x^4","A",0
83,1,173,0,0.812940," ","integrate(log(c*(b*x^2+a)^p)^2/x^7,x, algorithm=""maxima"")","-\frac{1}{6} \, b^{2} p^{2} {\left(\frac{2 \, {\left(2 \, \log\left(\frac{b x^{2}}{a} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{b x^{2}}{a}\right)\right)} b}{a^{3}} - \frac{3 \, b \log\left(b x^{2} + a\right)}{a^{3}} - \frac{b x^{2} \log\left(b x^{2} + a\right)^{2} - 6 \, b x^{2} \log\left(x\right) - a}{a^{3} x^{2}}\right)} - \frac{1}{6} \, b p {\left(\frac{2 \, b^{2} \log\left(b x^{2} + a\right)}{a^{3}} - \frac{2 \, b^{2} \log\left(x^{2}\right)}{a^{3}} - \frac{2 \, b x^{2} - a}{a^{2} x^{4}}\right)} \log\left({\left(b x^{2} + a\right)}^{p} c\right) - \frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)^{2}}{6 \, x^{6}}"," ",0,"-1/6*b^2*p^2*(2*(2*log(b*x^2/a + 1)*log(x) + dilog(-b*x^2/a))*b/a^3 - 3*b*log(b*x^2 + a)/a^3 - (b*x^2*log(b*x^2 + a)^2 - 6*b*x^2*log(x) - a)/(a^3*x^2)) - 1/6*b*p*(2*b^2*log(b*x^2 + a)/a^3 - 2*b^2*log(x^2)/a^3 - (2*b*x^2 - a)/(a^2*x^4))*log((b*x^2 + a)^p*c) - 1/6*log((b*x^2 + a)^p*c)^2/x^6","A",0
84,0,0,0,0.000000," ","integrate(x^4*log(c*(b*x^2+a)^p)^2,x, algorithm=""maxima"")","\frac{1}{5} \, p^{2} x^{5} \log\left(b x^{2} + a\right)^{2} + \int \frac{5 \, b x^{6} \log\left(c\right)^{2} + 5 \, a x^{4} \log\left(c\right)^{2} - 2 \, {\left({\left(2 \, p^{2} - 5 \, p \log\left(c\right)\right)} b x^{6} - 5 \, a p x^{4} \log\left(c\right)\right)} \log\left(b x^{2} + a\right)}{5 \, {\left(b x^{2} + a\right)}}\,{d x}"," ",0,"1/5*p^2*x^5*log(b*x^2 + a)^2 + integrate(1/5*(5*b*x^6*log(c)^2 + 5*a*x^4*log(c)^2 - 2*((2*p^2 - 5*p*log(c))*b*x^6 - 5*a*p*x^4*log(c))*log(b*x^2 + a))/(b*x^2 + a), x)","F",0
85,0,0,0,0.000000," ","integrate(x^2*log(c*(b*x^2+a)^p)^2,x, algorithm=""maxima"")","\frac{1}{3} \, p^{2} x^{3} \log\left(b x^{2} + a\right)^{2} + \int \frac{3 \, b x^{4} \log\left(c\right)^{2} + 3 \, a x^{2} \log\left(c\right)^{2} - 2 \, {\left({\left(2 \, p^{2} - 3 \, p \log\left(c\right)\right)} b x^{4} - 3 \, a p x^{2} \log\left(c\right)\right)} \log\left(b x^{2} + a\right)}{3 \, {\left(b x^{2} + a\right)}}\,{d x}"," ",0,"1/3*p^2*x^3*log(b*x^2 + a)^2 + integrate(1/3*(3*b*x^4*log(c)^2 + 3*a*x^2*log(c)^2 - 2*((2*p^2 - 3*p*log(c))*b*x^4 - 3*a*p*x^2*log(c))*log(b*x^2 + a))/(b*x^2 + a), x)","F",0
86,0,0,0,0.000000," ","integrate(log(c*(b*x^2+a)^p)^2,x, algorithm=""maxima"")","p^{2} x \log\left(b x^{2} + a\right)^{2} + \int \frac{b x^{2} \log\left(c\right)^{2} + a \log\left(c\right)^{2} - 2 \, {\left({\left(2 \, p^{2} - p \log\left(c\right)\right)} b x^{2} - a p \log\left(c\right)\right)} \log\left(b x^{2} + a\right)}{b x^{2} + a}\,{d x}"," ",0,"p^2*x*log(b*x^2 + a)^2 + integrate((b*x^2*log(c)^2 + a*log(c)^2 - 2*((2*p^2 - p*log(c))*b*x^2 - a*p*log(c))*log(b*x^2 + a))/(b*x^2 + a), x)","F",0
87,0,0,0,0.000000," ","integrate(log(c*(b*x^2+a)^p)^2/x^2,x, algorithm=""maxima"")","-\frac{p^{2} \log\left(b x^{2} + a\right)^{2}}{x} + \int \frac{b x^{2} \log\left(c\right)^{2} + a \log\left(c\right)^{2} + 2 \, {\left({\left(2 \, p^{2} + p \log\left(c\right)\right)} b x^{2} + a p \log\left(c\right)\right)} \log\left(b x^{2} + a\right)}{b x^{4} + a x^{2}}\,{d x}"," ",0,"-p^2*log(b*x^2 + a)^2/x + integrate((b*x^2*log(c)^2 + a*log(c)^2 + 2*((2*p^2 + p*log(c))*b*x^2 + a*p*log(c))*log(b*x^2 + a))/(b*x^4 + a*x^2), x)","F",0
88,0,0,0,0.000000," ","integrate(log(c*(b*x^2+a)^p)^2/x^4,x, algorithm=""maxima"")","-\frac{p^{2} \log\left(b x^{2} + a\right)^{2}}{3 \, x^{3}} + \int \frac{3 \, b x^{2} \log\left(c\right)^{2} + 3 \, a \log\left(c\right)^{2} + 2 \, {\left({\left(2 \, p^{2} + 3 \, p \log\left(c\right)\right)} b x^{2} + 3 \, a p \log\left(c\right)\right)} \log\left(b x^{2} + a\right)}{3 \, {\left(b x^{6} + a x^{4}\right)}}\,{d x}"," ",0,"-1/3*p^2*log(b*x^2 + a)^2/x^3 + integrate(1/3*(3*b*x^2*log(c)^2 + 3*a*log(c)^2 + 2*((2*p^2 + 3*p*log(c))*b*x^2 + 3*a*p*log(c))*log(b*x^2 + a))/(b*x^6 + a*x^4), x)","F",0
89,0,0,0,0.000000," ","integrate(log(c*(b*x^2+a)^p)^2/x^6,x, algorithm=""maxima"")","-\frac{p^{2} \log\left(b x^{2} + a\right)^{2}}{5 \, x^{5}} + \int \frac{5 \, b x^{2} \log\left(c\right)^{2} + 5 \, a \log\left(c\right)^{2} + 2 \, {\left({\left(2 \, p^{2} + 5 \, p \log\left(c\right)\right)} b x^{2} + 5 \, a p \log\left(c\right)\right)} \log\left(b x^{2} + a\right)}{5 \, {\left(b x^{8} + a x^{6}\right)}}\,{d x}"," ",0,"-1/5*p^2*log(b*x^2 + a)^2/x^5 + integrate(1/5*(5*b*x^2*log(c)^2 + 5*a*log(c)^2 + 2*((2*p^2 + 5*p*log(c))*b*x^2 + 5*a*p*log(c))*log(b*x^2 + a))/(b*x^8 + a*x^6), x)","F",0
90,0,0,0,0.000000," ","integrate(log(c*(b*x^2+a)^p)^2/x^8,x, algorithm=""maxima"")","-\frac{p^{2} \log\left(b x^{2} + a\right)^{2}}{7 \, x^{7}} + \int \frac{7 \, b x^{2} \log\left(c\right)^{2} + 7 \, a \log\left(c\right)^{2} + 2 \, {\left({\left(2 \, p^{2} + 7 \, p \log\left(c\right)\right)} b x^{2} + 7 \, a p \log\left(c\right)\right)} \log\left(b x^{2} + a\right)}{7 \, {\left(b x^{10} + a x^{8}\right)}}\,{d x}"," ",0,"-1/7*p^2*log(b*x^2 + a)^2/x^7 + integrate(1/7*(7*b*x^2*log(c)^2 + 7*a*log(c)^2 + 2*((2*p^2 + 7*p*log(c))*b*x^2 + 7*a*p*log(c))*log(b*x^2 + a))/(b*x^10 + a*x^8), x)","F",0
91,1,239,0,0.720881," ","integrate(x^5*log(c*(b*x^2+a)^p)^3,x, algorithm=""maxima"")","\frac{1}{6} \, x^{6} \log\left({\left(b x^{2} + a\right)}^{p} c\right)^{3} + \frac{1}{12} \, b p {\left(\frac{6 \, a^{3} \log\left(b x^{2} + a\right)}{b^{4}} - \frac{2 \, b^{2} x^{6} - 3 \, a b x^{4} + 6 \, a^{2} x^{2}}{b^{3}}\right)} \log\left({\left(b x^{2} + a\right)}^{p} c\right)^{2} - \frac{1}{216} \, b p {\left(\frac{{\left(8 \, b^{3} x^{6} - 57 \, a b^{2} x^{4} - 36 \, a^{3} \log\left(b x^{2} + a\right)^{3} + 510 \, a^{2} b x^{2} - 198 \, a^{3} \log\left(b x^{2} + a\right)^{2} - 510 \, a^{3} \log\left(b x^{2} + a\right)\right)} p^{2}}{b^{4}} - \frac{6 \, {\left(4 \, b^{3} x^{6} - 15 \, a b^{2} x^{4} + 66 \, a^{2} b x^{2} - 18 \, a^{3} \log\left(b x^{2} + a\right)^{2} - 66 \, a^{3} \log\left(b x^{2} + a\right)\right)} p \log\left({\left(b x^{2} + a\right)}^{p} c\right)}{b^{4}}\right)}"," ",0,"1/6*x^6*log((b*x^2 + a)^p*c)^3 + 1/12*b*p*(6*a^3*log(b*x^2 + a)/b^4 - (2*b^2*x^6 - 3*a*b*x^4 + 6*a^2*x^2)/b^3)*log((b*x^2 + a)^p*c)^2 - 1/216*b*p*((8*b^3*x^6 - 57*a*b^2*x^4 - 36*a^3*log(b*x^2 + a)^3 + 510*a^2*b*x^2 - 198*a^3*log(b*x^2 + a)^2 - 510*a^3*log(b*x^2 + a))*p^2/b^4 - 6*(4*b^3*x^6 - 15*a*b^2*x^4 + 66*a^2*b*x^2 - 18*a^3*log(b*x^2 + a)^2 - 66*a^3*log(b*x^2 + a))*p*log((b*x^2 + a)^p*c)/b^4)","A",0
92,1,203,0,0.758793," ","integrate(x^3*log(c*(b*x^2+a)^p)^3,x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \log\left({\left(b x^{2} + a\right)}^{p} c\right)^{3} - \frac{3}{8} \, b p {\left(\frac{2 \, a^{2} \log\left(b x^{2} + a\right)}{b^{3}} + \frac{b x^{4} - 2 \, a x^{2}}{b^{2}}\right)} \log\left({\left(b x^{2} + a\right)}^{p} c\right)^{2} - \frac{1}{16} \, b p {\left(\frac{{\left(3 \, b^{2} x^{4} + 4 \, a^{2} \log\left(b x^{2} + a\right)^{3} - 42 \, a b x^{2} + 18 \, a^{2} \log\left(b x^{2} + a\right)^{2} + 42 \, a^{2} \log\left(b x^{2} + a\right)\right)} p^{2}}{b^{3}} - \frac{6 \, {\left(b^{2} x^{4} - 6 \, a b x^{2} + 2 \, a^{2} \log\left(b x^{2} + a\right)^{2} + 6 \, a^{2} \log\left(b x^{2} + a\right)\right)} p \log\left({\left(b x^{2} + a\right)}^{p} c\right)}{b^{3}}\right)}"," ",0,"1/4*x^4*log((b*x^2 + a)^p*c)^3 - 3/8*b*p*(2*a^2*log(b*x^2 + a)/b^3 + (b*x^4 - 2*a*x^2)/b^2)*log((b*x^2 + a)^p*c)^2 - 1/16*b*p*((3*b^2*x^4 + 4*a^2*log(b*x^2 + a)^3 - 42*a*b*x^2 + 18*a^2*log(b*x^2 + a)^2 + 42*a^2*log(b*x^2 + a))*p^2/b^3 - 6*(b^2*x^4 - 6*a*b*x^2 + 2*a^2*log(b*x^2 + a)^2 + 6*a^2*log(b*x^2 + a))*p*log((b*x^2 + a)^p*c)/b^3)","A",0
93,1,164,0,0.747950," ","integrate(x*log(c*(b*x^2+a)^p)^3,x, algorithm=""maxima"")","-\frac{3}{2} \, b p {\left(\frac{x^{2}}{b} - \frac{a \log\left(b x^{2} + a\right)}{b^{2}}\right)} \log\left({\left(b x^{2} + a\right)}^{p} c\right)^{2} + \frac{1}{2} \, x^{2} \log\left({\left(b x^{2} + a\right)}^{p} c\right)^{3} + \frac{1}{2} \, b p {\left(\frac{{\left(a \log\left(b x^{2} + a\right)^{3} - 6 \, b x^{2} + 3 \, a \log\left(b x^{2} + a\right)^{2} + 6 \, a \log\left(b x^{2} + a\right)\right)} p^{2}}{b^{2}} + \frac{3 \, {\left(2 \, b x^{2} - a \log\left(b x^{2} + a\right)^{2} - 2 \, a \log\left(b x^{2} + a\right)\right)} p \log\left({\left(b x^{2} + a\right)}^{p} c\right)}{b^{2}}\right)}"," ",0,"-3/2*b*p*(x^2/b - a*log(b*x^2 + a)/b^2)*log((b*x^2 + a)^p*c)^2 + 1/2*x^2*log((b*x^2 + a)^p*c)^3 + 1/2*b*p*((a*log(b*x^2 + a)^3 - 6*b*x^2 + 3*a*log(b*x^2 + a)^2 + 6*a*log(b*x^2 + a))*p^2/b^2 + 3*(2*b*x^2 - a*log(b*x^2 + a)^2 - 2*a*log(b*x^2 + a))*p*log((b*x^2 + a)^p*c)/b^2)","A",0
94,1,217,0,0.646090," ","integrate(log(c*(b*x^2+a)^p)^3/x,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\log\left(b x^{2} + a\right)^{3} \log\left(-\frac{b x^{2} + a}{a} + 1\right) + 3 \, {\rm Li}_2\left(\frac{b x^{2} + a}{a}\right) \log\left(b x^{2} + a\right)^{2} - 6 \, \log\left(b x^{2} + a\right) {\rm Li}_{3}(\frac{b x^{2} + a}{a}) + 6 \, {\rm Li}_{4}(\frac{b x^{2} + a}{a})\right)} p^{3} + \frac{3}{2} \, {\left(\log\left(b x^{2} + a\right)^{2} \log\left(-\frac{b x^{2} + a}{a} + 1\right) + 2 \, {\rm Li}_2\left(\frac{b x^{2} + a}{a}\right) \log\left(b x^{2} + a\right) - 2 \, {\rm Li}_{3}(\frac{b x^{2} + a}{a})\right)} p^{2} \log\left(c\right) + \frac{3}{2} \, {\left(\log\left(b x^{2} + a\right) \log\left(-\frac{b x^{2} + a}{a} + 1\right) + {\rm Li}_2\left(\frac{b x^{2} + a}{a}\right)\right)} p \log\left(c\right)^{2} + \log\left(c\right)^{3} \log\left(x\right)"," ",0,"1/2*(log(b*x^2 + a)^3*log(-(b*x^2 + a)/a + 1) + 3*dilog((b*x^2 + a)/a)*log(b*x^2 + a)^2 - 6*log(b*x^2 + a)*polylog(3, (b*x^2 + a)/a) + 6*polylog(4, (b*x^2 + a)/a))*p^3 + 3/2*(log(b*x^2 + a)^2*log(-(b*x^2 + a)/a + 1) + 2*dilog((b*x^2 + a)/a)*log(b*x^2 + a) - 2*polylog(3, (b*x^2 + a)/a))*p^2*log(c) + 3/2*(log(b*x^2 + a)*log(-(b*x^2 + a)/a + 1) + dilog((b*x^2 + a)/a))*p*log(c)^2 + log(c)^3*log(x)","B",0
95,1,202,0,1.132678," ","integrate(log(c*(b*x^2+a)^p)^3/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{3 \, {\left(\log\left(b x^{2} + a\right)^{2} \log\left(-\frac{b x^{2} + a}{a} + 1\right) + 2 \, {\rm Li}_2\left(\frac{b x^{2} + a}{a}\right) \log\left(b x^{2} + a\right) - 2 \, {\rm Li}_{3}(\frac{b x^{2} + a}{a})\right)} p^{2}}{a} + \frac{6 \, {\left(\log\left(b x^{2} + a\right) \log\left(-\frac{b x^{2} + a}{a} + 1\right) + {\rm Li}_2\left(\frac{b x^{2} + a}{a}\right)\right)} p \log\left(c\right)}{a} + \frac{6 \, \log\left(c\right)^{2} \log\left(x\right)}{a} - \frac{p^{2} \log\left(b x^{2} + a\right)^{3} + 3 \, p \log\left(b x^{2} + a\right)^{2} \log\left(c\right) + 3 \, \log\left(b x^{2} + a\right) \log\left(c\right)^{2}}{a}\right)} b p - \frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)^{3}}{2 \, x^{2}}"," ",0,"1/2*(3*(log(b*x^2 + a)^2*log(-(b*x^2 + a)/a + 1) + 2*dilog((b*x^2 + a)/a)*log(b*x^2 + a) - 2*polylog(3, (b*x^2 + a)/a))*p^2/a + 6*(log(b*x^2 + a)*log(-(b*x^2 + a)/a + 1) + dilog((b*x^2 + a)/a))*p*log(c)/a + 6*log(c)^2*log(x)/a - (p^2*log(b*x^2 + a)^3 + 3*p*log(b*x^2 + a)^2*log(c) + 3*log(b*x^2 + a)*log(c)^2)/a)*b*p - 1/2*log((b*x^2 + a)^p*c)^3/x^2","A",0
96,1,270,0,1.355937," ","integrate(log(c*(b*x^2+a)^p)^3/x^5,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(\frac{3 \, {\left(\log\left(b x^{2} + a\right)^{2} \log\left(-\frac{b x^{2} + a}{a} + 1\right) + 2 \, {\rm Li}_2\left(\frac{b x^{2} + a}{a}\right) \log\left(b x^{2} + a\right) - 2 \, {\rm Li}_{3}(\frac{b x^{2} + a}{a})\right)} b p^{2}}{a^{2}} - \frac{6 \, {\left(p^{2} - p \log\left(c\right)\right)} {\left(\log\left(b x^{2} + a\right) \log\left(-\frac{b x^{2} + a}{a} + 1\right) + {\rm Li}_2\left(\frac{b x^{2} + a}{a}\right)\right)} b}{a^{2}} - \frac{6 \, {\left(2 \, p \log\left(c\right) - \log\left(c\right)^{2}\right)} b \log\left(x\right)}{a^{2}} - \frac{b p^{2} x^{2} \log\left(b x^{2} + a\right)^{3} - 3 \, {\left({\left(p^{2} - p \log\left(c\right)\right)} b x^{2} + a p^{2}\right)} \log\left(b x^{2} + a\right)^{2} - 3 \, a \log\left(c\right)^{2} - 3 \, {\left({\left(2 \, p \log\left(c\right) - \log\left(c\right)^{2}\right)} b x^{2} + 2 \, a p \log\left(c\right)\right)} \log\left(b x^{2} + a\right)}{a^{2} x^{2}}\right)} b p - \frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)^{3}}{4 \, x^{4}}"," ",0,"-1/4*(3*(log(b*x^2 + a)^2*log(-(b*x^2 + a)/a + 1) + 2*dilog((b*x^2 + a)/a)*log(b*x^2 + a) - 2*polylog(3, (b*x^2 + a)/a))*b*p^2/a^2 - 6*(p^2 - p*log(c))*(log(b*x^2 + a)*log(-(b*x^2 + a)/a + 1) + dilog((b*x^2 + a)/a))*b/a^2 - 6*(2*p*log(c) - log(c)^2)*b*log(x)/a^2 - (b*p^2*x^2*log(b*x^2 + a)^3 - 3*((p^2 - p*log(c))*b*x^2 + a*p^2)*log(b*x^2 + a)^2 - 3*a*log(c)^2 - 3*((2*p*log(c) - log(c)^2)*b*x^2 + 2*a*p*log(c))*log(b*x^2 + a))/(a^2*x^2))*b*p - 1/4*log((b*x^2 + a)^p*c)^3/x^4","A",0
97,1,338,0,1.268629," ","integrate(log(c*(b*x^2+a)^p)^3/x^7,x, algorithm=""maxima"")","\frac{1}{12} \, {\left(\frac{6 \, {\left(\log\left(b x^{2} + a\right)^{2} \log\left(-\frac{b x^{2} + a}{a} + 1\right) + 2 \, {\rm Li}_2\left(\frac{b x^{2} + a}{a}\right) \log\left(b x^{2} + a\right) - 2 \, {\rm Li}_{3}(\frac{b x^{2} + a}{a})\right)} b^{2} p^{2}}{a^{3}} - \frac{6 \, {\left(3 \, p^{2} - 2 \, p \log\left(c\right)\right)} {\left(\log\left(b x^{2} + a\right) \log\left(-\frac{b x^{2} + a}{a} + 1\right) + {\rm Li}_2\left(\frac{b x^{2} + a}{a}\right)\right)} b^{2}}{a^{3}} + \frac{12 \, {\left(p^{2} - 3 \, p \log\left(c\right) + \log\left(c\right)^{2}\right)} b^{2} \log\left(x\right)}{a^{3}} - \frac{2 \, b^{2} p^{2} x^{4} \log\left(b x^{2} + a\right)^{3} + 6 \, {\left(p \log\left(c\right) - \log\left(c\right)^{2}\right)} a b x^{2} + 3 \, a^{2} \log\left(c\right)^{2} - 3 \, {\left({\left(3 \, p^{2} - 2 \, p \log\left(c\right)\right)} b^{2} x^{4} + 2 \, a b p^{2} x^{2} - a^{2} p^{2}\right)} \log\left(b x^{2} + a\right)^{2} + 6 \, {\left({\left(p^{2} - 3 \, p \log\left(c\right) + \log\left(c\right)^{2}\right)} b^{2} x^{4} + {\left(p^{2} - 2 \, p \log\left(c\right)\right)} a b x^{2} + a^{2} p \log\left(c\right)\right)} \log\left(b x^{2} + a\right)}{a^{3} x^{4}}\right)} b p - \frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)^{3}}{6 \, x^{6}}"," ",0,"1/12*(6*(log(b*x^2 + a)^2*log(-(b*x^2 + a)/a + 1) + 2*dilog((b*x^2 + a)/a)*log(b*x^2 + a) - 2*polylog(3, (b*x^2 + a)/a))*b^2*p^2/a^3 - 6*(3*p^2 - 2*p*log(c))*(log(b*x^2 + a)*log(-(b*x^2 + a)/a + 1) + dilog((b*x^2 + a)/a))*b^2/a^3 + 12*(p^2 - 3*p*log(c) + log(c)^2)*b^2*log(x)/a^3 - (2*b^2*p^2*x^4*log(b*x^2 + a)^3 + 6*(p*log(c) - log(c)^2)*a*b*x^2 + 3*a^2*log(c)^2 - 3*((3*p^2 - 2*p*log(c))*b^2*x^4 + 2*a*b*p^2*x^2 - a^2*p^2)*log(b*x^2 + a)^2 + 6*((p^2 - 3*p*log(c) + log(c)^2)*b^2*x^4 + (p^2 - 2*p*log(c))*a*b*x^2 + a^2*p*log(c))*log(b*x^2 + a))/(a^3*x^4))*b*p - 1/6*log((b*x^2 + a)^p*c)^3/x^6","A",0
98,0,0,0,0.000000," ","integrate(x^2*log(c*(b*x^2+a)^p)^3,x, algorithm=""maxima"")","\frac{1}{3} \, p^{3} x^{3} \log\left(b x^{2} + a\right)^{3} + \int \frac{b x^{4} \log\left(c\right)^{3} + a x^{2} \log\left(c\right)^{3} - {\left({\left(2 \, p^{3} - 3 \, p^{2} \log\left(c\right)\right)} b x^{4} - 3 \, a p^{2} x^{2} \log\left(c\right)\right)} \log\left(b x^{2} + a\right)^{2} + 3 \, {\left(b p x^{4} \log\left(c\right)^{2} + a p x^{2} \log\left(c\right)^{2}\right)} \log\left(b x^{2} + a\right)}{b x^{2} + a}\,{d x}"," ",0,"1/3*p^3*x^3*log(b*x^2 + a)^3 + integrate((b*x^4*log(c)^3 + a*x^2*log(c)^3 - ((2*p^3 - 3*p^2*log(c))*b*x^4 - 3*a*p^2*x^2*log(c))*log(b*x^2 + a)^2 + 3*(b*p*x^4*log(c)^2 + a*p*x^2*log(c)^2)*log(b*x^2 + a))/(b*x^2 + a), x)","F",0
99,0,0,0,0.000000," ","integrate(log(c*(b*x^2+a)^p)^3,x, algorithm=""maxima"")","p^{3} x \log\left(b x^{2} + a\right)^{3} + \int \frac{b x^{2} \log\left(c\right)^{3} + a \log\left(c\right)^{3} - 3 \, {\left({\left(2 \, p^{3} - p^{2} \log\left(c\right)\right)} b x^{2} - a p^{2} \log\left(c\right)\right)} \log\left(b x^{2} + a\right)^{2} + 3 \, {\left(b p x^{2} \log\left(c\right)^{2} + a p \log\left(c\right)^{2}\right)} \log\left(b x^{2} + a\right)}{b x^{2} + a}\,{d x}"," ",0,"p^3*x*log(b*x^2 + a)^3 + integrate((b*x^2*log(c)^3 + a*log(c)^3 - 3*((2*p^3 - p^2*log(c))*b*x^2 - a*p^2*log(c))*log(b*x^2 + a)^2 + 3*(b*p*x^2*log(c)^2 + a*p*log(c)^2)*log(b*x^2 + a))/(b*x^2 + a), x)","F",0
100,-2,0,0,0.000000," ","integrate(log(c*(b*x^2+a)^p)^3/x^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
101,0,0,0,0.000000," ","integrate(log(c*(b*x^2+a)^p)^3/x^4,x, algorithm=""maxima"")","-\frac{p^{3} \log\left(b x^{2} + a\right)^{3}}{3 \, x^{3}} + \int \frac{b x^{2} \log\left(c\right)^{3} + a \log\left(c\right)^{3} + {\left({\left(2 \, p^{3} + 3 \, p^{2} \log\left(c\right)\right)} b x^{2} + 3 \, a p^{2} \log\left(c\right)\right)} \log\left(b x^{2} + a\right)^{2} + 3 \, {\left(b p x^{2} \log\left(c\right)^{2} + a p \log\left(c\right)^{2}\right)} \log\left(b x^{2} + a\right)}{b x^{6} + a x^{4}}\,{d x}"," ",0,"-1/3*p^3*log(b*x^2 + a)^3/x^3 + integrate((b*x^2*log(c)^3 + a*log(c)^3 + ((2*p^3 + 3*p^2*log(c))*b*x^2 + 3*a*p^2*log(c))*log(b*x^2 + a)^2 + 3*(b*p*x^2*log(c)^2 + a*p*log(c)^2)*log(b*x^2 + a))/(b*x^6 + a*x^4), x)","F",0
102,0,0,0,0.000000," ","integrate(x^3/log(c*(b*x^2+a)^p),x, algorithm=""maxima"")","\int \frac{x^{3}}{\log\left({\left(b x^{2} + a\right)}^{p} c\right)}\,{d x}"," ",0,"integrate(x^3/log((b*x^2 + a)^p*c), x)","F",0
103,0,0,0,0.000000," ","integrate(x/log(c*(b*x^2+a)^p),x, algorithm=""maxima"")","\int \frac{x}{\log\left({\left(b x^{2} + a\right)}^{p} c\right)}\,{d x}"," ",0,"integrate(x/log((b*x^2 + a)^p*c), x)","F",0
104,0,0,0,0.000000," ","integrate(1/x/log(c*(b*x^2+a)^p),x, algorithm=""maxima"")","\int \frac{1}{x \log\left({\left(b x^{2} + a\right)}^{p} c\right)}\,{d x}"," ",0,"integrate(1/(x*log((b*x^2 + a)^p*c)), x)","F",0
105,0,0,0,0.000000," ","integrate(1/x^3/log(c*(b*x^2+a)^p),x, algorithm=""maxima"")","\int \frac{1}{x^{3} \log\left({\left(b x^{2} + a\right)}^{p} c\right)}\,{d x}"," ",0,"integrate(1/(x^3*log((b*x^2 + a)^p*c)), x)","F",0
106,0,0,0,0.000000," ","integrate(x^2/log(c*(b*x^2+a)^p),x, algorithm=""maxima"")","\int \frac{x^{2}}{\log\left({\left(b x^{2} + a\right)}^{p} c\right)}\,{d x}"," ",0,"integrate(x^2/log((b*x^2 + a)^p*c), x)","F",0
107,0,0,0,0.000000," ","integrate(1/log(c*(b*x^2+a)^p),x, algorithm=""maxima"")","\int \frac{1}{\log\left({\left(b x^{2} + a\right)}^{p} c\right)}\,{d x}"," ",0,"integrate(1/log((b*x^2 + a)^p*c), x)","F",0
108,0,0,0,0.000000," ","integrate(1/x^2/log(c*(b*x^2+a)^p),x, algorithm=""maxima"")","\int \frac{1}{x^{2} \log\left({\left(b x^{2} + a\right)}^{p} c\right)}\,{d x}"," ",0,"integrate(1/(x^2*log((b*x^2 + a)^p*c)), x)","F",0
109,0,0,0,0.000000," ","integrate(x^3/log(c*(b*x^2+a)^p)^2,x, algorithm=""maxima"")","-\frac{b x^{4} + a x^{2}}{2 \, {\left(b p^{2} \log\left(b x^{2} + a\right) + b p \log\left(c\right)\right)}} + \int \frac{2 \, b x^{3} + a x}{b p^{2} \log\left(b x^{2} + a\right) + b p \log\left(c\right)}\,{d x}"," ",0,"-1/2*(b*x^4 + a*x^2)/(b*p^2*log(b*x^2 + a) + b*p*log(c)) + integrate((2*b*x^3 + a*x)/(b*p^2*log(b*x^2 + a) + b*p*log(c)), x)","F",0
110,0,0,0,0.000000," ","integrate(x/log(c*(b*x^2+a)^p)^2,x, algorithm=""maxima"")","-\frac{b x^{2} + a}{2 \, {\left(b p^{2} \log\left(b x^{2} + a\right) + b p \log\left(c\right)\right)}} + \int \frac{x}{p^{2} \log\left(b x^{2} + a\right) + p \log\left(c\right)}\,{d x}"," ",0,"-1/2*(b*x^2 + a)/(b*p^2*log(b*x^2 + a) + b*p*log(c)) + integrate(x/(p^2*log(b*x^2 + a) + p*log(c)), x)","F",0
111,0,0,0,0.000000," ","integrate(1/x/log(c*(b*x^2+a)^p)^2,x, algorithm=""maxima"")","-a \int \frac{1}{b p^{2} x^{3} \log\left(b x^{2} + a\right) + b p x^{3} \log\left(c\right)}\,{d x} - \frac{b x^{2} + a}{2 \, {\left(b p^{2} x^{2} \log\left(b x^{2} + a\right) + b p x^{2} \log\left(c\right)\right)}}"," ",0,"-a*integrate(1/(b*p^2*x^3*log(b*x^2 + a) + b*p*x^3*log(c)), x) - 1/2*(b*x^2 + a)/(b*p^2*x^2*log(b*x^2 + a) + b*p*x^2*log(c))","F",0
112,0,0,0,0.000000," ","integrate(1/x^3/log(c*(b*x^2+a)^p)^2,x, algorithm=""maxima"")","-\frac{b x^{2} + a}{2 \, {\left(b p^{2} x^{4} \log\left(b x^{2} + a\right) + b p x^{4} \log\left(c\right)\right)}} - \int \frac{b x^{2} + 2 \, a}{b p^{2} x^{5} \log\left(b x^{2} + a\right) + b p x^{5} \log\left(c\right)}\,{d x}"," ",0,"-1/2*(b*x^2 + a)/(b*p^2*x^4*log(b*x^2 + a) + b*p*x^4*log(c)) - integrate((b*x^2 + 2*a)/(b*p^2*x^5*log(b*x^2 + a) + b*p*x^5*log(c)), x)","F",0
113,0,0,0,0.000000," ","integrate(x^2/log(c*(b*x^2+a)^p)^2,x, algorithm=""maxima"")","-\frac{b x^{3} + a x}{2 \, {\left(b p^{2} \log\left(b x^{2} + a\right) + b p \log\left(c\right)\right)}} + \int \frac{3 \, b x^{2} + a}{2 \, {\left(b p^{2} \log\left(b x^{2} + a\right) + b p \log\left(c\right)\right)}}\,{d x}"," ",0,"-1/2*(b*x^3 + a*x)/(b*p^2*log(b*x^2 + a) + b*p*log(c)) + integrate(1/2*(3*b*x^2 + a)/(b*p^2*log(b*x^2 + a) + b*p*log(c)), x)","F",0
114,0,0,0,0.000000," ","integrate(1/log(c*(b*x^2+a)^p)^2,x, algorithm=""maxima"")","-\frac{b x^{2} + a}{2 \, {\left(b p^{2} x \log\left(b x^{2} + a\right) + b p x \log\left(c\right)\right)}} + \int \frac{b x^{2} - a}{2 \, {\left(b p^{2} x^{2} \log\left(b x^{2} + a\right) + b p x^{2} \log\left(c\right)\right)}}\,{d x}"," ",0,"-1/2*(b*x^2 + a)/(b*p^2*x*log(b*x^2 + a) + b*p*x*log(c)) + integrate(1/2*(b*x^2 - a)/(b*p^2*x^2*log(b*x^2 + a) + b*p*x^2*log(c)), x)","F",0
115,0,0,0,0.000000," ","integrate(1/x^2/log(c*(b*x^2+a)^p)^2,x, algorithm=""maxima"")","-\frac{b x^{2} + a}{2 \, {\left(b p^{2} x^{3} \log\left(b x^{2} + a\right) + b p x^{3} \log\left(c\right)\right)}} - \int \frac{b x^{2} + 3 \, a}{2 \, {\left(b p^{2} x^{4} \log\left(b x^{2} + a\right) + b p x^{4} \log\left(c\right)\right)}}\,{d x}"," ",0,"-1/2*(b*x^2 + a)/(b*p^2*x^3*log(b*x^2 + a) + b*p*x^3*log(c)) - integrate(1/2*(b*x^2 + 3*a)/(b*p^2*x^4*log(b*x^2 + a) + b*p*x^4*log(c)), x)","F",0
116,0,0,0,0.000000," ","integrate(x^3/log(c*(b*x^2+a)^p)^3,x, algorithm=""maxima"")","-\frac{b^{2} {\left(p + 2 \, \log\left(c\right)\right)} x^{4} + a b {\left(p + 3 \, \log\left(c\right)\right)} x^{2} + a^{2} \log\left(c\right) + {\left(2 \, b^{2} p x^{4} + 3 \, a b p x^{2} + a^{2} p\right)} \log\left(b x^{2} + a\right)}{4 \, {\left(b^{2} p^{4} \log\left(b x^{2} + a\right)^{2} + 2 \, b^{2} p^{3} \log\left(b x^{2} + a\right) \log\left(c\right) + b^{2} p^{2} \log\left(c\right)^{2}\right)}} + \int \frac{4 \, b x^{3} + 3 \, a x}{2 \, {\left(b p^{3} \log\left(b x^{2} + a\right) + b p^{2} \log\left(c\right)\right)}}\,{d x}"," ",0,"-1/4*(b^2*(p + 2*log(c))*x^4 + a*b*(p + 3*log(c))*x^2 + a^2*log(c) + (2*b^2*p*x^4 + 3*a*b*p*x^2 + a^2*p)*log(b*x^2 + a))/(b^2*p^4*log(b*x^2 + a)^2 + 2*b^2*p^3*log(b*x^2 + a)*log(c) + b^2*p^2*log(c)^2) + integrate(1/2*(4*b*x^3 + 3*a*x)/(b*p^3*log(b*x^2 + a) + b*p^2*log(c)), x)","F",0
117,0,0,0,0.000000," ","integrate(x/log(c*(b*x^2+a)^p)^3,x, algorithm=""maxima"")","-\frac{b {\left(p + \log\left(c\right)\right)} x^{2} + a {\left(p + \log\left(c\right)\right)} + {\left(b p x^{2} + a p\right)} \log\left(b x^{2} + a\right)}{4 \, {\left(b p^{4} \log\left(b x^{2} + a\right)^{2} + 2 \, b p^{3} \log\left(b x^{2} + a\right) \log\left(c\right) + b p^{2} \log\left(c\right)^{2}\right)}} + \int \frac{x}{2 \, {\left(p^{3} \log\left(b x^{2} + a\right) + p^{2} \log\left(c\right)\right)}}\,{d x}"," ",0,"-1/4*(b*(p + log(c))*x^2 + a*(p + log(c)) + (b*p*x^2 + a*p)*log(b*x^2 + a))/(b*p^4*log(b*x^2 + a)^2 + 2*b*p^3*log(b*x^2 + a)*log(c) + b*p^2*log(c)^2) + integrate(1/2*x/(p^3*log(b*x^2 + a) + p^2*log(c)), x)","F",0
118,0,0,0,0.000000," ","integrate(1/x/log(c*(b*x^2+a)^p)^3,x, algorithm=""maxima"")","-\frac{b^{2} p x^{4} + a b {\left(p - \log\left(c\right)\right)} x^{2} - a^{2} \log\left(c\right) - {\left(a b p x^{2} + a^{2} p\right)} \log\left(b x^{2} + a\right)}{4 \, {\left(b^{2} p^{4} x^{4} \log\left(b x^{2} + a\right)^{2} + 2 \, b^{2} p^{3} x^{4} \log\left(b x^{2} + a\right) \log\left(c\right) + b^{2} p^{2} x^{4} \log\left(c\right)^{2}\right)}} + \int \frac{a b x^{2} + 2 \, a^{2}}{2 \, {\left(b^{2} p^{3} x^{5} \log\left(b x^{2} + a\right) + b^{2} p^{2} x^{5} \log\left(c\right)\right)}}\,{d x}"," ",0,"-1/4*(b^2*p*x^4 + a*b*(p - log(c))*x^2 - a^2*log(c) - (a*b*p*x^2 + a^2*p)*log(b*x^2 + a))/(b^2*p^4*x^4*log(b*x^2 + a)^2 + 2*b^2*p^3*x^4*log(b*x^2 + a)*log(c) + b^2*p^2*x^4*log(c)^2) + integrate(1/2*(a*b*x^2 + 2*a^2)/(b^2*p^3*x^5*log(b*x^2 + a) + b^2*p^2*x^5*log(c)), x)","F",0
119,0,0,0,0.000000," ","integrate(1/x^3/log(c*(b*x^2+a)^p)^3,x, algorithm=""maxima"")","-\frac{b^{2} {\left(p - \log\left(c\right)\right)} x^{4} + a b {\left(p - 3 \, \log\left(c\right)\right)} x^{2} - 2 \, a^{2} \log\left(c\right) - {\left(b^{2} p x^{4} + 3 \, a b p x^{2} + 2 \, a^{2} p\right)} \log\left(b x^{2} + a\right)}{4 \, {\left(b^{2} p^{4} x^{6} \log\left(b x^{2} + a\right)^{2} + 2 \, b^{2} p^{3} x^{6} \log\left(b x^{2} + a\right) \log\left(c\right) + b^{2} p^{2} x^{6} \log\left(c\right)^{2}\right)}} + \int \frac{b^{2} x^{4} + 6 \, a b x^{2} + 6 \, a^{2}}{2 \, {\left(b^{2} p^{3} x^{7} \log\left(b x^{2} + a\right) + b^{2} p^{2} x^{7} \log\left(c\right)\right)}}\,{d x}"," ",0,"-1/4*(b^2*(p - log(c))*x^4 + a*b*(p - 3*log(c))*x^2 - 2*a^2*log(c) - (b^2*p*x^4 + 3*a*b*p*x^2 + 2*a^2*p)*log(b*x^2 + a))/(b^2*p^4*x^6*log(b*x^2 + a)^2 + 2*b^2*p^3*x^6*log(b*x^2 + a)*log(c) + b^2*p^2*x^6*log(c)^2) + integrate(1/2*(b^2*x^4 + 6*a*b*x^2 + 6*a^2)/(b^2*p^3*x^7*log(b*x^2 + a) + b^2*p^2*x^7*log(c)), x)","F",0
120,0,0,0,0.000000," ","integrate(x^2/log(c*(b*x^2+a)^p)^3,x, algorithm=""maxima"")","-\frac{b^{2} {\left(2 \, p + 3 \, \log\left(c\right)\right)} x^{4} + 2 \, a b {\left(p + 2 \, \log\left(c\right)\right)} x^{2} + a^{2} \log\left(c\right) + {\left(3 \, b^{2} p x^{4} + 4 \, a b p x^{2} + a^{2} p\right)} \log\left(b x^{2} + a\right)}{8 \, {\left(b^{2} p^{4} x \log\left(b x^{2} + a\right)^{2} + 2 \, b^{2} p^{3} x \log\left(b x^{2} + a\right) \log\left(c\right) + b^{2} p^{2} x \log\left(c\right)^{2}\right)}} + \int \frac{9 \, b^{2} x^{4} + 4 \, a b x^{2} - a^{2}}{8 \, {\left(b^{2} p^{3} x^{2} \log\left(b x^{2} + a\right) + b^{2} p^{2} x^{2} \log\left(c\right)\right)}}\,{d x}"," ",0,"-1/8*(b^2*(2*p + 3*log(c))*x^4 + 2*a*b*(p + 2*log(c))*x^2 + a^2*log(c) + (3*b^2*p*x^4 + 4*a*b*p*x^2 + a^2*p)*log(b*x^2 + a))/(b^2*p^4*x*log(b*x^2 + a)^2 + 2*b^2*p^3*x*log(b*x^2 + a)*log(c) + b^2*p^2*x*log(c)^2) + integrate(1/8*(9*b^2*x^4 + 4*a*b*x^2 - a^2)/(b^2*p^3*x^2*log(b*x^2 + a) + b^2*p^2*x^2*log(c)), x)","F",0
121,0,0,0,0.000000," ","integrate(1/log(c*(b*x^2+a)^p)^3,x, algorithm=""maxima"")","-\frac{b^{2} {\left(2 \, p + \log\left(c\right)\right)} x^{4} + 2 \, a b p x^{2} - a^{2} \log\left(c\right) + {\left(b^{2} p x^{4} - a^{2} p\right)} \log\left(b x^{2} + a\right)}{8 \, {\left(b^{2} p^{4} x^{3} \log\left(b x^{2} + a\right)^{2} + 2 \, b^{2} p^{3} x^{3} \log\left(b x^{2} + a\right) \log\left(c\right) + b^{2} p^{2} x^{3} \log\left(c\right)^{2}\right)}} + \int \frac{b^{2} x^{4} + 3 \, a^{2}}{8 \, {\left(b^{2} p^{3} x^{4} \log\left(b x^{2} + a\right) + b^{2} p^{2} x^{4} \log\left(c\right)\right)}}\,{d x}"," ",0,"-1/8*(b^2*(2*p + log(c))*x^4 + 2*a*b*p*x^2 - a^2*log(c) + (b^2*p*x^4 - a^2*p)*log(b*x^2 + a))/(b^2*p^4*x^3*log(b*x^2 + a)^2 + 2*b^2*p^3*x^3*log(b*x^2 + a)*log(c) + b^2*p^2*x^3*log(c)^2) + integrate(1/8*(b^2*x^4 + 3*a^2)/(b^2*p^3*x^4*log(b*x^2 + a) + b^2*p^2*x^4*log(c)), x)","F",0
122,0,0,0,0.000000," ","integrate(1/x^2/log(c*(b*x^2+a)^p)^3,x, algorithm=""maxima"")","-\frac{b^{2} {\left(2 \, p - \log\left(c\right)\right)} x^{4} + 2 \, a b {\left(p - 2 \, \log\left(c\right)\right)} x^{2} - 3 \, a^{2} \log\left(c\right) - {\left(b^{2} p x^{4} + 4 \, a b p x^{2} + 3 \, a^{2} p\right)} \log\left(b x^{2} + a\right)}{8 \, {\left(b^{2} p^{4} x^{5} \log\left(b x^{2} + a\right)^{2} + 2 \, b^{2} p^{3} x^{5} \log\left(b x^{2} + a\right) \log\left(c\right) + b^{2} p^{2} x^{5} \log\left(c\right)^{2}\right)}} + \int \frac{b^{2} x^{4} + 12 \, a b x^{2} + 15 \, a^{2}}{8 \, {\left(b^{2} p^{3} x^{6} \log\left(b x^{2} + a\right) + b^{2} p^{2} x^{6} \log\left(c\right)\right)}}\,{d x}"," ",0,"-1/8*(b^2*(2*p - log(c))*x^4 + 2*a*b*(p - 2*log(c))*x^2 - 3*a^2*log(c) - (b^2*p*x^4 + 4*a*b*p*x^2 + 3*a^2*p)*log(b*x^2 + a))/(b^2*p^4*x^5*log(b*x^2 + a)^2 + 2*b^2*p^3*x^5*log(b*x^2 + a)*log(c) + b^2*p^2*x^5*log(c)^2) + integrate(1/8*(b^2*x^4 + 12*a*b*x^2 + 15*a^2)/(b^2*p^3*x^6*log(b*x^2 + a) + b^2*p^2*x^6*log(c)), x)","F",0
123,0,0,0,0.000000," ","integrate(x^3/log(c*(b*x^2+a)),x, algorithm=""maxima"")","\int \frac{x^{3}}{\log\left({\left(b x^{2} + a\right)} c\right)}\,{d x}"," ",0,"integrate(x^3/log((b*x^2 + a)*c), x)","F",0
124,0,0,0,0.000000," ","integrate(x/log(c*(b*x^2+a)),x, algorithm=""maxima"")","\int \frac{x}{\log\left({\left(b x^{2} + a\right)} c\right)}\,{d x}"," ",0,"integrate(x/log((b*x^2 + a)*c), x)","F",0
125,0,0,0,0.000000," ","integrate(x^3/log(c*(b*x^2+a))^2,x, algorithm=""maxima"")","-\frac{b x^{4} + a x^{2}}{2 \, {\left(b \log\left(b x^{2} + a\right) + b \log\left(c\right)\right)}} + \int \frac{2 \, b x^{3} + a x}{b \log\left(b x^{2} + a\right) + b \log\left(c\right)}\,{d x}"," ",0,"-1/2*(b*x^4 + a*x^2)/(b*log(b*x^2 + a) + b*log(c)) + integrate((2*b*x^3 + a*x)/(b*log(b*x^2 + a) + b*log(c)), x)","F",0
126,0,0,0,0.000000," ","integrate(x/log(c*(b*x^2+a))^2,x, algorithm=""maxima"")","-\frac{b x^{2} + a}{2 \, {\left(b \log\left(b x^{2} + a\right) + b \log\left(c\right)\right)}} + \int \frac{x}{\log\left(b x^{2} + a\right) + \log\left(c\right)}\,{d x}"," ",0,"-1/2*(b*x^2 + a)/(b*log(b*x^2 + a) + b*log(c)) + integrate(x/(log(b*x^2 + a) + log(c)), x)","F",0
127,0,0,0,0.000000," ","integrate(x^3/log(c*(b*x^2+a))^3,x, algorithm=""maxima"")","-\frac{b^{2} x^{4} {\left(2 \, \log\left(c\right) + 1\right)} + a b x^{2} {\left(3 \, \log\left(c\right) + 1\right)} + a^{2} \log\left(c\right) + {\left(2 \, b^{2} x^{4} + 3 \, a b x^{2} + a^{2}\right)} \log\left(b x^{2} + a\right)}{4 \, {\left(b^{2} \log\left(b x^{2} + a\right)^{2} + 2 \, b^{2} \log\left(b x^{2} + a\right) \log\left(c\right) + b^{2} \log\left(c\right)^{2}\right)}} + \int \frac{4 \, b x^{3} + 3 \, a x}{2 \, {\left(b \log\left(b x^{2} + a\right) + b \log\left(c\right)\right)}}\,{d x}"," ",0,"-1/4*(b^2*x^4*(2*log(c) + 1) + a*b*x^2*(3*log(c) + 1) + a^2*log(c) + (2*b^2*x^4 + 3*a*b*x^2 + a^2)*log(b*x^2 + a))/(b^2*log(b*x^2 + a)^2 + 2*b^2*log(b*x^2 + a)*log(c) + b^2*log(c)^2) + integrate(1/2*(4*b*x^3 + 3*a*x)/(b*log(b*x^2 + a) + b*log(c)), x)","F",0
128,0,0,0,0.000000," ","integrate(x/log(c*(b*x^2+a))^3,x, algorithm=""maxima"")","-\frac{b x^{2} {\left(\log\left(c\right) + 1\right)} + a {\left(\log\left(c\right) + 1\right)} + {\left(b x^{2} + a\right)} \log\left(b x^{2} + a\right)}{4 \, {\left(b \log\left(b x^{2} + a\right)^{2} + 2 \, b \log\left(b x^{2} + a\right) \log\left(c\right) + b \log\left(c\right)^{2}\right)}} + \int \frac{x}{2 \, {\left(\log\left(b x^{2} + a\right) + \log\left(c\right)\right)}}\,{d x}"," ",0,"-1/4*(b*x^2*(log(c) + 1) + a*(log(c) + 1) + (b*x^2 + a)*log(b*x^2 + a))/(b*log(b*x^2 + a)^2 + 2*b*log(b*x^2 + a)*log(c) + b*log(c)^2) + integrate(1/2*x/(log(b*x^2 + a) + log(c)), x)","F",0
129,1,120,0,0.664182," ","integrate(x^5*log(c*(e*x^3+d)^p)^2,x, algorithm=""maxima"")","\frac{1}{6} \, x^{6} \log\left({\left(e x^{3} + d\right)}^{p} c\right)^{2} - \frac{1}{6} \, e p {\left(\frac{2 \, d^{2} \log\left(e x^{3} + d\right)}{e^{3}} + \frac{e x^{6} - 2 \, d x^{3}}{e^{2}}\right)} \log\left({\left(e x^{3} + d\right)}^{p} c\right) + \frac{{\left(e^{2} x^{6} - 6 \, d e x^{3} + 2 \, d^{2} \log\left(e x^{3} + d\right)^{2} + 6 \, d^{2} \log\left(e x^{3} + d\right)\right)} p^{2}}{12 \, e^{2}}"," ",0,"1/6*x^6*log((e*x^3 + d)^p*c)^2 - 1/6*e*p*(2*d^2*log(e*x^3 + d)/e^3 + (e*x^6 - 2*d*x^3)/e^2)*log((e*x^3 + d)^p*c) + 1/12*(e^2*x^6 - 6*d*e*x^3 + 2*d^2*log(e*x^3 + d)^2 + 6*d^2*log(e*x^3 + d))*p^2/e^2","A",0
130,1,97,0,0.661736," ","integrate(x^2*log(c*(e*x^3+d)^p)^2,x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \log\left({\left(e x^{3} + d\right)}^{p} c\right)^{2} - \frac{2}{3} \, {\left(\frac{x^{3}}{e} - \frac{d \log\left(e x^{3} + d\right)}{e^{2}}\right)} e p \log\left({\left(e x^{3} + d\right)}^{p} c\right) + \frac{{\left(2 \, e x^{3} - d \log\left(e x^{3} + d\right)^{2} - 2 \, d \log\left(e x^{3} + d\right)\right)} p^{2}}{3 \, e}"," ",0,"1/3*x^3*log((e*x^3 + d)^p*c)^2 - 2/3*(x^3/e - d*log(e*x^3 + d)/e^2)*e*p*log((e*x^3 + d)^p*c) + 1/3*(2*e*x^3 - d*log(e*x^3 + d)^2 - 2*d*log(e*x^3 + d))*p^2/e","A",0
131,0,0,0,0.000000," ","integrate(log(c*(e*x^3+d)^p)^2/x,x, algorithm=""maxima"")","\int \frac{\log\left({\left(e x^{3} + d\right)}^{p} c\right)^{2}}{x}\,{d x}"," ",0,"integrate(log((e*x^3 + d)^p*c)^2/x, x)","F",0
132,1,118,0,0.821102," ","integrate(log(c*(e*x^3+d)^p)^2/x^4,x, algorithm=""maxima"")","\frac{1}{3} \, e^{2} p^{2} {\left(\frac{\log\left(e x^{3} + d\right)^{2}}{d e} - \frac{2 \, {\left(3 \, \log\left(\frac{e x^{3}}{d} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{e x^{3}}{d}\right)\right)}}{d e}\right)} - \frac{2}{3} \, e p {\left(\frac{\log\left(e x^{3} + d\right)}{d} - \frac{\log\left(x^{3}\right)}{d}\right)} \log\left({\left(e x^{3} + d\right)}^{p} c\right) - \frac{\log\left({\left(e x^{3} + d\right)}^{p} c\right)^{2}}{3 \, x^{3}}"," ",0,"1/3*e^2*p^2*(log(e*x^3 + d)^2/(d*e) - 2*(3*log(e*x^3/d + 1)*log(x) + dilog(-e*x^3/d))/(d*e)) - 2/3*e*p*(log(e*x^3 + d)/d - log(x^3)/d)*log((e*x^3 + d)^p*c) - 1/3*log((e*x^3 + d)^p*c)^2/x^3","A",0
133,0,0,0,0.000000," ","integrate(x*log(c*(e*x^3+d)^p)^2,x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \log\left({\left(e x^{3} + d\right)}^{p}\right)^{2} + \int \frac{e x^{4} \log\left(c\right)^{2} + d x \log\left(c\right)^{2} - {\left({\left(3 \, e p - 2 \, e \log\left(c\right)\right)} x^{4} - 2 \, d x \log\left(c\right)\right)} \log\left({\left(e x^{3} + d\right)}^{p}\right)}{e x^{3} + d}\,{d x}"," ",0,"1/2*x^2*log((e*x^3 + d)^p)^2 + integrate((e*x^4*log(c)^2 + d*x*log(c)^2 - ((3*e*p - 2*e*log(c))*x^4 - 2*d*x*log(c))*log((e*x^3 + d)^p))/(e*x^3 + d), x)","F",0
134,0,0,0,0.000000," ","integrate(log(c*(e*x^3+d)^p)^2,x, algorithm=""maxima"")","x \log\left({\left(e x^{3} + d\right)}^{p}\right)^{2} + \int \frac{e x^{3} \log\left(c\right)^{2} + d \log\left(c\right)^{2} - 2 \, {\left({\left(3 \, e p - e \log\left(c\right)\right)} x^{3} - d \log\left(c\right)\right)} \log\left({\left(e x^{3} + d\right)}^{p}\right)}{e x^{3} + d}\,{d x}"," ",0,"x*log((e*x^3 + d)^p)^2 + integrate((e*x^3*log(c)^2 + d*log(c)^2 - 2*((3*e*p - e*log(c))*x^3 - d*log(c))*log((e*x^3 + d)^p))/(e*x^3 + d), x)","F",0
135,0,0,0,0.000000," ","integrate(log(c*(e*x^3+d)^p)^2/x^2,x, algorithm=""maxima"")","-\frac{\log\left({\left(e x^{3} + d\right)}^{p}\right)^{2}}{x} + \int \frac{e x^{3} \log\left(c\right)^{2} + d \log\left(c\right)^{2} + 2 \, {\left({\left(3 \, e p + e \log\left(c\right)\right)} x^{3} + d \log\left(c\right)\right)} \log\left({\left(e x^{3} + d\right)}^{p}\right)}{e x^{5} + d x^{2}}\,{d x}"," ",0,"-log((e*x^3 + d)^p)^2/x + integrate((e*x^3*log(c)^2 + d*log(c)^2 + 2*((3*e*p + e*log(c))*x^3 + d*log(c))*log((e*x^3 + d)^p))/(e*x^5 + d*x^2), x)","F",0
136,0,0,0,0.000000," ","integrate(log(c*(e*x^3+d)^p)^2/x^3,x, algorithm=""maxima"")","-\frac{\log\left({\left(e x^{3} + d\right)}^{p}\right)^{2}}{2 \, x^{2}} + \int \frac{e x^{3} \log\left(c\right)^{2} + d \log\left(c\right)^{2} + {\left({\left(3 \, e p + 2 \, e \log\left(c\right)\right)} x^{3} + 2 \, d \log\left(c\right)\right)} \log\left({\left(e x^{3} + d\right)}^{p}\right)}{e x^{6} + d x^{3}}\,{d x}"," ",0,"-1/2*log((e*x^3 + d)^p)^2/x^2 + integrate((e*x^3*log(c)^2 + d*log(c)^2 + ((3*e*p + 2*e*log(c))*x^3 + 2*d*log(c))*log((e*x^3 + d)^p))/(e*x^6 + d*x^3), x)","F",0
137,0,0,0,0.000000," ","integrate(log(c*(e*x^3+d)^p)^2/x^5,x, algorithm=""maxima"")","-\frac{\log\left({\left(e x^{3} + d\right)}^{p}\right)^{2}}{4 \, x^{4}} + \int \frac{2 \, e x^{3} \log\left(c\right)^{2} + 2 \, d \log\left(c\right)^{2} + {\left({\left(3 \, e p + 4 \, e \log\left(c\right)\right)} x^{3} + 4 \, d \log\left(c\right)\right)} \log\left({\left(e x^{3} + d\right)}^{p}\right)}{2 \, {\left(e x^{8} + d x^{5}\right)}}\,{d x}"," ",0,"-1/4*log((e*x^3 + d)^p)^2/x^4 + integrate(1/2*(2*e*x^3*log(c)^2 + 2*d*log(c)^2 + ((3*e*p + 4*e*log(c))*x^3 + 4*d*log(c))*log((e*x^3 + d)^p))/(e*x^8 + d*x^5), x)","F",0
138,0,0,0,0.000000," ","integrate(x^8/log(c*(e*x^3+d)^p),x, algorithm=""maxima"")","\int \frac{x^{8}}{\log\left({\left(e x^{3} + d\right)}^{p} c\right)}\,{d x}"," ",0,"integrate(x^8/log((e*x^3 + d)^p*c), x)","F",0
139,0,0,0,0.000000," ","integrate(x^5/log(c*(e*x^3+d)^p),x, algorithm=""maxima"")","\int \frac{x^{5}}{\log\left({\left(e x^{3} + d\right)}^{p} c\right)}\,{d x}"," ",0,"integrate(x^5/log((e*x^3 + d)^p*c), x)","F",0
140,0,0,0,0.000000," ","integrate(x^2/log(c*(e*x^3+d)^p),x, algorithm=""maxima"")","\int \frac{x^{2}}{\log\left({\left(e x^{3} + d\right)}^{p} c\right)}\,{d x}"," ",0,"integrate(x^2/log((e*x^3 + d)^p*c), x)","F",0
141,0,0,0,0.000000," ","integrate(1/x/log(c*(e*x^3+d)^p),x, algorithm=""maxima"")","\int \frac{1}{x \log\left({\left(e x^{3} + d\right)}^{p} c\right)}\,{d x}"," ",0,"integrate(1/(x*log((e*x^3 + d)^p*c)), x)","F",0
142,0,0,0,0.000000," ","integrate(1/x^4/log(c*(e*x^3+d)^p),x, algorithm=""maxima"")","\int \frac{1}{x^{4} \log\left({\left(e x^{3} + d\right)}^{p} c\right)}\,{d x}"," ",0,"integrate(1/(x^4*log((e*x^3 + d)^p*c)), x)","F",0
143,0,0,0,0.000000," ","integrate(x^3/log(c*(e*x^3+d)^p),x, algorithm=""maxima"")","\int \frac{x^{3}}{\log\left({\left(e x^{3} + d\right)}^{p} c\right)}\,{d x}"," ",0,"integrate(x^3/log((e*x^3 + d)^p*c), x)","F",0
144,0,0,0,0.000000," ","integrate(x/log(c*(e*x^3+d)^p),x, algorithm=""maxima"")","\int \frac{x}{\log\left({\left(e x^{3} + d\right)}^{p} c\right)}\,{d x}"," ",0,"integrate(x/log((e*x^3 + d)^p*c), x)","F",0
145,0,0,0,0.000000," ","integrate(1/log(c*(e*x^3+d)^p),x, algorithm=""maxima"")","\int \frac{1}{\log\left({\left(e x^{3} + d\right)}^{p} c\right)}\,{d x}"," ",0,"integrate(1/log((e*x^3 + d)^p*c), x)","F",0
146,0,0,0,0.000000," ","integrate(1/x^2/log(c*(e*x^3+d)^p),x, algorithm=""maxima"")","\int \frac{1}{x^{2} \log\left({\left(e x^{3} + d\right)}^{p} c\right)}\,{d x}"," ",0,"integrate(1/(x^2*log((e*x^3 + d)^p*c)), x)","F",0
147,0,0,0,0.000000," ","integrate(1/x^3/log(c*(e*x^3+d)^p),x, algorithm=""maxima"")","\int \frac{1}{x^{3} \log\left({\left(e x^{3} + d\right)}^{p} c\right)}\,{d x}"," ",0,"integrate(1/(x^3*log((e*x^3 + d)^p*c)), x)","F",0
148,0,0,0,0.000000," ","integrate(x^8/log(c*(e*x^3+d)^p)^2,x, algorithm=""maxima"")","-\frac{e x^{9} + d x^{6}}{3 \, {\left(e p \log\left({\left(e x^{3} + d\right)}^{p}\right) + e p \log\left(c\right)\right)}} + \int \frac{3 \, e x^{8} + 2 \, d x^{5}}{e p \log\left({\left(e x^{3} + d\right)}^{p}\right) + e p \log\left(c\right)}\,{d x}"," ",0,"-1/3*(e*x^9 + d*x^6)/(e*p*log((e*x^3 + d)^p) + e*p*log(c)) + integrate((3*e*x^8 + 2*d*x^5)/(e*p*log((e*x^3 + d)^p) + e*p*log(c)), x)","F",0
149,0,0,0,0.000000," ","integrate(x^5/log(c*(e*x^3+d)^p)^2,x, algorithm=""maxima"")","-\frac{e x^{6} + d x^{3}}{3 \, {\left(e p \log\left({\left(e x^{3} + d\right)}^{p}\right) + e p \log\left(c\right)\right)}} + \int \frac{2 \, e x^{5} + d x^{2}}{e p \log\left({\left(e x^{3} + d\right)}^{p}\right) + e p \log\left(c\right)}\,{d x}"," ",0,"-1/3*(e*x^6 + d*x^3)/(e*p*log((e*x^3 + d)^p) + e*p*log(c)) + integrate((2*e*x^5 + d*x^2)/(e*p*log((e*x^3 + d)^p) + e*p*log(c)), x)","F",0
150,0,0,0,0.000000," ","integrate(x^2/log(c*(e*x^3+d)^p)^2,x, algorithm=""maxima"")","-\frac{e x^{3} + d}{3 \, {\left(e p \log\left({\left(e x^{3} + d\right)}^{p}\right) + e p \log\left(c\right)\right)}} + \int \frac{x^{2}}{p \log\left({\left(e x^{3} + d\right)}^{p}\right) + p \log\left(c\right)}\,{d x}"," ",0,"-1/3*(e*x^3 + d)/(e*p*log((e*x^3 + d)^p) + e*p*log(c)) + integrate(x^2/(p*log((e*x^3 + d)^p) + p*log(c)), x)","F",0
151,0,0,0,0.000000," ","integrate(1/x/log(c*(e*x^3+d)^p)^2,x, algorithm=""maxima"")","-d \int \frac{1}{e p x^{4} \log\left({\left(e x^{3} + d\right)}^{p}\right) + e p x^{4} \log\left(c\right)}\,{d x} - \frac{e x^{3} + d}{3 \, {\left(e p x^{3} \log\left({\left(e x^{3} + d\right)}^{p}\right) + e p x^{3} \log\left(c\right)\right)}}"," ",0,"-d*integrate(1/(e*p*x^4*log((e*x^3 + d)^p) + e*p*x^4*log(c)), x) - 1/3*(e*x^3 + d)/(e*p*x^3*log((e*x^3 + d)^p) + e*p*x^3*log(c))","F",0
152,0,0,0,0.000000," ","integrate(1/x^4/log(c*(e*x^3+d)^p)^2,x, algorithm=""maxima"")","-\frac{e x^{3} + d}{3 \, {\left(e p x^{6} \log\left({\left(e x^{3} + d\right)}^{p}\right) + e p x^{6} \log\left(c\right)\right)}} - \int \frac{e x^{3} + 2 \, d}{e p x^{7} \log\left({\left(e x^{3} + d\right)}^{p}\right) + e p x^{7} \log\left(c\right)}\,{d x}"," ",0,"-1/3*(e*x^3 + d)/(e*p*x^6*log((e*x^3 + d)^p) + e*p*x^6*log(c)) - integrate((e*x^3 + 2*d)/(e*p*x^7*log((e*x^3 + d)^p) + e*p*x^7*log(c)), x)","F",0
153,0,0,0,0.000000," ","integrate(x^3/log(c*(e*x^3+d)^p)^2,x, algorithm=""maxima"")","-\frac{e x^{4} + d x}{3 \, {\left(e p \log\left({\left(e x^{3} + d\right)}^{p}\right) + e p \log\left(c\right)\right)}} + \int \frac{4 \, e x^{3} + d}{3 \, {\left(e p \log\left({\left(e x^{3} + d\right)}^{p}\right) + e p \log\left(c\right)\right)}}\,{d x}"," ",0,"-1/3*(e*x^4 + d*x)/(e*p*log((e*x^3 + d)^p) + e*p*log(c)) + integrate(1/3*(4*e*x^3 + d)/(e*p*log((e*x^3 + d)^p) + e*p*log(c)), x)","F",0
154,0,0,0,0.000000," ","integrate(x/log(c*(e*x^3+d)^p)^2,x, algorithm=""maxima"")","-\frac{e x^{3} + d}{3 \, {\left(e p x \log\left({\left(e x^{3} + d\right)}^{p}\right) + e p x \log\left(c\right)\right)}} + \int \frac{2 \, e x^{3} - d}{3 \, {\left(e p x^{2} \log\left({\left(e x^{3} + d\right)}^{p}\right) + e p x^{2} \log\left(c\right)\right)}}\,{d x}"," ",0,"-1/3*(e*x^3 + d)/(e*p*x*log((e*x^3 + d)^p) + e*p*x*log(c)) + integrate(1/3*(2*e*x^3 - d)/(e*p*x^2*log((e*x^3 + d)^p) + e*p*x^2*log(c)), x)","F",0
155,0,0,0,0.000000," ","integrate(1/log(c*(e*x^3+d)^p)^2,x, algorithm=""maxima"")","-\frac{e x^{3} + d}{3 \, {\left(e p x^{2} \log\left({\left(e x^{3} + d\right)}^{p}\right) + e p x^{2} \log\left(c\right)\right)}} + \int \frac{e x^{3} - 2 \, d}{3 \, {\left(e p x^{3} \log\left({\left(e x^{3} + d\right)}^{p}\right) + e p x^{3} \log\left(c\right)\right)}}\,{d x}"," ",0,"-1/3*(e*x^3 + d)/(e*p*x^2*log((e*x^3 + d)^p) + e*p*x^2*log(c)) + integrate(1/3*(e*x^3 - 2*d)/(e*p*x^3*log((e*x^3 + d)^p) + e*p*x^3*log(c)), x)","F",0
156,0,0,0,0.000000," ","integrate(1/x^2/log(c*(e*x^3+d)^p)^2,x, algorithm=""maxima"")","-\frac{e x^{3} + d}{3 \, {\left(e p x^{4} \log\left({\left(e x^{3} + d\right)}^{p}\right) + e p x^{4} \log\left(c\right)\right)}} - \int \frac{e x^{3} + 4 \, d}{3 \, {\left(e p x^{5} \log\left({\left(e x^{3} + d\right)}^{p}\right) + e p x^{5} \log\left(c\right)\right)}}\,{d x}"," ",0,"-1/3*(e*x^3 + d)/(e*p*x^4*log((e*x^3 + d)^p) + e*p*x^4*log(c)) - integrate(1/3*(e*x^3 + 4*d)/(e*p*x^5*log((e*x^3 + d)^p) + e*p*x^5*log(c)), x)","F",0
157,0,0,0,0.000000," ","integrate(1/x^3/log(c*(e*x^3+d)^p)^2,x, algorithm=""maxima"")","-\frac{e x^{3} + d}{3 \, {\left(e p x^{5} \log\left({\left(e x^{3} + d\right)}^{p}\right) + e p x^{5} \log\left(c\right)\right)}} - \int \frac{2 \, e x^{3} + 5 \, d}{3 \, {\left(e p x^{6} \log\left({\left(e x^{3} + d\right)}^{p}\right) + e p x^{6} \log\left(c\right)\right)}}\,{d x}"," ",0,"-1/3*(e*x^3 + d)/(e*p*x^5*log((e*x^3 + d)^p) + e*p*x^5*log(c)) - integrate(1/3*(2*e*x^3 + 5*d)/(e*p*x^6*log((e*x^3 + d)^p) + e*p*x^6*log(c)), x)","F",0
158,0,0,0,0.000000," ","integrate((f*x)^m*log(c*(e*x^2+d)^p)^3,x, algorithm=""maxima"")","\frac{f^{m} p^{3} x x^{m} \log\left(e x^{2} + d\right)^{3}}{m + 1} + \int \frac{3 \, {\left({\left(m p^{2} + p^{2}\right)} d f^{m} \log\left(c\right) - {\left(2 \, e f^{m} p^{3} - {\left(m p^{2} + p^{2}\right)} e f^{m} \log\left(c\right)\right)} x^{2}\right)} x^{m} \log\left(e x^{2} + d\right)^{2} + 3 \, {\left({\left(m p + p\right)} e f^{m} x^{2} \log\left(c\right)^{2} + {\left(m p + p\right)} d f^{m} \log\left(c\right)^{2}\right)} x^{m} \log\left(e x^{2} + d\right) + {\left(e f^{m} {\left(m + 1\right)} x^{2} \log\left(c\right)^{3} + d f^{m} {\left(m + 1\right)} \log\left(c\right)^{3}\right)} x^{m}}{e {\left(m + 1\right)} x^{2} + d {\left(m + 1\right)}}\,{d x}"," ",0,"f^m*p^3*x*x^m*log(e*x^2 + d)^3/(m + 1) + integrate((3*((m*p^2 + p^2)*d*f^m*log(c) - (2*e*f^m*p^3 - (m*p^2 + p^2)*e*f^m*log(c))*x^2)*x^m*log(e*x^2 + d)^2 + 3*((m*p + p)*e*f^m*x^2*log(c)^2 + (m*p + p)*d*f^m*log(c)^2)*x^m*log(e*x^2 + d) + (e*f^m*(m + 1)*x^2*log(c)^3 + d*f^m*(m + 1)*log(c)^3)*x^m)/(e*(m + 1)*x^2 + d*(m + 1)), x)","F",0
159,0,0,0,0.000000," ","integrate((f*x)^m*log(c*(e*x^2+d)^p)^2,x, algorithm=""maxima"")","\frac{f^{m} p^{2} x x^{m} \log\left(e x^{2} + d\right)^{2}}{m + 1} + \int \frac{2 \, {\left({\left(m p + p\right)} d f^{m} \log\left(c\right) - {\left(2 \, e f^{m} p^{2} - {\left(m p + p\right)} e f^{m} \log\left(c\right)\right)} x^{2}\right)} x^{m} \log\left(e x^{2} + d\right) + {\left(e f^{m} {\left(m + 1\right)} x^{2} \log\left(c\right)^{2} + d f^{m} {\left(m + 1\right)} \log\left(c\right)^{2}\right)} x^{m}}{e {\left(m + 1\right)} x^{2} + d {\left(m + 1\right)}}\,{d x}"," ",0,"f^m*p^2*x*x^m*log(e*x^2 + d)^2/(m + 1) + integrate((2*((m*p + p)*d*f^m*log(c) - (2*e*f^m*p^2 - (m*p + p)*e*f^m*log(c))*x^2)*x^m*log(e*x^2 + d) + (e*f^m*(m + 1)*x^2*log(c)^2 + d*f^m*(m + 1)*log(c)^2)*x^m)/(e*(m + 1)*x^2 + d*(m + 1)), x)","F",0
160,0,0,0,0.000000," ","integrate((f*x)^m*log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","\frac{f^{m} p x x^{m} \log\left(e x^{2} + d\right)}{m + 1} + \int \frac{{\left(d f^{m} {\left(m + 1\right)} \log\left(c\right) + {\left(e f^{m} {\left(m + 1\right)} \log\left(c\right) - 2 \, e f^{m} p\right)} x^{2}\right)} x^{m}}{e {\left(m + 1\right)} x^{2} + d {\left(m + 1\right)}}\,{d x}"," ",0,"f^m*p*x*x^m*log(e*x^2 + d)/(m + 1) + integrate((d*f^m*(m + 1)*log(c) + (e*f^m*(m + 1)*log(c) - 2*e*f^m*p)*x^2)*x^m/(e*(m + 1)*x^2 + d*(m + 1)), x)","F",0
161,0,0,0,0.000000," ","integrate((f*x)^m/log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","\int \frac{\left(f x\right)^{m}}{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}\,{d x}"," ",0,"integrate((f*x)^m/log((e*x^2 + d)^p*c), x)","F",0
162,0,0,0,0.000000," ","integrate((f*x)^m/log(c*(e*x^2+d)^p)^2,x, algorithm=""maxima"")","-\frac{{\left(e f^{m} x^{2} + d f^{m}\right)} x^{m}}{2 \, {\left(e p^{2} x \log\left(e x^{2} + d\right) + e p x \log\left(c\right)\right)}} + \int \frac{{\left(e f^{m} {\left(m + 1\right)} x^{2} + d f^{m} {\left(m - 1\right)}\right)} x^{m}}{2 \, {\left(e p^{2} x^{2} \log\left(e x^{2} + d\right) + e p x^{2} \log\left(c\right)\right)}}\,{d x}"," ",0,"-1/2*(e*f^m*x^2 + d*f^m)*x^m/(e*p^2*x*log(e*x^2 + d) + e*p*x*log(c)) + integrate(1/2*(e*f^m*(m + 1)*x^2 + d*f^m*(m - 1))*x^m/(e*p^2*x^2*log(e*x^2 + d) + e*p*x^2*log(c)), x)","F",0
163,1,239,0,0.558171," ","integrate((f*x)^(-1+3*n)*log(c*(d+e*x^n)^p)^2,x, algorithm=""maxima"")","\frac{e p {\left(\frac{6 \, d^{3} f^{3 \, n} \log\left(\frac{e x^{n} + d}{e}\right)}{e^{4} n} - \frac{2 \, e^{2} f^{3 \, n} x^{3 \, n} - 3 \, d e f^{3 \, n} x^{2 \, n} + 6 \, d^{2} f^{3 \, n} x^{n}}{e^{3} n}\right)} \log\left({\left(e x^{n} + d\right)}^{p} c\right)}{9 \, f} + \frac{\left(f x\right)^{3 \, n} \log\left({\left(e x^{n} + d\right)}^{p} c\right)^{2}}{3 \, f n} - \frac{{\left(18 \, d^{3} f^{3 \, n} \log\left(e x^{n} + d\right)^{2} - 4 \, e^{3} f^{3 \, n} x^{3 \, n} + 15 \, d e^{2} f^{3 \, n} x^{2 \, n} - 66 \, d^{2} e f^{3 \, n} x^{n} - 6 \, {\left(6 \, f^{3 \, n} \log\left(e\right) - 11 \, f^{3 \, n}\right)} d^{3} \log\left(e x^{n} + d\right)\right)} p^{2}}{54 \, e^{3} f n}"," ",0,"1/9*e*p*(6*d^3*f^(3*n)*log((e*x^n + d)/e)/(e^4*n) - (2*e^2*f^(3*n)*x^(3*n) - 3*d*e*f^(3*n)*x^(2*n) + 6*d^2*f^(3*n)*x^n)/(e^3*n))*log((e*x^n + d)^p*c)/f + 1/3*(f*x)^(3*n)*log((e*x^n + d)^p*c)^2/(f*n) - 1/54*(18*d^3*f^(3*n)*log(e*x^n + d)^2 - 4*e^3*f^(3*n)*x^(3*n) + 15*d*e^2*f^(3*n)*x^(2*n) - 66*d^2*e*f^(3*n)*x^n - 6*(6*f^(3*n)*log(e) - 11*f^(3*n))*d^3*log(e*x^n + d))*p^2/(e^3*f*n)","A",0
164,1,200,0,0.566445," ","integrate((f*x)^(-1+2*n)*log(c*(d+e*x^n)^p)^2,x, algorithm=""maxima"")","-\frac{e p {\left(\frac{2 \, d^{2} f^{2 \, n} \log\left(\frac{e x^{n} + d}{e}\right)}{e^{3} n} + \frac{e f^{2 \, n} x^{2 \, n} - 2 \, d f^{2 \, n} x^{n}}{e^{2} n}\right)} \log\left({\left(e x^{n} + d\right)}^{p} c\right)}{2 \, f} + \frac{\left(f x\right)^{2 \, n} \log\left({\left(e x^{n} + d\right)}^{p} c\right)^{2}}{2 \, f n} + \frac{{\left(2 \, d^{2} f^{2 \, n} \log\left(e x^{n} + d\right)^{2} + e^{2} f^{2 \, n} x^{2 \, n} - 6 \, d e f^{2 \, n} x^{n} - 2 \, {\left(2 \, f^{2 \, n} \log\left(e\right) - 3 \, f^{2 \, n}\right)} d^{2} \log\left(e x^{n} + d\right)\right)} p^{2}}{4 \, e^{2} f n}"," ",0,"-1/2*e*p*(2*d^2*f^(2*n)*log((e*x^n + d)/e)/(e^3*n) + (e*f^(2*n)*x^(2*n) - 2*d*f^(2*n)*x^n)/(e^2*n))*log((e*x^n + d)^p*c)/f + 1/2*(f*x)^(2*n)*log((e*x^n + d)^p*c)^2/(f*n) + 1/4*(2*d^2*f^(2*n)*log(e*x^n + d)^2 + e^2*f^(2*n)*x^(2*n) - 6*d*e*f^(2*n)*x^n - 2*(2*f^(2*n)*log(e) - 3*f^(2*n))*d^2*log(e*x^n + d))*p^2/(e^2*f*n)","A",0
165,1,146,0,0.544456," ","integrate((f*x)^(-1+n)*log(c*(d+e*x^n)^p)^2,x, algorithm=""maxima"")","-\frac{2 \, e p {\left(\frac{f^{n} x^{n}}{e n} - \frac{d f^{n} \log\left(\frac{e x^{n} + d}{e}\right)}{e^{2} n}\right)} \log\left({\left(e x^{n} + d\right)}^{p} c\right)}{f} + \frac{\left(f x\right)^{n} \log\left({\left(e x^{n} + d\right)}^{p} c\right)^{2}}{f n} - \frac{{\left(d f^{n} \log\left(e x^{n} + d\right)^{2} - 2 \, e f^{n} x^{n} - 2 \, {\left(f^{n} \log\left(e\right) - f^{n}\right)} d \log\left(e x^{n} + d\right)\right)} p^{2}}{e f n}"," ",0,"-2*e*p*(f^n*x^n/(e*n) - d*f^n*log((e*x^n + d)/e)/(e^2*n))*log((e*x^n + d)^p*c)/f + (f*x)^n*log((e*x^n + d)^p*c)^2/(f*n) - (d*f^n*log(e*x^n + d)^2 - 2*e*f^n*x^n - 2*(f^n*log(e) - f^n)*d*log(e*x^n + d))*p^2/(e*f*n)","A",0
166,0,0,0,0.000000," ","integrate(log(c*(d+e*x^n)^p)^2/f/x,x, algorithm=""maxima"")","\frac{d {\left(\frac{\log\left(x\right)}{d} - \frac{\log\left(\frac{e x^{n} + d}{e}\right)}{d n}\right)} \log\left(c\right)^{2} + \log\left({\left(e x^{n} + d\right)}^{p}\right)^{2} \log\left(x\right) + \frac{\log\left(c\right)^{2} \log\left(\frac{e x^{n} + d}{e}\right)}{n} - \int \frac{2 \, {\left({\left(e n p \log\left(x\right) - e \log\left(c\right)\right)} x^{n} - d \log\left(c\right)\right)} \log\left({\left(e x^{n} + d\right)}^{p}\right)}{e x x^{n} + d x}\,{d x}}{f}"," ",0,"(log((e*x^n + d)^p)^2*log(x) - integrate(-(e*x^n*log(c)^2 + d*log(c)^2 - 2*((e*n*p*log(x) - e*log(c))*x^n - d*log(c))*log((e*x^n + d)^p))/(e*x*x^n + d*x), x))/f","F",0
167,0,0,0,0.000000," ","integrate((f*x)^(-1-n)*log(c*(d+e*x^n)^p)^2,x, algorithm=""maxima"")","-\frac{{\left(e n^{2} p^{2} x^{n} \log\left(x\right)^{2} - e p^{2} x^{n} \log\left(e x^{n} + d\right)^{2} + d \log\left({\left(e x^{n} + d\right)}^{p}\right)^{2} + d \log\left(c\right)^{2} - 2 \, {\left(e n p x^{n} \log\left(x\right) - e p x^{n} \log\left(e x^{n} + d\right) - d \log\left(c\right)\right)} \log\left({\left(e x^{n} + d\right)}^{p}\right)\right)} f^{-n - 1}}{d n x^{n}} + \int \frac{2 \, {\left(e n p^{2} \log\left(x\right) + e p \log\left(c\right)\right)}}{e f^{n + 1} x x^{n} + d f^{n + 1} x}\,{d x}"," ",0,"-(e*n^2*p^2*x^n*log(x)^2 - e*p^2*x^n*log(e*x^n + d)^2 + d*log((e*x^n + d)^p)^2 + d*log(c)^2 - 2*(e*n*p*x^n*log(x) - e*p*x^n*log(e*x^n + d) - d*log(c))*log((e*x^n + d)^p))*f^(-n - 1)/(d*n*x^n) + integrate(2*(e*n*p^2*log(x) + e*p*log(c))/(e*f^(n + 1)*x*x^n + d*f^(n + 1)*x), x)","F",0
168,0,0,0,0.000000," ","integrate((f*x)^(-1-2*n)*log(c*(d+e*x^n)^p)^2,x, algorithm=""maxima"")","\frac{{\left(e^{2} n^{2} p^{2} x^{2 \, n} \log\left(x\right)^{2} - e^{2} p^{2} x^{2 \, n} \log\left(e x^{n} + d\right)^{2} - 2 \, d e p x^{n} \log\left(c\right) - d^{2} \log\left({\left(e x^{n} + d\right)}^{p}\right)^{2} - d^{2} \log\left(c\right)^{2} - 2 \, {\left(e^{2} n p x^{2 \, n} \log\left(x\right) - e^{2} p x^{2 \, n} \log\left(e x^{n} + d\right) + d e p x^{n} + d^{2} \log\left(c\right)\right)} \log\left({\left(e x^{n} + d\right)}^{p}\right)\right)} f^{-2 \, n - 1}}{2 \, d^{2} n x^{2 \, n}} - \int \frac{e^{2} n p^{2} \log\left(x\right) - e^{2} p^{2} + e^{2} p \log\left(c\right)}{d e f^{2 \, n + 1} x x^{n} + d^{2} f^{2 \, n + 1} x}\,{d x}"," ",0,"1/2*(e^2*n^2*p^2*x^(2*n)*log(x)^2 - e^2*p^2*x^(2*n)*log(e*x^n + d)^2 - 2*d*e*p*x^n*log(c) - d^2*log((e*x^n + d)^p)^2 - d^2*log(c)^2 - 2*(e^2*n*p*x^(2*n)*log(x) - e^2*p*x^(2*n)*log(e*x^n + d) + d*e*p*x^n + d^2*log(c))*log((e*x^n + d)^p))*f^(-2*n - 1)/(d^2*n*x^(2*n)) - integrate((e^2*n*p^2*log(x) - e^2*p^2 + e^2*p*log(c))/(d*e*f^(2*n + 1)*x*x^n + d^2*f^(2*n + 1)*x), x)","F",0
169,0,0,0,0.000000," ","integrate(log(1+e*x^n)/x,x, algorithm=""maxima"")","-\frac{1}{2} \, n \log\left(x\right)^{2} + n \int \frac{\log\left(x\right)}{e x x^{n} + x}\,{d x} + \log\left(e x^{n} + 1\right) \log\left(x\right)"," ",0,"-1/2*n*log(x)^2 + n*integrate(log(x)/(e*x*x^n + x), x) + log(e*x^n + 1)*log(x)","F",0
170,0,0,0,0.000000," ","integrate(log(2+e*x^n)/x,x, algorithm=""maxima"")","-\frac{1}{2} \, n \log\left(x\right)^{2} + 2 \, n \int \frac{\log\left(x\right)}{e x x^{n} + 2 \, x}\,{d x} + \log\left(e x^{n} + 2\right) \log\left(x\right)"," ",0,"-1/2*n*log(x)^2 + 2*n*integrate(log(x)/(e*x*x^n + 2*x), x) + log(e*x^n + 2)*log(x)","F",0
171,0,0,0,0.000000," ","integrate(log(6+2*e*x^n)/x,x, algorithm=""maxima"")","-\frac{1}{2} \, n \log\left(x\right)^{2} + 3 \, n \int \frac{\log\left(x\right)}{e x x^{n} + 3 \, x}\,{d x} + \log\left(2\right) \log\left(x\right) + \log\left(e x^{n} + 3\right) \log\left(x\right)"," ",0,"-1/2*n*log(x)^2 + 3*n*integrate(log(x)/(e*x*x^n + 3*x), x) + log(2)*log(x) + log(e*x^n + 3)*log(x)","F",0
172,0,0,0,0.000000," ","integrate(log(c*(d+e*x^n))/x,x, algorithm=""maxima"")","d n \int \frac{\log\left(x\right)}{e x x^{n} + d x}\,{d x} - \frac{1}{2} \, n \log\left(x\right)^{2} + \log\left(e x^{n} + d\right) \log\left(x\right) + \log\left(c\right) \log\left(x\right)"," ",0,"d*n*integrate(log(x)/(e*x*x^n + d*x), x) - 1/2*n*log(x)^2 + log(e*x^n + d)*log(x) + log(c)*log(x)","F",0
173,0,0,0,0.000000," ","integrate(log(c*(d+e*x^n)^p)/x,x, algorithm=""maxima"")","d n p \int \frac{\log\left(x\right)}{e x x^{n} + d x}\,{d x} - \frac{1}{2} \, n p \log\left(x\right)^{2} + \log\left({\left(e x^{n} + d\right)}^{p}\right) \log\left(x\right) + \log\left(c\right) \log\left(x\right)"," ",0,"d*n*p*integrate(log(x)/(e*x*x^n + d*x), x) - 1/2*n*p*log(x)^2 + log((e*x^n + d)^p)*log(x) + log(c)*log(x)","F",0
174,0,0,0,0.000000," ","integrate(log(c*(d+e*x^n)^p)^2/x,x, algorithm=""maxima"")","\log\left({\left(e x^{n} + d\right)}^{p}\right)^{2} \log\left(x\right) - \int -\frac{e x^{n} \log\left(c\right)^{2} + d \log\left(c\right)^{2} - 2 \, {\left({\left(e n p \log\left(x\right) - e \log\left(c\right)\right)} x^{n} - d \log\left(c\right)\right)} \log\left({\left(e x^{n} + d\right)}^{p}\right)}{e x x^{n} + d x}\,{d x}"," ",0,"log((e*x^n + d)^p)^2*log(x) - integrate(-(e*x^n*log(c)^2 + d*log(c)^2 - 2*((e*n*p*log(x) - e*log(c))*x^n - d*log(c))*log((e*x^n + d)^p))/(e*x*x^n + d*x), x)","F",0
175,0,0,0,0.000000," ","integrate(log(c*(d+e*x^n)^p)^3/x,x, algorithm=""maxima"")","\log\left({\left(e x^{n} + d\right)}^{p}\right)^{3} \log\left(x\right) - \int -\frac{e x^{n} \log\left(c\right)^{3} + d \log\left(c\right)^{3} - 3 \, {\left({\left(e n p \log\left(x\right) - e \log\left(c\right)\right)} x^{n} - d \log\left(c\right)\right)} \log\left({\left(e x^{n} + d\right)}^{p}\right)^{2} + 3 \, {\left(e x^{n} \log\left(c\right)^{2} + d \log\left(c\right)^{2}\right)} \log\left({\left(e x^{n} + d\right)}^{p}\right)}{e x x^{n} + d x}\,{d x}"," ",0,"log((e*x^n + d)^p)^3*log(x) - integrate(-(e*x^n*log(c)^3 + d*log(c)^3 - 3*((e*n*p*log(x) - e*log(c))*x^n - d*log(c))*log((e*x^n + d)^p)^2 + 3*(e*x^n*log(c)^2 + d*log(c)^2)*log((e*x^n + d)^p))/(e*x*x^n + d*x), x)","F",0
176,1,214,0,0.448521," ","integrate((e*x+d)^3*log(c*(b*x+a)^p),x, algorithm=""maxima"")","-\frac{1}{48} \, b p {\left(\frac{3 \, b^{3} e^{3} x^{4} + 4 \, {\left(4 \, b^{3} d e^{2} - a b^{2} e^{3}\right)} x^{3} + 6 \, {\left(6 \, b^{3} d^{2} e - 4 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} x^{2} + 12 \, {\left(4 \, b^{3} d^{3} - 6 \, a b^{2} d^{2} e + 4 \, a^{2} b d e^{2} - a^{3} e^{3}\right)} x}{b^{4}} - \frac{12 \, {\left(4 \, a b^{3} d^{3} - 6 \, a^{2} b^{2} d^{2} e + 4 \, a^{3} b d e^{2} - a^{4} e^{3}\right)} \log\left(b x + a\right)}{b^{5}}\right)} + \frac{1}{4} \, {\left(e^{3} x^{4} + 4 \, d e^{2} x^{3} + 6 \, d^{2} e x^{2} + 4 \, d^{3} x\right)} \log\left({\left(b x + a\right)}^{p} c\right)"," ",0,"-1/48*b*p*((3*b^3*e^3*x^4 + 4*(4*b^3*d*e^2 - a*b^2*e^3)*x^3 + 6*(6*b^3*d^2*e - 4*a*b^2*d*e^2 + a^2*b*e^3)*x^2 + 12*(4*b^3*d^3 - 6*a*b^2*d^2*e + 4*a^2*b*d*e^2 - a^3*e^3)*x)/b^4 - 12*(4*a*b^3*d^3 - 6*a^2*b^2*d^2*e + 4*a^3*b*d*e^2 - a^4*e^3)*log(b*x + a)/b^5) + 1/4*(e^3*x^4 + 4*d*e^2*x^3 + 6*d^2*e*x^2 + 4*d^3*x)*log((b*x + a)^p*c)","A",0
177,1,136,0,0.444361," ","integrate((e*x+d)^2*log(c*(b*x+a)^p),x, algorithm=""maxima"")","-\frac{1}{18} \, b p {\left(\frac{2 \, b^{2} e^{2} x^{3} + 3 \, {\left(3 \, b^{2} d e - a b e^{2}\right)} x^{2} + 6 \, {\left(3 \, b^{2} d^{2} - 3 \, a b d e + a^{2} e^{2}\right)} x}{b^{3}} - \frac{6 \, {\left(3 \, a b^{2} d^{2} - 3 \, a^{2} b d e + a^{3} e^{2}\right)} \log\left(b x + a\right)}{b^{4}}\right)} + \frac{1}{3} \, {\left(e^{2} x^{3} + 3 \, d e x^{2} + 3 \, d^{2} x\right)} \log\left({\left(b x + a\right)}^{p} c\right)"," ",0,"-1/18*b*p*((2*b^2*e^2*x^3 + 3*(3*b^2*d*e - a*b*e^2)*x^2 + 6*(3*b^2*d^2 - 3*a*b*d*e + a^2*e^2)*x)/b^3 - 6*(3*a*b^2*d^2 - 3*a^2*b*d*e + a^3*e^2)*log(b*x + a)/b^4) + 1/3*(e^2*x^3 + 3*d*e*x^2 + 3*d^2*x)*log((b*x + a)^p*c)","A",0
178,1,74,0,0.439798," ","integrate((e*x+d)*log(c*(b*x+a)^p),x, algorithm=""maxima"")","-\frac{1}{4} \, b p {\left(\frac{b e x^{2} + 2 \, {\left(2 \, b d - a e\right)} x}{b^{2}} - \frac{2 \, {\left(2 \, a b d - a^{2} e\right)} \log\left(b x + a\right)}{b^{3}}\right)} + \frac{1}{2} \, {\left(e x^{2} + 2 \, d x\right)} \log\left({\left(b x + a\right)}^{p} c\right)"," ",0,"-1/4*b*p*((b*e*x^2 + 2*(2*b*d - a*e)*x)/b^2 - 2*(2*a*b*d - a^2*e)*log(b*x + a)/b^3) + 1/2*(e*x^2 + 2*d*x)*log((b*x + a)^p*c)","A",0
179,1,35,0,0.430549," ","integrate(log(c*(b*x+a)^p),x, algorithm=""maxima"")","-b p {\left(\frac{x}{b} - \frac{a \log\left(b x + a\right)}{b^{2}}\right)} + x \log\left({\left(b x + a\right)}^{p} c\right)"," ",0,"-b*p*(x/b - a*log(b*x + a)/b^2) + x*log((b*x + a)^p*c)","A",0
180,1,118,0,0.467616," ","integrate(log(c*(b*x+a)^p)/(e*x+d),x, algorithm=""maxima"")","\frac{b p {\left(\frac{\log\left(b x + a\right) \log\left(e x + d\right)}{b} - \frac{\log\left(e x + d\right) \log\left(-\frac{b e x + b d}{b d - a e} + 1\right) + {\rm Li}_2\left(\frac{b e x + b d}{b d - a e}\right)}{b}\right)}}{e} - \frac{p \log\left(b x + a\right) \log\left(e x + d\right)}{e} + \frac{\log\left({\left(b x + a\right)}^{p} c\right) \log\left(e x + d\right)}{e}"," ",0,"b*p*(log(b*x + a)*log(e*x + d)/b - (log(e*x + d)*log(-(b*e*x + b*d)/(b*d - a*e) + 1) + dilog((b*e*x + b*d)/(b*d - a*e)))/b)/e - p*log(b*x + a)*log(e*x + d)/e + log((b*x + a)^p*c)*log(e*x + d)/e","B",0
181,1,65,0,0.443918," ","integrate(log(c*(b*x+a)^p)/(e*x+d)^2,x, algorithm=""maxima"")","\frac{b p {\left(\frac{\log\left(b x + a\right)}{b d - a e} - \frac{\log\left(e x + d\right)}{b d - a e}\right)}}{e} - \frac{\log\left({\left(b x + a\right)}^{p} c\right)}{{\left(e x + d\right)} e}"," ",0,"b*p*(log(b*x + a)/(b*d - a*e) - log(e*x + d)/(b*d - a*e))/e - log((b*x + a)^p*c)/((e*x + d)*e)","A",0
182,1,120,0,0.447271," ","integrate(log(c*(b*x+a)^p)/(e*x+d)^3,x, algorithm=""maxima"")","\frac{b p {\left(\frac{b \log\left(b x + a\right)}{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}} - \frac{b \log\left(e x + d\right)}{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}} + \frac{1}{b d^{2} - a d e + {\left(b d e - a e^{2}\right)} x}\right)}}{2 \, e} - \frac{\log\left({\left(b x + a\right)}^{p} c\right)}{2 \, {\left(e x + d\right)}^{2} e}"," ",0,"1/2*b*p*(b*log(b*x + a)/(b^2*d^2 - 2*a*b*d*e + a^2*e^2) - b*log(e*x + d)/(b^2*d^2 - 2*a*b*d*e + a^2*e^2) + 1/(b*d^2 - a*d*e + (b*d*e - a*e^2)*x))/e - 1/2*log((b*x + a)^p*c)/((e*x + d)^2*e)","A",0
183,1,232,0,0.469898," ","integrate(log(c*(b*x+a)^p)/(e*x+d)^4,x, algorithm=""maxima"")","\frac{{\left(\frac{2 \, b^{2} \log\left(b x + a\right)}{b^{3} d^{3} - 3 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} - a^{3} e^{3}} - \frac{2 \, b^{2} \log\left(e x + d\right)}{b^{3} d^{3} - 3 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} - a^{3} e^{3}} + \frac{2 \, b e x + 3 \, b d - a e}{b^{2} d^{4} - 2 \, a b d^{3} e + a^{2} d^{2} e^{2} + {\left(b^{2} d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4}\right)} x^{2} + 2 \, {\left(b^{2} d^{3} e - 2 \, a b d^{2} e^{2} + a^{2} d e^{3}\right)} x}\right)} b p}{6 \, e} - \frac{\log\left({\left(b x + a\right)}^{p} c\right)}{3 \, {\left(e x + d\right)}^{3} e}"," ",0,"1/6*(2*b^2*log(b*x + a)/(b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3) - 2*b^2*log(e*x + d)/(b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3) + (2*b*e*x + 3*b*d - a*e)/(b^2*d^4 - 2*a*b*d^3*e + a^2*d^2*e^2 + (b^2*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4)*x^2 + 2*(b^2*d^3*e - 2*a*b*d^2*e^2 + a^2*d*e^3)*x))*b*p/e - 1/3*log((b*x + a)^p*c)/((e*x + d)^3*e)","A",0
184,1,177,0,0.985755," ","integrate((e*x+d)^3*log(c*(b*x^2+a)^p),x, algorithm=""maxima"")","\frac{1}{24} \, b p {\left(\frac{48 \, {\left(a b d^{3} - a^{2} d e^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{2}} - \frac{3 \, b e^{3} x^{4} + 16 \, b d e^{2} x^{3} + 6 \, {\left(6 \, b d^{2} e - a e^{3}\right)} x^{2} + 48 \, {\left(b d^{3} - a d e^{2}\right)} x}{b^{2}} + \frac{6 \, {\left(6 \, a b d^{2} e - a^{2} e^{3}\right)} \log\left(b x^{2} + a\right)}{b^{3}}\right)} + \frac{1}{4} \, {\left(e^{3} x^{4} + 4 \, d e^{2} x^{3} + 6 \, d^{2} e x^{2} + 4 \, d^{3} x\right)} \log\left({\left(b x^{2} + a\right)}^{p} c\right)"," ",0,"1/24*b*p*(48*(a*b*d^3 - a^2*d*e^2)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^2) - (3*b*e^3*x^4 + 16*b*d*e^2*x^3 + 6*(6*b*d^2*e - a*e^3)*x^2 + 48*(b*d^3 - a*d*e^2)*x)/b^2 + 6*(6*a*b*d^2*e - a^2*e^3)*log(b*x^2 + a)/b^3) + 1/4*(e^3*x^4 + 4*d*e^2*x^3 + 6*d^2*e*x^2 + 4*d^3*x)*log((b*x^2 + a)^p*c)","A",0
185,1,131,0,0.990375," ","integrate((e*x+d)^2*log(c*(b*x^2+a)^p),x, algorithm=""maxima"")","\frac{1}{9} \, {\left(\frac{9 \, a d e \log\left(b x^{2} + a\right)}{b^{2}} + \frac{6 \, {\left(3 \, a b d^{2} - a^{2} e^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{2}} - \frac{2 \, b e^{2} x^{3} + 9 \, b d e x^{2} + 6 \, {\left(3 \, b d^{2} - a e^{2}\right)} x}{b^{2}}\right)} b p + \frac{1}{3} \, {\left(e^{2} x^{3} + 3 \, d e x^{2} + 3 \, d^{2} x\right)} \log\left({\left(b x^{2} + a\right)}^{p} c\right)"," ",0,"1/9*(9*a*d*e*log(b*x^2 + a)/b^2 + 6*(3*a*b*d^2 - a^2*e^2)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^2) - (2*b*e^2*x^3 + 9*b*d*e*x^2 + 6*(3*b*d^2 - a*e^2)*x)/b^2)*b*p + 1/3*(e^2*x^3 + 3*d*e*x^2 + 3*d^2*x)*log((b*x^2 + a)^p*c)","A",0
186,1,80,0,0.982290," ","integrate((e*x+d)*log(c*(b*x^2+a)^p),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{4 \, a d \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b} + \frac{a e \log\left(b x^{2} + a\right)}{b^{2}} - \frac{e x^{2} + 4 \, d x}{b}\right)} b p + \frac{1}{2} \, {\left(e x^{2} + 2 \, d x\right)} \log\left({\left(b x^{2} + a\right)}^{p} c\right)"," ",0,"1/2*(4*a*d*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b) + a*e*log(b*x^2 + a)/b^2 - (e*x^2 + 4*d*x)/b)*b*p + 1/2*(e*x^2 + 2*d*x)*log((b*x^2 + a)^p*c)","A",0
187,1,45,0,0.991442," ","integrate(log(c*(b*x^2+a)^p),x, algorithm=""maxima"")","2 \, b p {\left(\frac{a \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b} - \frac{x}{b}\right)} + x \log\left({\left(b x^{2} + a\right)}^{p} c\right)"," ",0,"2*b*p*(a*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b) - x/b) + x*log((b*x^2 + a)^p*c)","A",0
188,0,0,0,0.000000," ","integrate(log(c*(b*x^2+a)^p)/(e*x+d),x, algorithm=""maxima"")","\int \frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)}{e x + d}\,{d x}"," ",0,"integrate(log((b*x^2 + a)^p*c)/(e*x + d), x)","F",0
189,1,108,0,1.507975," ","integrate(log(c*(b*x^2+a)^p)/(e*x+d)^2,x, algorithm=""maxima"")","\frac{{\left(\frac{2 \, a e \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{{\left(b d^{2} + a e^{2}\right)} \sqrt{a b}} + \frac{d \log\left(b x^{2} + a\right)}{b d^{2} + a e^{2}} - \frac{2 \, d \log\left(e x + d\right)}{b d^{2} + a e^{2}}\right)} b p}{e} - \frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)}{{\left(e x + d\right)} e}"," ",0,"(2*a*e*arctan(b*x/sqrt(a*b))/((b*d^2 + a*e^2)*sqrt(a*b)) + d*log(b*x^2 + a)/(b*d^2 + a*e^2) - 2*d*log(e*x + d)/(b*d^2 + a*e^2))*b*p/e - log((b*x^2 + a)^p*c)/((e*x + d)*e)","A",0
190,1,206,0,1.074795," ","integrate(log(c*(b*x^2+a)^p)/(e*x+d)^3,x, algorithm=""maxima"")","\frac{{\left(\frac{4 \, a b d e \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{{\left(b^{2} d^{4} + 2 \, a b d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{a b}} + \frac{{\left(b d^{2} - a e^{2}\right)} \log\left(b x^{2} + a\right)}{b^{2} d^{4} + 2 \, a b d^{2} e^{2} + a^{2} e^{4}} - \frac{2 \, {\left(b d^{2} - a e^{2}\right)} \log\left(e x + d\right)}{b^{2} d^{4} + 2 \, a b d^{2} e^{2} + a^{2} e^{4}} + \frac{2 \, d}{b d^{3} + a d e^{2} + {\left(b d^{2} e + a e^{3}\right)} x}\right)} b p}{2 \, e} - \frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)}{2 \, {\left(e x + d\right)}^{2} e}"," ",0,"1/2*(4*a*b*d*e*arctan(b*x/sqrt(a*b))/((b^2*d^4 + 2*a*b*d^2*e^2 + a^2*e^4)*sqrt(a*b)) + (b*d^2 - a*e^2)*log(b*x^2 + a)/(b^2*d^4 + 2*a*b*d^2*e^2 + a^2*e^4) - 2*(b*d^2 - a*e^2)*log(e*x + d)/(b^2*d^4 + 2*a*b*d^2*e^2 + a^2*e^4) + 2*d/(b*d^3 + a*d*e^2 + (b*d^2*e + a*e^3)*x))*b*p/e - 1/2*log((b*x^2 + a)^p*c)/((e*x + d)^2*e)","A",0
191,1,332,0,1.020873," ","integrate((e*x+d)^3*log(c*(b*x^3+a)^p),x, algorithm=""maxima"")","\frac{1}{16} \, b p {\left(\frac{4 \, \sqrt{3} {\left(6 \, a b d^{2} e \left(\frac{a}{b}\right)^{\frac{2}{3}} + 4 \, a b d^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}} - a^{2} e^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{a b^{2}} - \frac{3 \, b e^{3} x^{4} + 16 \, b d e^{2} x^{3} + 36 \, b d^{2} e x^{2} + 12 \, {\left(4 \, b d^{3} - a e^{3}\right)} x}{b^{2}} + \frac{2 \, {\left(8 \, a b d e^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} + 6 \, a b d^{2} e \left(\frac{a}{b}\right)^{\frac{1}{3}} - 4 \, a b d^{3} + a^{2} e^{3}\right)} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{4 \, {\left(4 \, a b d e^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} - 6 \, a b d^{2} e \left(\frac{a}{b}\right)^{\frac{1}{3}} + 4 \, a b d^{3} - a^{2} e^{3}\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}\right)} + \frac{1}{4} \, {\left(e^{3} x^{4} + 4 \, d e^{2} x^{3} + 6 \, d^{2} e x^{2} + 4 \, d^{3} x\right)} \log\left({\left(b x^{3} + a\right)}^{p} c\right)"," ",0,"1/16*b*p*(4*sqrt(3)*(6*a*b*d^2*e*(a/b)^(2/3) + 4*a*b*d^3*(a/b)^(1/3) - a^2*e^3*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b^2) - (3*b*e^3*x^4 + 16*b*d*e^2*x^3 + 36*b*d^2*e*x^2 + 12*(4*b*d^3 - a*e^3)*x)/b^2 + 2*(8*a*b*d*e^2*(a/b)^(2/3) + 6*a*b*d^2*e*(a/b)^(1/3) - 4*a*b*d^3 + a^2*e^3)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^3*(a/b)^(2/3)) + 4*(4*a*b*d*e^2*(a/b)^(2/3) - 6*a*b*d^2*e*(a/b)^(1/3) + 4*a*b*d^3 - a^2*e^3)*log(x + (a/b)^(1/3))/(b^3*(a/b)^(2/3))) + 1/4*(e^3*x^4 + 4*d*e^2*x^3 + 6*d^2*e*x^2 + 4*d^3*x)*log((b*x^3 + a)^p*c)","A",0
192,1,249,0,1.020325," ","integrate((e*x+d)^2*log(c*(b*x^3+a)^p),x, algorithm=""maxima"")","-\frac{1}{6} \, b p {\left(\frac{2 \, e^{2} x^{3} + 9 \, d e x^{2} + 18 \, d^{2} x}{b} - \frac{6 \, \sqrt{3} {\left(a b d e \left(\frac{a}{b}\right)^{\frac{2}{3}} + a b d^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{a b^{2}} - \frac{{\left(2 \, a e^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} + 3 \, a d e \left(\frac{a}{b}\right)^{\frac{1}{3}} - 3 \, a d^{2}\right)} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{2 \, {\left(a e^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} - 3 \, a d e \left(\frac{a}{b}\right)^{\frac{1}{3}} + 3 \, a d^{2}\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}\right)} + \frac{1}{3} \, {\left(e^{2} x^{3} + 3 \, d e x^{2} + 3 \, d^{2} x\right)} \log\left({\left(b x^{3} + a\right)}^{p} c\right)"," ",0,"-1/6*b*p*((2*e^2*x^3 + 9*d*e*x^2 + 18*d^2*x)/b - 6*sqrt(3)*(a*b*d*e*(a/b)^(2/3) + a*b*d^2*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(a*b^2) - (2*a*e^2*(a/b)^(2/3) + 3*a*d*e*(a/b)^(1/3) - 3*a*d^2)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^2*(a/b)^(2/3)) - 2*(a*e^2*(a/b)^(2/3) - 3*a*d*e*(a/b)^(1/3) + 3*a*d^2)*log(x + (a/b)^(1/3))/(b^2*(a/b)^(2/3))) + 1/3*(e^2*x^3 + 3*d*e*x^2 + 3*d^2*x)*log((b*x^3 + a)^p*c)","A",0
193,1,187,0,1.013536," ","integrate((e*x+d)*log(c*(b*x^3+a)^p),x, algorithm=""maxima"")","-\frac{1}{4} \, b p {\left(\frac{3 \, {\left(e x^{2} + 4 \, d x\right)}}{b} - \frac{2 \, \sqrt{3} {\left(a e \left(\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, a d\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{{\left(a e \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, a d\right)} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{2 \, {\left(a e \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, a d\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}\right)} + \frac{1}{2} \, {\left(e x^{2} + 2 \, d x\right)} \log\left({\left(b x^{3} + a\right)}^{p} c\right)"," ",0,"-1/4*b*p*(3*(e*x^2 + 4*d*x)/b - 2*sqrt(3)*(a*e*(a/b)^(1/3) + 2*a*d)*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^2*(a/b)^(2/3)) - (a*e*(a/b)^(1/3) - 2*a*d)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^2*(a/b)^(2/3)) + 2*(a*e*(a/b)^(1/3) - 2*a*d)*log(x + (a/b)^(1/3))/(b^2*(a/b)^(2/3))) + 1/2*(e*x^2 + 2*d*x)*log((b*x^3 + a)^p*c)","A",0
194,1,125,0,1.008586," ","integrate(log(c*(b*x^3+a)^p),x, algorithm=""maxima"")","-\frac{1}{2} \, b p {\left(\frac{6 \, x}{b} - \frac{2 \, \sqrt{3} a \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} + \frac{a \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{2 \, a \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{b^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}\right)} + x \log\left({\left(b x^{3} + a\right)}^{p} c\right)"," ",0,"-1/2*b*p*(6*x/b - 2*sqrt(3)*a*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/(b^2*(a/b)^(2/3)) + a*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^2*(a/b)^(2/3)) - 2*a*log(x + (a/b)^(1/3))/(b^2*(a/b)^(2/3))) + x*log((b*x^3 + a)^p*c)","A",0
195,0,0,0,0.000000," ","integrate(log(c*(b*x^3+a)^p)/(e*x+d),x, algorithm=""maxima"")","\int \frac{\log\left({\left(b x^{3} + a\right)}^{p} c\right)}{e x + d}\,{d x}"," ",0,"integrate(log((b*x^3 + a)^p*c)/(e*x + d), x)","F",0
196,1,311,0,1.010981," ","integrate(log(c*(b*x^3+a)^p)/(e*x+d)^2,x, algorithm=""maxima"")","-\frac{{\left(\frac{6 \, d^{2} \log\left(e x + d\right)}{b d^{3} - a e^{3}} + \frac{2 \, \sqrt{3} {\left(a e^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} - a d e \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{{\left(b^{2} d^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}} - a b e^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{{\left(2 \, b d^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} - a e^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}} - a d e\right)} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{b^{2} d^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}} - a b e^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{2 \, {\left(b d^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} + a e^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}} + a d e\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{b^{2} d^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}} - a b e^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}\right)} b p}{2 \, e} - \frac{\log\left({\left(b x^{3} + a\right)}^{p} c\right)}{{\left(e x + d\right)} e}"," ",0,"-1/2*(6*d^2*log(e*x + d)/(b*d^3 - a*e^3) + 2*sqrt(3)*(a*e^2*(a/b)^(2/3) - a*d*e*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/((b^2*d^3*(a/b)^(2/3) - a*b*e^3*(a/b)^(2/3))*(a/b)^(1/3)) - (2*b*d^2*(a/b)^(2/3) - a*e^2*(a/b)^(1/3) - a*d*e)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^2*d^3*(a/b)^(2/3) - a*b*e^3*(a/b)^(2/3)) - 2*(b*d^2*(a/b)^(2/3) + a*e^2*(a/b)^(1/3) + a*d*e)*log(x + (a/b)^(1/3))/(b^2*d^3*(a/b)^(2/3) - a*b*e^3*(a/b)^(2/3)))*b*p/e - log((b*x^3 + a)^p*c)/((e*x + d)*e)","A",0
197,1,517,0,1.027830," ","integrate(log(c*(b*x^3+a)^p)/(e*x+d)^3,x, algorithm=""maxima"")","-\frac{{\left(\frac{2 \, \sqrt{3} {\left(3 \, a b d^{2} e^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a b d^{3} e \left(\frac{a}{b}\right)^{\frac{1}{3}} - a^{2} e^{4} \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)} \arctan\left(\frac{\sqrt{3} {\left(2 \, x - \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}}{3 \, \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)}{{\left(b^{3} d^{6} \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a b^{2} d^{3} e^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}} + a^{2} b e^{6} \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)} \left(\frac{a}{b}\right)^{\frac{1}{3}}} - \frac{6 \, d^{2}}{b d^{4} - a d e^{3} + {\left(b d^{3} e - a e^{4}\right)} x} + \frac{6 \, {\left(b d^{4} + 2 \, a d e^{3}\right)} \log\left(e x + d\right)}{b^{2} d^{6} - 2 \, a b d^{3} e^{3} + a^{2} e^{6}} - \frac{{\left(2 \, b^{2} d^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}} + 4 \, a b d e^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}} - 3 \, a b d^{2} e^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}} - 2 \, a b d^{3} e - a^{2} e^{4}\right)} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{b^{3} d^{6} \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a b^{2} d^{3} e^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}} + a^{2} b e^{6} \left(\frac{a}{b}\right)^{\frac{2}{3}}} - \frac{2 \, {\left(b^{2} d^{4} \left(\frac{a}{b}\right)^{\frac{2}{3}} + 2 \, a b d e^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}} + 3 \, a b d^{2} e^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}} + 2 \, a b d^{3} e + a^{2} e^{4}\right)} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{b^{3} d^{6} \left(\frac{a}{b}\right)^{\frac{2}{3}} - 2 \, a b^{2} d^{3} e^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}} + a^{2} b e^{6} \left(\frac{a}{b}\right)^{\frac{2}{3}}}\right)} b p}{4 \, e} - \frac{\log\left({\left(b x^{3} + a\right)}^{p} c\right)}{2 \, {\left(e x + d\right)}^{2} e}"," ",0,"-1/4*(2*sqrt(3)*(3*a*b*d^2*e^2*(a/b)^(2/3) - 2*a*b*d^3*e*(a/b)^(1/3) - a^2*e^4*(a/b)^(1/3))*arctan(1/3*sqrt(3)*(2*x - (a/b)^(1/3))/(a/b)^(1/3))/((b^3*d^6*(a/b)^(2/3) - 2*a*b^2*d^3*e^3*(a/b)^(2/3) + a^2*b*e^6*(a/b)^(2/3))*(a/b)^(1/3)) - 6*d^2/(b*d^4 - a*d*e^3 + (b*d^3*e - a*e^4)*x) + 6*(b*d^4 + 2*a*d*e^3)*log(e*x + d)/(b^2*d^6 - 2*a*b*d^3*e^3 + a^2*e^6) - (2*b^2*d^4*(a/b)^(2/3) + 4*a*b*d*e^3*(a/b)^(2/3) - 3*a*b*d^2*e^2*(a/b)^(1/3) - 2*a*b*d^3*e - a^2*e^4)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3))/(b^3*d^6*(a/b)^(2/3) - 2*a*b^2*d^3*e^3*(a/b)^(2/3) + a^2*b*e^6*(a/b)^(2/3)) - 2*(b^2*d^4*(a/b)^(2/3) + 2*a*b*d*e^3*(a/b)^(2/3) + 3*a*b*d^2*e^2*(a/b)^(1/3) + 2*a*b*d^3*e + a^2*e^4)*log(x + (a/b)^(1/3))/(b^3*d^6*(a/b)^(2/3) - 2*a*b^2*d^3*e^3*(a/b)^(2/3) + a^2*b*e^6*(a/b)^(2/3)))*b*p/e - 1/2*log((b*x^3 + a)^p*c)/((e*x + d)^2*e)","A",0
198,1,166,0,0.462988," ","integrate((e*x+d)^3*log(c*(a+b/x)^p),x, algorithm=""maxima"")","\frac{1}{24} \, b p {\left(\frac{2 \, a^{2} e^{3} x^{3} + 3 \, {\left(4 \, a^{2} d e^{2} - a b e^{3}\right)} x^{2} + 6 \, {\left(6 \, a^{2} d^{2} e - 4 \, a b d e^{2} + b^{2} e^{3}\right)} x}{a^{3}} + \frac{6 \, {\left(4 \, a^{3} d^{3} - 6 \, a^{2} b d^{2} e + 4 \, a b^{2} d e^{2} - b^{3} e^{3}\right)} \log\left(a x + b\right)}{a^{4}}\right)} + \frac{1}{4} \, {\left(e^{3} x^{4} + 4 \, d e^{2} x^{3} + 6 \, d^{2} e x^{2} + 4 \, d^{3} x\right)} \log\left({\left(a + \frac{b}{x}\right)}^{p} c\right)"," ",0,"1/24*b*p*((2*a^2*e^3*x^3 + 3*(4*a^2*d*e^2 - a*b*e^3)*x^2 + 6*(6*a^2*d^2*e - 4*a*b*d*e^2 + b^2*e^3)*x)/a^3 + 6*(4*a^3*d^3 - 6*a^2*b*d^2*e + 4*a*b^2*d*e^2 - b^3*e^3)*log(a*x + b)/a^4) + 1/4*(e^3*x^4 + 4*d*e^2*x^3 + 6*d^2*e*x^2 + 4*d^3*x)*log((a + b/x)^p*c)","A",0
199,1,102,0,0.454510," ","integrate((e*x+d)^2*log(c*(a+b/x)^p),x, algorithm=""maxima"")","\frac{1}{6} \, b p {\left(\frac{a e^{2} x^{2} + 2 \, {\left(3 \, a d e - b e^{2}\right)} x}{a^{2}} + \frac{2 \, {\left(3 \, a^{2} d^{2} - 3 \, a b d e + b^{2} e^{2}\right)} \log\left(a x + b\right)}{a^{3}}\right)} + \frac{1}{3} \, {\left(e^{2} x^{3} + 3 \, d e x^{2} + 3 \, d^{2} x\right)} \log\left({\left(a + \frac{b}{x}\right)}^{p} c\right)"," ",0,"1/6*b*p*((a*e^2*x^2 + 2*(3*a*d*e - b*e^2)*x)/a^2 + 2*(3*a^2*d^2 - 3*a*b*d*e + b^2*e^2)*log(a*x + b)/a^3) + 1/3*(e^2*x^3 + 3*d*e*x^2 + 3*d^2*x)*log((a + b/x)^p*c)","A",0
200,1,55,0,0.457081," ","integrate((e*x+d)*log(c*(a+b/x)^p),x, algorithm=""maxima"")","\frac{1}{2} \, b p {\left(\frac{e x}{a} + \frac{{\left(2 \, a d - b e\right)} \log\left(a x + b\right)}{a^{2}}\right)} + \frac{1}{2} \, {\left(e x^{2} + 2 \, d x\right)} \log\left({\left(a + \frac{b}{x}\right)}^{p} c\right)"," ",0,"1/2*b*p*(e*x/a + (2*a*d - b*e)*log(a*x + b)/a^2) + 1/2*(e*x^2 + 2*d*x)*log((a + b/x)^p*c)","A",0
201,1,159,0,0.491816," ","integrate(log(c*(a+b/x)^p)/(e*x+d),x, algorithm=""maxima"")","\frac{b p {\left(\frac{\log\left(e x + d\right) \log\left(a + \frac{b}{x}\right)}{b} - \frac{\log\left(e x + d\right) \log\left(-\frac{a e x + a d}{a d - b e} + 1\right) + {\rm Li}_2\left(\frac{a e x + a d}{a d - b e}\right)}{b} + \frac{\log\left(e x + d\right) \log\left(-\frac{e x + d}{d} + 1\right) + {\rm Li}_2\left(\frac{e x + d}{d}\right)}{b}\right)}}{e} - \frac{p \log\left(e x + d\right) \log\left(a + \frac{b}{x}\right)}{e} + \frac{\log\left({\left(a + \frac{b}{x}\right)}^{p} c\right) \log\left(e x + d\right)}{e}"," ",0,"b*p*(log(e*x + d)*log(a + b/x)/b - (log(e*x + d)*log(-(a*e*x + a*d)/(a*d - b*e) + 1) + dilog((a*e*x + a*d)/(a*d - b*e)))/b + (log(e*x + d)*log(-(e*x + d)/d + 1) + dilog((e*x + d)/d))/b)/e - p*log(e*x + d)*log(a + b/x)/e + log((a + b/x)^p*c)*log(e*x + d)/e","A",0
202,1,85,0,0.457706," ","integrate(log(c*(a+b/x)^p)/(e*x+d)^2,x, algorithm=""maxima"")","\frac{b p {\left(\frac{a \log\left(a x + b\right)}{a b d - b^{2} e} - \frac{e \log\left(e x + d\right)}{a d^{2} - b d e} - \frac{\log\left(x\right)}{b d}\right)}}{e} - \frac{\log\left({\left(a + \frac{b}{x}\right)}^{p} c\right)}{{\left(e x + d\right)} e}"," ",0,"b*p*(a*log(a*x + b)/(a*b*d - b^2*e) - e*log(e*x + d)/(a*d^2 - b*d*e) - log(x)/(b*d))/e - log((a + b/x)^p*c)/((e*x + d)*e)","A",0
203,1,160,0,0.478878," ","integrate(log(c*(a+b/x)^p)/(e*x+d)^3,x, algorithm=""maxima"")","\frac{{\left(\frac{a^{2} \log\left(a x + b\right)}{a^{2} b d^{2} - 2 \, a b^{2} d e + b^{3} e^{2}} - \frac{{\left(2 \, a d e - b e^{2}\right)} \log\left(e x + d\right)}{a^{2} d^{4} - 2 \, a b d^{3} e + b^{2} d^{2} e^{2}} + \frac{e}{a d^{3} - b d^{2} e + {\left(a d^{2} e - b d e^{2}\right)} x} - \frac{\log\left(x\right)}{b d^{2}}\right)} b p}{2 \, e} - \frac{\log\left({\left(a + \frac{b}{x}\right)}^{p} c\right)}{2 \, {\left(e x + d\right)}^{2} e}"," ",0,"1/2*(a^2*log(a*x + b)/(a^2*b*d^2 - 2*a*b^2*d*e + b^3*e^2) - (2*a*d*e - b*e^2)*log(e*x + d)/(a^2*d^4 - 2*a*b*d^3*e + b^2*d^2*e^2) + e/(a*d^3 - b*d^2*e + (a*d^2*e - b*d*e^2)*x) - log(x)/(b*d^2))*b*p/e - 1/2*log((a + b/x)^p*c)/((e*x + d)^2*e)","A",0
204,1,299,0,0.520217," ","integrate(log(c*(a+b/x)^p)/(e*x+d)^4,x, algorithm=""maxima"")","\frac{{\left(\frac{2 \, a^{3} \log\left(a x + b\right)}{a^{3} b d^{3} - 3 \, a^{2} b^{2} d^{2} e + 3 \, a b^{3} d e^{2} - b^{4} e^{3}} - \frac{2 \, {\left(3 \, a^{2} d^{2} e - 3 \, a b d e^{2} + b^{2} e^{3}\right)} \log\left(e x + d\right)}{a^{3} d^{6} - 3 \, a^{2} b d^{5} e + 3 \, a b^{2} d^{4} e^{2} - b^{3} d^{3} e^{3}} + \frac{5 \, a d^{2} e - 3 \, b d e^{2} + 2 \, {\left(2 \, a d e^{2} - b e^{3}\right)} x}{a^{2} d^{6} - 2 \, a b d^{5} e + b^{2} d^{4} e^{2} + {\left(a^{2} d^{4} e^{2} - 2 \, a b d^{3} e^{3} + b^{2} d^{2} e^{4}\right)} x^{2} + 2 \, {\left(a^{2} d^{5} e - 2 \, a b d^{4} e^{2} + b^{2} d^{3} e^{3}\right)} x} - \frac{2 \, \log\left(x\right)}{b d^{3}}\right)} b p}{6 \, e} - \frac{\log\left({\left(a + \frac{b}{x}\right)}^{p} c\right)}{3 \, {\left(e x + d\right)}^{3} e}"," ",0,"1/6*(2*a^3*log(a*x + b)/(a^3*b*d^3 - 3*a^2*b^2*d^2*e + 3*a*b^3*d*e^2 - b^4*e^3) - 2*(3*a^2*d^2*e - 3*a*b*d*e^2 + b^2*e^3)*log(e*x + d)/(a^3*d^6 - 3*a^2*b*d^5*e + 3*a*b^2*d^4*e^2 - b^3*d^3*e^3) + (5*a*d^2*e - 3*b*d*e^2 + 2*(2*a*d*e^2 - b*e^3)*x)/(a^2*d^6 - 2*a*b*d^5*e + b^2*d^4*e^2 + (a^2*d^4*e^2 - 2*a*b*d^3*e^3 + b^2*d^2*e^4)*x^2 + 2*(a^2*d^5*e - 2*a*b*d^4*e^2 + b^2*d^3*e^3)*x) - 2*log(x)/(b*d^3))*b*p/e - 1/3*log((a + b/x)^p*c)/((e*x + d)^3*e)","A",0
205,1,82,0,0.478746," ","integrate(log(a+b/x)/(d*x+c),x, algorithm=""maxima"")","-\frac{\log\left(\frac{d x}{c} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{d x}{c}\right)}{d} + \frac{\log\left(a x + b\right) \log\left(\frac{a d x + b d}{a c - b d} + 1\right) + {\rm Li}_2\left(-\frac{a d x + b d}{a c - b d}\right)}{d}"," ",0,"-(log(d*x/c + 1)*log(x) + dilog(-d*x/c))/d + (log(a*x + b)*log((a*d*x + b*d)/(a*c - b*d) + 1) + dilog(-(a*d*x + b*d)/(a*c - b*d)))/d","A",0
206,0,0,0,0.000000," ","integrate((e*x+d)^m*log(c*(b*x^3+a)^p),x, algorithm=""maxima"")","\frac{{\left(e x + d\right)} {\left(e x + d\right)}^{m} \log\left({\left(b x^{3} + a\right)}^{p}\right)}{e {\left(m + 1\right)}} + \int -\frac{{\left(3 \, b d p x^{2} - {\left(e {\left(m + 1\right)} \log\left(c\right) - 3 \, e p\right)} b x^{3} - a e {\left(m + 1\right)} \log\left(c\right)\right)} {\left(e x + d\right)}^{m}}{b e {\left(m + 1\right)} x^{3} + a e {\left(m + 1\right)}}\,{d x}"," ",0,"(e*x + d)*(e*x + d)^m*log((b*x^3 + a)^p)/(e*(m + 1)) + integrate(-(3*b*d*p*x^2 - (e*(m + 1)*log(c) - 3*e*p)*b*x^3 - a*e*(m + 1)*log(c))*(e*x + d)^m/(b*e*(m + 1)*x^3 + a*e*(m + 1)), x)","F",0
207,0,0,0,0.000000," ","integrate((e*x+d)^m*log(c*(b*x^2+a)^p),x, algorithm=""maxima"")","\frac{{\left(e p x + d p\right)} {\left(e x + d\right)}^{m} \log\left(b x^{2} + a\right)}{e {\left(m + 1\right)}} + \int -\frac{{\left(2 \, b d p x - {\left(e {\left(m + 1\right)} \log\left(c\right) - 2 \, e p\right)} b x^{2} - a e {\left(m + 1\right)} \log\left(c\right)\right)} {\left(e x + d\right)}^{m}}{b e {\left(m + 1\right)} x^{2} + a e {\left(m + 1\right)}}\,{d x}"," ",0,"(e*p*x + d*p)*(e*x + d)^m*log(b*x^2 + a)/(e*(m + 1)) + integrate(-(2*b*d*p*x - (e*(m + 1)*log(c) - 2*e*p)*b*x^2 - a*e*(m + 1)*log(c))*(e*x + d)^m/(b*e*(m + 1)*x^2 + a*e*(m + 1)), x)","F",0
208,0,0,0,0.000000," ","integrate((e*x+d)^m*log(c*(b*x+a)^p),x, algorithm=""maxima"")","\frac{{\left(e x + d\right)} {\left(e x + d\right)}^{m} \log\left({\left(b x + a\right)}^{p}\right)}{e {\left(m + 1\right)}} + \int \frac{{\left(a e {\left(m + 1\right)} \log\left(c\right) - b d p + {\left(e {\left(m + 1\right)} \log\left(c\right) - e p\right)} b x\right)} {\left(e x + d\right)}^{m}}{b e {\left(m + 1\right)} x + a e {\left(m + 1\right)}}\,{d x}"," ",0,"(e*x + d)*(e*x + d)^m*log((b*x + a)^p)/(e*(m + 1)) + integrate((a*e*(m + 1)*log(c) - b*d*p + (e*(m + 1)*log(c) - e*p)*b*x)*(e*x + d)^m/(b*e*(m + 1)*x + a*e*(m + 1)), x)","F",0
209,0,0,0,0.000000," ","integrate((e*x+d)^m*log(c*(a+b/x)^p),x, algorithm=""maxima"")","\frac{{\left(e x + d\right)} {\left(e x + d\right)}^{m} \log\left({\left(a x + b\right)}^{p}\right)}{e {\left(m + 1\right)}} - \int -\frac{{\left(b e {\left(m + 1\right)} \log\left(c\right) - a d p + {\left(e {\left(m + 1\right)} \log\left(c\right) - e p\right)} a x - {\left(a e {\left(m + 1\right)} x + b e {\left(m + 1\right)}\right)} \log\left(x^{p}\right)\right)} {\left(e x + d\right)}^{m}}{a e {\left(m + 1\right)} x + b e {\left(m + 1\right)}}\,{d x}"," ",0,"(e*x + d)*(e*x + d)^m*log((a*x + b)^p)/(e*(m + 1)) - integrate(-(b*e*(m + 1)*log(c) - a*d*p + (e*(m + 1)*log(c) - e*p)*a*x - (a*e*(m + 1)*x + b*e*(m + 1))*log(x^p))*(e*x + d)^m/(a*e*(m + 1)*x + b*e*(m + 1)), x)","F",0
210,0,0,0,0.000000," ","integrate((e*x+d)^m*log(c*(a+b/x^2)^p),x, algorithm=""maxima"")","\frac{{\left(e p x + d p\right)} {\left(e x + d\right)}^{m} \log\left(a x^{2} + b\right)}{e {\left(m + 1\right)}} - \int \frac{{\left(2 \, a d p x - {\left(e {\left(m + 1\right)} \log\left(c\right) - 2 \, e p\right)} a x^{2} - b e {\left(m + 1\right)} \log\left(c\right) + 2 \, {\left(a e {\left(m + 1\right)} x^{2} + b e {\left(m + 1\right)}\right)} \log\left(x^{p}\right)\right)} {\left(e x + d\right)}^{m}}{a e {\left(m + 1\right)} x^{2} + b e {\left(m + 1\right)}}\,{d x}"," ",0,"(e*p*x + d*p)*(e*x + d)^m*log(a*x^2 + b)/(e*(m + 1)) - integrate((2*a*d*p*x - (e*(m + 1)*log(c) - 2*e*p)*a*x^2 - b*e*(m + 1)*log(c) + 2*(a*e*(m + 1)*x^2 + b*e*(m + 1))*log(x^p))*(e*x + d)^m/(a*e*(m + 1)*x^2 + b*e*(m + 1)), x)","F",0
211,0,0,0,0.000000," ","integrate((g*x+f)^m*log(c*(d+e*x^n)^p),x, algorithm=""maxima"")","\frac{{\left(g x + f\right)} {\left(g x + f\right)}^{m} \log\left({\left(e x^{n} + d\right)}^{p}\right)}{g {\left(m + 1\right)}} + \int \frac{{\left(d g {\left(m + 1\right)} x \log\left(c\right) - {\left(e f n p + {\left(e g n p - e g {\left(m + 1\right)} \log\left(c\right)\right)} x\right)} x^{n}\right)} {\left(g x + f\right)}^{m}}{e g {\left(m + 1\right)} x x^{n} + d g {\left(m + 1\right)} x}\,{d x}"," ",0,"(g*x + f)*(g*x + f)^m*log((e*x^n + d)^p)/(g*(m + 1)) + integrate((d*g*(m + 1)*x*log(c) - (e*f*n*p + (e*g*n*p - e*g*(m + 1)*log(c))*x)*x^n)*(g*x + f)^m/(e*g*(m + 1)*x*x^n + d*g*(m + 1)*x), x)","F",0
212,0,0,0,0.000000," ","integrate((g*x+f)^3*log(c*(d+e*x^n)^p),x, algorithm=""maxima"")","-\frac{1}{16} \, {\left(g^{3} n p - 4 \, g^{3} \log\left(c\right)\right)} x^{4} - \frac{1}{3} \, {\left(f g^{2} n p - 3 \, f g^{2} \log\left(c\right)\right)} x^{3} - \frac{3}{4} \, {\left(f^{2} g n p - 2 \, f^{2} g \log\left(c\right)\right)} x^{2} - {\left(f^{3} n p - f^{3} \log\left(c\right)\right)} x + \frac{1}{4} \, {\left(g^{3} x^{4} + 4 \, f g^{2} x^{3} + 6 \, f^{2} g x^{2} + 4 \, f^{3} x\right)} \log\left({\left(e x^{n} + d\right)}^{p}\right) + \int \frac{d g^{3} n p x^{3} + 4 \, d f g^{2} n p x^{2} + 6 \, d f^{2} g n p x + 4 \, d f^{3} n p}{4 \, {\left(e x^{n} + d\right)}}\,{d x}"," ",0,"-1/16*(g^3*n*p - 4*g^3*log(c))*x^4 - 1/3*(f*g^2*n*p - 3*f*g^2*log(c))*x^3 - 3/4*(f^2*g*n*p - 2*f^2*g*log(c))*x^2 - (f^3*n*p - f^3*log(c))*x + 1/4*(g^3*x^4 + 4*f*g^2*x^3 + 6*f^2*g*x^2 + 4*f^3*x)*log((e*x^n + d)^p) + integrate(1/4*(d*g^3*n*p*x^3 + 4*d*f*g^2*n*p*x^2 + 6*d*f^2*g*n*p*x + 4*d*f^3*n*p)/(e*x^n + d), x)","F",0
213,0,0,0,0.000000," ","integrate((g*x+f)^2*log(c*(d+e*x^n)^p),x, algorithm=""maxima"")","-\frac{1}{9} \, {\left(g^{2} n p - 3 \, g^{2} \log\left(c\right)\right)} x^{3} - \frac{1}{2} \, {\left(f g n p - 2 \, f g \log\left(c\right)\right)} x^{2} - {\left(f^{2} n p - f^{2} \log\left(c\right)\right)} x + \frac{1}{3} \, {\left(g^{2} x^{3} + 3 \, f g x^{2} + 3 \, f^{2} x\right)} \log\left({\left(e x^{n} + d\right)}^{p}\right) + \int \frac{d g^{2} n p x^{2} + 3 \, d f g n p x + 3 \, d f^{2} n p}{3 \, {\left(e x^{n} + d\right)}}\,{d x}"," ",0,"-1/9*(g^2*n*p - 3*g^2*log(c))*x^3 - 1/2*(f*g*n*p - 2*f*g*log(c))*x^2 - (f^2*n*p - f^2*log(c))*x + 1/3*(g^2*x^3 + 3*f*g*x^2 + 3*f^2*x)*log((e*x^n + d)^p) + integrate(1/3*(d*g^2*n*p*x^2 + 3*d*f*g*n*p*x + 3*d*f^2*n*p)/(e*x^n + d), x)","F",0
214,0,0,0,0.000000," ","integrate((g*x+f)*log(c*(d+e*x^n)^p),x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(g n p - 2 \, g \log\left(c\right)\right)} x^{2} - {\left(f n p - f \log\left(c\right)\right)} x + \frac{1}{2} \, {\left(g x^{2} + 2 \, f x\right)} \log\left({\left(e x^{n} + d\right)}^{p}\right) + \int \frac{d g n p x + 2 \, d f n p}{2 \, {\left(e x^{n} + d\right)}}\,{d x}"," ",0,"-1/4*(g*n*p - 2*g*log(c))*x^2 - (f*n*p - f*log(c))*x + 1/2*(g*x^2 + 2*f*x)*log((e*x^n + d)^p) + integrate(1/2*(d*g*n*p*x + 2*d*f*n*p)/(e*x^n + d), x)","F",0
215,0,0,0,0.000000," ","integrate(log(c*(d+e*x^n)^p),x, algorithm=""maxima"")","d n p \int \frac{1}{e x^{n} + d}\,{d x} - {\left(n p - \log\left(c\right)\right)} x + x \log\left({\left(e x^{n} + d\right)}^{p}\right)"," ",0,"d*n*p*integrate(1/(e*x^n + d), x) - (n*p - log(c))*x + x*log((e*x^n + d)^p)","F",0
216,0,0,0,0.000000," ","integrate(log(c*(d+e*x^n)^p)/(g*x+f),x, algorithm=""maxima"")","\int \frac{\log\left({\left(e x^{n} + d\right)}^{p} c\right)}{g x + f}\,{d x}"," ",0,"integrate(log((e*x^n + d)^p*c)/(g*x + f), x)","F",0
217,0,0,0,0.000000," ","integrate(log(c*(d+e*x^n)^p)/(g*x+f)^2,x, algorithm=""maxima"")","-d n p \int \frac{1}{d g^{2} x^{2} + d f g x + {\left(e g^{2} x^{2} + e f g x\right)} x^{n}}\,{d x} - \frac{n p \log\left(g x + f\right)}{f g} - \frac{f \log\left({\left(e x^{n} + d\right)}^{p}\right) + f \log\left(c\right) - {\left(g n p x + f n p\right)} \log\left(x\right)}{f g^{2} x + f^{2} g}"," ",0,"-d*n*p*integrate(1/(d*g^2*x^2 + d*f*g*x + (e*g^2*x^2 + e*f*g*x)*x^n), x) - n*p*log(g*x + f)/(f*g) - (f*log((e*x^n + d)^p) + f*log(c) - (g*n*p*x + f*n*p)*log(x))/(f*g^2*x + f^2*g)","F",0
218,0,0,0,0.000000," ","integrate(log(c*(d+e*x^n)^p)/(g*x+f)^3,x, algorithm=""maxima"")","-d n p \int \frac{1}{2 \, {\left(d g^{3} x^{3} + 2 \, d f g^{2} x^{2} + d f^{2} g x + {\left(e g^{3} x^{3} + 2 \, e f g^{2} x^{2} + e f^{2} g x\right)} x^{n}\right)}}\,{d x} + \frac{f g n p x + f^{2} n p - f^{2} \log\left({\left(e x^{n} + d\right)}^{p}\right) - f^{2} \log\left(c\right) + {\left(g^{2} n p x^{2} + 2 \, f g n p x + f^{2} n p\right)} \log\left(x\right)}{2 \, {\left(f^{2} g^{3} x^{2} + 2 \, f^{3} g^{2} x + f^{4} g\right)}} - \frac{n p \log\left(g x + f\right)}{2 \, f^{2} g}"," ",0,"-d*n*p*integrate(1/2/(d*g^3*x^3 + 2*d*f*g^2*x^2 + d*f^2*g*x + (e*g^3*x^3 + 2*e*f*g^2*x^2 + e*f^2*g*x)*x^n), x) + 1/2*(f*g*n*p*x + f^2*n*p - f^2*log((e*x^n + d)^p) - f^2*log(c) + (g^2*n*p*x^2 + 2*f*g*n*p*x + f^2*n*p)*log(x))/(f^2*g^3*x^2 + 2*f^3*g^2*x + f^4*g) - 1/2*n*p*log(g*x + f)/(f^2*g)","F",0
219,0,0,0,0.000000," ","integrate(x^3*log(c*(b*x+a)^p)/(e*x+d),x, algorithm=""maxima"")","\int \frac{x^{3} \log\left({\left(b x + a\right)}^{p} c\right)}{e x + d}\,{d x}"," ",0,"integrate(x^3*log((b*x + a)^p*c)/(e*x + d), x)","F",0
220,0,0,0,0.000000," ","integrate(x^2*log(c*(b*x+a)^p)/(e*x+d),x, algorithm=""maxima"")","\int \frac{x^{2} \log\left({\left(b x + a\right)}^{p} c\right)}{e x + d}\,{d x}"," ",0,"integrate(x^2*log((b*x + a)^p*c)/(e*x + d), x)","F",0
221,0,0,0,0.000000," ","integrate(x*log(c*(b*x+a)^p)/(e*x+d),x, algorithm=""maxima"")","\int \frac{x \log\left({\left(b x + a\right)}^{p} c\right)}{e x + d}\,{d x}"," ",0,"integrate(x*log((b*x + a)^p*c)/(e*x + d), x)","F",0
222,1,118,0,0.472560," ","integrate(log(c*(b*x+a)^p)/(e*x+d),x, algorithm=""maxima"")","\frac{b p {\left(\frac{\log\left(b x + a\right) \log\left(e x + d\right)}{b} - \frac{\log\left(e x + d\right) \log\left(-\frac{b e x + b d}{b d - a e} + 1\right) + {\rm Li}_2\left(\frac{b e x + b d}{b d - a e}\right)}{b}\right)}}{e} - \frac{p \log\left(b x + a\right) \log\left(e x + d\right)}{e} + \frac{\log\left({\left(b x + a\right)}^{p} c\right) \log\left(e x + d\right)}{e}"," ",0,"b*p*(log(b*x + a)*log(e*x + d)/b - (log(e*x + d)*log(-(b*e*x + b*d)/(b*d - a*e) + 1) + dilog((b*e*x + b*d)/(b*d - a*e)))/b)/e - p*log(b*x + a)*log(e*x + d)/e + log((b*x + a)^p*c)*log(e*x + d)/e","B",0
223,1,123,0,0.646552," ","integrate(log(c*(b*x+a)^p)/x/(e*x+d),x, algorithm=""maxima"")","-b p {\left(\frac{\log\left(\frac{b x}{a} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{b x}{a}\right)}{b d} - \frac{\log\left(e x + d\right) \log\left(-\frac{b e x + b d}{b d - a e} + 1\right) + {\rm Li}_2\left(\frac{b e x + b d}{b d - a e}\right)}{b d}\right)} - {\left(\frac{\log\left(e x + d\right)}{d} - \frac{\log\left(x\right)}{d}\right)} \log\left({\left(b x + a\right)}^{p} c\right)"," ",0,"-b*p*((log(b*x/a + 1)*log(x) + dilog(-b*x/a))/(b*d) - (log(e*x + d)*log(-(b*e*x + b*d)/(b*d - a*e) + 1) + dilog((b*e*x + b*d)/(b*d - a*e)))/(b*d)) - (log(e*x + d)/d - log(x)/d)*log((b*x + a)^p*c)","A",0
224,1,156,0,0.649710," ","integrate(log(c*(b*x+a)^p)/x^2/(e*x+d),x, algorithm=""maxima"")","b p {\left(\frac{{\left(\log\left(\frac{b x}{a} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{b x}{a}\right)\right)} e}{b d^{2}} - \frac{{\left(\log\left(e x + d\right) \log\left(-\frac{b e x + b d}{b d - a e} + 1\right) + {\rm Li}_2\left(\frac{b e x + b d}{b d - a e}\right)\right)} e}{b d^{2}} - \frac{\log\left(b x + a\right)}{a d} + \frac{\log\left(x\right)}{a d}\right)} + {\left(\frac{e \log\left(e x + d\right)}{d^{2}} - \frac{e \log\left(x\right)}{d^{2}} - \frac{1}{d x}\right)} \log\left({\left(b x + a\right)}^{p} c\right)"," ",0,"b*p*((log(b*x/a + 1)*log(x) + dilog(-b*x/a))*e/(b*d^2) - (log(e*x + d)*log(-(b*e*x + b*d)/(b*d - a*e) + 1) + dilog((b*e*x + b*d)/(b*d - a*e)))*e/(b*d^2) - log(b*x + a)/(a*d) + log(x)/(a*d)) + (e*log(e*x + d)/d^2 - e*log(x)/d^2 - 1/(d*x))*log((b*x + a)^p*c)","A",0
225,1,216,0,1.009045," ","integrate(log(c*(b*x+a)^p)/x^3/(e*x+d),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(2 \, e {\left(\frac{\log\left(b x + a\right)}{a d^{2}} - \frac{\log\left(x\right)}{a d^{2}}\right)} - \frac{2 \, {\left(\log\left(\frac{b x}{a} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{b x}{a}\right)\right)} e^{2}}{b d^{3}} + \frac{2 \, {\left(\log\left(e x + d\right) \log\left(-\frac{b e x + b d}{b d - a e} + 1\right) + {\rm Li}_2\left(\frac{b e x + b d}{b d - a e}\right)\right)} e^{2}}{b d^{3}} + \frac{b \log\left(b x + a\right)}{a^{2} d} - \frac{b \log\left(x\right)}{a^{2} d} - \frac{1}{a d x}\right)} b p - \frac{1}{2} \, {\left(\frac{2 \, e^{2} \log\left(e x + d\right)}{d^{3}} - \frac{2 \, e^{2} \log\left(x\right)}{d^{3}} - \frac{2 \, e x - d}{d^{2} x^{2}}\right)} \log\left({\left(b x + a\right)}^{p} c\right)"," ",0,"1/2*(2*e*(log(b*x + a)/(a*d^2) - log(x)/(a*d^2)) - 2*(log(b*x/a + 1)*log(x) + dilog(-b*x/a))*e^2/(b*d^3) + 2*(log(e*x + d)*log(-(b*e*x + b*d)/(b*d - a*e) + 1) + dilog((b*e*x + b*d)/(b*d - a*e)))*e^2/(b*d^3) + b*log(b*x + a)/(a^2*d) - b*log(x)/(a^2*d) - 1/(a*d*x))*b*p - 1/2*(2*e^2*log(e*x + d)/d^3 - 2*e^2*log(x)/d^3 - (2*e*x - d)/(d^2*x^2))*log((b*x + a)^p*c)","A",0
226,0,0,0,0.000000," ","integrate(x^3*log(c*(b*x^2+a)^p)/(e*x+d),x, algorithm=""maxima"")","\int \frac{x^{3} \log\left({\left(b x^{2} + a\right)}^{p} c\right)}{e x + d}\,{d x}"," ",0,"integrate(x^3*log((b*x^2 + a)^p*c)/(e*x + d), x)","F",0
227,0,0,0,0.000000," ","integrate(x^2*log(c*(b*x^2+a)^p)/(e*x+d),x, algorithm=""maxima"")","\int \frac{x^{2} \log\left({\left(b x^{2} + a\right)}^{p} c\right)}{e x + d}\,{d x}"," ",0,"integrate(x^2*log((b*x^2 + a)^p*c)/(e*x + d), x)","F",0
228,0,0,0,0.000000," ","integrate(x*log(c*(b*x^2+a)^p)/(e*x+d),x, algorithm=""maxima"")","\int \frac{x \log\left({\left(b x^{2} + a\right)}^{p} c\right)}{e x + d}\,{d x}"," ",0,"integrate(x*log((b*x^2 + a)^p*c)/(e*x + d), x)","F",0
229,0,0,0,0.000000," ","integrate(log(c*(b*x^2+a)^p)/(e*x+d),x, algorithm=""maxima"")","\int \frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)}{e x + d}\,{d x}"," ",0,"integrate(log((b*x^2 + a)^p*c)/(e*x + d), x)","F",0
230,0,0,0,0.000000," ","integrate(log(c*(b*x^2+a)^p)/x/(e*x+d),x, algorithm=""maxima"")","\int \frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)}{{\left(e x + d\right)} x}\,{d x}"," ",0,"integrate(log((b*x^2 + a)^p*c)/((e*x + d)*x), x)","F",0
231,0,0,0,0.000000," ","integrate(log(c*(b*x^2+a)^p)/x^2/(e*x+d),x, algorithm=""maxima"")","\int \frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)}{{\left(e x + d\right)} x^{2}}\,{d x}"," ",0,"integrate(log((b*x^2 + a)^p*c)/((e*x + d)*x^2), x)","F",0
232,0,0,0,0.000000," ","integrate(log(c*(b*x^2+a)^p)/x^3/(e*x+d),x, algorithm=""maxima"")","\int \frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)}{{\left(e x + d\right)} x^{3}}\,{d x}"," ",0,"integrate(log((b*x^2 + a)^p*c)/((e*x + d)*x^3), x)","F",0
233,0,0,0,0.000000," ","integrate(x^3*log(c*(b*x^3+a)^p)/(e*x+d),x, algorithm=""maxima"")","\int \frac{x^{3} \log\left({\left(b x^{3} + a\right)}^{p} c\right)}{e x + d}\,{d x}"," ",0,"integrate(x^3*log((b*x^3 + a)^p*c)/(e*x + d), x)","F",0
234,0,0,0,0.000000," ","integrate(x^2*log(c*(b*x^3+a)^p)/(e*x+d),x, algorithm=""maxima"")","\int \frac{x^{2} \log\left({\left(b x^{3} + a\right)}^{p} c\right)}{e x + d}\,{d x}"," ",0,"integrate(x^2*log((b*x^3 + a)^p*c)/(e*x + d), x)","F",0
235,0,0,0,0.000000," ","integrate(x*log(c*(b*x^3+a)^p)/(e*x+d),x, algorithm=""maxima"")","\int \frac{x \log\left({\left(b x^{3} + a\right)}^{p} c\right)}{e x + d}\,{d x}"," ",0,"integrate(x*log((b*x^3 + a)^p*c)/(e*x + d), x)","F",0
236,0,0,0,0.000000," ","integrate(log(c*(b*x^3+a)^p)/(e*x+d),x, algorithm=""maxima"")","\int \frac{\log\left({\left(b x^{3} + a\right)}^{p} c\right)}{e x + d}\,{d x}"," ",0,"integrate(log((b*x^3 + a)^p*c)/(e*x + d), x)","F",0
237,0,0,0,0.000000," ","integrate(log(c*(b*x^3+a)^p)/x/(e*x+d),x, algorithm=""maxima"")","\int \frac{\log\left({\left(b x^{3} + a\right)}^{p} c\right)}{{\left(e x + d\right)} x}\,{d x}"," ",0,"integrate(log((b*x^3 + a)^p*c)/((e*x + d)*x), x)","F",0
238,0,0,0,0.000000," ","integrate(log(c*(b*x^3+a)^p)/x^2/(e*x+d),x, algorithm=""maxima"")","\int \frac{\log\left({\left(b x^{3} + a\right)}^{p} c\right)}{{\left(e x + d\right)} x^{2}}\,{d x}"," ",0,"integrate(log((b*x^3 + a)^p*c)/((e*x + d)*x^2), x)","F",0
239,0,0,0,0.000000," ","integrate(log(c*(b*x^3+a)^p)/x^3/(e*x+d),x, algorithm=""maxima"")","\int \frac{\log\left({\left(b x^{3} + a\right)}^{p} c\right)}{{\left(e x + d\right)} x^{3}}\,{d x}"," ",0,"integrate(log((b*x^3 + a)^p*c)/((e*x + d)*x^3), x)","F",0
240,0,0,0,0.000000," ","integrate(x^3*log(c*(a+b/x)^p)/(e*x+d),x, algorithm=""maxima"")","\int \frac{x^{3} \log\left({\left(a + \frac{b}{x}\right)}^{p} c\right)}{e x + d}\,{d x}"," ",0,"integrate(x^3*log((a + b/x)^p*c)/(e*x + d), x)","F",0
241,0,0,0,0.000000," ","integrate(x^2*log(c*(a+b/x)^p)/(e*x+d),x, algorithm=""maxima"")","\int \frac{x^{2} \log\left({\left(a + \frac{b}{x}\right)}^{p} c\right)}{e x + d}\,{d x}"," ",0,"integrate(x^2*log((a + b/x)^p*c)/(e*x + d), x)","F",0
242,0,0,0,0.000000," ","integrate(x*log(c*(a+b/x)^p)/(e*x+d),x, algorithm=""maxima"")","\int \frac{x \log\left({\left(a + \frac{b}{x}\right)}^{p} c\right)}{e x + d}\,{d x}"," ",0,"integrate(x*log((a + b/x)^p*c)/(e*x + d), x)","F",0
243,1,159,0,0.735211," ","integrate(log(c*(a+b/x)^p)/(e*x+d),x, algorithm=""maxima"")","\frac{b p {\left(\frac{\log\left(e x + d\right) \log\left(a + \frac{b}{x}\right)}{b} - \frac{\log\left(e x + d\right) \log\left(-\frac{a e x + a d}{a d - b e} + 1\right) + {\rm Li}_2\left(\frac{a e x + a d}{a d - b e}\right)}{b} + \frac{\log\left(e x + d\right) \log\left(-\frac{e x + d}{d} + 1\right) + {\rm Li}_2\left(\frac{e x + d}{d}\right)}{b}\right)}}{e} - \frac{p \log\left(e x + d\right) \log\left(a + \frac{b}{x}\right)}{e} + \frac{\log\left({\left(a + \frac{b}{x}\right)}^{p} c\right) \log\left(e x + d\right)}{e}"," ",0,"b*p*(log(e*x + d)*log(a + b/x)/b - (log(e*x + d)*log(-(a*e*x + a*d)/(a*d - b*e) + 1) + dilog((a*e*x + a*d)/(a*d - b*e)))/b + (log(e*x + d)*log(-(e*x + d)/d + 1) + dilog((e*x + d)/d))/b)/e - p*log(e*x + d)*log(a + b/x)/e + log((a + b/x)^p*c)*log(e*x + d)/e","A",0
244,1,179,0,1.052873," ","integrate(log(c*(a+b/x)^p)/x/(e*x+d),x, algorithm=""maxima"")","-\frac{1}{2} \, b p {\left(\frac{2 \, \log\left(e x + d\right) \log\left(x\right) - \log\left(x\right)^{2}}{b d} + \frac{2 \, {\left(\log\left(\frac{a x}{b} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{a x}{b}\right)\right)}}{b d} - \frac{2 \, {\left(\log\left(\frac{e x}{d} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{e x}{d}\right)\right)}}{b d} - \frac{2 \, {\left(\log\left(e x + d\right) \log\left(-\frac{a e x + a d}{a d - b e} + 1\right) + {\rm Li}_2\left(\frac{a e x + a d}{a d - b e}\right)\right)}}{b d}\right)} - {\left(\frac{\log\left(e x + d\right)}{d} - \frac{\log\left(x\right)}{d}\right)} \log\left({\left(a + \frac{b}{x}\right)}^{p} c\right)"," ",0,"-1/2*b*p*((2*log(e*x + d)*log(x) - log(x)^2)/(b*d) + 2*(log(a*x/b + 1)*log(x) + dilog(-a*x/b))/(b*d) - 2*(log(e*x/d + 1)*log(x) + dilog(-e*x/d))/(b*d) - 2*(log(e*x + d)*log(-(a*e*x + a*d)/(a*d - b*e) + 1) + dilog((a*e*x + a*d)/(a*d - b*e)))/(b*d)) - (log(e*x + d)/d - log(x)/d)*log((a + b/x)^p*c)","A",0
245,1,230,0,0.876660," ","integrate(log(c*(a+b/x)^p)/x^2/(e*x+d),x, algorithm=""maxima"")","\frac{1}{2} \, b p {\left(\frac{2 \, {\left(\log\left(\frac{a x}{b} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{a x}{b}\right)\right)} e}{b d^{2}} - \frac{2 \, {\left(\log\left(\frac{e x}{d} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{e x}{d}\right)\right)} e}{b d^{2}} - \frac{2 \, {\left(\log\left(e x + d\right) \log\left(-\frac{a e x + a d}{a d - b e} + 1\right) + {\rm Li}_2\left(\frac{a e x + a d}{a d - b e}\right)\right)} e}{b d^{2}} - \frac{2 \, a \log\left(a x + b\right)}{b^{2} d} + \frac{2 \, a \log\left(x\right)}{b^{2} d} + \frac{2 \, e \log\left(e x + d\right) \log\left(x\right) - e \log\left(x\right)^{2}}{b d^{2}} + \frac{2}{b d x}\right)} + {\left(\frac{e \log\left(e x + d\right)}{d^{2}} - \frac{e \log\left(x\right)}{d^{2}} - \frac{1}{d x}\right)} \log\left({\left(a + \frac{b}{x}\right)}^{p} c\right)"," ",0,"1/2*b*p*(2*(log(a*x/b + 1)*log(x) + dilog(-a*x/b))*e/(b*d^2) - 2*(log(e*x/d + 1)*log(x) + dilog(-e*x/d))*e/(b*d^2) - 2*(log(e*x + d)*log(-(a*e*x + a*d)/(a*d - b*e) + 1) + dilog((a*e*x + a*d)/(a*d - b*e)))*e/(b*d^2) - 2*a*log(a*x + b)/(b^2*d) + 2*a*log(x)/(b^2*d) + (2*e*log(e*x + d)*log(x) - e*log(x)^2)/(b*d^2) + 2/(b*d*x)) + (e*log(e*x + d)/d^2 - e*log(x)/d^2 - 1/(d*x))*log((a + b/x)^p*c)","A",0
246,1,307,0,1.013735," ","integrate(log(c*(a+b/x)^p)/x^3/(e*x+d),x, algorithm=""maxima"")","\frac{1}{4} \, {\left(4 \, e {\left(\frac{a \log\left(a x + b\right)}{b^{2} d^{2}} - \frac{a \log\left(x\right)}{b^{2} d^{2}} - \frac{1}{b d^{2} x}\right)} - \frac{4 \, {\left(\log\left(\frac{a x}{b} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{a x}{b}\right)\right)} e^{2}}{b d^{3}} + \frac{4 \, {\left(\log\left(\frac{e x}{d} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{e x}{d}\right)\right)} e^{2}}{b d^{3}} + \frac{4 \, {\left(\log\left(e x + d\right) \log\left(-\frac{a e x + a d}{a d - b e} + 1\right) + {\rm Li}_2\left(\frac{a e x + a d}{a d - b e}\right)\right)} e^{2}}{b d^{3}} + \frac{2 \, a^{2} \log\left(a x + b\right)}{b^{3} d} - \frac{2 \, a^{2} \log\left(x\right)}{b^{3} d} - \frac{2 \, {\left(2 \, e^{2} \log\left(e x + d\right) \log\left(x\right) - e^{2} \log\left(x\right)^{2}\right)}}{b d^{3}} - \frac{2 \, a x - b}{b^{2} d x^{2}}\right)} b p - \frac{1}{2} \, {\left(\frac{2 \, e^{2} \log\left(e x + d\right)}{d^{3}} - \frac{2 \, e^{2} \log\left(x\right)}{d^{3}} - \frac{2 \, e x - d}{d^{2} x^{2}}\right)} \log\left({\left(a + \frac{b}{x}\right)}^{p} c\right)"," ",0,"1/4*(4*e*(a*log(a*x + b)/(b^2*d^2) - a*log(x)/(b^2*d^2) - 1/(b*d^2*x)) - 4*(log(a*x/b + 1)*log(x) + dilog(-a*x/b))*e^2/(b*d^3) + 4*(log(e*x/d + 1)*log(x) + dilog(-e*x/d))*e^2/(b*d^3) + 4*(log(e*x + d)*log(-(a*e*x + a*d)/(a*d - b*e) + 1) + dilog((a*e*x + a*d)/(a*d - b*e)))*e^2/(b*d^3) + 2*a^2*log(a*x + b)/(b^3*d) - 2*a^2*log(x)/(b^3*d) - 2*(2*e^2*log(e*x + d)*log(x) - e^2*log(x)^2)/(b*d^3) - (2*a*x - b)/(b^2*d*x^2))*b*p - 1/2*(2*e^2*log(e*x + d)/d^3 - 2*e^2*log(x)/d^3 - (2*e*x - d)/(d^2*x^2))*log((a + b/x)^p*c)","A",0
247,0,0,0,0.000000," ","integrate(x^3*log(c*(a+b/x^2)^p)/(e*x+d),x, algorithm=""maxima"")","\int \frac{x^{3} \log\left({\left(a + \frac{b}{x^{2}}\right)}^{p} c\right)}{e x + d}\,{d x}"," ",0,"integrate(x^3*log((a + b/x^2)^p*c)/(e*x + d), x)","F",0
248,0,0,0,0.000000," ","integrate(x^2*log(c*(a+b/x^2)^p)/(e*x+d),x, algorithm=""maxima"")","\int \frac{x^{2} \log\left({\left(a + \frac{b}{x^{2}}\right)}^{p} c\right)}{e x + d}\,{d x}"," ",0,"integrate(x^2*log((a + b/x^2)^p*c)/(e*x + d), x)","F",0
249,0,0,0,0.000000," ","integrate(x*log(c*(a+b/x^2)^p)/(e*x+d),x, algorithm=""maxima"")","\int \frac{x \log\left({\left(a + \frac{b}{x^{2}}\right)}^{p} c\right)}{e x + d}\,{d x}"," ",0,"integrate(x*log((a + b/x^2)^p*c)/(e*x + d), x)","F",0
250,0,0,0,0.000000," ","integrate(log(c*(a+b/x^2)^p)/(e*x+d),x, algorithm=""maxima"")","\int \frac{\log\left({\left(a + \frac{b}{x^{2}}\right)}^{p} c\right)}{e x + d}\,{d x}"," ",0,"integrate(log((a + b/x^2)^p*c)/(e*x + d), x)","F",0
251,0,0,0,0.000000," ","integrate(log(c*(a+b/x^2)^p)/x/(e*x+d),x, algorithm=""maxima"")","\int \frac{\log\left({\left(a + \frac{b}{x^{2}}\right)}^{p} c\right)}{{\left(e x + d\right)} x}\,{d x}"," ",0,"integrate(log((a + b/x^2)^p*c)/((e*x + d)*x), x)","F",0
252,0,0,0,0.000000," ","integrate(log(c*(a+b/x^2)^p)/x^2/(e*x+d),x, algorithm=""maxima"")","\int \frac{\log\left({\left(a + \frac{b}{x^{2}}\right)}^{p} c\right)}{{\left(e x + d\right)} x^{2}}\,{d x}"," ",0,"integrate(log((a + b/x^2)^p*c)/((e*x + d)*x^2), x)","F",0
253,0,0,0,0.000000," ","integrate(log(c*(a+b/x^2)^p)/x^3/(e*x+d),x, algorithm=""maxima"")","\int \frac{\log\left({\left(a + \frac{b}{x^{2}}\right)}^{p} c\right)}{{\left(e x + d\right)} x^{3}}\,{d x}"," ",0,"integrate(log((a + b/x^2)^p*c)/((e*x + d)*x^3), x)","F",0
254,0,0,0,0.000000," ","integrate(x^3*log(c*(a+b/x^3)^p)/(e*x+d),x, algorithm=""maxima"")","\int \frac{x^{3} \log\left({\left(a + \frac{b}{x^{3}}\right)}^{p} c\right)}{e x + d}\,{d x}"," ",0,"integrate(x^3*log((a + b/x^3)^p*c)/(e*x + d), x)","F",0
255,0,0,0,0.000000," ","integrate(x^2*log(c*(a+b/x^3)^p)/(e*x+d),x, algorithm=""maxima"")","\int \frac{x^{2} \log\left({\left(a + \frac{b}{x^{3}}\right)}^{p} c\right)}{e x + d}\,{d x}"," ",0,"integrate(x^2*log((a + b/x^3)^p*c)/(e*x + d), x)","F",0
256,0,0,0,0.000000," ","integrate(x*log(c*(a+b/x^3)^p)/(e*x+d),x, algorithm=""maxima"")","\int \frac{x \log\left({\left(a + \frac{b}{x^{3}}\right)}^{p} c\right)}{e x + d}\,{d x}"," ",0,"integrate(x*log((a + b/x^3)^p*c)/(e*x + d), x)","F",0
257,0,0,0,0.000000," ","integrate(log(c*(a+b/x^3)^p)/(e*x+d),x, algorithm=""maxima"")","\int \frac{\log\left({\left(a + \frac{b}{x^{3}}\right)}^{p} c\right)}{e x + d}\,{d x}"," ",0,"integrate(log((a + b/x^3)^p*c)/(e*x + d), x)","F",0
258,0,0,0,0.000000," ","integrate(log(c*(a+b/x^3)^p)/x/(e*x+d),x, algorithm=""maxima"")","\int \frac{\log\left({\left(a + \frac{b}{x^{3}}\right)}^{p} c\right)}{{\left(e x + d\right)} x}\,{d x}"," ",0,"integrate(log((a + b/x^3)^p*c)/((e*x + d)*x), x)","F",0
259,0,0,0,0.000000," ","integrate(log(c*(a+b/x^3)^p)/x^2/(e*x+d),x, algorithm=""maxima"")","\int \frac{\log\left({\left(a + \frac{b}{x^{3}}\right)}^{p} c\right)}{{\left(e x + d\right)} x^{2}}\,{d x}"," ",0,"integrate(log((a + b/x^3)^p*c)/((e*x + d)*x^2), x)","F",0
260,0,0,0,0.000000," ","integrate(log(c*(a+b/x^3)^p)/x^3/(e*x+d),x, algorithm=""maxima"")","\int \frac{\log\left({\left(a + \frac{b}{x^{3}}\right)}^{p} c\right)}{{\left(e x + d\right)} x^{3}}\,{d x}"," ",0,"integrate(log((a + b/x^3)^p*c)/((e*x + d)*x^3), x)","F",0
261,0,0,0,0.000000," ","integrate(log(c*(e*x^3+d)^p)/(g*x^2+f),x, algorithm=""maxima"")","\int \frac{\log\left({\left(e x^{3} + d\right)}^{p} c\right)}{g x^{2} + f}\,{d x}"," ",0,"integrate(log((e*x^3 + d)^p*c)/(g*x^2 + f), x)","F",0
262,0,0,0,0.000000," ","integrate(log(c*(e*x^2+d)^p)/(g*x^2+f),x, algorithm=""maxima"")","\int \frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g x^{2} + f}\,{d x}"," ",0,"integrate(log((e*x^2 + d)^p*c)/(g*x^2 + f), x)","F",0
263,1,309,0,1.290388," ","integrate(log(c*(e*x+d)^p)/(g*x^2+f),x, algorithm=""maxima"")","\frac{e p {\left(\frac{2 \, \arctan\left(\frac{g x}{\sqrt{f g}}\right) \log\left(e x + d\right)}{e} + \frac{\arctan\left(\frac{{\left(e^{2} x + d e\right)} \sqrt{f} \sqrt{g}}{e^{2} f + d^{2} g}, \frac{d e g x + d^{2} g}{e^{2} f + d^{2} g}\right) \log\left(g x^{2} + f\right) - \arctan\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log\left(\frac{e^{2} g x^{2} + 2 \, d e g x + d^{2} g}{e^{2} f + d^{2} g}\right) - i \, {\rm Li}_2\left(\frac{d e g x + e^{2} f - {\left(i \, e^{2} x - i \, d e\right)} \sqrt{f} \sqrt{g}}{e^{2} f + 2 i \, d e \sqrt{f} \sqrt{g} - d^{2} g}\right) + i \, {\rm Li}_2\left(\frac{d e g x + e^{2} f + {\left(i \, e^{2} x - i \, d e\right)} \sqrt{f} \sqrt{g}}{e^{2} f - 2 i \, d e \sqrt{f} \sqrt{g} - d^{2} g}\right)}{e}\right)}}{2 \, \sqrt{f g}} - \frac{p \arctan\left(\frac{g x}{\sqrt{f g}}\right) \log\left(e x + d\right)}{\sqrt{f g}} + \frac{\arctan\left(\frac{g x}{\sqrt{f g}}\right) \log\left({\left(e x + d\right)}^{p} c\right)}{\sqrt{f g}}"," ",0,"1/2*e*p*(2*arctan(g*x/sqrt(f*g))*log(e*x + d)/e + (arctan2((e^2*x + d*e)*sqrt(f)*sqrt(g)/(e^2*f + d^2*g), (d*e*g*x + d^2*g)/(e^2*f + d^2*g))*log(g*x^2 + f) - arctan(sqrt(g)*x/sqrt(f))*log((e^2*g*x^2 + 2*d*e*g*x + d^2*g)/(e^2*f + d^2*g)) - I*dilog((d*e*g*x + e^2*f - (I*e^2*x - I*d*e)*sqrt(f)*sqrt(g))/(e^2*f + 2*I*d*e*sqrt(f)*sqrt(g) - d^2*g)) + I*dilog((d*e*g*x + e^2*f + (I*e^2*x - I*d*e)*sqrt(f)*sqrt(g))/(e^2*f - 2*I*d*e*sqrt(f)*sqrt(g) - d^2*g)))/e)/sqrt(f*g) - p*arctan(g*x/sqrt(f*g))*log(e*x + d)/sqrt(f*g) + arctan(g*x/sqrt(f*g))*log((e*x + d)^p*c)/sqrt(f*g)","C",0
264,1,377,0,1.265661," ","integrate(log(c*(d+e/x)^p)/(g*x^2+f),x, algorithm=""maxima"")","\frac{e p {\left(\frac{4 \, \arctan\left(\frac{g x}{\sqrt{f g}}\right) \log\left(d + \frac{e}{x}\right)}{e} - \frac{{\left(\pi - 2 \, \arctan\left(\frac{{\left(d^{2} x + d e\right)} \sqrt{f} \sqrt{g}}{d^{2} f + e^{2} g}, \frac{d e g x + e^{2} g}{d^{2} f + e^{2} g}\right)\right)} \log\left(g x^{2} + f\right) - 4 \, \arctan\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) + 2 \, \arctan\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log\left(\frac{d^{2} g x^{2} + 2 \, d e g x + e^{2} g}{d^{2} f + e^{2} g}\right) + 2 i \, {\rm Li}_2\left(\frac{i \, \sqrt{g} x + \sqrt{f}}{\sqrt{f}}\right) - 2 i \, {\rm Li}_2\left(-\frac{i \, \sqrt{g} x - \sqrt{f}}{\sqrt{f}}\right) + 2 i \, {\rm Li}_2\left(\frac{d e g x + d^{2} f - {\left(i \, d^{2} x - i \, d e\right)} \sqrt{f} \sqrt{g}}{d^{2} f + 2 i \, d e \sqrt{f} \sqrt{g} - e^{2} g}\right) - 2 i \, {\rm Li}_2\left(\frac{d e g x + d^{2} f + {\left(i \, d^{2} x - i \, d e\right)} \sqrt{f} \sqrt{g}}{d^{2} f - 2 i \, d e \sqrt{f} \sqrt{g} - e^{2} g}\right)}{e}\right)}}{4 \, \sqrt{f g}} - \frac{p \arctan\left(\frac{g x}{\sqrt{f g}}\right) \log\left(d + \frac{e}{x}\right)}{\sqrt{f g}} + \frac{\arctan\left(\frac{g x}{\sqrt{f g}}\right) \log\left(c {\left(d + \frac{e}{x}\right)}^{p}\right)}{\sqrt{f g}}"," ",0,"1/4*e*p*(4*arctan(g*x/sqrt(f*g))*log(d + e/x)/e - ((pi - 2*arctan2((d^2*x + d*e)*sqrt(f)*sqrt(g)/(d^2*f + e^2*g), (d*e*g*x + e^2*g)/(d^2*f + e^2*g)))*log(g*x^2 + f) - 4*arctan(sqrt(g)*x/sqrt(f))*log(sqrt(g)*x/sqrt(f)) + 2*arctan(sqrt(g)*x/sqrt(f))*log((d^2*g*x^2 + 2*d*e*g*x + e^2*g)/(d^2*f + e^2*g)) + 2*I*dilog((I*sqrt(g)*x + sqrt(f))/sqrt(f)) - 2*I*dilog(-(I*sqrt(g)*x - sqrt(f))/sqrt(f)) + 2*I*dilog((d*e*g*x + d^2*f - (I*d^2*x - I*d*e)*sqrt(f)*sqrt(g))/(d^2*f + 2*I*d*e*sqrt(f)*sqrt(g) - e^2*g)) - 2*I*dilog((d*e*g*x + d^2*f + (I*d^2*x - I*d*e)*sqrt(f)*sqrt(g))/(d^2*f - 2*I*d*e*sqrt(f)*sqrt(g) - e^2*g)))/e)/sqrt(f*g) - p*arctan(g*x/sqrt(f*g))*log(d + e/x)/sqrt(f*g) + arctan(g*x/sqrt(f*g))*log(c*(d + e/x)^p)/sqrt(f*g)","A",0
265,0,0,0,0.000000," ","integrate(log(c*(d+e/x^2)^p)/(g*x^2+f),x, algorithm=""maxima"")","\int \frac{\log\left(c {\left(d + \frac{e}{x^{2}}\right)}^{p}\right)}{g x^{2} + f}\,{d x}"," ",0,"integrate(log(c*(d + e/x^2)^p)/(g*x^2 + f), x)","F",0
266,0,0,0,0.000000," ","integrate(log(c*(d+e*x^(1/2))^p)/(g*x^2+f),x, algorithm=""maxima"")","\int \frac{\log\left({\left(e \sqrt{x} + d\right)}^{p} c\right)}{g x^{2} + f}\,{d x}"," ",0,"integrate(log((e*sqrt(x) + d)^p*c)/(g*x^2 + f), x)","F",0
267,0,0,0,0.000000," ","integrate(log(c*(d+e/x^(1/2))^p)/(g*x^2+f),x, algorithm=""maxima"")","\int \frac{\log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{p}\right)}{g x^{2} + f}\,{d x}"," ",0,"integrate(log(c*(d + e/sqrt(x))^p)/(g*x^2 + f), x)","F",0
268,1,227,0,1.014995," ","integrate((g*x^2+f)^3*log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","\frac{2}{3675} \, e p {\left(\frac{105 \, {\left(35 \, d e^{3} f^{3} - 35 \, d^{2} e^{2} f^{2} g + 21 \, d^{3} e f g^{2} - 5 \, d^{4} g^{3}\right)} \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e^{4}} - \frac{75 \, e^{3} g^{3} x^{7} + 21 \, {\left(21 \, e^{3} f g^{2} - 5 \, d e^{2} g^{3}\right)} x^{5} + 35 \, {\left(35 \, e^{3} f^{2} g - 21 \, d e^{2} f g^{2} + 5 \, d^{2} e g^{3}\right)} x^{3} + 105 \, {\left(35 \, e^{3} f^{3} - 35 \, d e^{2} f^{2} g + 21 \, d^{2} e f g^{2} - 5 \, d^{3} g^{3}\right)} x}{e^{4}}\right)} + \frac{1}{35} \, {\left(5 \, g^{3} x^{7} + 21 \, f g^{2} x^{5} + 35 \, f^{2} g x^{3} + 35 \, f^{3} x\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)"," ",0,"2/3675*e*p*(105*(35*d*e^3*f^3 - 35*d^2*e^2*f^2*g + 21*d^3*e*f*g^2 - 5*d^4*g^3)*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e^4) - (75*e^3*g^3*x^7 + 21*(21*e^3*f*g^2 - 5*d*e^2*g^3)*x^5 + 35*(35*e^3*f^2*g - 21*d*e^2*f*g^2 + 5*d^2*e*g^3)*x^3 + 105*(35*e^3*f^3 - 35*d*e^2*f^2*g + 21*d^2*e*f*g^2 - 5*d^3*g^3)*x)/e^4) + 1/35*(5*g^3*x^7 + 21*f*g^2*x^5 + 35*f^2*g*x^3 + 35*f^3*x)*log((e*x^2 + d)^p*c)","A",0
269,1,150,0,1.014115," ","integrate((g*x^2+f)^2*log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","\frac{2}{225} \, e p {\left(\frac{15 \, {\left(15 \, d e^{2} f^{2} - 10 \, d^{2} e f g + 3 \, d^{3} g^{2}\right)} \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e^{3}} - \frac{9 \, e^{2} g^{2} x^{5} + 5 \, {\left(10 \, e^{2} f g - 3 \, d e g^{2}\right)} x^{3} + 15 \, {\left(15 \, e^{2} f^{2} - 10 \, d e f g + 3 \, d^{2} g^{2}\right)} x}{e^{3}}\right)} + \frac{1}{15} \, {\left(3 \, g^{2} x^{5} + 10 \, f g x^{3} + 15 \, f^{2} x\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)"," ",0,"2/225*e*p*(15*(15*d*e^2*f^2 - 10*d^2*e*f*g + 3*d^3*g^2)*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e^3) - (9*e^2*g^2*x^5 + 5*(10*e^2*f*g - 3*d*e*g^2)*x^3 + 15*(15*e^2*f^2 - 10*d*e*f*g + 3*d^2*g^2)*x)/e^3) + 1/15*(3*g^2*x^5 + 10*f*g*x^3 + 15*f^2*x)*log((e*x^2 + d)^p*c)","A",0
270,1,85,0,1.038067," ","integrate((g*x^2+f)*log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","\frac{2}{9} \, e p {\left(\frac{3 \, {\left(3 \, d e f - d^{2} g\right)} \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e^{2}} - \frac{e g x^{3} + 3 \, {\left(3 \, e f - d g\right)} x}{e^{2}}\right)} + \frac{1}{3} \, {\left(g x^{3} + 3 \, f x\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)"," ",0,"2/9*e*p*(3*(3*d*e*f - d^2*g)*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e^2) - (e*g*x^3 + 3*(3*e*f - d*g)*x)/e^2) + 1/3*(g*x^3 + 3*f*x)*log((e*x^2 + d)^p*c)","A",0
271,0,0,0,0.000000," ","integrate(log(c*(e*x^2+d)^p)/(g*x^2+f),x, algorithm=""maxima"")","\int \frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g x^{2} + f}\,{d x}"," ",0,"integrate(log((e*x^2 + d)^p*c)/(g*x^2 + f), x)","F",0
272,0,0,0,0.000000," ","integrate(log(c*(e*x^2+d)^p)/(g*x^2+f)^2,x, algorithm=""maxima"")","\int \frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}{{\left(g x^{2} + f\right)}^{2}}\,{d x}"," ",0,"integrate(log((e*x^2 + d)^p*c)/(g*x^2 + f)^2, x)","F",0
273,0,0,0,0.000000," ","integrate((g*x^2+f)^2*log(c*(e*x^2+d)^p)^2,x, algorithm=""maxima"")","\frac{1}{15} \, {\left(3 \, g^{2} p^{2} x^{5} + 10 \, f g p^{2} x^{3} + 15 \, f^{2} p^{2} x\right)} \log\left(e x^{2} + d\right)^{2} + \int \frac{15 \, e g^{2} x^{6} \log\left(c\right)^{2} + 15 \, {\left(2 \, e f g + d g^{2}\right)} x^{4} \log\left(c\right)^{2} + 15 \, d f^{2} \log\left(c\right)^{2} + 15 \, {\left(e f^{2} + 2 \, d f g\right)} x^{2} \log\left(c\right)^{2} - 2 \, {\left(3 \, {\left(2 \, e g^{2} p^{2} - 5 \, e g^{2} p \log\left(c\right)\right)} x^{6} + 5 \, {\left(4 \, e f g p^{2} - 3 \, {\left(2 \, e f g p + d g^{2} p\right)} \log\left(c\right)\right)} x^{4} - 15 \, d f^{2} p \log\left(c\right) + 15 \, {\left(2 \, e f^{2} p^{2} - {\left(e f^{2} p + 2 \, d f g p\right)} \log\left(c\right)\right)} x^{2}\right)} \log\left(e x^{2} + d\right)}{15 \, {\left(e x^{2} + d\right)}}\,{d x}"," ",0,"1/15*(3*g^2*p^2*x^5 + 10*f*g*p^2*x^3 + 15*f^2*p^2*x)*log(e*x^2 + d)^2 + integrate(1/15*(15*e*g^2*x^6*log(c)^2 + 15*(2*e*f*g + d*g^2)*x^4*log(c)^2 + 15*d*f^2*log(c)^2 + 15*(e*f^2 + 2*d*f*g)*x^2*log(c)^2 - 2*(3*(2*e*g^2*p^2 - 5*e*g^2*p*log(c))*x^6 + 5*(4*e*f*g*p^2 - 3*(2*e*f*g*p + d*g^2*p)*log(c))*x^4 - 15*d*f^2*p*log(c) + 15*(2*e*f^2*p^2 - (e*f^2*p + 2*d*f*g*p)*log(c))*x^2)*log(e*x^2 + d))/(e*x^2 + d), x)","F",0
274,0,0,0,0.000000," ","integrate((g*x^2+f)*log(c*(e*x^2+d)^p)^2,x, algorithm=""maxima"")","\frac{1}{3} \, {\left(g p^{2} x^{3} + 3 \, f p^{2} x\right)} \log\left(e x^{2} + d\right)^{2} + \int \frac{3 \, e g x^{4} \log\left(c\right)^{2} + 3 \, {\left(e f + d g\right)} x^{2} \log\left(c\right)^{2} + 3 \, d f \log\left(c\right)^{2} - 2 \, {\left({\left(2 \, e g p^{2} - 3 \, e g p \log\left(c\right)\right)} x^{4} - 3 \, d f p \log\left(c\right) + 3 \, {\left(2 \, e f p^{2} - {\left(e f p + d g p\right)} \log\left(c\right)\right)} x^{2}\right)} \log\left(e x^{2} + d\right)}{3 \, {\left(e x^{2} + d\right)}}\,{d x}"," ",0,"1/3*(g*p^2*x^3 + 3*f*p^2*x)*log(e*x^2 + d)^2 + integrate(1/3*(3*e*g*x^4*log(c)^2 + 3*(e*f + d*g)*x^2*log(c)^2 + 3*d*f*log(c)^2 - 2*((2*e*g*p^2 - 3*e*g*p*log(c))*x^4 - 3*d*f*p*log(c) + 3*(2*e*f*p^2 - (e*f*p + d*g*p)*log(c))*x^2)*log(e*x^2 + d))/(e*x^2 + d), x)","F",0
275,0,0,0,0.000000," ","integrate(log(c*(e*x^2+d)^p)^2/(g*x^2+f),x, algorithm=""maxima"")","\int \frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)^{2}}{g x^{2} + f}\,{d x}"," ",0,"integrate(log((e*x^2 + d)^p*c)^2/(g*x^2 + f), x)","F",0
276,0,0,0,0.000000," ","integrate(log(c*(e*x^2+d)^p)^2/(g*x^2+f)^2,x, algorithm=""maxima"")","\int \frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)^{2}}{{\left(g x^{2} + f\right)}^{2}}\,{d x}"," ",0,"integrate(log((e*x^2 + d)^p*c)^2/(g*x^2 + f)^2, x)","F",0
277,0,0,0,0.000000," ","integrate((g*x^2+f)*log(c*(e*x^2+d)^p)^3,x, algorithm=""maxima"")","\frac{1}{3} \, {\left(g p^{3} x^{3} + 3 \, f p^{3} x\right)} \log\left(e x^{2} + d\right)^{3} + \int \frac{e g x^{4} \log\left(c\right)^{3} + {\left(e f + d g\right)} x^{2} \log\left(c\right)^{3} + d f \log\left(c\right)^{3} - {\left({\left(2 \, e g p^{3} - 3 \, e g p^{2} \log\left(c\right)\right)} x^{4} - 3 \, d f p^{2} \log\left(c\right) + 3 \, {\left(2 \, e f p^{3} - {\left(e f p^{2} + d g p^{2}\right)} \log\left(c\right)\right)} x^{2}\right)} \log\left(e x^{2} + d\right)^{2} + 3 \, {\left(e g p x^{4} \log\left(c\right)^{2} + d f p \log\left(c\right)^{2} + {\left(e f p + d g p\right)} x^{2} \log\left(c\right)^{2}\right)} \log\left(e x^{2} + d\right)}{e x^{2} + d}\,{d x}"," ",0,"1/3*(g*p^3*x^3 + 3*f*p^3*x)*log(e*x^2 + d)^3 + integrate((e*g*x^4*log(c)^3 + (e*f + d*g)*x^2*log(c)^3 + d*f*log(c)^3 - ((2*e*g*p^3 - 3*e*g*p^2*log(c))*x^4 - 3*d*f*p^2*log(c) + 3*(2*e*f*p^3 - (e*f*p^2 + d*g*p^2)*log(c))*x^2)*log(e*x^2 + d)^2 + 3*(e*g*p*x^4*log(c)^2 + d*f*p*log(c)^2 + (e*f*p + d*g*p)*x^2*log(c)^2)*log(e*x^2 + d))/(e*x^2 + d), x)","F",0
278,0,0,0,0.000000," ","integrate(log(c*(e*x^2+d)^p)^3/(g*x^2+f),x, algorithm=""maxima"")","\int \frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)^{3}}{g x^{2} + f}\,{d x}"," ",0,"integrate(log((e*x^2 + d)^p*c)^3/(g*x^2 + f), x)","F",0
279,0,0,0,0.000000," ","integrate(log(c*(e*x^2+d)^p)^3/(g*x^2+f)^2,x, algorithm=""maxima"")","\int \frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)^{3}}{{\left(g x^{2} + f\right)}^{2}}\,{d x}"," ",0,"integrate(log((e*x^2 + d)^p*c)^3/(g*x^2 + f)^2, x)","F",0
280,0,0,0,0.000000," ","integrate((g*x^2+f)^2/log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","\int \frac{{\left(g x^{2} + f\right)}^{2}}{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}\,{d x}"," ",0,"integrate((g*x^2 + f)^2/log((e*x^2 + d)^p*c), x)","F",0
281,0,0,0,0.000000," ","integrate((g*x^2+f)/log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","\int \frac{g x^{2} + f}{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}\,{d x}"," ",0,"integrate((g*x^2 + f)/log((e*x^2 + d)^p*c), x)","F",0
282,0,0,0,0.000000," ","integrate(1/(g*x^2+f)/log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","\int \frac{1}{{\left(g x^{2} + f\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}\,{d x}"," ",0,"integrate(1/((g*x^2 + f)*log((e*x^2 + d)^p*c)), x)","F",0
283,0,0,0,0.000000," ","integrate(1/(g*x^2+f)^2/log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","\int \frac{1}{{\left(g x^{2} + f\right)}^{2} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}\,{d x}"," ",0,"integrate(1/((g*x^2 + f)^2*log((e*x^2 + d)^p*c)), x)","F",0
284,0,0,0,0.000000," ","integrate((g*x^2+f)^2/log(c*(e*x^2+d)^p)^2,x, algorithm=""maxima"")","-\frac{e g^{2} x^{6} + {\left(2 \, e f g + d g^{2}\right)} x^{4} + d f^{2} + {\left(e f^{2} + 2 \, d f g\right)} x^{2}}{2 \, {\left(e p^{2} x \log\left(e x^{2} + d\right) + e p x \log\left(c\right)\right)}} + \int \frac{5 \, e g^{2} x^{6} + 3 \, {\left(2 \, e f g + d g^{2}\right)} x^{4} - d f^{2} + {\left(e f^{2} + 2 \, d f g\right)} x^{2}}{2 \, {\left(e p^{2} x^{2} \log\left(e x^{2} + d\right) + e p x^{2} \log\left(c\right)\right)}}\,{d x}"," ",0,"-1/2*(e*g^2*x^6 + (2*e*f*g + d*g^2)*x^4 + d*f^2 + (e*f^2 + 2*d*f*g)*x^2)/(e*p^2*x*log(e*x^2 + d) + e*p*x*log(c)) + integrate(1/2*(5*e*g^2*x^6 + 3*(2*e*f*g + d*g^2)*x^4 - d*f^2 + (e*f^2 + 2*d*f*g)*x^2)/(e*p^2*x^2*log(e*x^2 + d) + e*p*x^2*log(c)), x)","F",0
285,0,0,0,0.000000," ","integrate((g*x^2+f)/log(c*(e*x^2+d)^p)^2,x, algorithm=""maxima"")","-\frac{e g x^{4} + {\left(e f + d g\right)} x^{2} + d f}{2 \, {\left(e p^{2} x \log\left(e x^{2} + d\right) + e p x \log\left(c\right)\right)}} + \int \frac{3 \, e g x^{4} + {\left(e f + d g\right)} x^{2} - d f}{2 \, {\left(e p^{2} x^{2} \log\left(e x^{2} + d\right) + e p x^{2} \log\left(c\right)\right)}}\,{d x}"," ",0,"-1/2*(e*g*x^4 + (e*f + d*g)*x^2 + d*f)/(e*p^2*x*log(e*x^2 + d) + e*p*x*log(c)) + integrate(1/2*(3*e*g*x^4 + (e*f + d*g)*x^2 - d*f)/(e*p^2*x^2*log(e*x^2 + d) + e*p*x^2*log(c)), x)","F",0
286,0,0,0,0.000000," ","integrate(1/(g*x^2+f)/log(c*(e*x^2+d)^p)^2,x, algorithm=""maxima"")","-\frac{e x^{2} + d}{2 \, {\left(e g p x^{3} \log\left(c\right) + e f p x \log\left(c\right) + {\left(e g p^{2} x^{3} + e f p^{2} x\right)} \log\left(e x^{2} + d\right)\right)}} - \int \frac{e g x^{4} - {\left(e f - 3 \, d g\right)} x^{2} + d f}{2 \, {\left(e g^{2} p x^{6} \log\left(c\right) + 2 \, e f g p x^{4} \log\left(c\right) + e f^{2} p x^{2} \log\left(c\right) + {\left(e g^{2} p^{2} x^{6} + 2 \, e f g p^{2} x^{4} + e f^{2} p^{2} x^{2}\right)} \log\left(e x^{2} + d\right)\right)}}\,{d x}"," ",0,"-1/2*(e*x^2 + d)/(e*g*p*x^3*log(c) + e*f*p*x*log(c) + (e*g*p^2*x^3 + e*f*p^2*x)*log(e*x^2 + d)) - integrate(1/2*(e*g*x^4 - (e*f - 3*d*g)*x^2 + d*f)/(e*g^2*p*x^6*log(c) + 2*e*f*g*p*x^4*log(c) + e*f^2*p*x^2*log(c) + (e*g^2*p^2*x^6 + 2*e*f*g*p^2*x^4 + e*f^2*p^2*x^2)*log(e*x^2 + d)), x)","F",0
287,0,0,0,0.000000," ","integrate(1/(g*x^2+f)^2/log(c*(e*x^2+d)^p)^2,x, algorithm=""maxima"")","-\frac{e x^{2} + d}{2 \, {\left(e g^{2} p x^{5} \log\left(c\right) + 2 \, e f g p x^{3} \log\left(c\right) + e f^{2} p x \log\left(c\right) + {\left(e g^{2} p^{2} x^{5} + 2 \, e f g p^{2} x^{3} + e f^{2} p^{2} x\right)} \log\left(e x^{2} + d\right)\right)}} - \int \frac{3 \, e g x^{4} - {\left(e f - 5 \, d g\right)} x^{2} + d f}{2 \, {\left(e g^{3} p x^{8} \log\left(c\right) + 3 \, e f g^{2} p x^{6} \log\left(c\right) + 3 \, e f^{2} g p x^{4} \log\left(c\right) + e f^{3} p x^{2} \log\left(c\right) + {\left(e g^{3} p^{2} x^{8} + 3 \, e f g^{2} p^{2} x^{6} + 3 \, e f^{2} g p^{2} x^{4} + e f^{3} p^{2} x^{2}\right)} \log\left(e x^{2} + d\right)\right)}}\,{d x}"," ",0,"-1/2*(e*x^2 + d)/(e*g^2*p*x^5*log(c) + 2*e*f*g*p*x^3*log(c) + e*f^2*p*x*log(c) + (e*g^2*p^2*x^5 + 2*e*f*g*p^2*x^3 + e*f^2*p^2*x)*log(e*x^2 + d)) - integrate(1/2*(3*e*g*x^4 - (e*f - 5*d*g)*x^2 + d*f)/(e*g^3*p*x^8*log(c) + 3*e*f*g^2*p*x^6*log(c) + 3*e*f^2*g*p*x^4*log(c) + e*f^3*p*x^2*log(c) + (e*g^3*p^2*x^8 + 3*e*f*g^2*p^2*x^6 + 3*e*f^2*g*p^2*x^4 + e*f^3*p^2*x^2)*log(e*x^2 + d)), x)","F",0
288,1,278,0,0.998441," ","integrate((g*x^3+f)^3*log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","\frac{1}{29400} \, e p {\left(\frac{8400 \, {\left(7 \, d e^{3} f^{3} - 3 \, d^{4} f g^{2}\right)} \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e^{4}} - \frac{588 \, e^{4} g^{3} x^{10} - 735 \, d e^{3} g^{3} x^{8} + 3600 \, e^{4} f g^{2} x^{7} + 980 \, d^{2} e^{2} g^{3} x^{6} - 5040 \, d e^{3} f g^{2} x^{5} + 8400 \, d^{2} e^{2} f g^{2} x^{3} + 735 \, {\left(15 \, e^{4} f^{2} g - 2 \, d^{3} e g^{3}\right)} x^{4} - 1470 \, {\left(15 \, d e^{3} f^{2} g - 2 \, d^{4} g^{3}\right)} x^{2} + 8400 \, {\left(7 \, e^{4} f^{3} - 3 \, d^{3} e f g^{2}\right)} x}{e^{5}} - \frac{1470 \, {\left(15 \, d^{2} e^{3} f^{2} g - 2 \, d^{5} g^{3}\right)} \log\left(e x^{2} + d\right)}{e^{6}}\right)} + \frac{1}{140} \, {\left(14 \, g^{3} x^{10} + 60 \, f g^{2} x^{7} + 105 \, f^{2} g x^{4} + 140 \, f^{3} x\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)"," ",0,"1/29400*e*p*(8400*(7*d*e^3*f^3 - 3*d^4*f*g^2)*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e^4) - (588*e^4*g^3*x^10 - 735*d*e^3*g^3*x^8 + 3600*e^4*f*g^2*x^7 + 980*d^2*e^2*g^3*x^6 - 5040*d*e^3*f*g^2*x^5 + 8400*d^2*e^2*f*g^2*x^3 + 735*(15*e^4*f^2*g - 2*d^3*e*g^3)*x^4 - 1470*(15*d*e^3*f^2*g - 2*d^4*g^3)*x^2 + 8400*(7*e^4*f^3 - 3*d^3*e*f*g^2)*x)/e^5 - 1470*(15*d^2*e^3*f^2*g - 2*d^5*g^3)*log(e*x^2 + d)/e^6) + 1/140*(14*g^3*x^10 + 60*f*g^2*x^7 + 105*f^2*g*x^4 + 140*f^3*x)*log((e*x^2 + d)^p*c)","A",0
289,1,178,0,0.994642," ","integrate((g*x^3+f)^2*log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","-\frac{1}{2940} \, {\left(\frac{1470 \, d^{2} f g \log\left(e x^{2} + d\right)}{e^{3}} - \frac{840 \, {\left(7 \, d e^{3} f^{2} - d^{4} g^{2}\right)} \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e^{4}} + \frac{120 \, e^{3} g^{2} x^{7} - 168 \, d e^{2} g^{2} x^{5} + 735 \, e^{3} f g x^{4} + 280 \, d^{2} e g^{2} x^{3} - 1470 \, d e^{2} f g x^{2} + 840 \, {\left(7 \, e^{3} f^{2} - d^{3} g^{2}\right)} x}{e^{4}}\right)} e p + \frac{1}{14} \, {\left(2 \, g^{2} x^{7} + 7 \, f g x^{4} + 14 \, f^{2} x\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)"," ",0,"-1/2940*(1470*d^2*f*g*log(e*x^2 + d)/e^3 - 840*(7*d*e^3*f^2 - d^4*g^2)*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e^4) + (120*e^3*g^2*x^7 - 168*d*e^2*g^2*x^5 + 735*e^3*f*g*x^4 + 280*d^2*e*g^2*x^3 - 1470*d*e^2*f*g*x^2 + 840*(7*e^3*f^2 - d^3*g^2)*x)/e^4)*e*p + 1/14*(2*g^2*x^7 + 7*f*g*x^4 + 14*f^2*x)*log((e*x^2 + d)^p*c)","A",0
290,1,92,0,0.995869," ","integrate((g*x^3+f)*log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","\frac{1}{8} \, {\left(\frac{16 \, d f \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e} - \frac{2 \, d^{2} g \log\left(e x^{2} + d\right)}{e^{3}} - \frac{e g x^{4} - 2 \, d g x^{2} + 16 \, e f x}{e^{2}}\right)} e p + \frac{1}{4} \, {\left(g x^{4} + 4 \, f x\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)"," ",0,"1/8*(16*d*f*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e) - 2*d^2*g*log(e*x^2 + d)/e^3 - (e*g*x^4 - 2*d*g*x^2 + 16*e*f*x)/e^2)*e*p + 1/4*(g*x^4 + 4*f*x)*log((e*x^2 + d)^p*c)","A",0
291,0,0,0,0.000000," ","integrate(log(c*(e*x^2+d)^p)/(g*x^3+f),x, algorithm=""maxima"")","\int \frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g x^{3} + f}\,{d x}"," ",0,"integrate(log((e*x^2 + d)^p*c)/(g*x^3 + f), x)","F",0
292,0,0,0,0.000000," ","integrate(log(c*(e*x^2+d)^p)/(g*x^3+f)^2,x, algorithm=""maxima"")","\int \frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}{{\left(g x^{3} + f\right)}^{2}}\,{d x}"," ",0,"integrate(log((e*x^2 + d)^p*c)/(g*x^3 + f)^2, x)","F",0
293,0,0,0,0.000000," ","integrate((g*x^3+f)^3*log(c*(e*x^2+d)^p)^2,x, algorithm=""maxima"")","\frac{1}{140} \, {\left(14 \, g^{3} p^{2} x^{10} + 60 \, f g^{2} p^{2} x^{7} + 105 \, f^{2} g p^{2} x^{4} + 140 \, f^{3} p^{2} x\right)} \log\left(e x^{2} + d\right)^{2} + \int \frac{35 \, e g^{3} x^{11} \log\left(c\right)^{2} + 35 \, d g^{3} x^{9} \log\left(c\right)^{2} + 105 \, e f g^{2} x^{8} \log\left(c\right)^{2} + 105 \, d f g^{2} x^{6} \log\left(c\right)^{2} + 105 \, e f^{2} g x^{5} \log\left(c\right)^{2} + 105 \, d f^{2} g x^{3} \log\left(c\right)^{2} + 35 \, e f^{3} x^{2} \log\left(c\right)^{2} + 35 \, d f^{3} \log\left(c\right)^{2} + {\left(70 \, d g^{3} p x^{9} \log\left(c\right) - 14 \, {\left(e g^{3} p^{2} - 5 \, e g^{3} p \log\left(c\right)\right)} x^{11} + 210 \, d f g^{2} p x^{6} \log\left(c\right) - 30 \, {\left(2 \, e f g^{2} p^{2} - 7 \, e f g^{2} p \log\left(c\right)\right)} x^{8} + 210 \, d f^{2} g p x^{3} \log\left(c\right) - 105 \, {\left(e f^{2} g p^{2} - 2 \, e f^{2} g p \log\left(c\right)\right)} x^{5} + 70 \, d f^{3} p \log\left(c\right) - 70 \, {\left(2 \, e f^{3} p^{2} - e f^{3} p \log\left(c\right)\right)} x^{2}\right)} \log\left(e x^{2} + d\right)}{35 \, {\left(e x^{2} + d\right)}}\,{d x}"," ",0,"1/140*(14*g^3*p^2*x^10 + 60*f*g^2*p^2*x^7 + 105*f^2*g*p^2*x^4 + 140*f^3*p^2*x)*log(e*x^2 + d)^2 + integrate(1/35*(35*e*g^3*x^11*log(c)^2 + 35*d*g^3*x^9*log(c)^2 + 105*e*f*g^2*x^8*log(c)^2 + 105*d*f*g^2*x^6*log(c)^2 + 105*e*f^2*g*x^5*log(c)^2 + 105*d*f^2*g*x^3*log(c)^2 + 35*e*f^3*x^2*log(c)^2 + 35*d*f^3*log(c)^2 + (70*d*g^3*p*x^9*log(c) - 14*(e*g^3*p^2 - 5*e*g^3*p*log(c))*x^11 + 210*d*f*g^2*p*x^6*log(c) - 30*(2*e*f*g^2*p^2 - 7*e*f*g^2*p*log(c))*x^8 + 210*d*f^2*g*p*x^3*log(c) - 105*(e*f^2*g*p^2 - 2*e*f^2*g*p*log(c))*x^5 + 70*d*f^3*p*log(c) - 70*(2*e*f^3*p^2 - e*f^3*p*log(c))*x^2)*log(e*x^2 + d))/(e*x^2 + d), x)","F",0
294,0,0,0,0.000000," ","integrate((g*x^3+f)^2*log(c*(e*x^2+d)^p)^2,x, algorithm=""maxima"")","\frac{1}{14} \, {\left(2 \, g^{2} p^{2} x^{7} + 7 \, f g p^{2} x^{4} + 14 \, f^{2} p^{2} x\right)} \log\left(e x^{2} + d\right)^{2} + \int \frac{7 \, e g^{2} x^{8} \log\left(c\right)^{2} + 7 \, d g^{2} x^{6} \log\left(c\right)^{2} + 14 \, e f g x^{5} \log\left(c\right)^{2} + 14 \, d f g x^{3} \log\left(c\right)^{2} + 7 \, e f^{2} x^{2} \log\left(c\right)^{2} + 7 \, d f^{2} \log\left(c\right)^{2} + 2 \, {\left(7 \, d g^{2} p x^{6} \log\left(c\right) - {\left(2 \, e g^{2} p^{2} - 7 \, e g^{2} p \log\left(c\right)\right)} x^{8} + 14 \, d f g p x^{3} \log\left(c\right) - 7 \, {\left(e f g p^{2} - 2 \, e f g p \log\left(c\right)\right)} x^{5} + 7 \, d f^{2} p \log\left(c\right) - 7 \, {\left(2 \, e f^{2} p^{2} - e f^{2} p \log\left(c\right)\right)} x^{2}\right)} \log\left(e x^{2} + d\right)}{7 \, {\left(e x^{2} + d\right)}}\,{d x}"," ",0,"1/14*(2*g^2*p^2*x^7 + 7*f*g*p^2*x^4 + 14*f^2*p^2*x)*log(e*x^2 + d)^2 + integrate(1/7*(7*e*g^2*x^8*log(c)^2 + 7*d*g^2*x^6*log(c)^2 + 14*e*f*g*x^5*log(c)^2 + 14*d*f*g*x^3*log(c)^2 + 7*e*f^2*x^2*log(c)^2 + 7*d*f^2*log(c)^2 + 2*(7*d*g^2*p*x^6*log(c) - (2*e*g^2*p^2 - 7*e*g^2*p*log(c))*x^8 + 14*d*f*g*p*x^3*log(c) - 7*(e*f*g*p^2 - 2*e*f*g*p*log(c))*x^5 + 7*d*f^2*p*log(c) - 7*(2*e*f^2*p^2 - e*f^2*p*log(c))*x^2)*log(e*x^2 + d))/(e*x^2 + d), x)","F",0
295,0,0,0,0.000000," ","integrate((g*x^3+f)*log(c*(e*x^2+d)^p)^2,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(g p^{2} x^{4} + 4 \, f p^{2} x\right)} \log\left(e x^{2} + d\right)^{2} + \int \frac{e g x^{5} \log\left(c\right)^{2} + d g x^{3} \log\left(c\right)^{2} + e f x^{2} \log\left(c\right)^{2} + d f \log\left(c\right)^{2} + {\left(2 \, d g p x^{3} \log\left(c\right) - {\left(e g p^{2} - 2 \, e g p \log\left(c\right)\right)} x^{5} + 2 \, d f p \log\left(c\right) - 2 \, {\left(2 \, e f p^{2} - e f p \log\left(c\right)\right)} x^{2}\right)} \log\left(e x^{2} + d\right)}{e x^{2} + d}\,{d x}"," ",0,"1/4*(g*p^2*x^4 + 4*f*p^2*x)*log(e*x^2 + d)^2 + integrate((e*g*x^5*log(c)^2 + d*g*x^3*log(c)^2 + e*f*x^2*log(c)^2 + d*f*log(c)^2 + (2*d*g*p*x^3*log(c) - (e*g*p^2 - 2*e*g*p*log(c))*x^5 + 2*d*f*p*log(c) - 2*(2*e*f*p^2 - e*f*p*log(c))*x^2)*log(e*x^2 + d))/(e*x^2 + d), x)","F",0
296,0,0,0,0.000000," ","integrate(log(c*(e*x^2+d)^p)^2/(g*x^3+f),x, algorithm=""maxima"")","\int \frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)^{2}}{g x^{3} + f}\,{d x}"," ",0,"integrate(log((e*x^2 + d)^p*c)^2/(g*x^3 + f), x)","F",0
297,-1,0,0,0.000000," ","integrate(log(c*(e*x^2+d)^p)^2/(g*x^3+f)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
298,-2,0,0,0.000000," ","integrate((g*x^3+f)^2*log(c*(e*x^2+d)^p)^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*sqrt(e)>0)', see `assume?` for more details)Is 4*d^2-4*sqrt(e) positive or negative?","F(-2)",0
299,-2,0,0,0.000000," ","integrate((g*x^3+f)*log(c*(e*x^2+d)^p)^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*sqrt(e)>0)', see `assume?` for more details)Is 4*d^2-4*sqrt(e) positive or negative?","F(-2)",0
300,0,0,0,0.000000," ","integrate(log(c*(e*x^2+d)^p)^3/(g*x^3+f),x, algorithm=""maxima"")","\int \frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)^{3}}{g x^{3} + f}\,{d x}"," ",0,"integrate(log((e*x^2 + d)^p*c)^3/(g*x^3 + f), x)","F",0
301,-1,0,0,0.000000," ","integrate(log(c*(e*x^2+d)^p)^3/(g*x^3+f)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
302,0,0,0,0.000000," ","integrate((g*x^3+f)^2/log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","\int \frac{{\left(g x^{3} + f\right)}^{2}}{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}\,{d x}"," ",0,"integrate((g*x^3 + f)^2/log((e*x^2 + d)^p*c), x)","F",0
303,0,0,0,0.000000," ","integrate((g*x^3+f)/log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","\int \frac{g x^{3} + f}{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}\,{d x}"," ",0,"integrate((g*x^3 + f)/log((e*x^2 + d)^p*c), x)","F",0
304,0,0,0,0.000000," ","integrate(1/(g*x^3+f)/log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","\int \frac{1}{{\left(g x^{3} + f\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}\,{d x}"," ",0,"integrate(1/((g*x^3 + f)*log((e*x^2 + d)^p*c)), x)","F",0
305,0,0,0,0.000000," ","integrate(1/(g*x^3+f)^2/log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","\int \frac{1}{{\left(g x^{3} + f\right)}^{2} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}\,{d x}"," ",0,"integrate(1/((g*x^3 + f)^2*log((e*x^2 + d)^p*c)), x)","F",0
306,0,0,0,0.000000," ","integrate((g*x^3+f)^2/log(c*(e*x^2+d)^p)^2,x, algorithm=""maxima"")","-\frac{e g^{2} x^{8} + d g^{2} x^{6} + 2 \, e f g x^{5} + 2 \, d f g x^{3} + e f^{2} x^{2} + d f^{2}}{2 \, {\left(e p^{2} x \log\left(e x^{2} + d\right) + e p x \log\left(c\right)\right)}} + \int \frac{7 \, e g^{2} x^{8} + 5 \, d g^{2} x^{6} + 8 \, e f g x^{5} + 4 \, d f g x^{3} + e f^{2} x^{2} - d f^{2}}{2 \, {\left(e p^{2} x^{2} \log\left(e x^{2} + d\right) + e p x^{2} \log\left(c\right)\right)}}\,{d x}"," ",0,"-1/2*(e*g^2*x^8 + d*g^2*x^6 + 2*e*f*g*x^5 + 2*d*f*g*x^3 + e*f^2*x^2 + d*f^2)/(e*p^2*x*log(e*x^2 + d) + e*p*x*log(c)) + integrate(1/2*(7*e*g^2*x^8 + 5*d*g^2*x^6 + 8*e*f*g*x^5 + 4*d*f*g*x^3 + e*f^2*x^2 - d*f^2)/(e*p^2*x^2*log(e*x^2 + d) + e*p*x^2*log(c)), x)","F",0
307,0,0,0,0.000000," ","integrate((g*x^3+f)/log(c*(e*x^2+d)^p)^2,x, algorithm=""maxima"")","-\frac{e g x^{5} + d g x^{3} + e f x^{2} + d f}{2 \, {\left(e p^{2} x \log\left(e x^{2} + d\right) + e p x \log\left(c\right)\right)}} + \int \frac{4 \, e g x^{5} + 2 \, d g x^{3} + e f x^{2} - d f}{2 \, {\left(e p^{2} x^{2} \log\left(e x^{2} + d\right) + e p x^{2} \log\left(c\right)\right)}}\,{d x}"," ",0,"-1/2*(e*g*x^5 + d*g*x^3 + e*f*x^2 + d*f)/(e*p^2*x*log(e*x^2 + d) + e*p*x*log(c)) + integrate(1/2*(4*e*g*x^5 + 2*d*g*x^3 + e*f*x^2 - d*f)/(e*p^2*x^2*log(e*x^2 + d) + e*p*x^2*log(c)), x)","F",0
308,0,0,0,0.000000," ","integrate(1/(g*x^3+f)/log(c*(e*x^2+d)^p)^2,x, algorithm=""maxima"")","-\frac{e x^{2} + d}{2 \, {\left(e g p x^{4} \log\left(c\right) + e f p x \log\left(c\right) + {\left(e g p^{2} x^{4} + e f p^{2} x\right)} \log\left(e x^{2} + d\right)\right)}} - \int \frac{2 \, e g x^{5} + 4 \, d g x^{3} - e f x^{2} + d f}{2 \, {\left(e g^{2} p x^{8} \log\left(c\right) + 2 \, e f g p x^{5} \log\left(c\right) + e f^{2} p x^{2} \log\left(c\right) + {\left(e g^{2} p^{2} x^{8} + 2 \, e f g p^{2} x^{5} + e f^{2} p^{2} x^{2}\right)} \log\left(e x^{2} + d\right)\right)}}\,{d x}"," ",0,"-1/2*(e*x^2 + d)/(e*g*p*x^4*log(c) + e*f*p*x*log(c) + (e*g*p^2*x^4 + e*f*p^2*x)*log(e*x^2 + d)) - integrate(1/2*(2*e*g*x^5 + 4*d*g*x^3 - e*f*x^2 + d*f)/(e*g^2*p*x^8*log(c) + 2*e*f*g*p*x^5*log(c) + e*f^2*p*x^2*log(c) + (e*g^2*p^2*x^8 + 2*e*f*g*p^2*x^5 + e*f^2*p^2*x^2)*log(e*x^2 + d)), x)","F",0
309,0,0,0,0.000000," ","integrate(1/(g*x^3+f)^2/log(c*(e*x^2+d)^p)^2,x, algorithm=""maxima"")","-\frac{e x^{2} + d}{2 \, {\left(e g^{2} p x^{7} \log\left(c\right) + 2 \, e f g p x^{4} \log\left(c\right) + e f^{2} p x \log\left(c\right) + {\left(e g^{2} p^{2} x^{7} + 2 \, e f g p^{2} x^{4} + e f^{2} p^{2} x\right)} \log\left(e x^{2} + d\right)\right)}} - \int \frac{5 \, e g x^{5} + 7 \, d g x^{3} - e f x^{2} + d f}{2 \, {\left(e g^{3} p x^{11} \log\left(c\right) + 3 \, e f g^{2} p x^{8} \log\left(c\right) + 3 \, e f^{2} g p x^{5} \log\left(c\right) + e f^{3} p x^{2} \log\left(c\right) + {\left(e g^{3} p^{2} x^{11} + 3 \, e f g^{2} p^{2} x^{8} + 3 \, e f^{2} g p^{2} x^{5} + e f^{3} p^{2} x^{2}\right)} \log\left(e x^{2} + d\right)\right)}}\,{d x}"," ",0,"-1/2*(e*x^2 + d)/(e*g^2*p*x^7*log(c) + 2*e*f*g*p*x^4*log(c) + e*f^2*p*x*log(c) + (e*g^2*p^2*x^7 + 2*e*f*g*p^2*x^4 + e*f^2*p^2*x)*log(e*x^2 + d)) - integrate(1/2*(5*e*g*x^5 + 7*d*g*x^3 - e*f*x^2 + d*f)/(e*g^3*p*x^11*log(c) + 3*e*f*g^2*p*x^8*log(c) + 3*e*f^2*g*p*x^5*log(c) + e*f^3*p*x^2*log(c) + (e*g^3*p^2*x^11 + 3*e*f*g^2*p^2*x^8 + 3*e*f^2*g*p^2*x^5 + e*f^3*p^2*x^2)*log(e*x^2 + d)), x)","F",0
310,1,132,0,0.464806," ","integrate(x^5*(g*x^2+f)*log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","-\frac{1}{288} \, e p {\left(\frac{9 \, e^{3} g x^{8} + 4 \, {\left(4 \, e^{3} f - 3 \, d e^{2} g\right)} x^{6} - 6 \, {\left(4 \, d e^{2} f - 3 \, d^{2} e g\right)} x^{4} + 12 \, {\left(4 \, d^{2} e f - 3 \, d^{3} g\right)} x^{2}}{e^{4}} - \frac{12 \, {\left(4 \, d^{3} e f - 3 \, d^{4} g\right)} \log\left(e x^{2} + d\right)}{e^{5}}\right)} + \frac{1}{24} \, {\left(3 \, g x^{8} + 4 \, f x^{6}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)"," ",0,"-1/288*e*p*((9*e^3*g*x^8 + 4*(4*e^3*f - 3*d*e^2*g)*x^6 - 6*(4*d*e^2*f - 3*d^2*e*g)*x^4 + 12*(4*d^2*e*f - 3*d^3*g)*x^2)/e^4 - 12*(4*d^3*e*f - 3*d^4*g)*log(e*x^2 + d)/e^5) + 1/24*(3*g*x^8 + 4*f*x^6)*log((e*x^2 + d)^p*c)","A",0
311,1,108,0,0.455974," ","integrate(x^3*(g*x^2+f)*log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","-\frac{1}{72} \, e p {\left(\frac{4 \, e^{2} g x^{6} + 3 \, {\left(3 \, e^{2} f - 2 \, d e g\right)} x^{4} - 6 \, {\left(3 \, d e f - 2 \, d^{2} g\right)} x^{2}}{e^{3}} + \frac{6 \, {\left(3 \, d^{2} e f - 2 \, d^{3} g\right)} \log\left(e x^{2} + d\right)}{e^{4}}\right)} + \frac{1}{12} \, {\left(2 \, g x^{6} + 3 \, f x^{4}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)"," ",0,"-1/72*e*p*((4*e^2*g*x^6 + 3*(3*e^2*f - 2*d*e*g)*x^4 - 6*(3*d*e*f - 2*d^2*g)*x^2)/e^3 + 6*(3*d^2*e*f - 2*d^3*g)*log(e*x^2 + d)/e^4) + 1/12*(2*g*x^6 + 3*f*x^4)*log((e*x^2 + d)^p*c)","A",0
312,1,99,0,0.470218," ","integrate(x*(g*x^2+f)*log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","-\frac{e p {\left(\frac{e g^{2} x^{4} + 2 \, {\left(2 \, e f g - d g^{2}\right)} x^{2}}{e^{2}} + \frac{2 \, {\left(e^{2} f^{2} - 2 \, d e f g + d^{2} g^{2}\right)} \log\left(e x^{2} + d\right)}{e^{3}}\right)}}{8 \, g} + \frac{{\left(g x^{2} + f\right)}^{2} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{4 \, g}"," ",0,"-1/8*e*p*((e*g^2*x^4 + 2*(2*e*f*g - d*g^2)*x^2)/e^2 + 2*(e^2*f^2 - 2*d*e*f*g + d^2*g^2)*log(e*x^2 + d)/e^3)/g + 1/4*(g*x^2 + f)^2*log((e*x^2 + d)^p*c)/g","A",0
313,1,91,0,1.261033," ","integrate((g*x^2+f)*log(c*(e*x^2+d)^p)/x,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\log\left(e x^{2} + d\right) \log\left(-\frac{e x^{2} + d}{d} + 1\right) + {\rm Li}_2\left(\frac{e x^{2} + d}{d}\right)\right)} f p + f \log\left(c\right) \log\left(x\right) - \frac{{\left(e g p - e g \log\left(c\right)\right)} x^{2} - {\left(e g p x^{2} + d g p\right)} \log\left(e x^{2} + d\right)}{2 \, e}"," ",0,"1/2*(log(e*x^2 + d)*log(-(e*x^2 + d)/d + 1) + dilog((e*x^2 + d)/d))*f*p + f*log(c)*log(x) - 1/2*((e*g*p - e*g*log(c))*x^2 - (e*g*p*x^2 + d*g*p)*log(e*x^2 + d))/e","A",0
314,1,93,0,1.265428," ","integrate((g*x^2+f)*log(c*(e*x^2+d)^p)/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\log\left(e x^{2} + d\right) \log\left(-\frac{e x^{2} + d}{d} + 1\right) + {\rm Li}_2\left(\frac{e x^{2} + d}{d}\right)\right)} g p + \frac{{\left(e f p + d g \log\left(c\right)\right)} \log\left(x\right)}{d} - \frac{d f \log\left(c\right) + {\left(e f p x^{2} + d f p\right)} \log\left(e x^{2} + d\right)}{2 \, d x^{2}}"," ",0,"1/2*(log(e*x^2 + d)*log(-(e*x^2 + d)/d + 1) + dilog((e*x^2 + d)/d))*g*p + (e*f*p + d*g*log(c))*log(x)/d - 1/2*(d*f*log(c) + (e*f*p*x^2 + d*f*p)*log(e*x^2 + d))/(d*x^2)","A",0
315,1,77,0,0.471190," ","integrate((g*x^2+f)*log(c*(e*x^2+d)^p)/x^5,x, algorithm=""maxima"")","\frac{1}{4} \, e p {\left(\frac{{\left(e f - 2 \, d g\right)} \log\left(e x^{2} + d\right)}{d^{2}} - \frac{{\left(e f - 2 \, d g\right)} \log\left(x^{2}\right)}{d^{2}} - \frac{f}{d x^{2}}\right)} - \frac{{\left(2 \, g x^{2} + f\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{4 \, x^{4}}"," ",0,"1/4*e*p*((e*f - 2*d*g)*log(e*x^2 + d)/d^2 - (e*f - 2*d*g)*log(x^2)/d^2 - f/(d*x^2)) - 1/4*(2*g*x^2 + f)*log((e*x^2 + d)^p*c)/x^4","A",0
316,1,104,0,0.448196," ","integrate((g*x^2+f)*log(c*(e*x^2+d)^p)/x^7,x, algorithm=""maxima"")","-\frac{1}{12} \, e p {\left(\frac{{\left(2 \, e^{2} f - 3 \, d e g\right)} \log\left(e x^{2} + d\right)}{d^{3}} - \frac{{\left(2 \, e^{2} f - 3 \, d e g\right)} \log\left(x^{2}\right)}{d^{3}} - \frac{{\left(2 \, e f - 3 \, d g\right)} x^{2} - d f}{d^{2} x^{4}}\right)} - \frac{{\left(3 \, g x^{2} + 2 \, f\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{12 \, x^{6}}"," ",0,"-1/12*e*p*((2*e^2*f - 3*d*e*g)*log(e*x^2 + d)/d^3 - (2*e^2*f - 3*d*e*g)*log(x^2)/d^3 - ((2*e*f - 3*d*g)*x^2 - d*f)/(d^2*x^4)) - 1/12*(3*g*x^2 + 2*f)*log((e*x^2 + d)^p*c)/x^6","A",0
317,1,132,0,0.454539," ","integrate((g*x^2+f)*log(c*(e*x^2+d)^p)/x^9,x, algorithm=""maxima"")","\frac{1}{48} \, e p {\left(\frac{2 \, {\left(3 \, e^{3} f - 4 \, d e^{2} g\right)} \log\left(e x^{2} + d\right)}{d^{4}} - \frac{2 \, {\left(3 \, e^{3} f - 4 \, d e^{2} g\right)} \log\left(x^{2}\right)}{d^{4}} - \frac{2 \, {\left(3 \, e^{2} f - 4 \, d e g\right)} x^{4} + 2 \, d^{2} f - {\left(3 \, d e f - 4 \, d^{2} g\right)} x^{2}}{d^{3} x^{6}}\right)} - \frac{{\left(4 \, g x^{2} + 3 \, f\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{24 \, x^{8}}"," ",0,"1/48*e*p*(2*(3*e^3*f - 4*d*e^2*g)*log(e*x^2 + d)/d^4 - 2*(3*e^3*f - 4*d*e^2*g)*log(x^2)/d^4 - (2*(3*e^2*f - 4*d*e*g)*x^4 + 2*d^2*f - (3*d*e*f - 4*d^2*g)*x^2)/(d^3*x^6)) - 1/24*(4*g*x^2 + 3*f)*log((e*x^2 + d)^p*c)/x^8","A",0
318,1,112,0,0.985387," ","integrate(x^2*(g*x^2+f)*log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","-\frac{2}{225} \, e p {\left(\frac{15 \, {\left(5 \, d^{2} e f - 3 \, d^{3} g\right)} \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e^{3}} + \frac{9 \, e^{2} g x^{5} + 5 \, {\left(5 \, e^{2} f - 3 \, d e g\right)} x^{3} - 15 \, {\left(5 \, d e f - 3 \, d^{2} g\right)} x}{e^{3}}\right)} + \frac{1}{15} \, {\left(3 \, g x^{5} + 5 \, f x^{3}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)"," ",0,"-2/225*e*p*(15*(5*d^2*e*f - 3*d^3*g)*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e^3) + (9*e^2*g*x^5 + 5*(5*e^2*f - 3*d*e*g)*x^3 - 15*(5*d*e*f - 3*d^2*g)*x)/e^3) + 1/15*(3*g*x^5 + 5*f*x^3)*log((e*x^2 + d)^p*c)","A",0
319,1,85,0,0.993411," ","integrate((g*x^2+f)*log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","\frac{2}{9} \, e p {\left(\frac{3 \, {\left(3 \, d e f - d^{2} g\right)} \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e^{2}} - \frac{e g x^{3} + 3 \, {\left(3 \, e f - d g\right)} x}{e^{2}}\right)} + \frac{1}{3} \, {\left(g x^{3} + 3 \, f x\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)"," ",0,"2/9*e*p*(3*(3*d*e*f - d^2*g)*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e^2) - (e*g*x^3 + 3*(3*e*f - d*g)*x)/e^2) + 1/3*(g*x^3 + 3*f*x)*log((e*x^2 + d)^p*c)","A",0
320,1,61,0,0.993771," ","integrate((g*x^2+f)*log(c*(e*x^2+d)^p)/x^2,x, algorithm=""maxima"")","-2 \, e p {\left(\frac{g x}{e} - \frac{{\left(e f + d g\right)} \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e}\right)} + {\left(g x - \frac{f}{x}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)"," ",0,"-2*e*p*(g*x/e - (e*f + d*g)*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e)) + (g*x - f/x)*log((e*x^2 + d)^p*c)","A",0
321,1,65,0,0.989436," ","integrate((g*x^2+f)*log(c*(e*x^2+d)^p)/x^4,x, algorithm=""maxima"")","-\frac{2}{3} \, e p {\left(\frac{{\left(e f - 3 \, d g\right)} \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d} + \frac{f}{d x}\right)} - \frac{{\left(3 \, g x^{2} + f\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{3 \, x^{3}}"," ",0,"-2/3*e*p*((e*f - 3*d*g)*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d) + f/(d*x)) - 1/3*(3*g*x^2 + f)*log((e*x^2 + d)^p*c)/x^3","A",0
322,1,88,0,1.005589," ","integrate((g*x^2+f)*log(c*(e*x^2+d)^p)/x^6,x, algorithm=""maxima"")","\frac{2}{15} \, e p {\left(\frac{{\left(3 \, e^{2} f - 5 \, d e g\right)} \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d^{2}} + \frac{{\left(3 \, e f - 5 \, d g\right)} x^{2} - d f}{d^{2} x^{3}}\right)} - \frac{{\left(5 \, g x^{2} + 3 \, f\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{15 \, x^{5}}"," ",0,"2/15*e*p*((3*e^2*f - 5*d*e*g)*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d^2) + ((3*e*f - 5*d*g)*x^2 - d*f)/(d^2*x^3)) - 1/15*(5*g*x^2 + 3*f)*log((e*x^2 + d)^p*c)/x^5","A",0
323,1,223,0,0.470853," ","integrate(x^5*(g*x^2+f)^2*log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","-\frac{1}{3600} \, e p {\left(\frac{72 \, e^{4} g^{2} x^{10} + 45 \, {\left(5 \, e^{4} f g - 2 \, d e^{3} g^{2}\right)} x^{8} + 20 \, {\left(10 \, e^{4} f^{2} - 15 \, d e^{3} f g + 6 \, d^{2} e^{2} g^{2}\right)} x^{6} - 30 \, {\left(10 \, d e^{3} f^{2} - 15 \, d^{2} e^{2} f g + 6 \, d^{3} e g^{2}\right)} x^{4} + 60 \, {\left(10 \, d^{2} e^{2} f^{2} - 15 \, d^{3} e f g + 6 \, d^{4} g^{2}\right)} x^{2}}{e^{5}} - \frac{60 \, {\left(10 \, d^{3} e^{2} f^{2} - 15 \, d^{4} e f g + 6 \, d^{5} g^{2}\right)} \log\left(e x^{2} + d\right)}{e^{6}}\right)} + \frac{1}{60} \, {\left(6 \, g^{2} x^{10} + 15 \, f g x^{8} + 10 \, f^{2} x^{6}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)"," ",0,"-1/3600*e*p*((72*e^4*g^2*x^10 + 45*(5*e^4*f*g - 2*d*e^3*g^2)*x^8 + 20*(10*e^4*f^2 - 15*d*e^3*f*g + 6*d^2*e^2*g^2)*x^6 - 30*(10*d*e^3*f^2 - 15*d^2*e^2*f*g + 6*d^3*e*g^2)*x^4 + 60*(10*d^2*e^2*f^2 - 15*d^3*e*f*g + 6*d^4*g^2)*x^2)/e^5 - 60*(10*d^3*e^2*f^2 - 15*d^4*e*f*g + 6*d^5*g^2)*log(e*x^2 + d)/e^6) + 1/60*(6*g^2*x^10 + 15*f*g*x^8 + 10*f^2*x^6)*log((e*x^2 + d)^p*c)","A",0
324,1,185,0,0.474262," ","integrate(x^3*(g*x^2+f)^2*log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","-\frac{1}{288} \, e p {\left(\frac{9 \, e^{3} g^{2} x^{8} + 4 \, {\left(8 \, e^{3} f g - 3 \, d e^{2} g^{2}\right)} x^{6} + 6 \, {\left(6 \, e^{3} f^{2} - 8 \, d e^{2} f g + 3 \, d^{2} e g^{2}\right)} x^{4} - 12 \, {\left(6 \, d e^{2} f^{2} - 8 \, d^{2} e f g + 3 \, d^{3} g^{2}\right)} x^{2}}{e^{4}} + \frac{12 \, {\left(6 \, d^{2} e^{2} f^{2} - 8 \, d^{3} e f g + 3 \, d^{4} g^{2}\right)} \log\left(e x^{2} + d\right)}{e^{5}}\right)} + \frac{1}{24} \, {\left(3 \, g^{2} x^{8} + 8 \, f g x^{6} + 6 \, f^{2} x^{4}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)"," ",0,"-1/288*e*p*((9*e^3*g^2*x^8 + 4*(8*e^3*f*g - 3*d*e^2*g^2)*x^6 + 6*(6*e^3*f^2 - 8*d*e^2*f*g + 3*d^2*e*g^2)*x^4 - 12*(6*d*e^2*f^2 - 8*d^2*e*f*g + 3*d^3*g^2)*x^2)/e^4 + 12*(6*d^2*e^2*f^2 - 8*d^3*e*f*g + 3*d^4*g^2)*log(e*x^2 + d)/e^5) + 1/24*(3*g^2*x^8 + 8*f*g*x^6 + 6*f^2*x^4)*log((e*x^2 + d)^p*c)","A",0
325,1,152,0,0.479804," ","integrate(x*(g*x^2+f)^2*log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","\frac{{\left(g x^{2} + f\right)}^{3} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{6 \, g} - \frac{e p {\left(\frac{2 \, e^{2} g^{3} x^{6} + 3 \, {\left(3 \, e^{2} f g^{2} - d e g^{3}\right)} x^{4} + 6 \, {\left(3 \, e^{2} f^{2} g - 3 \, d e f g^{2} + d^{2} g^{3}\right)} x^{2}}{e^{3}} + \frac{6 \, {\left(e^{3} f^{3} - 3 \, d e^{2} f^{2} g + 3 \, d^{2} e f g^{2} - d^{3} g^{3}\right)} \log\left(e x^{2} + d\right)}{e^{4}}\right)}}{36 \, g}"," ",0,"1/6*(g*x^2 + f)^3*log((e*x^2 + d)^p*c)/g - 1/36*e*p*((2*e^2*g^3*x^6 + 3*(3*e^2*f*g^2 - d*e*g^3)*x^4 + 6*(3*e^2*f^2*g - 3*d*e*f*g^2 + d^2*g^3)*x^2)/e^3 + 6*(e^3*f^3 - 3*d*e^2*f^2*g + 3*d^2*e*f*g^2 - d^3*g^3)*log(e*x^2 + d)/e^4)/g","A",0
326,1,161,0,1.298140," ","integrate((g*x^2+f)^2*log(c*(e*x^2+d)^p)/x,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\log\left(e x^{2} + d\right) \log\left(-\frac{e x^{2} + d}{d} + 1\right) + {\rm Li}_2\left(\frac{e x^{2} + d}{d}\right)\right)} f^{2} p + f^{2} \log\left(c\right) \log\left(x\right) - \frac{{\left(e^{2} g^{2} p - 2 \, e^{2} g^{2} \log\left(c\right)\right)} x^{4} + 2 \, {\left(4 \, e^{2} f g p - d e g^{2} p - 4 \, e^{2} f g \log\left(c\right)\right)} x^{2} - 2 \, {\left(e^{2} g^{2} p x^{4} + 4 \, e^{2} f g p x^{2} + 4 \, d e f g p - d^{2} g^{2} p\right)} \log\left(e x^{2} + d\right)}{8 \, e^{2}}"," ",0,"1/2*(log(e*x^2 + d)*log(-(e*x^2 + d)/d + 1) + dilog((e*x^2 + d)/d))*f^2*p + f^2*log(c)*log(x) - 1/8*((e^2*g^2*p - 2*e^2*g^2*log(c))*x^4 + 2*(4*e^2*f*g*p - d*e*g^2*p - 4*e^2*f*g*log(c))*x^2 - 2*(e^2*g^2*p*x^4 + 4*e^2*f*g*p*x^2 + 4*d*e*f*g*p - d^2*g^2*p)*log(e*x^2 + d))/e^2","A",0
327,1,155,0,0.749072," ","integrate((g*x^2+f)^2*log(c*(e*x^2+d)^p)/x^3,x, algorithm=""maxima"")","{\left(\log\left(e x^{2} + d\right) \log\left(-\frac{e x^{2} + d}{d} + 1\right) + {\rm Li}_2\left(\frac{e x^{2} + d}{d}\right)\right)} f g p + \frac{{\left(e f^{2} p + 2 \, d f g \log\left(c\right)\right)} \log\left(x\right)}{d} - \frac{{\left(d e g^{2} p - d e g^{2} \log\left(c\right)\right)} x^{4} + d e f^{2} \log\left(c\right) - {\left(d e g^{2} p x^{4} - d e f^{2} p - {\left(e^{2} f^{2} p - d^{2} g^{2} p\right)} x^{2}\right)} \log\left(e x^{2} + d\right)}{2 \, d e x^{2}}"," ",0,"(log(e*x^2 + d)*log(-(e*x^2 + d)/d + 1) + dilog((e*x^2 + d)/d))*f*g*p + (e*f^2*p + 2*d*f*g*log(c))*log(x)/d - 1/2*((d*e*g^2*p - d*e*g^2*log(c))*x^4 + d*e*f^2*log(c) - (d*e*g^2*p*x^4 - d*e*f^2*p - (e^2*f^2*p - d^2*g^2*p)*x^2)*log(e*x^2 + d))/(d*e*x^2)","A",0
328,1,166,0,1.304792," ","integrate((g*x^2+f)^2*log(c*(e*x^2+d)^p)/x^5,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\log\left(e x^{2} + d\right) \log\left(-\frac{e x^{2} + d}{d} + 1\right) + {\rm Li}_2\left(\frac{e x^{2} + d}{d}\right)\right)} g^{2} p - \frac{{\left(e^{2} f^{2} p - 4 \, d e f g p - 2 \, d^{2} g^{2} \log\left(c\right)\right)} \log\left(x\right)}{2 \, d^{2}} - \frac{d^{2} f^{2} \log\left(c\right) + {\left(d e f^{2} p + 4 \, d^{2} f g \log\left(c\right)\right)} x^{2} + {\left(4 \, d^{2} f g p x^{2} + d^{2} f^{2} p - {\left(e^{2} f^{2} p - 4 \, d e f g p\right)} x^{4}\right)} \log\left(e x^{2} + d\right)}{4 \, d^{2} x^{4}}"," ",0,"1/2*(log(e*x^2 + d)*log(-(e*x^2 + d)/d + 1) + dilog((e*x^2 + d)/d))*g^2*p - 1/2*(e^2*f^2*p - 4*d*e*f*g*p - 2*d^2*g^2*log(c))*log(x)/d^2 - 1/4*(d^2*f^2*log(c) + (d*e*f^2*p + 4*d^2*f*g*log(c))*x^2 + (4*d^2*f*g*p*x^2 + d^2*f^2*p - (e^2*f^2*p - 4*d*e*f*g*p)*x^4)*log(e*x^2 + d))/(d^2*x^4)","A",0
329,1,137,0,0.487603," ","integrate((g*x^2+f)^2*log(c*(e*x^2+d)^p)/x^7,x, algorithm=""maxima"")","-\frac{1}{12} \, e p {\left(\frac{2 \, {\left(e^{2} f^{2} - 3 \, d e f g + 3 \, d^{2} g^{2}\right)} \log\left(e x^{2} + d\right)}{d^{3}} - \frac{2 \, {\left(e^{2} f^{2} - 3 \, d e f g + 3 \, d^{2} g^{2}\right)} \log\left(x^{2}\right)}{d^{3}} + \frac{d f^{2} - 2 \, {\left(e f^{2} - 3 \, d f g\right)} x^{2}}{d^{2} x^{4}}\right)} - \frac{{\left(3 \, g^{2} x^{4} + 3 \, f g x^{2} + f^{2}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{6 \, x^{6}}"," ",0,"-1/12*e*p*(2*(e^2*f^2 - 3*d*e*f*g + 3*d^2*g^2)*log(e*x^2 + d)/d^3 - 2*(e^2*f^2 - 3*d*e*f*g + 3*d^2*g^2)*log(x^2)/d^3 + (d*f^2 - 2*(e*f^2 - 3*d*f*g)*x^2)/(d^2*x^4)) - 1/6*(3*g^2*x^4 + 3*f*g*x^2 + f^2)*log((e*x^2 + d)^p*c)/x^6","A",0
330,1,183,0,0.491417," ","integrate((g*x^2+f)^2*log(c*(e*x^2+d)^p)/x^9,x, algorithm=""maxima"")","\frac{1}{48} \, e p {\left(\frac{2 \, {\left(3 \, e^{3} f^{2} - 8 \, d e^{2} f g + 6 \, d^{2} e g^{2}\right)} \log\left(e x^{2} + d\right)}{d^{4}} - \frac{2 \, {\left(3 \, e^{3} f^{2} - 8 \, d e^{2} f g + 6 \, d^{2} e g^{2}\right)} \log\left(x^{2}\right)}{d^{4}} - \frac{2 \, {\left(3 \, e^{2} f^{2} - 8 \, d e f g + 6 \, d^{2} g^{2}\right)} x^{4} + 2 \, d^{2} f^{2} - {\left(3 \, d e f^{2} - 8 \, d^{2} f g\right)} x^{2}}{d^{3} x^{6}}\right)} - \frac{{\left(6 \, g^{2} x^{4} + 8 \, f g x^{2} + 3 \, f^{2}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{24 \, x^{8}}"," ",0,"1/48*e*p*(2*(3*e^3*f^2 - 8*d*e^2*f*g + 6*d^2*e*g^2)*log(e*x^2 + d)/d^4 - 2*(3*e^3*f^2 - 8*d*e^2*f*g + 6*d^2*e*g^2)*log(x^2)/d^4 - (2*(3*e^2*f^2 - 8*d*e*f*g + 6*d^2*g^2)*x^4 + 2*d^2*f^2 - (3*d*e*f^2 - 8*d^2*f*g)*x^2)/(d^3*x^6)) - 1/24*(6*g^2*x^4 + 8*f*g*x^2 + 3*f^2)*log((e*x^2 + d)^p*c)/x^8","A",0
331,1,223,0,0.497267," ","integrate((g*x^2+f)^2*log(c*(e*x^2+d)^p)/x^11,x, algorithm=""maxima"")","-\frac{1}{120} \, e p {\left(\frac{2 \, {\left(6 \, e^{4} f^{2} - 15 \, d e^{3} f g + 10 \, d^{2} e^{2} g^{2}\right)} \log\left(e x^{2} + d\right)}{d^{5}} - \frac{2 \, {\left(6 \, e^{4} f^{2} - 15 \, d e^{3} f g + 10 \, d^{2} e^{2} g^{2}\right)} \log\left(x^{2}\right)}{d^{5}} - \frac{2 \, {\left(6 \, e^{3} f^{2} - 15 \, d e^{2} f g + 10 \, d^{2} e g^{2}\right)} x^{6} - 3 \, d^{3} f^{2} - {\left(6 \, d e^{2} f^{2} - 15 \, d^{2} e f g + 10 \, d^{3} g^{2}\right)} x^{4} + 2 \, {\left(2 \, d^{2} e f^{2} - 5 \, d^{3} f g\right)} x^{2}}{d^{4} x^{8}}\right)} - \frac{{\left(10 \, g^{2} x^{4} + 15 \, f g x^{2} + 6 \, f^{2}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{60 \, x^{10}}"," ",0,"-1/120*e*p*(2*(6*e^4*f^2 - 15*d*e^3*f*g + 10*d^2*e^2*g^2)*log(e*x^2 + d)/d^5 - 2*(6*e^4*f^2 - 15*d*e^3*f*g + 10*d^2*e^2*g^2)*log(x^2)/d^5 - (2*(6*e^3*f^2 - 15*d*e^2*f*g + 10*d^2*e*g^2)*x^6 - 3*d^3*f^2 - (6*d*e^2*f^2 - 15*d^2*e*f*g + 10*d^3*g^2)*x^4 + 2*(2*d^2*e*f^2 - 5*d^3*f*g)*x^2)/(d^4*x^8)) - 1/60*(10*g^2*x^4 + 15*f*g*x^2 + 6*f^2)*log((e*x^2 + d)^p*c)/x^10","A",0
332,1,189,0,1.019344," ","integrate(x^2*(g*x^2+f)^2*log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","-\frac{2}{11025} \, e p {\left(\frac{105 \, {\left(35 \, d^{2} e^{2} f^{2} - 42 \, d^{3} e f g + 15 \, d^{4} g^{2}\right)} \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e^{4}} + \frac{225 \, e^{3} g^{2} x^{7} + 63 \, {\left(14 \, e^{3} f g - 5 \, d e^{2} g^{2}\right)} x^{5} + 35 \, {\left(35 \, e^{3} f^{2} - 42 \, d e^{2} f g + 15 \, d^{2} e g^{2}\right)} x^{3} - 105 \, {\left(35 \, d e^{2} f^{2} - 42 \, d^{2} e f g + 15 \, d^{3} g^{2}\right)} x}{e^{4}}\right)} + \frac{1}{105} \, {\left(15 \, g^{2} x^{7} + 42 \, f g x^{5} + 35 \, f^{2} x^{3}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)"," ",0,"-2/11025*e*p*(105*(35*d^2*e^2*f^2 - 42*d^3*e*f*g + 15*d^4*g^2)*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e^4) + (225*e^3*g^2*x^7 + 63*(14*e^3*f*g - 5*d*e^2*g^2)*x^5 + 35*(35*e^3*f^2 - 42*d*e^2*f*g + 15*d^2*e*g^2)*x^3 - 105*(35*d*e^2*f^2 - 42*d^2*e*f*g + 15*d^3*g^2)*x)/e^4) + 1/105*(15*g^2*x^7 + 42*f*g*x^5 + 35*f^2*x^3)*log((e*x^2 + d)^p*c)","A",0
333,1,150,0,1.015927," ","integrate((g*x^2+f)^2*log(c*(e*x^2+d)^p),x, algorithm=""maxima"")","\frac{2}{225} \, e p {\left(\frac{15 \, {\left(15 \, d e^{2} f^{2} - 10 \, d^{2} e f g + 3 \, d^{3} g^{2}\right)} \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e^{3}} - \frac{9 \, e^{2} g^{2} x^{5} + 5 \, {\left(10 \, e^{2} f g - 3 \, d e g^{2}\right)} x^{3} + 15 \, {\left(15 \, e^{2} f^{2} - 10 \, d e f g + 3 \, d^{2} g^{2}\right)} x}{e^{3}}\right)} + \frac{1}{15} \, {\left(3 \, g^{2} x^{5} + 10 \, f g x^{3} + 15 \, f^{2} x\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)"," ",0,"2/225*e*p*(15*(15*d*e^2*f^2 - 10*d^2*e*f*g + 3*d^3*g^2)*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e^3) - (9*e^2*g^2*x^5 + 5*(10*e^2*f*g - 3*d*e*g^2)*x^3 + 15*(15*e^2*f^2 - 10*d*e*f*g + 3*d^2*g^2)*x)/e^3) + 1/15*(3*g^2*x^5 + 10*f*g*x^3 + 15*f^2*x)*log((e*x^2 + d)^p*c)","A",0
334,1,112,0,1.042160," ","integrate((g*x^2+f)^2*log(c*(e*x^2+d)^p)/x^2,x, algorithm=""maxima"")","\frac{2}{9} \, e p {\left(\frac{3 \, {\left(3 \, e^{2} f^{2} + 6 \, d e f g - d^{2} g^{2}\right)} \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e^{2}} - \frac{e g^{2} x^{3} + 3 \, {\left(6 \, e f g - d g^{2}\right)} x}{e^{2}}\right)} + \frac{1}{3} \, {\left(g^{2} x^{3} + 6 \, f g x - \frac{3 \, f^{2}}{x}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)"," ",0,"2/9*e*p*(3*(3*e^2*f^2 + 6*d*e*f*g - d^2*g^2)*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e^2) - (e*g^2*x^3 + 3*(6*e*f*g - d*g^2)*x)/e^2) + 1/3*(g^2*x^3 + 6*f*g*x - 3*f^2/x)*log((e*x^2 + d)^p*c)","A",0
335,1,105,0,1.011771," ","integrate((g*x^2+f)^2*log(c*(e*x^2+d)^p)/x^4,x, algorithm=""maxima"")","-\frac{2}{3} \, {\left(\frac{3 \, g^{2} x}{e} + \frac{f^{2}}{d x} + \frac{{\left(e^{2} f^{2} - 6 \, d e f g - 3 \, d^{2} g^{2}\right)} \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d e}\right)} e p + \frac{1}{3} \, {\left(3 \, g^{2} x - \frac{6 \, f g x^{2} + f^{2}}{x^{3}}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)"," ",0,"-2/3*(3*g^2*x/e + f^2/(d*x) + (e^2*f^2 - 6*d*e*f*g - 3*d^2*g^2)*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d*e))*e*p + 1/3*(3*g^2*x - (6*f*g*x^2 + f^2)/x^3)*log((e*x^2 + d)^p*c)","A",0
336,1,116,0,1.031934," ","integrate((g*x^2+f)^2*log(c*(e*x^2+d)^p)/x^6,x, algorithm=""maxima"")","\frac{2}{15} \, e p {\left(\frac{{\left(3 \, e^{2} f^{2} - 10 \, d e f g + 15 \, d^{2} g^{2}\right)} \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d^{2}} - \frac{d f^{2} - {\left(3 \, e f^{2} - 10 \, d f g\right)} x^{2}}{d^{2} x^{3}}\right)} - \frac{{\left(15 \, g^{2} x^{4} + 10 \, f g x^{2} + 3 \, f^{2}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{15 \, x^{5}}"," ",0,"2/15*e*p*((3*e^2*f^2 - 10*d*e*f*g + 15*d^2*g^2)*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d^2) - (d*f^2 - (3*e*f^2 - 10*d*f*g)*x^2)/(d^2*x^3)) - 1/15*(15*g^2*x^4 + 10*f*g*x^2 + 3*f^2)*log((e*x^2 + d)^p*c)/x^5","A",0
337,1,151,0,1.030585," ","integrate((g*x^2+f)^2*log(c*(e*x^2+d)^p)/x^8,x, algorithm=""maxima"")","-\frac{2}{105} \, e p {\left(\frac{{\left(15 \, e^{3} f^{2} - 42 \, d e^{2} f g + 35 \, d^{2} e g^{2}\right)} \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d^{3}} + \frac{{\left(15 \, e^{2} f^{2} - 42 \, d e f g + 35 \, d^{2} g^{2}\right)} x^{4} + 3 \, d^{2} f^{2} - {\left(5 \, d e f^{2} - 14 \, d^{2} f g\right)} x^{2}}{d^{3} x^{5}}\right)} - \frac{{\left(35 \, g^{2} x^{4} + 42 \, f g x^{2} + 15 \, f^{2}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{105 \, x^{7}}"," ",0,"-2/105*e*p*((15*e^3*f^2 - 42*d*e^2*f*g + 35*d^2*e*g^2)*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d^3) + ((15*e^2*f^2 - 42*d*e*f*g + 35*d^2*g^2)*x^4 + 3*d^2*f^2 - (5*d*e*f^2 - 14*d^2*f*g)*x^2)/(d^3*x^5)) - 1/105*(35*g^2*x^4 + 42*f*g*x^2 + 15*f^2)*log((e*x^2 + d)^p*c)/x^7","A",0
338,1,182,0,1.305132," ","integrate(x^5*log(c*(e*x^2+d)^p)/(g*x^2+f),x, algorithm=""maxima"")","\frac{{\left(\log\left(e x^{2} + d\right) \log\left(\frac{e g x^{2} + d g}{e f - d g} + 1\right) + {\rm Li}_2\left(-\frac{e g x^{2} + d g}{e f - d g}\right)\right)} f^{2} p}{2 \, g^{3}} + \frac{f^{2} \log\left(g x^{2} + f\right) \log\left(c\right)}{2 \, g^{3}} - \frac{{\left(e^{2} g p - 2 \, e^{2} g \log\left(c\right)\right)} x^{4} - 2 \, {\left(2 \, e^{2} f p + d e g p - 2 \, e^{2} f \log\left(c\right)\right)} x^{2} - 2 \, {\left(e^{2} g p x^{4} - 2 \, e^{2} f p x^{2} - 2 \, d e f p - d^{2} g p\right)} \log\left(e x^{2} + d\right)}{8 \, e^{2} g^{2}}"," ",0,"1/2*(log(e*x^2 + d)*log((e*g*x^2 + d*g)/(e*f - d*g) + 1) + dilog(-(e*g*x^2 + d*g)/(e*f - d*g)))*f^2*p/g^3 + 1/2*f^2*log(g*x^2 + f)*log(c)/g^3 - 1/8*((e^2*g*p - 2*e^2*g*log(c))*x^4 - 2*(2*e^2*f*p + d*e*g*p - 2*e^2*f*log(c))*x^2 - 2*(e^2*g*p*x^4 - 2*e^2*f*p*x^2 - 2*d*e*f*p - d^2*g*p)*log(e*x^2 + d))/(e^2*g^2)","A",0
339,1,123,0,1.319841," ","integrate(x^3*log(c*(e*x^2+d)^p)/(g*x^2+f),x, algorithm=""maxima"")","-\frac{{\left(\log\left(e x^{2} + d\right) \log\left(\frac{e g x^{2} + d g}{e f - d g} + 1\right) + {\rm Li}_2\left(-\frac{e g x^{2} + d g}{e f - d g}\right)\right)} f p}{2 \, g^{2}} - \frac{f \log\left(g x^{2} + f\right) \log\left(c\right)}{2 \, g^{2}} - \frac{{\left(e p - e \log\left(c\right)\right)} x^{2} - {\left(e p x^{2} + d p\right)} \log\left(e x^{2} + d\right)}{2 \, e g}"," ",0,"-1/2*(log(e*x^2 + d)*log((e*g*x^2 + d*g)/(e*f - d*g) + 1) + dilog(-(e*g*x^2 + d*g)/(e*f - d*g)))*f*p/g^2 - 1/2*f*log(g*x^2 + f)*log(c)/g^2 - 1/2*((e*p - e*log(c))*x^2 - (e*p*x^2 + d*p)*log(e*x^2 + d))/(e*g)","A",0
340,1,138,0,0.485967," ","integrate(x*log(c*(e*x^2+d)^p)/(g*x^2+f),x, algorithm=""maxima"")","\frac{e p {\left(\frac{\log\left(e x^{2} + d\right) \log\left(g x^{2} + f\right)}{e} - \frac{\log\left(g x^{2} + f\right) \log\left(-\frac{e g x^{2} + e f}{e f - d g} + 1\right) + {\rm Li}_2\left(\frac{e g x^{2} + e f}{e f - d g}\right)}{e}\right)}}{2 \, g} - \frac{p \log\left(e x^{2} + d\right) \log\left(g x^{2} + f\right)}{2 \, g} + \frac{\log\left(g x^{2} + f\right) \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{2 \, g}"," ",0,"1/2*e*p*(log(e*x^2 + d)*log(g*x^2 + f)/e - (log(g*x^2 + f)*log(-(e*g*x^2 + e*f)/(e*f - d*g) + 1) + dilog((e*g*x^2 + e*f)/(e*f - d*g)))/e)/g - 1/2*p*log(e*x^2 + d)*log(g*x^2 + f)/g + 1/2*log(g*x^2 + f)*log((e*x^2 + d)^p*c)/g","B",0
341,1,140,0,1.258921," ","integrate(log(c*(e*x^2+d)^p)/x/(g*x^2+f),x, algorithm=""maxima"")","-\frac{1}{2} \, e p {\left(\frac{2 \, \log\left(\frac{e x^{2}}{d} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{e x^{2}}{d}\right)}{e f} - \frac{\log\left(g x^{2} + f\right) \log\left(-\frac{e g x^{2} + e f}{e f - d g} + 1\right) + {\rm Li}_2\left(\frac{e g x^{2} + e f}{e f - d g}\right)}{e f}\right)} - \frac{1}{2} \, {\left(\frac{\log\left(g x^{2} + f\right)}{f} - \frac{\log\left(x^{2}\right)}{f}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)"," ",0,"-1/2*e*p*((2*log(e*x^2/d + 1)*log(x) + dilog(-e*x^2/d))/(e*f) - (log(g*x^2 + f)*log(-(e*g*x^2 + e*f)/(e*f - d*g) + 1) + dilog((e*g*x^2 + e*f)/(e*f - d*g)))/(e*f)) - 1/2*(log(g*x^2 + f)/f - log(x^2)/f)*log((e*x^2 + d)^p*c)","A",0
342,1,178,0,1.260064," ","integrate(log(c*(e*x^2+d)^p)/x^3/(g*x^2+f),x, algorithm=""maxima"")","\frac{1}{2} \, e p {\left(\frac{{\left(2 \, \log\left(\frac{e x^{2}}{d} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{e x^{2}}{d}\right)\right)} g}{e f^{2}} - \frac{{\left(\log\left(g x^{2} + f\right) \log\left(-\frac{e g x^{2} + e f}{e f - d g} + 1\right) + {\rm Li}_2\left(\frac{e g x^{2} + e f}{e f - d g}\right)\right)} g}{e f^{2}} - \frac{\log\left(e x^{2} + d\right)}{d f} + \frac{2 \, \log\left(x\right)}{d f}\right)} + \frac{1}{2} \, {\left(\frac{g \log\left(g x^{2} + f\right)}{f^{2}} - \frac{g \log\left(x^{2}\right)}{f^{2}} - \frac{1}{f x^{2}}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)"," ",0,"1/2*e*p*((2*log(e*x^2/d + 1)*log(x) + dilog(-e*x^2/d))*g/(e*f^2) - (log(g*x^2 + f)*log(-(e*g*x^2 + e*f)/(e*f - d*g) + 1) + dilog((e*g*x^2 + e*f)/(e*f - d*g)))*g/(e*f^2) - log(e*x^2 + d)/(d*f) + 2*log(x)/(d*f)) + 1/2*(g*log(g*x^2 + f)/f^2 - g*log(x^2)/f^2 - 1/(f*x^2))*log((e*x^2 + d)^p*c)","A",0
343,0,0,0,0.000000," ","integrate(x^4*log(c*(e*x^2+d)^p)/(g*x^2+f),x, algorithm=""maxima"")","\int \frac{x^{4} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g x^{2} + f}\,{d x}"," ",0,"integrate(x^4*log((e*x^2 + d)^p*c)/(g*x^2 + f), x)","F",0
344,0,0,0,0.000000," ","integrate(x^2*log(c*(e*x^2+d)^p)/(g*x^2+f),x, algorithm=""maxima"")","\int \frac{x^{2} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g x^{2} + f}\,{d x}"," ",0,"integrate(x^2*log((e*x^2 + d)^p*c)/(g*x^2 + f), x)","F",0
345,0,0,0,0.000000," ","integrate(log(c*(e*x^2+d)^p)/(g*x^2+f),x, algorithm=""maxima"")","\int \frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g x^{2} + f}\,{d x}"," ",0,"integrate(log((e*x^2 + d)^p*c)/(g*x^2 + f), x)","F",0
346,0,0,0,0.000000," ","integrate(log(c*(e*x^2+d)^p)/x^2/(g*x^2+f),x, algorithm=""maxima"")","\int \frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}{{\left(g x^{2} + f\right)} x^{2}}\,{d x}"," ",0,"integrate(log((e*x^2 + d)^p*c)/((g*x^2 + f)*x^2), x)","F",0
347,0,0,0,0.000000," ","integrate(log(c*(e*x^2+d)^p)/x^4/(g*x^2+f),x, algorithm=""maxima"")","\int \frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}{{\left(g x^{2} + f\right)} x^{4}}\,{d x}"," ",0,"integrate(log((e*x^2 + d)^p*c)/((g*x^2 + f)*x^4), x)","F",0
348,1,337,0,0.798776," ","integrate(x^5*log(c*(e*x^2+d)^p)/(g*x^2+f)^2,x, algorithm=""maxima"")","-\frac{{\left(e f^{2} p + 2 \, {\left(e f^{2} - d f g\right)} \log\left(c\right)\right)} \log\left(g x^{2} + f\right)}{2 \, {\left(e f g^{3} - d g^{4}\right)}} - \frac{{\left(e^{2} f g^{2} p - d e g^{3} p - {\left(e^{2} f g^{2} - d e g^{3}\right)} \log\left(c\right)\right)} x^{4} + {\left(e^{2} f^{2} g p - d e f g^{2} p - {\left(e^{2} f^{2} g - d e f g^{2}\right)} \log\left(c\right)\right)} x^{2} - {\left(2 \, d e f^{2} g p - d^{2} f g^{2} p + {\left(e^{2} f g^{2} p - d e g^{3} p\right)} x^{4} + {\left(2 \, e^{2} f^{2} g p - d^{2} g^{3} p\right)} x^{2}\right)} \log\left(e x^{2} + d\right) + {\left(e^{2} f^{3} - d e f^{2} g\right)} \log\left(c\right)}{2 \, {\left(e^{2} f^{2} g^{3} - d e f g^{4} + {\left(e^{2} f g^{4} - d e g^{5}\right)} x^{2}\right)}} - \frac{{\left(\log\left(e x^{2} + d\right) \log\left(\frac{e g x^{2} + d g}{e f - d g} + 1\right) + {\rm Li}_2\left(-\frac{e g x^{2} + d g}{e f - d g}\right)\right)} f p}{g^{3}}"," ",0,"-1/2*(e*f^2*p + 2*(e*f^2 - d*f*g)*log(c))*log(g*x^2 + f)/(e*f*g^3 - d*g^4) - 1/2*((e^2*f*g^2*p - d*e*g^3*p - (e^2*f*g^2 - d*e*g^3)*log(c))*x^4 + (e^2*f^2*g*p - d*e*f*g^2*p - (e^2*f^2*g - d*e*f*g^2)*log(c))*x^2 - (2*d*e*f^2*g*p - d^2*f*g^2*p + (e^2*f*g^2*p - d*e*g^3*p)*x^4 + (2*e^2*f^2*g*p - d^2*g^3*p)*x^2)*log(e*x^2 + d) + (e^2*f^3 - d*e*f^2*g)*log(c))/(e^2*f^2*g^3 - d*e*f*g^4 + (e^2*f*g^4 - d*e*g^5)*x^2) - (log(e*x^2 + d)*log((e*g*x^2 + d*g)/(e*f - d*g) + 1) + dilog(-(e*g*x^2 + d*g)/(e*f - d*g)))*f*p/g^3","A",0
349,1,181,0,1.292440," ","integrate(x^3*log(c*(e*x^2+d)^p)/(g*x^2+f)^2,x, algorithm=""maxima"")","\frac{{\left(e f p + {\left(e f - d g\right)} \log\left(c\right)\right)} \log\left(g x^{2} + f\right)}{2 \, {\left(e f g^{2} - d g^{3}\right)}} - \frac{{\left(e f g p x^{2} + d f g p\right)} \log\left(e x^{2} + d\right) - {\left(e f^{2} - d f g\right)} \log\left(c\right)}{2 \, {\left(e f^{2} g^{2} - d f g^{3} + {\left(e f g^{3} - d g^{4}\right)} x^{2}\right)}} + \frac{{\left(\log\left(e x^{2} + d\right) \log\left(\frac{e g x^{2} + d g}{e f - d g} + 1\right) + {\rm Li}_2\left(-\frac{e g x^{2} + d g}{e f - d g}\right)\right)} p}{2 \, g^{2}}"," ",0,"1/2*(e*f*p + (e*f - d*g)*log(c))*log(g*x^2 + f)/(e*f*g^2 - d*g^3) - 1/2*((e*f*g*p*x^2 + d*f*g*p)*log(e*x^2 + d) - (e*f^2 - d*f*g)*log(c))/(e*f^2*g^2 - d*f*g^3 + (e*f*g^3 - d*g^4)*x^2) + 1/2*(log(e*x^2 + d)*log((e*g*x^2 + d*g)/(e*f - d*g) + 1) + dilog(-(e*g*x^2 + d*g)/(e*f - d*g)))*p/g^2","A",0
350,1,74,0,0.464568," ","integrate(x*log(c*(e*x^2+d)^p)/(g*x^2+f)^2,x, algorithm=""maxima"")","\frac{e p {\left(\frac{\log\left(e x^{2} + d\right)}{e f - d g} - \frac{\log\left(g x^{2} + f\right)}{e f - d g}\right)}}{2 \, g} - \frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}{2 \, {\left(g x^{2} + f\right)} g}"," ",0,"1/2*e*p*(log(e*x^2 + d)/(e*f - d*g) - log(g*x^2 + f)/(e*f - d*g))/g - 1/2*log((e*x^2 + d)^p*c)/((g*x^2 + f)*g)","A",0
351,1,197,0,1.270022," ","integrate(log(c*(e*x^2+d)^p)/x/(g*x^2+f)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, e p {\left(\frac{\log\left(e x^{2} + d\right)}{e f^{2} - d f g} - \frac{\log\left(g x^{2} + f\right)}{e f^{2} - d f g} + \frac{2 \, \log\left(\frac{e x^{2}}{d} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{e x^{2}}{d}\right)}{e f^{2}} - \frac{\log\left(g x^{2} + f\right) \log\left(-\frac{e g x^{2} + e f}{e f - d g} + 1\right) + {\rm Li}_2\left(\frac{e g x^{2} + e f}{e f - d g}\right)}{e f^{2}}\right)} + \frac{1}{2} \, {\left(\frac{1}{f g x^{2} + f^{2}} - \frac{\log\left(g x^{2} + f\right)}{f^{2}} + \frac{\log\left(x^{2}\right)}{f^{2}}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)"," ",0,"-1/2*e*p*(log(e*x^2 + d)/(e*f^2 - d*f*g) - log(g*x^2 + f)/(e*f^2 - d*f*g) + (2*log(e*x^2/d + 1)*log(x) + dilog(-e*x^2/d))/(e*f^2) - (log(g*x^2 + f)*log(-(e*g*x^2 + e*f)/(e*f - d*g) + 1) + dilog((e*g*x^2 + e*f)/(e*f - d*g)))/(e*f^2)) + 1/2*(1/(f*g*x^2 + f^2) - log(g*x^2 + f)/f^2 + log(x^2)/f^2)*log((e*x^2 + d)^p*c)","A",0
352,1,295,0,0.736162," ","integrate(log(c*(e*x^2+d)^p)/x^3/(g*x^2+f)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(f {\left(\frac{e \log\left(e x^{2} + d\right)}{d e f^{3} - d^{2} f^{2} g} - \frac{g \log\left(g x^{2} + f\right)}{e f^{4} - d f^{3} g} - \frac{\log\left(x^{2}\right)}{d f^{3}}\right)} - 2 \, g {\left(\frac{\log\left(e x^{2} + d\right)}{e f^{3} - d f^{2} g} - \frac{\log\left(g x^{2} + f\right)}{e f^{3} - d f^{2} g}\right)} - \frac{2 \, {\left(2 \, \log\left(\frac{e x^{2}}{d} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{e x^{2}}{d}\right)\right)} g}{e f^{3}} + \frac{2 \, {\left(\log\left(g x^{2} + f\right) \log\left(-\frac{e g x^{2} + e f}{e f - d g} + 1\right) + {\rm Li}_2\left(\frac{e g x^{2} + e f}{e f - d g}\right)\right)} g}{e f^{3}}\right)} e p - \frac{1}{2} \, {\left(\frac{2 \, g x^{2} + f}{f^{2} g x^{4} + f^{3} x^{2}} - \frac{2 \, g \log\left(g x^{2} + f\right)}{f^{3}} + \frac{2 \, g \log\left(x^{2}\right)}{f^{3}}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)"," ",0,"-1/2*(f*(e*log(e*x^2 + d)/(d*e*f^3 - d^2*f^2*g) - g*log(g*x^2 + f)/(e*f^4 - d*f^3*g) - log(x^2)/(d*f^3)) - 2*g*(log(e*x^2 + d)/(e*f^3 - d*f^2*g) - log(g*x^2 + f)/(e*f^3 - d*f^2*g)) - 2*(2*log(e*x^2/d + 1)*log(x) + dilog(-e*x^2/d))*g/(e*f^3) + 2*(log(g*x^2 + f)*log(-(e*g*x^2 + e*f)/(e*f - d*g) + 1) + dilog((e*g*x^2 + e*f)/(e*f - d*g)))*g/(e*f^3))*e*p - 1/2*((2*g*x^2 + f)/(f^2*g*x^4 + f^3*x^2) - 2*g*log(g*x^2 + f)/f^3 + 2*g*log(x^2)/f^3)*log((e*x^2 + d)^p*c)","A",0
353,0,0,0,0.000000," ","integrate(x^4*log(c*(e*x^2+d)^p)/(g*x^2+f)^2,x, algorithm=""maxima"")","\int \frac{x^{4} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{{\left(g x^{2} + f\right)}^{2}}\,{d x}"," ",0,"integrate(x^4*log((e*x^2 + d)^p*c)/(g*x^2 + f)^2, x)","F",0
354,0,0,0,0.000000," ","integrate(x^2*log(c*(e*x^2+d)^p)/(g*x^2+f)^2,x, algorithm=""maxima"")","\int \frac{x^{2} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{{\left(g x^{2} + f\right)}^{2}}\,{d x}"," ",0,"integrate(x^2*log((e*x^2 + d)^p*c)/(g*x^2 + f)^2, x)","F",0
355,0,0,0,0.000000," ","integrate(log(c*(e*x^2+d)^p)/(g*x^2+f)^2,x, algorithm=""maxima"")","\int \frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}{{\left(g x^{2} + f\right)}^{2}}\,{d x}"," ",0,"integrate(log((e*x^2 + d)^p*c)/(g*x^2 + f)^2, x)","F",0
356,0,0,0,0.000000," ","integrate(log(c*(e*x^2+d)^p)/x^2/(g*x^2+f)^2,x, algorithm=""maxima"")","\int \frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}{{\left(g x^{2} + f\right)}^{2} x^{2}}\,{d x}"," ",0,"integrate(log((e*x^2 + d)^p*c)/((g*x^2 + f)^2*x^2), x)","F",0
357,0,0,0,0.000000," ","integrate(log(c*(b*x^2+a)^n)/(b*x^2+a),x, algorithm=""maxima"")","\int \frac{\log\left({\left(b x^{2} + a\right)}^{n} c\right)}{b x^{2} + a}\,{d x}"," ",0,"integrate(log((b*x^2 + a)^n*c)/(b*x^2 + a), x)","F",0
358,1,208,0,1.063596," ","integrate(log(-x^2+1)/(-x^2+2),x, algorithm=""maxima"")","\frac{1}{4} \, \sqrt{2} {\left({\left(\log\left(2 \, x + 2 \, \sqrt{2}\right) - \log\left(2 \, x - 2 \, \sqrt{2}\right)\right)} \log\left(-x^{2} + 1\right) - \log\left(x + \sqrt{2}\right) \log\left(-\frac{x + \sqrt{2}}{\sqrt{2} + 1} + 1\right) + \log\left(x - \sqrt{2}\right) \log\left(\frac{x - \sqrt{2}}{\sqrt{2} + 1} + 1\right) - \log\left(x + \sqrt{2}\right) \log\left(-\frac{x + \sqrt{2}}{\sqrt{2} - 1} + 1\right) + \log\left(x - \sqrt{2}\right) \log\left(\frac{x - \sqrt{2}}{\sqrt{2} - 1} + 1\right) - {\rm Li}_2\left(\frac{x + \sqrt{2}}{\sqrt{2} + 1}\right) + {\rm Li}_2\left(-\frac{x - \sqrt{2}}{\sqrt{2} + 1}\right) - {\rm Li}_2\left(\frac{x + \sqrt{2}}{\sqrt{2} - 1}\right) + {\rm Li}_2\left(-\frac{x - \sqrt{2}}{\sqrt{2} - 1}\right)\right)}"," ",0,"1/4*sqrt(2)*((log(2*x + 2*sqrt(2)) - log(2*x - 2*sqrt(2)))*log(-x^2 + 1) - log(x + sqrt(2))*log(-(x + sqrt(2))/(sqrt(2) + 1) + 1) + log(x - sqrt(2))*log((x - sqrt(2))/(sqrt(2) + 1) + 1) - log(x + sqrt(2))*log(-(x + sqrt(2))/(sqrt(2) - 1) + 1) + log(x - sqrt(2))*log((x - sqrt(2))/(sqrt(2) - 1) + 1) - dilog((x + sqrt(2))/(sqrt(2) + 1)) + dilog(-(x - sqrt(2))/(sqrt(2) + 1)) - dilog((x + sqrt(2))/(sqrt(2) - 1)) + dilog(-(x - sqrt(2))/(sqrt(2) - 1)))","A",0
359,0,0,0,0.000000," ","integrate(log(e*x^2+d)/(-x^2+1),x, algorithm=""maxima"")","-\int \frac{\log\left(e x^{2} + d\right)}{x^{2} - 1}\,{d x}"," ",0,"-integrate(log(e*x^2 + d)/(x^2 - 1), x)","F",0
360,0,0,0,0.000000," ","integrate((f+g*x^(3*n))*log(c*(d+e*x^n)^p)/x,x, algorithm=""maxima"")","-\frac{9 \, e^{3} f n^{2} p \log\left(x\right)^{2} - 3 \, d e^{2} g p x^{2 \, n} + 6 \, d^{2} e g p x^{n} + 2 \, {\left(e^{3} g p - 3 \, e^{3} g \log\left(c\right)\right)} x^{3 \, n} - 6 \, {\left(3 \, e^{3} f n \log\left(x\right) + e^{3} g x^{3 \, n}\right)} \log\left({\left(e x^{n} + d\right)}^{p}\right) - 6 \, {\left(d^{3} g n p + 3 \, e^{3} f n \log\left(c\right)\right)} \log\left(x\right)}{18 \, e^{3} n} + \int \frac{3 \, d e^{3} f n p \log\left(x\right) - d^{4} g p}{3 \, {\left(e^{4} x x^{n} + d e^{3} x\right)}}\,{d x}"," ",0,"-1/18*(9*e^3*f*n^2*p*log(x)^2 - 3*d*e^2*g*p*x^(2*n) + 6*d^2*e*g*p*x^n + 2*(e^3*g*p - 3*e^3*g*log(c))*x^(3*n) - 6*(3*e^3*f*n*log(x) + e^3*g*x^(3*n))*log((e*x^n + d)^p) - 6*(d^3*g*n*p + 3*e^3*f*n*log(c))*log(x))/(e^3*n) + integrate(1/3*(3*d*e^3*f*n*p*log(x) - d^4*g*p)/(e^4*x*x^n + d*e^3*x), x)","F",0
361,0,0,0,0.000000," ","integrate((f+g*x^(2*n))*log(c*(d+e*x^n)^p)/x,x, algorithm=""maxima"")","-\frac{2 \, e^{2} f n^{2} p \log\left(x\right)^{2} - 2 \, d e g p x^{n} + {\left(e^{2} g p - 2 \, e^{2} g \log\left(c\right)\right)} x^{2 \, n} - 2 \, {\left(2 \, e^{2} f n \log\left(x\right) + e^{2} g x^{2 \, n}\right)} \log\left({\left(e x^{n} + d\right)}^{p}\right) + 2 \, {\left(d^{2} g n p - 2 \, e^{2} f n \log\left(c\right)\right)} \log\left(x\right)}{4 \, e^{2} n} + \int \frac{2 \, d e^{2} f n p \log\left(x\right) + d^{3} g p}{2 \, {\left(e^{3} x x^{n} + d e^{2} x\right)}}\,{d x}"," ",0,"-1/4*(2*e^2*f*n^2*p*log(x)^2 - 2*d*e*g*p*x^n + (e^2*g*p - 2*e^2*g*log(c))*x^(2*n) - 2*(2*e^2*f*n*log(x) + e^2*g*x^(2*n))*log((e*x^n + d)^p) + 2*(d^2*g*n*p - 2*e^2*f*n*log(c))*log(x))/(e^2*n) + integrate(1/2*(2*d*e^2*f*n*p*log(x) + d^3*g*p)/(e^3*x*x^n + d*e^2*x), x)","F",0
362,0,0,0,0.000000," ","integrate((f+g*x^n)*log(c*(d+e*x^n)^p)/x,x, algorithm=""maxima"")","-\frac{e f n^{2} p \log\left(x\right)^{2} + 2 \, {\left(e g p - e g \log\left(c\right)\right)} x^{n} - 2 \, {\left(e f n \log\left(x\right) + e g x^{n}\right)} \log\left({\left(e x^{n} + d\right)}^{p}\right) - 2 \, {\left(d g n p + e f n \log\left(c\right)\right)} \log\left(x\right)}{2 \, e n} + \int \frac{d e f n p \log\left(x\right) - d^{2} g p}{e^{2} x x^{n} + d e x}\,{d x}"," ",0,"-1/2*(e*f*n^2*p*log(x)^2 + 2*(e*g*p - e*g*log(c))*x^n - 2*(e*f*n*log(x) + e*g*x^n)*log((e*x^n + d)^p) - 2*(d*g*n*p + e*f*n*log(c))*log(x))/(e*n) + integrate((d*e*f*n*p*log(x) - d^2*g*p)/(e^2*x*x^n + d*e*x), x)","F",0
363,0,0,0,0.000000," ","integrate((f+g/(x^n))*log(c*(d+e*x^n)^p)/x,x, algorithm=""maxima"")","-\frac{{\left(f n^{2} p \log\left(x\right)^{2} - 2 \, f n \log\left(c\right) \log\left(x\right)\right)} x^{n} - 2 \, {\left(f n x^{n} \log\left(x\right) - g\right)} \log\left({\left(e x^{n} + d\right)}^{p}\right) + 2 \, g \log\left(c\right)}{2 \, n x^{n}} + \int \frac{d f n p \log\left(x\right) + e g p}{e x x^{n} + d x}\,{d x}"," ",0,"-1/2*((f*n^2*p*log(x)^2 - 2*f*n*log(c)*log(x))*x^n - 2*(f*n*x^n*log(x) - g)*log((e*x^n + d)^p) + 2*g*log(c))/(n*x^n) + integrate((d*f*n*p*log(x) + e*g*p)/(e*x*x^n + d*x), x)","F",0
364,0,0,0,0.000000," ","integrate((f+g/(x^(2*n)))*log(c*(d+e*x^n)^p)/x,x, algorithm=""maxima"")","-\frac{e g p x^{n} + d g \log\left(c\right) + {\left(d f n^{2} p \log\left(x\right)^{2} - 2 \, d f n \log\left(c\right) \log\left(x\right)\right)} x^{2 \, n} - {\left(2 \, d f n x^{2 \, n} \log\left(x\right) - d g\right)} \log\left({\left(e x^{n} + d\right)}^{p}\right)}{2 \, d n x^{2 \, n}} + \int \frac{2 \, d^{2} f n p \log\left(x\right) - e^{2} g p}{2 \, {\left(d e x x^{n} + d^{2} x\right)}}\,{d x}"," ",0,"-1/2*(e*g*p*x^n + d*g*log(c) + (d*f*n^2*p*log(x)^2 - 2*d*f*n*log(c)*log(x))*x^(2*n) - (2*d*f*n*x^(2*n)*log(x) - d*g)*log((e*x^n + d)^p))/(d*n*x^(2*n)) + integrate(1/2*(2*d^2*f*n*p*log(x) - e^2*g*p)/(d*e*x*x^n + d^2*x), x)","F",0
365,0,0,0,0.000000," ","integrate((f+g*x^(3*n))^2*log(c*(d+e*x^n)^p)/x,x, algorithm=""maxima"")","-\frac{180 \, e^{6} f^{2} n^{2} p \log\left(x\right)^{2} - 12 \, d e^{5} g^{2} p x^{5 \, n} + 15 \, d^{2} e^{4} g^{2} p x^{4 \, n} + 10 \, {\left(e^{6} g^{2} p - 6 \, e^{6} g^{2} \log\left(c\right)\right)} x^{6 \, n} + 20 \, {\left(4 \, e^{6} f g p - d^{3} e^{3} g^{2} p - 12 \, e^{6} f g \log\left(c\right)\right)} x^{3 \, n} - 30 \, {\left(4 \, d e^{5} f g p - d^{4} e^{2} g^{2} p\right)} x^{2 \, n} + 60 \, {\left(4 \, d^{2} e^{4} f g p - d^{5} e g^{2} p\right)} x^{n} - 60 \, {\left(6 \, e^{6} f^{2} n \log\left(x\right) + e^{6} g^{2} x^{6 \, n} + 4 \, e^{6} f g x^{3 \, n}\right)} \log\left({\left(e x^{n} + d\right)}^{p}\right) - 60 \, {\left(4 \, d^{3} e^{3} f g n p - d^{6} g^{2} n p + 6 \, e^{6} f^{2} n \log\left(c\right)\right)} \log\left(x\right)}{360 \, e^{6} n} + \int \frac{6 \, d e^{6} f^{2} n p \log\left(x\right) - 4 \, d^{4} e^{3} f g p + d^{7} g^{2} p}{6 \, {\left(e^{7} x x^{n} + d e^{6} x\right)}}\,{d x}"," ",0,"-1/360*(180*e^6*f^2*n^2*p*log(x)^2 - 12*d*e^5*g^2*p*x^(5*n) + 15*d^2*e^4*g^2*p*x^(4*n) + 10*(e^6*g^2*p - 6*e^6*g^2*log(c))*x^(6*n) + 20*(4*e^6*f*g*p - d^3*e^3*g^2*p - 12*e^6*f*g*log(c))*x^(3*n) - 30*(4*d*e^5*f*g*p - d^4*e^2*g^2*p)*x^(2*n) + 60*(4*d^2*e^4*f*g*p - d^5*e*g^2*p)*x^n - 60*(6*e^6*f^2*n*log(x) + e^6*g^2*x^(6*n) + 4*e^6*f*g*x^(3*n))*log((e*x^n + d)^p) - 60*(4*d^3*e^3*f*g*n*p - d^6*g^2*n*p + 6*e^6*f^2*n*log(c))*log(x))/(e^6*n) + integrate(1/6*(6*d*e^6*f^2*n*p*log(x) - 4*d^4*e^3*f*g*p + d^7*g^2*p)/(e^7*x*x^n + d*e^6*x), x)","F",0
366,0,0,0,0.000000," ","integrate((f+g*x^(2*n))^2*log(c*(d+e*x^n)^p)/x,x, algorithm=""maxima"")","-\frac{24 \, e^{4} f^{2} n^{2} p \log\left(x\right)^{2} - 4 \, d e^{3} g^{2} p x^{3 \, n} + 3 \, {\left(e^{4} g^{2} p - 4 \, e^{4} g^{2} \log\left(c\right)\right)} x^{4 \, n} + 6 \, {\left(4 \, e^{4} f g p + d^{2} e^{2} g^{2} p - 8 \, e^{4} f g \log\left(c\right)\right)} x^{2 \, n} - 12 \, {\left(4 \, d e^{3} f g p + d^{3} e g^{2} p\right)} x^{n} - 12 \, {\left(4 \, e^{4} f^{2} n \log\left(x\right) + e^{4} g^{2} x^{4 \, n} + 4 \, e^{4} f g x^{2 \, n}\right)} \log\left({\left(e x^{n} + d\right)}^{p}\right) + 12 \, {\left(4 \, d^{2} e^{2} f g n p + d^{4} g^{2} n p - 4 \, e^{4} f^{2} n \log\left(c\right)\right)} \log\left(x\right)}{48 \, e^{4} n} + \int \frac{4 \, d e^{4} f^{2} n p \log\left(x\right) + 4 \, d^{3} e^{2} f g p + d^{5} g^{2} p}{4 \, {\left(e^{5} x x^{n} + d e^{4} x\right)}}\,{d x}"," ",0,"-1/48*(24*e^4*f^2*n^2*p*log(x)^2 - 4*d*e^3*g^2*p*x^(3*n) + 3*(e^4*g^2*p - 4*e^4*g^2*log(c))*x^(4*n) + 6*(4*e^4*f*g*p + d^2*e^2*g^2*p - 8*e^4*f*g*log(c))*x^(2*n) - 12*(4*d*e^3*f*g*p + d^3*e*g^2*p)*x^n - 12*(4*e^4*f^2*n*log(x) + e^4*g^2*x^(4*n) + 4*e^4*f*g*x^(2*n))*log((e*x^n + d)^p) + 12*(4*d^2*e^2*f*g*n*p + d^4*g^2*n*p - 4*e^4*f^2*n*log(c))*log(x))/(e^4*n) + integrate(1/4*(4*d*e^4*f^2*n*p*log(x) + 4*d^3*e^2*f*g*p + d^5*g^2*p)/(e^5*x*x^n + d*e^4*x), x)","F",0
367,0,0,0,0.000000," ","integrate((f+g*x^n)^2*log(c*(d+e*x^n)^p)/x,x, algorithm=""maxima"")","-\frac{2 \, e^{2} f^{2} n^{2} p \log\left(x\right)^{2} + {\left(e^{2} g^{2} p - 2 \, e^{2} g^{2} \log\left(c\right)\right)} x^{2 \, n} + 2 \, {\left(4 \, e^{2} f g p - d e g^{2} p - 4 \, e^{2} f g \log\left(c\right)\right)} x^{n} - 2 \, {\left(2 \, e^{2} f^{2} n \log\left(x\right) + e^{2} g^{2} x^{2 \, n} + 4 \, e^{2} f g x^{n}\right)} \log\left({\left(e x^{n} + d\right)}^{p}\right) - 2 \, {\left(4 \, d e f g n p - d^{2} g^{2} n p + 2 \, e^{2} f^{2} n \log\left(c\right)\right)} \log\left(x\right)}{4 \, e^{2} n} + \int \frac{2 \, d e^{2} f^{2} n p \log\left(x\right) - 4 \, d^{2} e f g p + d^{3} g^{2} p}{2 \, {\left(e^{3} x x^{n} + d e^{2} x\right)}}\,{d x}"," ",0,"-1/4*(2*e^2*f^2*n^2*p*log(x)^2 + (e^2*g^2*p - 2*e^2*g^2*log(c))*x^(2*n) + 2*(4*e^2*f*g*p - d*e*g^2*p - 4*e^2*f*g*log(c))*x^n - 2*(2*e^2*f^2*n*log(x) + e^2*g^2*x^(2*n) + 4*e^2*f*g*x^n)*log((e*x^n + d)^p) - 2*(4*d*e*f*g*n*p - d^2*g^2*n*p + 2*e^2*f^2*n*log(c))*log(x))/(e^2*n) + integrate(1/2*(2*d*e^2*f^2*n*p*log(x) - 4*d^2*e*f*g*p + d^3*g^2*p)/(e^3*x*x^n + d*e^2*x), x)","F",0
368,0,0,0,0.000000," ","integrate((f+g/(x^n))^2*log(c*(d+e*x^n)^p)/x,x, algorithm=""maxima"")","-\frac{d g^{2} \log\left(c\right) + {\left(d f^{2} n^{2} p \log\left(x\right)^{2} - 2 \, d f^{2} n \log\left(c\right) \log\left(x\right)\right)} x^{2 \, n} + {\left(e g^{2} p + 4 \, d f g \log\left(c\right)\right)} x^{n} - {\left(2 \, d f^{2} n x^{2 \, n} \log\left(x\right) - 4 \, d f g x^{n} - d g^{2}\right)} \log\left({\left(e x^{n} + d\right)}^{p}\right)}{2 \, d n x^{2 \, n}} + \int \frac{2 \, d^{2} f^{2} n p \log\left(x\right) + 4 \, d e f g p - e^{2} g^{2} p}{2 \, {\left(d e x x^{n} + d^{2} x\right)}}\,{d x}"," ",0,"-1/2*(d*g^2*log(c) + (d*f^2*n^2*p*log(x)^2 - 2*d*f^2*n*log(c)*log(x))*x^(2*n) + (e*g^2*p + 4*d*f*g*log(c))*x^n - (2*d*f^2*n*x^(2*n)*log(x) - 4*d*f*g*x^n - d*g^2)*log((e*x^n + d)^p))/(d*n*x^(2*n)) + integrate(1/2*(2*d^2*f^2*n*p*log(x) + 4*d*e*f*g*p - e^2*g^2*p)/(d*e*x*x^n + d^2*x), x)","F",0
369,0,0,0,0.000000," ","integrate((f+g/(x^(2*n)))^2*log(c*(d+e*x^n)^p)/x,x, algorithm=""maxima"")","-\frac{2 \, d^{2} e g^{2} p x^{n} + 6 \, d^{3} g^{2} \log\left(c\right) + 12 \, {\left(d^{3} f^{2} n^{2} p \log\left(x\right)^{2} - 2 \, d^{3} f^{2} n \log\left(c\right) \log\left(x\right)\right)} x^{4 \, n} + 6 \, {\left(4 \, d^{2} e f g p + e^{3} g^{2} p\right)} x^{3 \, n} - 3 \, {\left(d e^{2} g^{2} p - 8 \, d^{3} f g \log\left(c\right)\right)} x^{2 \, n} - 6 \, {\left(4 \, d^{3} f^{2} n x^{4 \, n} \log\left(x\right) - 4 \, d^{3} f g x^{2 \, n} - d^{3} g^{2}\right)} \log\left({\left(e x^{n} + d\right)}^{p}\right)}{24 \, d^{3} n x^{4 \, n}} + \int \frac{4 \, d^{4} f^{2} n p \log\left(x\right) - 4 \, d^{2} e^{2} f g p - e^{4} g^{2} p}{4 \, {\left(d^{3} e x x^{n} + d^{4} x\right)}}\,{d x}"," ",0,"-1/24*(2*d^2*e*g^2*p*x^n + 6*d^3*g^2*log(c) + 12*(d^3*f^2*n^2*p*log(x)^2 - 2*d^3*f^2*n*log(c)*log(x))*x^(4*n) + 6*(4*d^2*e*f*g*p + e^3*g^2*p)*x^(3*n) - 3*(d*e^2*g^2*p - 8*d^3*f*g*log(c))*x^(2*n) - 6*(4*d^3*f^2*n*x^(4*n)*log(x) - 4*d^3*f*g*x^(2*n) - d^3*g^2)*log((e*x^n + d)^p))/(d^3*n*x^(4*n)) + integrate(1/4*(4*d^4*f^2*n*p*log(x) - 4*d^2*e^2*f*g*p - e^4*g^2*p)/(d^3*e*x*x^n + d^4*x), x)","F",0
370,0,0,0,0.000000," ","integrate(log(c*(d+e*x^n)^p)/x/(f+g*x^(2*n)),x, algorithm=""maxima"")","\int \frac{\log\left({\left(e x^{n} + d\right)}^{p} c\right)}{{\left(g x^{2 \, n} + f\right)} x}\,{d x}"," ",0,"integrate(log((e*x^n + d)^p*c)/((g*x^(2*n) + f)*x), x)","F",0
371,1,154,0,0.891341," ","integrate(log(c*(d+e*x^n)^p)/x/(f+g*x^n),x, algorithm=""maxima"")","-e n p {\left(\frac{\log\left(x^{n}\right) \log\left(\frac{e x^{n}}{d} + 1\right) + {\rm Li}_2\left(-\frac{e x^{n}}{d}\right)}{e f n^{2}} - \frac{\log\left(g x^{n} + f\right) \log\left(-\frac{e g x^{n} + e f}{e f - d g} + 1\right) + {\rm Li}_2\left(\frac{e g x^{n} + e f}{e f - d g}\right)}{e f n^{2}}\right)} - {\left(\frac{\log\left(g x^{n} + f\right)}{f n} - \frac{\log\left(x^{n}\right)}{f n}\right)} \log\left({\left(e x^{n} + d\right)}^{p} c\right)"," ",0,"-e*n*p*((log(x^n)*log(e*x^n/d + 1) + dilog(-e*x^n/d))/(e*f*n^2) - (log(g*x^n + f)*log(-(e*g*x^n + e*f)/(e*f - d*g) + 1) + dilog((e*g*x^n + e*f)/(e*f - d*g)))/(e*f*n^2)) - (log(g*x^n + f)/(f*n) - log(x^n)/(f*n))*log((e*x^n + d)^p*c)","A",0
372,1,112,0,0.862551," ","integrate(log(c*(d+e*x^n)^p)/x/(f+g/(x^n)),x, algorithm=""maxima"")","{\left(\frac{\log\left(f + \frac{g}{x^{n}}\right)}{f n} - \frac{\log\left(\frac{1}{x^{n}}\right)}{f n}\right)} \log\left({\left(e x^{n} + d\right)}^{p} c\right) - \frac{{\left(\log\left(f x^{n} + g\right) \log\left(\frac{e f x^{n} + e g}{d f - e g} + 1\right) + {\rm Li}_2\left(-\frac{e f x^{n} + e g}{d f - e g}\right)\right)} p}{f n}"," ",0,"(log(f + g/x^n)/(f*n) - log(1/(x^n))/(f*n))*log((e*x^n + d)^p*c) - (log(f*x^n + g)*log((e*f*x^n + e*g)/(d*f - e*g) + 1) + dilog(-(e*f*x^n + e*g)/(d*f - e*g)))*p/(f*n)","A",0
373,0,0,0,0.000000," ","integrate(log(c*(d+e*x^n)^p)/x/(f+g/(x^(2*n))),x, algorithm=""maxima"")","\int \frac{\log\left({\left(e x^{n} + d\right)}^{p} c\right)}{{\left(f + \frac{g}{x^{2 \, n}}\right)} x}\,{d x}"," ",0,"integrate(log((e*x^n + d)^p*c)/((f + g/x^(2*n))*x), x)","F",0
374,0,0,0,0.000000," ","integrate(log(c*(d+e*x^n)^p)/x/(f+g*x^(2*n))^2,x, algorithm=""maxima"")","\int \frac{\log\left({\left(e x^{n} + d\right)}^{p} c\right)}{{\left(g x^{2 \, n} + f\right)}^{2} x}\,{d x}"," ",0,"integrate(log((e*x^n + d)^p*c)/((g*x^(2*n) + f)^2*x), x)","F",0
375,1,233,0,0.897307," ","integrate(log(c*(d+e*x^n)^p)/x/(f+g*x^n)^2,x, algorithm=""maxima"")","-e n p {\left(\frac{\log\left(\frac{e x^{n} + d}{e}\right)}{e f^{2} n^{2} - d f g n^{2}} - \frac{\log\left(\frac{g x^{n} + f}{g}\right)}{e f^{2} n^{2} - d f g n^{2}} + \frac{\log\left(x^{n}\right) \log\left(\frac{e x^{n}}{d} + 1\right) + {\rm Li}_2\left(-\frac{e x^{n}}{d}\right)}{e f^{2} n^{2}} - \frac{\log\left(g x^{n} + f\right) \log\left(-\frac{e g x^{n} + e f}{e f - d g} + 1\right) + {\rm Li}_2\left(\frac{e g x^{n} + e f}{e f - d g}\right)}{e f^{2} n^{2}}\right)} + {\left(\frac{1}{f g n x^{n} + f^{2} n} - \frac{\log\left(g x^{n} + f\right)}{f^{2} n} + \frac{\log\left(x^{n}\right)}{f^{2} n}\right)} \log\left({\left(e x^{n} + d\right)}^{p} c\right)"," ",0,"-e*n*p*(log((e*x^n + d)/e)/(e*f^2*n^2 - d*f*g*n^2) - log((g*x^n + f)/g)/(e*f^2*n^2 - d*f*g*n^2) + (log(x^n)*log(e*x^n/d + 1) + dilog(-e*x^n/d))/(e*f^2*n^2) - (log(g*x^n + f)*log(-(e*g*x^n + e*f)/(e*f - d*g) + 1) + dilog((e*g*x^n + e*f)/(e*f - d*g)))/(e*f^2*n^2)) + (1/(f*g*n*x^n + f^2*n) - log(g*x^n + f)/(f^2*n) + log(x^n)/(f^2*n))*log((e*x^n + d)^p*c)","A",0
376,1,209,0,0.882678," ","integrate(log(c*(d+e*x^n)^p)/x/(f+g/(x^n))^2,x, algorithm=""maxima"")","e n p {\left(\frac{d \log\left(\frac{e x^{n} + d}{e}\right)}{d e f^{2} n^{2} - e^{2} f g n^{2}} - \frac{g \log\left(\frac{f x^{n} + g}{f}\right)}{d f^{3} n^{2} - e f^{2} g n^{2}} - \frac{\log\left(f x^{n} + g\right) \log\left(\frac{e f x^{n} + e g}{d f - e g} + 1\right) + {\rm Li}_2\left(-\frac{e f x^{n} + e g}{d f - e g}\right)}{e f^{2} n^{2}}\right)} - {\left(\frac{1}{f^{2} n + \frac{f g n}{x^{n}}} - \frac{\log\left(f + \frac{g}{x^{n}}\right)}{f^{2} n} + \frac{\log\left(\frac{1}{x^{n}}\right)}{f^{2} n}\right)} \log\left({\left(e x^{n} + d\right)}^{p} c\right)"," ",0,"e*n*p*(d*log((e*x^n + d)/e)/(d*e*f^2*n^2 - e^2*f*g*n^2) - g*log((f*x^n + g)/f)/(d*f^3*n^2 - e*f^2*g*n^2) - (log(f*x^n + g)*log((e*f*x^n + e*g)/(d*f - e*g) + 1) + dilog(-(e*f*x^n + e*g)/(d*f - e*g)))/(e*f^2*n^2)) - (1/(f^2*n + f*g*n/x^n) - log(f + g/x^n)/(f^2*n) + log(1/(x^n))/(f^2*n))*log((e*x^n + d)^p*c)","A",0
377,0,0,0,0.000000," ","integrate(log(c*(d+e*x^n)^p)/x/(f+g/(x^(2*n)))^2,x, algorithm=""maxima"")","\int \frac{\log\left({\left(e x^{n} + d\right)}^{p} c\right)}{{\left(f + \frac{g}{x^{2 \, n}}\right)}^{2} x}\,{d x}"," ",0,"integrate(log((e*x^n + d)^p*c)/((f + g/x^(2*n))^2*x), x)","F",0
378,1,106,0,0.878766," ","integrate(log(c*(d+e*x^n))/x/(c*e+(c*d-1)/(x^n)),x, algorithm=""maxima"")","{\left(\frac{\log\left(c e + \frac{c d - 1}{x^{n}}\right)}{c e n} - \frac{\log\left(\frac{1}{x^{n}}\right)}{c e n}\right)} \log\left({\left(e x^{n} + d\right)} c\right) - \frac{\log\left(c e x^{n} + c d\right) \log\left(c e x^{n} + c d - 1\right) + {\rm Li}_2\left(-c e x^{n} - c d + 1\right)}{c e n}"," ",0,"(log(c*e + (c*d - 1)/x^n)/(c*e*n) - log(1/(x^n))/(c*e*n))*log((e*x^n + d)*c) - (log(c*e*x^n + c*d)*log(c*e*x^n + c*d - 1) + dilog(-c*e*x^n - c*d + 1))/(c*e*n)","B",0
379,1,109,0,0.516917," ","integrate(x^(-1+n)*log(c*(d+e*x^n))/(-1+c*d+c*e*x^n),x, algorithm=""maxima"")","\frac{\log\left(c e x^{n} + c d - 1\right) \log\left({\left(e x^{n} + d\right)} c\right)}{c e n} - \frac{\log\left(c e x^{n} + c d - 1\right) \log\left(e x^{n} + d\right)}{c e n} + \frac{\log\left(-c e x^{n} - c d + 1\right) \log\left(e x^{n} + d\right) + {\rm Li}_2\left(c e x^{n} + c d\right)}{c e n}"," ",0,"log(c*e*x^n + c*d - 1)*log((e*x^n + d)*c)/(c*e*n) - log(c*e*x^n + c*d - 1)*log(e*x^n + d)/(c*e*n) + (log(-c*e*x^n - c*d + 1)*log(e*x^n + d) + dilog(c*e*x^n + c*d))/(c*e*n)","B",0
380,0,0,0,0.000000," ","integrate(log(c*(d+e/(x^n)))/x/(c*e-(-c*d+1)*x^n),x, algorithm=""maxima"")","n \int \frac{\log\left(x\right)}{c d x x^{n} + c e x}\,{d x} + \frac{\log\left(d x^{n} + e\right) \log\left(x\right) + \log\left(c\right) \log\left(x\right) - \log\left(x\right) \log\left(x^{n}\right)}{c e} - \frac{\log\left(c\right) \log\left(\frac{c e + {\left(c d - 1\right)} x^{n}}{c d - 1}\right)}{c e n} - \frac{\log\left(d x^{n} + e\right) \log\left(\frac{c d e + {\left(c d^{2} - d\right)} x^{n} - e}{e} + 1\right) + {\rm Li}_2\left(-\frac{c d e + {\left(c d^{2} - d\right)} x^{n} - e}{e}\right)}{c e n} + \frac{\log\left(x^{n}\right) \log\left(\frac{{\left(c d - 1\right)} x^{n}}{c e} + 1\right) + {\rm Li}_2\left(-\frac{{\left(c d - 1\right)} x^{n}}{c e}\right)}{c e n}"," ",0,"n*integrate(log(x)/(c*d*x*x^n + c*e*x), x) + (log(d*x^n + e)*log(x) + log(c)*log(x) - log(x)*log(x^n))/(c*e) - log(c)*log((c*e + (c*d - 1)*x^n)/(c*d - 1))/(c*e*n) - (log(d*x^n + e)*log((c*d*e + (c*d^2 - d)*x^n - e)/e + 1) + dilog(-(c*d*e + (c*d^2 - d)*x^n - e)/e))/(c*e*n) + (log(x^n)*log((c*d - 1)*x^n/(c*e) + 1) + dilog(-(c*d - 1)*x^n/(c*e)))/(c*e*n)","F",0
381,-2,0,0,0.000000," ","integrate((f+g*x^(2*n))^2*log(c*(d+e*x^n)^p)^q/x,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: In function CAR, the value of the first argument is  0which is not of the expected type LIST","F(-2)",0
382,-2,0,0,0.000000," ","integrate((f+g*x^n)^2*log(c*(d+e*x^n)^p)^q/x,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: In function CAR, the value of the first argument is  0which is not of the expected type LIST","F(-2)",0
383,-2,0,0,0.000000," ","integrate((f+g/(x^n))^2*log(c*(d+e*x^n)^p)^q/x,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: In function CAR, the value of the first argument is  0which is not of the expected type LIST","F(-2)",0
384,-2,0,0,0.000000," ","integrate((f+g/(x^(2*n)))^2*log(c*(d+e*x^n)^p)^q/x,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: In function CAR, the value of the first argument is  0which is not of the expected type LIST","F(-2)",0
385,-2,0,0,0.000000," ","integrate(log(c*(d+e*x^n)^p)^q/x/(f+g*x^(2*n)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: In function CAR, the value of the first argument is  0which is not of the expected type LIST","F(-2)",0
386,-2,0,0,0.000000," ","integrate(log(c*(d+e*x^n)^p)^q/x/(f+g*x^n),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: In function CAR, the value of the first argument is  0which is not of the expected type LIST","F(-2)",0
387,-2,0,0,0.000000," ","integrate(log(c*(d+e*x^n)^p)^q/x/(f+g/(x^n)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: In function CAR, the value of the first argument is  0which is not of the expected type LIST","F(-2)",0
388,-2,0,0,0.000000," ","integrate(log(c*(d+e*x^n)^p)^q/x/(f+g/(x^(2*n))),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: In function CAR, the value of the first argument is  0which is not of the expected type LIST","F(-2)",0
389,0,0,0,0.000000," ","integrate(log(x)*log(d+e*x^m)/x,x, algorithm=""maxima"")","-\frac{1}{6} \, m \log\left(x\right)^{3} + d m \int \frac{\log\left(x\right)^{2}}{2 \, {\left(e x x^{m} + d x\right)}}\,{d x} + \frac{1}{2} \, \log\left(e x^{m} + d\right) \log\left(x\right)^{2}"," ",0,"-1/6*m*log(x)^3 + d*m*integrate(1/2*log(x)^2/(e*x*x^m + d*x), x) + 1/2*log(e*x^m + d)*log(x)^2","F",0
390,1,59,0,0.460751," ","integrate(log((a+x)/x)/x,x, algorithm=""maxima"")","-{\left(\log\left(a + x\right) - \log\left(x\right)\right)} \log\left(x\right) + \log\left(a + x\right) \log\left(x\right) - \frac{1}{2} \, \log\left(x\right)^{2} + \log\left(x\right) \log\left(\frac{a + x}{x}\right) - \log\left(x\right) \log\left(\frac{x}{a} + 1\right) - {\rm Li}_2\left(-\frac{x}{a}\right)"," ",0,"-(log(a + x) - log(x))*log(x) + log(a + x)*log(x) - 1/2*log(x)^2 + log(x)*log((a + x)/x) - log(x)*log(x/a + 1) - dilog(-x/a)","B",0
391,1,69,0,0.473139," ","integrate(log((x^2+a)/x^2)/x,x, algorithm=""maxima"")","-{\left(\log\left(x^{2} + a\right) - 2 \, \log\left(x\right)\right)} \log\left(x\right) + \log\left(x^{2} + a\right) \log\left(x\right) - \log\left(x\right)^{2} - \log\left(x\right) \log\left(\frac{x^{2}}{a} + 1\right) + \log\left(x\right) \log\left(\frac{x^{2} + a}{x^{2}}\right) - \frac{1}{2} \, {\rm Li}_2\left(-\frac{x^{2}}{a}\right)"," ",0,"-(log(x^2 + a) - 2*log(x))*log(x) + log(x^2 + a)*log(x) - log(x)^2 - log(x)*log(x^2/a + 1) + log(x)*log((x^2 + a)/x^2) - 1/2*dilog(-x^2/a)","B",0
392,0,0,0,0.000000," ","integrate(log((a+x^n)/(x^n))/x,x, algorithm=""maxima"")","a n \int \frac{\log\left(x\right)}{a x + x x^{n}}\,{d x} + \log\left(a + x^{n}\right) \log\left(x\right) - \log\left(x\right) \log\left(x^{n}\right)"," ",0,"a*n*integrate(log(x)/(a*x + x*x^n), x) + log(a + x^n)*log(x) - log(x)*log(x^n)","F",0
393,1,67,0,0.484096," ","integrate(log((b*x+a)/x)/x,x, algorithm=""maxima"")","-{\left(\log\left(b x + a\right) - \log\left(x\right)\right)} \log\left(x\right) + \log\left(b x + a\right) \log\left(x\right) - \log\left(\frac{b x}{a} + 1\right) \log\left(x\right) - \frac{1}{2} \, \log\left(x\right)^{2} + \log\left(x\right) \log\left(\frac{b x + a}{x}\right) - {\rm Li}_2\left(-\frac{b x}{a}\right)"," ",0,"-(log(b*x + a) - log(x))*log(x) + log(b*x + a)*log(x) - log(b*x/a + 1)*log(x) - 1/2*log(x)^2 + log(x)*log((b*x + a)/x) - dilog(-b*x/a)","A",0
394,1,77,0,0.474762," ","integrate(log((b*x^2+a)/x^2)/x,x, algorithm=""maxima"")","-{\left(\log\left(b x^{2} + a\right) - 2 \, \log\left(x\right)\right)} \log\left(x\right) + \log\left(b x^{2} + a\right) \log\left(x\right) - \log\left(\frac{b x^{2}}{a} + 1\right) \log\left(x\right) - \log\left(x\right)^{2} + \log\left(x\right) \log\left(\frac{b x^{2} + a}{x^{2}}\right) - \frac{1}{2} \, {\rm Li}_2\left(-\frac{b x^{2}}{a}\right)"," ",0,"-(log(b*x^2 + a) - 2*log(x))*log(x) + log(b*x^2 + a)*log(x) - log(b*x^2/a + 1)*log(x) - log(x)^2 + log(x)*log((b*x^2 + a)/x^2) - 1/2*dilog(-b*x^2/a)","B",0
395,0,0,0,0.000000," ","integrate(log((a+b*x^n)/(x^n))/x,x, algorithm=""maxima"")","a n \int \frac{\log\left(x\right)}{b x x^{n} + a x}\,{d x} + \log\left(b x^{n} + a\right) \log\left(x\right) - \log\left(x\right) \log\left(x^{n}\right)"," ",0,"a*n*integrate(log(x)/(b*x*x^n + a*x), x) + log(b*x^n + a)*log(x) - log(x)*log(x^n)","F",0
396,1,124,0,0.494828," ","integrate(log((b*x+a)/x)/(d*x+c),x, algorithm=""maxima"")","-\frac{{\left(\log\left(b x + a\right) - \log\left(x\right)\right)} \log\left(d x + c\right)}{d} + \frac{\log\left(d x + c\right) \log\left(\frac{b x + a}{x}\right)}{d} - \frac{\log\left(\frac{d x}{c} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{d x}{c}\right)}{d} + \frac{\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)}{d}"," ",0,"-(log(b*x + a) - log(x))*log(d*x + c)/d + log(d*x + c)*log((b*x + a)/x)/d - (log(d*x/c + 1)*log(x) + dilog(-d*x/c))/d + (log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))/d","A",0
397,0,0,0,0.000000," ","integrate(log((b*x^2+a)/x^2)/(d*x+c),x, algorithm=""maxima"")","\int \frac{\log\left(\frac{b x^{2} + a}{x^{2}}\right)}{d x + c}\,{d x}"," ",0,"integrate(log((b*x^2 + a)/x^2)/(d*x + c), x)","F",0
398,0,0,0,0.000000," ","integrate(log((a+b*x^n)/(x^n))/(d*x+c),x, algorithm=""maxima"")","\int \frac{\log\left(\frac{b x^{n} + a}{x^{n}}\right)}{d x + c}\,{d x}"," ",0,"integrate(log((b*x^n + a)/x^n)/(d*x + c), x)","F",0
399,0,0,0,0.000000," ","integrate((f*x)^q*(a+b*log(c*(d+e*x^m)^n)),x, algorithm=""maxima"")","{\left(d^{2} f^{q} m^{2} n \int \frac{x^{q}}{{\left(m {\left(q + 1\right)} - q^{2} - 2 \, q - 1\right)} e^{2} x^{2 \, m} + 2 \, {\left(m {\left(q + 1\right)} - q^{2} - 2 \, q - 1\right)} d e x^{m} + {\left(m {\left(q + 1\right)} - q^{2} - 2 \, q - 1\right)} d^{2}}\,{d x} - \frac{{\left({\left(m {\left(q + 1\right)} - q^{2} - 2 \, q - 1\right)} e f^{q} x x^{m} + {\left(m {\left(q + 1\right)} - q^{2} - 2 \, q - 1\right)} d f^{q} x\right)} x^{q} \log\left({\left(e x^{m} + d\right)}^{n}\right) + {\left({\left({\left(m {\left(q + 1\right)} - q^{2} - 2 \, q - 1\right)} e f^{q} \log\left(c\right) - {\left(m^{2} n - m n {\left(q + 1\right)}\right)} e f^{q}\right)} x x^{m} - {\left(d f^{q} m^{2} n - {\left(m {\left(q + 1\right)} - q^{2} - 2 \, q - 1\right)} d f^{q} \log\left(c\right)\right)} x\right)} x^{q}}{{\left(q^{3} - {\left(q^{2} + 2 \, q + 1\right)} m + 3 \, q^{2} + 3 \, q + 1\right)} e x^{m} + {\left(q^{3} - {\left(q^{2} + 2 \, q + 1\right)} m + 3 \, q^{2} + 3 \, q + 1\right)} d}\right)} b + \frac{\left(f x\right)^{q + 1} a}{f {\left(q + 1\right)}}"," ",0,"(d^2*f^q*m^2*n*integrate(x^q/((m*(q + 1) - q^2 - 2*q - 1)*e^2*x^(2*m) + 2*(m*(q + 1) - q^2 - 2*q - 1)*d*e*x^m + (m*(q + 1) - q^2 - 2*q - 1)*d^2), x) - (((m*(q + 1) - q^2 - 2*q - 1)*e*f^q*x*x^m + (m*(q + 1) - q^2 - 2*q - 1)*d*f^q*x)*x^q*log((e*x^m + d)^n) + (((m*(q + 1) - q^2 - 2*q - 1)*e*f^q*log(c) - (m^2*n - m*n*(q + 1))*e*f^q)*x*x^m - (d*f^q*m^2*n - (m*(q + 1) - q^2 - 2*q - 1)*d*f^q*log(c))*x)*x^q)/((q^3 - (q^2 + 2*q + 1)*m + 3*q^2 + 3*q + 1)*e*x^m + (q^3 - (q^2 + 2*q + 1)*m + 3*q^2 + 3*q + 1)*d))*b + (f*x)^(q + 1)*a/(f*(q + 1))","F",0
400,1,128,0,0.496856," ","integrate(x^3*(a+b*log(c*(d+e*x^(1/2))^n)),x, algorithm=""maxima"")","\frac{1}{4} \, b x^{4} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right) + \frac{1}{4} \, a x^{4} - \frac{1}{3360} \, b e n {\left(\frac{840 \, d^{8} \log\left(e \sqrt{x} + d\right)}{e^{9}} + \frac{105 \, e^{7} x^{4} - 120 \, d e^{6} x^{\frac{7}{2}} + 140 \, d^{2} e^{5} x^{3} - 168 \, d^{3} e^{4} x^{\frac{5}{2}} + 210 \, d^{4} e^{3} x^{2} - 280 \, d^{5} e^{2} x^{\frac{3}{2}} + 420 \, d^{6} e x - 840 \, d^{7} \sqrt{x}}{e^{8}}\right)}"," ",0,"1/4*b*x^4*log((e*sqrt(x) + d)^n*c) + 1/4*a*x^4 - 1/3360*b*e*n*(840*d^8*log(e*sqrt(x) + d)/e^9 + (105*e^7*x^4 - 120*d*e^6*x^(7/2) + 140*d^2*e^5*x^3 - 168*d^3*e^4*x^(5/2) + 210*d^4*e^3*x^2 - 280*d^5*e^2*x^(3/2) + 420*d^6*e*x - 840*d^7*sqrt(x))/e^8)","A",0
401,1,106,0,0.485565," ","integrate(x^2*(a+b*log(c*(d+e*x^(1/2))^n)),x, algorithm=""maxima"")","\frac{1}{3} \, b x^{3} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right) + \frac{1}{3} \, a x^{3} - \frac{1}{180} \, b e n {\left(\frac{60 \, d^{6} \log\left(e \sqrt{x} + d\right)}{e^{7}} + \frac{10 \, e^{5} x^{3} - 12 \, d e^{4} x^{\frac{5}{2}} + 15 \, d^{2} e^{3} x^{2} - 20 \, d^{3} e^{2} x^{\frac{3}{2}} + 30 \, d^{4} e x - 60 \, d^{5} \sqrt{x}}{e^{6}}\right)}"," ",0,"1/3*b*x^3*log((e*sqrt(x) + d)^n*c) + 1/3*a*x^3 - 1/180*b*e*n*(60*d^6*log(e*sqrt(x) + d)/e^7 + (10*e^5*x^3 - 12*d*e^4*x^(5/2) + 15*d^2*e^3*x^2 - 20*d^3*e^2*x^(3/2) + 30*d^4*e*x - 60*d^5*sqrt(x))/e^6)","A",0
402,1,84,0,0.496118," ","integrate(x*(a+b*log(c*(d+e*x^(1/2))^n)),x, algorithm=""maxima"")","-\frac{1}{24} \, b e n {\left(\frac{12 \, d^{4} \log\left(e \sqrt{x} + d\right)}{e^{5}} + \frac{3 \, e^{3} x^{2} - 4 \, d e^{2} x^{\frac{3}{2}} + 6 \, d^{2} e x - 12 \, d^{3} \sqrt{x}}{e^{4}}\right)} + \frac{1}{2} \, b x^{2} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right) + \frac{1}{2} \, a x^{2}"," ",0,"-1/24*b*e*n*(12*d^4*log(e*sqrt(x) + d)/e^5 + (3*e^3*x^2 - 4*d*e^2*x^(3/2) + 6*d^2*e*x - 12*d^3*sqrt(x))/e^4) + 1/2*b*x^2*log((e*sqrt(x) + d)^n*c) + 1/2*a*x^2","A",0
403,1,57,0,0.470976," ","integrate(a+b*log(c*(d+e*x^(1/2))^n),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(e n {\left(\frac{2 \, d^{2} \log\left(e \sqrt{x} + d\right)}{e^{3}} + \frac{e x - 2 \, d \sqrt{x}}{e^{2}}\right)} - 2 \, x \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)\right)} b + a x"," ",0,"-1/2*(e*n*(2*d^2*log(e*sqrt(x) + d)/e^3 + (e*x - 2*d*sqrt(x))/e^2) - 2*x*log((e*sqrt(x) + d)^n*c))*b + a*x","A",0
404,1,107,0,1.140956," ","integrate((a+b*log(c*(d+e*x^(1/2))^n))/x,x, algorithm=""maxima"")","-2 \, {\left(\log\left(\frac{e \sqrt{x}}{d} + 1\right) \log\left(\sqrt{x}\right) + {\rm Li}_2\left(-\frac{e \sqrt{x}}{d}\right)\right)} b n + \frac{b d n \log\left(e \sqrt{x} + d\right) \log\left(x\right) + {\left(b d \log\left(c\right) + a d\right)} \log\left(x\right) - \frac{b e n x \log\left(x\right) - 2 \, b e n x}{\sqrt{x}}}{d} + \frac{2 \, {\left(b e n \sqrt{x} \log\left(\sqrt{x}\right) - b e n \sqrt{x}\right)}}{d}"," ",0,"-2*(log(e*sqrt(x)/d + 1)*log(sqrt(x)) + dilog(-e*sqrt(x)/d))*b*n + (b*d*n*log(e*sqrt(x) + d)*log(x) + (b*d*log(c) + a*d)*log(x) - (b*e*n*x*log(x) - 2*b*e*n*x)/sqrt(x))/d + 2*(b*e*n*sqrt(x)*log(sqrt(x)) - b*e*n*sqrt(x))/d","B",0
405,1,61,0,0.480585," ","integrate((a+b*log(c*(d+e*x^(1/2))^n))/x^2,x, algorithm=""maxima"")","\frac{1}{2} \, b e n {\left(\frac{2 \, e \log\left(e \sqrt{x} + d\right)}{d^{2}} - \frac{e \log\left(x\right)}{d^{2}} - \frac{2}{d \sqrt{x}}\right)} - \frac{b \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)}{x} - \frac{a}{x}"," ",0,"1/2*b*e*n*(2*e*log(e*sqrt(x) + d)/d^2 - e*log(x)/d^2 - 2/(d*sqrt(x))) - b*log((e*sqrt(x) + d)^n*c)/x - a/x","A",0
406,1,84,0,0.488894," ","integrate((a+b*log(c*(d+e*x^(1/2))^n))/x^3,x, algorithm=""maxima"")","\frac{1}{12} \, b e n {\left(\frac{6 \, e^{3} \log\left(e \sqrt{x} + d\right)}{d^{4}} - \frac{3 \, e^{3} \log\left(x\right)}{d^{4}} - \frac{6 \, e^{2} x - 3 \, d e \sqrt{x} + 2 \, d^{2}}{d^{3} x^{\frac{3}{2}}}\right)} - \frac{b \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)}{2 \, x^{2}} - \frac{a}{2 \, x^{2}}"," ",0,"1/12*b*e*n*(6*e^3*log(e*sqrt(x) + d)/d^4 - 3*e^3*log(x)/d^4 - (6*e^2*x - 3*d*e*sqrt(x) + 2*d^2)/(d^3*x^(3/2))) - 1/2*b*log((e*sqrt(x) + d)^n*c)/x^2 - 1/2*a/x^2","A",0
407,1,106,0,0.492572," ","integrate((a+b*log(c*(d+e*x^(1/2))^n))/x^4,x, algorithm=""maxima"")","\frac{1}{180} \, b e n {\left(\frac{60 \, e^{5} \log\left(e \sqrt{x} + d\right)}{d^{6}} - \frac{30 \, e^{5} \log\left(x\right)}{d^{6}} - \frac{60 \, e^{4} x^{2} - 30 \, d e^{3} x^{\frac{3}{2}} + 20 \, d^{2} e^{2} x - 15 \, d^{3} e \sqrt{x} + 12 \, d^{4}}{d^{5} x^{\frac{5}{2}}}\right)} - \frac{b \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)}{3 \, x^{3}} - \frac{a}{3 \, x^{3}}"," ",0,"1/180*b*e*n*(60*e^5*log(e*sqrt(x) + d)/d^6 - 30*e^5*log(x)/d^6 - (60*e^4*x^2 - 30*d*e^3*x^(3/2) + 20*d^2*e^2*x - 15*d^3*e*sqrt(x) + 12*d^4)/(d^5*x^(5/2))) - 1/3*b*log((e*sqrt(x) + d)^n*c)/x^3 - 1/3*a/x^3","A",0
408,1,324,0,0.518280," ","integrate(x^2*(a+b*log(c*(d+e*x^(1/2))^n))^2,x, algorithm=""maxima"")","\frac{1}{3} \, b^{2} x^{3} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)^{2} + \frac{2}{3} \, a b x^{3} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right) + \frac{1}{3} \, a^{2} x^{3} - \frac{1}{90} \, a b e n {\left(\frac{60 \, d^{6} \log\left(e \sqrt{x} + d\right)}{e^{7}} + \frac{10 \, e^{5} x^{3} - 12 \, d e^{4} x^{\frac{5}{2}} + 15 \, d^{2} e^{3} x^{2} - 20 \, d^{3} e^{2} x^{\frac{3}{2}} + 30 \, d^{4} e x - 60 \, d^{5} \sqrt{x}}{e^{6}}\right)} - \frac{1}{5400} \, {\left(60 \, e n {\left(\frac{60 \, d^{6} \log\left(e \sqrt{x} + d\right)}{e^{7}} + \frac{10 \, e^{5} x^{3} - 12 \, d e^{4} x^{\frac{5}{2}} + 15 \, d^{2} e^{3} x^{2} - 20 \, d^{3} e^{2} x^{\frac{3}{2}} + 30 \, d^{4} e x - 60 \, d^{5} \sqrt{x}}{e^{6}}\right)} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right) - \frac{{\left(100 \, e^{6} x^{3} - 264 \, d e^{5} x^{\frac{5}{2}} + 555 \, d^{2} e^{4} x^{2} + 1800 \, d^{6} \log\left(e \sqrt{x} + d\right)^{2} - 1140 \, d^{3} e^{3} x^{\frac{3}{2}} + 2610 \, d^{4} e^{2} x + 8820 \, d^{6} \log\left(e \sqrt{x} + d\right) - 8820 \, d^{5} e \sqrt{x}\right)} n^{2}}{e^{6}}\right)} b^{2}"," ",0,"1/3*b^2*x^3*log((e*sqrt(x) + d)^n*c)^2 + 2/3*a*b*x^3*log((e*sqrt(x) + d)^n*c) + 1/3*a^2*x^3 - 1/90*a*b*e*n*(60*d^6*log(e*sqrt(x) + d)/e^7 + (10*e^5*x^3 - 12*d*e^4*x^(5/2) + 15*d^2*e^3*x^2 - 20*d^3*e^2*x^(3/2) + 30*d^4*e*x - 60*d^5*sqrt(x))/e^6) - 1/5400*(60*e*n*(60*d^6*log(e*sqrt(x) + d)/e^7 + (10*e^5*x^3 - 12*d*e^4*x^(5/2) + 15*d^2*e^3*x^2 - 20*d^3*e^2*x^(3/2) + 30*d^4*e*x - 60*d^5*sqrt(x))/e^6)*log((e*sqrt(x) + d)^n*c) - (100*e^6*x^3 - 264*d*e^5*x^(5/2) + 555*d^2*e^4*x^2 + 1800*d^6*log(e*sqrt(x) + d)^2 - 1140*d^3*e^3*x^(3/2) + 2610*d^4*e^2*x + 8820*d^6*log(e*sqrt(x) + d) - 8820*d^5*e*sqrt(x))*n^2/e^6)*b^2","A",0
409,1,257,0,0.553664," ","integrate(x*(a+b*log(c*(d+e*x^(1/2))^n))^2,x, algorithm=""maxima"")","\frac{1}{2} \, b^{2} x^{2} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)^{2} - \frac{1}{12} \, a b e n {\left(\frac{12 \, d^{4} \log\left(e \sqrt{x} + d\right)}{e^{5}} + \frac{3 \, e^{3} x^{2} - 4 \, d e^{2} x^{\frac{3}{2}} + 6 \, d^{2} e x - 12 \, d^{3} \sqrt{x}}{e^{4}}\right)} + a b x^{2} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right) + \frac{1}{2} \, a^{2} x^{2} - \frac{1}{144} \, {\left(12 \, e n {\left(\frac{12 \, d^{4} \log\left(e \sqrt{x} + d\right)}{e^{5}} + \frac{3 \, e^{3} x^{2} - 4 \, d e^{2} x^{\frac{3}{2}} + 6 \, d^{2} e x - 12 \, d^{3} \sqrt{x}}{e^{4}}\right)} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right) - \frac{{\left(9 \, e^{4} x^{2} + 72 \, d^{4} \log\left(e \sqrt{x} + d\right)^{2} - 28 \, d e^{3} x^{\frac{3}{2}} + 78 \, d^{2} e^{2} x + 300 \, d^{4} \log\left(e \sqrt{x} + d\right) - 300 \, d^{3} e \sqrt{x}\right)} n^{2}}{e^{4}}\right)} b^{2}"," ",0,"1/2*b^2*x^2*log((e*sqrt(x) + d)^n*c)^2 - 1/12*a*b*e*n*(12*d^4*log(e*sqrt(x) + d)/e^5 + (3*e^3*x^2 - 4*d*e^2*x^(3/2) + 6*d^2*e*x - 12*d^3*sqrt(x))/e^4) + a*b*x^2*log((e*sqrt(x) + d)^n*c) + 1/2*a^2*x^2 - 1/144*(12*e*n*(12*d^4*log(e*sqrt(x) + d)/e^5 + (3*e^3*x^2 - 4*d*e^2*x^(3/2) + 6*d^2*e*x - 12*d^3*sqrt(x))/e^4)*log((e*sqrt(x) + d)^n*c) - (9*e^4*x^2 + 72*d^4*log(e*sqrt(x) + d)^2 - 28*d*e^3*x^(3/2) + 78*d^2*e^2*x + 300*d^4*log(e*sqrt(x) + d) - 300*d^3*e*sqrt(x))*n^2/e^4)*b^2","A",0
410,1,179,0,0.540397," ","integrate((a+b*log(c*(d+e*x^(1/2))^n))^2,x, algorithm=""maxima"")","-{\left(e n {\left(\frac{2 \, d^{2} \log\left(e \sqrt{x} + d\right)}{e^{3}} + \frac{e x - 2 \, d \sqrt{x}}{e^{2}}\right)} - 2 \, x \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)\right)} a b - \frac{1}{2} \, {\left(2 \, e n {\left(\frac{2 \, d^{2} \log\left(e \sqrt{x} + d\right)}{e^{3}} + \frac{e x - 2 \, d \sqrt{x}}{e^{2}}\right)} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right) - 2 \, x \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)^{2} - \frac{{\left(2 \, d^{2} \log\left(e \sqrt{x} + d\right)^{2} + e^{2} x + 6 \, d^{2} \log\left(e \sqrt{x} + d\right) - 6 \, d e \sqrt{x}\right)} n^{2}}{e^{2}}\right)} b^{2} + a^{2} x"," ",0,"-(e*n*(2*d^2*log(e*sqrt(x) + d)/e^3 + (e*x - 2*d*sqrt(x))/e^2) - 2*x*log((e*sqrt(x) + d)^n*c))*a*b - 1/2*(2*e*n*(2*d^2*log(e*sqrt(x) + d)/e^3 + (e*x - 2*d*sqrt(x))/e^2)*log((e*sqrt(x) + d)^n*c) - 2*x*log((e*sqrt(x) + d)^n*c)^2 - (2*d^2*log(e*sqrt(x) + d)^2 + e^2*x + 6*d^2*log(e*sqrt(x) + d) - 6*d*e*sqrt(x))*n^2/e^2)*b^2 + a^2*x","A",0
411,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(1/2))^n))^2/x,x, algorithm=""maxima"")","b^{2} n^{2} \log\left(e \sqrt{x} + d\right)^{2} \log\left(x\right) + \int -\frac{{\left(b^{2} e n x \log\left(x\right) - 2 \, {\left(b^{2} e \log\left(c\right) + a b e\right)} x - 2 \, {\left(b^{2} d \log\left(c\right) + a b d\right)} \sqrt{x}\right)} n \log\left(e \sqrt{x} + d\right) - {\left(b^{2} e \log\left(c\right)^{2} + 2 \, a b e \log\left(c\right) + a^{2} e\right)} x - {\left(b^{2} d \log\left(c\right)^{2} + 2 \, a b d \log\left(c\right) + a^{2} d\right)} \sqrt{x}}{e x^{2} + d x^{\frac{3}{2}}}\,{d x}"," ",0,"b^2*n^2*log(e*sqrt(x) + d)^2*log(x) + integrate(-((b^2*e*n*x*log(x) - 2*(b^2*e*log(c) + a*b*e)*x - 2*(b^2*d*log(c) + a*b*d)*sqrt(x))*n*log(e*sqrt(x) + d) - (b^2*e*log(c)^2 + 2*a*b*e*log(c) + a^2*e)*x - (b^2*d*log(c)^2 + 2*a*b*d*log(c) + a^2*d)*sqrt(x))/(e*x^2 + d*x^(3/2)), x)","F",0
412,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(1/2))^n))^2/x^2,x, algorithm=""maxima"")","\frac{2 \, {\left(\log\left(\frac{e \sqrt{x}}{d} + 1\right) \log\left(\sqrt{x}\right) + {\rm Li}_2\left(-\frac{e \sqrt{x}}{d}\right)\right)} b^{2} e^{2} n^{2}}{d^{2}} + \frac{2 \, {\left(a b e^{2} n - {\left(e^{2} n^{2} - e^{2} n \log\left(c\right)\right)} b^{2}\right)} \log\left(e \sqrt{x} + d\right)}{d^{2}} - \frac{2 \, {\left(b^{2} e^{2} n \log\left(c\right) + a b e^{2} n\right)} \log\left(\sqrt{x}\right)}{d^{2}} + \frac{b^{2} e^{4} n^{2} x + b^{2} d^{2} e^{2} n^{2} \log\left(x\right)}{d^{4}} + \frac{2 \, b^{2} e^{5} n^{2} x^{\frac{3}{2}} - 6 \, b^{2} d^{2} e^{3} n^{2} \sqrt{x} \log\left(\sqrt{x}\right) - 3 \, b^{2} d e^{4} n^{2} x + 12 \, b^{2} d^{2} e^{3} n^{2} \sqrt{x}}{3 \, d^{5}} - \frac{3 \, b^{2} d^{3} e^{2} n^{2} x^{\frac{3}{2}} \log\left(e \sqrt{x} + d\right)^{2} + 2 \, b^{2} e^{5} n^{2} x^{3} - 3 \, b^{2} d^{2} e^{3} n^{2} x^{2} \log\left(x\right) + 3 \, b^{2} d^{5} n^{2} \sqrt{x} \log\left(e \sqrt{x} + d\right)^{2} + 12 \, b^{2} d^{2} e^{3} n^{2} x^{2} - 3 \, {\left(2 \, b^{2} d^{3} e^{2} n x^{\frac{3}{2}} \log\left(e \sqrt{x} + d\right) - 2 \, b^{2} d^{4} e n x - {\left(b^{2} d^{3} e^{2} n x \log\left(x\right) + 2 \, b^{2} d^{5} \log\left(c\right) + 2 \, a b d^{5}\right)} \sqrt{x}\right)} n \log\left(e \sqrt{x} + d\right) + 6 \, {\left(b^{2} d^{4} e n \log\left(c\right) + a b d^{4} e n\right)} x}{3 \, d^{5} x^{\frac{3}{2}}}"," ",0,"2*(log(e*sqrt(x)/d + 1)*log(sqrt(x)) + dilog(-e*sqrt(x)/d))*b^2*e^2*n^2/d^2 + 2*(a*b*e^2*n - (e^2*n^2 - e^2*n*log(c))*b^2)*log(e*sqrt(x) + d)/d^2 - 2*(b^2*e^2*n*log(c) + a*b*e^2*n)*log(sqrt(x))/d^2 + integrate((b^2*e^4*n^2*x + b^2*d^2*e^2*n^2)/x, x)/d^4 + 1/3*(2*b^2*e^5*n^2*x^(3/2) - 6*b^2*d^2*e^3*n^2*sqrt(x)*log(sqrt(x)) - 3*b^2*d*e^4*n^2*x + 12*b^2*d^2*e^3*n^2*sqrt(x))/d^5 - 1/3*(3*b^2*d^3*e^2*n^2*x^(3/2)*log(e*sqrt(x) + d)^2 + 2*b^2*e^5*n^2*x^3 - 3*b^2*d^2*e^3*n^2*x^2*log(x) + 3*b^2*d^5*n^2*sqrt(x)*log(e*sqrt(x) + d)^2 + 12*b^2*d^2*e^3*n^2*x^2 - 3*(2*b^2*d^3*e^2*n*x^(3/2)*log(e*sqrt(x) + d) - 2*b^2*d^4*e*n*x - (b^2*d^3*e^2*n*x*log(x) + 2*b^2*d^5*log(c) + 2*a*b*d^5)*sqrt(x))*n*log(e*sqrt(x) + d) + 6*(b^2*d^4*e*n*log(c) + a*b*d^4*e*n)*x)/(d^5*x^(3/2))","F",0
413,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(1/2))^n))^2/x^3,x, algorithm=""maxima"")","-\frac{b^{2} n^{2} \log\left(e \sqrt{x} + d\right)^{2}}{2 \, x^{2}} + \int \frac{{\left(b^{2} e n x + 4 \, {\left(b^{2} e \log\left(c\right) + a b e\right)} x + 4 \, {\left(b^{2} d \log\left(c\right) + a b d\right)} \sqrt{x}\right)} n \log\left(e \sqrt{x} + d\right) + 2 \, {\left(b^{2} e \log\left(c\right)^{2} + 2 \, a b e \log\left(c\right) + a^{2} e\right)} x + 2 \, {\left(b^{2} d \log\left(c\right)^{2} + 2 \, a b d \log\left(c\right) + a^{2} d\right)} \sqrt{x}}{2 \, {\left(e x^{4} + d x^{\frac{7}{2}}\right)}}\,{d x}"," ",0,"-1/2*b^2*n^2*log(e*sqrt(x) + d)^2/x^2 + integrate(1/2*((b^2*e*n*x + 4*(b^2*e*log(c) + a*b*e)*x + 4*(b^2*d*log(c) + a*b*d)*sqrt(x))*n*log(e*sqrt(x) + d) + 2*(b^2*e*log(c)^2 + 2*a*b*e*log(c) + a^2*e)*x + 2*(b^2*d*log(c)^2 + 2*a*b*d*log(c) + a^2*d)*sqrt(x))/(e*x^4 + d*x^(7/2)), x)","F",0
414,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(1/2))^n))^2/x^4,x, algorithm=""maxima"")","-\frac{b^{2} n^{2} \log\left(e \sqrt{x} + d\right)^{2}}{3 \, x^{3}} + \int \frac{{\left(b^{2} e n x + 6 \, {\left(b^{2} e \log\left(c\right) + a b e\right)} x + 6 \, {\left(b^{2} d \log\left(c\right) + a b d\right)} \sqrt{x}\right)} n \log\left(e \sqrt{x} + d\right) + 3 \, {\left(b^{2} e \log\left(c\right)^{2} + 2 \, a b e \log\left(c\right) + a^{2} e\right)} x + 3 \, {\left(b^{2} d \log\left(c\right)^{2} + 2 \, a b d \log\left(c\right) + a^{2} d\right)} \sqrt{x}}{3 \, {\left(e x^{5} + d x^{\frac{9}{2}}\right)}}\,{d x}"," ",0,"-1/3*b^2*n^2*log(e*sqrt(x) + d)^2/x^3 + integrate(1/3*((b^2*e*n*x + 6*(b^2*e*log(c) + a*b*e)*x + 6*(b^2*d*log(c) + a*b*d)*sqrt(x))*n*log(e*sqrt(x) + d) + 3*(b^2*e*log(c)^2 + 2*a*b*e*log(c) + a^2*e)*x + 3*(b^2*d*log(c)^2 + 2*a*b*d*log(c) + a^2*d)*sqrt(x))/(e*x^5 + d*x^(9/2)), x)","F",0
415,1,666,0,0.563967," ","integrate(x^2*(a+b*log(c*(d+e*x^(1/2))^n))^3,x, algorithm=""maxima"")","\frac{1}{3} \, b^{3} x^{3} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)^{3} + a b^{2} x^{3} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)^{2} + a^{2} b x^{3} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right) + \frac{1}{3} \, a^{3} x^{3} - \frac{1}{60} \, a^{2} b e n {\left(\frac{60 \, d^{6} \log\left(e \sqrt{x} + d\right)}{e^{7}} + \frac{10 \, e^{5} x^{3} - 12 \, d e^{4} x^{\frac{5}{2}} + 15 \, d^{2} e^{3} x^{2} - 20 \, d^{3} e^{2} x^{\frac{3}{2}} + 30 \, d^{4} e x - 60 \, d^{5} \sqrt{x}}{e^{6}}\right)} - \frac{1}{1800} \, {\left(60 \, e n {\left(\frac{60 \, d^{6} \log\left(e \sqrt{x} + d\right)}{e^{7}} + \frac{10 \, e^{5} x^{3} - 12 \, d e^{4} x^{\frac{5}{2}} + 15 \, d^{2} e^{3} x^{2} - 20 \, d^{3} e^{2} x^{\frac{3}{2}} + 30 \, d^{4} e x - 60 \, d^{5} \sqrt{x}}{e^{6}}\right)} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right) - \frac{{\left(100 \, e^{6} x^{3} - 264 \, d e^{5} x^{\frac{5}{2}} + 555 \, d^{2} e^{4} x^{2} + 1800 \, d^{6} \log\left(e \sqrt{x} + d\right)^{2} - 1140 \, d^{3} e^{3} x^{\frac{3}{2}} + 2610 \, d^{4} e^{2} x + 8820 \, d^{6} \log\left(e \sqrt{x} + d\right) - 8820 \, d^{5} e \sqrt{x}\right)} n^{2}}{e^{6}}\right)} a b^{2} - \frac{1}{108000} \, {\left(1800 \, e n {\left(\frac{60 \, d^{6} \log\left(e \sqrt{x} + d\right)}{e^{7}} + \frac{10 \, e^{5} x^{3} - 12 \, d e^{4} x^{\frac{5}{2}} + 15 \, d^{2} e^{3} x^{2} - 20 \, d^{3} e^{2} x^{\frac{3}{2}} + 30 \, d^{4} e x - 60 \, d^{5} \sqrt{x}}{e^{6}}\right)} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)^{2} + e n {\left(\frac{{\left(1000 \, e^{6} x^{3} + 36000 \, d^{6} \log\left(e \sqrt{x} + d\right)^{3} - 4368 \, d e^{5} x^{\frac{5}{2}} + 13785 \, d^{2} e^{4} x^{2} + 264600 \, d^{6} \log\left(e \sqrt{x} + d\right)^{2} - 41180 \, d^{3} e^{3} x^{\frac{3}{2}} + 140070 \, d^{4} e^{2} x + 809340 \, d^{6} \log\left(e \sqrt{x} + d\right) - 809340 \, d^{5} e \sqrt{x}\right)} n^{2}}{e^{7}} - \frac{60 \, {\left(100 \, e^{6} x^{3} - 264 \, d e^{5} x^{\frac{5}{2}} + 555 \, d^{2} e^{4} x^{2} + 1800 \, d^{6} \log\left(e \sqrt{x} + d\right)^{2} - 1140 \, d^{3} e^{3} x^{\frac{3}{2}} + 2610 \, d^{4} e^{2} x + 8820 \, d^{6} \log\left(e \sqrt{x} + d\right) - 8820 \, d^{5} e \sqrt{x}\right)} n \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)}{e^{7}}\right)}\right)} b^{3}"," ",0,"1/3*b^3*x^3*log((e*sqrt(x) + d)^n*c)^3 + a*b^2*x^3*log((e*sqrt(x) + d)^n*c)^2 + a^2*b*x^3*log((e*sqrt(x) + d)^n*c) + 1/3*a^3*x^3 - 1/60*a^2*b*e*n*(60*d^6*log(e*sqrt(x) + d)/e^7 + (10*e^5*x^3 - 12*d*e^4*x^(5/2) + 15*d^2*e^3*x^2 - 20*d^3*e^2*x^(3/2) + 30*d^4*e*x - 60*d^5*sqrt(x))/e^6) - 1/1800*(60*e*n*(60*d^6*log(e*sqrt(x) + d)/e^7 + (10*e^5*x^3 - 12*d*e^4*x^(5/2) + 15*d^2*e^3*x^2 - 20*d^3*e^2*x^(3/2) + 30*d^4*e*x - 60*d^5*sqrt(x))/e^6)*log((e*sqrt(x) + d)^n*c) - (100*e^6*x^3 - 264*d*e^5*x^(5/2) + 555*d^2*e^4*x^2 + 1800*d^6*log(e*sqrt(x) + d)^2 - 1140*d^3*e^3*x^(3/2) + 2610*d^4*e^2*x + 8820*d^6*log(e*sqrt(x) + d) - 8820*d^5*e*sqrt(x))*n^2/e^6)*a*b^2 - 1/108000*(1800*e*n*(60*d^6*log(e*sqrt(x) + d)/e^7 + (10*e^5*x^3 - 12*d*e^4*x^(5/2) + 15*d^2*e^3*x^2 - 20*d^3*e^2*x^(3/2) + 30*d^4*e*x - 60*d^5*sqrt(x))/e^6)*log((e*sqrt(x) + d)^n*c)^2 + e*n*((1000*e^6*x^3 + 36000*d^6*log(e*sqrt(x) + d)^3 - 4368*d*e^5*x^(5/2) + 13785*d^2*e^4*x^2 + 264600*d^6*log(e*sqrt(x) + d)^2 - 41180*d^3*e^3*x^(3/2) + 140070*d^4*e^2*x + 809340*d^6*log(e*sqrt(x) + d) - 809340*d^5*e*sqrt(x))*n^2/e^7 - 60*(100*e^6*x^3 - 264*d*e^5*x^(5/2) + 555*d^2*e^4*x^2 + 1800*d^6*log(e*sqrt(x) + d)^2 - 1140*d^3*e^3*x^(3/2) + 2610*d^4*e^2*x + 8820*d^6*log(e*sqrt(x) + d) - 8820*d^5*e*sqrt(x))*n*log((e*sqrt(x) + d)^n*c)/e^7))*b^3","A",0
416,1,536,0,0.570081," ","integrate(x*(a+b*log(c*(d+e*x^(1/2))^n))^3,x, algorithm=""maxima"")","\frac{1}{2} \, b^{3} x^{2} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)^{3} + \frac{3}{2} \, a b^{2} x^{2} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)^{2} - \frac{1}{8} \, a^{2} b e n {\left(\frac{12 \, d^{4} \log\left(e \sqrt{x} + d\right)}{e^{5}} + \frac{3 \, e^{3} x^{2} - 4 \, d e^{2} x^{\frac{3}{2}} + 6 \, d^{2} e x - 12 \, d^{3} \sqrt{x}}{e^{4}}\right)} + \frac{3}{2} \, a^{2} b x^{2} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right) + \frac{1}{2} \, a^{3} x^{2} - \frac{1}{48} \, {\left(12 \, e n {\left(\frac{12 \, d^{4} \log\left(e \sqrt{x} + d\right)}{e^{5}} + \frac{3 \, e^{3} x^{2} - 4 \, d e^{2} x^{\frac{3}{2}} + 6 \, d^{2} e x - 12 \, d^{3} \sqrt{x}}{e^{4}}\right)} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right) - \frac{{\left(9 \, e^{4} x^{2} + 72 \, d^{4} \log\left(e \sqrt{x} + d\right)^{2} - 28 \, d e^{3} x^{\frac{3}{2}} + 78 \, d^{2} e^{2} x + 300 \, d^{4} \log\left(e \sqrt{x} + d\right) - 300 \, d^{3} e \sqrt{x}\right)} n^{2}}{e^{4}}\right)} a b^{2} - \frac{1}{576} \, {\left(72 \, e n {\left(\frac{12 \, d^{4} \log\left(e \sqrt{x} + d\right)}{e^{5}} + \frac{3 \, e^{3} x^{2} - 4 \, d e^{2} x^{\frac{3}{2}} + 6 \, d^{2} e x - 12 \, d^{3} \sqrt{x}}{e^{4}}\right)} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)^{2} + e n {\left(\frac{{\left(288 \, d^{4} \log\left(e \sqrt{x} + d\right)^{3} + 27 \, e^{4} x^{2} + 1800 \, d^{4} \log\left(e \sqrt{x} + d\right)^{2} - 148 \, d e^{3} x^{\frac{3}{2}} + 690 \, d^{2} e^{2} x + 4980 \, d^{4} \log\left(e \sqrt{x} + d\right) - 4980 \, d^{3} e \sqrt{x}\right)} n^{2}}{e^{5}} - \frac{12 \, {\left(9 \, e^{4} x^{2} + 72 \, d^{4} \log\left(e \sqrt{x} + d\right)^{2} - 28 \, d e^{3} x^{\frac{3}{2}} + 78 \, d^{2} e^{2} x + 300 \, d^{4} \log\left(e \sqrt{x} + d\right) - 300 \, d^{3} e \sqrt{x}\right)} n \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)}{e^{5}}\right)}\right)} b^{3}"," ",0,"1/2*b^3*x^2*log((e*sqrt(x) + d)^n*c)^3 + 3/2*a*b^2*x^2*log((e*sqrt(x) + d)^n*c)^2 - 1/8*a^2*b*e*n*(12*d^4*log(e*sqrt(x) + d)/e^5 + (3*e^3*x^2 - 4*d*e^2*x^(3/2) + 6*d^2*e*x - 12*d^3*sqrt(x))/e^4) + 3/2*a^2*b*x^2*log((e*sqrt(x) + d)^n*c) + 1/2*a^3*x^2 - 1/48*(12*e*n*(12*d^4*log(e*sqrt(x) + d)/e^5 + (3*e^3*x^2 - 4*d*e^2*x^(3/2) + 6*d^2*e*x - 12*d^3*sqrt(x))/e^4)*log((e*sqrt(x) + d)^n*c) - (9*e^4*x^2 + 72*d^4*log(e*sqrt(x) + d)^2 - 28*d*e^3*x^(3/2) + 78*d^2*e^2*x + 300*d^4*log(e*sqrt(x) + d) - 300*d^3*e*sqrt(x))*n^2/e^4)*a*b^2 - 1/576*(72*e*n*(12*d^4*log(e*sqrt(x) + d)/e^5 + (3*e^3*x^2 - 4*d*e^2*x^(3/2) + 6*d^2*e*x - 12*d^3*sqrt(x))/e^4)*log((e*sqrt(x) + d)^n*c)^2 + e*n*((288*d^4*log(e*sqrt(x) + d)^3 + 27*e^4*x^2 + 1800*d^4*log(e*sqrt(x) + d)^2 - 148*d*e^3*x^(3/2) + 690*d^2*e^2*x + 4980*d^4*log(e*sqrt(x) + d) - 4980*d^3*e*sqrt(x))*n^2/e^5 - 12*(9*e^4*x^2 + 72*d^4*log(e*sqrt(x) + d)^2 - 28*d*e^3*x^(3/2) + 78*d^2*e^2*x + 300*d^4*log(e*sqrt(x) + d) - 300*d^3*e*sqrt(x))*n*log((e*sqrt(x) + d)^n*c)/e^5))*b^3","A",0
417,1,381,0,0.901573," ","integrate((a+b*log(c*(d+e*x^(1/2))^n))^3,x, algorithm=""maxima"")","-\frac{3}{2} \, {\left(e n {\left(\frac{2 \, d^{2} \log\left(e \sqrt{x} + d\right)}{e^{3}} + \frac{e x - 2 \, d \sqrt{x}}{e^{2}}\right)} - 2 \, x \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)\right)} a^{2} b - \frac{3}{2} \, {\left(2 \, e n {\left(\frac{2 \, d^{2} \log\left(e \sqrt{x} + d\right)}{e^{3}} + \frac{e x - 2 \, d \sqrt{x}}{e^{2}}\right)} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right) - 2 \, x \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)^{2} - \frac{{\left(2 \, d^{2} \log\left(e \sqrt{x} + d\right)^{2} + e^{2} x + 6 \, d^{2} \log\left(e \sqrt{x} + d\right) - 6 \, d e \sqrt{x}\right)} n^{2}}{e^{2}}\right)} a b^{2} - \frac{1}{4} \, {\left(6 \, e n {\left(\frac{2 \, d^{2} \log\left(e \sqrt{x} + d\right)}{e^{3}} + \frac{e x - 2 \, d \sqrt{x}}{e^{2}}\right)} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)^{2} - 4 \, x \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)^{3} + e n {\left(\frac{{\left(4 \, d^{2} \log\left(e \sqrt{x} + d\right)^{3} + 18 \, d^{2} \log\left(e \sqrt{x} + d\right)^{2} + 3 \, e^{2} x + 42 \, d^{2} \log\left(e \sqrt{x} + d\right) - 42 \, d e \sqrt{x}\right)} n^{2}}{e^{3}} - \frac{6 \, {\left(2 \, d^{2} \log\left(e \sqrt{x} + d\right)^{2} + e^{2} x + 6 \, d^{2} \log\left(e \sqrt{x} + d\right) - 6 \, d e \sqrt{x}\right)} n \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)}{e^{3}}\right)}\right)} b^{3} + a^{3} x"," ",0,"-3/2*(e*n*(2*d^2*log(e*sqrt(x) + d)/e^3 + (e*x - 2*d*sqrt(x))/e^2) - 2*x*log((e*sqrt(x) + d)^n*c))*a^2*b - 3/2*(2*e*n*(2*d^2*log(e*sqrt(x) + d)/e^3 + (e*x - 2*d*sqrt(x))/e^2)*log((e*sqrt(x) + d)^n*c) - 2*x*log((e*sqrt(x) + d)^n*c)^2 - (2*d^2*log(e*sqrt(x) + d)^2 + e^2*x + 6*d^2*log(e*sqrt(x) + d) - 6*d*e*sqrt(x))*n^2/e^2)*a*b^2 - 1/4*(6*e*n*(2*d^2*log(e*sqrt(x) + d)/e^3 + (e*x - 2*d*sqrt(x))/e^2)*log((e*sqrt(x) + d)^n*c)^2 - 4*x*log((e*sqrt(x) + d)^n*c)^3 + e*n*((4*d^2*log(e*sqrt(x) + d)^3 + 18*d^2*log(e*sqrt(x) + d)^2 + 3*e^2*x + 42*d^2*log(e*sqrt(x) + d) - 42*d*e*sqrt(x))*n^2/e^3 - 6*(2*d^2*log(e*sqrt(x) + d)^2 + e^2*x + 6*d^2*log(e*sqrt(x) + d) - 6*d*e*sqrt(x))*n*log((e*sqrt(x) + d)^n*c)/e^3))*b^3 + a^3*x","A",0
418,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(1/2))^n))^3/x,x, algorithm=""maxima"")","b^{3} n^{3} \log\left(e \sqrt{x} + d\right)^{3} \log\left(x\right) + \int -\frac{3 \, {\left(b^{3} e n x \log\left(x\right) - 2 \, {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x - 2 \, {\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} \sqrt{x}\right)} n^{2} \log\left(e \sqrt{x} + d\right)^{2} - 6 \, {\left({\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} x + {\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} \sqrt{x}\right)} n \log\left(e \sqrt{x} + d\right) - 2 \, {\left(b^{3} e \log\left(c\right)^{3} + 3 \, a b^{2} e \log\left(c\right)^{2} + 3 \, a^{2} b e \log\left(c\right) + a^{3} e\right)} x - 2 \, {\left(b^{3} d \log\left(c\right)^{3} + 3 \, a b^{2} d \log\left(c\right)^{2} + 3 \, a^{2} b d \log\left(c\right) + a^{3} d\right)} \sqrt{x}}{2 \, {\left(e x^{2} + d x^{\frac{3}{2}}\right)}}\,{d x}"," ",0,"b^3*n^3*log(e*sqrt(x) + d)^3*log(x) + integrate(-1/2*(3*(b^3*e*n*x*log(x) - 2*(b^3*e*log(c) + a*b^2*e)*x - 2*(b^3*d*log(c) + a*b^2*d)*sqrt(x))*n^2*log(e*sqrt(x) + d)^2 - 6*((b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*x + (b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*sqrt(x))*n*log(e*sqrt(x) + d) - 2*(b^3*e*log(c)^3 + 3*a*b^2*e*log(c)^2 + 3*a^2*b*e*log(c) + a^3*e)*x - 2*(b^3*d*log(c)^3 + 3*a*b^2*d*log(c)^2 + 3*a^2*b*d*log(c) + a^3*d)*sqrt(x))/(e*x^2 + d*x^(3/2)), x)","F",0
419,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(1/2))^n))^3/x^2,x, algorithm=""maxima"")","-\frac{2 \, b^{3} d^{2} n^{3} \sqrt{x} \log\left(e \sqrt{x} + d\right)^{3} - 3 \, {\left(2 \, b^{3} e^{2} n x^{\frac{3}{2}} \log\left(e \sqrt{x} + d\right) - 2 \, b^{3} d e n x - {\left(b^{3} e^{2} n x \log\left(x\right) + 2 \, b^{3} d^{2} \log\left(c\right) + 2 \, a b^{2} d^{2}\right)} \sqrt{x}\right)} n^{2} \log\left(e \sqrt{x} + d\right)^{2}}{2 \, d^{2} x^{\frac{3}{2}}} - \int \frac{3 \, {\left(2 \, b^{3} e^{3} n^{2} x^{\frac{5}{2}} \log\left(e \sqrt{x} + d\right) - 2 \, b^{3} d e^{2} n^{2} x^{2} - 2 \, {\left(b^{3} d^{2} e \log\left(c\right)^{2} + 2 \, a b^{2} d^{2} e \log\left(c\right) + a^{2} b d^{2} e\right)} x^{\frac{3}{2}} - 2 \, {\left(b^{3} d^{3} \log\left(c\right)^{2} + 2 \, a b^{2} d^{3} \log\left(c\right) + a^{2} b d^{3}\right)} x - {\left(b^{3} e^{3} n^{2} x^{2} \log\left(x\right) + 2 \, {\left(b^{3} d^{2} e n \log\left(c\right) + a b^{2} d^{2} e n\right)} x\right)} \sqrt{x}\right)} n \log\left(e \sqrt{x} + d\right) - 2 \, {\left(b^{3} d^{2} e \log\left(c\right)^{3} + 3 \, a b^{2} d^{2} e \log\left(c\right)^{2} + 3 \, a^{2} b d^{2} e \log\left(c\right) + a^{3} d^{2} e\right)} x^{\frac{3}{2}} - 2 \, {\left(b^{3} d^{3} \log\left(c\right)^{3} + 3 \, a b^{2} d^{3} \log\left(c\right)^{2} + 3 \, a^{2} b d^{3} \log\left(c\right) + a^{3} d^{3}\right)} x}{2 \, {\left(d^{2} e x^{\frac{7}{2}} + d^{3} x^{3}\right)}}\,{d x}"," ",0,"-1/2*(2*b^3*d^2*n^3*sqrt(x)*log(e*sqrt(x) + d)^3 - 3*(2*b^3*e^2*n*x^(3/2)*log(e*sqrt(x) + d) - 2*b^3*d*e*n*x - (b^3*e^2*n*x*log(x) + 2*b^3*d^2*log(c) + 2*a*b^2*d^2)*sqrt(x))*n^2*log(e*sqrt(x) + d)^2)/(d^2*x^(3/2)) - integrate(1/2*(3*(2*b^3*e^3*n^2*x^(5/2)*log(e*sqrt(x) + d) - 2*b^3*d*e^2*n^2*x^2 - 2*(b^3*d^2*e*log(c)^2 + 2*a*b^2*d^2*e*log(c) + a^2*b*d^2*e)*x^(3/2) - 2*(b^3*d^3*log(c)^2 + 2*a*b^2*d^3*log(c) + a^2*b*d^3)*x - (b^3*e^3*n^2*x^2*log(x) + 2*(b^3*d^2*e*n*log(c) + a*b^2*d^2*e*n)*x)*sqrt(x))*n*log(e*sqrt(x) + d) - 2*(b^3*d^2*e*log(c)^3 + 3*a*b^2*d^2*e*log(c)^2 + 3*a^2*b*d^2*e*log(c) + a^3*d^2*e)*x^(3/2) - 2*(b^3*d^3*log(c)^3 + 3*a*b^2*d^3*log(c)^2 + 3*a^2*b*d^3*log(c) + a^3*d^3)*x)/(d^2*e*x^(7/2) + d^3*x^3), x)","F",0
420,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(1/2))^n))^3/x^3,x, algorithm=""maxima"")","-\frac{b^{3} n^{3} \log\left(e \sqrt{x} + d\right)^{3}}{2 \, x^{2}} + \int \frac{3 \, {\left(b^{3} e n x + 4 \, {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x + 4 \, {\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} \sqrt{x}\right)} n^{2} \log\left(e \sqrt{x} + d\right)^{2} + 12 \, {\left({\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} x + {\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} \sqrt{x}\right)} n \log\left(e \sqrt{x} + d\right) + 4 \, {\left(b^{3} e \log\left(c\right)^{3} + 3 \, a b^{2} e \log\left(c\right)^{2} + 3 \, a^{2} b e \log\left(c\right) + a^{3} e\right)} x + 4 \, {\left(b^{3} d \log\left(c\right)^{3} + 3 \, a b^{2} d \log\left(c\right)^{2} + 3 \, a^{2} b d \log\left(c\right) + a^{3} d\right)} \sqrt{x}}{4 \, {\left(e x^{4} + d x^{\frac{7}{2}}\right)}}\,{d x}"," ",0,"-1/2*b^3*n^3*log(e*sqrt(x) + d)^3/x^2 + integrate(1/4*(3*(b^3*e*n*x + 4*(b^3*e*log(c) + a*b^2*e)*x + 4*(b^3*d*log(c) + a*b^2*d)*sqrt(x))*n^2*log(e*sqrt(x) + d)^2 + 12*((b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*x + (b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*sqrt(x))*n*log(e*sqrt(x) + d) + 4*(b^3*e*log(c)^3 + 3*a*b^2*e*log(c)^2 + 3*a^2*b*e*log(c) + a^3*e)*x + 4*(b^3*d*log(c)^3 + 3*a*b^2*d*log(c)^2 + 3*a^2*b*d*log(c) + a^3*d)*sqrt(x))/(e*x^4 + d*x^(7/2)), x)","F",0
421,1,118,0,0.733653," ","integrate(x^3*(a+b*log(c*(d+e/x^(1/2))^n)),x, algorithm=""maxima"")","\frac{1}{4} \, b x^{4} \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right) + \frac{1}{4} \, a x^{4} - \frac{1}{1680} \, b e n {\left(\frac{420 \, e^{7} \log\left(d \sqrt{x} + e\right)}{d^{8}} - \frac{60 \, d^{6} x^{\frac{7}{2}} - 70 \, d^{5} e x^{3} + 84 \, d^{4} e^{2} x^{\frac{5}{2}} - 105 \, d^{3} e^{3} x^{2} + 140 \, d^{2} e^{4} x^{\frac{3}{2}} - 210 \, d e^{5} x + 420 \, e^{6} \sqrt{x}}{d^{7}}\right)}"," ",0,"1/4*b*x^4*log(c*(d + e/sqrt(x))^n) + 1/4*a*x^4 - 1/1680*b*e*n*(420*e^7*log(d*sqrt(x) + e)/d^8 - (60*d^6*x^(7/2) - 70*d^5*e*x^3 + 84*d^4*e^2*x^(5/2) - 105*d^3*e^3*x^2 + 140*d^2*e^4*x^(3/2) - 210*d*e^5*x + 420*e^6*sqrt(x))/d^7)","A",0
422,1,96,0,0.710676," ","integrate(x^2*(a+b*log(c*(d+e/x^(1/2))^n)),x, algorithm=""maxima"")","\frac{1}{3} \, b x^{3} \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right) + \frac{1}{3} \, a x^{3} - \frac{1}{180} \, b e n {\left(\frac{60 \, e^{5} \log\left(d \sqrt{x} + e\right)}{d^{6}} - \frac{12 \, d^{4} x^{\frac{5}{2}} - 15 \, d^{3} e x^{2} + 20 \, d^{2} e^{2} x^{\frac{3}{2}} - 30 \, d e^{3} x + 60 \, e^{4} \sqrt{x}}{d^{5}}\right)}"," ",0,"1/3*b*x^3*log(c*(d + e/sqrt(x))^n) + 1/3*a*x^3 - 1/180*b*e*n*(60*e^5*log(d*sqrt(x) + e)/d^6 - (12*d^4*x^(5/2) - 15*d^3*e*x^2 + 20*d^2*e^2*x^(3/2) - 30*d*e^3*x + 60*e^4*sqrt(x))/d^5)","A",0
423,1,74,0,0.709558," ","integrate(x*(a+b*log(c*(d+e/x^(1/2))^n)),x, algorithm=""maxima"")","-\frac{1}{12} \, b e n {\left(\frac{6 \, e^{3} \log\left(d \sqrt{x} + e\right)}{d^{4}} - \frac{2 \, d^{2} x^{\frac{3}{2}} - 3 \, d e x + 6 \, e^{2} \sqrt{x}}{d^{3}}\right)} + \frac{1}{2} \, b x^{2} \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right) + \frac{1}{2} \, a x^{2}"," ",0,"-1/12*b*e*n*(6*e^3*log(d*sqrt(x) + e)/d^4 - (2*d^2*x^(3/2) - 3*d*e*x + 6*e^2*sqrt(x))/d^3) + 1/2*b*x^2*log(c*(d + e/sqrt(x))^n) + 1/2*a*x^2","A",0
424,1,48,0,0.664524," ","integrate(a+b*log(c*(d+e/x^(1/2))^n),x, algorithm=""maxima"")","-{\left(e n {\left(\frac{e \log\left(d \sqrt{x} + e\right)}{d^{2}} - \frac{\sqrt{x}}{d}\right)} - x \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)\right)} b + a x"," ",0,"-(e*n*(e*log(d*sqrt(x) + e)/d^2 - sqrt(x)/d) - x*log(c*(d + e/sqrt(x))^n))*b + a*x","A",0
425,1,123,0,2.686644," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))/x,x, algorithm=""maxima"")","-2 \, {\left(\log\left(\frac{d \sqrt{x}}{e} + 1\right) \log\left(\sqrt{x}\right) + {\rm Li}_2\left(-\frac{d \sqrt{x}}{e}\right)\right)} b n + \frac{4 \, b e n \log\left(d \sqrt{x} + e\right) \log\left(x\right) + b e n \log\left(x\right)^{2} + 4 \, b d n \sqrt{x} \log\left(x\right) - 4 \, b e \log\left(x\right) \log\left(x^{\frac{1}{2} \, n}\right) - 8 \, b d n \sqrt{x} + 4 \, {\left(b e \log\left(c\right) + a e\right)} \log\left(x\right) - \frac{4 \, {\left(b d n x \log\left(x\right) - 2 \, b d n x\right)}}{\sqrt{x}}}{4 \, e}"," ",0,"-2*(log(d*sqrt(x)/e + 1)*log(sqrt(x)) + dilog(-d*sqrt(x)/e))*b*n + 1/4*(4*b*e*n*log(d*sqrt(x) + e)*log(x) + b*e*n*log(x)^2 + 4*b*d*n*sqrt(x)*log(x) - 4*b*e*log(x)*log(x^(1/2*n)) - 8*b*d*n*sqrt(x) + 4*(b*e*log(c) + a*e)*log(x) - 4*(b*d*n*x*log(x) - 2*b*d*n*x)/sqrt(x))/e","B",0
426,1,75,0,0.812361," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))/x^2,x, algorithm=""maxima"")","\frac{1}{2} \, b e n {\left(\frac{2 \, d^{2} \log\left(d \sqrt{x} + e\right)}{e^{3}} - \frac{d^{2} \log\left(x\right)}{e^{3}} - \frac{2 \, d \sqrt{x} - e}{e^{2} x}\right)} - \frac{b \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)}{x} - \frac{a}{x}"," ",0,"1/2*b*e*n*(2*d^2*log(d*sqrt(x) + e)/e^3 - d^2*log(x)/e^3 - (2*d*sqrt(x) - e)/(e^2*x)) - b*log(c*(d + e/sqrt(x))^n)/x - a/x","A",0
427,1,95,0,0.621906," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))/x^3,x, algorithm=""maxima"")","\frac{1}{24} \, b e n {\left(\frac{12 \, d^{4} \log\left(d \sqrt{x} + e\right)}{e^{5}} - \frac{6 \, d^{4} \log\left(x\right)}{e^{5}} - \frac{12 \, d^{3} x^{\frac{3}{2}} - 6 \, d^{2} e x + 4 \, d e^{2} \sqrt{x} - 3 \, e^{3}}{e^{4} x^{2}}\right)} - \frac{b \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)}{2 \, x^{2}} - \frac{a}{2 \, x^{2}}"," ",0,"1/24*b*e*n*(12*d^4*log(d*sqrt(x) + e)/e^5 - 6*d^4*log(x)/e^5 - (12*d^3*x^(3/2) - 6*d^2*e*x + 4*d*e^2*sqrt(x) - 3*e^3)/(e^4*x^2)) - 1/2*b*log(c*(d + e/sqrt(x))^n)/x^2 - 1/2*a/x^2","A",0
428,1,117,0,0.806862," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))/x^4,x, algorithm=""maxima"")","\frac{1}{180} \, b e n {\left(\frac{60 \, d^{6} \log\left(d \sqrt{x} + e\right)}{e^{7}} - \frac{30 \, d^{6} \log\left(x\right)}{e^{7}} - \frac{60 \, d^{5} x^{\frac{5}{2}} - 30 \, d^{4} e x^{2} + 20 \, d^{3} e^{2} x^{\frac{3}{2}} - 15 \, d^{2} e^{3} x + 12 \, d e^{4} \sqrt{x} - 10 \, e^{5}}{e^{6} x^{3}}\right)} - \frac{b \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)}{3 \, x^{3}} - \frac{a}{3 \, x^{3}}"," ",0,"1/180*b*e*n*(60*d^6*log(d*sqrt(x) + e)/e^7 - 30*d^6*log(x)/e^7 - (60*d^5*x^(5/2) - 30*d^4*e*x^2 + 20*d^3*e^2*x^(3/2) - 15*d^2*e^3*x + 12*d*e^4*sqrt(x) - 10*e^5)/(e^6*x^3)) - 1/3*b*log(c*(d + e/sqrt(x))^n)/x^3 - 1/3*a/x^3","A",0
429,0,0,0,0.000000," ","integrate(x^2*(a+b*log(c*(d+e/x^(1/2))^n))^2,x, algorithm=""maxima"")","\frac{1}{3} \, b^{2} n^{2} x^{3} \log\left(d \sqrt{x} + e\right)^{2} - \int -\frac{3 \, {\left(b^{2} d \log\left(c\right)^{2} + 2 \, a b d \log\left(c\right) + a^{2} d\right)} x^{3} + 3 \, {\left(b^{2} e \log\left(c\right)^{2} + 2 \, a b e \log\left(c\right) + a^{2} e\right)} x^{\frac{5}{2}} - {\left(b^{2} d n x^{3} - 6 \, {\left(b^{2} d \log\left(c\right) + a b d\right)} x^{3} - 6 \, {\left(b^{2} e \log\left(c\right) + a b e\right)} x^{\frac{5}{2}} + 6 \, {\left(b^{2} d x^{3} + b^{2} e x^{\frac{5}{2}}\right)} \log\left(x^{\frac{1}{2} \, n}\right)\right)} n \log\left(d \sqrt{x} + e\right) + 3 \, {\left(b^{2} d x^{3} + b^{2} e x^{\frac{5}{2}}\right)} \log\left(x^{\frac{1}{2} \, n}\right)^{2} - 6 \, {\left({\left(b^{2} d \log\left(c\right) + a b d\right)} x^{3} + {\left(b^{2} e \log\left(c\right) + a b e\right)} x^{\frac{5}{2}}\right)} \log\left(x^{\frac{1}{2} \, n}\right)}{3 \, {\left(d x + e \sqrt{x}\right)}}\,{d x}"," ",0,"1/3*b^2*n^2*x^3*log(d*sqrt(x) + e)^2 - integrate(-1/3*(3*(b^2*d*log(c)^2 + 2*a*b*d*log(c) + a^2*d)*x^3 + 3*(b^2*e*log(c)^2 + 2*a*b*e*log(c) + a^2*e)*x^(5/2) - (b^2*d*n*x^3 - 6*(b^2*d*log(c) + a*b*d)*x^3 - 6*(b^2*e*log(c) + a*b*e)*x^(5/2) + 6*(b^2*d*x^3 + b^2*e*x^(5/2))*log(x^(1/2*n)))*n*log(d*sqrt(x) + e) + 3*(b^2*d*x^3 + b^2*e*x^(5/2))*log(x^(1/2*n))^2 - 6*((b^2*d*log(c) + a*b*d)*x^3 + (b^2*e*log(c) + a*b*e)*x^(5/2))*log(x^(1/2*n)))/(d*x + e*sqrt(x)), x)","F",0
430,0,0,0,0.000000," ","integrate(x*(a+b*log(c*(d+e/x^(1/2))^n))^2,x, algorithm=""maxima"")","\frac{1}{2} \, b^{2} n^{2} x^{2} \log\left(d \sqrt{x} + e\right)^{2} - \int -\frac{2 \, {\left(b^{2} d \log\left(c\right)^{2} + 2 \, a b d \log\left(c\right) + a^{2} d\right)} x^{2} - {\left(b^{2} d n x^{2} - 4 \, {\left(b^{2} d \log\left(c\right) + a b d\right)} x^{2} - 4 \, {\left(b^{2} e \log\left(c\right) + a b e\right)} x^{\frac{3}{2}} + 4 \, {\left(b^{2} d x^{2} + b^{2} e x^{\frac{3}{2}}\right)} \log\left(x^{\frac{1}{2} \, n}\right)\right)} n \log\left(d \sqrt{x} + e\right) + 2 \, {\left(b^{2} d x^{2} + b^{2} e x^{\frac{3}{2}}\right)} \log\left(x^{\frac{1}{2} \, n}\right)^{2} + 2 \, {\left(b^{2} e \log\left(c\right)^{2} + 2 \, a b e \log\left(c\right) + a^{2} e\right)} x^{\frac{3}{2}} - 4 \, {\left({\left(b^{2} d \log\left(c\right) + a b d\right)} x^{2} + {\left(b^{2} e \log\left(c\right) + a b e\right)} x^{\frac{3}{2}}\right)} \log\left(x^{\frac{1}{2} \, n}\right)}{2 \, {\left(d x + e \sqrt{x}\right)}}\,{d x}"," ",0,"1/2*b^2*n^2*x^2*log(d*sqrt(x) + e)^2 - integrate(-1/2*(2*(b^2*d*log(c)^2 + 2*a*b*d*log(c) + a^2*d)*x^2 - (b^2*d*n*x^2 - 4*(b^2*d*log(c) + a*b*d)*x^2 - 4*(b^2*e*log(c) + a*b*e)*x^(3/2) + 4*(b^2*d*x^2 + b^2*e*x^(3/2))*log(x^(1/2*n)))*n*log(d*sqrt(x) + e) + 2*(b^2*d*x^2 + b^2*e*x^(3/2))*log(x^(1/2*n))^2 + 2*(b^2*e*log(c)^2 + 2*a*b*e*log(c) + a^2*e)*x^(3/2) - 4*((b^2*d*log(c) + a*b*d)*x^2 + (b^2*e*log(c) + a*b*e)*x^(3/2))*log(x^(1/2*n)))/(d*x + e*sqrt(x)), x)","F",0
431,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))^2,x, algorithm=""maxima"")","-2 \, {\left(e n {\left(\frac{e \log\left(d \sqrt{x} + e\right)}{d^{2}} - \frac{\sqrt{x}}{d}\right)} - x \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)\right)} a b + {\left(n^{2} x \log\left(d \sqrt{x} + e\right)^{2} - \int -\frac{d x \log\left(c\right)^{2} + e \sqrt{x} \log\left(c\right)^{2} - {\left(d n x - 2 \, d x \log\left(c\right) - 2 \, e \sqrt{x} \log\left(c\right) + 2 \, {\left(d x + e \sqrt{x}\right)} \log\left(x^{\frac{1}{2} \, n}\right)\right)} n \log\left(d \sqrt{x} + e\right) + {\left(d x + e \sqrt{x}\right)} \log\left(x^{\frac{1}{2} \, n}\right)^{2} - 2 \, {\left(d x \log\left(c\right) + e \sqrt{x} \log\left(c\right)\right)} \log\left(x^{\frac{1}{2} \, n}\right)}{d x + e \sqrt{x}}\,{d x}\right)} b^{2} + a^{2} x"," ",0,"-2*(e*n*(e*log(d*sqrt(x) + e)/d^2 - sqrt(x)/d) - x*log(c*(d + e/sqrt(x))^n))*a*b + (n^2*x*log(d*sqrt(x) + e)^2 - integrate(-(d*x*log(c)^2 + e*sqrt(x)*log(c)^2 - (d*n*x - 2*d*x*log(c) - 2*e*sqrt(x)*log(c) + 2*(d*x + e*sqrt(x))*log(x^(1/2*n)))*n*log(d*sqrt(x) + e) + (d*x + e*sqrt(x))*log(x^(1/2*n))^2 - 2*(d*x*log(c) + e*sqrt(x)*log(c))*log(x^(1/2*n)))/(d*x + e*sqrt(x)), x))*b^2 + a^2*x","F",0
432,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))^2/x,x, algorithm=""maxima"")","b^{2} n^{2} \log\left(d \sqrt{x} + e\right)^{2} \log\left(x\right) - \int \frac{{\left(b^{2} d n x \log\left(x\right) - 2 \, {\left(b^{2} d \log\left(c\right) + a b d\right)} x + 2 \, {\left(b^{2} d x + b^{2} e \sqrt{x}\right)} \log\left(x^{\frac{1}{2} \, n}\right) - 2 \, {\left(b^{2} e \log\left(c\right) + a b e\right)} \sqrt{x}\right)} n \log\left(d \sqrt{x} + e\right) - {\left(b^{2} d x + b^{2} e \sqrt{x}\right)} \log\left(x^{\frac{1}{2} \, n}\right)^{2} - {\left(b^{2} d \log\left(c\right)^{2} + 2 \, a b d \log\left(c\right) + a^{2} d\right)} x + 2 \, {\left({\left(b^{2} d \log\left(c\right) + a b d\right)} x + {\left(b^{2} e \log\left(c\right) + a b e\right)} \sqrt{x}\right)} \log\left(x^{\frac{1}{2} \, n}\right) - {\left(b^{2} e \log\left(c\right)^{2} + 2 \, a b e \log\left(c\right) + a^{2} e\right)} \sqrt{x}}{d x^{2} + e x^{\frac{3}{2}}}\,{d x}"," ",0,"b^2*n^2*log(d*sqrt(x) + e)^2*log(x) - integrate(((b^2*d*n*x*log(x) - 2*(b^2*d*log(c) + a*b*d)*x + 2*(b^2*d*x + b^2*e*sqrt(x))*log(x^(1/2*n)) - 2*(b^2*e*log(c) + a*b*e)*sqrt(x))*n*log(d*sqrt(x) + e) - (b^2*d*x + b^2*e*sqrt(x))*log(x^(1/2*n))^2 - (b^2*d*log(c)^2 + 2*a*b*d*log(c) + a^2*d)*x + 2*((b^2*d*log(c) + a*b*d)*x + (b^2*e*log(c) + a*b*e)*sqrt(x))*log(x^(1/2*n)) - (b^2*e*log(c)^2 + 2*a*b*e*log(c) + a^2*e)*sqrt(x))/(d*x^2 + e*x^(3/2)), x)","F",0
433,1,248,0,0.785708," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))^2/x^2,x, algorithm=""maxima"")","a b e n {\left(\frac{2 \, d^{2} \log\left(d \sqrt{x} + e\right)}{e^{3}} - \frac{d^{2} \log\left(x\right)}{e^{3}} - \frac{2 \, d \sqrt{x} - e}{e^{2} x}\right)} + \frac{1}{4} \, {\left(4 \, e n {\left(\frac{2 \, d^{2} \log\left(d \sqrt{x} + e\right)}{e^{3}} - \frac{d^{2} \log\left(x\right)}{e^{3}} - \frac{2 \, d \sqrt{x} - e}{e^{2} x}\right)} \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right) - \frac{{\left(4 \, d^{2} x \log\left(d \sqrt{x} + e\right)^{2} + d^{2} x \log\left(x\right)^{2} - 6 \, d^{2} x \log\left(x\right) - 12 \, d e \sqrt{x} + 2 \, e^{2} - 4 \, {\left(d^{2} x \log\left(x\right) - 3 \, d^{2} x\right)} \log\left(d \sqrt{x} + e\right)\right)} n^{2}}{e^{2} x}\right)} b^{2} - \frac{b^{2} \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)^{2}}{x} - \frac{2 \, a b \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)}{x} - \frac{a^{2}}{x}"," ",0,"a*b*e*n*(2*d^2*log(d*sqrt(x) + e)/e^3 - d^2*log(x)/e^3 - (2*d*sqrt(x) - e)/(e^2*x)) + 1/4*(4*e*n*(2*d^2*log(d*sqrt(x) + e)/e^3 - d^2*log(x)/e^3 - (2*d*sqrt(x) - e)/(e^2*x))*log(c*(d + e/sqrt(x))^n) - (4*d^2*x*log(d*sqrt(x) + e)^2 + d^2*x*log(x)^2 - 6*d^2*x*log(x) - 12*d*e*sqrt(x) + 2*e^2 - 4*(d^2*x*log(x) - 3*d^2*x)*log(d*sqrt(x) + e))*n^2/(e^2*x))*b^2 - b^2*log(c*(d + e/sqrt(x))^n)^2/x - 2*a*b*log(c*(d + e/sqrt(x))^n)/x - a^2/x","A",0
434,1,321,0,0.880471," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))^2/x^3,x, algorithm=""maxima"")","\frac{1}{12} \, a b e n {\left(\frac{12 \, d^{4} \log\left(d \sqrt{x} + e\right)}{e^{5}} - \frac{6 \, d^{4} \log\left(x\right)}{e^{5}} - \frac{12 \, d^{3} x^{\frac{3}{2}} - 6 \, d^{2} e x + 4 \, d e^{2} \sqrt{x} - 3 \, e^{3}}{e^{4} x^{2}}\right)} + \frac{1}{144} \, {\left(12 \, e n {\left(\frac{12 \, d^{4} \log\left(d \sqrt{x} + e\right)}{e^{5}} - \frac{6 \, d^{4} \log\left(x\right)}{e^{5}} - \frac{12 \, d^{3} x^{\frac{3}{2}} - 6 \, d^{2} e x + 4 \, d e^{2} \sqrt{x} - 3 \, e^{3}}{e^{4} x^{2}}\right)} \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right) - \frac{{\left(72 \, d^{4} x^{2} \log\left(d \sqrt{x} + e\right)^{2} + 18 \, d^{4} x^{2} \log\left(x\right)^{2} - 150 \, d^{4} x^{2} \log\left(x\right) - 300 \, d^{3} e x^{\frac{3}{2}} + 78 \, d^{2} e^{2} x - 28 \, d e^{3} \sqrt{x} + 9 \, e^{4} - 12 \, {\left(6 \, d^{4} x^{2} \log\left(x\right) - 25 \, d^{4} x^{2}\right)} \log\left(d \sqrt{x} + e\right)\right)} n^{2}}{e^{4} x^{2}}\right)} b^{2} - \frac{b^{2} \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)^{2}}{2 \, x^{2}} - \frac{a b \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)}{x^{2}} - \frac{a^{2}}{2 \, x^{2}}"," ",0,"1/12*a*b*e*n*(12*d^4*log(d*sqrt(x) + e)/e^5 - 6*d^4*log(x)/e^5 - (12*d^3*x^(3/2) - 6*d^2*e*x + 4*d*e^2*sqrt(x) - 3*e^3)/(e^4*x^2)) + 1/144*(12*e*n*(12*d^4*log(d*sqrt(x) + e)/e^5 - 6*d^4*log(x)/e^5 - (12*d^3*x^(3/2) - 6*d^2*e*x + 4*d*e^2*sqrt(x) - 3*e^3)/(e^4*x^2))*log(c*(d + e/sqrt(x))^n) - (72*d^4*x^2*log(d*sqrt(x) + e)^2 + 18*d^4*x^2*log(x)^2 - 150*d^4*x^2*log(x) - 300*d^3*e*x^(3/2) + 78*d^2*e^2*x - 28*d*e^3*sqrt(x) + 9*e^4 - 12*(6*d^4*x^2*log(x) - 25*d^4*x^2)*log(d*sqrt(x) + e))*n^2/(e^4*x^2))*b^2 - 1/2*b^2*log(c*(d + e/sqrt(x))^n)^2/x^2 - a*b*log(c*(d + e/sqrt(x))^n)/x^2 - 1/2*a^2/x^2","A",0
435,1,387,0,0.666857," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))^2/x^4,x, algorithm=""maxima"")","\frac{1}{90} \, a b e n {\left(\frac{60 \, d^{6} \log\left(d \sqrt{x} + e\right)}{e^{7}} - \frac{30 \, d^{6} \log\left(x\right)}{e^{7}} - \frac{60 \, d^{5} x^{\frac{5}{2}} - 30 \, d^{4} e x^{2} + 20 \, d^{3} e^{2} x^{\frac{3}{2}} - 15 \, d^{2} e^{3} x + 12 \, d e^{4} \sqrt{x} - 10 \, e^{5}}{e^{6} x^{3}}\right)} + \frac{1}{5400} \, {\left(60 \, e n {\left(\frac{60 \, d^{6} \log\left(d \sqrt{x} + e\right)}{e^{7}} - \frac{30 \, d^{6} \log\left(x\right)}{e^{7}} - \frac{60 \, d^{5} x^{\frac{5}{2}} - 30 \, d^{4} e x^{2} + 20 \, d^{3} e^{2} x^{\frac{3}{2}} - 15 \, d^{2} e^{3} x + 12 \, d e^{4} \sqrt{x} - 10 \, e^{5}}{e^{6} x^{3}}\right)} \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right) - \frac{{\left(1800 \, d^{6} x^{3} \log\left(d \sqrt{x} + e\right)^{2} + 450 \, d^{6} x^{3} \log\left(x\right)^{2} - 4410 \, d^{6} x^{3} \log\left(x\right) - 8820 \, d^{5} e x^{\frac{5}{2}} + 2610 \, d^{4} e^{2} x^{2} - 1140 \, d^{3} e^{3} x^{\frac{3}{2}} + 555 \, d^{2} e^{4} x - 264 \, d e^{5} \sqrt{x} + 100 \, e^{6} - 180 \, {\left(10 \, d^{6} x^{3} \log\left(x\right) - 49 \, d^{6} x^{3}\right)} \log\left(d \sqrt{x} + e\right)\right)} n^{2}}{e^{6} x^{3}}\right)} b^{2} - \frac{b^{2} \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)^{2}}{3 \, x^{3}} - \frac{2 \, a b \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)}{3 \, x^{3}} - \frac{a^{2}}{3 \, x^{3}}"," ",0,"1/90*a*b*e*n*(60*d^6*log(d*sqrt(x) + e)/e^7 - 30*d^6*log(x)/e^7 - (60*d^5*x^(5/2) - 30*d^4*e*x^2 + 20*d^3*e^2*x^(3/2) - 15*d^2*e^3*x + 12*d*e^4*sqrt(x) - 10*e^5)/(e^6*x^3)) + 1/5400*(60*e*n*(60*d^6*log(d*sqrt(x) + e)/e^7 - 30*d^6*log(x)/e^7 - (60*d^5*x^(5/2) - 30*d^4*e*x^2 + 20*d^3*e^2*x^(3/2) - 15*d^2*e^3*x + 12*d*e^4*sqrt(x) - 10*e^5)/(e^6*x^3))*log(c*(d + e/sqrt(x))^n) - (1800*d^6*x^3*log(d*sqrt(x) + e)^2 + 450*d^6*x^3*log(x)^2 - 4410*d^6*x^3*log(x) - 8820*d^5*e*x^(5/2) + 2610*d^4*e^2*x^2 - 1140*d^3*e^3*x^(3/2) + 555*d^2*e^4*x - 264*d*e^5*sqrt(x) + 100*e^6 - 180*(10*d^6*x^3*log(x) - 49*d^6*x^3)*log(d*sqrt(x) + e))*n^2/(e^6*x^3))*b^2 - 1/3*b^2*log(c*(d + e/sqrt(x))^n)^2/x^3 - 2/3*a*b*log(c*(d + e/sqrt(x))^n)/x^3 - 1/3*a^2/x^3","A",0
436,0,0,0,0.000000," ","integrate(x*(a+b*log(c*(d+e/x^(1/2))^n))^3,x, algorithm=""maxima"")","\frac{1}{2} \, b^{3} n^{3} x^{2} \log\left(d \sqrt{x} + e\right)^{3} - \int \frac{3 \, {\left(b^{3} d n x^{2} - 4 \, {\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x^{2} - 4 \, {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{3}{2}} + 4 \, {\left(b^{3} d x^{2} + b^{3} e x^{\frac{3}{2}}\right)} \log\left(x^{\frac{1}{2} \, n}\right)\right)} n^{2} \log\left(d \sqrt{x} + e\right)^{2} + 4 \, {\left(b^{3} d x^{2} + b^{3} e x^{\frac{3}{2}}\right)} \log\left(x^{\frac{1}{2} \, n}\right)^{3} - 4 \, {\left(b^{3} d \log\left(c\right)^{3} + 3 \, a b^{2} d \log\left(c\right)^{2} + 3 \, a^{2} b d \log\left(c\right) + a^{3} d\right)} x^{2} - 12 \, {\left({\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} x^{2} + {\left(b^{3} d x^{2} + b^{3} e x^{\frac{3}{2}}\right)} \log\left(x^{\frac{1}{2} \, n}\right)^{2} + {\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} x^{\frac{3}{2}} - 2 \, {\left({\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x^{2} + {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{3}{2}}\right)} \log\left(x^{\frac{1}{2} \, n}\right)\right)} n \log\left(d \sqrt{x} + e\right) - 12 \, {\left({\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x^{2} + {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{3}{2}}\right)} \log\left(x^{\frac{1}{2} \, n}\right)^{2} - 4 \, {\left(b^{3} e \log\left(c\right)^{3} + 3 \, a b^{2} e \log\left(c\right)^{2} + 3 \, a^{2} b e \log\left(c\right) + a^{3} e\right)} x^{\frac{3}{2}} + 12 \, {\left({\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} x^{2} + {\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} x^{\frac{3}{2}}\right)} \log\left(x^{\frac{1}{2} \, n}\right)}{4 \, {\left(d x + e \sqrt{x}\right)}}\,{d x}"," ",0,"1/2*b^3*n^3*x^2*log(d*sqrt(x) + e)^3 - integrate(1/4*(3*(b^3*d*n*x^2 - 4*(b^3*d*log(c) + a*b^2*d)*x^2 - 4*(b^3*e*log(c) + a*b^2*e)*x^(3/2) + 4*(b^3*d*x^2 + b^3*e*x^(3/2))*log(x^(1/2*n)))*n^2*log(d*sqrt(x) + e)^2 + 4*(b^3*d*x^2 + b^3*e*x^(3/2))*log(x^(1/2*n))^3 - 4*(b^3*d*log(c)^3 + 3*a*b^2*d*log(c)^2 + 3*a^2*b*d*log(c) + a^3*d)*x^2 - 12*((b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*x^2 + (b^3*d*x^2 + b^3*e*x^(3/2))*log(x^(1/2*n))^2 + (b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*x^(3/2) - 2*((b^3*d*log(c) + a*b^2*d)*x^2 + (b^3*e*log(c) + a*b^2*e)*x^(3/2))*log(x^(1/2*n)))*n*log(d*sqrt(x) + e) - 12*((b^3*d*log(c) + a*b^2*d)*x^2 + (b^3*e*log(c) + a*b^2*e)*x^(3/2))*log(x^(1/2*n))^2 - 4*(b^3*e*log(c)^3 + 3*a*b^2*e*log(c)^2 + 3*a^2*b*e*log(c) + a^3*e)*x^(3/2) + 12*((b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*x^2 + (b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*x^(3/2))*log(x^(1/2*n)))/(d*x + e*sqrt(x)), x)","F",0
437,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))^3,x, algorithm=""maxima"")","b^{3} n^{3} x \log\left(d \sqrt{x} + e\right)^{3} - 3 \, {\left(e n {\left(\frac{e \log\left(d \sqrt{x} + e\right)}{d^{2}} - \frac{\sqrt{x}}{d}\right)} - x \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)\right)} a^{2} b + a^{3} x - \int \frac{3 \, {\left(b^{3} d n x - 2 \, {\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x + 2 \, {\left(b^{3} d x + b^{3} e \sqrt{x}\right)} \log\left(x^{\frac{1}{2} \, n}\right) - 2 \, {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} \sqrt{x}\right)} n^{2} \log\left(d \sqrt{x} + e\right)^{2} + 2 \, {\left(b^{3} d x + b^{3} e \sqrt{x}\right)} \log\left(x^{\frac{1}{2} \, n}\right)^{3} - 6 \, {\left({\left(b^{3} d x + b^{3} e \sqrt{x}\right)} \log\left(x^{\frac{1}{2} \, n}\right)^{2} + {\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right)\right)} x - 2 \, {\left({\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x + {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} \sqrt{x}\right)} \log\left(x^{\frac{1}{2} \, n}\right) + {\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right)\right)} \sqrt{x}\right)} n \log\left(d \sqrt{x} + e\right) - 6 \, {\left({\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x + {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} \sqrt{x}\right)} \log\left(x^{\frac{1}{2} \, n}\right)^{2} - 2 \, {\left(b^{3} d \log\left(c\right)^{3} + 3 \, a b^{2} d \log\left(c\right)^{2}\right)} x + 6 \, {\left({\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right)\right)} x + {\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right)\right)} \sqrt{x}\right)} \log\left(x^{\frac{1}{2} \, n}\right) - 2 \, {\left(b^{3} e \log\left(c\right)^{3} + 3 \, a b^{2} e \log\left(c\right)^{2}\right)} \sqrt{x}}{2 \, {\left(d x + e \sqrt{x}\right)}}\,{d x}"," ",0,"b^3*n^3*x*log(d*sqrt(x) + e)^3 - 3*(e*n*(e*log(d*sqrt(x) + e)/d^2 - sqrt(x)/d) - x*log(c*(d + e/sqrt(x))^n))*a^2*b + a^3*x - integrate(1/2*(3*(b^3*d*n*x - 2*(b^3*d*log(c) + a*b^2*d)*x + 2*(b^3*d*x + b^3*e*sqrt(x))*log(x^(1/2*n)) - 2*(b^3*e*log(c) + a*b^2*e)*sqrt(x))*n^2*log(d*sqrt(x) + e)^2 + 2*(b^3*d*x + b^3*e*sqrt(x))*log(x^(1/2*n))^3 - 6*((b^3*d*x + b^3*e*sqrt(x))*log(x^(1/2*n))^2 + (b^3*d*log(c)^2 + 2*a*b^2*d*log(c))*x - 2*((b^3*d*log(c) + a*b^2*d)*x + (b^3*e*log(c) + a*b^2*e)*sqrt(x))*log(x^(1/2*n)) + (b^3*e*log(c)^2 + 2*a*b^2*e*log(c))*sqrt(x))*n*log(d*sqrt(x) + e) - 6*((b^3*d*log(c) + a*b^2*d)*x + (b^3*e*log(c) + a*b^2*e)*sqrt(x))*log(x^(1/2*n))^2 - 2*(b^3*d*log(c)^3 + 3*a*b^2*d*log(c)^2)*x + 6*((b^3*d*log(c)^2 + 2*a*b^2*d*log(c))*x + (b^3*e*log(c)^2 + 2*a*b^2*e*log(c))*sqrt(x))*log(x^(1/2*n)) - 2*(b^3*e*log(c)^3 + 3*a*b^2*e*log(c)^2)*sqrt(x))/(d*x + e*sqrt(x)), x)","F",0
438,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))^3/x,x, algorithm=""maxima"")","b^{3} n^{3} \log\left(d \sqrt{x} + e\right)^{3} \log\left(x\right) - \int \frac{3 \, {\left(b^{3} d n x \log\left(x\right) - 2 \, {\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x + 2 \, {\left(b^{3} d x + b^{3} e \sqrt{x}\right)} \log\left(x^{\frac{1}{2} \, n}\right) - 2 \, {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} \sqrt{x}\right)} n^{2} \log\left(d \sqrt{x} + e\right)^{2} + 2 \, {\left(b^{3} d x + b^{3} e \sqrt{x}\right)} \log\left(x^{\frac{1}{2} \, n}\right)^{3} - 6 \, {\left({\left(b^{3} d x + b^{3} e \sqrt{x}\right)} \log\left(x^{\frac{1}{2} \, n}\right)^{2} + {\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} x - 2 \, {\left({\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x + {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} \sqrt{x}\right)} \log\left(x^{\frac{1}{2} \, n}\right) + {\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} \sqrt{x}\right)} n \log\left(d \sqrt{x} + e\right) - 6 \, {\left({\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x + {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} \sqrt{x}\right)} \log\left(x^{\frac{1}{2} \, n}\right)^{2} - 2 \, {\left(b^{3} d \log\left(c\right)^{3} + 3 \, a b^{2} d \log\left(c\right)^{2} + 3 \, a^{2} b d \log\left(c\right) + a^{3} d\right)} x + 6 \, {\left({\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} x + {\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} \sqrt{x}\right)} \log\left(x^{\frac{1}{2} \, n}\right) - 2 \, {\left(b^{3} e \log\left(c\right)^{3} + 3 \, a b^{2} e \log\left(c\right)^{2} + 3 \, a^{2} b e \log\left(c\right) + a^{3} e\right)} \sqrt{x}}{2 \, {\left(d x^{2} + e x^{\frac{3}{2}}\right)}}\,{d x}"," ",0,"b^3*n^3*log(d*sqrt(x) + e)^3*log(x) - integrate(1/2*(3*(b^3*d*n*x*log(x) - 2*(b^3*d*log(c) + a*b^2*d)*x + 2*(b^3*d*x + b^3*e*sqrt(x))*log(x^(1/2*n)) - 2*(b^3*e*log(c) + a*b^2*e)*sqrt(x))*n^2*log(d*sqrt(x) + e)^2 + 2*(b^3*d*x + b^3*e*sqrt(x))*log(x^(1/2*n))^3 - 6*((b^3*d*x + b^3*e*sqrt(x))*log(x^(1/2*n))^2 + (b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*x - 2*((b^3*d*log(c) + a*b^2*d)*x + (b^3*e*log(c) + a*b^2*e)*sqrt(x))*log(x^(1/2*n)) + (b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*sqrt(x))*n*log(d*sqrt(x) + e) - 6*((b^3*d*log(c) + a*b^2*d)*x + (b^3*e*log(c) + a*b^2*e)*sqrt(x))*log(x^(1/2*n))^2 - 2*(b^3*d*log(c)^3 + 3*a*b^2*d*log(c)^2 + 3*a^2*b*d*log(c) + a^3*d)*x + 6*((b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*x + (b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*sqrt(x))*log(x^(1/2*n)) - 2*(b^3*e*log(c)^3 + 3*a*b^2*e*log(c)^2 + 3*a^2*b*e*log(c) + a^3*e)*sqrt(x))/(d*x^2 + e*x^(3/2)), x)","F",0
439,1,568,0,0.821990," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))^3/x^2,x, algorithm=""maxima"")","\frac{3}{2} \, a^{2} b e n {\left(\frac{2 \, d^{2} \log\left(d \sqrt{x} + e\right)}{e^{3}} - \frac{d^{2} \log\left(x\right)}{e^{3}} - \frac{2 \, d \sqrt{x} - e}{e^{2} x}\right)} - \frac{b^{3} \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)^{3}}{x} + \frac{3}{4} \, {\left(4 \, e n {\left(\frac{2 \, d^{2} \log\left(d \sqrt{x} + e\right)}{e^{3}} - \frac{d^{2} \log\left(x\right)}{e^{3}} - \frac{2 \, d \sqrt{x} - e}{e^{2} x}\right)} \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right) - \frac{{\left(4 \, d^{2} x \log\left(d \sqrt{x} + e\right)^{2} + d^{2} x \log\left(x\right)^{2} - 6 \, d^{2} x \log\left(x\right) - 12 \, d e \sqrt{x} + 2 \, e^{2} - 4 \, {\left(d^{2} x \log\left(x\right) - 3 \, d^{2} x\right)} \log\left(d \sqrt{x} + e\right)\right)} n^{2}}{e^{2} x}\right)} a b^{2} + \frac{1}{8} \, {\left(12 \, e n {\left(\frac{2 \, d^{2} \log\left(d \sqrt{x} + e\right)}{e^{3}} - \frac{d^{2} \log\left(x\right)}{e^{3}} - \frac{2 \, d \sqrt{x} - e}{e^{2} x}\right)} \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)^{2} + e n {\left(\frac{{\left(8 \, d^{2} x \log\left(d \sqrt{x} + e\right)^{3} - d^{2} x \log\left(x\right)^{3} + 9 \, d^{2} x \log\left(x\right)^{2} - 42 \, d^{2} x \log\left(x\right) - 12 \, {\left(d^{2} x \log\left(x\right) - 3 \, d^{2} x\right)} \log\left(d \sqrt{x} + e\right)^{2} - 84 \, d e \sqrt{x} + 6 \, e^{2} + 6 \, {\left(d^{2} x \log\left(x\right)^{2} - 6 \, d^{2} x \log\left(x\right) + 14 \, d^{2} x\right)} \log\left(d \sqrt{x} + e\right)\right)} n^{2}}{e^{3} x} - \frac{6 \, {\left(4 \, d^{2} x \log\left(d \sqrt{x} + e\right)^{2} + d^{2} x \log\left(x\right)^{2} - 6 \, d^{2} x \log\left(x\right) - 12 \, d e \sqrt{x} + 2 \, e^{2} - 4 \, {\left(d^{2} x \log\left(x\right) - 3 \, d^{2} x\right)} \log\left(d \sqrt{x} + e\right)\right)} n \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)}{e^{3} x}\right)}\right)} b^{3} - \frac{3 \, a b^{2} \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)^{2}}{x} - \frac{3 \, a^{2} b \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)}{x} - \frac{a^{3}}{x}"," ",0,"3/2*a^2*b*e*n*(2*d^2*log(d*sqrt(x) + e)/e^3 - d^2*log(x)/e^3 - (2*d*sqrt(x) - e)/(e^2*x)) - b^3*log(c*(d + e/sqrt(x))^n)^3/x + 3/4*(4*e*n*(2*d^2*log(d*sqrt(x) + e)/e^3 - d^2*log(x)/e^3 - (2*d*sqrt(x) - e)/(e^2*x))*log(c*(d + e/sqrt(x))^n) - (4*d^2*x*log(d*sqrt(x) + e)^2 + d^2*x*log(x)^2 - 6*d^2*x*log(x) - 12*d*e*sqrt(x) + 2*e^2 - 4*(d^2*x*log(x) - 3*d^2*x)*log(d*sqrt(x) + e))*n^2/(e^2*x))*a*b^2 + 1/8*(12*e*n*(2*d^2*log(d*sqrt(x) + e)/e^3 - d^2*log(x)/e^3 - (2*d*sqrt(x) - e)/(e^2*x))*log(c*(d + e/sqrt(x))^n)^2 + e*n*((8*d^2*x*log(d*sqrt(x) + e)^3 - d^2*x*log(x)^3 + 9*d^2*x*log(x)^2 - 42*d^2*x*log(x) - 12*(d^2*x*log(x) - 3*d^2*x)*log(d*sqrt(x) + e)^2 - 84*d*e*sqrt(x) + 6*e^2 + 6*(d^2*x*log(x)^2 - 6*d^2*x*log(x) + 14*d^2*x)*log(d*sqrt(x) + e))*n^2/(e^3*x) - 6*(4*d^2*x*log(d*sqrt(x) + e)^2 + d^2*x*log(x)^2 - 6*d^2*x*log(x) - 12*d*e*sqrt(x) + 2*e^2 - 4*(d^2*x*log(x) - 3*d^2*x)*log(d*sqrt(x) + e))*n*log(c*(d + e/sqrt(x))^n)/(e^3*x)))*b^3 - 3*a*b^2*log(c*(d + e/sqrt(x))^n)^2/x - 3*a^2*b*log(c*(d + e/sqrt(x))^n)/x - a^3/x","B",0
440,1,732,0,0.893343," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))^3/x^3,x, algorithm=""maxima"")","\frac{1}{8} \, a^{2} b e n {\left(\frac{12 \, d^{4} \log\left(d \sqrt{x} + e\right)}{e^{5}} - \frac{6 \, d^{4} \log\left(x\right)}{e^{5}} - \frac{12 \, d^{3} x^{\frac{3}{2}} - 6 \, d^{2} e x + 4 \, d e^{2} \sqrt{x} - 3 \, e^{3}}{e^{4} x^{2}}\right)} + \frac{1}{48} \, {\left(12 \, e n {\left(\frac{12 \, d^{4} \log\left(d \sqrt{x} + e\right)}{e^{5}} - \frac{6 \, d^{4} \log\left(x\right)}{e^{5}} - \frac{12 \, d^{3} x^{\frac{3}{2}} - 6 \, d^{2} e x + 4 \, d e^{2} \sqrt{x} - 3 \, e^{3}}{e^{4} x^{2}}\right)} \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right) - \frac{{\left(72 \, d^{4} x^{2} \log\left(d \sqrt{x} + e\right)^{2} + 18 \, d^{4} x^{2} \log\left(x\right)^{2} - 150 \, d^{4} x^{2} \log\left(x\right) - 300 \, d^{3} e x^{\frac{3}{2}} + 78 \, d^{2} e^{2} x - 28 \, d e^{3} \sqrt{x} + 9 \, e^{4} - 12 \, {\left(6 \, d^{4} x^{2} \log\left(x\right) - 25 \, d^{4} x^{2}\right)} \log\left(d \sqrt{x} + e\right)\right)} n^{2}}{e^{4} x^{2}}\right)} a b^{2} + \frac{1}{576} \, {\left(72 \, e n {\left(\frac{12 \, d^{4} \log\left(d \sqrt{x} + e\right)}{e^{5}} - \frac{6 \, d^{4} \log\left(x\right)}{e^{5}} - \frac{12 \, d^{3} x^{\frac{3}{2}} - 6 \, d^{2} e x + 4 \, d e^{2} \sqrt{x} - 3 \, e^{3}}{e^{4} x^{2}}\right)} \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)^{2} + e n {\left(\frac{{\left(288 \, d^{4} x^{2} \log\left(d \sqrt{x} + e\right)^{3} - 36 \, d^{4} x^{2} \log\left(x\right)^{3} + 450 \, d^{4} x^{2} \log\left(x\right)^{2} - 2490 \, d^{4} x^{2} \log\left(x\right) - 4980 \, d^{3} e x^{\frac{3}{2}} + 690 \, d^{2} e^{2} x - 148 \, d e^{3} \sqrt{x} + 27 \, e^{4} - 72 \, {\left(6 \, d^{4} x^{2} \log\left(x\right) - 25 \, d^{4} x^{2}\right)} \log\left(d \sqrt{x} + e\right)^{2} + 12 \, {\left(18 \, d^{4} x^{2} \log\left(x\right)^{2} - 150 \, d^{4} x^{2} \log\left(x\right) + 415 \, d^{4} x^{2}\right)} \log\left(d \sqrt{x} + e\right)\right)} n^{2}}{e^{5} x^{2}} - \frac{12 \, {\left(72 \, d^{4} x^{2} \log\left(d \sqrt{x} + e\right)^{2} + 18 \, d^{4} x^{2} \log\left(x\right)^{2} - 150 \, d^{4} x^{2} \log\left(x\right) - 300 \, d^{3} e x^{\frac{3}{2}} + 78 \, d^{2} e^{2} x - 28 \, d e^{3} \sqrt{x} + 9 \, e^{4} - 12 \, {\left(6 \, d^{4} x^{2} \log\left(x\right) - 25 \, d^{4} x^{2}\right)} \log\left(d \sqrt{x} + e\right)\right)} n \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)}{e^{5} x^{2}}\right)}\right)} b^{3} - \frac{b^{3} \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)^{3}}{2 \, x^{2}} - \frac{3 \, a b^{2} \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)^{2}}{2 \, x^{2}} - \frac{3 \, a^{2} b \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)}{2 \, x^{2}} - \frac{a^{3}}{2 \, x^{2}}"," ",0,"1/8*a^2*b*e*n*(12*d^4*log(d*sqrt(x) + e)/e^5 - 6*d^4*log(x)/e^5 - (12*d^3*x^(3/2) - 6*d^2*e*x + 4*d*e^2*sqrt(x) - 3*e^3)/(e^4*x^2)) + 1/48*(12*e*n*(12*d^4*log(d*sqrt(x) + e)/e^5 - 6*d^4*log(x)/e^5 - (12*d^3*x^(3/2) - 6*d^2*e*x + 4*d*e^2*sqrt(x) - 3*e^3)/(e^4*x^2))*log(c*(d + e/sqrt(x))^n) - (72*d^4*x^2*log(d*sqrt(x) + e)^2 + 18*d^4*x^2*log(x)^2 - 150*d^4*x^2*log(x) - 300*d^3*e*x^(3/2) + 78*d^2*e^2*x - 28*d*e^3*sqrt(x) + 9*e^4 - 12*(6*d^4*x^2*log(x) - 25*d^4*x^2)*log(d*sqrt(x) + e))*n^2/(e^4*x^2))*a*b^2 + 1/576*(72*e*n*(12*d^4*log(d*sqrt(x) + e)/e^5 - 6*d^4*log(x)/e^5 - (12*d^3*x^(3/2) - 6*d^2*e*x + 4*d*e^2*sqrt(x) - 3*e^3)/(e^4*x^2))*log(c*(d + e/sqrt(x))^n)^2 + e*n*((288*d^4*x^2*log(d*sqrt(x) + e)^3 - 36*d^4*x^2*log(x)^3 + 450*d^4*x^2*log(x)^2 - 2490*d^4*x^2*log(x) - 4980*d^3*e*x^(3/2) + 690*d^2*e^2*x - 148*d*e^3*sqrt(x) + 27*e^4 - 72*(6*d^4*x^2*log(x) - 25*d^4*x^2)*log(d*sqrt(x) + e)^2 + 12*(18*d^4*x^2*log(x)^2 - 150*d^4*x^2*log(x) + 415*d^4*x^2)*log(d*sqrt(x) + e))*n^2/(e^5*x^2) - 12*(72*d^4*x^2*log(d*sqrt(x) + e)^2 + 18*d^4*x^2*log(x)^2 - 150*d^4*x^2*log(x) - 300*d^3*e*x^(3/2) + 78*d^2*e^2*x - 28*d*e^3*sqrt(x) + 9*e^4 - 12*(6*d^4*x^2*log(x) - 25*d^4*x^2)*log(d*sqrt(x) + e))*n*log(c*(d + e/sqrt(x))^n)/(e^5*x^2)))*b^3 - 1/2*b^3*log(c*(d + e/sqrt(x))^n)^3/x^2 - 3/2*a*b^2*log(c*(d + e/sqrt(x))^n)^2/x^2 - 3/2*a^2*b*log(c*(d + e/sqrt(x))^n)/x^2 - 1/2*a^3/x^2","A",0
441,1,864,0,1.068479," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))^3/x^4,x, algorithm=""maxima"")","\frac{1}{60} \, a^{2} b e n {\left(\frac{60 \, d^{6} \log\left(d \sqrt{x} + e\right)}{e^{7}} - \frac{30 \, d^{6} \log\left(x\right)}{e^{7}} - \frac{60 \, d^{5} x^{\frac{5}{2}} - 30 \, d^{4} e x^{2} + 20 \, d^{3} e^{2} x^{\frac{3}{2}} - 15 \, d^{2} e^{3} x + 12 \, d e^{4} \sqrt{x} - 10 \, e^{5}}{e^{6} x^{3}}\right)} + \frac{1}{1800} \, {\left(60 \, e n {\left(\frac{60 \, d^{6} \log\left(d \sqrt{x} + e\right)}{e^{7}} - \frac{30 \, d^{6} \log\left(x\right)}{e^{7}} - \frac{60 \, d^{5} x^{\frac{5}{2}} - 30 \, d^{4} e x^{2} + 20 \, d^{3} e^{2} x^{\frac{3}{2}} - 15 \, d^{2} e^{3} x + 12 \, d e^{4} \sqrt{x} - 10 \, e^{5}}{e^{6} x^{3}}\right)} \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right) - \frac{{\left(1800 \, d^{6} x^{3} \log\left(d \sqrt{x} + e\right)^{2} + 450 \, d^{6} x^{3} \log\left(x\right)^{2} - 4410 \, d^{6} x^{3} \log\left(x\right) - 8820 \, d^{5} e x^{\frac{5}{2}} + 2610 \, d^{4} e^{2} x^{2} - 1140 \, d^{3} e^{3} x^{\frac{3}{2}} + 555 \, d^{2} e^{4} x - 264 \, d e^{5} \sqrt{x} + 100 \, e^{6} - 180 \, {\left(10 \, d^{6} x^{3} \log\left(x\right) - 49 \, d^{6} x^{3}\right)} \log\left(d \sqrt{x} + e\right)\right)} n^{2}}{e^{6} x^{3}}\right)} a b^{2} + \frac{1}{108000} \, {\left(1800 \, e n {\left(\frac{60 \, d^{6} \log\left(d \sqrt{x} + e\right)}{e^{7}} - \frac{30 \, d^{6} \log\left(x\right)}{e^{7}} - \frac{60 \, d^{5} x^{\frac{5}{2}} - 30 \, d^{4} e x^{2} + 20 \, d^{3} e^{2} x^{\frac{3}{2}} - 15 \, d^{2} e^{3} x + 12 \, d e^{4} \sqrt{x} - 10 \, e^{5}}{e^{6} x^{3}}\right)} \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)^{2} + e n {\left(\frac{{\left(36000 \, d^{6} x^{3} \log\left(d \sqrt{x} + e\right)^{3} - 4500 \, d^{6} x^{3} \log\left(x\right)^{3} + 66150 \, d^{6} x^{3} \log\left(x\right)^{2} - 404670 \, d^{6} x^{3} \log\left(x\right) - 809340 \, d^{5} e x^{\frac{5}{2}} + 140070 \, d^{4} e^{2} x^{2} - 41180 \, d^{3} e^{3} x^{\frac{3}{2}} + 13785 \, d^{2} e^{4} x - 4368 \, d e^{5} \sqrt{x} + 1000 \, e^{6} - 5400 \, {\left(10 \, d^{6} x^{3} \log\left(x\right) - 49 \, d^{6} x^{3}\right)} \log\left(d \sqrt{x} + e\right)^{2} + 60 \, {\left(450 \, d^{6} x^{3} \log\left(x\right)^{2} - 4410 \, d^{6} x^{3} \log\left(x\right) + 13489 \, d^{6} x^{3}\right)} \log\left(d \sqrt{x} + e\right)\right)} n^{2}}{e^{7} x^{3}} - \frac{60 \, {\left(1800 \, d^{6} x^{3} \log\left(d \sqrt{x} + e\right)^{2} + 450 \, d^{6} x^{3} \log\left(x\right)^{2} - 4410 \, d^{6} x^{3} \log\left(x\right) - 8820 \, d^{5} e x^{\frac{5}{2}} + 2610 \, d^{4} e^{2} x^{2} - 1140 \, d^{3} e^{3} x^{\frac{3}{2}} + 555 \, d^{2} e^{4} x - 264 \, d e^{5} \sqrt{x} + 100 \, e^{6} - 180 \, {\left(10 \, d^{6} x^{3} \log\left(x\right) - 49 \, d^{6} x^{3}\right)} \log\left(d \sqrt{x} + e\right)\right)} n \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)}{e^{7} x^{3}}\right)}\right)} b^{3} - \frac{b^{3} \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)^{3}}{3 \, x^{3}} - \frac{a b^{2} \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)^{2}}{x^{3}} - \frac{a^{2} b \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{n}\right)}{x^{3}} - \frac{a^{3}}{3 \, x^{3}}"," ",0,"1/60*a^2*b*e*n*(60*d^6*log(d*sqrt(x) + e)/e^7 - 30*d^6*log(x)/e^7 - (60*d^5*x^(5/2) - 30*d^4*e*x^2 + 20*d^3*e^2*x^(3/2) - 15*d^2*e^3*x + 12*d*e^4*sqrt(x) - 10*e^5)/(e^6*x^3)) + 1/1800*(60*e*n*(60*d^6*log(d*sqrt(x) + e)/e^7 - 30*d^6*log(x)/e^7 - (60*d^5*x^(5/2) - 30*d^4*e*x^2 + 20*d^3*e^2*x^(3/2) - 15*d^2*e^3*x + 12*d*e^4*sqrt(x) - 10*e^5)/(e^6*x^3))*log(c*(d + e/sqrt(x))^n) - (1800*d^6*x^3*log(d*sqrt(x) + e)^2 + 450*d^6*x^3*log(x)^2 - 4410*d^6*x^3*log(x) - 8820*d^5*e*x^(5/2) + 2610*d^4*e^2*x^2 - 1140*d^3*e^3*x^(3/2) + 555*d^2*e^4*x - 264*d*e^5*sqrt(x) + 100*e^6 - 180*(10*d^6*x^3*log(x) - 49*d^6*x^3)*log(d*sqrt(x) + e))*n^2/(e^6*x^3))*a*b^2 + 1/108000*(1800*e*n*(60*d^6*log(d*sqrt(x) + e)/e^7 - 30*d^6*log(x)/e^7 - (60*d^5*x^(5/2) - 30*d^4*e*x^2 + 20*d^3*e^2*x^(3/2) - 15*d^2*e^3*x + 12*d*e^4*sqrt(x) - 10*e^5)/(e^6*x^3))*log(c*(d + e/sqrt(x))^n)^2 + e*n*((36000*d^6*x^3*log(d*sqrt(x) + e)^3 - 4500*d^6*x^3*log(x)^3 + 66150*d^6*x^3*log(x)^2 - 404670*d^6*x^3*log(x) - 809340*d^5*e*x^(5/2) + 140070*d^4*e^2*x^2 - 41180*d^3*e^3*x^(3/2) + 13785*d^2*e^4*x - 4368*d*e^5*sqrt(x) + 1000*e^6 - 5400*(10*d^6*x^3*log(x) - 49*d^6*x^3)*log(d*sqrt(x) + e)^2 + 60*(450*d^6*x^3*log(x)^2 - 4410*d^6*x^3*log(x) + 13489*d^6*x^3)*log(d*sqrt(x) + e))*n^2/(e^7*x^3) - 60*(1800*d^6*x^3*log(d*sqrt(x) + e)^2 + 450*d^6*x^3*log(x)^2 - 4410*d^6*x^3*log(x) - 8820*d^5*e*x^(5/2) + 2610*d^4*e^2*x^2 - 1140*d^3*e^3*x^(3/2) + 555*d^2*e^4*x - 264*d*e^5*sqrt(x) + 100*e^6 - 180*(10*d^6*x^3*log(x) - 49*d^6*x^3)*log(d*sqrt(x) + e))*n*log(c*(d + e/sqrt(x))^n)/(e^7*x^3)))*b^3 - 1/3*b^3*log(c*(d + e/sqrt(x))^n)^3/x^3 - a*b^2*log(c*(d + e/sqrt(x))^n)^2/x^3 - a^2*b*log(c*(d + e/sqrt(x))^n)/x^3 - 1/3*a^3/x^3","A",0
442,1,172,0,0.869414," ","integrate(x^3*(a+b*log(c*(d+e*x^(1/3))^n)),x, algorithm=""maxima"")","\frac{1}{4} \, b x^{4} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right) + \frac{1}{4} \, a x^{4} - \frac{1}{110880} \, b e n {\left(\frac{27720 \, d^{12} \log\left(e x^{\frac{1}{3}} + d\right)}{e^{13}} + \frac{2310 \, e^{11} x^{4} - 2520 \, d e^{10} x^{\frac{11}{3}} + 2772 \, d^{2} e^{9} x^{\frac{10}{3}} - 3080 \, d^{3} e^{8} x^{3} + 3465 \, d^{4} e^{7} x^{\frac{8}{3}} - 3960 \, d^{5} e^{6} x^{\frac{7}{3}} + 4620 \, d^{6} e^{5} x^{2} - 5544 \, d^{7} e^{4} x^{\frac{5}{3}} + 6930 \, d^{8} e^{3} x^{\frac{4}{3}} - 9240 \, d^{9} e^{2} x + 13860 \, d^{10} e x^{\frac{2}{3}} - 27720 \, d^{11} x^{\frac{1}{3}}}{e^{12}}\right)}"," ",0,"1/4*b*x^4*log((e*x^(1/3) + d)^n*c) + 1/4*a*x^4 - 1/110880*b*e*n*(27720*d^12*log(e*x^(1/3) + d)/e^13 + (2310*e^11*x^4 - 2520*d*e^10*x^(11/3) + 2772*d^2*e^9*x^(10/3) - 3080*d^3*e^8*x^3 + 3465*d^4*e^7*x^(8/3) - 3960*d^5*e^6*x^(7/3) + 4620*d^6*e^5*x^2 - 5544*d^7*e^4*x^(5/3) + 6930*d^8*e^3*x^(4/3) - 9240*d^9*e^2*x + 13860*d^10*e*x^(2/3) - 27720*d^11*x^(1/3))/e^12)","A",0
443,1,140,0,0.721674," ","integrate(x^2*(a+b*log(c*(d+e*x^(1/3))^n)),x, algorithm=""maxima"")","\frac{1}{3} \, b x^{3} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right) + \frac{1}{3} \, a x^{3} + \frac{1}{7560} \, b e n {\left(\frac{2520 \, d^{9} \log\left(e x^{\frac{1}{3}} + d\right)}{e^{10}} - \frac{280 \, e^{8} x^{3} - 315 \, d e^{7} x^{\frac{8}{3}} + 360 \, d^{2} e^{6} x^{\frac{7}{3}} - 420 \, d^{3} e^{5} x^{2} + 504 \, d^{4} e^{4} x^{\frac{5}{3}} - 630 \, d^{5} e^{3} x^{\frac{4}{3}} + 840 \, d^{6} e^{2} x - 1260 \, d^{7} e x^{\frac{2}{3}} + 2520 \, d^{8} x^{\frac{1}{3}}}{e^{9}}\right)}"," ",0,"1/3*b*x^3*log((e*x^(1/3) + d)^n*c) + 1/3*a*x^3 + 1/7560*b*e*n*(2520*d^9*log(e*x^(1/3) + d)/e^10 - (280*e^8*x^3 - 315*d*e^7*x^(8/3) + 360*d^2*e^6*x^(7/3) - 420*d^3*e^5*x^2 + 504*d^4*e^4*x^(5/3) - 630*d^5*e^3*x^(4/3) + 840*d^6*e^2*x - 1260*d^7*e*x^(2/3) + 2520*d^8*x^(1/3))/e^9)","A",0
444,1,106,0,0.676893," ","integrate(x*(a+b*log(c*(d+e*x^(1/3))^n)),x, algorithm=""maxima"")","-\frac{1}{120} \, b e n {\left(\frac{60 \, d^{6} \log\left(e x^{\frac{1}{3}} + d\right)}{e^{7}} + \frac{10 \, e^{5} x^{2} - 12 \, d e^{4} x^{\frac{5}{3}} + 15 \, d^{2} e^{3} x^{\frac{4}{3}} - 20 \, d^{3} e^{2} x + 30 \, d^{4} e x^{\frac{2}{3}} - 60 \, d^{5} x^{\frac{1}{3}}}{e^{6}}\right)} + \frac{1}{2} \, b x^{2} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right) + \frac{1}{2} \, a x^{2}"," ",0,"-1/120*b*e*n*(60*d^6*log(e*x^(1/3) + d)/e^7 + (10*e^5*x^2 - 12*d*e^4*x^(5/3) + 15*d^2*e^3*x^(4/3) - 20*d^3*e^2*x + 30*d^4*e*x^(2/3) - 60*d^5*x^(1/3))/e^6) + 1/2*b*x^2*log((e*x^(1/3) + d)^n*c) + 1/2*a*x^2","A",0
445,1,70,0,0.809233," ","integrate(a+b*log(c*(d+e*x^(1/3))^n),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(e n {\left(\frac{6 \, d^{3} \log\left(e x^{\frac{1}{3}} + d\right)}{e^{4}} - \frac{2 \, e^{2} x - 3 \, d e x^{\frac{2}{3}} + 6 \, d^{2} x^{\frac{1}{3}}}{e^{3}}\right)} + 6 \, x \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)\right)} b + a x"," ",0,"1/6*(e*n*(6*d^3*log(e*x^(1/3) + d)/e^4 - (2*e^2*x - 3*d*e*x^(2/3) + 6*d^2*x^(1/3))/e^3) + 6*x*log((e*x^(1/3) + d)^n*c))*b + a*x","A",0
446,1,166,0,1.499830," ","integrate((a+b*log(c*(d+e*x^(1/3))^n))/x,x, algorithm=""maxima"")","-3 \, {\left(\log\left(\frac{e x^{\frac{1}{3}}}{d} + 1\right) \log\left(x^{\frac{1}{3}}\right) + {\rm Li}_2\left(-\frac{e x^{\frac{1}{3}}}{d}\right)\right)} b n + \frac{4 \, b d^{2} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n}\right) \log\left(x\right) + 4 \, {\left(b d^{2} \log\left(c\right) + a d^{2}\right)} \log\left(x\right) + \frac{2 \, b e^{2} n x \log\left(x\right) - 3 \, b e^{2} n x}{x^{\frac{1}{3}}} - \frac{4 \, {\left(b d e n x \log\left(x\right) - 3 \, b d e n x\right)}}{x^{\frac{2}{3}}}}{4 \, d^{2}} + \frac{3 \, {\left(b e^{2} n x^{\frac{2}{3}} - 4 \, b d e n x^{\frac{1}{3}} - 2 \, {\left(b e^{2} n x^{\frac{2}{3}} - 2 \, b d e n x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3}}\right)\right)}}{4 \, d^{2}}"," ",0,"-3*(log(e*x^(1/3)/d + 1)*log(x^(1/3)) + dilog(-e*x^(1/3)/d))*b*n + 1/4*(4*b*d^2*log((e*x^(1/3) + d)^n)*log(x) + 4*(b*d^2*log(c) + a*d^2)*log(x) + (2*b*e^2*n*x*log(x) - 3*b*e^2*n*x)/x^(1/3) - 4*(b*d*e*n*x*log(x) - 3*b*d*e*n*x)/x^(2/3))/d^2 + 3/4*(b*e^2*n*x^(2/3) - 4*b*d*e*n*x^(1/3) - 2*(b*e^2*n*x^(2/3) - 2*b*d*e*n*x^(1/3))*log(x^(1/3)))/d^2","B",0
447,1,75,0,0.619768," ","integrate((a+b*log(c*(d+e*x^(1/3))^n))/x^2,x, algorithm=""maxima"")","-\frac{1}{6} \, b e n {\left(\frac{6 \, e^{2} \log\left(e x^{\frac{1}{3}} + d\right)}{d^{3}} - \frac{2 \, e^{2} \log\left(x\right)}{d^{3}} - \frac{3 \, {\left(2 \, e x^{\frac{1}{3}} - d\right)}}{d^{2} x^{\frac{2}{3}}}\right)} - \frac{b \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)}{x} - \frac{a}{x}"," ",0,"-1/6*b*e*n*(6*e^2*log(e*x^(1/3) + d)/d^3 - 2*e^2*log(x)/d^3 - 3*(2*e*x^(1/3) - d)/(d^2*x^(2/3))) - b*log((e*x^(1/3) + d)^n*c)/x - a/x","A",0
448,1,106,0,0.716626," ","integrate((a+b*log(c*(d+e*x^(1/3))^n))/x^3,x, algorithm=""maxima"")","\frac{1}{120} \, b e n {\left(\frac{60 \, e^{5} \log\left(e x^{\frac{1}{3}} + d\right)}{d^{6}} - \frac{20 \, e^{5} \log\left(x\right)}{d^{6}} - \frac{60 \, e^{4} x^{\frac{4}{3}} - 30 \, d e^{3} x + 20 \, d^{2} e^{2} x^{\frac{2}{3}} - 15 \, d^{3} e x^{\frac{1}{3}} + 12 \, d^{4}}{d^{5} x^{\frac{5}{3}}}\right)} - \frac{b \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)}{2 \, x^{2}} - \frac{a}{2 \, x^{2}}"," ",0,"1/120*b*e*n*(60*e^5*log(e*x^(1/3) + d)/d^6 - 20*e^5*log(x)/d^6 - (60*e^4*x^(4/3) - 30*d*e^3*x + 20*d^2*e^2*x^(2/3) - 15*d^3*e*x^(1/3) + 12*d^4)/(d^5*x^(5/3))) - 1/2*b*log((e*x^(1/3) + d)^n*c)/x^2 - 1/2*a/x^2","A",0
449,1,139,0,0.971771," ","integrate((a+b*log(c*(d+e*x^(1/3))^n))/x^4,x, algorithm=""maxima"")","-\frac{1}{2520} \, b e n {\left(\frac{840 \, e^{8} \log\left(e x^{\frac{1}{3}} + d\right)}{d^{9}} - \frac{280 \, e^{8} \log\left(x\right)}{d^{9}} - \frac{840 \, e^{7} x^{\frac{7}{3}} - 420 \, d e^{6} x^{2} + 280 \, d^{2} e^{5} x^{\frac{5}{3}} - 210 \, d^{3} e^{4} x^{\frac{4}{3}} + 168 \, d^{4} e^{3} x - 140 \, d^{5} e^{2} x^{\frac{2}{3}} + 120 \, d^{6} e x^{\frac{1}{3}} - 105 \, d^{7}}{d^{8} x^{\frac{8}{3}}}\right)} - \frac{b \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)}{3 \, x^{3}} - \frac{a}{3 \, x^{3}}"," ",0,"-1/2520*b*e*n*(840*e^8*log(e*x^(1/3) + d)/d^9 - 280*e^8*log(x)/d^9 - (840*e^7*x^(7/3) - 420*d*e^6*x^2 + 280*d^2*e^5*x^(5/3) - 210*d^3*e^4*x^(4/3) + 168*d^4*e^3*x - 140*d^5*e^2*x^(2/3) + 120*d^6*e*x^(1/3) - 105*d^7)/(d^8*x^(8/3))) - 1/3*b*log((e*x^(1/3) + d)^n*c)/x^3 - 1/3*a/x^3","A",0
450,1,424,0,0.587889," ","integrate(x^2*(a+b*log(c*(d+e*x^(1/3))^n))^2,x, algorithm=""maxima"")","\frac{1}{3} \, b^{2} x^{3} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)^{2} + \frac{2}{3} \, a b x^{3} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right) + \frac{1}{3} \, a^{2} x^{3} + \frac{1}{3780} \, a b e n {\left(\frac{2520 \, d^{9} \log\left(e x^{\frac{1}{3}} + d\right)}{e^{10}} - \frac{280 \, e^{8} x^{3} - 315 \, d e^{7} x^{\frac{8}{3}} + 360 \, d^{2} e^{6} x^{\frac{7}{3}} - 420 \, d^{3} e^{5} x^{2} + 504 \, d^{4} e^{4} x^{\frac{5}{3}} - 630 \, d^{5} e^{3} x^{\frac{4}{3}} + 840 \, d^{6} e^{2} x - 1260 \, d^{7} e x^{\frac{2}{3}} + 2520 \, d^{8} x^{\frac{1}{3}}}{e^{9}}\right)} + \frac{1}{9525600} \, {\left(2520 \, e n {\left(\frac{2520 \, d^{9} \log\left(e x^{\frac{1}{3}} + d\right)}{e^{10}} - \frac{280 \, e^{8} x^{3} - 315 \, d e^{7} x^{\frac{8}{3}} + 360 \, d^{2} e^{6} x^{\frac{7}{3}} - 420 \, d^{3} e^{5} x^{2} + 504 \, d^{4} e^{4} x^{\frac{5}{3}} - 630 \, d^{5} e^{3} x^{\frac{4}{3}} + 840 \, d^{6} e^{2} x - 1260 \, d^{7} e x^{\frac{2}{3}} + 2520 \, d^{8} x^{\frac{1}{3}}}{e^{9}}\right)} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right) + \frac{{\left(78400 \, e^{9} x^{3} - 187425 \, d e^{8} x^{\frac{8}{3}} + 343800 \, d^{2} e^{7} x^{\frac{7}{3}} - 577500 \, d^{3} e^{6} x^{2} - 3175200 \, d^{9} \log\left(e x^{\frac{1}{3}} + d\right)^{2} + 947016 \, d^{4} e^{5} x^{\frac{5}{3}} - 1580670 \, d^{5} e^{4} x^{\frac{4}{3}} + 2813160 \, d^{6} e^{3} x - 17965080 \, d^{9} \log\left(e x^{\frac{1}{3}} + d\right) - 5807340 \, d^{7} e^{2} x^{\frac{2}{3}} + 17965080 \, d^{8} e x^{\frac{1}{3}}\right)} n^{2}}{e^{9}}\right)} b^{2}"," ",0,"1/3*b^2*x^3*log((e*x^(1/3) + d)^n*c)^2 + 2/3*a*b*x^3*log((e*x^(1/3) + d)^n*c) + 1/3*a^2*x^3 + 1/3780*a*b*e*n*(2520*d^9*log(e*x^(1/3) + d)/e^10 - (280*e^8*x^3 - 315*d*e^7*x^(8/3) + 360*d^2*e^6*x^(7/3) - 420*d^3*e^5*x^2 + 504*d^4*e^4*x^(5/3) - 630*d^5*e^3*x^(4/3) + 840*d^6*e^2*x - 1260*d^7*e*x^(2/3) + 2520*d^8*x^(1/3))/e^9) + 1/9525600*(2520*e*n*(2520*d^9*log(e*x^(1/3) + d)/e^10 - (280*e^8*x^3 - 315*d*e^7*x^(8/3) + 360*d^2*e^6*x^(7/3) - 420*d^3*e^5*x^2 + 504*d^4*e^4*x^(5/3) - 630*d^5*e^3*x^(4/3) + 840*d^6*e^2*x - 1260*d^7*e*x^(2/3) + 2520*d^8*x^(1/3))/e^9)*log((e*x^(1/3) + d)^n*c) + (78400*e^9*x^3 - 187425*d*e^8*x^(8/3) + 343800*d^2*e^7*x^(7/3) - 577500*d^3*e^6*x^2 - 3175200*d^9*log(e*x^(1/3) + d)^2 + 947016*d^4*e^5*x^(5/3) - 1580670*d^5*e^4*x^(4/3) + 2813160*d^6*e^3*x - 17965080*d^9*log(e*x^(1/3) + d) - 5807340*d^7*e^2*x^(2/3) + 17965080*d^8*e*x^(1/3))*n^2/e^9)*b^2","A",0
451,1,323,0,0.553426," ","integrate(x*(a+b*log(c*(d+e*x^(1/3))^n))^2,x, algorithm=""maxima"")","\frac{1}{2} \, b^{2} x^{2} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)^{2} - \frac{1}{60} \, a b e n {\left(\frac{60 \, d^{6} \log\left(e x^{\frac{1}{3}} + d\right)}{e^{7}} + \frac{10 \, e^{5} x^{2} - 12 \, d e^{4} x^{\frac{5}{3}} + 15 \, d^{2} e^{3} x^{\frac{4}{3}} - 20 \, d^{3} e^{2} x + 30 \, d^{4} e x^{\frac{2}{3}} - 60 \, d^{5} x^{\frac{1}{3}}}{e^{6}}\right)} + a b x^{2} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right) + \frac{1}{2} \, a^{2} x^{2} - \frac{1}{3600} \, {\left(60 \, e n {\left(\frac{60 \, d^{6} \log\left(e x^{\frac{1}{3}} + d\right)}{e^{7}} + \frac{10 \, e^{5} x^{2} - 12 \, d e^{4} x^{\frac{5}{3}} + 15 \, d^{2} e^{3} x^{\frac{4}{3}} - 20 \, d^{3} e^{2} x + 30 \, d^{4} e x^{\frac{2}{3}} - 60 \, d^{5} x^{\frac{1}{3}}}{e^{6}}\right)} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right) - \frac{{\left(100 \, e^{6} x^{2} + 1800 \, d^{6} \log\left(e x^{\frac{1}{3}} + d\right)^{2} - 264 \, d e^{5} x^{\frac{5}{3}} + 555 \, d^{2} e^{4} x^{\frac{4}{3}} - 1140 \, d^{3} e^{3} x + 8820 \, d^{6} \log\left(e x^{\frac{1}{3}} + d\right) + 2610 \, d^{4} e^{2} x^{\frac{2}{3}} - 8820 \, d^{5} e x^{\frac{1}{3}}\right)} n^{2}}{e^{6}}\right)} b^{2}"," ",0,"1/2*b^2*x^2*log((e*x^(1/3) + d)^n*c)^2 - 1/60*a*b*e*n*(60*d^6*log(e*x^(1/3) + d)/e^7 + (10*e^5*x^2 - 12*d*e^4*x^(5/3) + 15*d^2*e^3*x^(4/3) - 20*d^3*e^2*x + 30*d^4*e*x^(2/3) - 60*d^5*x^(1/3))/e^6) + a*b*x^2*log((e*x^(1/3) + d)^n*c) + 1/2*a^2*x^2 - 1/3600*(60*e*n*(60*d^6*log(e*x^(1/3) + d)/e^7 + (10*e^5*x^2 - 12*d*e^4*x^(5/3) + 15*d^2*e^3*x^(4/3) - 20*d^3*e^2*x + 30*d^4*e*x^(2/3) - 60*d^5*x^(1/3))/e^6)*log((e*x^(1/3) + d)^n*c) - (100*e^6*x^2 + 1800*d^6*log(e*x^(1/3) + d)^2 - 264*d*e^5*x^(5/3) + 555*d^2*e^4*x^(4/3) - 1140*d^3*e^3*x + 8820*d^6*log(e*x^(1/3) + d) + 2610*d^4*e^2*x^(2/3) - 8820*d^5*e*x^(1/3))*n^2/e^6)*b^2","A",0
452,1,217,0,0.567443," ","integrate((a+b*log(c*(d+e*x^(1/3))^n))^2,x, algorithm=""maxima"")","\frac{1}{3} \, {\left(e n {\left(\frac{6 \, d^{3} \log\left(e x^{\frac{1}{3}} + d\right)}{e^{4}} - \frac{2 \, e^{2} x - 3 \, d e x^{\frac{2}{3}} + 6 \, d^{2} x^{\frac{1}{3}}}{e^{3}}\right)} + 6 \, x \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)\right)} a b + \frac{1}{18} \, {\left(6 \, e n {\left(\frac{6 \, d^{3} \log\left(e x^{\frac{1}{3}} + d\right)}{e^{4}} - \frac{2 \, e^{2} x - 3 \, d e x^{\frac{2}{3}} + 6 \, d^{2} x^{\frac{1}{3}}}{e^{3}}\right)} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right) + 18 \, x \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)^{2} - \frac{{\left(18 \, d^{3} \log\left(e x^{\frac{1}{3}} + d\right)^{2} - 4 \, e^{3} x + 66 \, d^{3} \log\left(e x^{\frac{1}{3}} + d\right) + 15 \, d e^{2} x^{\frac{2}{3}} - 66 \, d^{2} e x^{\frac{1}{3}}\right)} n^{2}}{e^{3}}\right)} b^{2} + a^{2} x"," ",0,"1/3*(e*n*(6*d^3*log(e*x^(1/3) + d)/e^4 - (2*e^2*x - 3*d*e*x^(2/3) + 6*d^2*x^(1/3))/e^3) + 6*x*log((e*x^(1/3) + d)^n*c))*a*b + 1/18*(6*e*n*(6*d^3*log(e*x^(1/3) + d)/e^4 - (2*e^2*x - 3*d*e*x^(2/3) + 6*d^2*x^(1/3))/e^3)*log((e*x^(1/3) + d)^n*c) + 18*x*log((e*x^(1/3) + d)^n*c)^2 - (18*d^3*log(e*x^(1/3) + d)^2 - 4*e^3*x + 66*d^3*log(e*x^(1/3) + d) + 15*d*e^2*x^(2/3) - 66*d^2*e*x^(1/3))*n^2/e^3)*b^2 + a^2*x","A",0
453,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(1/3))^n))^2/x,x, algorithm=""maxima"")","b^{2} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n}\right)^{2} \log\left(x\right) + \int \frac{3 \, {\left(b^{2} e \log\left(c\right)^{2} + 2 \, a b e \log\left(c\right) + a^{2} e\right)} x - 2 \, {\left(b^{2} e n x \log\left(x\right) - 3 \, {\left(b^{2} e \log\left(c\right) + a b e\right)} x - 3 \, {\left(b^{2} d \log\left(c\right) + a b d\right)} x^{\frac{2}{3}}\right)} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n}\right) + 3 \, {\left(b^{2} d \log\left(c\right)^{2} + 2 \, a b d \log\left(c\right) + a^{2} d\right)} x^{\frac{2}{3}}}{3 \, {\left(e x^{2} + d x^{\frac{5}{3}}\right)}}\,{d x}"," ",0,"b^2*log((e*x^(1/3) + d)^n)^2*log(x) + integrate(1/3*(3*(b^2*e*log(c)^2 + 2*a*b*e*log(c) + a^2*e)*x - 2*(b^2*e*n*x*log(x) - 3*(b^2*e*log(c) + a*b*e)*x - 3*(b^2*d*log(c) + a*b*d)*x^(2/3))*log((e*x^(1/3) + d)^n) + 3*(b^2*d*log(c)^2 + 2*a*b*d*log(c) + a^2*d)*x^(2/3))/(e*x^2 + d*x^(5/3)), x)","F",0
454,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(1/3))^n))^2/x^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(\log\left(\frac{e x^{\frac{1}{3}}}{d} + 1\right) \log\left(x^{\frac{1}{3}}\right) + {\rm Li}_2\left(-\frac{e x^{\frac{1}{3}}}{d}\right)\right)} b^{2} e^{3} n^{2}}{d^{3}} - \frac{{\left(2 \, a b e^{3} n - {\left(3 \, e^{3} n^{2} - 2 \, e^{3} n \log\left(c\right)\right)} b^{2}\right)} \log\left(e x^{\frac{1}{3}} + d\right)}{d^{3}} + \frac{2 \, {\left(b^{2} e^{3} n \log\left(c\right) + a b e^{3} n\right)} \log\left(x^{\frac{1}{3}}\right)}{d^{3}} + \frac{b^{2} e^{6} n^{2} x - b^{2} d^{3} e^{3} n^{2} \log\left(x\right)}{d^{6}} - \frac{12 \, b^{2} e^{8} n^{2} x^{\frac{5}{3}} - 15 \, b^{2} d e^{7} n^{2} x^{\frac{4}{3}} + 20 \, b^{2} d^{2} e^{6} n^{2} x - 40 \, b^{2} d^{3} e^{5} n^{2} x^{\frac{2}{3}} + 100 \, b^{2} d^{4} e^{4} n^{2} x^{\frac{1}{3}} + 20 \, {\left(b^{2} d^{3} e^{5} n^{2} x^{\frac{2}{3}} - 2 \, b^{2} d^{4} e^{4} n^{2} x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3}}\right)}{20 \, d^{8}} + \frac{60 \, b^{2} d^{5} e^{3} n^{2} x^{\frac{5}{3}} \log\left(e x^{\frac{1}{3}} + d\right)^{2} - 45 \, b^{2} d e^{7} n^{2} x^{3} - 40 \, b^{2} d^{4} e^{4} n^{2} x^{2} \log\left(x\right) + 300 \, b^{2} d^{4} e^{4} n^{2} x^{2} - 60 \, b^{2} d^{8} x^{\frac{2}{3}} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n}\right)^{2} - 60 \, {\left(b^{2} d^{7} e n \log\left(c\right) + a b d^{7} e n\right)} x - 20 \, {\left(6 \, b^{2} d^{5} e^{3} n x^{\frac{5}{3}} \log\left(e x^{\frac{1}{3}} + d\right) - 6 \, b^{2} d^{6} e^{2} n x^{\frac{4}{3}} + 3 \, b^{2} d^{7} e n x - 2 \, {\left(b^{2} d^{5} e^{3} n x \log\left(x\right) - 3 \, b^{2} d^{8} \log\left(c\right) - 3 \, a b d^{8}\right)} x^{\frac{2}{3}}\right)} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n}\right) - 60 \, {\left(b^{2} d^{8} \log\left(c\right)^{2} + 2 \, a b d^{8} \log\left(c\right) + a^{2} d^{8}\right)} x^{\frac{2}{3}} + 4 \, {\left(9 \, b^{2} e^{8} n^{2} x^{3} + 5 \, b^{2} d^{3} e^{5} n^{2} x^{2} \log\left(x\right) - 15 \, b^{2} d^{3} e^{5} n^{2} x^{2} + 30 \, {\left(b^{2} d^{6} e^{2} n \log\left(c\right) + a b d^{6} e^{2} n\right)} x\right)} x^{\frac{1}{3}} - \frac{60 \, {\left(b^{2} d^{3} e^{5} n^{2} x^{3} + b^{2} d^{6} e^{2} n^{2} x^{2}\right)}}{x^{\frac{2}{3}}}}{60 \, d^{8} x^{\frac{5}{3}}}"," ",0,"-2*(log(e*x^(1/3)/d + 1)*log(x^(1/3)) + dilog(-e*x^(1/3)/d))*b^2*e^3*n^2/d^3 - (2*a*b*e^3*n - (3*e^3*n^2 - 2*e^3*n*log(c))*b^2)*log(e*x^(1/3) + d)/d^3 + 2*(b^2*e^3*n*log(c) + a*b*e^3*n)*log(x^(1/3))/d^3 + integrate((b^2*e^6*n^2*x - b^2*d^3*e^3*n^2)/x, x)/d^6 - 1/20*(12*b^2*e^8*n^2*x^(5/3) - 15*b^2*d*e^7*n^2*x^(4/3) + 20*b^2*d^2*e^6*n^2*x - 40*b^2*d^3*e^5*n^2*x^(2/3) + 100*b^2*d^4*e^4*n^2*x^(1/3) + 20*(b^2*d^3*e^5*n^2*x^(2/3) - 2*b^2*d^4*e^4*n^2*x^(1/3))*log(x^(1/3)))/d^8 + 1/60*(60*b^2*d^5*e^3*n^2*x^(5/3)*log(e*x^(1/3) + d)^2 - 45*b^2*d*e^7*n^2*x^3 - 40*b^2*d^4*e^4*n^2*x^2*log(x) + 300*b^2*d^4*e^4*n^2*x^2 - 60*b^2*d^8*x^(2/3)*log((e*x^(1/3) + d)^n)^2 - 60*(b^2*d^7*e*n*log(c) + a*b*d^7*e*n)*x - 20*(6*b^2*d^5*e^3*n*x^(5/3)*log(e*x^(1/3) + d) - 6*b^2*d^6*e^2*n*x^(4/3) + 3*b^2*d^7*e*n*x - 2*(b^2*d^5*e^3*n*x*log(x) - 3*b^2*d^8*log(c) - 3*a*b*d^8)*x^(2/3))*log((e*x^(1/3) + d)^n) - 60*(b^2*d^8*log(c)^2 + 2*a*b*d^8*log(c) + a^2*d^8)*x^(2/3) + 4*(9*b^2*e^8*n^2*x^3 + 5*b^2*d^3*e^5*n^2*x^2*log(x) - 15*b^2*d^3*e^5*n^2*x^2 + 30*(b^2*d^6*e^2*n*log(c) + a*b*d^6*e^2*n)*x)*x^(1/3) - 60*(b^2*d^3*e^5*n^2*x^3 + b^2*d^6*e^2*n^2*x^2)/x^(2/3))/(d^8*x^(5/3))","F",0
455,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(1/3))^n))^2/x^3,x, algorithm=""maxima"")","-\frac{b^{2} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n}\right)^{2}}{2 \, x^{2}} + \int \frac{3 \, {\left(b^{2} e \log\left(c\right)^{2} + 2 \, a b e \log\left(c\right) + a^{2} e\right)} x + {\left(b^{2} e n x + 6 \, {\left(b^{2} e \log\left(c\right) + a b e\right)} x + 6 \, {\left(b^{2} d \log\left(c\right) + a b d\right)} x^{\frac{2}{3}}\right)} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n}\right) + 3 \, {\left(b^{2} d \log\left(c\right)^{2} + 2 \, a b d \log\left(c\right) + a^{2} d\right)} x^{\frac{2}{3}}}{3 \, {\left(e x^{4} + d x^{\frac{11}{3}}\right)}}\,{d x}"," ",0,"-1/2*b^2*log((e*x^(1/3) + d)^n)^2/x^2 + integrate(1/3*(3*(b^2*e*log(c)^2 + 2*a*b*e*log(c) + a^2*e)*x + (b^2*e*n*x + 6*(b^2*e*log(c) + a*b*e)*x + 6*(b^2*d*log(c) + a*b*d)*x^(2/3))*log((e*x^(1/3) + d)^n) + 3*(b^2*d*log(c)^2 + 2*a*b*d*log(c) + a^2*d)*x^(2/3))/(e*x^4 + d*x^(11/3)), x)","F",0
456,1,1064,0,0.675890," ","integrate(x^3*(a+b*log(c*(d+e*x^(1/3))^n))^3,x, algorithm=""maxima"")","\frac{1}{4} \, b^{3} x^{4} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)^{3} + \frac{3}{4} \, a b^{2} x^{4} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)^{2} + \frac{3}{4} \, a^{2} b x^{4} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right) + \frac{1}{4} \, a^{3} x^{4} - \frac{1}{36960} \, a^{2} b e n {\left(\frac{27720 \, d^{12} \log\left(e x^{\frac{1}{3}} + d\right)}{e^{13}} + \frac{2310 \, e^{11} x^{4} - 2520 \, d e^{10} x^{\frac{11}{3}} + 2772 \, d^{2} e^{9} x^{\frac{10}{3}} - 3080 \, d^{3} e^{8} x^{3} + 3465 \, d^{4} e^{7} x^{\frac{8}{3}} - 3960 \, d^{5} e^{6} x^{\frac{7}{3}} + 4620 \, d^{6} e^{5} x^{2} - 5544 \, d^{7} e^{4} x^{\frac{5}{3}} + 6930 \, d^{8} e^{3} x^{\frac{4}{3}} - 9240 \, d^{9} e^{2} x + 13860 \, d^{10} e x^{\frac{2}{3}} - 27720 \, d^{11} x^{\frac{1}{3}}}{e^{12}}\right)} - \frac{1}{512265600} \, {\left(27720 \, e n {\left(\frac{27720 \, d^{12} \log\left(e x^{\frac{1}{3}} + d\right)}{e^{13}} + \frac{2310 \, e^{11} x^{4} - 2520 \, d e^{10} x^{\frac{11}{3}} + 2772 \, d^{2} e^{9} x^{\frac{10}{3}} - 3080 \, d^{3} e^{8} x^{3} + 3465 \, d^{4} e^{7} x^{\frac{8}{3}} - 3960 \, d^{5} e^{6} x^{\frac{7}{3}} + 4620 \, d^{6} e^{5} x^{2} - 5544 \, d^{7} e^{4} x^{\frac{5}{3}} + 6930 \, d^{8} e^{3} x^{\frac{4}{3}} - 9240 \, d^{9} e^{2} x + 13860 \, d^{10} e x^{\frac{2}{3}} - 27720 \, d^{11} x^{\frac{1}{3}}}{e^{12}}\right)} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right) - \frac{{\left(5336100 \, e^{12} x^{4} - 12171600 \, d e^{11} x^{\frac{11}{3}} + 21072744 \, d^{2} e^{10} x^{\frac{10}{3}} - 32900560 \, d^{3} e^{9} x^{3} + 49019355 \, d^{4} e^{8} x^{\frac{8}{3}} - 71703720 \, d^{5} e^{7} x^{\frac{7}{3}} + 104998740 \, d^{6} e^{6} x^{2} + 384199200 \, d^{12} \log\left(e x^{\frac{1}{3}} + d\right)^{2} - 156734424 \, d^{7} e^{5} x^{\frac{5}{3}} + 243942930 \, d^{8} e^{4} x^{\frac{4}{3}} - 410634840 \, d^{9} e^{3} x + 2384502120 \, d^{12} \log\left(e x^{\frac{1}{3}} + d\right) + 808051860 \, d^{10} e^{2} x^{\frac{2}{3}} - 2384502120 \, d^{11} e x^{\frac{1}{3}}\right)} n^{2}}{e^{12}}\right)} a b^{2} - \frac{1}{14200002432000} \, {\left(384199200 \, e n {\left(\frac{27720 \, d^{12} \log\left(e x^{\frac{1}{3}} + d\right)}{e^{13}} + \frac{2310 \, e^{11} x^{4} - 2520 \, d e^{10} x^{\frac{11}{3}} + 2772 \, d^{2} e^{9} x^{\frac{10}{3}} - 3080 \, d^{3} e^{8} x^{3} + 3465 \, d^{4} e^{7} x^{\frac{8}{3}} - 3960 \, d^{5} e^{6} x^{\frac{7}{3}} + 4620 \, d^{6} e^{5} x^{2} - 5544 \, d^{7} e^{4} x^{\frac{5}{3}} + 6930 \, d^{8} e^{3} x^{\frac{4}{3}} - 9240 \, d^{9} e^{2} x + 13860 \, d^{10} e x^{\frac{2}{3}} - 27720 \, d^{11} x^{\frac{1}{3}}}{e^{12}}\right)} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)^{2} + e n {\left(\frac{{\left(12326391000 \, e^{12} x^{4} - 44119404000 \, d e^{11} x^{\frac{11}{3}} + 106944990768 \, d^{2} e^{10} x^{\frac{10}{3}} - 220161492320 \, d^{3} e^{9} x^{3} + 3550000608000 \, d^{12} \log\left(e x^{\frac{1}{3}} + d\right)^{3} + 417533743935 \, d^{4} e^{8} x^{\frac{8}{3}} - 761128152840 \, d^{5} e^{7} x^{\frac{7}{3}} + 1373077023780 \, d^{6} e^{6} x^{2} + 33049199383200 \, d^{12} \log\left(e x^{\frac{1}{3}} + d\right)^{2} - 2516628075192 \, d^{7} e^{5} x^{\frac{5}{3}} + 4836309598890 \, d^{8} e^{4} x^{\frac{4}{3}} - 10242678720120 \, d^{9} e^{3} x + 119225632485960 \, d^{12} \log\left(e x^{\frac{1}{3}} + d\right) + 26563616859780 \, d^{10} e^{2} x^{\frac{2}{3}} - 119225632485960 \, d^{11} e x^{\frac{1}{3}}\right)} n^{2}}{e^{13}} - \frac{27720 \, {\left(5336100 \, e^{12} x^{4} - 12171600 \, d e^{11} x^{\frac{11}{3}} + 21072744 \, d^{2} e^{10} x^{\frac{10}{3}} - 32900560 \, d^{3} e^{9} x^{3} + 49019355 \, d^{4} e^{8} x^{\frac{8}{3}} - 71703720 \, d^{5} e^{7} x^{\frac{7}{3}} + 104998740 \, d^{6} e^{6} x^{2} + 384199200 \, d^{12} \log\left(e x^{\frac{1}{3}} + d\right)^{2} - 156734424 \, d^{7} e^{5} x^{\frac{5}{3}} + 243942930 \, d^{8} e^{4} x^{\frac{4}{3}} - 410634840 \, d^{9} e^{3} x + 2384502120 \, d^{12} \log\left(e x^{\frac{1}{3}} + d\right) + 808051860 \, d^{10} e^{2} x^{\frac{2}{3}} - 2384502120 \, d^{11} e x^{\frac{1}{3}}\right)} n \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)}{e^{13}}\right)}\right)} b^{3}"," ",0,"1/4*b^3*x^4*log((e*x^(1/3) + d)^n*c)^3 + 3/4*a*b^2*x^4*log((e*x^(1/3) + d)^n*c)^2 + 3/4*a^2*b*x^4*log((e*x^(1/3) + d)^n*c) + 1/4*a^3*x^4 - 1/36960*a^2*b*e*n*(27720*d^12*log(e*x^(1/3) + d)/e^13 + (2310*e^11*x^4 - 2520*d*e^10*x^(11/3) + 2772*d^2*e^9*x^(10/3) - 3080*d^3*e^8*x^3 + 3465*d^4*e^7*x^(8/3) - 3960*d^5*e^6*x^(7/3) + 4620*d^6*e^5*x^2 - 5544*d^7*e^4*x^(5/3) + 6930*d^8*e^3*x^(4/3) - 9240*d^9*e^2*x + 13860*d^10*e*x^(2/3) - 27720*d^11*x^(1/3))/e^12) - 1/512265600*(27720*e*n*(27720*d^12*log(e*x^(1/3) + d)/e^13 + (2310*e^11*x^4 - 2520*d*e^10*x^(11/3) + 2772*d^2*e^9*x^(10/3) - 3080*d^3*e^8*x^3 + 3465*d^4*e^7*x^(8/3) - 3960*d^5*e^6*x^(7/3) + 4620*d^6*e^5*x^2 - 5544*d^7*e^4*x^(5/3) + 6930*d^8*e^3*x^(4/3) - 9240*d^9*e^2*x + 13860*d^10*e*x^(2/3) - 27720*d^11*x^(1/3))/e^12)*log((e*x^(1/3) + d)^n*c) - (5336100*e^12*x^4 - 12171600*d*e^11*x^(11/3) + 21072744*d^2*e^10*x^(10/3) - 32900560*d^3*e^9*x^3 + 49019355*d^4*e^8*x^(8/3) - 71703720*d^5*e^7*x^(7/3) + 104998740*d^6*e^6*x^2 + 384199200*d^12*log(e*x^(1/3) + d)^2 - 156734424*d^7*e^5*x^(5/3) + 243942930*d^8*e^4*x^(4/3) - 410634840*d^9*e^3*x + 2384502120*d^12*log(e*x^(1/3) + d) + 808051860*d^10*e^2*x^(2/3) - 2384502120*d^11*e*x^(1/3))*n^2/e^12)*a*b^2 - 1/14200002432000*(384199200*e*n*(27720*d^12*log(e*x^(1/3) + d)/e^13 + (2310*e^11*x^4 - 2520*d*e^10*x^(11/3) + 2772*d^2*e^9*x^(10/3) - 3080*d^3*e^8*x^3 + 3465*d^4*e^7*x^(8/3) - 3960*d^5*e^6*x^(7/3) + 4620*d^6*e^5*x^2 - 5544*d^7*e^4*x^(5/3) + 6930*d^8*e^3*x^(4/3) - 9240*d^9*e^2*x + 13860*d^10*e*x^(2/3) - 27720*d^11*x^(1/3))/e^12)*log((e*x^(1/3) + d)^n*c)^2 + e*n*((12326391000*e^12*x^4 - 44119404000*d*e^11*x^(11/3) + 106944990768*d^2*e^10*x^(10/3) - 220161492320*d^3*e^9*x^3 + 3550000608000*d^12*log(e*x^(1/3) + d)^3 + 417533743935*d^4*e^8*x^(8/3) - 761128152840*d^5*e^7*x^(7/3) + 1373077023780*d^6*e^6*x^2 + 33049199383200*d^12*log(e*x^(1/3) + d)^2 - 2516628075192*d^7*e^5*x^(5/3) + 4836309598890*d^8*e^4*x^(4/3) - 10242678720120*d^9*e^3*x + 119225632485960*d^12*log(e*x^(1/3) + d) + 26563616859780*d^10*e^2*x^(2/3) - 119225632485960*d^11*e*x^(1/3))*n^2/e^13 - 27720*(5336100*e^12*x^4 - 12171600*d*e^11*x^(11/3) + 21072744*d^2*e^10*x^(10/3) - 32900560*d^3*e^9*x^3 + 49019355*d^4*e^8*x^(8/3) - 71703720*d^5*e^7*x^(7/3) + 104998740*d^6*e^6*x^2 + 384199200*d^12*log(e*x^(1/3) + d)^2 - 156734424*d^7*e^5*x^(5/3) + 243942930*d^8*e^4*x^(4/3) - 410634840*d^9*e^3*x + 2384502120*d^12*log(e*x^(1/3) + d) + 808051860*d^10*e^2*x^(2/3) - 2384502120*d^11*e*x^(1/3))*n*log((e*x^(1/3) + d)^n*c)/e^13))*b^3","A",0
457,1,867,0,0.645376," ","integrate(x^2*(a+b*log(c*(d+e*x^(1/3))^n))^3,x, algorithm=""maxima"")","\frac{1}{3} \, b^{3} x^{3} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)^{3} + a b^{2} x^{3} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)^{2} + a^{2} b x^{3} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right) + \frac{1}{3} \, a^{3} x^{3} + \frac{1}{2520} \, a^{2} b e n {\left(\frac{2520 \, d^{9} \log\left(e x^{\frac{1}{3}} + d\right)}{e^{10}} - \frac{280 \, e^{8} x^{3} - 315 \, d e^{7} x^{\frac{8}{3}} + 360 \, d^{2} e^{6} x^{\frac{7}{3}} - 420 \, d^{3} e^{5} x^{2} + 504 \, d^{4} e^{4} x^{\frac{5}{3}} - 630 \, d^{5} e^{3} x^{\frac{4}{3}} + 840 \, d^{6} e^{2} x - 1260 \, d^{7} e x^{\frac{2}{3}} + 2520 \, d^{8} x^{\frac{1}{3}}}{e^{9}}\right)} + \frac{1}{3175200} \, {\left(2520 \, e n {\left(\frac{2520 \, d^{9} \log\left(e x^{\frac{1}{3}} + d\right)}{e^{10}} - \frac{280 \, e^{8} x^{3} - 315 \, d e^{7} x^{\frac{8}{3}} + 360 \, d^{2} e^{6} x^{\frac{7}{3}} - 420 \, d^{3} e^{5} x^{2} + 504 \, d^{4} e^{4} x^{\frac{5}{3}} - 630 \, d^{5} e^{3} x^{\frac{4}{3}} + 840 \, d^{6} e^{2} x - 1260 \, d^{7} e x^{\frac{2}{3}} + 2520 \, d^{8} x^{\frac{1}{3}}}{e^{9}}\right)} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right) + \frac{{\left(78400 \, e^{9} x^{3} - 187425 \, d e^{8} x^{\frac{8}{3}} + 343800 \, d^{2} e^{7} x^{\frac{7}{3}} - 577500 \, d^{3} e^{6} x^{2} - 3175200 \, d^{9} \log\left(e x^{\frac{1}{3}} + d\right)^{2} + 947016 \, d^{4} e^{5} x^{\frac{5}{3}} - 1580670 \, d^{5} e^{4} x^{\frac{4}{3}} + 2813160 \, d^{6} e^{3} x - 17965080 \, d^{9} \log\left(e x^{\frac{1}{3}} + d\right) - 5807340 \, d^{7} e^{2} x^{\frac{2}{3}} + 17965080 \, d^{8} e x^{\frac{1}{3}}\right)} n^{2}}{e^{9}}\right)} a b^{2} + \frac{1}{8001504000} \, {\left(3175200 \, e n {\left(\frac{2520 \, d^{9} \log\left(e x^{\frac{1}{3}} + d\right)}{e^{10}} - \frac{280 \, e^{8} x^{3} - 315 \, d e^{7} x^{\frac{8}{3}} + 360 \, d^{2} e^{6} x^{\frac{7}{3}} - 420 \, d^{3} e^{5} x^{2} + 504 \, d^{4} e^{4} x^{\frac{5}{3}} - 630 \, d^{5} e^{3} x^{\frac{4}{3}} + 840 \, d^{6} e^{2} x - 1260 \, d^{7} e x^{\frac{2}{3}} + 2520 \, d^{8} x^{\frac{1}{3}}}{e^{9}}\right)} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)^{2} - e n {\left(\frac{{\left(21952000 \, e^{9} x^{3} - 2667168000 \, d^{9} \log\left(e x^{\frac{1}{3}} + d\right)^{3} - 83734875 \, d e^{8} x^{\frac{8}{3}} + 219465000 \, d^{2} e^{7} x^{\frac{7}{3}} - 498592500 \, d^{3} e^{6} x^{2} - 22636000800 \, d^{9} \log\left(e x^{\frac{1}{3}} + d\right)^{2} + 1075607064 \, d^{4} e^{5} x^{\frac{5}{3}} - 2340330930 \, d^{5} e^{4} x^{\frac{4}{3}} + 5483495640 \, d^{6} e^{3} x - 76356985320 \, d^{9} \log\left(e x^{\frac{1}{3}} + d\right) - 15542491860 \, d^{7} e^{2} x^{\frac{2}{3}} + 76356985320 \, d^{8} e x^{\frac{1}{3}}\right)} n^{2}}{e^{10}} - \frac{2520 \, {\left(78400 \, e^{9} x^{3} - 187425 \, d e^{8} x^{\frac{8}{3}} + 343800 \, d^{2} e^{7} x^{\frac{7}{3}} - 577500 \, d^{3} e^{6} x^{2} - 3175200 \, d^{9} \log\left(e x^{\frac{1}{3}} + d\right)^{2} + 947016 \, d^{4} e^{5} x^{\frac{5}{3}} - 1580670 \, d^{5} e^{4} x^{\frac{4}{3}} + 2813160 \, d^{6} e^{3} x - 17965080 \, d^{9} \log\left(e x^{\frac{1}{3}} + d\right) - 5807340 \, d^{7} e^{2} x^{\frac{2}{3}} + 17965080 \, d^{8} e x^{\frac{1}{3}}\right)} n \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)}{e^{10}}\right)}\right)} b^{3}"," ",0,"1/3*b^3*x^3*log((e*x^(1/3) + d)^n*c)^3 + a*b^2*x^3*log((e*x^(1/3) + d)^n*c)^2 + a^2*b*x^3*log((e*x^(1/3) + d)^n*c) + 1/3*a^3*x^3 + 1/2520*a^2*b*e*n*(2520*d^9*log(e*x^(1/3) + d)/e^10 - (280*e^8*x^3 - 315*d*e^7*x^(8/3) + 360*d^2*e^6*x^(7/3) - 420*d^3*e^5*x^2 + 504*d^4*e^4*x^(5/3) - 630*d^5*e^3*x^(4/3) + 840*d^6*e^2*x - 1260*d^7*e*x^(2/3) + 2520*d^8*x^(1/3))/e^9) + 1/3175200*(2520*e*n*(2520*d^9*log(e*x^(1/3) + d)/e^10 - (280*e^8*x^3 - 315*d*e^7*x^(8/3) + 360*d^2*e^6*x^(7/3) - 420*d^3*e^5*x^2 + 504*d^4*e^4*x^(5/3) - 630*d^5*e^3*x^(4/3) + 840*d^6*e^2*x - 1260*d^7*e*x^(2/3) + 2520*d^8*x^(1/3))/e^9)*log((e*x^(1/3) + d)^n*c) + (78400*e^9*x^3 - 187425*d*e^8*x^(8/3) + 343800*d^2*e^7*x^(7/3) - 577500*d^3*e^6*x^2 - 3175200*d^9*log(e*x^(1/3) + d)^2 + 947016*d^4*e^5*x^(5/3) - 1580670*d^5*e^4*x^(4/3) + 2813160*d^6*e^3*x - 17965080*d^9*log(e*x^(1/3) + d) - 5807340*d^7*e^2*x^(2/3) + 17965080*d^8*e*x^(1/3))*n^2/e^9)*a*b^2 + 1/8001504000*(3175200*e*n*(2520*d^9*log(e*x^(1/3) + d)/e^10 - (280*e^8*x^3 - 315*d*e^7*x^(8/3) + 360*d^2*e^6*x^(7/3) - 420*d^3*e^5*x^2 + 504*d^4*e^4*x^(5/3) - 630*d^5*e^3*x^(4/3) + 840*d^6*e^2*x - 1260*d^7*e*x^(2/3) + 2520*d^8*x^(1/3))/e^9)*log((e*x^(1/3) + d)^n*c)^2 - e*n*((21952000*e^9*x^3 - 2667168000*d^9*log(e*x^(1/3) + d)^3 - 83734875*d*e^8*x^(8/3) + 219465000*d^2*e^7*x^(7/3) - 498592500*d^3*e^6*x^2 - 22636000800*d^9*log(e*x^(1/3) + d)^2 + 1075607064*d^4*e^5*x^(5/3) - 2340330930*d^5*e^4*x^(4/3) + 5483495640*d^6*e^3*x - 76356985320*d^9*log(e*x^(1/3) + d) - 15542491860*d^7*e^2*x^(2/3) + 76356985320*d^8*e*x^(1/3))*n^2/e^10 - 2520*(78400*e^9*x^3 - 187425*d*e^8*x^(8/3) + 343800*d^2*e^7*x^(7/3) - 577500*d^3*e^6*x^2 - 3175200*d^9*log(e*x^(1/3) + d)^2 + 947016*d^4*e^5*x^(5/3) - 1580670*d^5*e^4*x^(4/3) + 2813160*d^6*e^3*x - 17965080*d^9*log(e*x^(1/3) + d) - 5807340*d^7*e^2*x^(2/3) + 17965080*d^8*e*x^(1/3))*n*log((e*x^(1/3) + d)^n*c)/e^10))*b^3","A",0
458,1,668,0,0.644207," ","integrate(x*(a+b*log(c*(d+e*x^(1/3))^n))^3,x, algorithm=""maxima"")","\frac{1}{2} \, b^{3} x^{2} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)^{3} + \frac{3}{2} \, a b^{2} x^{2} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)^{2} - \frac{1}{40} \, a^{2} b e n {\left(\frac{60 \, d^{6} \log\left(e x^{\frac{1}{3}} + d\right)}{e^{7}} + \frac{10 \, e^{5} x^{2} - 12 \, d e^{4} x^{\frac{5}{3}} + 15 \, d^{2} e^{3} x^{\frac{4}{3}} - 20 \, d^{3} e^{2} x + 30 \, d^{4} e x^{\frac{2}{3}} - 60 \, d^{5} x^{\frac{1}{3}}}{e^{6}}\right)} + \frac{3}{2} \, a^{2} b x^{2} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right) + \frac{1}{2} \, a^{3} x^{2} - \frac{1}{1200} \, {\left(60 \, e n {\left(\frac{60 \, d^{6} \log\left(e x^{\frac{1}{3}} + d\right)}{e^{7}} + \frac{10 \, e^{5} x^{2} - 12 \, d e^{4} x^{\frac{5}{3}} + 15 \, d^{2} e^{3} x^{\frac{4}{3}} - 20 \, d^{3} e^{2} x + 30 \, d^{4} e x^{\frac{2}{3}} - 60 \, d^{5} x^{\frac{1}{3}}}{e^{6}}\right)} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right) - \frac{{\left(100 \, e^{6} x^{2} + 1800 \, d^{6} \log\left(e x^{\frac{1}{3}} + d\right)^{2} - 264 \, d e^{5} x^{\frac{5}{3}} + 555 \, d^{2} e^{4} x^{\frac{4}{3}} - 1140 \, d^{3} e^{3} x + 8820 \, d^{6} \log\left(e x^{\frac{1}{3}} + d\right) + 2610 \, d^{4} e^{2} x^{\frac{2}{3}} - 8820 \, d^{5} e x^{\frac{1}{3}}\right)} n^{2}}{e^{6}}\right)} a b^{2} - \frac{1}{72000} \, {\left(1800 \, e n {\left(\frac{60 \, d^{6} \log\left(e x^{\frac{1}{3}} + d\right)}{e^{7}} + \frac{10 \, e^{5} x^{2} - 12 \, d e^{4} x^{\frac{5}{3}} + 15 \, d^{2} e^{3} x^{\frac{4}{3}} - 20 \, d^{3} e^{2} x + 30 \, d^{4} e x^{\frac{2}{3}} - 60 \, d^{5} x^{\frac{1}{3}}}{e^{6}}\right)} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)^{2} + e n {\left(\frac{{\left(36000 \, d^{6} \log\left(e x^{\frac{1}{3}} + d\right)^{3} + 1000 \, e^{6} x^{2} + 264600 \, d^{6} \log\left(e x^{\frac{1}{3}} + d\right)^{2} - 4368 \, d e^{5} x^{\frac{5}{3}} + 13785 \, d^{2} e^{4} x^{\frac{4}{3}} - 41180 \, d^{3} e^{3} x + 809340 \, d^{6} \log\left(e x^{\frac{1}{3}} + d\right) + 140070 \, d^{4} e^{2} x^{\frac{2}{3}} - 809340 \, d^{5} e x^{\frac{1}{3}}\right)} n^{2}}{e^{7}} - \frac{60 \, {\left(100 \, e^{6} x^{2} + 1800 \, d^{6} \log\left(e x^{\frac{1}{3}} + d\right)^{2} - 264 \, d e^{5} x^{\frac{5}{3}} + 555 \, d^{2} e^{4} x^{\frac{4}{3}} - 1140 \, d^{3} e^{3} x + 8820 \, d^{6} \log\left(e x^{\frac{1}{3}} + d\right) + 2610 \, d^{4} e^{2} x^{\frac{2}{3}} - 8820 \, d^{5} e x^{\frac{1}{3}}\right)} n \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)}{e^{7}}\right)}\right)} b^{3}"," ",0,"1/2*b^3*x^2*log((e*x^(1/3) + d)^n*c)^3 + 3/2*a*b^2*x^2*log((e*x^(1/3) + d)^n*c)^2 - 1/40*a^2*b*e*n*(60*d^6*log(e*x^(1/3) + d)/e^7 + (10*e^5*x^2 - 12*d*e^4*x^(5/3) + 15*d^2*e^3*x^(4/3) - 20*d^3*e^2*x + 30*d^4*e*x^(2/3) - 60*d^5*x^(1/3))/e^6) + 3/2*a^2*b*x^2*log((e*x^(1/3) + d)^n*c) + 1/2*a^3*x^2 - 1/1200*(60*e*n*(60*d^6*log(e*x^(1/3) + d)/e^7 + (10*e^5*x^2 - 12*d*e^4*x^(5/3) + 15*d^2*e^3*x^(4/3) - 20*d^3*e^2*x + 30*d^4*e*x^(2/3) - 60*d^5*x^(1/3))/e^6)*log((e*x^(1/3) + d)^n*c) - (100*e^6*x^2 + 1800*d^6*log(e*x^(1/3) + d)^2 - 264*d*e^5*x^(5/3) + 555*d^2*e^4*x^(4/3) - 1140*d^3*e^3*x + 8820*d^6*log(e*x^(1/3) + d) + 2610*d^4*e^2*x^(2/3) - 8820*d^5*e*x^(1/3))*n^2/e^6)*a*b^2 - 1/72000*(1800*e*n*(60*d^6*log(e*x^(1/3) + d)/e^7 + (10*e^5*x^2 - 12*d*e^4*x^(5/3) + 15*d^2*e^3*x^(4/3) - 20*d^3*e^2*x + 30*d^4*e*x^(2/3) - 60*d^5*x^(1/3))/e^6)*log((e*x^(1/3) + d)^n*c)^2 + e*n*((36000*d^6*log(e*x^(1/3) + d)^3 + 1000*e^6*x^2 + 264600*d^6*log(e*x^(1/3) + d)^2 - 4368*d*e^5*x^(5/3) + 13785*d^2*e^4*x^(4/3) - 41180*d^3*e^3*x + 809340*d^6*log(e*x^(1/3) + d) + 140070*d^4*e^2*x^(2/3) - 809340*d^5*e*x^(1/3))*n^2/e^7 - 60*(100*e^6*x^2 + 1800*d^6*log(e*x^(1/3) + d)^2 - 264*d*e^5*x^(5/3) + 555*d^2*e^4*x^(4/3) - 1140*d^3*e^3*x + 8820*d^6*log(e*x^(1/3) + d) + 2610*d^4*e^2*x^(2/3) - 8820*d^5*e*x^(1/3))*n*log((e*x^(1/3) + d)^n*c)/e^7))*b^3","A",0
459,1,455,0,0.613123," ","integrate((a+b*log(c*(d+e*x^(1/3))^n))^3,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(e n {\left(\frac{6 \, d^{3} \log\left(e x^{\frac{1}{3}} + d\right)}{e^{4}} - \frac{2 \, e^{2} x - 3 \, d e x^{\frac{2}{3}} + 6 \, d^{2} x^{\frac{1}{3}}}{e^{3}}\right)} + 6 \, x \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)\right)} a^{2} b + \frac{1}{6} \, {\left(6 \, e n {\left(\frac{6 \, d^{3} \log\left(e x^{\frac{1}{3}} + d\right)}{e^{4}} - \frac{2 \, e^{2} x - 3 \, d e x^{\frac{2}{3}} + 6 \, d^{2} x^{\frac{1}{3}}}{e^{3}}\right)} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right) + 18 \, x \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)^{2} - \frac{{\left(18 \, d^{3} \log\left(e x^{\frac{1}{3}} + d\right)^{2} - 4 \, e^{3} x + 66 \, d^{3} \log\left(e x^{\frac{1}{3}} + d\right) + 15 \, d e^{2} x^{\frac{2}{3}} - 66 \, d^{2} e x^{\frac{1}{3}}\right)} n^{2}}{e^{3}}\right)} a b^{2} + \frac{1}{36} \, {\left(18 \, e n {\left(\frac{6 \, d^{3} \log\left(e x^{\frac{1}{3}} + d\right)}{e^{4}} - \frac{2 \, e^{2} x - 3 \, d e x^{\frac{2}{3}} + 6 \, d^{2} x^{\frac{1}{3}}}{e^{3}}\right)} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)^{2} + 36 \, x \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)^{3} + e n {\left(\frac{{\left(36 \, d^{3} \log\left(e x^{\frac{1}{3}} + d\right)^{3} + 198 \, d^{3} \log\left(e x^{\frac{1}{3}} + d\right)^{2} - 8 \, e^{3} x + 510 \, d^{3} \log\left(e x^{\frac{1}{3}} + d\right) + 57 \, d e^{2} x^{\frac{2}{3}} - 510 \, d^{2} e x^{\frac{1}{3}}\right)} n^{2}}{e^{4}} - \frac{6 \, {\left(18 \, d^{3} \log\left(e x^{\frac{1}{3}} + d\right)^{2} - 4 \, e^{3} x + 66 \, d^{3} \log\left(e x^{\frac{1}{3}} + d\right) + 15 \, d e^{2} x^{\frac{2}{3}} - 66 \, d^{2} e x^{\frac{1}{3}}\right)} n \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)}{e^{4}}\right)}\right)} b^{3} + a^{3} x"," ",0,"1/2*(e*n*(6*d^3*log(e*x^(1/3) + d)/e^4 - (2*e^2*x - 3*d*e*x^(2/3) + 6*d^2*x^(1/3))/e^3) + 6*x*log((e*x^(1/3) + d)^n*c))*a^2*b + 1/6*(6*e*n*(6*d^3*log(e*x^(1/3) + d)/e^4 - (2*e^2*x - 3*d*e*x^(2/3) + 6*d^2*x^(1/3))/e^3)*log((e*x^(1/3) + d)^n*c) + 18*x*log((e*x^(1/3) + d)^n*c)^2 - (18*d^3*log(e*x^(1/3) + d)^2 - 4*e^3*x + 66*d^3*log(e*x^(1/3) + d) + 15*d*e^2*x^(2/3) - 66*d^2*e*x^(1/3))*n^2/e^3)*a*b^2 + 1/36*(18*e*n*(6*d^3*log(e*x^(1/3) + d)/e^4 - (2*e^2*x - 3*d*e*x^(2/3) + 6*d^2*x^(1/3))/e^3)*log((e*x^(1/3) + d)^n*c)^2 + 36*x*log((e*x^(1/3) + d)^n*c)^3 + e*n*((36*d^3*log(e*x^(1/3) + d)^3 + 198*d^3*log(e*x^(1/3) + d)^2 - 8*e^3*x + 510*d^3*log(e*x^(1/3) + d) + 57*d*e^2*x^(2/3) - 510*d^2*e*x^(1/3))*n^2/e^4 - 6*(18*d^3*log(e*x^(1/3) + d)^2 - 4*e^3*x + 66*d^3*log(e*x^(1/3) + d) + 15*d*e^2*x^(2/3) - 66*d^2*e*x^(1/3))*n*log((e*x^(1/3) + d)^n*c)/e^4))*b^3 + a^3*x","A",0
460,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(1/3))^n))^3/x,x, algorithm=""maxima"")","b^{3} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n}\right)^{3} \log\left(x\right) + \int -\frac{{\left(b^{3} e n x \log\left(x\right) - 3 \, {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x - 3 \, {\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x^{\frac{2}{3}}\right)} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n}\right)^{2} - {\left(b^{3} e \log\left(c\right)^{3} + 3 \, a b^{2} e \log\left(c\right)^{2} + 3 \, a^{2} b e \log\left(c\right) + a^{3} e\right)} x - 3 \, {\left({\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} x + {\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} x^{\frac{2}{3}}\right)} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n}\right) - {\left(b^{3} d \log\left(c\right)^{3} + 3 \, a b^{2} d \log\left(c\right)^{2} + 3 \, a^{2} b d \log\left(c\right) + a^{3} d\right)} x^{\frac{2}{3}}}{e x^{2} + d x^{\frac{5}{3}}}\,{d x}"," ",0,"b^3*log((e*x^(1/3) + d)^n)^3*log(x) + integrate(-((b^3*e*n*x*log(x) - 3*(b^3*e*log(c) + a*b^2*e)*x - 3*(b^3*d*log(c) + a*b^2*d)*x^(2/3))*log((e*x^(1/3) + d)^n)^2 - (b^3*e*log(c)^3 + 3*a*b^2*e*log(c)^2 + 3*a^2*b*e*log(c) + a^3*e)*x - 3*((b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*x + (b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*x^(2/3))*log((e*x^(1/3) + d)^n) - (b^3*d*log(c)^3 + 3*a*b^2*d*log(c)^2 + 3*a^2*b*d*log(c) + a^3*d)*x^(2/3))/(e*x^2 + d*x^(5/3)), x)","F",0
461,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(1/3))^n))^3/x^2,x, algorithm=""maxima"")","-\frac{2 \, b^{3} d^{3} x^{\frac{2}{3}} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n}\right)^{3} + {\left(6 \, b^{3} e^{3} n x^{\frac{5}{3}} \log\left(e x^{\frac{1}{3}} + d\right) - 6 \, b^{3} d e^{2} n x^{\frac{4}{3}} + 3 \, b^{3} d^{2} e n x - 2 \, {\left(b^{3} e^{3} n x \log\left(x\right) - 3 \, b^{3} d^{3} \log\left(c\right) - 3 \, a b^{2} d^{3}\right)} x^{\frac{2}{3}}\right)} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n}\right)^{2}}{2 \, d^{3} x^{\frac{5}{3}}} + \int \frac{3 \, {\left(b^{3} d^{3} e \log\left(c\right)^{3} + 3 \, a b^{2} d^{3} e \log\left(c\right)^{2} + 3 \, a^{2} b d^{3} e \log\left(c\right) + a^{3} d^{3} e\right)} x^{\frac{5}{3}} + 3 \, {\left(b^{3} d^{4} \log\left(c\right)^{3} + 3 \, a b^{2} d^{4} \log\left(c\right)^{2} + 3 \, a^{2} b d^{4} \log\left(c\right) + a^{3} d^{4}\right)} x^{\frac{4}{3}} + {\left(6 \, b^{3} e^{4} n^{2} x^{\frac{8}{3}} \log\left(e x^{\frac{1}{3}} + d\right) - 6 \, b^{3} d e^{3} n^{2} x^{\frac{7}{3}} + 3 \, b^{3} d^{2} e^{2} n^{2} x^{2} + 9 \, {\left(b^{3} d^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} d^{3} e \log\left(c\right) + a^{2} b d^{3} e\right)} x^{\frac{5}{3}} + 9 \, {\left(b^{3} d^{4} \log\left(c\right)^{2} + 2 \, a b^{2} d^{4} \log\left(c\right) + a^{2} b d^{4}\right)} x^{\frac{4}{3}} - 2 \, {\left(b^{3} e^{4} n^{2} x^{2} \log\left(x\right) - 3 \, {\left(b^{3} d^{3} e n \log\left(c\right) + a b^{2} d^{3} e n\right)} x\right)} x^{\frac{2}{3}}\right)} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n}\right)}{3 \, {\left(d^{3} e x^{\frac{11}{3}} + d^{4} x^{\frac{10}{3}}\right)}}\,{d x}"," ",0,"-1/2*(2*b^3*d^3*x^(2/3)*log((e*x^(1/3) + d)^n)^3 + (6*b^3*e^3*n*x^(5/3)*log(e*x^(1/3) + d) - 6*b^3*d*e^2*n*x^(4/3) + 3*b^3*d^2*e*n*x - 2*(b^3*e^3*n*x*log(x) - 3*b^3*d^3*log(c) - 3*a*b^2*d^3)*x^(2/3))*log((e*x^(1/3) + d)^n)^2)/(d^3*x^(5/3)) + integrate(1/3*(3*(b^3*d^3*e*log(c)^3 + 3*a*b^2*d^3*e*log(c)^2 + 3*a^2*b*d^3*e*log(c) + a^3*d^3*e)*x^(5/3) + 3*(b^3*d^4*log(c)^3 + 3*a*b^2*d^4*log(c)^2 + 3*a^2*b*d^4*log(c) + a^3*d^4)*x^(4/3) + (6*b^3*e^4*n^2*x^(8/3)*log(e*x^(1/3) + d) - 6*b^3*d*e^3*n^2*x^(7/3) + 3*b^3*d^2*e^2*n^2*x^2 + 9*(b^3*d^3*e*log(c)^2 + 2*a*b^2*d^3*e*log(c) + a^2*b*d^3*e)*x^(5/3) + 9*(b^3*d^4*log(c)^2 + 2*a*b^2*d^4*log(c) + a^2*b*d^4)*x^(4/3) - 2*(b^3*e^4*n^2*x^2*log(x) - 3*(b^3*d^3*e*n*log(c) + a*b^2*d^3*e*n)*x)*x^(2/3))*log((e*x^(1/3) + d)^n))/(d^3*e*x^(11/3) + d^4*x^(10/3)), x)","F",0
462,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(1/3))^n))^3/x^3,x, algorithm=""maxima"")","-\frac{b^{3} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n}\right)^{3}}{2 \, x^{2}} + \int \frac{{\left(b^{3} e n x + 6 \, {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x + 6 \, {\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x^{\frac{2}{3}}\right)} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n}\right)^{2} + 2 \, {\left(b^{3} e \log\left(c\right)^{3} + 3 \, a b^{2} e \log\left(c\right)^{2} + 3 \, a^{2} b e \log\left(c\right) + a^{3} e\right)} x + 6 \, {\left({\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} x + {\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} x^{\frac{2}{3}}\right)} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n}\right) + 2 \, {\left(b^{3} d \log\left(c\right)^{3} + 3 \, a b^{2} d \log\left(c\right)^{2} + 3 \, a^{2} b d \log\left(c\right) + a^{3} d\right)} x^{\frac{2}{3}}}{2 \, {\left(e x^{4} + d x^{\frac{11}{3}}\right)}}\,{d x}"," ",0,"-1/2*b^3*log((e*x^(1/3) + d)^n)^3/x^2 + integrate(1/2*((b^3*e*n*x + 6*(b^3*e*log(c) + a*b^2*e)*x + 6*(b^3*d*log(c) + a*b^2*d)*x^(2/3))*log((e*x^(1/3) + d)^n)^2 + 2*(b^3*e*log(c)^3 + 3*a*b^2*e*log(c)^2 + 3*a^2*b*e*log(c) + a^3*e)*x + 6*((b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*x + (b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*x^(2/3))*log((e*x^(1/3) + d)^n) + 2*(b^3*d*log(c)^3 + 3*a*b^2*d*log(c)^2 + 3*a^2*b*d*log(c) + a^3*d)*x^(2/3))/(e*x^4 + d*x^(11/3)), x)","F",0
463,1,108,0,0.486052," ","integrate(x^3*(a+b*log(c*(d+e*x^(2/3))^n)),x, algorithm=""maxima"")","\frac{1}{4} \, b x^{4} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right) + \frac{1}{4} \, a x^{4} - \frac{1}{240} \, b e n {\left(\frac{60 \, d^{6} \log\left(e x^{\frac{2}{3}} + d\right)}{e^{7}} + \frac{10 \, e^{5} x^{4} - 12 \, d e^{4} x^{\frac{10}{3}} + 15 \, d^{2} e^{3} x^{\frac{8}{3}} - 20 \, d^{3} e^{2} x^{2} + 30 \, d^{4} e x^{\frac{4}{3}} - 60 \, d^{5} x^{\frac{2}{3}}}{e^{6}}\right)}"," ",0,"1/4*b*x^4*log((e*x^(2/3) + d)^n*c) + 1/4*a*x^4 - 1/240*b*e*n*(60*d^6*log(e*x^(2/3) + d)/e^7 + (10*e^5*x^4 - 12*d*e^4*x^(10/3) + 15*d^2*e^3*x^(8/3) - 20*d^3*e^2*x^2 + 30*d^4*e*x^(4/3) - 60*d^5*x^(2/3))/e^6)","A",0
464,1,104,0,1.003894," ","integrate(x^2*(a+b*log(c*(d+e*x^(2/3))^n)),x, algorithm=""maxima"")","\frac{1}{3} \, b x^{3} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right) + \frac{1}{3} \, a x^{3} + \frac{2}{945} \, b e n {\left(\frac{315 \, d^{5} \arctan\left(\frac{e x^{\frac{1}{3}}}{\sqrt{d e}}\right)}{\sqrt{d e} e^{5}} - \frac{35 \, e^{4} x^{3} - 45 \, d e^{3} x^{\frac{7}{3}} + 63 \, d^{2} e^{2} x^{\frac{5}{3}} - 105 \, d^{3} e x + 315 \, d^{4} x^{\frac{1}{3}}}{e^{5}}\right)}"," ",0,"1/3*b*x^3*log((e*x^(2/3) + d)^n*c) + 1/3*a*x^3 + 2/945*b*e*n*(315*d^5*arctan(e*x^(1/3)/sqrt(d*e))/(sqrt(d*e)*e^5) - (35*e^4*x^3 - 45*d*e^3*x^(7/3) + 63*d^2*e^2*x^(5/3) - 105*d^3*e*x + 315*d^4*x^(1/3))/e^5)","A",0
465,1,76,0,0.476205," ","integrate(x*(a+b*log(c*(d+e*x^(2/3))^n)),x, algorithm=""maxima"")","\frac{1}{12} \, b e n {\left(\frac{6 \, d^{3} \log\left(e x^{\frac{2}{3}} + d\right)}{e^{4}} - \frac{2 \, e^{2} x^{2} - 3 \, d e x^{\frac{4}{3}} + 6 \, d^{2} x^{\frac{2}{3}}}{e^{3}}\right)} + \frac{1}{2} \, b x^{2} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right) + \frac{1}{2} \, a x^{2}"," ",0,"1/12*b*e*n*(6*d^3*log(e*x^(2/3) + d)/e^4 - (2*e^2*x^2 - 3*d*e*x^(4/3) + 6*d^2*x^(2/3))/e^3) + 1/2*b*x^2*log((e*x^(2/3) + d)^n*c) + 1/2*a*x^2","A",0
466,1,66,0,0.996859," ","integrate(a+b*log(c*(d+e*x^(2/3))^n),x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(2 \, e n {\left(\frac{3 \, d^{2} \arctan\left(\frac{e x^{\frac{1}{3}}}{\sqrt{d e}}\right)}{\sqrt{d e} e^{2}} + \frac{e x - 3 \, d x^{\frac{1}{3}}}{e^{2}}\right)} - 3 \, x \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)\right)} b + a x"," ",0,"-1/3*(2*e*n*(3*d^2*arctan(e*x^(1/3)/sqrt(d*e))/(sqrt(d*e)*e^2) + (e*x - 3*d*x^(1/3))/e^2) - 3*x*log((e*x^(2/3) + d)^n*c))*b + a*x","A",0
467,1,113,0,1.008343," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))/x,x, algorithm=""maxima"")","-\frac{3}{2} \, {\left(2 \, \log\left(\frac{e x^{\frac{2}{3}}}{d} + 1\right) \log\left(x^{\frac{1}{3}}\right) + {\rm Li}_2\left(-\frac{e x^{\frac{2}{3}}}{d}\right)\right)} b n + \frac{2 \, b d n \log\left(e x^{\frac{2}{3}} + d\right) \log\left(x\right) + 2 \, {\left(b d \log\left(c\right) + a d\right)} \log\left(x\right) - \frac{2 \, b e n x \log\left(x\right) - 3 \, b e n x}{x^{\frac{1}{3}}}}{2 \, d} + \frac{3 \, {\left(2 \, b e n x^{\frac{2}{3}} \log\left(x^{\frac{1}{3}}\right) - b e n x^{\frac{2}{3}}\right)}}{2 \, d}"," ",0,"-3/2*(2*log(e*x^(2/3)/d + 1)*log(x^(1/3)) + dilog(-e*x^(2/3)/d))*b*n + 1/2*(2*b*d*n*log(e*x^(2/3) + d)*log(x) + 2*(b*d*log(c) + a*d)*log(x) - (2*b*e*n*x*log(x) - 3*b*e*n*x)/x^(1/3))/d + 3/2*(2*b*e*n*x^(2/3)*log(x^(1/3)) - b*e*n*x^(2/3))/d","B",0
468,1,59,0,1.008654," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))/x^2,x, algorithm=""maxima"")","-2 \, b e n {\left(\frac{e \arctan\left(\frac{e x^{\frac{1}{3}}}{\sqrt{d e}}\right)}{\sqrt{d e} d} + \frac{1}{d x^{\frac{1}{3}}}\right)} - \frac{b \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)}{x} - \frac{a}{x}"," ",0,"-2*b*e*n*(e*arctan(e*x^(1/3)/sqrt(d*e))/(sqrt(d*e)*d) + 1/(d*x^(1/3))) - b*log((e*x^(2/3) + d)^n*c)/x - a/x","A",0
469,1,77,0,0.483974," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))/x^3,x, algorithm=""maxima"")","-\frac{1}{4} \, b e n {\left(\frac{2 \, e^{2} \log\left(e x^{\frac{2}{3}} + d\right)}{d^{3}} - \frac{2 \, e^{2} \log\left(x^{\frac{2}{3}}\right)}{d^{3}} - \frac{2 \, e x^{\frac{2}{3}} - d}{d^{2} x^{\frac{4}{3}}}\right)} - \frac{b \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)}{2 \, x^{2}} - \frac{a}{2 \, x^{2}}"," ",0,"-1/4*b*e*n*(2*e^2*log(e*x^(2/3) + d)/d^3 - 2*e^2*log(x^(2/3))/d^3 - (2*e*x^(2/3) - d)/(d^2*x^(4/3))) - 1/2*b*log((e*x^(2/3) + d)^n*c)/x^2 - 1/2*a/x^2","A",0
470,1,94,0,1.017328," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))/x^4,x, algorithm=""maxima"")","\frac{2}{315} \, b e n {\left(\frac{105 \, e^{4} \arctan\left(\frac{e x^{\frac{1}{3}}}{\sqrt{d e}}\right)}{\sqrt{d e} d^{4}} + \frac{105 \, e^{3} x^{2} - 35 \, d e^{2} x^{\frac{4}{3}} + 21 \, d^{2} e x^{\frac{2}{3}} - 15 \, d^{3}}{d^{4} x^{\frac{7}{3}}}\right)} - \frac{b \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)}{3 \, x^{3}} - \frac{a}{3 \, x^{3}}"," ",0,"2/315*b*e*n*(105*e^4*arctan(e*x^(1/3)/sqrt(d*e))/(sqrt(d*e)*d^4) + (105*e^3*x^2 - 35*d*e^2*x^(4/3) + 21*d^2*e*x^(2/3) - 15*d^3)/(d^4*x^(7/3))) - 1/3*b*log((e*x^(2/3) + d)^n*c)/x^3 - 1/3*a/x^3","A",0
471,1,330,0,0.524261," ","integrate(x^3*(a+b*log(c*(d+e*x^(2/3))^n))^2,x, algorithm=""maxima"")","\frac{1}{4} \, b^{2} x^{4} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{2} + \frac{1}{2} \, a b x^{4} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right) + \frac{1}{4} \, a^{2} x^{4} - \frac{1}{120} \, a b e n {\left(\frac{60 \, d^{6} \log\left(e x^{\frac{2}{3}} + d\right)}{e^{7}} + \frac{10 \, e^{5} x^{4} - 12 \, d e^{4} x^{\frac{10}{3}} + 15 \, d^{2} e^{3} x^{\frac{8}{3}} - 20 \, d^{3} e^{2} x^{2} + 30 \, d^{4} e x^{\frac{4}{3}} - 60 \, d^{5} x^{\frac{2}{3}}}{e^{6}}\right)} - \frac{1}{7200} \, {\left(60 \, e n {\left(\frac{60 \, d^{6} \log\left(e x^{\frac{2}{3}} + d\right)}{e^{7}} + \frac{10 \, e^{5} x^{4} - 12 \, d e^{4} x^{\frac{10}{3}} + 15 \, d^{2} e^{3} x^{\frac{8}{3}} - 20 \, d^{3} e^{2} x^{2} + 30 \, d^{4} e x^{\frac{4}{3}} - 60 \, d^{5} x^{\frac{2}{3}}}{e^{6}}\right)} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right) - \frac{{\left(100 \, e^{6} x^{4} - 264 \, d e^{5} x^{\frac{10}{3}} + 555 \, d^{2} e^{4} x^{\frac{8}{3}} - 1140 \, d^{3} e^{3} x^{2} + 1800 \, d^{6} \log\left(e x^{\frac{2}{3}} + d\right)^{2} + 2610 \, d^{4} e^{2} x^{\frac{4}{3}} + 8820 \, d^{6} \log\left(e x^{\frac{2}{3}} + d\right) - 8820 \, d^{5} e x^{\frac{2}{3}}\right)} n^{2}}{e^{6}}\right)} b^{2}"," ",0,"1/4*b^2*x^4*log((e*x^(2/3) + d)^n*c)^2 + 1/2*a*b*x^4*log((e*x^(2/3) + d)^n*c) + 1/4*a^2*x^4 - 1/120*a*b*e*n*(60*d^6*log(e*x^(2/3) + d)/e^7 + (10*e^5*x^4 - 12*d*e^4*x^(10/3) + 15*d^2*e^3*x^(8/3) - 20*d^3*e^2*x^2 + 30*d^4*e*x^(4/3) - 60*d^5*x^(2/3))/e^6) - 1/7200*(60*e*n*(60*d^6*log(e*x^(2/3) + d)/e^7 + (10*e^5*x^4 - 12*d*e^4*x^(10/3) + 15*d^2*e^3*x^(8/3) - 20*d^3*e^2*x^2 + 30*d^4*e*x^(4/3) - 60*d^5*x^(2/3))/e^6)*log((e*x^(2/3) + d)^n*c) - (100*e^6*x^4 - 264*d*e^5*x^(10/3) + 555*d^2*e^4*x^(8/3) - 1140*d^3*e^3*x^2 + 1800*d^6*log(e*x^(2/3) + d)^2 + 2610*d^4*e^2*x^(4/3) + 8820*d^6*log(e*x^(2/3) + d) - 8820*d^5*e*x^(2/3))*n^2/e^6)*b^2","A",0
472,1,231,0,0.510161," ","integrate(x*(a+b*log(c*(d+e*x^(2/3))^n))^2,x, algorithm=""maxima"")","\frac{1}{2} \, b^{2} x^{2} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{2} + \frac{1}{6} \, a b e n {\left(\frac{6 \, d^{3} \log\left(e x^{\frac{2}{3}} + d\right)}{e^{4}} - \frac{2 \, e^{2} x^{2} - 3 \, d e x^{\frac{4}{3}} + 6 \, d^{2} x^{\frac{2}{3}}}{e^{3}}\right)} + a b x^{2} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right) + \frac{1}{2} \, a^{2} x^{2} + \frac{1}{36} \, {\left(6 \, e n {\left(\frac{6 \, d^{3} \log\left(e x^{\frac{2}{3}} + d\right)}{e^{4}} - \frac{2 \, e^{2} x^{2} - 3 \, d e x^{\frac{4}{3}} + 6 \, d^{2} x^{\frac{2}{3}}}{e^{3}}\right)} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right) + \frac{{\left(4 \, e^{3} x^{2} - 18 \, d^{3} \log\left(e x^{\frac{2}{3}} + d\right)^{2} - 15 \, d e^{2} x^{\frac{4}{3}} - 66 \, d^{3} \log\left(e x^{\frac{2}{3}} + d\right) + 66 \, d^{2} e x^{\frac{2}{3}}\right)} n^{2}}{e^{3}}\right)} b^{2}"," ",0,"1/2*b^2*x^2*log((e*x^(2/3) + d)^n*c)^2 + 1/6*a*b*e*n*(6*d^3*log(e*x^(2/3) + d)/e^4 - (2*e^2*x^2 - 3*d*e*x^(4/3) + 6*d^2*x^(2/3))/e^3) + a*b*x^2*log((e*x^(2/3) + d)^n*c) + 1/2*a^2*x^2 + 1/36*(6*e*n*(6*d^3*log(e*x^(2/3) + d)/e^4 - (2*e^2*x^2 - 3*d*e*x^(4/3) + 6*d^2*x^(2/3))/e^3)*log((e*x^(2/3) + d)^n*c) + (4*e^3*x^2 - 18*d^3*log(e*x^(2/3) + d)^2 - 15*d*e^2*x^(4/3) - 66*d^3*log(e*x^(2/3) + d) + 66*d^2*e*x^(2/3))*n^2/e^3)*b^2","A",0
473,1,148,0,0.789115," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))^2/x,x, algorithm=""maxima"")","\frac{3}{2} \, {\left(\log\left(e x^{\frac{2}{3}} + d\right)^{2} \log\left(-\frac{e x^{\frac{2}{3}} + d}{d} + 1\right) + 2 \, {\rm Li}_2\left(\frac{e x^{\frac{2}{3}} + d}{d}\right) \log\left(e x^{\frac{2}{3}} + d\right) - 2 \, {\rm Li}_{3}(\frac{e x^{\frac{2}{3}} + d}{d})\right)} b^{2} n^{2} + a^{2} \log\left(x\right) + 3 \, {\left(b^{2} n \log\left(c\right) + a b n\right)} {\left(\log\left(e x^{\frac{2}{3}} + d\right) \log\left(-\frac{e x^{\frac{2}{3}} + d}{d} + 1\right) + {\rm Li}_2\left(\frac{e x^{\frac{2}{3}} + d}{d}\right)\right)} + {\left(b^{2} \log\left(c\right)^{2} + 2 \, a b \log\left(c\right)\right)} \log\left(x\right)"," ",0,"3/2*(log(e*x^(2/3) + d)^2*log(-(e*x^(2/3) + d)/d + 1) + 2*dilog((e*x^(2/3) + d)/d)*log(e*x^(2/3) + d) - 2*polylog(3, (e*x^(2/3) + d)/d))*b^2*n^2 + a^2*log(x) + 3*(b^2*n*log(c) + a*b*n)*(log(e*x^(2/3) + d)*log(-(e*x^(2/3) + d)/d + 1) + dilog((e*x^(2/3) + d)/d)) + (b^2*log(c)^2 + 2*a*b*log(c))*log(x)","A",0
474,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))^2/x^3,x, algorithm=""maxima"")","-\frac{b^{2} n^{2} \log\left(e x^{\frac{2}{3}} + d\right)^{2}}{2 \, x^{2}} + \int \frac{2 \, {\left(b^{2} e n x + 3 \, {\left(b^{2} e \log\left(c\right) + a b e\right)} x + 3 \, {\left(b^{2} d \log\left(c\right) + a b d\right)} x^{\frac{1}{3}}\right)} n \log\left(e x^{\frac{2}{3}} + d\right) + 3 \, {\left(b^{2} e \log\left(c\right)^{2} + 2 \, a b e \log\left(c\right) + a^{2} e\right)} x + 3 \, {\left(b^{2} d \log\left(c\right)^{2} + 2 \, a b d \log\left(c\right) + a^{2} d\right)} x^{\frac{1}{3}}}{3 \, {\left(e x^{4} + d x^{\frac{10}{3}}\right)}}\,{d x}"," ",0,"-1/2*b^2*n^2*log(e*x^(2/3) + d)^2/x^2 + integrate(1/3*(2*(b^2*e*n*x + 3*(b^2*e*log(c) + a*b*e)*x + 3*(b^2*d*log(c) + a*b*d)*x^(1/3))*n*log(e*x^(2/3) + d) + 3*(b^2*e*log(c)^2 + 2*a*b*e*log(c) + a^2*e)*x + 3*(b^2*d*log(c)^2 + 2*a*b*d*log(c) + a^2*d)*x^(1/3))/(e*x^4 + d*x^(10/3)), x)","F",0
475,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))^2/x^5,x, algorithm=""maxima"")","-\frac{b^{2} n^{2} \log\left(e x^{\frac{2}{3}} + d\right)^{2}}{4 \, x^{4}} + \int \frac{{\left(b^{2} e n x + 6 \, {\left(b^{2} e \log\left(c\right) + a b e\right)} x + 6 \, {\left(b^{2} d \log\left(c\right) + a b d\right)} x^{\frac{1}{3}}\right)} n \log\left(e x^{\frac{2}{3}} + d\right) + 3 \, {\left(b^{2} e \log\left(c\right)^{2} + 2 \, a b e \log\left(c\right) + a^{2} e\right)} x + 3 \, {\left(b^{2} d \log\left(c\right)^{2} + 2 \, a b d \log\left(c\right) + a^{2} d\right)} x^{\frac{1}{3}}}{3 \, {\left(e x^{6} + d x^{\frac{16}{3}}\right)}}\,{d x}"," ",0,"-1/4*b^2*n^2*log(e*x^(2/3) + d)^2/x^4 + integrate(1/3*((b^2*e*n*x + 6*(b^2*e*log(c) + a*b*e)*x + 6*(b^2*d*log(c) + a*b*d)*x^(1/3))*n*log(e*x^(2/3) + d) + 3*(b^2*e*log(c)^2 + 2*a*b*e*log(c) + a^2*e)*x + 3*(b^2*d*log(c)^2 + 2*a*b*d*log(c) + a^2*d)*x^(1/3))/(e*x^6 + d*x^(16/3)), x)","F",0
476,0,0,0,0.000000," ","integrate(x^2*(a+b*log(c*(d+e*x^(2/3))^n))^2,x, algorithm=""maxima"")","\frac{1}{3} \, b^{2} n^{2} x^{3} \log\left(e x^{\frac{2}{3}} + d\right)^{2} + \int \frac{9 \, {\left(b^{2} e \log\left(c\right)^{2} + 2 \, a b e \log\left(c\right) + a^{2} e\right)} x^{3} + 9 \, {\left(b^{2} d \log\left(c\right)^{2} + 2 \, a b d \log\left(c\right) + a^{2} d\right)} x^{\frac{7}{3}} - 2 \, {\left(2 \, b^{2} e n x^{3} - 9 \, {\left(b^{2} e \log\left(c\right) + a b e\right)} x^{3} - 9 \, {\left(b^{2} d \log\left(c\right) + a b d\right)} x^{\frac{7}{3}}\right)} n \log\left(e x^{\frac{2}{3}} + d\right)}{9 \, {\left(e x + d x^{\frac{1}{3}}\right)}}\,{d x}"," ",0,"1/3*b^2*n^2*x^3*log(e*x^(2/3) + d)^2 + integrate(1/9*(9*(b^2*e*log(c)^2 + 2*a*b*e*log(c) + a^2*e)*x^3 + 9*(b^2*d*log(c)^2 + 2*a*b*d*log(c) + a^2*d)*x^(7/3) - 2*(2*b^2*e*n*x^3 - 9*(b^2*e*log(c) + a*b*e)*x^3 - 9*(b^2*d*log(c) + a*b*d)*x^(7/3))*n*log(e*x^(2/3) + d))/(e*x + d*x^(1/3)), x)","F",0
477,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))^2,x, algorithm=""maxima"")","-\frac{2}{3} \, {\left(2 \, e n {\left(\frac{3 \, d^{2} \arctan\left(\frac{e x^{\frac{1}{3}}}{\sqrt{d e}}\right)}{\sqrt{d e} e^{2}} + \frac{e x - 3 \, d x^{\frac{1}{3}}}{e^{2}}\right)} - 3 \, x \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)\right)} a b + {\left(n^{2} x \log\left(e x^{\frac{2}{3}} + d\right)^{2} + \int \frac{3 \, e x \log\left(c\right)^{2} + 3 \, d x^{\frac{1}{3}} \log\left(c\right)^{2} - 2 \, {\left(2 \, e n x - 3 \, e x \log\left(c\right) - 3 \, d x^{\frac{1}{3}} \log\left(c\right)\right)} n \log\left(e x^{\frac{2}{3}} + d\right)}{3 \, {\left(e x + d x^{\frac{1}{3}}\right)}}\,{d x}\right)} b^{2} + a^{2} x"," ",0,"-2/3*(2*e*n*(3*d^2*arctan(e*x^(1/3)/sqrt(d*e))/(sqrt(d*e)*e^2) + (e*x - 3*d*x^(1/3))/e^2) - 3*x*log((e*x^(2/3) + d)^n*c))*a*b + (n^2*x*log(e*x^(2/3) + d)^2 + integrate(1/3*(3*e*x*log(c)^2 + 3*d*x^(1/3)*log(c)^2 - 2*(2*e*n*x - 3*e*x*log(c) - 3*d*x^(1/3)*log(c))*n*log(e*x^(2/3) + d))/(e*x + d*x^(1/3)), x))*b^2 + a^2*x","F",0
478,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))^2/x^2,x, algorithm=""maxima"")","-\frac{b^{2} n^{2} \log\left(e x^{\frac{2}{3}} + d\right)^{2}}{x} + \int \frac{2 \, {\left(2 \, b^{2} e n x + 3 \, {\left(b^{2} e \log\left(c\right) + a b e\right)} x + 3 \, {\left(b^{2} d \log\left(c\right) + a b d\right)} x^{\frac{1}{3}}\right)} n \log\left(e x^{\frac{2}{3}} + d\right) + 3 \, {\left(b^{2} e \log\left(c\right)^{2} + 2 \, a b e \log\left(c\right) + a^{2} e\right)} x + 3 \, {\left(b^{2} d \log\left(c\right)^{2} + 2 \, a b d \log\left(c\right) + a^{2} d\right)} x^{\frac{1}{3}}}{3 \, {\left(e x^{3} + d x^{\frac{7}{3}}\right)}}\,{d x}"," ",0,"-b^2*n^2*log(e*x^(2/3) + d)^2/x + integrate(1/3*(2*(2*b^2*e*n*x + 3*(b^2*e*log(c) + a*b*e)*x + 3*(b^2*d*log(c) + a*b*d)*x^(1/3))*n*log(e*x^(2/3) + d) + 3*(b^2*e*log(c)^2 + 2*a*b*e*log(c) + a^2*e)*x + 3*(b^2*d*log(c)^2 + 2*a*b*d*log(c) + a^2*d)*x^(1/3))/(e*x^3 + d*x^(7/3)), x)","F",0
479,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))^2/x^4,x, algorithm=""maxima"")","-\frac{b^{2} n^{2} \log\left(e x^{\frac{2}{3}} + d\right)^{2}}{3 \, x^{3}} + \int \frac{2 \, {\left(2 \, b^{2} e n x + 9 \, {\left(b^{2} e \log\left(c\right) + a b e\right)} x + 9 \, {\left(b^{2} d \log\left(c\right) + a b d\right)} x^{\frac{1}{3}}\right)} n \log\left(e x^{\frac{2}{3}} + d\right) + 9 \, {\left(b^{2} e \log\left(c\right)^{2} + 2 \, a b e \log\left(c\right) + a^{2} e\right)} x + 9 \, {\left(b^{2} d \log\left(c\right)^{2} + 2 \, a b d \log\left(c\right) + a^{2} d\right)} x^{\frac{1}{3}}}{9 \, {\left(e x^{5} + d x^{\frac{13}{3}}\right)}}\,{d x}"," ",0,"-1/3*b^2*n^2*log(e*x^(2/3) + d)^2/x^3 + integrate(1/9*(2*(2*b^2*e*n*x + 9*(b^2*e*log(c) + a*b*e)*x + 9*(b^2*d*log(c) + a*b*d)*x^(1/3))*n*log(e*x^(2/3) + d) + 9*(b^2*e*log(c)^2 + 2*a*b*e*log(c) + a^2*e)*x + 9*(b^2*d*log(c)^2 + 2*a*b*d*log(c) + a^2*d)*x^(1/3))/(e*x^5 + d*x^(13/3)), x)","F",0
480,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))^2/x^6,x, algorithm=""maxima"")","-\frac{b^{2} n^{2} \log\left(e x^{\frac{2}{3}} + d\right)^{2}}{5 \, x^{5}} + \int \frac{2 \, {\left(2 \, b^{2} e n x + 15 \, {\left(b^{2} e \log\left(c\right) + a b e\right)} x + 15 \, {\left(b^{2} d \log\left(c\right) + a b d\right)} x^{\frac{1}{3}}\right)} n \log\left(e x^{\frac{2}{3}} + d\right) + 15 \, {\left(b^{2} e \log\left(c\right)^{2} + 2 \, a b e \log\left(c\right) + a^{2} e\right)} x + 15 \, {\left(b^{2} d \log\left(c\right)^{2} + 2 \, a b d \log\left(c\right) + a^{2} d\right)} x^{\frac{1}{3}}}{15 \, {\left(e x^{7} + d x^{\frac{19}{3}}\right)}}\,{d x}"," ",0,"-1/5*b^2*n^2*log(e*x^(2/3) + d)^2/x^5 + integrate(1/15*(2*(2*b^2*e*n*x + 15*(b^2*e*log(c) + a*b*e)*x + 15*(b^2*d*log(c) + a*b*d)*x^(1/3))*n*log(e*x^(2/3) + d) + 15*(b^2*e*log(c)^2 + 2*a*b*e*log(c) + a^2*e)*x + 15*(b^2*d*log(c)^2 + 2*a*b*d*log(c) + a^2*d)*x^(1/3))/(e*x^7 + d*x^(19/3)), x)","F",0
481,1,680,0,0.588299," ","integrate(x^3*(a+b*log(c*(d+e*x^(2/3))^n))^3,x, algorithm=""maxima"")","\frac{1}{4} \, b^{3} x^{4} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{3} + \frac{3}{4} \, a b^{2} x^{4} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{2} + \frac{3}{4} \, a^{2} b x^{4} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right) + \frac{1}{4} \, a^{3} x^{4} - \frac{1}{80} \, a^{2} b e n {\left(\frac{60 \, d^{6} \log\left(e x^{\frac{2}{3}} + d\right)}{e^{7}} + \frac{10 \, e^{5} x^{4} - 12 \, d e^{4} x^{\frac{10}{3}} + 15 \, d^{2} e^{3} x^{\frac{8}{3}} - 20 \, d^{3} e^{2} x^{2} + 30 \, d^{4} e x^{\frac{4}{3}} - 60 \, d^{5} x^{\frac{2}{3}}}{e^{6}}\right)} - \frac{1}{2400} \, {\left(60 \, e n {\left(\frac{60 \, d^{6} \log\left(e x^{\frac{2}{3}} + d\right)}{e^{7}} + \frac{10 \, e^{5} x^{4} - 12 \, d e^{4} x^{\frac{10}{3}} + 15 \, d^{2} e^{3} x^{\frac{8}{3}} - 20 \, d^{3} e^{2} x^{2} + 30 \, d^{4} e x^{\frac{4}{3}} - 60 \, d^{5} x^{\frac{2}{3}}}{e^{6}}\right)} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right) - \frac{{\left(100 \, e^{6} x^{4} - 264 \, d e^{5} x^{\frac{10}{3}} + 555 \, d^{2} e^{4} x^{\frac{8}{3}} - 1140 \, d^{3} e^{3} x^{2} + 1800 \, d^{6} \log\left(e x^{\frac{2}{3}} + d\right)^{2} + 2610 \, d^{4} e^{2} x^{\frac{4}{3}} + 8820 \, d^{6} \log\left(e x^{\frac{2}{3}} + d\right) - 8820 \, d^{5} e x^{\frac{2}{3}}\right)} n^{2}}{e^{6}}\right)} a b^{2} - \frac{1}{144000} \, {\left(1800 \, e n {\left(\frac{60 \, d^{6} \log\left(e x^{\frac{2}{3}} + d\right)}{e^{7}} + \frac{10 \, e^{5} x^{4} - 12 \, d e^{4} x^{\frac{10}{3}} + 15 \, d^{2} e^{3} x^{\frac{8}{3}} - 20 \, d^{3} e^{2} x^{2} + 30 \, d^{4} e x^{\frac{4}{3}} - 60 \, d^{5} x^{\frac{2}{3}}}{e^{6}}\right)} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{2} + e n {\left(\frac{{\left(1000 \, e^{6} x^{4} - 4368 \, d e^{5} x^{\frac{10}{3}} + 36000 \, d^{6} \log\left(e x^{\frac{2}{3}} + d\right)^{3} + 13785 \, d^{2} e^{4} x^{\frac{8}{3}} - 41180 \, d^{3} e^{3} x^{2} + 264600 \, d^{6} \log\left(e x^{\frac{2}{3}} + d\right)^{2} + 140070 \, d^{4} e^{2} x^{\frac{4}{3}} + 809340 \, d^{6} \log\left(e x^{\frac{2}{3}} + d\right) - 809340 \, d^{5} e x^{\frac{2}{3}}\right)} n^{2}}{e^{7}} - \frac{60 \, {\left(100 \, e^{6} x^{4} - 264 \, d e^{5} x^{\frac{10}{3}} + 555 \, d^{2} e^{4} x^{\frac{8}{3}} - 1140 \, d^{3} e^{3} x^{2} + 1800 \, d^{6} \log\left(e x^{\frac{2}{3}} + d\right)^{2} + 2610 \, d^{4} e^{2} x^{\frac{4}{3}} + 8820 \, d^{6} \log\left(e x^{\frac{2}{3}} + d\right) - 8820 \, d^{5} e x^{\frac{2}{3}}\right)} n \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)}{e^{7}}\right)}\right)} b^{3}"," ",0,"1/4*b^3*x^4*log((e*x^(2/3) + d)^n*c)^3 + 3/4*a*b^2*x^4*log((e*x^(2/3) + d)^n*c)^2 + 3/4*a^2*b*x^4*log((e*x^(2/3) + d)^n*c) + 1/4*a^3*x^4 - 1/80*a^2*b*e*n*(60*d^6*log(e*x^(2/3) + d)/e^7 + (10*e^5*x^4 - 12*d*e^4*x^(10/3) + 15*d^2*e^3*x^(8/3) - 20*d^3*e^2*x^2 + 30*d^4*e*x^(4/3) - 60*d^5*x^(2/3))/e^6) - 1/2400*(60*e*n*(60*d^6*log(e*x^(2/3) + d)/e^7 + (10*e^5*x^4 - 12*d*e^4*x^(10/3) + 15*d^2*e^3*x^(8/3) - 20*d^3*e^2*x^2 + 30*d^4*e*x^(4/3) - 60*d^5*x^(2/3))/e^6)*log((e*x^(2/3) + d)^n*c) - (100*e^6*x^4 - 264*d*e^5*x^(10/3) + 555*d^2*e^4*x^(8/3) - 1140*d^3*e^3*x^2 + 1800*d^6*log(e*x^(2/3) + d)^2 + 2610*d^4*e^2*x^(4/3) + 8820*d^6*log(e*x^(2/3) + d) - 8820*d^5*e*x^(2/3))*n^2/e^6)*a*b^2 - 1/144000*(1800*e*n*(60*d^6*log(e*x^(2/3) + d)/e^7 + (10*e^5*x^4 - 12*d*e^4*x^(10/3) + 15*d^2*e^3*x^(8/3) - 20*d^3*e^2*x^2 + 30*d^4*e*x^(4/3) - 60*d^5*x^(2/3))/e^6)*log((e*x^(2/3) + d)^n*c)^2 + e*n*((1000*e^6*x^4 - 4368*d*e^5*x^(10/3) + 36000*d^6*log(e*x^(2/3) + d)^3 + 13785*d^2*e^4*x^(8/3) - 41180*d^3*e^3*x^2 + 264600*d^6*log(e*x^(2/3) + d)^2 + 140070*d^4*e^2*x^(4/3) + 809340*d^6*log(e*x^(2/3) + d) - 809340*d^5*e*x^(2/3))*n^2/e^7 - 60*(100*e^6*x^4 - 264*d*e^5*x^(10/3) + 555*d^2*e^4*x^(8/3) - 1140*d^3*e^3*x^2 + 1800*d^6*log(e*x^(2/3) + d)^2 + 2610*d^4*e^2*x^(4/3) + 8820*d^6*log(e*x^(2/3) + d) - 8820*d^5*e*x^(2/3))*n*log((e*x^(2/3) + d)^n*c)/e^7))*b^3","A",0
482,1,484,0,0.569680," ","integrate(x*(a+b*log(c*(d+e*x^(2/3))^n))^3,x, algorithm=""maxima"")","\frac{1}{2} \, b^{3} x^{2} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{3} + \frac{3}{2} \, a b^{2} x^{2} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{2} + \frac{1}{4} \, a^{2} b e n {\left(\frac{6 \, d^{3} \log\left(e x^{\frac{2}{3}} + d\right)}{e^{4}} - \frac{2 \, e^{2} x^{2} - 3 \, d e x^{\frac{4}{3}} + 6 \, d^{2} x^{\frac{2}{3}}}{e^{3}}\right)} + \frac{3}{2} \, a^{2} b x^{2} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right) + \frac{1}{2} \, a^{3} x^{2} + \frac{1}{12} \, {\left(6 \, e n {\left(\frac{6 \, d^{3} \log\left(e x^{\frac{2}{3}} + d\right)}{e^{4}} - \frac{2 \, e^{2} x^{2} - 3 \, d e x^{\frac{4}{3}} + 6 \, d^{2} x^{\frac{2}{3}}}{e^{3}}\right)} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right) + \frac{{\left(4 \, e^{3} x^{2} - 18 \, d^{3} \log\left(e x^{\frac{2}{3}} + d\right)^{2} - 15 \, d e^{2} x^{\frac{4}{3}} - 66 \, d^{3} \log\left(e x^{\frac{2}{3}} + d\right) + 66 \, d^{2} e x^{\frac{2}{3}}\right)} n^{2}}{e^{3}}\right)} a b^{2} + \frac{1}{72} \, {\left(18 \, e n {\left(\frac{6 \, d^{3} \log\left(e x^{\frac{2}{3}} + d\right)}{e^{4}} - \frac{2 \, e^{2} x^{2} - 3 \, d e x^{\frac{4}{3}} + 6 \, d^{2} x^{\frac{2}{3}}}{e^{3}}\right)} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{2} + e n {\left(\frac{{\left(36 \, d^{3} \log\left(e x^{\frac{2}{3}} + d\right)^{3} - 8 \, e^{3} x^{2} + 198 \, d^{3} \log\left(e x^{\frac{2}{3}} + d\right)^{2} + 57 \, d e^{2} x^{\frac{4}{3}} + 510 \, d^{3} \log\left(e x^{\frac{2}{3}} + d\right) - 510 \, d^{2} e x^{\frac{2}{3}}\right)} n^{2}}{e^{4}} + \frac{6 \, {\left(4 \, e^{3} x^{2} - 18 \, d^{3} \log\left(e x^{\frac{2}{3}} + d\right)^{2} - 15 \, d e^{2} x^{\frac{4}{3}} - 66 \, d^{3} \log\left(e x^{\frac{2}{3}} + d\right) + 66 \, d^{2} e x^{\frac{2}{3}}\right)} n \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)}{e^{4}}\right)}\right)} b^{3}"," ",0,"1/2*b^3*x^2*log((e*x^(2/3) + d)^n*c)^3 + 3/2*a*b^2*x^2*log((e*x^(2/3) + d)^n*c)^2 + 1/4*a^2*b*e*n*(6*d^3*log(e*x^(2/3) + d)/e^4 - (2*e^2*x^2 - 3*d*e*x^(4/3) + 6*d^2*x^(2/3))/e^3) + 3/2*a^2*b*x^2*log((e*x^(2/3) + d)^n*c) + 1/2*a^3*x^2 + 1/12*(6*e*n*(6*d^3*log(e*x^(2/3) + d)/e^4 - (2*e^2*x^2 - 3*d*e*x^(4/3) + 6*d^2*x^(2/3))/e^3)*log((e*x^(2/3) + d)^n*c) + (4*e^3*x^2 - 18*d^3*log(e*x^(2/3) + d)^2 - 15*d*e^2*x^(4/3) - 66*d^3*log(e*x^(2/3) + d) + 66*d^2*e*x^(2/3))*n^2/e^3)*a*b^2 + 1/72*(18*e*n*(6*d^3*log(e*x^(2/3) + d)/e^4 - (2*e^2*x^2 - 3*d*e*x^(4/3) + 6*d^2*x^(2/3))/e^3)*log((e*x^(2/3) + d)^n*c)^2 + e*n*((36*d^3*log(e*x^(2/3) + d)^3 - 8*e^3*x^2 + 198*d^3*log(e*x^(2/3) + d)^2 + 57*d*e^2*x^(4/3) + 510*d^3*log(e*x^(2/3) + d) - 510*d^2*e*x^(2/3))*n^2/e^4 + 6*(4*e^3*x^2 - 18*d^3*log(e*x^(2/3) + d)^2 - 15*d*e^2*x^(4/3) - 66*d^3*log(e*x^(2/3) + d) + 66*d^2*e*x^(2/3))*n*log((e*x^(2/3) + d)^n*c)/e^4))*b^3","A",0
483,1,282,0,0.798782," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))^3/x,x, algorithm=""maxima"")","\frac{3}{2} \, {\left(\log\left(e x^{\frac{2}{3}} + d\right)^{3} \log\left(-\frac{e x^{\frac{2}{3}} + d}{d} + 1\right) + 3 \, {\rm Li}_2\left(\frac{e x^{\frac{2}{3}} + d}{d}\right) \log\left(e x^{\frac{2}{3}} + d\right)^{2} - 6 \, \log\left(e x^{\frac{2}{3}} + d\right) {\rm Li}_{3}(\frac{e x^{\frac{2}{3}} + d}{d}) + 6 \, {\rm Li}_{4}(\frac{e x^{\frac{2}{3}} + d}{d})\right)} b^{3} n^{3} + a^{3} \log\left(x\right) + \frac{9}{2} \, {\left(b^{3} n^{2} \log\left(c\right) + a b^{2} n^{2}\right)} {\left(\log\left(e x^{\frac{2}{3}} + d\right)^{2} \log\left(-\frac{e x^{\frac{2}{3}} + d}{d} + 1\right) + 2 \, {\rm Li}_2\left(\frac{e x^{\frac{2}{3}} + d}{d}\right) \log\left(e x^{\frac{2}{3}} + d\right) - 2 \, {\rm Li}_{3}(\frac{e x^{\frac{2}{3}} + d}{d})\right)} + \frac{9}{2} \, {\left(b^{3} n \log\left(c\right)^{2} + 2 \, a b^{2} n \log\left(c\right) + a^{2} b n\right)} {\left(\log\left(e x^{\frac{2}{3}} + d\right) \log\left(-\frac{e x^{\frac{2}{3}} + d}{d} + 1\right) + {\rm Li}_2\left(\frac{e x^{\frac{2}{3}} + d}{d}\right)\right)} + {\left(b^{3} \log\left(c\right)^{3} + 3 \, a b^{2} \log\left(c\right)^{2} + 3 \, a^{2} b \log\left(c\right)\right)} \log\left(x\right)"," ",0,"3/2*(log(e*x^(2/3) + d)^3*log(-(e*x^(2/3) + d)/d + 1) + 3*dilog((e*x^(2/3) + d)/d)*log(e*x^(2/3) + d)^2 - 6*log(e*x^(2/3) + d)*polylog(3, (e*x^(2/3) + d)/d) + 6*polylog(4, (e*x^(2/3) + d)/d))*b^3*n^3 + a^3*log(x) + 9/2*(b^3*n^2*log(c) + a*b^2*n^2)*(log(e*x^(2/3) + d)^2*log(-(e*x^(2/3) + d)/d + 1) + 2*dilog((e*x^(2/3) + d)/d)*log(e*x^(2/3) + d) - 2*polylog(3, (e*x^(2/3) + d)/d)) + 9/2*(b^3*n*log(c)^2 + 2*a*b^2*n*log(c) + a^2*b*n)*(log(e*x^(2/3) + d)*log(-(e*x^(2/3) + d)/d + 1) + dilog((e*x^(2/3) + d)/d)) + (b^3*log(c)^3 + 3*a*b^2*log(c)^2 + 3*a^2*b*log(c))*log(x)","B",0
484,1,740,0,1.008590," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))^3/x^3,x, algorithm=""maxima"")","\frac{3 \, {\left(\log\left(e x^{\frac{2}{3}} + d\right)^{2} \log\left(-\frac{e x^{\frac{2}{3}} + d}{d} + 1\right) + 2 \, {\rm Li}_2\left(\frac{e x^{\frac{2}{3}} + d}{d}\right) \log\left(e x^{\frac{2}{3}} + d\right) - 2 \, {\rm Li}_{3}(\frac{e x^{\frac{2}{3}} + d}{d})\right)} b^{3} e^{3} n^{3}}{2 \, d^{3}} - \frac{3}{4} \, a^{2} b e n {\left(\frac{2 \, e^{2} \log\left(e x^{\frac{2}{3}} + d\right)}{d^{3}} - \frac{2 \, e^{2} \log\left(x^{\frac{2}{3}}\right)}{d^{3}} - \frac{2 \, e x^{\frac{2}{3}} - d}{d^{2} x^{\frac{4}{3}}}\right)} - \frac{3 \, a^{2} b \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)}{2 \, x^{2}} - \frac{a^{3}}{2 \, x^{2}} + \frac{3 \, {\left(2 \, a b^{2} e^{3} n^{2} - {\left(3 \, e^{3} n^{3} - 2 \, e^{3} n^{2} \log\left(c\right)\right)} b^{3}\right)} {\left(\log\left(e x^{\frac{2}{3}} + d\right) \log\left(-\frac{e x^{\frac{2}{3}} + d}{d} + 1\right) + {\rm Li}_2\left(\frac{e x^{\frac{2}{3}} + d}{d}\right)\right)}}{2 \, d^{3}} - \frac{{\left({\left(3 \, e^{3} n^{2} - 2 \, e^{3} n \log\left(c\right)\right)} a b^{2} - {\left(e^{3} n^{3} - 3 \, e^{3} n^{2} \log\left(c\right) + e^{3} n \log\left(c\right)^{2}\right)} b^{3}\right)} \log\left(x\right)}{d^{3}} - \frac{2 \, b^{3} d^{3} \log\left(c\right)^{3} + 6 \, a b^{2} d^{3} \log\left(c\right)^{2} + 2 \, {\left(b^{3} e^{3} n^{3} x^{2} + b^{3} d^{3} n^{3}\right)} \log\left(e x^{\frac{2}{3}} + d\right)^{3} - 3 \, {\left(2 \, b^{3} d e^{2} n^{3} x^{\frac{4}{3}} - b^{3} d^{2} e n^{3} x^{\frac{2}{3}} - 2 \, b^{3} d^{3} n^{2} \log\left(c\right) - 2 \, a b^{2} d^{3} n^{2} - {\left(2 \, a b^{2} e^{3} n^{2} - {\left(3 \, e^{3} n^{3} - 2 \, e^{3} n^{2} \log\left(c\right)\right)} b^{3}\right)} x^{2}\right)} \log\left(e x^{\frac{2}{3}} + d\right)^{2} + 6 \, {\left({\left(d e^{2} n^{2} - 2 \, d e^{2} n \log\left(c\right)\right)} a b^{2} + {\left(d e^{2} n^{2} \log\left(c\right) - d e^{2} n \log\left(c\right)^{2}\right)} b^{3}\right)} x^{\frac{4}{3}} + 6 \, {\left(b^{3} d^{3} n \log\left(c\right)^{2} + 2 \, a b^{2} d^{3} n \log\left(c\right) - {\left({\left(3 \, e^{3} n^{2} - 2 \, e^{3} n \log\left(c\right)\right)} a b^{2} - {\left(e^{3} n^{3} - 3 \, e^{3} n^{2} \log\left(c\right) + e^{3} n \log\left(c\right)^{2}\right)} b^{3}\right)} x^{2} - {\left(2 \, a b^{2} d e^{2} n^{2} - {\left(d e^{2} n^{3} - 2 \, d e^{2} n^{2} \log\left(c\right)\right)} b^{3}\right)} x^{\frac{4}{3}} + {\left(b^{3} d^{2} e n^{2} \log\left(c\right) + a b^{2} d^{2} e n^{2}\right)} x^{\frac{2}{3}}\right)} \log\left(e x^{\frac{2}{3}} + d\right) + 3 \, {\left(b^{3} d^{2} e n \log\left(c\right)^{2} + 2 \, a b^{2} d^{2} e n \log\left(c\right)\right)} x^{\frac{2}{3}}}{4 \, d^{3} x^{2}}"," ",0,"3/2*(log(e*x^(2/3) + d)^2*log(-(e*x^(2/3) + d)/d + 1) + 2*dilog((e*x^(2/3) + d)/d)*log(e*x^(2/3) + d) - 2*polylog(3, (e*x^(2/3) + d)/d))*b^3*e^3*n^3/d^3 - 3/4*a^2*b*e*n*(2*e^2*log(e*x^(2/3) + d)/d^3 - 2*e^2*log(x^(2/3))/d^3 - (2*e*x^(2/3) - d)/(d^2*x^(4/3))) - 3/2*a^2*b*log((e*x^(2/3) + d)^n*c)/x^2 - 1/2*a^3/x^2 + 3/2*(2*a*b^2*e^3*n^2 - (3*e^3*n^3 - 2*e^3*n^2*log(c))*b^3)*(log(e*x^(2/3) + d)*log(-(e*x^(2/3) + d)/d + 1) + dilog((e*x^(2/3) + d)/d))/d^3 - ((3*e^3*n^2 - 2*e^3*n*log(c))*a*b^2 - (e^3*n^3 - 3*e^3*n^2*log(c) + e^3*n*log(c)^2)*b^3)*log(x)/d^3 - 1/4*(2*b^3*d^3*log(c)^3 + 6*a*b^2*d^3*log(c)^2 + 2*(b^3*e^3*n^3*x^2 + b^3*d^3*n^3)*log(e*x^(2/3) + d)^3 - 3*(2*b^3*d*e^2*n^3*x^(4/3) - b^3*d^2*e*n^3*x^(2/3) - 2*b^3*d^3*n^2*log(c) - 2*a*b^2*d^3*n^2 - (2*a*b^2*e^3*n^2 - (3*e^3*n^3 - 2*e^3*n^2*log(c))*b^3)*x^2)*log(e*x^(2/3) + d)^2 + 6*((d*e^2*n^2 - 2*d*e^2*n*log(c))*a*b^2 + (d*e^2*n^2*log(c) - d*e^2*n*log(c)^2)*b^3)*x^(4/3) + 6*(b^3*d^3*n*log(c)^2 + 2*a*b^2*d^3*n*log(c) - ((3*e^3*n^2 - 2*e^3*n*log(c))*a*b^2 - (e^3*n^3 - 3*e^3*n^2*log(c) + e^3*n*log(c)^2)*b^3)*x^2 - (2*a*b^2*d*e^2*n^2 - (d*e^2*n^3 - 2*d*e^2*n^2*log(c))*b^3)*x^(4/3) + (b^3*d^2*e*n^2*log(c) + a*b^2*d^2*e*n^2)*x^(2/3))*log(e*x^(2/3) + d) + 3*(b^3*d^2*e*n*log(c)^2 + 2*a*b^2*d^2*e*n*log(c))*x^(2/3))/(d^3*x^2)","A",0
485,0,0,0,0.000000," ","integrate(x^2*(a+b*log(c*(d+e*x^(2/3))^n))^3,x, algorithm=""maxima"")","\frac{1}{3} \, b^{3} n^{3} x^{3} \log\left(e x^{\frac{2}{3}} + d\right)^{3} + \int -\frac{{\left(2 \, b^{3} e n x^{3} - 9 \, {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{3} - 9 \, {\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x^{\frac{7}{3}}\right)} n^{2} \log\left(e x^{\frac{2}{3}} + d\right)^{2} - 3 \, {\left(b^{3} e \log\left(c\right)^{3} + 3 \, a b^{2} e \log\left(c\right)^{2} + 3 \, a^{2} b e \log\left(c\right) + a^{3} e\right)} x^{3} - 3 \, {\left(b^{3} d \log\left(c\right)^{3} + 3 \, a b^{2} d \log\left(c\right)^{2} + 3 \, a^{2} b d \log\left(c\right) + a^{3} d\right)} x^{\frac{7}{3}} - 9 \, {\left({\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} x^{3} + {\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} x^{\frac{7}{3}}\right)} n \log\left(e x^{\frac{2}{3}} + d\right)}{3 \, {\left(e x + d x^{\frac{1}{3}}\right)}}\,{d x}"," ",0,"1/3*b^3*n^3*x^3*log(e*x^(2/3) + d)^3 + integrate(-1/3*((2*b^3*e*n*x^3 - 9*(b^3*e*log(c) + a*b^2*e)*x^3 - 9*(b^3*d*log(c) + a*b^2*d)*x^(7/3))*n^2*log(e*x^(2/3) + d)^2 - 3*(b^3*e*log(c)^3 + 3*a*b^2*e*log(c)^2 + 3*a^2*b*e*log(c) + a^3*e)*x^3 - 3*(b^3*d*log(c)^3 + 3*a*b^2*d*log(c)^2 + 3*a^2*b*d*log(c) + a^3*d)*x^(7/3) - 9*((b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*x^3 + (b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*x^(7/3))*n*log(e*x^(2/3) + d))/(e*x + d*x^(1/3)), x)","F",0
486,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))^3,x, algorithm=""maxima"")","b^{3} n^{3} x \log\left(e x^{\frac{2}{3}} + d\right)^{3} - {\left(2 \, e n {\left(\frac{3 \, d^{2} \arctan\left(\frac{e x^{\frac{1}{3}}}{\sqrt{d e}}\right)}{\sqrt{d e} e^{2}} + \frac{e x - 3 \, d x^{\frac{1}{3}}}{e^{2}}\right)} - 3 \, x \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)\right)} a^{2} b + a^{3} x + \int -\frac{{\left(2 \, b^{3} e n x - 3 \, {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x - 3 \, {\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x^{\frac{1}{3}}\right)} n^{2} \log\left(e x^{\frac{2}{3}} + d\right)^{2} - 3 \, {\left({\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right)\right)} x + {\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right)\right)} x^{\frac{1}{3}}\right)} n \log\left(e x^{\frac{2}{3}} + d\right) - {\left(b^{3} e \log\left(c\right)^{3} + 3 \, a b^{2} e \log\left(c\right)^{2}\right)} x - {\left(b^{3} d \log\left(c\right)^{3} + 3 \, a b^{2} d \log\left(c\right)^{2}\right)} x^{\frac{1}{3}}}{e x + d x^{\frac{1}{3}}}\,{d x}"," ",0,"b^3*n^3*x*log(e*x^(2/3) + d)^3 - (2*e*n*(3*d^2*arctan(e*x^(1/3)/sqrt(d*e))/(sqrt(d*e)*e^2) + (e*x - 3*d*x^(1/3))/e^2) - 3*x*log((e*x^(2/3) + d)^n*c))*a^2*b + a^3*x + integrate(-((2*b^3*e*n*x - 3*(b^3*e*log(c) + a*b^2*e)*x - 3*(b^3*d*log(c) + a*b^2*d)*x^(1/3))*n^2*log(e*x^(2/3) + d)^2 - 3*((b^3*e*log(c)^2 + 2*a*b^2*e*log(c))*x + (b^3*d*log(c)^2 + 2*a*b^2*d*log(c))*x^(1/3))*n*log(e*x^(2/3) + d) - (b^3*e*log(c)^3 + 3*a*b^2*e*log(c)^2)*x - (b^3*d*log(c)^3 + 3*a*b^2*d*log(c)^2)*x^(1/3))/(e*x + d*x^(1/3)), x)","F",0
487,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))^3/x^2,x, algorithm=""maxima"")","-\frac{b^{3} n^{3} \log\left(e x^{\frac{2}{3}} + d\right)^{3}}{x} + \int \frac{{\left(2 \, b^{3} e n x + 3 \, {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x + 3 \, {\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x^{\frac{1}{3}}\right)} n^{2} \log\left(e x^{\frac{2}{3}} + d\right)^{2} + 3 \, {\left({\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} x + {\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} x^{\frac{1}{3}}\right)} n \log\left(e x^{\frac{2}{3}} + d\right) + {\left(b^{3} e \log\left(c\right)^{3} + 3 \, a b^{2} e \log\left(c\right)^{2} + 3 \, a^{2} b e \log\left(c\right) + a^{3} e\right)} x + {\left(b^{3} d \log\left(c\right)^{3} + 3 \, a b^{2} d \log\left(c\right)^{2} + 3 \, a^{2} b d \log\left(c\right) + a^{3} d\right)} x^{\frac{1}{3}}}{e x^{3} + d x^{\frac{7}{3}}}\,{d x}"," ",0,"-b^3*n^3*log(e*x^(2/3) + d)^3/x + integrate(((2*b^3*e*n*x + 3*(b^3*e*log(c) + a*b^2*e)*x + 3*(b^3*d*log(c) + a*b^2*d)*x^(1/3))*n^2*log(e*x^(2/3) + d)^2 + 3*((b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*x + (b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*x^(1/3))*n*log(e*x^(2/3) + d) + (b^3*e*log(c)^3 + 3*a*b^2*e*log(c)^2 + 3*a^2*b*e*log(c) + a^3*e)*x + (b^3*d*log(c)^3 + 3*a*b^2*d*log(c)^2 + 3*a^2*b*d*log(c) + a^3*d)*x^(1/3))/(e*x^3 + d*x^(7/3)), x)","F",0
488,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))^3/x^4,x, algorithm=""maxima"")","-\frac{b^{3} n^{3} \log\left(e x^{\frac{2}{3}} + d\right)^{3}}{3 \, x^{3}} + \int \frac{{\left(2 \, b^{3} e n x + 9 \, {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x + 9 \, {\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x^{\frac{1}{3}}\right)} n^{2} \log\left(e x^{\frac{2}{3}} + d\right)^{2} + 9 \, {\left({\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} x + {\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} x^{\frac{1}{3}}\right)} n \log\left(e x^{\frac{2}{3}} + d\right) + 3 \, {\left(b^{3} e \log\left(c\right)^{3} + 3 \, a b^{2} e \log\left(c\right)^{2} + 3 \, a^{2} b e \log\left(c\right) + a^{3} e\right)} x + 3 \, {\left(b^{3} d \log\left(c\right)^{3} + 3 \, a b^{2} d \log\left(c\right)^{2} + 3 \, a^{2} b d \log\left(c\right) + a^{3} d\right)} x^{\frac{1}{3}}}{3 \, {\left(e x^{5} + d x^{\frac{13}{3}}\right)}}\,{d x}"," ",0,"-1/3*b^3*n^3*log(e*x^(2/3) + d)^3/x^3 + integrate(1/3*((2*b^3*e*n*x + 9*(b^3*e*log(c) + a*b^2*e)*x + 9*(b^3*d*log(c) + a*b^2*d)*x^(1/3))*n^2*log(e*x^(2/3) + d)^2 + 9*((b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*x + (b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*x^(1/3))*n*log(e*x^(2/3) + d) + 3*(b^3*e*log(c)^3 + 3*a*b^2*e*log(c)^2 + 3*a^2*b*e*log(c) + a^3*e)*x + 3*(b^3*d*log(c)^3 + 3*a*b^2*d*log(c)^2 + 3*a^2*b*d*log(c) + a^3*d)*x^(1/3))/(e*x^5 + d*x^(13/3)), x)","F",0
489,1,162,0,0.473431," ","integrate(x^3*(a+b*log(c*(d+e/x^(1/3))^n)),x, algorithm=""maxima"")","\frac{1}{4} \, b x^{4} \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right) + \frac{1}{4} \, a x^{4} - \frac{1}{110880} \, b e n {\left(\frac{27720 \, e^{11} \log\left(d x^{\frac{1}{3}} + e\right)}{d^{12}} - \frac{2520 \, d^{10} x^{\frac{11}{3}} - 2772 \, d^{9} e x^{\frac{10}{3}} + 3080 \, d^{8} e^{2} x^{3} - 3465 \, d^{7} e^{3} x^{\frac{8}{3}} + 3960 \, d^{6} e^{4} x^{\frac{7}{3}} - 4620 \, d^{5} e^{5} x^{2} + 5544 \, d^{4} e^{6} x^{\frac{5}{3}} - 6930 \, d^{3} e^{7} x^{\frac{4}{3}} + 9240 \, d^{2} e^{8} x - 13860 \, d e^{9} x^{\frac{2}{3}} + 27720 \, e^{10} x^{\frac{1}{3}}}{d^{11}}\right)}"," ",0,"1/4*b*x^4*log(c*(d + e/x^(1/3))^n) + 1/4*a*x^4 - 1/110880*b*e*n*(27720*e^11*log(d*x^(1/3) + e)/d^12 - (2520*d^10*x^(11/3) - 2772*d^9*e*x^(10/3) + 3080*d^8*e^2*x^3 - 3465*d^7*e^3*x^(8/3) + 3960*d^6*e^4*x^(7/3) - 4620*d^5*e^5*x^2 + 5544*d^4*e^6*x^(5/3) - 6930*d^3*e^7*x^(4/3) + 9240*d^2*e^8*x - 13860*d*e^9*x^(2/3) + 27720*e^10*x^(1/3))/d^11)","A",0
490,1,128,0,0.471499," ","integrate(x^2*(a+b*log(c*(d+e/x^(1/3))^n)),x, algorithm=""maxima"")","\frac{1}{3} \, b x^{3} \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right) + \frac{1}{3} \, a x^{3} + \frac{1}{2520} \, b e n {\left(\frac{840 \, e^{8} \log\left(d x^{\frac{1}{3}} + e\right)}{d^{9}} + \frac{105 \, d^{7} x^{\frac{8}{3}} - 120 \, d^{6} e x^{\frac{7}{3}} + 140 \, d^{5} e^{2} x^{2} - 168 \, d^{4} e^{3} x^{\frac{5}{3}} + 210 \, d^{3} e^{4} x^{\frac{4}{3}} - 280 \, d^{2} e^{5} x + 420 \, d e^{6} x^{\frac{2}{3}} - 840 \, e^{7} x^{\frac{1}{3}}}{d^{8}}\right)}"," ",0,"1/3*b*x^3*log(c*(d + e/x^(1/3))^n) + 1/3*a*x^3 + 1/2520*b*e*n*(840*e^8*log(d*x^(1/3) + e)/d^9 + (105*d^7*x^(8/3) - 120*d^6*e*x^(7/3) + 140*d^5*e^2*x^2 - 168*d^4*e^3*x^(5/3) + 210*d^3*e^4*x^(4/3) - 280*d^2*e^5*x + 420*d*e^6*x^(2/3) - 840*e^7*x^(1/3))/d^8)","A",0
491,1,96,0,0.471755," ","integrate(x*(a+b*log(c*(d+e/x^(1/3))^n)),x, algorithm=""maxima"")","-\frac{1}{120} \, b e n {\left(\frac{60 \, e^{5} \log\left(d x^{\frac{1}{3}} + e\right)}{d^{6}} - \frac{12 \, d^{4} x^{\frac{5}{3}} - 15 \, d^{3} e x^{\frac{4}{3}} + 20 \, d^{2} e^{2} x - 30 \, d e^{3} x^{\frac{2}{3}} + 60 \, e^{4} x^{\frac{1}{3}}}{d^{5}}\right)} + \frac{1}{2} \, b x^{2} \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right) + \frac{1}{2} \, a x^{2}"," ",0,"-1/120*b*e*n*(60*e^5*log(d*x^(1/3) + e)/d^6 - (12*d^4*x^(5/3) - 15*d^3*e*x^(4/3) + 20*d^2*e^2*x - 30*d*e^3*x^(2/3) + 60*e^4*x^(1/3))/d^5) + 1/2*b*x^2*log(c*(d + e/x^(1/3))^n) + 1/2*a*x^2","A",0
492,1,59,0,0.451865," ","integrate(a+b*log(c*(d+e/x^(1/3))^n),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(e n {\left(\frac{2 \, e^{2} \log\left(d x^{\frac{1}{3}} + e\right)}{d^{3}} + \frac{d x^{\frac{2}{3}} - 2 \, e x^{\frac{1}{3}}}{d^{2}}\right)} + 2 \, x \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right)\right)} b + a x"," ",0,"1/2*(e*n*(2*e^2*log(d*x^(1/3) + e)/d^3 + (d*x^(2/3) - 2*e*x^(1/3))/d^2) + 2*x*log(c*(d + e/x^(1/3))^n))*b + a*x","A",0
493,1,185,0,1.916102," ","integrate((a+b*log(c*(d+e/x^(1/3))^n))/x,x, algorithm=""maxima"")","-3 \, {\left(\log\left(\frac{d x^{\frac{1}{3}}}{e} + 1\right) \log\left(x^{\frac{1}{3}}\right) + {\rm Li}_2\left(-\frac{d x^{\frac{1}{3}}}{e}\right)\right)} b n + \frac{2 \, b e^{2} n \log\left(x\right)^{2} + 12 \, b e^{2} \log\left({\left(d x^{\frac{1}{3}} + e\right)}^{n}\right) \log\left(x\right) - 12 \, b e^{2} \log\left(x\right) \log\left(x^{\frac{1}{3} \, n}\right) + 9 \, b d^{2} n x^{\frac{2}{3}} - 36 \, b d e n x^{\frac{1}{3}} - 6 \, {\left(b d^{2} n x^{\frac{2}{3}} - 2 \, b d e n x^{\frac{1}{3}}\right)} \log\left(x\right) + 12 \, {\left(b e^{2} \log\left(c\right) + a e^{2}\right)} \log\left(x\right) + \frac{3 \, {\left(2 \, b d^{2} n x \log\left(x\right) - 3 \, b d^{2} n x\right)}}{x^{\frac{1}{3}}} - \frac{12 \, {\left(b d e n x \log\left(x\right) - 3 \, b d e n x\right)}}{x^{\frac{2}{3}}}}{12 \, e^{2}}"," ",0,"-3*(log(d*x^(1/3)/e + 1)*log(x^(1/3)) + dilog(-d*x^(1/3)/e))*b*n + 1/12*(2*b*e^2*n*log(x)^2 + 12*b*e^2*log((d*x^(1/3) + e)^n)*log(x) - 12*b*e^2*log(x)*log(x^(1/3*n)) + 9*b*d^2*n*x^(2/3) - 36*b*d*e*n*x^(1/3) - 6*(b*d^2*n*x^(2/3) - 2*b*d*e*n*x^(1/3))*log(x) + 12*(b*e^2*log(c) + a*e^2)*log(x) + 3*(2*b*d^2*n*x*log(x) - 3*b*d^2*n*x)/x^(1/3) - 12*(b*d*e*n*x*log(x) - 3*b*d*e*n*x)/x^(2/3))/e^2","B",0
494,1,86,0,0.469384," ","integrate((a+b*log(c*(d+e/x^(1/3))^n))/x^2,x, algorithm=""maxima"")","-\frac{1}{6} \, b e n {\left(\frac{6 \, d^{3} \log\left(d x^{\frac{1}{3}} + e\right)}{e^{4}} - \frac{2 \, d^{3} \log\left(x\right)}{e^{4}} - \frac{6 \, d^{2} x^{\frac{2}{3}} - 3 \, d e x^{\frac{1}{3}} + 2 \, e^{2}}{e^{3} x}\right)} - \frac{b \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right)}{x} - \frac{a}{x}"," ",0,"-1/6*b*e*n*(6*d^3*log(d*x^(1/3) + e)/e^4 - 2*d^3*log(x)/e^4 - (6*d^2*x^(2/3) - 3*d*e*x^(1/3) + 2*e^2)/(e^3*x)) - b*log(c*(d + e/x^(1/3))^n)/x - a/x","A",0
495,1,117,0,0.474456," ","integrate((a+b*log(c*(d+e/x^(1/3))^n))/x^3,x, algorithm=""maxima"")","\frac{1}{120} \, b e n {\left(\frac{60 \, d^{6} \log\left(d x^{\frac{1}{3}} + e\right)}{e^{7}} - \frac{20 \, d^{6} \log\left(x\right)}{e^{7}} - \frac{60 \, d^{5} x^{\frac{5}{3}} - 30 \, d^{4} e x^{\frac{4}{3}} + 20 \, d^{3} e^{2} x - 15 \, d^{2} e^{3} x^{\frac{2}{3}} + 12 \, d e^{4} x^{\frac{1}{3}} - 10 \, e^{5}}{e^{6} x^{2}}\right)} - \frac{b \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right)}{2 \, x^{2}} - \frac{a}{2 \, x^{2}}"," ",0,"1/120*b*e*n*(60*d^6*log(d*x^(1/3) + e)/e^7 - 20*d^6*log(x)/e^7 - (60*d^5*x^(5/3) - 30*d^4*e*x^(4/3) + 20*d^3*e^2*x - 15*d^2*e^3*x^(2/3) + 12*d*e^4*x^(1/3) - 10*e^5)/(e^6*x^2)) - 1/2*b*log(c*(d + e/x^(1/3))^n)/x^2 - 1/2*a/x^2","A",0
496,1,150,0,0.475550," ","integrate((a+b*log(c*(d+e/x^(1/3))^n))/x^4,x, algorithm=""maxima"")","-\frac{1}{7560} \, b e n {\left(\frac{2520 \, d^{9} \log\left(d x^{\frac{1}{3}} + e\right)}{e^{10}} - \frac{840 \, d^{9} \log\left(x\right)}{e^{10}} - \frac{2520 \, d^{8} x^{\frac{8}{3}} - 1260 \, d^{7} e x^{\frac{7}{3}} + 840 \, d^{6} e^{2} x^{2} - 630 \, d^{5} e^{3} x^{\frac{5}{3}} + 504 \, d^{4} e^{4} x^{\frac{4}{3}} - 420 \, d^{3} e^{5} x + 360 \, d^{2} e^{6} x^{\frac{2}{3}} - 315 \, d e^{7} x^{\frac{1}{3}} + 280 \, e^{8}}{e^{9} x^{3}}\right)} - \frac{b \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right)}{3 \, x^{3}} - \frac{a}{3 \, x^{3}}"," ",0,"-1/7560*b*e*n*(2520*d^9*log(d*x^(1/3) + e)/e^10 - 840*d^9*log(x)/e^10 - (2520*d^8*x^(8/3) - 1260*d^7*e*x^(7/3) + 840*d^6*e^2*x^2 - 630*d^5*e^3*x^(5/3) + 504*d^4*e^4*x^(4/3) - 420*d^3*e^5*x + 360*d^2*e^6*x^(2/3) - 315*d*e^7*x^(1/3) + 280*e^8)/(e^9*x^3)) - 1/3*b*log(c*(d + e/x^(1/3))^n)/x^3 - 1/3*a/x^3","A",0
497,0,0,0,0.000000," ","integrate(x^2*(a+b*log(c*(d+e/x^(1/3))^n))^2,x, algorithm=""maxima"")","\frac{1}{3} \, b^{2} x^{3} \log\left({\left(d x^{\frac{1}{3}} + e\right)}^{n}\right)^{2} - \int -\frac{9 \, {\left(b^{2} d \log\left(c\right)^{2} + 2 \, a b d \log\left(c\right) + a^{2} d\right)} x^{3} + 9 \, {\left(b^{2} e \log\left(c\right)^{2} + 2 \, a b e \log\left(c\right) + a^{2} e\right)} x^{\frac{8}{3}} + 9 \, {\left(b^{2} d x^{3} + b^{2} e x^{\frac{8}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} - 2 \, {\left(b^{2} d n x^{3} - 9 \, {\left(b^{2} d \log\left(c\right) + a b d\right)} x^{3} - 9 \, {\left(b^{2} e \log\left(c\right) + a b e\right)} x^{\frac{8}{3}} + 9 \, {\left(b^{2} d x^{3} + b^{2} e x^{\frac{8}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)\right)} \log\left({\left(d x^{\frac{1}{3}} + e\right)}^{n}\right) - 18 \, {\left({\left(b^{2} d \log\left(c\right) + a b d\right)} x^{3} + {\left(b^{2} e \log\left(c\right) + a b e\right)} x^{\frac{8}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)}{9 \, {\left(d x + e x^{\frac{2}{3}}\right)}}\,{d x}"," ",0,"1/3*b^2*x^3*log((d*x^(1/3) + e)^n)^2 - integrate(-1/9*(9*(b^2*d*log(c)^2 + 2*a*b*d*log(c) + a^2*d)*x^3 + 9*(b^2*e*log(c)^2 + 2*a*b*e*log(c) + a^2*e)*x^(8/3) + 9*(b^2*d*x^3 + b^2*e*x^(8/3))*log(x^(1/3*n))^2 - 2*(b^2*d*n*x^3 - 9*(b^2*d*log(c) + a*b*d)*x^3 - 9*(b^2*e*log(c) + a*b*e)*x^(8/3) + 9*(b^2*d*x^3 + b^2*e*x^(8/3))*log(x^(1/3*n)))*log((d*x^(1/3) + e)^n) - 18*((b^2*d*log(c) + a*b*d)*x^3 + (b^2*e*log(c) + a*b*e)*x^(8/3))*log(x^(1/3*n)))/(d*x + e*x^(2/3)), x)","F",0
498,0,0,0,0.000000," ","integrate(x*(a+b*log(c*(d+e/x^(1/3))^n))^2,x, algorithm=""maxima"")","\frac{1}{2} \, b^{2} x^{2} \log\left({\left(d x^{\frac{1}{3}} + e\right)}^{n}\right)^{2} - \int -\frac{3 \, {\left(b^{2} d \log\left(c\right)^{2} + 2 \, a b d \log\left(c\right) + a^{2} d\right)} x^{2} + 3 \, {\left(b^{2} d x^{2} + b^{2} e x^{\frac{5}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} + 3 \, {\left(b^{2} e \log\left(c\right)^{2} + 2 \, a b e \log\left(c\right) + a^{2} e\right)} x^{\frac{5}{3}} - {\left(b^{2} d n x^{2} - 6 \, {\left(b^{2} d \log\left(c\right) + a b d\right)} x^{2} - 6 \, {\left(b^{2} e \log\left(c\right) + a b e\right)} x^{\frac{5}{3}} + 6 \, {\left(b^{2} d x^{2} + b^{2} e x^{\frac{5}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)\right)} \log\left({\left(d x^{\frac{1}{3}} + e\right)}^{n}\right) - 6 \, {\left({\left(b^{2} d \log\left(c\right) + a b d\right)} x^{2} + {\left(b^{2} e \log\left(c\right) + a b e\right)} x^{\frac{5}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)}{3 \, {\left(d x + e x^{\frac{2}{3}}\right)}}\,{d x}"," ",0,"1/2*b^2*x^2*log((d*x^(1/3) + e)^n)^2 - integrate(-1/3*(3*(b^2*d*log(c)^2 + 2*a*b*d*log(c) + a^2*d)*x^2 + 3*(b^2*d*x^2 + b^2*e*x^(5/3))*log(x^(1/3*n))^2 + 3*(b^2*e*log(c)^2 + 2*a*b*e*log(c) + a^2*e)*x^(5/3) - (b^2*d*n*x^2 - 6*(b^2*d*log(c) + a*b*d)*x^2 - 6*(b^2*e*log(c) + a*b*e)*x^(5/3) + 6*(b^2*d*x^2 + b^2*e*x^(5/3))*log(x^(1/3*n)))*log((d*x^(1/3) + e)^n) - 6*((b^2*d*log(c) + a*b*d)*x^2 + (b^2*e*log(c) + a*b*e)*x^(5/3))*log(x^(1/3*n)))/(d*x + e*x^(2/3)), x)","F",0
499,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(1/3))^n))^2,x, algorithm=""maxima"")","{\left(e n {\left(\frac{2 \, e^{2} \log\left(d x^{\frac{1}{3}} + e\right)}{d^{3}} + \frac{d x^{\frac{2}{3}} - 2 \, e x^{\frac{1}{3}}}{d^{2}}\right)} + 2 \, x \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right)\right)} a b + {\left(x \log\left({\left(d x^{\frac{1}{3}} + e\right)}^{n}\right)^{2} - \int -\frac{3 \, d x \log\left(c\right)^{2} + 3 \, e x^{\frac{2}{3}} \log\left(c\right)^{2} + 3 \, {\left(d x + e x^{\frac{2}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} - 2 \, {\left(d n x - 3 \, d x \log\left(c\right) - 3 \, e x^{\frac{2}{3}} \log\left(c\right) + 3 \, {\left(d x + e x^{\frac{2}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)\right)} \log\left({\left(d x^{\frac{1}{3}} + e\right)}^{n}\right) - 6 \, {\left(d x \log\left(c\right) + e x^{\frac{2}{3}} \log\left(c\right)\right)} \log\left(x^{\frac{1}{3} \, n}\right)}{3 \, {\left(d x + e x^{\frac{2}{3}}\right)}}\,{d x}\right)} b^{2} + a^{2} x"," ",0,"(e*n*(2*e^2*log(d*x^(1/3) + e)/d^3 + (d*x^(2/3) - 2*e*x^(1/3))/d^2) + 2*x*log(c*(d + e/x^(1/3))^n))*a*b + (x*log((d*x^(1/3) + e)^n)^2 - integrate(-1/3*(3*d*x*log(c)^2 + 3*e*x^(2/3)*log(c)^2 + 3*(d*x + e*x^(2/3))*log(x^(1/3*n))^2 - 2*(d*n*x - 3*d*x*log(c) - 3*e*x^(2/3)*log(c) + 3*(d*x + e*x^(2/3))*log(x^(1/3*n)))*log((d*x^(1/3) + e)^n) - 6*(d*x*log(c) + e*x^(2/3)*log(c))*log(x^(1/3*n)))/(d*x + e*x^(2/3)), x))*b^2 + a^2*x","F",0
500,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(1/3))^n))^2/x,x, algorithm=""maxima"")","b^{2} \log\left({\left(d x^{\frac{1}{3}} + e\right)}^{n}\right)^{2} \log\left(x\right) - \int -\frac{3 \, {\left(b^{2} d x + b^{2} e x^{\frac{2}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} + 3 \, {\left(b^{2} d \log\left(c\right)^{2} + 2 \, a b d \log\left(c\right) + a^{2} d\right)} x - 2 \, {\left(b^{2} d n x \log\left(x\right) - 3 \, {\left(b^{2} d \log\left(c\right) + a b d\right)} x + 3 \, {\left(b^{2} d x + b^{2} e x^{\frac{2}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right) - 3 \, {\left(b^{2} e \log\left(c\right) + a b e\right)} x^{\frac{2}{3}}\right)} \log\left({\left(d x^{\frac{1}{3}} + e\right)}^{n}\right) - 6 \, {\left({\left(b^{2} d \log\left(c\right) + a b d\right)} x + {\left(b^{2} e \log\left(c\right) + a b e\right)} x^{\frac{2}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right) + 3 \, {\left(b^{2} e \log\left(c\right)^{2} + 2 \, a b e \log\left(c\right) + a^{2} e\right)} x^{\frac{2}{3}}}{3 \, {\left(d x^{2} + e x^{\frac{5}{3}}\right)}}\,{d x}"," ",0,"b^2*log((d*x^(1/3) + e)^n)^2*log(x) - integrate(-1/3*(3*(b^2*d*x + b^2*e*x^(2/3))*log(x^(1/3*n))^2 + 3*(b^2*d*log(c)^2 + 2*a*b*d*log(c) + a^2*d)*x - 2*(b^2*d*n*x*log(x) - 3*(b^2*d*log(c) + a*b*d)*x + 3*(b^2*d*x + b^2*e*x^(2/3))*log(x^(1/3*n)) - 3*(b^2*e*log(c) + a*b*e)*x^(2/3))*log((d*x^(1/3) + e)^n) - 6*((b^2*d*log(c) + a*b*d)*x + (b^2*e*log(c) + a*b*e)*x^(2/3))*log(x^(1/3*n)) + 3*(b^2*e*log(c)^2 + 2*a*b*e*log(c) + a^2*e)*x^(2/3))/(d*x^2 + e*x^(5/3)), x)","F",0
501,1,284,0,0.518616," ","integrate((a+b*log(c*(d+e/x^(1/3))^n))^2/x^2,x, algorithm=""maxima"")","-\frac{1}{3} \, a b e n {\left(\frac{6 \, d^{3} \log\left(d x^{\frac{1}{3}} + e\right)}{e^{4}} - \frac{2 \, d^{3} \log\left(x\right)}{e^{4}} - \frac{6 \, d^{2} x^{\frac{2}{3}} - 3 \, d e x^{\frac{1}{3}} + 2 \, e^{2}}{e^{3} x}\right)} - \frac{1}{18} \, {\left(6 \, e n {\left(\frac{6 \, d^{3} \log\left(d x^{\frac{1}{3}} + e\right)}{e^{4}} - \frac{2 \, d^{3} \log\left(x\right)}{e^{4}} - \frac{6 \, d^{2} x^{\frac{2}{3}} - 3 \, d e x^{\frac{1}{3}} + 2 \, e^{2}}{e^{3} x}\right)} \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right) - \frac{{\left(18 \, d^{3} x \log\left(d x^{\frac{1}{3}} + e\right)^{2} + 2 \, d^{3} x \log\left(x\right)^{2} - 22 \, d^{3} x \log\left(x\right) - 66 \, d^{2} e x^{\frac{2}{3}} + 15 \, d e^{2} x^{\frac{1}{3}} - 4 \, e^{3} - 6 \, {\left(2 \, d^{3} x \log\left(x\right) - 11 \, d^{3} x\right)} \log\left(d x^{\frac{1}{3}} + e\right)\right)} n^{2}}{e^{3} x}\right)} b^{2} - \frac{b^{2} \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right)^{2}}{x} - \frac{2 \, a b \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right)}{x} - \frac{a^{2}}{x}"," ",0,"-1/3*a*b*e*n*(6*d^3*log(d*x^(1/3) + e)/e^4 - 2*d^3*log(x)/e^4 - (6*d^2*x^(2/3) - 3*d*e*x^(1/3) + 2*e^2)/(e^3*x)) - 1/18*(6*e*n*(6*d^3*log(d*x^(1/3) + e)/e^4 - 2*d^3*log(x)/e^4 - (6*d^2*x^(2/3) - 3*d*e*x^(1/3) + 2*e^2)/(e^3*x))*log(c*(d + e/x^(1/3))^n) - (18*d^3*x*log(d*x^(1/3) + e)^2 + 2*d^3*x*log(x)^2 - 22*d^3*x*log(x) - 66*d^2*e*x^(2/3) + 15*d*e^2*x^(1/3) - 4*e^3 - 6*(2*d^3*x*log(x) - 11*d^3*x)*log(d*x^(1/3) + e))*n^2/(e^3*x))*b^2 - b^2*log(c*(d + e/x^(1/3))^n)^2/x - 2*a*b*log(c*(d + e/x^(1/3))^n)/x - a^2/x","A",0
502,1,387,0,0.533150," ","integrate((a+b*log(c*(d+e/x^(1/3))^n))^2/x^3,x, algorithm=""maxima"")","\frac{1}{60} \, a b e n {\left(\frac{60 \, d^{6} \log\left(d x^{\frac{1}{3}} + e\right)}{e^{7}} - \frac{20 \, d^{6} \log\left(x\right)}{e^{7}} - \frac{60 \, d^{5} x^{\frac{5}{3}} - 30 \, d^{4} e x^{\frac{4}{3}} + 20 \, d^{3} e^{2} x - 15 \, d^{2} e^{3} x^{\frac{2}{3}} + 12 \, d e^{4} x^{\frac{1}{3}} - 10 \, e^{5}}{e^{6} x^{2}}\right)} + \frac{1}{3600} \, {\left(60 \, e n {\left(\frac{60 \, d^{6} \log\left(d x^{\frac{1}{3}} + e\right)}{e^{7}} - \frac{20 \, d^{6} \log\left(x\right)}{e^{7}} - \frac{60 \, d^{5} x^{\frac{5}{3}} - 30 \, d^{4} e x^{\frac{4}{3}} + 20 \, d^{3} e^{2} x - 15 \, d^{2} e^{3} x^{\frac{2}{3}} + 12 \, d e^{4} x^{\frac{1}{3}} - 10 \, e^{5}}{e^{6} x^{2}}\right)} \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right) - \frac{{\left(1800 \, d^{6} x^{2} \log\left(d x^{\frac{1}{3}} + e\right)^{2} + 200 \, d^{6} x^{2} \log\left(x\right)^{2} - 2940 \, d^{6} x^{2} \log\left(x\right) - 8820 \, d^{5} e x^{\frac{5}{3}} + 2610 \, d^{4} e^{2} x^{\frac{4}{3}} - 1140 \, d^{3} e^{3} x + 555 \, d^{2} e^{4} x^{\frac{2}{3}} - 264 \, d e^{5} x^{\frac{1}{3}} + 100 \, e^{6} - 60 \, {\left(20 \, d^{6} x^{2} \log\left(x\right) - 147 \, d^{6} x^{2}\right)} \log\left(d x^{\frac{1}{3}} + e\right)\right)} n^{2}}{e^{6} x^{2}}\right)} b^{2} - \frac{b^{2} \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right)^{2}}{2 \, x^{2}} - \frac{a b \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right)}{x^{2}} - \frac{a^{2}}{2 \, x^{2}}"," ",0,"1/60*a*b*e*n*(60*d^6*log(d*x^(1/3) + e)/e^7 - 20*d^6*log(x)/e^7 - (60*d^5*x^(5/3) - 30*d^4*e*x^(4/3) + 20*d^3*e^2*x - 15*d^2*e^3*x^(2/3) + 12*d*e^4*x^(1/3) - 10*e^5)/(e^6*x^2)) + 1/3600*(60*e*n*(60*d^6*log(d*x^(1/3) + e)/e^7 - 20*d^6*log(x)/e^7 - (60*d^5*x^(5/3) - 30*d^4*e*x^(4/3) + 20*d^3*e^2*x - 15*d^2*e^3*x^(2/3) + 12*d*e^4*x^(1/3) - 10*e^5)/(e^6*x^2))*log(c*(d + e/x^(1/3))^n) - (1800*d^6*x^2*log(d*x^(1/3) + e)^2 + 200*d^6*x^2*log(x)^2 - 2940*d^6*x^2*log(x) - 8820*d^5*e*x^(5/3) + 2610*d^4*e^2*x^(4/3) - 1140*d^3*e^3*x + 555*d^2*e^4*x^(2/3) - 264*d*e^5*x^(1/3) + 100*e^6 - 60*(20*d^6*x^2*log(x) - 147*d^6*x^2)*log(d*x^(1/3) + e))*n^2/(e^6*x^2))*b^2 - 1/2*b^2*log(c*(d + e/x^(1/3))^n)^2/x^2 - a*b*log(c*(d + e/x^(1/3))^n)/x^2 - 1/2*a^2/x^2","A",0
503,0,0,0,0.000000," ","integrate(x*(a+b*log(c*(d+e/x^(1/3))^n))^3,x, algorithm=""maxima"")","\frac{1}{2} \, b^{3} x^{2} \log\left({\left(d x^{\frac{1}{3}} + e\right)}^{n}\right)^{3} - \int \frac{2 \, {\left(b^{3} d x^{2} + b^{3} e x^{\frac{5}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{3} - 2 \, {\left(b^{3} d \log\left(c\right)^{3} + 3 \, a b^{2} d \log\left(c\right)^{2} + 3 \, a^{2} b d \log\left(c\right) + a^{3} d\right)} x^{2} + {\left(b^{3} d n x^{2} - 6 \, {\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x^{2} - 6 \, {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{5}{3}} + 6 \, {\left(b^{3} d x^{2} + b^{3} e x^{\frac{5}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)\right)} \log\left({\left(d x^{\frac{1}{3}} + e\right)}^{n}\right)^{2} - 6 \, {\left({\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x^{2} + {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{5}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} - 2 \, {\left(b^{3} e \log\left(c\right)^{3} + 3 \, a b^{2} e \log\left(c\right)^{2} + 3 \, a^{2} b e \log\left(c\right) + a^{3} e\right)} x^{\frac{5}{3}} - 6 \, {\left({\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} x^{2} + {\left(b^{3} d x^{2} + b^{3} e x^{\frac{5}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} + {\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} x^{\frac{5}{3}} - 2 \, {\left({\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x^{2} + {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{5}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)\right)} \log\left({\left(d x^{\frac{1}{3}} + e\right)}^{n}\right) + 6 \, {\left({\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} x^{2} + {\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} x^{\frac{5}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)}{2 \, {\left(d x + e x^{\frac{2}{3}}\right)}}\,{d x}"," ",0,"1/2*b^3*x^2*log((d*x^(1/3) + e)^n)^3 - integrate(1/2*(2*(b^3*d*x^2 + b^3*e*x^(5/3))*log(x^(1/3*n))^3 - 2*(b^3*d*log(c)^3 + 3*a*b^2*d*log(c)^2 + 3*a^2*b*d*log(c) + a^3*d)*x^2 + (b^3*d*n*x^2 - 6*(b^3*d*log(c) + a*b^2*d)*x^2 - 6*(b^3*e*log(c) + a*b^2*e)*x^(5/3) + 6*(b^3*d*x^2 + b^3*e*x^(5/3))*log(x^(1/3*n)))*log((d*x^(1/3) + e)^n)^2 - 6*((b^3*d*log(c) + a*b^2*d)*x^2 + (b^3*e*log(c) + a*b^2*e)*x^(5/3))*log(x^(1/3*n))^2 - 2*(b^3*e*log(c)^3 + 3*a*b^2*e*log(c)^2 + 3*a^2*b*e*log(c) + a^3*e)*x^(5/3) - 6*((b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*x^2 + (b^3*d*x^2 + b^3*e*x^(5/3))*log(x^(1/3*n))^2 + (b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*x^(5/3) - 2*((b^3*d*log(c) + a*b^2*d)*x^2 + (b^3*e*log(c) + a*b^2*e)*x^(5/3))*log(x^(1/3*n)))*log((d*x^(1/3) + e)^n) + 6*((b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*x^2 + (b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*x^(5/3))*log(x^(1/3*n)))/(d*x + e*x^(2/3)), x)","F",0
504,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(1/3))^n))^3,x, algorithm=""maxima"")","b^{3} x \log\left({\left(d x^{\frac{1}{3}} + e\right)}^{n}\right)^{3} + \frac{3}{2} \, {\left(e n {\left(\frac{2 \, e^{2} \log\left(d x^{\frac{1}{3}} + e\right)}{d^{3}} + \frac{d x^{\frac{2}{3}} - 2 \, e x^{\frac{1}{3}}}{d^{2}}\right)} + 2 \, x \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right)\right)} a^{2} b + a^{3} x - \int \frac{{\left(b^{3} d x + b^{3} e x^{\frac{2}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{3} + {\left(b^{3} d n x - 3 \, {\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x + 3 \, {\left(b^{3} d x + b^{3} e x^{\frac{2}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right) - 3 \, {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{2}{3}}\right)} \log\left({\left(d x^{\frac{1}{3}} + e\right)}^{n}\right)^{2} - 3 \, {\left({\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x + {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{2}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} - {\left(b^{3} d \log\left(c\right)^{3} + 3 \, a b^{2} d \log\left(c\right)^{2}\right)} x - 3 \, {\left({\left(b^{3} d x + b^{3} e x^{\frac{2}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} + {\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right)\right)} x - 2 \, {\left({\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x + {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{2}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right) + {\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right)\right)} x^{\frac{2}{3}}\right)} \log\left({\left(d x^{\frac{1}{3}} + e\right)}^{n}\right) + 3 \, {\left({\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right)\right)} x + {\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right)\right)} x^{\frac{2}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right) - {\left(b^{3} e \log\left(c\right)^{3} + 3 \, a b^{2} e \log\left(c\right)^{2}\right)} x^{\frac{2}{3}}}{d x + e x^{\frac{2}{3}}}\,{d x}"," ",0,"b^3*x*log((d*x^(1/3) + e)^n)^3 + 3/2*(e*n*(2*e^2*log(d*x^(1/3) + e)/d^3 + (d*x^(2/3) - 2*e*x^(1/3))/d^2) + 2*x*log(c*(d + e/x^(1/3))^n))*a^2*b + a^3*x - integrate(((b^3*d*x + b^3*e*x^(2/3))*log(x^(1/3*n))^3 + (b^3*d*n*x - 3*(b^3*d*log(c) + a*b^2*d)*x + 3*(b^3*d*x + b^3*e*x^(2/3))*log(x^(1/3*n)) - 3*(b^3*e*log(c) + a*b^2*e)*x^(2/3))*log((d*x^(1/3) + e)^n)^2 - 3*((b^3*d*log(c) + a*b^2*d)*x + (b^3*e*log(c) + a*b^2*e)*x^(2/3))*log(x^(1/3*n))^2 - (b^3*d*log(c)^3 + 3*a*b^2*d*log(c)^2)*x - 3*((b^3*d*x + b^3*e*x^(2/3))*log(x^(1/3*n))^2 + (b^3*d*log(c)^2 + 2*a*b^2*d*log(c))*x - 2*((b^3*d*log(c) + a*b^2*d)*x + (b^3*e*log(c) + a*b^2*e)*x^(2/3))*log(x^(1/3*n)) + (b^3*e*log(c)^2 + 2*a*b^2*e*log(c))*x^(2/3))*log((d*x^(1/3) + e)^n) + 3*((b^3*d*log(c)^2 + 2*a*b^2*d*log(c))*x + (b^3*e*log(c)^2 + 2*a*b^2*e*log(c))*x^(2/3))*log(x^(1/3*n)) - (b^3*e*log(c)^3 + 3*a*b^2*e*log(c)^2)*x^(2/3))/(d*x + e*x^(2/3)), x)","F",0
505,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(1/3))^n))^3/x,x, algorithm=""maxima"")","b^{3} \log\left({\left(d x^{\frac{1}{3}} + e\right)}^{n}\right)^{3} \log\left(x\right) - \int \frac{{\left(b^{3} d x + b^{3} e x^{\frac{2}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{3} + {\left(b^{3} d n x \log\left(x\right) - 3 \, {\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x + 3 \, {\left(b^{3} d x + b^{3} e x^{\frac{2}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right) - 3 \, {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{2}{3}}\right)} \log\left({\left(d x^{\frac{1}{3}} + e\right)}^{n}\right)^{2} - 3 \, {\left({\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x + {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{2}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} - {\left(b^{3} d \log\left(c\right)^{3} + 3 \, a b^{2} d \log\left(c\right)^{2} + 3 \, a^{2} b d \log\left(c\right) + a^{3} d\right)} x - 3 \, {\left({\left(b^{3} d x + b^{3} e x^{\frac{2}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} + {\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} x - 2 \, {\left({\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x + {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{2}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right) + {\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} x^{\frac{2}{3}}\right)} \log\left({\left(d x^{\frac{1}{3}} + e\right)}^{n}\right) + 3 \, {\left({\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} x + {\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} x^{\frac{2}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right) - {\left(b^{3} e \log\left(c\right)^{3} + 3 \, a b^{2} e \log\left(c\right)^{2} + 3 \, a^{2} b e \log\left(c\right) + a^{3} e\right)} x^{\frac{2}{3}}}{d x^{2} + e x^{\frac{5}{3}}}\,{d x}"," ",0,"b^3*log((d*x^(1/3) + e)^n)^3*log(x) - integrate(((b^3*d*x + b^3*e*x^(2/3))*log(x^(1/3*n))^3 + (b^3*d*n*x*log(x) - 3*(b^3*d*log(c) + a*b^2*d)*x + 3*(b^3*d*x + b^3*e*x^(2/3))*log(x^(1/3*n)) - 3*(b^3*e*log(c) + a*b^2*e)*x^(2/3))*log((d*x^(1/3) + e)^n)^2 - 3*((b^3*d*log(c) + a*b^2*d)*x + (b^3*e*log(c) + a*b^2*e)*x^(2/3))*log(x^(1/3*n))^2 - (b^3*d*log(c)^3 + 3*a*b^2*d*log(c)^2 + 3*a^2*b*d*log(c) + a^3*d)*x - 3*((b^3*d*x + b^3*e*x^(2/3))*log(x^(1/3*n))^2 + (b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*x - 2*((b^3*d*log(c) + a*b^2*d)*x + (b^3*e*log(c) + a*b^2*e)*x^(2/3))*log(x^(1/3*n)) + (b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*x^(2/3))*log((d*x^(1/3) + e)^n) + 3*((b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*x + (b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*x^(2/3))*log(x^(1/3*n)) - (b^3*e*log(c)^3 + 3*a*b^2*e*log(c)^2 + 3*a^2*b*e*log(c) + a^3*e)*x^(2/3))/(d*x^2 + e*x^(5/3)), x)","F",0
506,1,640,0,0.592429," ","integrate((a+b*log(c*(d+e/x^(1/3))^n))^3/x^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a^{2} b e n {\left(\frac{6 \, d^{3} \log\left(d x^{\frac{1}{3}} + e\right)}{e^{4}} - \frac{2 \, d^{3} \log\left(x\right)}{e^{4}} - \frac{6 \, d^{2} x^{\frac{2}{3}} - 3 \, d e x^{\frac{1}{3}} + 2 \, e^{2}}{e^{3} x}\right)} - \frac{b^{3} \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right)^{3}}{x} - \frac{1}{6} \, {\left(6 \, e n {\left(\frac{6 \, d^{3} \log\left(d x^{\frac{1}{3}} + e\right)}{e^{4}} - \frac{2 \, d^{3} \log\left(x\right)}{e^{4}} - \frac{6 \, d^{2} x^{\frac{2}{3}} - 3 \, d e x^{\frac{1}{3}} + 2 \, e^{2}}{e^{3} x}\right)} \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right) - \frac{{\left(18 \, d^{3} x \log\left(d x^{\frac{1}{3}} + e\right)^{2} + 2 \, d^{3} x \log\left(x\right)^{2} - 22 \, d^{3} x \log\left(x\right) - 66 \, d^{2} e x^{\frac{2}{3}} + 15 \, d e^{2} x^{\frac{1}{3}} - 4 \, e^{3} - 6 \, {\left(2 \, d^{3} x \log\left(x\right) - 11 \, d^{3} x\right)} \log\left(d x^{\frac{1}{3}} + e\right)\right)} n^{2}}{e^{3} x}\right)} a b^{2} - \frac{1}{108} \, {\left(54 \, e n {\left(\frac{6 \, d^{3} \log\left(d x^{\frac{1}{3}} + e\right)}{e^{4}} - \frac{2 \, d^{3} \log\left(x\right)}{e^{4}} - \frac{6 \, d^{2} x^{\frac{2}{3}} - 3 \, d e x^{\frac{1}{3}} + 2 \, e^{2}}{e^{3} x}\right)} \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right)^{2} + e n {\left(\frac{{\left(108 \, d^{3} x \log\left(d x^{\frac{1}{3}} + e\right)^{3} - 4 \, d^{3} x \log\left(x\right)^{3} + 66 \, d^{3} x \log\left(x\right)^{2} - 510 \, d^{3} x \log\left(x\right) - 1530 \, d^{2} e x^{\frac{2}{3}} + 171 \, d e^{2} x^{\frac{1}{3}} - 24 \, e^{3} - 54 \, {\left(2 \, d^{3} x \log\left(x\right) - 11 \, d^{3} x\right)} \log\left(d x^{\frac{1}{3}} + e\right)^{2} + 18 \, {\left(2 \, d^{3} x \log\left(x\right)^{2} - 22 \, d^{3} x \log\left(x\right) + 85 \, d^{3} x\right)} \log\left(d x^{\frac{1}{3}} + e\right)\right)} n^{2}}{e^{4} x} - \frac{18 \, {\left(18 \, d^{3} x \log\left(d x^{\frac{1}{3}} + e\right)^{2} + 2 \, d^{3} x \log\left(x\right)^{2} - 22 \, d^{3} x \log\left(x\right) - 66 \, d^{2} e x^{\frac{2}{3}} + 15 \, d e^{2} x^{\frac{1}{3}} - 4 \, e^{3} - 6 \, {\left(2 \, d^{3} x \log\left(x\right) - 11 \, d^{3} x\right)} \log\left(d x^{\frac{1}{3}} + e\right)\right)} n \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right)}{e^{4} x}\right)}\right)} b^{3} - \frac{3 \, a b^{2} \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right)^{2}}{x} - \frac{3 \, a^{2} b \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right)}{x} - \frac{a^{3}}{x}"," ",0,"-1/2*a^2*b*e*n*(6*d^3*log(d*x^(1/3) + e)/e^4 - 2*d^3*log(x)/e^4 - (6*d^2*x^(2/3) - 3*d*e*x^(1/3) + 2*e^2)/(e^3*x)) - b^3*log(c*(d + e/x^(1/3))^n)^3/x - 1/6*(6*e*n*(6*d^3*log(d*x^(1/3) + e)/e^4 - 2*d^3*log(x)/e^4 - (6*d^2*x^(2/3) - 3*d*e*x^(1/3) + 2*e^2)/(e^3*x))*log(c*(d + e/x^(1/3))^n) - (18*d^3*x*log(d*x^(1/3) + e)^2 + 2*d^3*x*log(x)^2 - 22*d^3*x*log(x) - 66*d^2*e*x^(2/3) + 15*d*e^2*x^(1/3) - 4*e^3 - 6*(2*d^3*x*log(x) - 11*d^3*x)*log(d*x^(1/3) + e))*n^2/(e^3*x))*a*b^2 - 1/108*(54*e*n*(6*d^3*log(d*x^(1/3) + e)/e^4 - 2*d^3*log(x)/e^4 - (6*d^2*x^(2/3) - 3*d*e*x^(1/3) + 2*e^2)/(e^3*x))*log(c*(d + e/x^(1/3))^n)^2 + e*n*((108*d^3*x*log(d*x^(1/3) + e)^3 - 4*d^3*x*log(x)^3 + 66*d^3*x*log(x)^2 - 510*d^3*x*log(x) - 1530*d^2*e*x^(2/3) + 171*d*e^2*x^(1/3) - 24*e^3 - 54*(2*d^3*x*log(x) - 11*d^3*x)*log(d*x^(1/3) + e)^2 + 18*(2*d^3*x*log(x)^2 - 22*d^3*x*log(x) + 85*d^3*x)*log(d*x^(1/3) + e))*n^2/(e^4*x) - 18*(18*d^3*x*log(d*x^(1/3) + e)^2 + 2*d^3*x*log(x)^2 - 22*d^3*x*log(x) - 66*d^2*e*x^(2/3) + 15*d*e^2*x^(1/3) - 4*e^3 - 6*(2*d^3*x*log(x) - 11*d^3*x)*log(d*x^(1/3) + e))*n*log(c*(d + e/x^(1/3))^n)/(e^4*x)))*b^3 - 3*a*b^2*log(c*(d + e/x^(1/3))^n)^2/x - 3*a^2*b*log(c*(d + e/x^(1/3))^n)/x - a^3/x","A",0
507,1,864,0,0.639674," ","integrate((a+b*log(c*(d+e/x^(1/3))^n))^3/x^3,x, algorithm=""maxima"")","\frac{1}{40} \, a^{2} b e n {\left(\frac{60 \, d^{6} \log\left(d x^{\frac{1}{3}} + e\right)}{e^{7}} - \frac{20 \, d^{6} \log\left(x\right)}{e^{7}} - \frac{60 \, d^{5} x^{\frac{5}{3}} - 30 \, d^{4} e x^{\frac{4}{3}} + 20 \, d^{3} e^{2} x - 15 \, d^{2} e^{3} x^{\frac{2}{3}} + 12 \, d e^{4} x^{\frac{1}{3}} - 10 \, e^{5}}{e^{6} x^{2}}\right)} + \frac{1}{1200} \, {\left(60 \, e n {\left(\frac{60 \, d^{6} \log\left(d x^{\frac{1}{3}} + e\right)}{e^{7}} - \frac{20 \, d^{6} \log\left(x\right)}{e^{7}} - \frac{60 \, d^{5} x^{\frac{5}{3}} - 30 \, d^{4} e x^{\frac{4}{3}} + 20 \, d^{3} e^{2} x - 15 \, d^{2} e^{3} x^{\frac{2}{3}} + 12 \, d e^{4} x^{\frac{1}{3}} - 10 \, e^{5}}{e^{6} x^{2}}\right)} \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right) - \frac{{\left(1800 \, d^{6} x^{2} \log\left(d x^{\frac{1}{3}} + e\right)^{2} + 200 \, d^{6} x^{2} \log\left(x\right)^{2} - 2940 \, d^{6} x^{2} \log\left(x\right) - 8820 \, d^{5} e x^{\frac{5}{3}} + 2610 \, d^{4} e^{2} x^{\frac{4}{3}} - 1140 \, d^{3} e^{3} x + 555 \, d^{2} e^{4} x^{\frac{2}{3}} - 264 \, d e^{5} x^{\frac{1}{3}} + 100 \, e^{6} - 60 \, {\left(20 \, d^{6} x^{2} \log\left(x\right) - 147 \, d^{6} x^{2}\right)} \log\left(d x^{\frac{1}{3}} + e\right)\right)} n^{2}}{e^{6} x^{2}}\right)} a b^{2} + \frac{1}{216000} \, {\left(5400 \, e n {\left(\frac{60 \, d^{6} \log\left(d x^{\frac{1}{3}} + e\right)}{e^{7}} - \frac{20 \, d^{6} \log\left(x\right)}{e^{7}} - \frac{60 \, d^{5} x^{\frac{5}{3}} - 30 \, d^{4} e x^{\frac{4}{3}} + 20 \, d^{3} e^{2} x - 15 \, d^{2} e^{3} x^{\frac{2}{3}} + 12 \, d e^{4} x^{\frac{1}{3}} - 10 \, e^{5}}{e^{6} x^{2}}\right)} \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right)^{2} + e n {\left(\frac{{\left(108000 \, d^{6} x^{2} \log\left(d x^{\frac{1}{3}} + e\right)^{3} - 4000 \, d^{6} x^{2} \log\left(x\right)^{3} + 88200 \, d^{6} x^{2} \log\left(x\right)^{2} - 809340 \, d^{6} x^{2} \log\left(x\right) - 2428020 \, d^{5} e x^{\frac{5}{3}} + 420210 \, d^{4} e^{2} x^{\frac{4}{3}} - 123540 \, d^{3} e^{3} x + 41355 \, d^{2} e^{4} x^{\frac{2}{3}} - 13104 \, d e^{5} x^{\frac{1}{3}} + 3000 \, e^{6} - 5400 \, {\left(20 \, d^{6} x^{2} \log\left(x\right) - 147 \, d^{6} x^{2}\right)} \log\left(d x^{\frac{1}{3}} + e\right)^{2} + 180 \, {\left(200 \, d^{6} x^{2} \log\left(x\right)^{2} - 2940 \, d^{6} x^{2} \log\left(x\right) + 13489 \, d^{6} x^{2}\right)} \log\left(d x^{\frac{1}{3}} + e\right)\right)} n^{2}}{e^{7} x^{2}} - \frac{180 \, {\left(1800 \, d^{6} x^{2} \log\left(d x^{\frac{1}{3}} + e\right)^{2} + 200 \, d^{6} x^{2} \log\left(x\right)^{2} - 2940 \, d^{6} x^{2} \log\left(x\right) - 8820 \, d^{5} e x^{\frac{5}{3}} + 2610 \, d^{4} e^{2} x^{\frac{4}{3}} - 1140 \, d^{3} e^{3} x + 555 \, d^{2} e^{4} x^{\frac{2}{3}} - 264 \, d e^{5} x^{\frac{1}{3}} + 100 \, e^{6} - 60 \, {\left(20 \, d^{6} x^{2} \log\left(x\right) - 147 \, d^{6} x^{2}\right)} \log\left(d x^{\frac{1}{3}} + e\right)\right)} n \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right)}{e^{7} x^{2}}\right)}\right)} b^{3} - \frac{b^{3} \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right)^{3}}{2 \, x^{2}} - \frac{3 \, a b^{2} \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right)^{2}}{2 \, x^{2}} - \frac{3 \, a^{2} b \log\left(c {\left(d + \frac{e}{x^{\frac{1}{3}}}\right)}^{n}\right)}{2 \, x^{2}} - \frac{a^{3}}{2 \, x^{2}}"," ",0,"1/40*a^2*b*e*n*(60*d^6*log(d*x^(1/3) + e)/e^7 - 20*d^6*log(x)/e^7 - (60*d^5*x^(5/3) - 30*d^4*e*x^(4/3) + 20*d^3*e^2*x - 15*d^2*e^3*x^(2/3) + 12*d*e^4*x^(1/3) - 10*e^5)/(e^6*x^2)) + 1/1200*(60*e*n*(60*d^6*log(d*x^(1/3) + e)/e^7 - 20*d^6*log(x)/e^7 - (60*d^5*x^(5/3) - 30*d^4*e*x^(4/3) + 20*d^3*e^2*x - 15*d^2*e^3*x^(2/3) + 12*d*e^4*x^(1/3) - 10*e^5)/(e^6*x^2))*log(c*(d + e/x^(1/3))^n) - (1800*d^6*x^2*log(d*x^(1/3) + e)^2 + 200*d^6*x^2*log(x)^2 - 2940*d^6*x^2*log(x) - 8820*d^5*e*x^(5/3) + 2610*d^4*e^2*x^(4/3) - 1140*d^3*e^3*x + 555*d^2*e^4*x^(2/3) - 264*d*e^5*x^(1/3) + 100*e^6 - 60*(20*d^6*x^2*log(x) - 147*d^6*x^2)*log(d*x^(1/3) + e))*n^2/(e^6*x^2))*a*b^2 + 1/216000*(5400*e*n*(60*d^6*log(d*x^(1/3) + e)/e^7 - 20*d^6*log(x)/e^7 - (60*d^5*x^(5/3) - 30*d^4*e*x^(4/3) + 20*d^3*e^2*x - 15*d^2*e^3*x^(2/3) + 12*d*e^4*x^(1/3) - 10*e^5)/(e^6*x^2))*log(c*(d + e/x^(1/3))^n)^2 + e*n*((108000*d^6*x^2*log(d*x^(1/3) + e)^3 - 4000*d^6*x^2*log(x)^3 + 88200*d^6*x^2*log(x)^2 - 809340*d^6*x^2*log(x) - 2428020*d^5*e*x^(5/3) + 420210*d^4*e^2*x^(4/3) - 123540*d^3*e^3*x + 41355*d^2*e^4*x^(2/3) - 13104*d*e^5*x^(1/3) + 3000*e^6 - 5400*(20*d^6*x^2*log(x) - 147*d^6*x^2)*log(d*x^(1/3) + e)^2 + 180*(200*d^6*x^2*log(x)^2 - 2940*d^6*x^2*log(x) + 13489*d^6*x^2)*log(d*x^(1/3) + e))*n^2/(e^7*x^2) - 180*(1800*d^6*x^2*log(d*x^(1/3) + e)^2 + 200*d^6*x^2*log(x)^2 - 2940*d^6*x^2*log(x) - 8820*d^5*e*x^(5/3) + 2610*d^4*e^2*x^(4/3) - 1140*d^3*e^3*x + 555*d^2*e^4*x^(2/3) - 264*d*e^5*x^(1/3) + 100*e^6 - 60*(20*d^6*x^2*log(x) - 147*d^6*x^2)*log(d*x^(1/3) + e))*n*log(c*(d + e/x^(1/3))^n)/(e^7*x^2)))*b^3 - 1/2*b^3*log(c*(d + e/x^(1/3))^n)^3/x^2 - 3/2*a*b^2*log(c*(d + e/x^(1/3))^n)^2/x^2 - 3/2*a^2*b*log(c*(d + e/x^(1/3))^n)/x^2 - 1/2*a^3/x^2","A",0
508,1,98,0,0.469589," ","integrate(x^3*(a+b*log(c*(d+e/x^(2/3))^n)),x, algorithm=""maxima"")","\frac{1}{4} \, b x^{4} \log\left(c {\left(d + \frac{e}{x^{\frac{2}{3}}}\right)}^{n}\right) + \frac{1}{4} \, a x^{4} - \frac{1}{240} \, b e n {\left(\frac{60 \, e^{5} \log\left(d x^{\frac{2}{3}} + e\right)}{d^{6}} - \frac{12 \, d^{4} x^{\frac{10}{3}} - 15 \, d^{3} e x^{\frac{8}{3}} + 20 \, d^{2} e^{2} x^{2} - 30 \, d e^{3} x^{\frac{4}{3}} + 60 \, e^{4} x^{\frac{2}{3}}}{d^{5}}\right)}"," ",0,"1/4*b*x^4*log(c*(d + e/x^(2/3))^n) + 1/4*a*x^4 - 1/240*b*e*n*(60*e^5*log(d*x^(2/3) + e)/d^6 - (12*d^4*x^(10/3) - 15*d^3*e*x^(8/3) + 20*d^2*e^2*x^2 - 30*d*e^3*x^(4/3) + 60*e^4*x^(2/3))/d^5)","A",0
509,1,92,0,0.997170," ","integrate(x^2*(a+b*log(c*(d+e/x^(2/3))^n)),x, algorithm=""maxima"")","\frac{1}{3} \, b x^{3} \log\left(c {\left(d + \frac{e}{x^{\frac{2}{3}}}\right)}^{n}\right) + \frac{1}{3} \, a x^{3} + \frac{2}{315} \, b e n {\left(\frac{105 \, e^{4} \arctan\left(\frac{d x^{\frac{1}{3}}}{\sqrt{d e}}\right)}{\sqrt{d e} d^{4}} + \frac{15 \, d^{3} x^{\frac{7}{3}} - 21 \, d^{2} e x^{\frac{5}{3}} + 35 \, d e^{2} x - 105 \, e^{3} x^{\frac{1}{3}}}{d^{4}}\right)}"," ",0,"1/3*b*x^3*log(c*(d + e/x^(2/3))^n) + 1/3*a*x^3 + 2/315*b*e*n*(105*e^4*arctan(d*x^(1/3)/sqrt(d*e))/(sqrt(d*e)*d^4) + (15*d^3*x^(7/3) - 21*d^2*e*x^(5/3) + 35*d*e^2*x - 105*e^3*x^(1/3))/d^4)","A",0
510,1,63,0,0.465714," ","integrate(x*(a+b*log(c*(d+e/x^(2/3))^n)),x, algorithm=""maxima"")","\frac{1}{4} \, b e n {\left(\frac{2 \, e^{2} \log\left(d x^{\frac{2}{3}} + e\right)}{d^{3}} + \frac{d x^{\frac{4}{3}} - 2 \, e x^{\frac{2}{3}}}{d^{2}}\right)} + \frac{1}{2} \, b x^{2} \log\left(c {\left(d + \frac{e}{x^{\frac{2}{3}}}\right)}^{n}\right) + \frac{1}{2} \, a x^{2}"," ",0,"1/4*b*e*n*(2*e^2*log(d*x^(2/3) + e)/d^3 + (d*x^(4/3) - 2*e*x^(2/3))/d^2) + 1/2*b*x^2*log(c*(d + e/x^(2/3))^n) + 1/2*a*x^2","A",0
511,1,57,0,0.985305," ","integrate(a+b*log(c*(d+e/x^(2/3))^n),x, algorithm=""maxima"")","-{\left(2 \, e n {\left(\frac{e \arctan\left(\frac{d x^{\frac{1}{3}}}{\sqrt{d e}}\right)}{\sqrt{d e} d} - \frac{x^{\frac{1}{3}}}{d}\right)} - x \log\left(c {\left(d + \frac{e}{x^{\frac{2}{3}}}\right)}^{n}\right)\right)} b + a x"," ",0,"-(2*e*n*(e*arctan(d*x^(1/3)/sqrt(d*e))/(sqrt(d*e)*d) - x^(1/3)/d) - x*log(c*(d + e/x^(2/3))^n))*b + a*x","A",0
512,1,126,0,1.743338," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))/x,x, algorithm=""maxima"")","-\frac{3}{2} \, {\left(2 \, \log\left(\frac{d x^{\frac{2}{3}}}{e} + 1\right) \log\left(x^{\frac{1}{3}}\right) + {\rm Li}_2\left(-\frac{d x^{\frac{2}{3}}}{e}\right)\right)} b n + \frac{6 \, b e n \log\left(d x^{\frac{2}{3}} + e\right) \log\left(x\right) + 2 \, b e n \log\left(x\right)^{2} + 6 \, b d n x^{\frac{2}{3}} \log\left(x\right) - 12 \, b e \log\left(x\right) \log\left(x^{\frac{1}{3} \, n}\right) - 9 \, b d n x^{\frac{2}{3}} + 6 \, {\left(b e \log\left(c\right) + a e\right)} \log\left(x\right) - \frac{3 \, {\left(2 \, b d n x \log\left(x\right) - 3 \, b d n x\right)}}{x^{\frac{1}{3}}}}{6 \, e}"," ",0,"-3/2*(2*log(d*x^(2/3)/e + 1)*log(x^(1/3)) + dilog(-d*x^(2/3)/e))*b*n + 1/6*(6*b*e*n*log(d*x^(2/3) + e)*log(x) + 2*b*e*n*log(x)^2 + 6*b*d*n*x^(2/3)*log(x) - 12*b*e*log(x)*log(x^(1/3*n)) - 9*b*d*n*x^(2/3) + 6*(b*e*log(c) + a*e)*log(x) - 3*(2*b*d*n*x*log(x) - 3*b*d*n*x)/x^(1/3))/e","B",0
513,1,72,0,0.991946," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))/x^2,x, algorithm=""maxima"")","-\frac{2}{3} \, b e n {\left(\frac{3 \, d^{2} \arctan\left(\frac{d x^{\frac{1}{3}}}{\sqrt{d e}}\right)}{\sqrt{d e} e^{2}} + \frac{3 \, d x^{\frac{2}{3}} - e}{e^{2} x}\right)} - \frac{b \log\left(c {\left(d + \frac{e}{x^{\frac{2}{3}}}\right)}^{n}\right)}{x} - \frac{a}{x}"," ",0,"-2/3*b*e*n*(3*d^2*arctan(d*x^(1/3)/sqrt(d*e))/(sqrt(d*e)*e^2) + (3*d*x^(2/3) - e)/(e^2*x)) - b*log(c*(d + e/x^(2/3))^n)/x - a/x","A",0
514,1,88,0,0.468980," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))/x^3,x, algorithm=""maxima"")","-\frac{1}{12} \, b e n {\left(\frac{6 \, d^{3} \log\left(d x^{\frac{2}{3}} + e\right)}{e^{4}} - \frac{6 \, d^{3} \log\left(x^{\frac{2}{3}}\right)}{e^{4}} - \frac{6 \, d^{2} x^{\frac{4}{3}} - 3 \, d e x^{\frac{2}{3}} + 2 \, e^{2}}{e^{3} x^{2}}\right)} - \frac{b \log\left(c {\left(d + \frac{e}{x^{\frac{2}{3}}}\right)}^{n}\right)}{2 \, x^{2}} - \frac{a}{2 \, x^{2}}"," ",0,"-1/12*b*e*n*(6*d^3*log(d*x^(2/3) + e)/e^4 - 6*d^3*log(x^(2/3))/e^4 - (6*d^2*x^(4/3) - 3*d*e*x^(2/3) + 2*e^2)/(e^3*x^2)) - 1/2*b*log(c*(d + e/x^(2/3))^n)/x^2 - 1/2*a/x^2","A",0
515,1,105,0,0.998137," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))/x^4,x, algorithm=""maxima"")","\frac{2}{945} \, b e n {\left(\frac{315 \, d^{5} \arctan\left(\frac{d x^{\frac{1}{3}}}{\sqrt{d e}}\right)}{\sqrt{d e} e^{5}} + \frac{315 \, d^{4} x^{\frac{8}{3}} - 105 \, d^{3} e x^{2} + 63 \, d^{2} e^{2} x^{\frac{4}{3}} - 45 \, d e^{3} x^{\frac{2}{3}} + 35 \, e^{4}}{e^{5} x^{3}}\right)} - \frac{b \log\left(c {\left(d + \frac{e}{x^{\frac{2}{3}}}\right)}^{n}\right)}{3 \, x^{3}} - \frac{a}{3 \, x^{3}}"," ",0,"2/945*b*e*n*(315*d^5*arctan(d*x^(1/3)/sqrt(d*e))/(sqrt(d*e)*e^5) + (315*d^4*x^(8/3) - 105*d^3*e*x^2 + 63*d^2*e^2*x^(4/3) - 45*d*e^3*x^(2/3) + 35*e^4)/(e^5*x^3)) - 1/3*b*log(c*(d + e/x^(2/3))^n)/x^3 - 1/3*a/x^3","A",0
516,0,0,0,0.000000," ","integrate(x^3*(a+b*log(c*(d+e/x^(2/3))^n))^2,x, algorithm=""maxima"")","\frac{1}{4} \, b^{2} n^{2} x^{4} \log\left(d x^{\frac{2}{3}} + e\right)^{2} - \int -\frac{3 \, {\left(b^{2} d \log\left(c\right)^{2} + 2 \, a b d \log\left(c\right) + a^{2} d\right)} x^{4} + 3 \, {\left(b^{2} e \log\left(c\right)^{2} + 2 \, a b e \log\left(c\right) + a^{2} e\right)} x^{\frac{10}{3}} - {\left(b^{2} d n x^{4} - 6 \, {\left(b^{2} d \log\left(c\right) + a b d\right)} x^{4} - 6 \, {\left(b^{2} e \log\left(c\right) + a b e\right)} x^{\frac{10}{3}} + 12 \, {\left(b^{2} d x^{4} + b^{2} e x^{\frac{10}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)\right)} n \log\left(d x^{\frac{2}{3}} + e\right) + 12 \, {\left(b^{2} d x^{4} + b^{2} e x^{\frac{10}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} - 12 \, {\left({\left(b^{2} d \log\left(c\right) + a b d\right)} x^{4} + {\left(b^{2} e \log\left(c\right) + a b e\right)} x^{\frac{10}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)}{3 \, {\left(d x + e x^{\frac{1}{3}}\right)}}\,{d x}"," ",0,"1/4*b^2*n^2*x^4*log(d*x^(2/3) + e)^2 - integrate(-1/3*(3*(b^2*d*log(c)^2 + 2*a*b*d*log(c) + a^2*d)*x^4 + 3*(b^2*e*log(c)^2 + 2*a*b*e*log(c) + a^2*e)*x^(10/3) - (b^2*d*n*x^4 - 6*(b^2*d*log(c) + a*b*d)*x^4 - 6*(b^2*e*log(c) + a*b*e)*x^(10/3) + 12*(b^2*d*x^4 + b^2*e*x^(10/3))*log(x^(1/3*n)))*n*log(d*x^(2/3) + e) + 12*(b^2*d*x^4 + b^2*e*x^(10/3))*log(x^(1/3*n))^2 - 12*((b^2*d*log(c) + a*b*d)*x^4 + (b^2*e*log(c) + a*b*e)*x^(10/3))*log(x^(1/3*n)))/(d*x + e*x^(1/3)), x)","F",0
517,0,0,0,0.000000," ","integrate(x*(a+b*log(c*(d+e/x^(2/3))^n))^2,x, algorithm=""maxima"")","\frac{1}{2} \, b^{2} n^{2} x^{2} \log\left(d x^{\frac{2}{3}} + e\right)^{2} - \int -\frac{3 \, {\left(b^{2} d \log\left(c\right)^{2} + 2 \, a b d \log\left(c\right) + a^{2} d\right)} x^{2} - 2 \, {\left(b^{2} d n x^{2} - 3 \, {\left(b^{2} d \log\left(c\right) + a b d\right)} x^{2} - 3 \, {\left(b^{2} e \log\left(c\right) + a b e\right)} x^{\frac{4}{3}} + 6 \, {\left(b^{2} d x^{2} + b^{2} e x^{\frac{4}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)\right)} n \log\left(d x^{\frac{2}{3}} + e\right) + 12 \, {\left(b^{2} d x^{2} + b^{2} e x^{\frac{4}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} + 3 \, {\left(b^{2} e \log\left(c\right)^{2} + 2 \, a b e \log\left(c\right) + a^{2} e\right)} x^{\frac{4}{3}} - 12 \, {\left({\left(b^{2} d \log\left(c\right) + a b d\right)} x^{2} + {\left(b^{2} e \log\left(c\right) + a b e\right)} x^{\frac{4}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)}{3 \, {\left(d x + e x^{\frac{1}{3}}\right)}}\,{d x}"," ",0,"1/2*b^2*n^2*x^2*log(d*x^(2/3) + e)^2 - integrate(-1/3*(3*(b^2*d*log(c)^2 + 2*a*b*d*log(c) + a^2*d)*x^2 - 2*(b^2*d*n*x^2 - 3*(b^2*d*log(c) + a*b*d)*x^2 - 3*(b^2*e*log(c) + a*b*e)*x^(4/3) + 6*(b^2*d*x^2 + b^2*e*x^(4/3))*log(x^(1/3*n)))*n*log(d*x^(2/3) + e) + 12*(b^2*d*x^2 + b^2*e*x^(4/3))*log(x^(1/3*n))^2 + 3*(b^2*e*log(c)^2 + 2*a*b*e*log(c) + a^2*e)*x^(4/3) - 12*((b^2*d*log(c) + a*b*d)*x^2 + (b^2*e*log(c) + a*b*e)*x^(4/3))*log(x^(1/3*n)))/(d*x + e*x^(1/3)), x)","F",0
518,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))^2/x,x, algorithm=""maxima"")","b^{2} n^{2} \log\left(d x^{\frac{2}{3}} + e\right)^{2} \log\left(x\right) - \int \frac{2 \, {\left(2 \, b^{2} d n x \log\left(x\right) - 3 \, {\left(b^{2} d \log\left(c\right) + a b d\right)} x + 6 \, {\left(b^{2} d x + b^{2} e x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right) - 3 \, {\left(b^{2} e \log\left(c\right) + a b e\right)} x^{\frac{1}{3}}\right)} n \log\left(d x^{\frac{2}{3}} + e\right) - 12 \, {\left(b^{2} d x + b^{2} e x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} - 3 \, {\left(b^{2} d \log\left(c\right)^{2} + 2 \, a b d \log\left(c\right) + a^{2} d\right)} x + 12 \, {\left({\left(b^{2} d \log\left(c\right) + a b d\right)} x + {\left(b^{2} e \log\left(c\right) + a b e\right)} x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right) - 3 \, {\left(b^{2} e \log\left(c\right)^{2} + 2 \, a b e \log\left(c\right) + a^{2} e\right)} x^{\frac{1}{3}}}{3 \, {\left(d x^{2} + e x^{\frac{4}{3}}\right)}}\,{d x}"," ",0,"b^2*n^2*log(d*x^(2/3) + e)^2*log(x) - integrate(1/3*(2*(2*b^2*d*n*x*log(x) - 3*(b^2*d*log(c) + a*b*d)*x + 6*(b^2*d*x + b^2*e*x^(1/3))*log(x^(1/3*n)) - 3*(b^2*e*log(c) + a*b*e)*x^(1/3))*n*log(d*x^(2/3) + e) - 12*(b^2*d*x + b^2*e*x^(1/3))*log(x^(1/3*n))^2 - 3*(b^2*d*log(c)^2 + 2*a*b*d*log(c) + a^2*d)*x + 12*((b^2*d*log(c) + a*b*d)*x + (b^2*e*log(c) + a*b*e)*x^(1/3))*log(x^(1/3*n)) - 3*(b^2*e*log(c)^2 + 2*a*b*e*log(c) + a^2*e)*x^(1/3))/(d*x^2 + e*x^(4/3)), x)","F",0
519,1,298,0,0.520147," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))^2/x^3,x, algorithm=""maxima"")","-\frac{1}{6} \, a b e n {\left(\frac{6 \, d^{3} \log\left(d x^{\frac{2}{3}} + e\right)}{e^{4}} - \frac{6 \, d^{3} \log\left(x^{\frac{2}{3}}\right)}{e^{4}} - \frac{6 \, d^{2} x^{\frac{4}{3}} - 3 \, d e x^{\frac{2}{3}} + 2 \, e^{2}}{e^{3} x^{2}}\right)} - \frac{1}{36} \, {\left(6 \, e n {\left(\frac{6 \, d^{3} \log\left(d x^{\frac{2}{3}} + e\right)}{e^{4}} - \frac{6 \, d^{3} \log\left(x^{\frac{2}{3}}\right)}{e^{4}} - \frac{6 \, d^{2} x^{\frac{4}{3}} - 3 \, d e x^{\frac{2}{3}} + 2 \, e^{2}}{e^{3} x^{2}}\right)} \log\left(c {\left(d + \frac{e}{x^{\frac{2}{3}}}\right)}^{n}\right) - \frac{{\left(18 \, d^{3} x^{2} \log\left(d x^{\frac{2}{3}} + e\right)^{2} + 8 \, d^{3} x^{2} \log\left(x\right)^{2} - 44 \, d^{3} x^{2} \log\left(x\right) - 66 \, d^{2} e x^{\frac{4}{3}} + 15 \, d e^{2} x^{\frac{2}{3}} - 4 \, e^{3} - 6 \, {\left(4 \, d^{3} x^{2} \log\left(x\right) - 11 \, d^{3} x^{2}\right)} \log\left(d x^{\frac{2}{3}} + e\right)\right)} n^{2}}{e^{3} x^{2}}\right)} b^{2} - \frac{b^{2} \log\left(c {\left(d + \frac{e}{x^{\frac{2}{3}}}\right)}^{n}\right)^{2}}{2 \, x^{2}} - \frac{a b \log\left(c {\left(d + \frac{e}{x^{\frac{2}{3}}}\right)}^{n}\right)}{x^{2}} - \frac{a^{2}}{2 \, x^{2}}"," ",0,"-1/6*a*b*e*n*(6*d^3*log(d*x^(2/3) + e)/e^4 - 6*d^3*log(x^(2/3))/e^4 - (6*d^2*x^(4/3) - 3*d*e*x^(2/3) + 2*e^2)/(e^3*x^2)) - 1/36*(6*e*n*(6*d^3*log(d*x^(2/3) + e)/e^4 - 6*d^3*log(x^(2/3))/e^4 - (6*d^2*x^(4/3) - 3*d*e*x^(2/3) + 2*e^2)/(e^3*x^2))*log(c*(d + e/x^(2/3))^n) - (18*d^3*x^2*log(d*x^(2/3) + e)^2 + 8*d^3*x^2*log(x)^2 - 44*d^3*x^2*log(x) - 66*d^2*e*x^(4/3) + 15*d*e^2*x^(2/3) - 4*e^3 - 6*(4*d^3*x^2*log(x) - 11*d^3*x^2)*log(d*x^(2/3) + e))*n^2/(e^3*x^2))*b^2 - 1/2*b^2*log(c*(d + e/x^(2/3))^n)^2/x^2 - a*b*log(c*(d + e/x^(2/3))^n)/x^2 - 1/2*a^2/x^2","A",0
520,1,397,0,0.536361," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))^2/x^5,x, algorithm=""maxima"")","\frac{1}{120} \, a b e n {\left(\frac{60 \, d^{6} \log\left(d x^{\frac{2}{3}} + e\right)}{e^{7}} - \frac{60 \, d^{6} \log\left(x^{\frac{2}{3}}\right)}{e^{7}} - \frac{60 \, d^{5} x^{\frac{10}{3}} - 30 \, d^{4} e x^{\frac{8}{3}} + 20 \, d^{3} e^{2} x^{2} - 15 \, d^{2} e^{3} x^{\frac{4}{3}} + 12 \, d e^{4} x^{\frac{2}{3}} - 10 \, e^{5}}{e^{6} x^{4}}\right)} + \frac{1}{7200} \, {\left(60 \, e n {\left(\frac{60 \, d^{6} \log\left(d x^{\frac{2}{3}} + e\right)}{e^{7}} - \frac{60 \, d^{6} \log\left(x^{\frac{2}{3}}\right)}{e^{7}} - \frac{60 \, d^{5} x^{\frac{10}{3}} - 30 \, d^{4} e x^{\frac{8}{3}} + 20 \, d^{3} e^{2} x^{2} - 15 \, d^{2} e^{3} x^{\frac{4}{3}} + 12 \, d e^{4} x^{\frac{2}{3}} - 10 \, e^{5}}{e^{6} x^{4}}\right)} \log\left(c {\left(d + \frac{e}{x^{\frac{2}{3}}}\right)}^{n}\right) - \frac{{\left(1800 \, d^{6} x^{4} \log\left(d x^{\frac{2}{3}} + e\right)^{2} + 800 \, d^{6} x^{4} \log\left(x\right)^{2} - 5880 \, d^{6} x^{4} \log\left(x\right) - 8820 \, d^{5} e x^{\frac{10}{3}} + 2610 \, d^{4} e^{2} x^{\frac{8}{3}} - 1140 \, d^{3} e^{3} x^{2} + 555 \, d^{2} e^{4} x^{\frac{4}{3}} - 264 \, d e^{5} x^{\frac{2}{3}} + 100 \, e^{6} - 60 \, {\left(40 \, d^{6} x^{4} \log\left(x\right) - 147 \, d^{6} x^{4}\right)} \log\left(d x^{\frac{2}{3}} + e\right)\right)} n^{2}}{e^{6} x^{4}}\right)} b^{2} - \frac{b^{2} \log\left(c {\left(d + \frac{e}{x^{\frac{2}{3}}}\right)}^{n}\right)^{2}}{4 \, x^{4}} - \frac{a b \log\left(c {\left(d + \frac{e}{x^{\frac{2}{3}}}\right)}^{n}\right)}{2 \, x^{4}} - \frac{a^{2}}{4 \, x^{4}}"," ",0,"1/120*a*b*e*n*(60*d^6*log(d*x^(2/3) + e)/e^7 - 60*d^6*log(x^(2/3))/e^7 - (60*d^5*x^(10/3) - 30*d^4*e*x^(8/3) + 20*d^3*e^2*x^2 - 15*d^2*e^3*x^(4/3) + 12*d*e^4*x^(2/3) - 10*e^5)/(e^6*x^4)) + 1/7200*(60*e*n*(60*d^6*log(d*x^(2/3) + e)/e^7 - 60*d^6*log(x^(2/3))/e^7 - (60*d^5*x^(10/3) - 30*d^4*e*x^(8/3) + 20*d^3*e^2*x^2 - 15*d^2*e^3*x^(4/3) + 12*d*e^4*x^(2/3) - 10*e^5)/(e^6*x^4))*log(c*(d + e/x^(2/3))^n) - (1800*d^6*x^4*log(d*x^(2/3) + e)^2 + 800*d^6*x^4*log(x)^2 - 5880*d^6*x^4*log(x) - 8820*d^5*e*x^(10/3) + 2610*d^4*e^2*x^(8/3) - 1140*d^3*e^3*x^2 + 555*d^2*e^4*x^(4/3) - 264*d*e^5*x^(2/3) + 100*e^6 - 60*(40*d^6*x^4*log(x) - 147*d^6*x^4)*log(d*x^(2/3) + e))*n^2/(e^6*x^4))*b^2 - 1/4*b^2*log(c*(d + e/x^(2/3))^n)^2/x^4 - 1/2*a*b*log(c*(d + e/x^(2/3))^n)/x^4 - 1/4*a^2/x^4","A",0
521,0,0,0,0.000000," ","integrate(x^2*(a+b*log(c*(d+e/x^(2/3))^n))^2,x, algorithm=""maxima"")","\frac{1}{3} \, b^{2} n^{2} x^{3} \log\left(d x^{\frac{2}{3}} + e\right)^{2} - \int -\frac{9 \, {\left(b^{2} d \log\left(c\right)^{2} + 2 \, a b d \log\left(c\right) + a^{2} d\right)} x^{3} + 9 \, {\left(b^{2} e \log\left(c\right)^{2} + 2 \, a b e \log\left(c\right) + a^{2} e\right)} x^{\frac{7}{3}} - 2 \, {\left(2 \, b^{2} d n x^{3} - 9 \, {\left(b^{2} d \log\left(c\right) + a b d\right)} x^{3} - 9 \, {\left(b^{2} e \log\left(c\right) + a b e\right)} x^{\frac{7}{3}} + 18 \, {\left(b^{2} d x^{3} + b^{2} e x^{\frac{7}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)\right)} n \log\left(d x^{\frac{2}{3}} + e\right) + 36 \, {\left(b^{2} d x^{3} + b^{2} e x^{\frac{7}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} - 36 \, {\left({\left(b^{2} d \log\left(c\right) + a b d\right)} x^{3} + {\left(b^{2} e \log\left(c\right) + a b e\right)} x^{\frac{7}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)}{9 \, {\left(d x + e x^{\frac{1}{3}}\right)}}\,{d x}"," ",0,"1/3*b^2*n^2*x^3*log(d*x^(2/3) + e)^2 - integrate(-1/9*(9*(b^2*d*log(c)^2 + 2*a*b*d*log(c) + a^2*d)*x^3 + 9*(b^2*e*log(c)^2 + 2*a*b*e*log(c) + a^2*e)*x^(7/3) - 2*(2*b^2*d*n*x^3 - 9*(b^2*d*log(c) + a*b*d)*x^3 - 9*(b^2*e*log(c) + a*b*e)*x^(7/3) + 18*(b^2*d*x^3 + b^2*e*x^(7/3))*log(x^(1/3*n)))*n*log(d*x^(2/3) + e) + 36*(b^2*d*x^3 + b^2*e*x^(7/3))*log(x^(1/3*n))^2 - 36*((b^2*d*log(c) + a*b*d)*x^3 + (b^2*e*log(c) + a*b*e)*x^(7/3))*log(x^(1/3*n)))/(d*x + e*x^(1/3)), x)","F",0
522,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))^2,x, algorithm=""maxima"")","-2 \, {\left(2 \, e n {\left(\frac{e \arctan\left(\frac{d x^{\frac{1}{3}}}{\sqrt{d e}}\right)}{\sqrt{d e} d} - \frac{x^{\frac{1}{3}}}{d}\right)} - x \log\left(c {\left(d + \frac{e}{x^{\frac{2}{3}}}\right)}^{n}\right)\right)} a b + {\left(n^{2} x \log\left(d x^{\frac{2}{3}} + e\right)^{2} - \int -\frac{3 \, d x \log\left(c\right)^{2} + 3 \, e x^{\frac{1}{3}} \log\left(c\right)^{2} - 2 \, {\left(2 \, d n x - 3 \, d x \log\left(c\right) - 3 \, e x^{\frac{1}{3}} \log\left(c\right) + 6 \, {\left(d x + e x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)\right)} n \log\left(d x^{\frac{2}{3}} + e\right) + 12 \, {\left(d x + e x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} - 12 \, {\left(d x \log\left(c\right) + e x^{\frac{1}{3}} \log\left(c\right)\right)} \log\left(x^{\frac{1}{3} \, n}\right)}{3 \, {\left(d x + e x^{\frac{1}{3}}\right)}}\,{d x}\right)} b^{2} + a^{2} x"," ",0,"-2*(2*e*n*(e*arctan(d*x^(1/3)/sqrt(d*e))/(sqrt(d*e)*d) - x^(1/3)/d) - x*log(c*(d + e/x^(2/3))^n))*a*b + (n^2*x*log(d*x^(2/3) + e)^2 - integrate(-1/3*(3*d*x*log(c)^2 + 3*e*x^(1/3)*log(c)^2 - 2*(2*d*n*x - 3*d*x*log(c) - 3*e*x^(1/3)*log(c) + 6*(d*x + e*x^(1/3))*log(x^(1/3*n)))*n*log(d*x^(2/3) + e) + 12*(d*x + e*x^(1/3))*log(x^(1/3*n))^2 - 12*(d*x*log(c) + e*x^(1/3)*log(c))*log(x^(1/3*n)))/(d*x + e*x^(1/3)), x))*b^2 + a^2*x","F",0
523,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))^2/x^2,x, algorithm=""maxima"")","-\frac{b^{2} n^{2} \log\left(d x^{\frac{2}{3}} + e\right)^{2}}{x} - \int -\frac{2 \, {\left(2 \, b^{2} d n x + 3 \, {\left(b^{2} d \log\left(c\right) + a b d\right)} x - 6 \, {\left(b^{2} d x + b^{2} e x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right) + 3 \, {\left(b^{2} e \log\left(c\right) + a b e\right)} x^{\frac{1}{3}}\right)} n \log\left(d x^{\frac{2}{3}} + e\right) + 12 \, {\left(b^{2} d x + b^{2} e x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} + 3 \, {\left(b^{2} d \log\left(c\right)^{2} + 2 \, a b d \log\left(c\right) + a^{2} d\right)} x - 12 \, {\left({\left(b^{2} d \log\left(c\right) + a b d\right)} x + {\left(b^{2} e \log\left(c\right) + a b e\right)} x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right) + 3 \, {\left(b^{2} e \log\left(c\right)^{2} + 2 \, a b e \log\left(c\right) + a^{2} e\right)} x^{\frac{1}{3}}}{3 \, {\left(d x^{3} + e x^{\frac{7}{3}}\right)}}\,{d x}"," ",0,"-b^2*n^2*log(d*x^(2/3) + e)^2/x - integrate(-1/3*(2*(2*b^2*d*n*x + 3*(b^2*d*log(c) + a*b*d)*x - 6*(b^2*d*x + b^2*e*x^(1/3))*log(x^(1/3*n)) + 3*(b^2*e*log(c) + a*b*e)*x^(1/3))*n*log(d*x^(2/3) + e) + 12*(b^2*d*x + b^2*e*x^(1/3))*log(x^(1/3*n))^2 + 3*(b^2*d*log(c)^2 + 2*a*b*d*log(c) + a^2*d)*x - 12*((b^2*d*log(c) + a*b*d)*x + (b^2*e*log(c) + a*b*e)*x^(1/3))*log(x^(1/3*n)) + 3*(b^2*e*log(c)^2 + 2*a*b*e*log(c) + a^2*e)*x^(1/3))/(d*x^3 + e*x^(7/3)), x)","F",0
524,0,0,0,0.000000," ","integrate(x^3*(a+b*log(c*(d+e/x^(2/3))^n))^3,x, algorithm=""maxima"")","\frac{1}{4} \, b^{3} n^{3} x^{4} \log\left(d x^{\frac{2}{3}} + e\right)^{3} - \int -\frac{2 \, {\left(b^{3} d \log\left(c\right)^{3} + 3 \, a b^{2} d \log\left(c\right)^{2} + 3 \, a^{2} b d \log\left(c\right) + a^{3} d\right)} x^{4} - {\left(b^{3} d n x^{4} - 6 \, {\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x^{4} - 6 \, {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{10}{3}} + 12 \, {\left(b^{3} d x^{4} + b^{3} e x^{\frac{10}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)\right)} n^{2} \log\left(d x^{\frac{2}{3}} + e\right)^{2} + 2 \, {\left(b^{3} e \log\left(c\right)^{3} + 3 \, a b^{2} e \log\left(c\right)^{2} + 3 \, a^{2} b e \log\left(c\right) + a^{3} e\right)} x^{\frac{10}{3}} - 16 \, {\left(b^{3} d x^{4} + b^{3} e x^{\frac{10}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{3} + 6 \, {\left({\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} x^{4} + {\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} x^{\frac{10}{3}} + 4 \, {\left(b^{3} d x^{4} + b^{3} e x^{\frac{10}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} - 4 \, {\left({\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x^{4} + {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{10}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)\right)} n \log\left(d x^{\frac{2}{3}} + e\right) + 24 \, {\left({\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x^{4} + {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{10}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} - 12 \, {\left({\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} x^{4} + {\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} x^{\frac{10}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)}{2 \, {\left(d x + e x^{\frac{1}{3}}\right)}}\,{d x}"," ",0,"1/4*b^3*n^3*x^4*log(d*x^(2/3) + e)^3 - integrate(-1/2*(2*(b^3*d*log(c)^3 + 3*a*b^2*d*log(c)^2 + 3*a^2*b*d*log(c) + a^3*d)*x^4 - (b^3*d*n*x^4 - 6*(b^3*d*log(c) + a*b^2*d)*x^4 - 6*(b^3*e*log(c) + a*b^2*e)*x^(10/3) + 12*(b^3*d*x^4 + b^3*e*x^(10/3))*log(x^(1/3*n)))*n^2*log(d*x^(2/3) + e)^2 + 2*(b^3*e*log(c)^3 + 3*a*b^2*e*log(c)^2 + 3*a^2*b*e*log(c) + a^3*e)*x^(10/3) - 16*(b^3*d*x^4 + b^3*e*x^(10/3))*log(x^(1/3*n))^3 + 6*((b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*x^4 + (b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*x^(10/3) + 4*(b^3*d*x^4 + b^3*e*x^(10/3))*log(x^(1/3*n))^2 - 4*((b^3*d*log(c) + a*b^2*d)*x^4 + (b^3*e*log(c) + a*b^2*e)*x^(10/3))*log(x^(1/3*n)))*n*log(d*x^(2/3) + e) + 24*((b^3*d*log(c) + a*b^2*d)*x^4 + (b^3*e*log(c) + a*b^2*e)*x^(10/3))*log(x^(1/3*n))^2 - 12*((b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*x^4 + (b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*x^(10/3))*log(x^(1/3*n)))/(d*x + e*x^(1/3)), x)","F",0
525,0,0,0,0.000000," ","integrate(x*(a+b*log(c*(d+e/x^(2/3))^n))^3,x, algorithm=""maxima"")","\frac{1}{2} \, b^{3} n^{3} x^{2} \log\left(d x^{\frac{2}{3}} + e\right)^{3} - \int \frac{{\left(b^{3} d n x^{2} - 3 \, {\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x^{2} - 3 \, {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{4}{3}} + 6 \, {\left(b^{3} d x^{2} + b^{3} e x^{\frac{4}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)\right)} n^{2} \log\left(d x^{\frac{2}{3}} + e\right)^{2} + 8 \, {\left(b^{3} d x^{2} + b^{3} e x^{\frac{4}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{3} - {\left(b^{3} d \log\left(c\right)^{3} + 3 \, a b^{2} d \log\left(c\right)^{2} + 3 \, a^{2} b d \log\left(c\right) + a^{3} d\right)} x^{2} - 3 \, {\left({\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} x^{2} + 4 \, {\left(b^{3} d x^{2} + b^{3} e x^{\frac{4}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} + {\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} x^{\frac{4}{3}} - 4 \, {\left({\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x^{2} + {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{4}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)\right)} n \log\left(d x^{\frac{2}{3}} + e\right) - 12 \, {\left({\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x^{2} + {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{4}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} - {\left(b^{3} e \log\left(c\right)^{3} + 3 \, a b^{2} e \log\left(c\right)^{2} + 3 \, a^{2} b e \log\left(c\right) + a^{3} e\right)} x^{\frac{4}{3}} + 6 \, {\left({\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} x^{2} + {\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} x^{\frac{4}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)}{d x + e x^{\frac{1}{3}}}\,{d x}"," ",0,"1/2*b^3*n^3*x^2*log(d*x^(2/3) + e)^3 - integrate(((b^3*d*n*x^2 - 3*(b^3*d*log(c) + a*b^2*d)*x^2 - 3*(b^3*e*log(c) + a*b^2*e)*x^(4/3) + 6*(b^3*d*x^2 + b^3*e*x^(4/3))*log(x^(1/3*n)))*n^2*log(d*x^(2/3) + e)^2 + 8*(b^3*d*x^2 + b^3*e*x^(4/3))*log(x^(1/3*n))^3 - (b^3*d*log(c)^3 + 3*a*b^2*d*log(c)^2 + 3*a^2*b*d*log(c) + a^3*d)*x^2 - 3*((b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*x^2 + 4*(b^3*d*x^2 + b^3*e*x^(4/3))*log(x^(1/3*n))^2 + (b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*x^(4/3) - 4*((b^3*d*log(c) + a*b^2*d)*x^2 + (b^3*e*log(c) + a*b^2*e)*x^(4/3))*log(x^(1/3*n)))*n*log(d*x^(2/3) + e) - 12*((b^3*d*log(c) + a*b^2*d)*x^2 + (b^3*e*log(c) + a*b^2*e)*x^(4/3))*log(x^(1/3*n))^2 - (b^3*e*log(c)^3 + 3*a*b^2*e*log(c)^2 + 3*a^2*b*e*log(c) + a^3*e)*x^(4/3) + 6*((b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*x^2 + (b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*x^(4/3))*log(x^(1/3*n)))/(d*x + e*x^(1/3)), x)","F",0
526,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))^3/x,x, algorithm=""maxima"")","b^{3} n^{3} \log\left(d x^{\frac{2}{3}} + e\right)^{3} \log\left(x\right) - \int \frac{{\left(2 \, b^{3} d n x \log\left(x\right) - 3 \, {\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x + 6 \, {\left(b^{3} d x + b^{3} e x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right) - 3 \, {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{1}{3}}\right)} n^{2} \log\left(d x^{\frac{2}{3}} + e\right)^{2} + 8 \, {\left(b^{3} d x + b^{3} e x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{3} - 3 \, {\left(4 \, {\left(b^{3} d x + b^{3} e x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} + {\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} x - 4 \, {\left({\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x + {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right) + {\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} x^{\frac{1}{3}}\right)} n \log\left(d x^{\frac{2}{3}} + e\right) - 12 \, {\left({\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x + {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} - {\left(b^{3} d \log\left(c\right)^{3} + 3 \, a b^{2} d \log\left(c\right)^{2} + 3 \, a^{2} b d \log\left(c\right) + a^{3} d\right)} x + 6 \, {\left({\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} x + {\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right) - {\left(b^{3} e \log\left(c\right)^{3} + 3 \, a b^{2} e \log\left(c\right)^{2} + 3 \, a^{2} b e \log\left(c\right) + a^{3} e\right)} x^{\frac{1}{3}}}{d x^{2} + e x^{\frac{4}{3}}}\,{d x}"," ",0,"b^3*n^3*log(d*x^(2/3) + e)^3*log(x) - integrate(((2*b^3*d*n*x*log(x) - 3*(b^3*d*log(c) + a*b^2*d)*x + 6*(b^3*d*x + b^3*e*x^(1/3))*log(x^(1/3*n)) - 3*(b^3*e*log(c) + a*b^2*e)*x^(1/3))*n^2*log(d*x^(2/3) + e)^2 + 8*(b^3*d*x + b^3*e*x^(1/3))*log(x^(1/3*n))^3 - 3*(4*(b^3*d*x + b^3*e*x^(1/3))*log(x^(1/3*n))^2 + (b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*x - 4*((b^3*d*log(c) + a*b^2*d)*x + (b^3*e*log(c) + a*b^2*e)*x^(1/3))*log(x^(1/3*n)) + (b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*x^(1/3))*n*log(d*x^(2/3) + e) - 12*((b^3*d*log(c) + a*b^2*d)*x + (b^3*e*log(c) + a*b^2*e)*x^(1/3))*log(x^(1/3*n))^2 - (b^3*d*log(c)^3 + 3*a*b^2*d*log(c)^2 + 3*a^2*b*d*log(c) + a^3*d)*x + 6*((b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*x + (b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*x^(1/3))*log(x^(1/3*n)) - (b^3*e*log(c)^3 + 3*a*b^2*e*log(c)^2 + 3*a^2*b*e*log(c) + a^3*e)*x^(1/3))/(d*x^2 + e*x^(4/3)), x)","F",0
527,1,684,0,0.616336," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))^3/x^3,x, algorithm=""maxima"")","-\frac{1}{4} \, a^{2} b e n {\left(\frac{6 \, d^{3} \log\left(d x^{\frac{2}{3}} + e\right)}{e^{4}} - \frac{6 \, d^{3} \log\left(x^{\frac{2}{3}}\right)}{e^{4}} - \frac{6 \, d^{2} x^{\frac{4}{3}} - 3 \, d e x^{\frac{2}{3}} + 2 \, e^{2}}{e^{3} x^{2}}\right)} - \frac{1}{12} \, {\left(6 \, e n {\left(\frac{6 \, d^{3} \log\left(d x^{\frac{2}{3}} + e\right)}{e^{4}} - \frac{6 \, d^{3} \log\left(x^{\frac{2}{3}}\right)}{e^{4}} - \frac{6 \, d^{2} x^{\frac{4}{3}} - 3 \, d e x^{\frac{2}{3}} + 2 \, e^{2}}{e^{3} x^{2}}\right)} \log\left(c {\left(d + \frac{e}{x^{\frac{2}{3}}}\right)}^{n}\right) - \frac{{\left(18 \, d^{3} x^{2} \log\left(d x^{\frac{2}{3}} + e\right)^{2} + 8 \, d^{3} x^{2} \log\left(x\right)^{2} - 44 \, d^{3} x^{2} \log\left(x\right) - 66 \, d^{2} e x^{\frac{4}{3}} + 15 \, d e^{2} x^{\frac{2}{3}} - 4 \, e^{3} - 6 \, {\left(4 \, d^{3} x^{2} \log\left(x\right) - 11 \, d^{3} x^{2}\right)} \log\left(d x^{\frac{2}{3}} + e\right)\right)} n^{2}}{e^{3} x^{2}}\right)} a b^{2} - \frac{1}{216} \, {\left(54 \, e n {\left(\frac{6 \, d^{3} \log\left(d x^{\frac{2}{3}} + e\right)}{e^{4}} - \frac{6 \, d^{3} \log\left(x^{\frac{2}{3}}\right)}{e^{4}} - \frac{6 \, d^{2} x^{\frac{4}{3}} - 3 \, d e x^{\frac{2}{3}} + 2 \, e^{2}}{e^{3} x^{2}}\right)} \log\left(c {\left(d + \frac{e}{x^{\frac{2}{3}}}\right)}^{n}\right)^{2} + e n {\left(\frac{{\left(108 \, d^{3} x^{2} \log\left(d x^{\frac{2}{3}} + e\right)^{3} - 32 \, d^{3} x^{2} \log\left(x\right)^{3} + 264 \, d^{3} x^{2} \log\left(x\right)^{2} - 1020 \, d^{3} x^{2} \log\left(x\right) - 1530 \, d^{2} e x^{\frac{4}{3}} + 171 \, d e^{2} x^{\frac{2}{3}} - 24 \, e^{3} - 54 \, {\left(4 \, d^{3} x^{2} \log\left(x\right) - 11 \, d^{3} x^{2}\right)} \log\left(d x^{\frac{2}{3}} + e\right)^{2} + 18 \, {\left(8 \, d^{3} x^{2} \log\left(x\right)^{2} - 44 \, d^{3} x^{2} \log\left(x\right) + 85 \, d^{3} x^{2}\right)} \log\left(d x^{\frac{2}{3}} + e\right)\right)} n^{2}}{e^{4} x^{2}} - \frac{18 \, {\left(18 \, d^{3} x^{2} \log\left(d x^{\frac{2}{3}} + e\right)^{2} + 8 \, d^{3} x^{2} \log\left(x\right)^{2} - 44 \, d^{3} x^{2} \log\left(x\right) - 66 \, d^{2} e x^{\frac{4}{3}} + 15 \, d e^{2} x^{\frac{2}{3}} - 4 \, e^{3} - 6 \, {\left(4 \, d^{3} x^{2} \log\left(x\right) - 11 \, d^{3} x^{2}\right)} \log\left(d x^{\frac{2}{3}} + e\right)\right)} n \log\left(c {\left(d + \frac{e}{x^{\frac{2}{3}}}\right)}^{n}\right)}{e^{4} x^{2}}\right)}\right)} b^{3} - \frac{b^{3} \log\left(c {\left(d + \frac{e}{x^{\frac{2}{3}}}\right)}^{n}\right)^{3}}{2 \, x^{2}} - \frac{3 \, a b^{2} \log\left(c {\left(d + \frac{e}{x^{\frac{2}{3}}}\right)}^{n}\right)^{2}}{2 \, x^{2}} - \frac{3 \, a^{2} b \log\left(c {\left(d + \frac{e}{x^{\frac{2}{3}}}\right)}^{n}\right)}{2 \, x^{2}} - \frac{a^{3}}{2 \, x^{2}}"," ",0,"-1/4*a^2*b*e*n*(6*d^3*log(d*x^(2/3) + e)/e^4 - 6*d^3*log(x^(2/3))/e^4 - (6*d^2*x^(4/3) - 3*d*e*x^(2/3) + 2*e^2)/(e^3*x^2)) - 1/12*(6*e*n*(6*d^3*log(d*x^(2/3) + e)/e^4 - 6*d^3*log(x^(2/3))/e^4 - (6*d^2*x^(4/3) - 3*d*e*x^(2/3) + 2*e^2)/(e^3*x^2))*log(c*(d + e/x^(2/3))^n) - (18*d^3*x^2*log(d*x^(2/3) + e)^2 + 8*d^3*x^2*log(x)^2 - 44*d^3*x^2*log(x) - 66*d^2*e*x^(4/3) + 15*d*e^2*x^(2/3) - 4*e^3 - 6*(4*d^3*x^2*log(x) - 11*d^3*x^2)*log(d*x^(2/3) + e))*n^2/(e^3*x^2))*a*b^2 - 1/216*(54*e*n*(6*d^3*log(d*x^(2/3) + e)/e^4 - 6*d^3*log(x^(2/3))/e^4 - (6*d^2*x^(4/3) - 3*d*e*x^(2/3) + 2*e^2)/(e^3*x^2))*log(c*(d + e/x^(2/3))^n)^2 + e*n*((108*d^3*x^2*log(d*x^(2/3) + e)^3 - 32*d^3*x^2*log(x)^3 + 264*d^3*x^2*log(x)^2 - 1020*d^3*x^2*log(x) - 1530*d^2*e*x^(4/3) + 171*d*e^2*x^(2/3) - 24*e^3 - 54*(4*d^3*x^2*log(x) - 11*d^3*x^2)*log(d*x^(2/3) + e)^2 + 18*(8*d^3*x^2*log(x)^2 - 44*d^3*x^2*log(x) + 85*d^3*x^2)*log(d*x^(2/3) + e))*n^2/(e^4*x^2) - 18*(18*d^3*x^2*log(d*x^(2/3) + e)^2 + 8*d^3*x^2*log(x)^2 - 44*d^3*x^2*log(x) - 66*d^2*e*x^(4/3) + 15*d*e^2*x^(2/3) - 4*e^3 - 6*(4*d^3*x^2*log(x) - 11*d^3*x^2)*log(d*x^(2/3) + e))*n*log(c*(d + e/x^(2/3))^n)/(e^4*x^2)))*b^3 - 1/2*b^3*log(c*(d + e/x^(2/3))^n)^3/x^2 - 3/2*a*b^2*log(c*(d + e/x^(2/3))^n)^2/x^2 - 3/2*a^2*b*log(c*(d + e/x^(2/3))^n)/x^2 - 1/2*a^3/x^2","A",0
528,0,0,0,0.000000," ","integrate(x^2*(a+b*log(c*(d+e/x^(2/3))^n))^3,x, algorithm=""maxima"")","\frac{1}{3} \, b^{3} n^{3} x^{3} \log\left(d x^{\frac{2}{3}} + e\right)^{3} - \int \frac{{\left(2 \, b^{3} d n x^{3} - 9 \, {\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x^{3} - 9 \, {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{7}{3}} + 18 \, {\left(b^{3} d x^{3} + b^{3} e x^{\frac{7}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)\right)} n^{2} \log\left(d x^{\frac{2}{3}} + e\right)^{2} - 3 \, {\left(b^{3} d \log\left(c\right)^{3} + 3 \, a b^{2} d \log\left(c\right)^{2} + 3 \, a^{2} b d \log\left(c\right) + a^{3} d\right)} x^{3} + 24 \, {\left(b^{3} d x^{3} + b^{3} e x^{\frac{7}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{3} - 3 \, {\left(b^{3} e \log\left(c\right)^{3} + 3 \, a b^{2} e \log\left(c\right)^{2} + 3 \, a^{2} b e \log\left(c\right) + a^{3} e\right)} x^{\frac{7}{3}} - 9 \, {\left({\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} x^{3} + {\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} x^{\frac{7}{3}} + 4 \, {\left(b^{3} d x^{3} + b^{3} e x^{\frac{7}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} - 4 \, {\left({\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x^{3} + {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{7}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)\right)} n \log\left(d x^{\frac{2}{3}} + e\right) - 36 \, {\left({\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x^{3} + {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{7}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} + 18 \, {\left({\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} x^{3} + {\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} x^{\frac{7}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)}{3 \, {\left(d x + e x^{\frac{1}{3}}\right)}}\,{d x}"," ",0,"1/3*b^3*n^3*x^3*log(d*x^(2/3) + e)^3 - integrate(1/3*((2*b^3*d*n*x^3 - 9*(b^3*d*log(c) + a*b^2*d)*x^3 - 9*(b^3*e*log(c) + a*b^2*e)*x^(7/3) + 18*(b^3*d*x^3 + b^3*e*x^(7/3))*log(x^(1/3*n)))*n^2*log(d*x^(2/3) + e)^2 - 3*(b^3*d*log(c)^3 + 3*a*b^2*d*log(c)^2 + 3*a^2*b*d*log(c) + a^3*d)*x^3 + 24*(b^3*d*x^3 + b^3*e*x^(7/3))*log(x^(1/3*n))^3 - 3*(b^3*e*log(c)^3 + 3*a*b^2*e*log(c)^2 + 3*a^2*b*e*log(c) + a^3*e)*x^(7/3) - 9*((b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*x^3 + (b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*x^(7/3) + 4*(b^3*d*x^3 + b^3*e*x^(7/3))*log(x^(1/3*n))^2 - 4*((b^3*d*log(c) + a*b^2*d)*x^3 + (b^3*e*log(c) + a*b^2*e)*x^(7/3))*log(x^(1/3*n)))*n*log(d*x^(2/3) + e) - 36*((b^3*d*log(c) + a*b^2*d)*x^3 + (b^3*e*log(c) + a*b^2*e)*x^(7/3))*log(x^(1/3*n))^2 + 18*((b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*x^3 + (b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*x^(7/3))*log(x^(1/3*n)))/(d*x + e*x^(1/3)), x)","F",0
529,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))^3,x, algorithm=""maxima"")","b^{3} n^{3} x \log\left(d x^{\frac{2}{3}} + e\right)^{3} - 3 \, {\left(2 \, e n {\left(\frac{e \arctan\left(\frac{d x^{\frac{1}{3}}}{\sqrt{d e}}\right)}{\sqrt{d e} d} - \frac{x^{\frac{1}{3}}}{d}\right)} - x \log\left(c {\left(d + \frac{e}{x^{\frac{2}{3}}}\right)}^{n}\right)\right)} a^{2} b + a^{3} x - \int \frac{{\left(2 \, b^{3} d n x - 3 \, {\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x + 6 \, {\left(b^{3} d x + b^{3} e x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right) - 3 \, {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{1}{3}}\right)} n^{2} \log\left(d x^{\frac{2}{3}} + e\right)^{2} + 8 \, {\left(b^{3} d x + b^{3} e x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{3} - 3 \, {\left(4 \, {\left(b^{3} d x + b^{3} e x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} + {\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right)\right)} x - 4 \, {\left({\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x + {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right) + {\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right)\right)} x^{\frac{1}{3}}\right)} n \log\left(d x^{\frac{2}{3}} + e\right) - 12 \, {\left({\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x + {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} - {\left(b^{3} d \log\left(c\right)^{3} + 3 \, a b^{2} d \log\left(c\right)^{2}\right)} x + 6 \, {\left({\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right)\right)} x + {\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right)\right)} x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right) - {\left(b^{3} e \log\left(c\right)^{3} + 3 \, a b^{2} e \log\left(c\right)^{2}\right)} x^{\frac{1}{3}}}{d x + e x^{\frac{1}{3}}}\,{d x}"," ",0,"b^3*n^3*x*log(d*x^(2/3) + e)^3 - 3*(2*e*n*(e*arctan(d*x^(1/3)/sqrt(d*e))/(sqrt(d*e)*d) - x^(1/3)/d) - x*log(c*(d + e/x^(2/3))^n))*a^2*b + a^3*x - integrate(((2*b^3*d*n*x - 3*(b^3*d*log(c) + a*b^2*d)*x + 6*(b^3*d*x + b^3*e*x^(1/3))*log(x^(1/3*n)) - 3*(b^3*e*log(c) + a*b^2*e)*x^(1/3))*n^2*log(d*x^(2/3) + e)^2 + 8*(b^3*d*x + b^3*e*x^(1/3))*log(x^(1/3*n))^3 - 3*(4*(b^3*d*x + b^3*e*x^(1/3))*log(x^(1/3*n))^2 + (b^3*d*log(c)^2 + 2*a*b^2*d*log(c))*x - 4*((b^3*d*log(c) + a*b^2*d)*x + (b^3*e*log(c) + a*b^2*e)*x^(1/3))*log(x^(1/3*n)) + (b^3*e*log(c)^2 + 2*a*b^2*e*log(c))*x^(1/3))*n*log(d*x^(2/3) + e) - 12*((b^3*d*log(c) + a*b^2*d)*x + (b^3*e*log(c) + a*b^2*e)*x^(1/3))*log(x^(1/3*n))^2 - (b^3*d*log(c)^3 + 3*a*b^2*d*log(c)^2)*x + 6*((b^3*d*log(c)^2 + 2*a*b^2*d*log(c))*x + (b^3*e*log(c)^2 + 2*a*b^2*e*log(c))*x^(1/3))*log(x^(1/3*n)) - (b^3*e*log(c)^3 + 3*a*b^2*e*log(c)^2)*x^(1/3))/(d*x + e*x^(1/3)), x)","F",0
530,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))^3/x^2,x, algorithm=""maxima"")","-\frac{b^{3} n^{3} \log\left(d x^{\frac{2}{3}} + e\right)^{3}}{x} - \int -\frac{{\left(2 \, b^{3} d n x + 3 \, {\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x - 6 \, {\left(b^{3} d x + b^{3} e x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right) + 3 \, {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{1}{3}}\right)} n^{2} \log\left(d x^{\frac{2}{3}} + e\right)^{2} - 8 \, {\left(b^{3} d x + b^{3} e x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{3} + 3 \, {\left(4 \, {\left(b^{3} d x + b^{3} e x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} + {\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} x - 4 \, {\left({\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x + {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right) + {\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} x^{\frac{1}{3}}\right)} n \log\left(d x^{\frac{2}{3}} + e\right) + 12 \, {\left({\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x + {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} + {\left(b^{3} d \log\left(c\right)^{3} + 3 \, a b^{2} d \log\left(c\right)^{2} + 3 \, a^{2} b d \log\left(c\right) + a^{3} d\right)} x - 6 \, {\left({\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} x + {\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right) + {\left(b^{3} e \log\left(c\right)^{3} + 3 \, a b^{2} e \log\left(c\right)^{2} + 3 \, a^{2} b e \log\left(c\right) + a^{3} e\right)} x^{\frac{1}{3}}}{d x^{3} + e x^{\frac{7}{3}}}\,{d x}"," ",0,"-b^3*n^3*log(d*x^(2/3) + e)^3/x - integrate(-((2*b^3*d*n*x + 3*(b^3*d*log(c) + a*b^2*d)*x - 6*(b^3*d*x + b^3*e*x^(1/3))*log(x^(1/3*n)) + 3*(b^3*e*log(c) + a*b^2*e)*x^(1/3))*n^2*log(d*x^(2/3) + e)^2 - 8*(b^3*d*x + b^3*e*x^(1/3))*log(x^(1/3*n))^3 + 3*(4*(b^3*d*x + b^3*e*x^(1/3))*log(x^(1/3*n))^2 + (b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*x - 4*((b^3*d*log(c) + a*b^2*d)*x + (b^3*e*log(c) + a*b^2*e)*x^(1/3))*log(x^(1/3*n)) + (b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*x^(1/3))*n*log(d*x^(2/3) + e) + 12*((b^3*d*log(c) + a*b^2*d)*x + (b^3*e*log(c) + a*b^2*e)*x^(1/3))*log(x^(1/3*n))^2 + (b^3*d*log(c)^3 + 3*a*b^2*d*log(c)^2 + 3*a^2*b*d*log(c) + a^3*d)*x - 6*((b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*x + (b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*x^(1/3))*log(x^(1/3*n)) + (b^3*e*log(c)^3 + 3*a*b^2*e*log(c)^2 + 3*a^2*b*e*log(c) + a^3*e)*x^(1/3))/(d*x^3 + e*x^(7/3)), x)","F",0
531,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))^3/x^4,x, algorithm=""maxima"")","-\frac{b^{3} n^{3} \log\left(d x^{\frac{2}{3}} + e\right)^{3}}{3 \, x^{3}} - \int -\frac{{\left(2 \, b^{3} d n x + 9 \, {\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x - 18 \, {\left(b^{3} d x + b^{3} e x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right) + 9 \, {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{1}{3}}\right)} n^{2} \log\left(d x^{\frac{2}{3}} + e\right)^{2} - 24 \, {\left(b^{3} d x + b^{3} e x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{3} + 9 \, {\left(4 \, {\left(b^{3} d x + b^{3} e x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} + {\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} x - 4 \, {\left({\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x + {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right) + {\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} x^{\frac{1}{3}}\right)} n \log\left(d x^{\frac{2}{3}} + e\right) + 36 \, {\left({\left(b^{3} d \log\left(c\right) + a b^{2} d\right)} x + {\left(b^{3} e \log\left(c\right) + a b^{2} e\right)} x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right)^{2} + 3 \, {\left(b^{3} d \log\left(c\right)^{3} + 3 \, a b^{2} d \log\left(c\right)^{2} + 3 \, a^{2} b d \log\left(c\right) + a^{3} d\right)} x - 18 \, {\left({\left(b^{3} d \log\left(c\right)^{2} + 2 \, a b^{2} d \log\left(c\right) + a^{2} b d\right)} x + {\left(b^{3} e \log\left(c\right)^{2} + 2 \, a b^{2} e \log\left(c\right) + a^{2} b e\right)} x^{\frac{1}{3}}\right)} \log\left(x^{\frac{1}{3} \, n}\right) + 3 \, {\left(b^{3} e \log\left(c\right)^{3} + 3 \, a b^{2} e \log\left(c\right)^{2} + 3 \, a^{2} b e \log\left(c\right) + a^{3} e\right)} x^{\frac{1}{3}}}{3 \, {\left(d x^{5} + e x^{\frac{13}{3}}\right)}}\,{d x}"," ",0,"-1/3*b^3*n^3*log(d*x^(2/3) + e)^3/x^3 - integrate(-1/3*((2*b^3*d*n*x + 9*(b^3*d*log(c) + a*b^2*d)*x - 18*(b^3*d*x + b^3*e*x^(1/3))*log(x^(1/3*n)) + 9*(b^3*e*log(c) + a*b^2*e)*x^(1/3))*n^2*log(d*x^(2/3) + e)^2 - 24*(b^3*d*x + b^3*e*x^(1/3))*log(x^(1/3*n))^3 + 9*(4*(b^3*d*x + b^3*e*x^(1/3))*log(x^(1/3*n))^2 + (b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*x - 4*((b^3*d*log(c) + a*b^2*d)*x + (b^3*e*log(c) + a*b^2*e)*x^(1/3))*log(x^(1/3*n)) + (b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*x^(1/3))*n*log(d*x^(2/3) + e) + 36*((b^3*d*log(c) + a*b^2*d)*x + (b^3*e*log(c) + a*b^2*e)*x^(1/3))*log(x^(1/3*n))^2 + 3*(b^3*d*log(c)^3 + 3*a*b^2*d*log(c)^2 + 3*a^2*b*d*log(c) + a^3*d)*x - 18*((b^3*d*log(c)^2 + 2*a*b^2*d*log(c) + a^2*b*d)*x + (b^3*e*log(c)^2 + 2*a*b^2*e*log(c) + a^2*b*e)*x^(1/3))*log(x^(1/3*n)) + 3*(b^3*e*log(c)^3 + 3*a*b^2*e*log(c)^2 + 3*a^2*b*e*log(c) + a^3*e)*x^(1/3))/(d*x^5 + e*x^(13/3)), x)","F",0
532,0,0,0,0.000000," ","integrate(x^3*(a+b*log(c*(d+e*x^(1/2))))^p,x, algorithm=""maxima"")","\int {\left(b \log\left({\left(e \sqrt{x} + d\right)} c\right) + a\right)}^{p} x^{3}\,{d x}"," ",0,"integrate((b*log((e*sqrt(x) + d)*c) + a)^p*x^3, x)","F",0
533,0,0,0,0.000000," ","integrate(x^2*(a+b*log(c*(d+e*x^(1/2))))^p,x, algorithm=""maxima"")","\int {\left(b \log\left({\left(e \sqrt{x} + d\right)} c\right) + a\right)}^{p} x^{2}\,{d x}"," ",0,"integrate((b*log((e*sqrt(x) + d)*c) + a)^p*x^2, x)","F",0
534,0,0,0,0.000000," ","integrate(x*(a+b*log(c*(d+e*x^(1/2))))^p,x, algorithm=""maxima"")","\int {\left(b \log\left({\left(e \sqrt{x} + d\right)} c\right) + a\right)}^{p} x\,{d x}"," ",0,"integrate((b*log((e*sqrt(x) + d)*c) + a)^p*x, x)","F",0
535,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(1/2))))^p,x, algorithm=""maxima"")","\int {\left(b \log\left({\left(e \sqrt{x} + d\right)} c\right) + a\right)}^{p}\,{d x}"," ",0,"integrate((b*log((e*sqrt(x) + d)*c) + a)^p, x)","F",0
536,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(1/2))))^p/x,x, algorithm=""maxima"")","\int \frac{{\left(b \log\left({\left(e \sqrt{x} + d\right)} c\right) + a\right)}^{p}}{x}\,{d x}"," ",0,"integrate((b*log((e*sqrt(x) + d)*c) + a)^p/x, x)","F",0
537,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(1/2))))^p/x^2,x, algorithm=""maxima"")","\int \frac{{\left(b \log\left({\left(e \sqrt{x} + d\right)} c\right) + a\right)}^{p}}{x^{2}}\,{d x}"," ",0,"integrate((b*log((e*sqrt(x) + d)*c) + a)^p/x^2, x)","F",0
538,0,0,0,0.000000," ","integrate(x^3*(a+b*log(c*(d+e*x^(1/2))^2))^p,x, algorithm=""maxima"")","\int {\left(b \log\left({\left(e \sqrt{x} + d\right)}^{2} c\right) + a\right)}^{p} x^{3}\,{d x}"," ",0,"integrate((b*log((e*sqrt(x) + d)^2*c) + a)^p*x^3, x)","F",0
539,0,0,0,0.000000," ","integrate(x^2*(a+b*log(c*(d+e*x^(1/2))^2))^p,x, algorithm=""maxima"")","\int {\left(b \log\left({\left(e \sqrt{x} + d\right)}^{2} c\right) + a\right)}^{p} x^{2}\,{d x}"," ",0,"integrate((b*log((e*sqrt(x) + d)^2*c) + a)^p*x^2, x)","F",0
540,0,0,0,0.000000," ","integrate(x*(a+b*log(c*(d+e*x^(1/2))^2))^p,x, algorithm=""maxima"")","\int {\left(b \log\left({\left(e \sqrt{x} + d\right)}^{2} c\right) + a\right)}^{p} x\,{d x}"," ",0,"integrate((b*log((e*sqrt(x) + d)^2*c) + a)^p*x, x)","F",0
541,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(1/2))^2))^p,x, algorithm=""maxima"")","\int {\left(b \log\left({\left(e \sqrt{x} + d\right)}^{2} c\right) + a\right)}^{p}\,{d x}"," ",0,"integrate((b*log((e*sqrt(x) + d)^2*c) + a)^p, x)","F",0
542,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(1/2))^2))^p/x,x, algorithm=""maxima"")","\int \frac{{\left(b \log\left({\left(e \sqrt{x} + d\right)}^{2} c\right) + a\right)}^{p}}{x}\,{d x}"," ",0,"integrate((b*log((e*sqrt(x) + d)^2*c) + a)^p/x, x)","F",0
543,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^(1/2))^2))^p/x^2,x, algorithm=""maxima"")","\int \frac{{\left(b \log\left({\left(e \sqrt{x} + d\right)}^{2} c\right) + a\right)}^{p}}{x^{2}}\,{d x}"," ",0,"integrate((b*log((e*sqrt(x) + d)^2*c) + a)^p/x^2, x)","F",0
544,0,0,0,0.000000," ","integrate(x*(a+b*log(c*(d+e/x^(1/2))))^p,x, algorithm=""maxima"")","\int {\left(b \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}\right) + a\right)}^{p} x\,{d x}"," ",0,"integrate((b*log(c*(d + e/sqrt(x))) + a)^p*x, x)","F",0
545,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(1/2))))^p,x, algorithm=""maxima"")","\int {\left(b \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}\right) + a\right)}^{p}\,{d x}"," ",0,"integrate((b*log(c*(d + e/sqrt(x))) + a)^p, x)","F",0
546,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(1/2))))^p/x,x, algorithm=""maxima"")","\int \frac{{\left(b \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}\right) + a\right)}^{p}}{x}\,{d x}"," ",0,"integrate((b*log(c*(d + e/sqrt(x))) + a)^p/x, x)","F",0
547,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(1/2))))^p/x^2,x, algorithm=""maxima"")","\int \frac{{\left(b \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}\right) + a\right)}^{p}}{x^{2}}\,{d x}"," ",0,"integrate((b*log(c*(d + e/sqrt(x))) + a)^p/x^2, x)","F",0
548,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(1/2))))^p/x^4,x, algorithm=""maxima"")","\int \frac{{\left(b \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}\right) + a\right)}^{p}}{x^{4}}\,{d x}"," ",0,"integrate((b*log(c*(d + e/sqrt(x))) + a)^p/x^4, x)","F",0
549,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(1/2))))^p/x^6,x, algorithm=""maxima"")","\int \frac{{\left(b \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}\right) + a\right)}^{p}}{x^{6}}\,{d x}"," ",0,"integrate((b*log(c*(d + e/sqrt(x))) + a)^p/x^6, x)","F",0
550,0,0,0,0.000000," ","integrate(x*(a+b*log(c*(d+e/x^(1/2))^2))^p,x, algorithm=""maxima"")","\int {\left(b \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{2}\right) + a\right)}^{p} x\,{d x}"," ",0,"integrate((b*log(c*(d + e/sqrt(x))^2) + a)^p*x, x)","F",0
551,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(1/2))^2))^p,x, algorithm=""maxima"")","\int {\left(b \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{2}\right) + a\right)}^{p}\,{d x}"," ",0,"integrate((b*log(c*(d + e/sqrt(x))^2) + a)^p, x)","F",0
552,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(1/2))^2))^p/x,x, algorithm=""maxima"")","\int \frac{{\left(b \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{2}\right) + a\right)}^{p}}{x}\,{d x}"," ",0,"integrate((b*log(c*(d + e/sqrt(x))^2) + a)^p/x, x)","F",0
553,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(1/2))^2))^p/x^2,x, algorithm=""maxima"")","\int \frac{{\left(b \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{2}\right) + a\right)}^{p}}{x^{2}}\,{d x}"," ",0,"integrate((b*log(c*(d + e/sqrt(x))^2) + a)^p/x^2, x)","F",0
554,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(1/2))^2))^p/x^4,x, algorithm=""maxima"")","\int \frac{{\left(b \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{2}\right) + a\right)}^{p}}{x^{4}}\,{d x}"," ",0,"integrate((b*log(c*(d + e/sqrt(x))^2) + a)^p/x^4, x)","F",0
555,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(1/2))^2))^p/x^6,x, algorithm=""maxima"")","\int \frac{{\left(b \log\left(c {\left(d + \frac{e}{\sqrt{x}}\right)}^{2}\right) + a\right)}^{p}}{x^{6}}\,{d x}"," ",0,"integrate((b*log(c*(d + e/sqrt(x))^2) + a)^p/x^6, x)","F",0
556,0,0,0,0.000000," ","integrate(x^3*(a+b*log(c*(d+e*x^(1/3))))^p,x, algorithm=""maxima"")","\int {\left(b \log\left({\left(e x^{\frac{1}{3}} + d\right)} c\right) + a\right)}^{p} x^{3}\,{d x}"," ",0,"integrate((b*log((e*x^(1/3) + d)*c) + a)^p*x^3, x)","F",0
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562,0,0,0,0.000000," ","integrate(x^3*(a+b*log(c*(d+e*x^(1/3))^2))^p,x, algorithm=""maxima"")","\int {\left(b \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{2} c\right) + a\right)}^{p} x^{3}\,{d x}"," ",0,"integrate((b*log((e*x^(1/3) + d)^2*c) + a)^p*x^3, x)","F",0
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604,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(2/3))^2))^p/x,x, algorithm=""maxima"")","\int \frac{{\left(b \log\left(c {\left(d + \frac{e}{x^{\frac{2}{3}}}\right)}^{2}\right) + a\right)}^{p}}{x}\,{d x}"," ",0,"integrate((b*log(c*(d + e/x^(2/3))^2) + a)^p/x, x)","F",0
605,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/x^(2/3))^2))^p/x^2,x, algorithm=""maxima"")","\int \frac{{\left(b \log\left(c {\left(d + \frac{e}{x^{\frac{2}{3}}}\right)}^{2}\right) + a\right)}^{p}}{x^{2}}\,{d x}"," ",0,"integrate((b*log(c*(d + e/x^(2/3))^2) + a)^p/x^2, x)","F",0
606,1,572,0,1.088113," ","integrate((g*x+f)*(a+b*log(c*(e*x^2+d)^p))/(h*x)^(1/2),x, algorithm=""maxima"")","\frac{2 \, b g x^{2} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{3 \, \sqrt{h x}} + \frac{2 \, a g x^{2}}{3 \, \sqrt{h x}} + \frac{2 \, \sqrt{h x} b f \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{h} - \frac{{\left(\frac{8 \, \sqrt{h x} h^{2}}{e} - \frac{{\left(\frac{\sqrt{2} h^{4} \log\left(\sqrt{e} h x + \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{3}{4}} e^{\frac{1}{4}}} - \frac{\sqrt{2} h^{4} \log\left(\sqrt{e} h x - \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{3}{4}} e^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} h^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} + 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{d}} + \frac{2 \, \sqrt{2} h^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} - 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{d}}\right)} d}{e}\right)} b e f p}{h^{3}} + \frac{2 \, \sqrt{h x} a f}{h} + \frac{{\left(\frac{3 \, d h^{4} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} + 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} - 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{e}} - \frac{\sqrt{2} \log\left(\sqrt{e} h x + \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{e} h x - \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{3}{4}}}\right)}}{e} - \frac{8 \, \left(h x\right)^{\frac{3}{2}} h^{2}}{e}\right)} b e g p}{9 \, h^{4}}"," ",0,"2/3*b*g*x^2*log((e*x^2 + d)^p*c)/sqrt(h*x) + 2/3*a*g*x^2/sqrt(h*x) + 2*sqrt(h*x)*b*f*log((e*x^2 + d)^p*c)/h - (8*sqrt(h*x)*h^2/e - (sqrt(2)*h^4*log(sqrt(e)*h*x + sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(3/4)*e^(1/4)) - sqrt(2)*h^4*log(sqrt(e)*h*x - sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(3/4)*e^(1/4)) + 2*sqrt(2)*h^3*arctan(1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) + 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(d)) + 2*sqrt(2)*h^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) - 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(d)))*d/e)*b*e*f*p/h^3 + 2*sqrt(h*x)*a*f/h + 1/9*(3*d*h^4*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) + 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(e)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) - 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(e)) - sqrt(2)*log(sqrt(e)*h*x + sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(1/4)*e^(3/4)) + sqrt(2)*log(sqrt(e)*h*x - sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(1/4)*e^(3/4)))/e - 8*(h*x)^(3/2)*h^2/e)*b*e*g*p/h^4","A",0
607,1,548,0,1.084605," ","integrate((g*x+f)*(a+b*log(c*(e*x^2+d)^p))/(h*x)^(3/2),x, algorithm=""maxima"")","\frac{b e f p {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} + 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} - 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{e}} - \frac{\sqrt{2} \log\left(\sqrt{e} h x + \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{e} h x - \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{3}{4}}}\right)}}{h} + \frac{2 \, b g x^{2} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{\left(h x\right)^{\frac{3}{2}}} + \frac{2 \, a g x^{2}}{\left(h x\right)^{\frac{3}{2}}} - \frac{2 \, b f \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{\sqrt{h x} h} - \frac{{\left(\frac{8 \, \sqrt{h x} h^{2}}{e} - \frac{{\left(\frac{\sqrt{2} h^{4} \log\left(\sqrt{e} h x + \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{3}{4}} e^{\frac{1}{4}}} - \frac{\sqrt{2} h^{4} \log\left(\sqrt{e} h x - \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{3}{4}} e^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} h^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} + 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{d}} + \frac{2 \, \sqrt{2} h^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} - 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{d}}\right)} d}{e}\right)} b e g p}{h^{4}} - \frac{2 \, a f}{\sqrt{h x} h}"," ",0,"b*e*f*p*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) + 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(e)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) - 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(e)) - sqrt(2)*log(sqrt(e)*h*x + sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(1/4)*e^(3/4)) + sqrt(2)*log(sqrt(e)*h*x - sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(1/4)*e^(3/4)))/h + 2*b*g*x^2*log((e*x^2 + d)^p*c)/(h*x)^(3/2) + 2*a*g*x^2/(h*x)^(3/2) - 2*b*f*log((e*x^2 + d)^p*c)/(sqrt(h*x)*h) - (8*sqrt(h*x)*h^2/e - (sqrt(2)*h^4*log(sqrt(e)*h*x + sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(3/4)*e^(1/4)) - sqrt(2)*h^4*log(sqrt(e)*h*x - sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(3/4)*e^(1/4)) + 2*sqrt(2)*h^3*arctan(1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) + 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(d)) + 2*sqrt(2)*h^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) - 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(d)))*d/e)*b*e*g*p/h^4 - 2*a*f/(sqrt(h*x)*h)","A",0
608,1,524,0,1.078705," ","integrate((g*x+f)*(a+b*log(c*(e*x^2+d)^p))/(h*x)^(5/2),x, algorithm=""maxima"")","\frac{b e g p {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} + 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} - 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{e}} - \frac{\sqrt{2} \log\left(\sqrt{e} h x + \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{e} h x - \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{3}{4}}}\right)}}{h^{2}} - \frac{2 \, b g x^{2} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{\left(h x\right)^{\frac{5}{2}}} + \frac{{\left(\frac{\sqrt{2} h^{2} \log\left(\sqrt{e} h x + \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{3}{4}} e^{\frac{1}{4}}} - \frac{\sqrt{2} h^{2} \log\left(\sqrt{e} h x - \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{3}{4}} e^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} h \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} + 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{d}} + \frac{2 \, \sqrt{2} h \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} - 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{d}}\right)} b e f p}{3 \, h^{3}} - \frac{2 \, a g x^{2}}{\left(h x\right)^{\frac{5}{2}}} - \frac{2 \, b f \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{3 \, \left(h x\right)^{\frac{3}{2}} h} - \frac{2 \, a f}{3 \, \left(h x\right)^{\frac{3}{2}} h}"," ",0,"b*e*g*p*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) + 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(e)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) - 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(e)) - sqrt(2)*log(sqrt(e)*h*x + sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(1/4)*e^(3/4)) + sqrt(2)*log(sqrt(e)*h*x - sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(1/4)*e^(3/4)))/h^2 - 2*b*g*x^2*log((e*x^2 + d)^p*c)/(h*x)^(5/2) + 1/3*(sqrt(2)*h^2*log(sqrt(e)*h*x + sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(3/4)*e^(1/4)) - sqrt(2)*h^2*log(sqrt(e)*h*x - sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(3/4)*e^(1/4)) + 2*sqrt(2)*h*arctan(1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) + 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(d)) + 2*sqrt(2)*h*arctan(-1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) - 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(d)))*b*e*f*p/h^3 - 2*a*g*x^2/(h*x)^(5/2) - 2/3*b*f*log((e*x^2 + d)^p*c)/((h*x)^(3/2)*h) - 2/3*a*f/((h*x)^(3/2)*h)","A",0
609,1,541,0,1.077972," ","integrate((g*x+f)*(a+b*log(c*(e*x^2+d)^p))/(h*x)^(7/2),x, algorithm=""maxima"")","-\frac{b e f p {\left(\frac{e {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} + 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} - 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{e}} - \frac{\sqrt{2} \log\left(\sqrt{e} h x + \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{e} h x - \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{3}{4}}}\right)}}{d} + \frac{8}{\sqrt{h x} d}\right)}}{5 \, h^{3}} - \frac{2 \, b g x^{2} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{3 \, \left(h x\right)^{\frac{7}{2}}} + \frac{{\left(\frac{\sqrt{2} h^{2} \log\left(\sqrt{e} h x + \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{3}{4}} e^{\frac{1}{4}}} - \frac{\sqrt{2} h^{2} \log\left(\sqrt{e} h x - \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{3}{4}} e^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} h \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} + 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{d}} + \frac{2 \, \sqrt{2} h \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} - 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{d}}\right)} b e g p}{3 \, h^{4}} - \frac{2 \, a g x^{2}}{3 \, \left(h x\right)^{\frac{7}{2}}} - \frac{2 \, b f \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{5 \, \left(h x\right)^{\frac{5}{2}} h} - \frac{2 \, a f}{5 \, \left(h x\right)^{\frac{5}{2}} h}"," ",0,"-1/5*b*e*f*p*(e*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) + 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(e)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) - 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(e)) - sqrt(2)*log(sqrt(e)*h*x + sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(1/4)*e^(3/4)) + sqrt(2)*log(sqrt(e)*h*x - sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(1/4)*e^(3/4)))/d + 8/(sqrt(h*x)*d))/h^3 - 2/3*b*g*x^2*log((e*x^2 + d)^p*c)/(h*x)^(7/2) + 1/3*(sqrt(2)*h^2*log(sqrt(e)*h*x + sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(3/4)*e^(1/4)) - sqrt(2)*h^2*log(sqrt(e)*h*x - sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(3/4)*e^(1/4)) + 2*sqrt(2)*h*arctan(1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) + 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(d)) + 2*sqrt(2)*h*arctan(-1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) - 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(d)))*b*e*g*p/h^4 - 2/3*a*g*x^2/(h*x)^(7/2) - 2/5*b*f*log((e*x^2 + d)^p*c)/((h*x)^(5/2)*h) - 2/5*a*f/((h*x)^(5/2)*h)","A",0
610,1,557,0,1.079399," ","integrate((g*x+f)*(a+b*log(c*(e*x^2+d)^p))/(h*x)^(9/2),x, algorithm=""maxima"")","-\frac{b e f p {\left(\frac{3 \, {\left(\frac{\sqrt{2} e^{\frac{3}{4}} \log\left(\sqrt{e} h x + \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{3}{4}}} - \frac{\sqrt{2} e^{\frac{3}{4}} \log\left(\sqrt{e} h x - \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{3}{4}}} + \frac{2 \, \sqrt{2} e \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} + 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{d} h} + \frac{2 \, \sqrt{2} e \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} - 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{d} h}\right)}}{d} + \frac{8}{\left(h x\right)^{\frac{3}{2}} d}\right)}}{21 \, h^{3}} - \frac{b e g p {\left(\frac{e {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} + 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} - 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{e}} - \frac{\sqrt{2} \log\left(\sqrt{e} h x + \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{e} h x - \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{3}{4}}}\right)}}{d} + \frac{8}{\sqrt{h x} d}\right)}}{5 \, h^{4}} - \frac{2 \, b g x^{2} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{5 \, \left(h x\right)^{\frac{9}{2}}} - \frac{2 \, a g x^{2}}{5 \, \left(h x\right)^{\frac{9}{2}}} - \frac{2 \, b f \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{7 \, \left(h x\right)^{\frac{7}{2}} h} - \frac{2 \, a f}{7 \, \left(h x\right)^{\frac{7}{2}} h}"," ",0,"-1/21*b*e*f*p*(3*(sqrt(2)*e^(3/4)*log(sqrt(e)*h*x + sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/(d*h^2)^(3/4) - sqrt(2)*e^(3/4)*log(sqrt(e)*h*x - sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/(d*h^2)^(3/4) + 2*sqrt(2)*e*arctan(1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) + 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(d)*h) + 2*sqrt(2)*e*arctan(-1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) - 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(d)*h))/d + 8/((h*x)^(3/2)*d))/h^3 - 1/5*b*e*g*p*(e*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) + 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(e)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) - 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(e)) - sqrt(2)*log(sqrt(e)*h*x + sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(1/4)*e^(3/4)) + sqrt(2)*log(sqrt(e)*h*x - sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(1/4)*e^(3/4)))/d + 8/(sqrt(h*x)*d))/h^4 - 2/5*b*g*x^2*log((e*x^2 + d)^p*c)/(h*x)^(9/2) - 2/5*a*g*x^2/(h*x)^(9/2) - 2/7*b*f*log((e*x^2 + d)^p*c)/((h*x)^(7/2)*h) - 2/7*a*f/((h*x)^(7/2)*h)","A",0
611,1,893,0,1.150670," ","integrate((g*x+f)^2*(a+b*log(c*(e*x^2+d)^p))/(h*x)^(1/2),x, algorithm=""maxima"")","\frac{2 \, b g^{2} x^{3} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{5 \, \sqrt{h x}} + \frac{2 \, a g^{2} x^{3}}{5 \, \sqrt{h x}} + \frac{4 \, b f g x^{2} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{3 \, \sqrt{h x}} + \frac{4 \, a f g x^{2}}{3 \, \sqrt{h x}} + \frac{2 \, \sqrt{h x} b f^{2} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{h} - \frac{{\left(\frac{8 \, \sqrt{h x} h^{2}}{e} - \frac{{\left(\frac{\sqrt{2} h^{4} \log\left(\sqrt{e} h x + \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{3}{4}} e^{\frac{1}{4}}} - \frac{\sqrt{2} h^{4} \log\left(\sqrt{e} h x - \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{3}{4}} e^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} h^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} + 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{d}} + \frac{2 \, \sqrt{2} h^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} - 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{d}}\right)} d}{e}\right)} b e f^{2} p}{h^{3}} + \frac{2 \, \sqrt{h x} a f^{2}}{h} + \frac{2 \, {\left(\frac{3 \, d h^{4} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} + 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} - 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{e}} - \frac{\sqrt{2} \log\left(\sqrt{e} h x + \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{e} h x - \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{3}{4}}}\right)}}{e} - \frac{8 \, \left(h x\right)^{\frac{3}{2}} h^{2}}{e}\right)} b e f g p}{9 \, h^{4}} - \frac{b {\left(\frac{5 \, {\left(\frac{\sqrt{2} h^{6} \log\left(\sqrt{e} h x + \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{3}{4}} e^{\frac{1}{4}}} - \frac{\sqrt{2} h^{6} \log\left(\sqrt{e} h x - \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{3}{4}} e^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} h^{5} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} + 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{d}} + \frac{2 \, \sqrt{2} h^{5} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} - 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{d}}\right)} d^{2}}{e^{2}} + \frac{8 \, {\left(\left(h x\right)^{\frac{5}{2}} e h^{2} - 5 \, \sqrt{h x} d h^{4}\right)}}{e^{2}}\right)} e g^{2} p}{25 \, h^{5}}"," ",0,"2/5*b*g^2*x^3*log((e*x^2 + d)^p*c)/sqrt(h*x) + 2/5*a*g^2*x^3/sqrt(h*x) + 4/3*b*f*g*x^2*log((e*x^2 + d)^p*c)/sqrt(h*x) + 4/3*a*f*g*x^2/sqrt(h*x) + 2*sqrt(h*x)*b*f^2*log((e*x^2 + d)^p*c)/h - (8*sqrt(h*x)*h^2/e - (sqrt(2)*h^4*log(sqrt(e)*h*x + sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(3/4)*e^(1/4)) - sqrt(2)*h^4*log(sqrt(e)*h*x - sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(3/4)*e^(1/4)) + 2*sqrt(2)*h^3*arctan(1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) + 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(d)) + 2*sqrt(2)*h^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) - 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(d)))*d/e)*b*e*f^2*p/h^3 + 2*sqrt(h*x)*a*f^2/h + 2/9*(3*d*h^4*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) + 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(e)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) - 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(e)) - sqrt(2)*log(sqrt(e)*h*x + sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(1/4)*e^(3/4)) + sqrt(2)*log(sqrt(e)*h*x - sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(1/4)*e^(3/4)))/e - 8*(h*x)^(3/2)*h^2/e)*b*e*f*g*p/h^4 - 1/25*b*(5*(sqrt(2)*h^6*log(sqrt(e)*h*x + sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(3/4)*e^(1/4)) - sqrt(2)*h^6*log(sqrt(e)*h*x - sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(3/4)*e^(1/4)) + 2*sqrt(2)*h^5*arctan(1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) + 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(d)) + 2*sqrt(2)*h^5*arctan(-1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) - 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(d)))*d^2/e^2 + 8*((h*x)^(5/2)*e*h^2 - 5*sqrt(h*x)*d*h^4)/e^2)*e*g^2*p/h^5","A",0
612,1,844,0,1.147650," ","integrate((g*x+f)^2*(a+b*log(c*(e*x^2+d)^p))/(h*x)^(3/2),x, algorithm=""maxima"")","\frac{2 \, b g^{2} x^{3} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{3 \, \left(h x\right)^{\frac{3}{2}}} + \frac{b e f^{2} p {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} + 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} - 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{e}} - \frac{\sqrt{2} \log\left(\sqrt{e} h x + \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{e} h x - \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{3}{4}}}\right)}}{h} + \frac{2 \, a g^{2} x^{3}}{3 \, \left(h x\right)^{\frac{3}{2}}} + \frac{4 \, b f g x^{2} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{\left(h x\right)^{\frac{3}{2}}} + \frac{4 \, a f g x^{2}}{\left(h x\right)^{\frac{3}{2}}} - \frac{2 \, b f^{2} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{\sqrt{h x} h} - \frac{2 \, {\left(\frac{8 \, \sqrt{h x} h^{2}}{e} - \frac{{\left(\frac{\sqrt{2} h^{4} \log\left(\sqrt{e} h x + \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{3}{4}} e^{\frac{1}{4}}} - \frac{\sqrt{2} h^{4} \log\left(\sqrt{e} h x - \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{3}{4}} e^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} h^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} + 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{d}} + \frac{2 \, \sqrt{2} h^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} - 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{d}}\right)} d}{e}\right)} b e f g p}{h^{4}} - \frac{2 \, a f^{2}}{\sqrt{h x} h} + \frac{{\left(\frac{3 \, d h^{4} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} + 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} - 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{e}} - \frac{\sqrt{2} \log\left(\sqrt{e} h x + \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{e} h x - \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{3}{4}}}\right)}}{e} - \frac{8 \, \left(h x\right)^{\frac{3}{2}} h^{2}}{e}\right)} b e g^{2} p}{9 \, h^{5}}"," ",0,"2/3*b*g^2*x^3*log((e*x^2 + d)^p*c)/(h*x)^(3/2) + b*e*f^2*p*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) + 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(e)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) - 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(e)) - sqrt(2)*log(sqrt(e)*h*x + sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(1/4)*e^(3/4)) + sqrt(2)*log(sqrt(e)*h*x - sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(1/4)*e^(3/4)))/h + 2/3*a*g^2*x^3/(h*x)^(3/2) + 4*b*f*g*x^2*log((e*x^2 + d)^p*c)/(h*x)^(3/2) + 4*a*f*g*x^2/(h*x)^(3/2) - 2*b*f^2*log((e*x^2 + d)^p*c)/(sqrt(h*x)*h) - 2*(8*sqrt(h*x)*h^2/e - (sqrt(2)*h^4*log(sqrt(e)*h*x + sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(3/4)*e^(1/4)) - sqrt(2)*h^4*log(sqrt(e)*h*x - sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(3/4)*e^(1/4)) + 2*sqrt(2)*h^3*arctan(1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) + 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(d)) + 2*sqrt(2)*h^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) - 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(d)))*d/e)*b*e*f*g*p/h^4 - 2*a*f^2/(sqrt(h*x)*h) + 1/9*(3*d*h^4*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) + 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(e)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) - 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(e)) - sqrt(2)*log(sqrt(e)*h*x + sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(1/4)*e^(3/4)) + sqrt(2)*log(sqrt(e)*h*x - sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(1/4)*e^(3/4)))/e - 8*(h*x)^(3/2)*h^2/e)*b*e*g^2*p/h^5","A",0
613,1,830,0,1.149443," ","integrate((g*x+f)^2*(a+b*log(c*(e*x^2+d)^p))/(h*x)^(5/2),x, algorithm=""maxima"")","\frac{2 \, b g^{2} x^{3} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{\left(h x\right)^{\frac{5}{2}}} + \frac{2 \, b e f g p {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} + 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} - 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{e}} - \frac{\sqrt{2} \log\left(\sqrt{e} h x + \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{e} h x - \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{3}{4}}}\right)}}{h^{2}} + \frac{2 \, a g^{2} x^{3}}{\left(h x\right)^{\frac{5}{2}}} - \frac{4 \, b f g x^{2} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{\left(h x\right)^{\frac{5}{2}}} + \frac{{\left(\frac{\sqrt{2} h^{2} \log\left(\sqrt{e} h x + \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{3}{4}} e^{\frac{1}{4}}} - \frac{\sqrt{2} h^{2} \log\left(\sqrt{e} h x - \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{3}{4}} e^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} h \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} + 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{d}} + \frac{2 \, \sqrt{2} h \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} - 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{d}}\right)} b e f^{2} p}{3 \, h^{3}} - \frac{4 \, a f g x^{2}}{\left(h x\right)^{\frac{5}{2}}} - \frac{2 \, b f^{2} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{3 \, \left(h x\right)^{\frac{3}{2}} h} - \frac{{\left(\frac{8 \, \sqrt{h x} h^{2}}{e} - \frac{{\left(\frac{\sqrt{2} h^{4} \log\left(\sqrt{e} h x + \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{3}{4}} e^{\frac{1}{4}}} - \frac{\sqrt{2} h^{4} \log\left(\sqrt{e} h x - \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{3}{4}} e^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} h^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} + 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{d}} + \frac{2 \, \sqrt{2} h^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} - 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{d}}\right)} d}{e}\right)} b e g^{2} p}{h^{5}} - \frac{2 \, a f^{2}}{3 \, \left(h x\right)^{\frac{3}{2}} h}"," ",0,"2*b*g^2*x^3*log((e*x^2 + d)^p*c)/(h*x)^(5/2) + 2*b*e*f*g*p*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) + 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(e)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) - 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(e)) - sqrt(2)*log(sqrt(e)*h*x + sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(1/4)*e^(3/4)) + sqrt(2)*log(sqrt(e)*h*x - sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(1/4)*e^(3/4)))/h^2 + 2*a*g^2*x^3/(h*x)^(5/2) - 4*b*f*g*x^2*log((e*x^2 + d)^p*c)/(h*x)^(5/2) + 1/3*(sqrt(2)*h^2*log(sqrt(e)*h*x + sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(3/4)*e^(1/4)) - sqrt(2)*h^2*log(sqrt(e)*h*x - sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(3/4)*e^(1/4)) + 2*sqrt(2)*h*arctan(1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) + 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(d)) + 2*sqrt(2)*h*arctan(-1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) - 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(d)))*b*e*f^2*p/h^3 - 4*a*f*g*x^2/(h*x)^(5/2) - 2/3*b*f^2*log((e*x^2 + d)^p*c)/((h*x)^(3/2)*h) - (8*sqrt(h*x)*h^2/e - (sqrt(2)*h^4*log(sqrt(e)*h*x + sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(3/4)*e^(1/4)) - sqrt(2)*h^4*log(sqrt(e)*h*x - sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(3/4)*e^(1/4)) + 2*sqrt(2)*h^3*arctan(1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) + 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(d)) + 2*sqrt(2)*h^3*arctan(-1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) - 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(d)))*d/e)*b*e*g^2*p/h^5 - 2/3*a*f^2/((h*x)^(3/2)*h)","A",0
614,1,813,0,1.146779," ","integrate((g*x+f)^2*(a+b*log(c*(e*x^2+d)^p))/(h*x)^(7/2),x, algorithm=""maxima"")","-\frac{2 \, b g^{2} x^{3} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{\left(h x\right)^{\frac{7}{2}}} - \frac{b e f^{2} p {\left(\frac{e {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} + 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} - 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{e}} - \frac{\sqrt{2} \log\left(\sqrt{e} h x + \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{e} h x - \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{3}{4}}}\right)}}{d} + \frac{8}{\sqrt{h x} d}\right)}}{5 \, h^{3}} + \frac{b e g^{2} p {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} + 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} - 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{e}} - \frac{\sqrt{2} \log\left(\sqrt{e} h x + \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{e} h x - \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{3}{4}}}\right)}}{h^{3}} - \frac{2 \, a g^{2} x^{3}}{\left(h x\right)^{\frac{7}{2}}} - \frac{4 \, b f g x^{2} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{3 \, \left(h x\right)^{\frac{7}{2}}} + \frac{2 \, {\left(\frac{\sqrt{2} h^{2} \log\left(\sqrt{e} h x + \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{3}{4}} e^{\frac{1}{4}}} - \frac{\sqrt{2} h^{2} \log\left(\sqrt{e} h x - \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{3}{4}} e^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} h \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} + 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{d}} + \frac{2 \, \sqrt{2} h \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} - 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{d}}\right)} b e f g p}{3 \, h^{4}} - \frac{4 \, a f g x^{2}}{3 \, \left(h x\right)^{\frac{7}{2}}} - \frac{2 \, b f^{2} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{5 \, \left(h x\right)^{\frac{5}{2}} h} - \frac{2 \, a f^{2}}{5 \, \left(h x\right)^{\frac{5}{2}} h}"," ",0,"-2*b*g^2*x^3*log((e*x^2 + d)^p*c)/(h*x)^(7/2) - 1/5*b*e*f^2*p*(e*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) + 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(e)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) - 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(e)) - sqrt(2)*log(sqrt(e)*h*x + sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(1/4)*e^(3/4)) + sqrt(2)*log(sqrt(e)*h*x - sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(1/4)*e^(3/4)))/d + 8/(sqrt(h*x)*d))/h^3 + b*e*g^2*p*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) + 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(e)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) - 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(e)) - sqrt(2)*log(sqrt(e)*h*x + sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(1/4)*e^(3/4)) + sqrt(2)*log(sqrt(e)*h*x - sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(1/4)*e^(3/4)))/h^3 - 2*a*g^2*x^3/(h*x)^(7/2) - 4/3*b*f*g*x^2*log((e*x^2 + d)^p*c)/(h*x)^(7/2) + 2/3*(sqrt(2)*h^2*log(sqrt(e)*h*x + sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(3/4)*e^(1/4)) - sqrt(2)*h^2*log(sqrt(e)*h*x - sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(3/4)*e^(1/4)) + 2*sqrt(2)*h*arctan(1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) + 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(d)) + 2*sqrt(2)*h*arctan(-1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) - 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(d)))*b*e*f*g*p/h^4 - 4/3*a*f*g*x^2/(h*x)^(7/2) - 2/5*b*f^2*log((e*x^2 + d)^p*c)/((h*x)^(5/2)*h) - 2/5*a*f^2/((h*x)^(5/2)*h)","A",0
615,1,838,0,1.155585," ","integrate((g*x+f)^2*(a+b*log(c*(e*x^2+d)^p))/(h*x)^(9/2),x, algorithm=""maxima"")","-\frac{b e f^{2} p {\left(\frac{3 \, {\left(\frac{\sqrt{2} e^{\frac{3}{4}} \log\left(\sqrt{e} h x + \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{3}{4}}} - \frac{\sqrt{2} e^{\frac{3}{4}} \log\left(\sqrt{e} h x - \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{3}{4}}} + \frac{2 \, \sqrt{2} e \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} + 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{d} h} + \frac{2 \, \sqrt{2} e \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} - 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{d} h}\right)}}{d} + \frac{8}{\left(h x\right)^{\frac{3}{2}} d}\right)}}{21 \, h^{3}} - \frac{2 \, b g^{2} x^{3} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{3 \, \left(h x\right)^{\frac{9}{2}}} - \frac{2 \, b e f g p {\left(\frac{e {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} + 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{e}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} - 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{e}} - \frac{\sqrt{2} \log\left(\sqrt{e} h x + \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{3}{4}}} + \frac{\sqrt{2} \log\left(\sqrt{e} h x - \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{3}{4}}}\right)}}{d} + \frac{8}{\sqrt{h x} d}\right)}}{5 \, h^{4}} - \frac{2 \, a g^{2} x^{3}}{3 \, \left(h x\right)^{\frac{9}{2}}} - \frac{4 \, b f g x^{2} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{5 \, \left(h x\right)^{\frac{9}{2}}} + \frac{{\left(\frac{\sqrt{2} h^{2} \log\left(\sqrt{e} h x + \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{3}{4}} e^{\frac{1}{4}}} - \frac{\sqrt{2} h^{2} \log\left(\sqrt{e} h x - \sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} \sqrt{h x} e^{\frac{1}{4}} + \sqrt{d} h\right)}{\left(d h^{2}\right)^{\frac{3}{4}} e^{\frac{1}{4}}} + \frac{2 \, \sqrt{2} h \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} + 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{d}} + \frac{2 \, \sqrt{2} h \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(d h^{2}\right)^{\frac{1}{4}} e^{\frac{1}{4}} - 2 \, \sqrt{h x} \sqrt{e}\right)}}{2 \, \sqrt{\sqrt{d} \sqrt{e} h}}\right)}{\sqrt{\sqrt{d} \sqrt{e} h} \sqrt{d}}\right)} b e g^{2} p}{3 \, h^{5}} - \frac{4 \, a f g x^{2}}{5 \, \left(h x\right)^{\frac{9}{2}}} - \frac{2 \, b f^{2} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{7 \, \left(h x\right)^{\frac{7}{2}} h} - \frac{2 \, a f^{2}}{7 \, \left(h x\right)^{\frac{7}{2}} h}"," ",0,"-1/21*b*e*f^2*p*(3*(sqrt(2)*e^(3/4)*log(sqrt(e)*h*x + sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/(d*h^2)^(3/4) - sqrt(2)*e^(3/4)*log(sqrt(e)*h*x - sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/(d*h^2)^(3/4) + 2*sqrt(2)*e*arctan(1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) + 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(d)*h) + 2*sqrt(2)*e*arctan(-1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) - 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(d)*h))/d + 8/((h*x)^(3/2)*d))/h^3 - 2/3*b*g^2*x^3*log((e*x^2 + d)^p*c)/(h*x)^(9/2) - 2/5*b*e*f*g*p*(e*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) + 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(e)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) - 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(e)) - sqrt(2)*log(sqrt(e)*h*x + sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(1/4)*e^(3/4)) + sqrt(2)*log(sqrt(e)*h*x - sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(1/4)*e^(3/4)))/d + 8/(sqrt(h*x)*d))/h^4 - 2/3*a*g^2*x^3/(h*x)^(9/2) - 4/5*b*f*g*x^2*log((e*x^2 + d)^p*c)/(h*x)^(9/2) + 1/3*(sqrt(2)*h^2*log(sqrt(e)*h*x + sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(3/4)*e^(1/4)) - sqrt(2)*h^2*log(sqrt(e)*h*x - sqrt(2)*(d*h^2)^(1/4)*sqrt(h*x)*e^(1/4) + sqrt(d)*h)/((d*h^2)^(3/4)*e^(1/4)) + 2*sqrt(2)*h*arctan(1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) + 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(d)) + 2*sqrt(2)*h*arctan(-1/2*sqrt(2)*(sqrt(2)*(d*h^2)^(1/4)*e^(1/4) - 2*sqrt(h*x)*sqrt(e))/sqrt(sqrt(d)*sqrt(e)*h))/(sqrt(sqrt(d)*sqrt(e)*h)*sqrt(d)))*b*e*g^2*p/h^5 - 4/5*a*f*g*x^2/(h*x)^(9/2) - 2/7*b*f^2*log((e*x^2 + d)^p*c)/((h*x)^(7/2)*h) - 2/7*a*f^2/((h*x)^(7/2)*h)","A",0
616,0,0,0,0.000000," ","integrate((h*x)^(1/2)*(a+b*log(c*(e*x^2+d)^p))/(g*x+f),x, algorithm=""maxima"")","b \int \frac{\sqrt{h} p \sqrt{x} \log\left(e x^{2} + d\right) + \sqrt{h} \sqrt{x} \log\left(c\right)}{g x + f}\,{d x} - \frac{2 \, {\left(\frac{f h^{2} \arctan\left(\frac{\sqrt{h x} g}{\sqrt{f g h}}\right)}{\sqrt{f g h} g} - \frac{\sqrt{h x} h}{g}\right)} a}{h}"," ",0,"b*integrate((sqrt(h)*p*sqrt(x)*log(e*x^2 + d) + sqrt(h)*sqrt(x)*log(c))/(g*x + f), x) - 2*(f*h^2*arctan(sqrt(h*x)*g/sqrt(f*g*h))/(sqrt(f*g*h)*g) - sqrt(h*x)*h/g)*a/h","F",0
617,0,0,0,0.000000," ","integrate((a+b*log(c*(e*x^2+d)^p))/(h*x)^(1/2)/(g*x+f),x, algorithm=""maxima"")","b \int \frac{\sqrt{h} p \log\left(e x^{2} + d\right) + \sqrt{h} \log\left(c\right)}{g h x^{\frac{3}{2}} + f h \sqrt{x}}\,{d x} + \frac{2 \, a \arctan\left(\frac{\sqrt{h x} g}{\sqrt{f g h}}\right)}{\sqrt{f g h}}"," ",0,"b*integrate((sqrt(h)*p*log(e*x^2 + d) + sqrt(h)*log(c))/(g*h*x^(3/2) + f*h*sqrt(x)), x) + 2*a*arctan(sqrt(h*x)*g/sqrt(f*g*h))/sqrt(f*g*h)","F",0
618,0,0,0,0.000000," ","integrate((a+b*log(c*(e*x^2+d)^p))/(h*x)^(3/2)/(g*x+f),x, algorithm=""maxima"")","b \int \frac{\sqrt{h} p \log\left(e x^{2} + d\right) + \sqrt{h} \log\left(c\right)}{g h^{2} x^{\frac{5}{2}} + f h^{2} x^{\frac{3}{2}}}\,{d x} - \frac{2 \, a {\left(\frac{g \arctan\left(\frac{\sqrt{h x} g}{\sqrt{f g h}}\right)}{\sqrt{f g h} f} + \frac{1}{\sqrt{h x} f}\right)}}{h}"," ",0,"b*integrate((sqrt(h)*p*log(e*x^2 + d) + sqrt(h)*log(c))/(g*h^2*x^(5/2) + f*h^2*x^(3/2)), x) - 2*a*(g*arctan(sqrt(h*x)*g/sqrt(f*g*h))/(sqrt(f*g*h)*f) + 1/(sqrt(h*x)*f))/h","F",0
619,0,0,0,0.000000," ","integrate(log(f*x^p)*log(1+e*x^m)/x,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(p \log\left(x\right)^{2} - 2 \, \log\left(f\right) \log\left(x\right) - 2 \, \log\left(x\right) \log\left(x^{p}\right)\right)} \log\left(e x^{m} + 1\right) - \int \frac{2 \, e m x^{m} \log\left(x\right) \log\left(x^{p}\right) - {\left(e m p \log\left(x\right)^{2} - 2 \, e m \log\left(f\right) \log\left(x\right)\right)} x^{m}}{2 \, {\left(e x x^{m} + x\right)}}\,{d x}"," ",0,"-1/2*(p*log(x)^2 - 2*log(f)*log(x) - 2*log(x)*log(x^p))*log(e*x^m + 1) - integrate(1/2*(2*e*m*x^m*log(x)*log(x^p) - (e*m*p*log(x)^2 - 2*e*m*log(f)*log(x))*x^m)/(e*x*x^m + x), x)","F",0
620,0,0,0,0.000000," ","integrate(x^(-1+m)*log(f*x^p)^2/(d+e*x^m),x, algorithm=""maxima"")","\int \frac{x^{m - 1} \log\left(f x^{p}\right)^{2}}{e x^{m} + d}\,{d x}"," ",0,"integrate(x^(m - 1)*log(f*x^p)^2/(e*x^m + d), x)","F",0
621,0,0,0,0.000000," ","integrate(log(f*x^p)^3*(a+b*log(c*(d+e*x^m)^n))/x,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(b p^{3} \log\left(x\right)^{4} - 4 \, b p^{2} \log\left(f\right) \log\left(x\right)^{3} + 6 \, b p \log\left(f\right)^{2} \log\left(x\right)^{2} - 4 \, b \log\left(f\right)^{3} \log\left(x\right) - 4 \, b \log\left(x\right) \log\left(x^{p}\right)^{3} + 6 \, {\left(b p \log\left(x\right)^{2} - 2 \, b \log\left(f\right) \log\left(x\right)\right)} \log\left(x^{p}\right)^{2} - 4 \, {\left(b p^{2} \log\left(x\right)^{3} - 3 \, b p \log\left(f\right) \log\left(x\right)^{2} + 3 \, b \log\left(f\right)^{2} \log\left(x\right)\right)} \log\left(x^{p}\right)\right)} \log\left({\left(e x^{m} + d\right)}^{n}\right) - \int -\frac{4 \, b d \log\left(c\right) \log\left(f\right)^{3} + 4 \, a d \log\left(f\right)^{3} + 4 \, {\left(b d \log\left(c\right) + a d - {\left(b e m n \log\left(x\right) - b e \log\left(c\right) - a e\right)} x^{m}\right)} \log\left(x^{p}\right)^{3} + 6 \, {\left(2 \, b d \log\left(c\right) \log\left(f\right) + 2 \, a d \log\left(f\right) + {\left(b e m n p \log\left(x\right)^{2} - 2 \, b e m n \log\left(f\right) \log\left(x\right) + 2 \, b e \log\left(c\right) \log\left(f\right) + 2 \, a e \log\left(f\right)\right)} x^{m}\right)} \log\left(x^{p}\right)^{2} + {\left(b e m n p^{3} \log\left(x\right)^{4} - 4 \, b e m n p^{2} \log\left(f\right) \log\left(x\right)^{3} + 6 \, b e m n p \log\left(f\right)^{2} \log\left(x\right)^{2} - 4 \, b e m n \log\left(f\right)^{3} \log\left(x\right) + 4 \, b e \log\left(c\right) \log\left(f\right)^{3} + 4 \, a e \log\left(f\right)^{3}\right)} x^{m} + 4 \, {\left(3 \, b d \log\left(c\right) \log\left(f\right)^{2} + 3 \, a d \log\left(f\right)^{2} - {\left(b e m n p^{2} \log\left(x\right)^{3} - 3 \, b e m n p \log\left(f\right) \log\left(x\right)^{2} + 3 \, b e m n \log\left(f\right)^{2} \log\left(x\right) - 3 \, b e \log\left(c\right) \log\left(f\right)^{2} - 3 \, a e \log\left(f\right)^{2}\right)} x^{m}\right)} \log\left(x^{p}\right)}{4 \, {\left(e x x^{m} + d x\right)}}\,{d x}"," ",0,"-1/4*(b*p^3*log(x)^4 - 4*b*p^2*log(f)*log(x)^3 + 6*b*p*log(f)^2*log(x)^2 - 4*b*log(f)^3*log(x) - 4*b*log(x)*log(x^p)^3 + 6*(b*p*log(x)^2 - 2*b*log(f)*log(x))*log(x^p)^2 - 4*(b*p^2*log(x)^3 - 3*b*p*log(f)*log(x)^2 + 3*b*log(f)^2*log(x))*log(x^p))*log((e*x^m + d)^n) - integrate(-1/4*(4*b*d*log(c)*log(f)^3 + 4*a*d*log(f)^3 + 4*(b*d*log(c) + a*d - (b*e*m*n*log(x) - b*e*log(c) - a*e)*x^m)*log(x^p)^3 + 6*(2*b*d*log(c)*log(f) + 2*a*d*log(f) + (b*e*m*n*p*log(x)^2 - 2*b*e*m*n*log(f)*log(x) + 2*b*e*log(c)*log(f) + 2*a*e*log(f))*x^m)*log(x^p)^2 + (b*e*m*n*p^3*log(x)^4 - 4*b*e*m*n*p^2*log(f)*log(x)^3 + 6*b*e*m*n*p*log(f)^2*log(x)^2 - 4*b*e*m*n*log(f)^3*log(x) + 4*b*e*log(c)*log(f)^3 + 4*a*e*log(f)^3)*x^m + 4*(3*b*d*log(c)*log(f)^2 + 3*a*d*log(f)^2 - (b*e*m*n*p^2*log(x)^3 - 3*b*e*m*n*p*log(f)*log(x)^2 + 3*b*e*m*n*log(f)^2*log(x) - 3*b*e*log(c)*log(f)^2 - 3*a*e*log(f)^2)*x^m)*log(x^p))/(e*x*x^m + d*x), x)","F",0
622,0,0,0,0.000000," ","integrate(log(f*x^p)^2*(a+b*log(c*(d+e*x^m)^n))/x,x, algorithm=""maxima"")","\frac{1}{3} \, {\left(b p^{2} \log\left(x\right)^{3} - 3 \, b p \log\left(f\right) \log\left(x\right)^{2} + 3 \, b \log\left(f\right)^{2} \log\left(x\right) + 3 \, b \log\left(x\right) \log\left(x^{p}\right)^{2} - 3 \, {\left(b p \log\left(x\right)^{2} - 2 \, b \log\left(f\right) \log\left(x\right)\right)} \log\left(x^{p}\right)\right)} \log\left({\left(e x^{m} + d\right)}^{n}\right) - \int -\frac{3 \, b d \log\left(c\right) \log\left(f\right)^{2} + 3 \, a d \log\left(f\right)^{2} + 3 \, {\left(b d \log\left(c\right) + a d - {\left(b e m n \log\left(x\right) - b e \log\left(c\right) - a e\right)} x^{m}\right)} \log\left(x^{p}\right)^{2} - {\left(b e m n p^{2} \log\left(x\right)^{3} - 3 \, b e m n p \log\left(f\right) \log\left(x\right)^{2} + 3 \, b e m n \log\left(f\right)^{2} \log\left(x\right) - 3 \, b e \log\left(c\right) \log\left(f\right)^{2} - 3 \, a e \log\left(f\right)^{2}\right)} x^{m} + 3 \, {\left(2 \, b d \log\left(c\right) \log\left(f\right) + 2 \, a d \log\left(f\right) + {\left(b e m n p \log\left(x\right)^{2} - 2 \, b e m n \log\left(f\right) \log\left(x\right) + 2 \, b e \log\left(c\right) \log\left(f\right) + 2 \, a e \log\left(f\right)\right)} x^{m}\right)} \log\left(x^{p}\right)}{3 \, {\left(e x x^{m} + d x\right)}}\,{d x}"," ",0,"1/3*(b*p^2*log(x)^3 - 3*b*p*log(f)*log(x)^2 + 3*b*log(f)^2*log(x) + 3*b*log(x)*log(x^p)^2 - 3*(b*p*log(x)^2 - 2*b*log(f)*log(x))*log(x^p))*log((e*x^m + d)^n) - integrate(-1/3*(3*b*d*log(c)*log(f)^2 + 3*a*d*log(f)^2 + 3*(b*d*log(c) + a*d - (b*e*m*n*log(x) - b*e*log(c) - a*e)*x^m)*log(x^p)^2 - (b*e*m*n*p^2*log(x)^3 - 3*b*e*m*n*p*log(f)*log(x)^2 + 3*b*e*m*n*log(f)^2*log(x) - 3*b*e*log(c)*log(f)^2 - 3*a*e*log(f)^2)*x^m + 3*(2*b*d*log(c)*log(f) + 2*a*d*log(f) + (b*e*m*n*p*log(x)^2 - 2*b*e*m*n*log(f)*log(x) + 2*b*e*log(c)*log(f) + 2*a*e*log(f))*x^m)*log(x^p))/(e*x*x^m + d*x), x)","F",0
623,0,0,0,0.000000," ","integrate(log(f*x^p)*(a+b*log(c*(d+e*x^m)^n))/x,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(b p \log\left(x\right)^{2} - 2 \, b \log\left(f\right) \log\left(x\right) - 2 \, b \log\left(x\right) \log\left(x^{p}\right)\right)} \log\left({\left(e x^{m} + d\right)}^{n}\right) - \int -\frac{2 \, b d \log\left(c\right) \log\left(f\right) + 2 \, a d \log\left(f\right) + {\left(b e m n p \log\left(x\right)^{2} - 2 \, b e m n \log\left(f\right) \log\left(x\right) + 2 \, b e \log\left(c\right) \log\left(f\right) + 2 \, a e \log\left(f\right)\right)} x^{m} + 2 \, {\left(b d \log\left(c\right) + a d - {\left(b e m n \log\left(x\right) - b e \log\left(c\right) - a e\right)} x^{m}\right)} \log\left(x^{p}\right)}{2 \, {\left(e x x^{m} + d x\right)}}\,{d x}"," ",0,"-1/2*(b*p*log(x)^2 - 2*b*log(f)*log(x) - 2*b*log(x)*log(x^p))*log((e*x^m + d)^n) - integrate(-1/2*(2*b*d*log(c)*log(f) + 2*a*d*log(f) + (b*e*m*n*p*log(x)^2 - 2*b*e*m*n*log(f)*log(x) + 2*b*e*log(c)*log(f) + 2*a*e*log(f))*x^m + 2*(b*d*log(c) + a*d - (b*e*m*n*log(x) - b*e*log(c) - a*e)*x^m)*log(x^p))/(e*x*x^m + d*x), x)","F",0
624,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^m)^n))/x,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(2 \, d m n \int \frac{\log\left(x\right)}{e x x^{m} + d x}\,{d x} - m n \log\left(x\right)^{2} + 2 \, \log\left({\left(e x^{m} + d\right)}^{n}\right) \log\left(x\right) + 2 \, \log\left(c\right) \log\left(x\right)\right)} b + a \log\left(x\right)"," ",0,"1/2*(2*d*m*n*integrate(log(x)/(e*x*x^m + d*x), x) - m*n*log(x)^2 + 2*log((e*x^m + d)^n)*log(x) + 2*log(c)*log(x))*b + a*log(x)","F",0
625,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^m)^n))/x/log(f*x^p),x, algorithm=""maxima"")","b \int \frac{\log\left({\left(e x^{m} + d\right)}^{n}\right) + \log\left(c\right)}{x \log\left(f\right) + x \log\left(x^{p}\right)}\,{d x} + \frac{a \log\left(\log\left(f x^{p}\right)\right)}{p}"," ",0,"b*integrate((log((e*x^m + d)^n) + log(c))/(x*log(f) + x*log(x^p)), x) + a*log(log(f*x^p))/p","F",0
626,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^m)^n))/x/log(f*x^p)^2,x, algorithm=""maxima"")","{\left(e m n \int \frac{x^{m}}{e p x x^{m} \log\left(f\right) + d p x \log\left(f\right) + {\left(e p x x^{m} + d p x\right)} \log\left(x^{p}\right)}\,{d x} - \frac{\log\left({\left(e x^{m} + d\right)}^{n}\right) + \log\left(c\right)}{p \log\left(f\right) + p \log\left(x^{p}\right)}\right)} b - \frac{a}{p \log\left(f x^{p}\right)}"," ",0,"(e*m*n*integrate(x^m/(e*p*x*x^m*log(f) + d*p*x*log(f) + (e*p*x*x^m + d*p*x)*log(x^p)), x) - (log((e*x^m + d)^n) + log(c))/(p*log(f) + p*log(x^p)))*b - a/(p*log(f*x^p))","F",0
627,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e*x^m)^n))/x/log(f*x^p)^3,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(2 \, d e m^{2} n \int \frac{x^{m}}{2 \, {\left(e^{2} p^{2} x x^{2 \, m} \log\left(f\right) + 2 \, d e p^{2} x x^{m} \log\left(f\right) + d^{2} p^{2} x \log\left(f\right) + {\left(e^{2} p^{2} x x^{2 \, m} + 2 \, d e p^{2} x x^{m} + d^{2} p^{2} x\right)} \log\left(x^{p}\right)\right)}}\,{d x} - \frac{e m n x^{m} \log\left(x^{p}\right) + d p \log\left(c\right) + {\left(e m n \log\left(f\right) + e p \log\left(c\right)\right)} x^{m} + {\left(e p x^{m} + d p\right)} \log\left({\left(e x^{m} + d\right)}^{n}\right)}{e p^{2} x^{m} \log\left(f\right)^{2} + d p^{2} \log\left(f\right)^{2} + {\left(e p^{2} x^{m} + d p^{2}\right)} \log\left(x^{p}\right)^{2} + 2 \, {\left(e p^{2} x^{m} \log\left(f\right) + d p^{2} \log\left(f\right)\right)} \log\left(x^{p}\right)}\right)} b - \frac{a}{2 \, p \log\left(f x^{p}\right)^{2}}"," ",0,"1/2*(2*d*e*m^2*n*integrate(1/2*x^m/(e^2*p^2*x*x^(2*m)*log(f) + 2*d*e*p^2*x*x^m*log(f) + d^2*p^2*x*log(f) + (e^2*p^2*x*x^(2*m) + 2*d*e*p^2*x*x^m + d^2*p^2*x)*log(x^p)), x) - (e*m*n*x^m*log(x^p) + d*p*log(c) + (e*m*n*log(f) + e*p*log(c))*x^m + (e*p*x^m + d*p)*log((e*x^m + d)^n))/(e*p^2*x^m*log(f)^2 + d*p^2*log(f)^2 + (e*p^2*x^m + d*p^2)*log(x^p)^2 + 2*(e*p^2*x^m*log(f) + d*p^2*log(f))*log(x^p)))*b - 1/2*a/(p*log(f*x^p)^2)","F",0
628,0,0,0,0.000000," ","integrate(log(c*(d+e*(g*x+f)^p)^q),x, algorithm=""maxima"")","d g p q \int \frac{x}{d g x + {\left(e g x + e f\right)} {\left(g x + f\right)}^{p} + d f}\,{d x} + \frac{f p q \log\left(g x + f\right) + g x \log\left({\left({\left(g x + f\right)}^{p} e + d\right)}^{q}\right) - {\left(g p q - g \log\left(c\right)\right)} x}{g}"," ",0,"d*g*p*q*integrate(x/(d*g*x + (e*g*x + e*f)*(g*x + f)^p + d*f), x) + (f*p*q*log(g*x + f) + g*x*log(((g*x + f)^p*e + d)^q) - (g*p*q - g*log(c))*x)/g","F",0
629,0,0,0,0.000000," ","integrate(log(c*(d+e*(g*x+f)^3)^q),x, algorithm=""maxima"")","-{\left(3 \, q - \log\left(c\right)\right)} x + 3 \, q \int \frac{e f g^{2} x^{2} + 2 \, e f^{2} g x + e f^{3} + d}{e g^{3} x^{3} + 3 \, e f g^{2} x^{2} + 3 \, e f^{2} g x + e f^{3} + d}\,{d x} + x \log\left({\left(e g^{3} x^{3} + 3 \, e f g^{2} x^{2} + 3 \, e f^{2} g x + e f^{3} + d\right)}^{q}\right)"," ",0,"-(3*q - log(c))*x + 3*q*integrate((e*f*g^2*x^2 + 2*e*f^2*g*x + e*f^3 + d)/(e*g^3*x^3 + 3*e*f*g^2*x^2 + 3*e*f^2*g*x + e*f^3 + d), x) + x*log((e*g^3*x^3 + 3*e*f*g^2*x^2 + 3*e*f^2*g*x + e*f^3 + d)^q)","F",0
630,1,100,0,1.480283," ","integrate(log(c*(d+e*(g*x+f)^2)^q),x, algorithm=""maxima"")","-e g q {\left(\frac{2 \, x}{e g} - \frac{f \log\left(e g^{2} x^{2} + 2 \, e f g x + e f^{2} + d\right)}{e g^{2}} - \frac{2 \, d \arctan\left(\frac{e g^{2} x + e f g}{\sqrt{d e} g}\right)}{\sqrt{d e} e g^{2}}\right)} + x \log\left({\left({\left(g x + f\right)}^{2} e + d\right)}^{q} c\right)"," ",0,"-e*g*q*(2*x/(e*g) - f*log(e*g^2*x^2 + 2*e*f*g*x + e*f^2 + d)/(e*g^2) - 2*d*arctan((e*g^2*x + e*f*g)/(sqrt(d*e)*g))/(sqrt(d*e)*e*g^2)) + x*log(((g*x + f)^2*e + d)^q*c)","A",0
631,1,54,0,0.511821," ","integrate(log(c*(d+e*(g*x+f))^q),x, algorithm=""maxima"")","-e g q {\left(\frac{x}{e g} - \frac{{\left(e f + d\right)} \log\left(e g x + e f + d\right)}{e^{2} g^{2}}\right)} + x \log\left({\left({\left(g x + f\right)} e + d\right)}^{q} c\right)"," ",0,"-e*g*q*(x/(e*g) - (e*f + d)*log(e*g*x + e*f + d)/(e^2*g^2)) + x*log(((g*x + f)*e + d)^q*c)","A",0
632,1,65,0,0.638888," ","integrate(log(c*(d+e/(g*x+f))^q),x, algorithm=""maxima"")","-e g q {\left(\frac{f \log\left(g x + f\right)}{e g^{2}} - \frac{{\left(d f + e\right)} \log\left(d g x + d f + e\right)}{d e g^{2}}\right)} + x \log\left(c {\left(d + \frac{e}{g x + f}\right)}^{q}\right)"," ",0,"-e*g*q*(f*log(g*x + f)/(e*g^2) - (d*f + e)*log(d*g*x + d*f + e)/(d*e*g^2)) + x*log(c*(d + e/(g*x + f))^q)","A",0
633,1,100,0,1.644761," ","integrate(log(c*(d+e/(g*x+f)^2)^q),x, algorithm=""maxima"")","e g q {\left(\frac{f \log\left(d g^{2} x^{2} + 2 \, d f g x + d f^{2} + e\right)}{e g^{2}} - \frac{2 \, f \log\left(g x + f\right)}{e g^{2}} + \frac{2 \, \arctan\left(\frac{d g^{2} x + d f g}{\sqrt{d e} g}\right)}{\sqrt{d e} g^{2}}\right)} + x \log\left(c {\left(d + \frac{e}{{\left(g x + f\right)}^{2}}\right)}^{q}\right)"," ",0,"e*g*q*(f*log(d*g^2*x^2 + 2*d*f*g*x + d*f^2 + e)/(e*g^2) - 2*f*log(g*x + f)/(e*g^2) + 2*arctan((d*g^2*x + d*f*g)/(sqrt(d*e)*g))/(sqrt(d*e)*g^2)) + x*log(c*(d + e/(g*x + f)^2)^q)","A",0
634,0,0,0,0.000000," ","integrate(log(c*(d+e/(g*x+f)^3)^q),x, algorithm=""maxima"")","3 \, q \int \frac{d f g^{2} x^{2} + 2 \, d f^{2} g x + d f^{3} + e}{d g^{3} x^{3} + 3 \, d f g^{2} x^{2} + 3 \, d f^{2} g x + d f^{3} + e}\,{d x} - \frac{3 \, f q \log\left(g x + f\right) - g x \log\left({\left(d g^{3} x^{3} + 3 \, d f g^{2} x^{2} + 3 \, d f^{2} g x + d f^{3} + e\right)}^{q}\right) + 3 \, g x \log\left({\left(g x + f\right)}^{q}\right) - g x \log\left(c\right)}{g}"," ",0,"3*q*integrate((d*f*g^2*x^2 + 2*d*f^2*g*x + d*f^3 + e)/(d*g^3*x^3 + 3*d*f*g^2*x^2 + 3*d*f^2*g*x + d*f^3 + e), x) - (3*f*q*log(g*x + f) - g*x*log((d*g^3*x^3 + 3*d*f*g^2*x^2 + 3*d*f^2*g*x + d*f^3 + e)^q) + 3*g*x*log((g*x + f)^q) - g*x*log(c))/g","F",0
635,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/(g*x+f))^p))^n,x, algorithm=""maxima"")","\int {\left(b \log\left(c {\left(d + \frac{e}{g x + f}\right)}^{p}\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((b*log(c*(d + e/(g*x + f))^p) + a)^n, x)","F",0
636,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/(g*x+f))^p))^4,x, algorithm=""maxima"")","-4 \, a^{3} b e g p {\left(\frac{f \log\left(g x + f\right)}{e g^{2}} - \frac{{\left(d f + e\right)} \log\left(d g x + d f + e\right)}{d e g^{2}}\right)} + 4 \, a^{3} b x \log\left(c {\left(d + \frac{e}{g x + f}\right)}^{p}\right) + a^{4} x + \frac{b^{4} d g x \log\left({\left(d g x + d f + e\right)}^{p}\right)^{4} - 4 \, {\left(b^{4} d f p \log\left(g x + f\right) + b^{4} d g x \log\left({\left(g x + f\right)}^{p}\right) - {\left(d f p + e p\right)} b^{4} \log\left(d g x + d f + e\right) - {\left(b^{4} d g \log\left(c\right) + a b^{3} d g\right)} x\right)} \log\left({\left(d g x + d f + e\right)}^{p}\right)^{3}}{d g} + \int \frac{{\left(d f + e\right)} b^{4} \log\left(c\right)^{4} + 4 \, {\left(d f + e\right)} a b^{3} \log\left(c\right)^{3} + 6 \, {\left(d f + e\right)} a^{2} b^{2} \log\left(c\right)^{2} + {\left(b^{4} d g x + {\left(d f + e\right)} b^{4}\right)} \log\left({\left(g x + f\right)}^{p}\right)^{4} - 4 \, {\left({\left(d f + e\right)} b^{4} \log\left(c\right) + {\left(d f + e\right)} a b^{3} + {\left(b^{4} d g \log\left(c\right) + a b^{3} d g\right)} x\right)} \log\left({\left(g x + f\right)}^{p}\right)^{3} + 6 \, {\left(2 \, b^{4} d f p^{2} \log\left(g x + f\right) + {\left(d f + e\right)} b^{4} \log\left(c\right)^{2} - 2 \, {\left(d f p^{2} + e p^{2}\right)} b^{4} \log\left(d g x + d f + e\right) + 2 \, {\left(d f + e\right)} a b^{3} \log\left(c\right) + {\left(d f + e\right)} a^{2} b^{2} + {\left(b^{4} d g x + {\left(d f + e\right)} b^{4}\right)} \log\left({\left(g x + f\right)}^{p}\right)^{2} + {\left(a^{2} b^{2} d g - 2 \, {\left(d g p - d g \log\left(c\right)\right)} a b^{3} - {\left(2 \, d g p \log\left(c\right) - d g \log\left(c\right)^{2}\right)} b^{4}\right)} x - 2 \, {\left({\left(d f + e\right)} b^{4} \log\left(c\right) + {\left(d f + e\right)} a b^{3} + {\left(a b^{3} d g - {\left(d g p - d g \log\left(c\right)\right)} b^{4}\right)} x\right)} \log\left({\left(g x + f\right)}^{p}\right)\right)} \log\left({\left(d g x + d f + e\right)}^{p}\right)^{2} + 6 \, {\left({\left(d f + e\right)} b^{4} \log\left(c\right)^{2} + 2 \, {\left(d f + e\right)} a b^{3} \log\left(c\right) + {\left(d f + e\right)} a^{2} b^{2} + {\left(b^{4} d g \log\left(c\right)^{2} + 2 \, a b^{3} d g \log\left(c\right) + a^{2} b^{2} d g\right)} x\right)} \log\left({\left(g x + f\right)}^{p}\right)^{2} + {\left(b^{4} d g \log\left(c\right)^{4} + 4 \, a b^{3} d g \log\left(c\right)^{3} + 6 \, a^{2} b^{2} d g \log\left(c\right)^{2}\right)} x + 4 \, {\left({\left(d f + e\right)} b^{4} \log\left(c\right)^{3} + 3 \, {\left(d f + e\right)} a b^{3} \log\left(c\right)^{2} + 3 \, {\left(d f + e\right)} a^{2} b^{2} \log\left(c\right) - {\left(b^{4} d g x + {\left(d f + e\right)} b^{4}\right)} \log\left({\left(g x + f\right)}^{p}\right)^{3} + 3 \, {\left({\left(d f + e\right)} b^{4} \log\left(c\right) + {\left(d f + e\right)} a b^{3} + {\left(b^{4} d g \log\left(c\right) + a b^{3} d g\right)} x\right)} \log\left({\left(g x + f\right)}^{p}\right)^{2} + {\left(b^{4} d g \log\left(c\right)^{3} + 3 \, a b^{3} d g \log\left(c\right)^{2} + 3 \, a^{2} b^{2} d g \log\left(c\right)\right)} x - 3 \, {\left({\left(d f + e\right)} b^{4} \log\left(c\right)^{2} + 2 \, {\left(d f + e\right)} a b^{3} \log\left(c\right) + {\left(d f + e\right)} a^{2} b^{2} + {\left(b^{4} d g \log\left(c\right)^{2} + 2 \, a b^{3} d g \log\left(c\right) + a^{2} b^{2} d g\right)} x\right)} \log\left({\left(g x + f\right)}^{p}\right)\right)} \log\left({\left(d g x + d f + e\right)}^{p}\right) - 4 \, {\left({\left(d f + e\right)} b^{4} \log\left(c\right)^{3} + 3 \, {\left(d f + e\right)} a b^{3} \log\left(c\right)^{2} + 3 \, {\left(d f + e\right)} a^{2} b^{2} \log\left(c\right) + {\left(b^{4} d g \log\left(c\right)^{3} + 3 \, a b^{3} d g \log\left(c\right)^{2} + 3 \, a^{2} b^{2} d g \log\left(c\right)\right)} x\right)} \log\left({\left(g x + f\right)}^{p}\right)}{d g x + d f + e}\,{d x}"," ",0,"-4*a^3*b*e*g*p*(f*log(g*x + f)/(e*g^2) - (d*f + e)*log(d*g*x + d*f + e)/(d*e*g^2)) + 4*a^3*b*x*log(c*(d + e/(g*x + f))^p) + a^4*x + (b^4*d*g*x*log((d*g*x + d*f + e)^p)^4 - 4*(b^4*d*f*p*log(g*x + f) + b^4*d*g*x*log((g*x + f)^p) - (d*f*p + e*p)*b^4*log(d*g*x + d*f + e) - (b^4*d*g*log(c) + a*b^3*d*g)*x)*log((d*g*x + d*f + e)^p)^3)/(d*g) + integrate(((d*f + e)*b^4*log(c)^4 + 4*(d*f + e)*a*b^3*log(c)^3 + 6*(d*f + e)*a^2*b^2*log(c)^2 + (b^4*d*g*x + (d*f + e)*b^4)*log((g*x + f)^p)^4 - 4*((d*f + e)*b^4*log(c) + (d*f + e)*a*b^3 + (b^4*d*g*log(c) + a*b^3*d*g)*x)*log((g*x + f)^p)^3 + 6*(2*b^4*d*f*p^2*log(g*x + f) + (d*f + e)*b^4*log(c)^2 - 2*(d*f*p^2 + e*p^2)*b^4*log(d*g*x + d*f + e) + 2*(d*f + e)*a*b^3*log(c) + (d*f + e)*a^2*b^2 + (b^4*d*g*x + (d*f + e)*b^4)*log((g*x + f)^p)^2 + (a^2*b^2*d*g - 2*(d*g*p - d*g*log(c))*a*b^3 - (2*d*g*p*log(c) - d*g*log(c)^2)*b^4)*x - 2*((d*f + e)*b^4*log(c) + (d*f + e)*a*b^3 + (a*b^3*d*g - (d*g*p - d*g*log(c))*b^4)*x)*log((g*x + f)^p))*log((d*g*x + d*f + e)^p)^2 + 6*((d*f + e)*b^4*log(c)^2 + 2*(d*f + e)*a*b^3*log(c) + (d*f + e)*a^2*b^2 + (b^4*d*g*log(c)^2 + 2*a*b^3*d*g*log(c) + a^2*b^2*d*g)*x)*log((g*x + f)^p)^2 + (b^4*d*g*log(c)^4 + 4*a*b^3*d*g*log(c)^3 + 6*a^2*b^2*d*g*log(c)^2)*x + 4*((d*f + e)*b^4*log(c)^3 + 3*(d*f + e)*a*b^3*log(c)^2 + 3*(d*f + e)*a^2*b^2*log(c) - (b^4*d*g*x + (d*f + e)*b^4)*log((g*x + f)^p)^3 + 3*((d*f + e)*b^4*log(c) + (d*f + e)*a*b^3 + (b^4*d*g*log(c) + a*b^3*d*g)*x)*log((g*x + f)^p)^2 + (b^4*d*g*log(c)^3 + 3*a*b^3*d*g*log(c)^2 + 3*a^2*b^2*d*g*log(c))*x - 3*((d*f + e)*b^4*log(c)^2 + 2*(d*f + e)*a*b^3*log(c) + (d*f + e)*a^2*b^2 + (b^4*d*g*log(c)^2 + 2*a*b^3*d*g*log(c) + a^2*b^2*d*g)*x)*log((g*x + f)^p))*log((d*g*x + d*f + e)^p) - 4*((d*f + e)*b^4*log(c)^3 + 3*(d*f + e)*a*b^3*log(c)^2 + 3*(d*f + e)*a^2*b^2*log(c) + (b^4*d*g*log(c)^3 + 3*a*b^3*d*g*log(c)^2 + 3*a^2*b^2*d*g*log(c))*x)*log((g*x + f)^p))/(d*g*x + d*f + e), x)","F",0
637,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/(g*x+f))^p))^3,x, algorithm=""maxima"")","-3 \, a^{2} b e g p {\left(\frac{f \log\left(g x + f\right)}{e g^{2}} - \frac{{\left(d f + e\right)} \log\left(d g x + d f + e\right)}{d e g^{2}}\right)} + 3 \, a^{2} b x \log\left(c {\left(d + \frac{e}{g x + f}\right)}^{p}\right) + a^{3} x + \frac{b^{3} d g x \log\left({\left(d g x + d f + e\right)}^{p}\right)^{3} - 3 \, {\left(b^{3} d f p \log\left(g x + f\right) + b^{3} d g x \log\left({\left(g x + f\right)}^{p}\right) - {\left(d f p + e p\right)} b^{3} \log\left(d g x + d f + e\right) - {\left(b^{3} d g \log\left(c\right) + a b^{2} d g\right)} x\right)} \log\left({\left(d g x + d f + e\right)}^{p}\right)^{2}}{d g} + \int \frac{{\left(d f + e\right)} b^{3} \log\left(c\right)^{3} + 3 \, {\left(d f + e\right)} a b^{2} \log\left(c\right)^{2} - {\left(b^{3} d g x + {\left(d f + e\right)} b^{3}\right)} \log\left({\left(g x + f\right)}^{p}\right)^{3} + 3 \, {\left({\left(d f + e\right)} b^{3} \log\left(c\right) + {\left(d f + e\right)} a b^{2} + {\left(b^{3} d g \log\left(c\right) + a b^{2} d g\right)} x\right)} \log\left({\left(g x + f\right)}^{p}\right)^{2} + {\left(b^{3} d g \log\left(c\right)^{3} + 3 \, a b^{2} d g \log\left(c\right)^{2}\right)} x + 3 \, {\left(2 \, b^{3} d f p^{2} \log\left(g x + f\right) + {\left(d f + e\right)} b^{3} \log\left(c\right)^{2} - 2 \, {\left(d f p^{2} + e p^{2}\right)} b^{3} \log\left(d g x + d f + e\right) + 2 \, {\left(d f + e\right)} a b^{2} \log\left(c\right) + {\left(b^{3} d g x + {\left(d f + e\right)} b^{3}\right)} \log\left({\left(g x + f\right)}^{p}\right)^{2} - {\left(2 \, {\left(d g p - d g \log\left(c\right)\right)} a b^{2} + {\left(2 \, d g p \log\left(c\right) - d g \log\left(c\right)^{2}\right)} b^{3}\right)} x - 2 \, {\left({\left(d f + e\right)} b^{3} \log\left(c\right) + {\left(d f + e\right)} a b^{2} + {\left(a b^{2} d g - {\left(d g p - d g \log\left(c\right)\right)} b^{3}\right)} x\right)} \log\left({\left(g x + f\right)}^{p}\right)\right)} \log\left({\left(d g x + d f + e\right)}^{p}\right) - 3 \, {\left({\left(d f + e\right)} b^{3} \log\left(c\right)^{2} + 2 \, {\left(d f + e\right)} a b^{2} \log\left(c\right) + {\left(b^{3} d g \log\left(c\right)^{2} + 2 \, a b^{2} d g \log\left(c\right)\right)} x\right)} \log\left({\left(g x + f\right)}^{p}\right)}{d g x + d f + e}\,{d x}"," ",0,"-3*a^2*b*e*g*p*(f*log(g*x + f)/(e*g^2) - (d*f + e)*log(d*g*x + d*f + e)/(d*e*g^2)) + 3*a^2*b*x*log(c*(d + e/(g*x + f))^p) + a^3*x + (b^3*d*g*x*log((d*g*x + d*f + e)^p)^3 - 3*(b^3*d*f*p*log(g*x + f) + b^3*d*g*x*log((g*x + f)^p) - (d*f*p + e*p)*b^3*log(d*g*x + d*f + e) - (b^3*d*g*log(c) + a*b^2*d*g)*x)*log((d*g*x + d*f + e)^p)^2)/(d*g) + integrate(((d*f + e)*b^3*log(c)^3 + 3*(d*f + e)*a*b^2*log(c)^2 - (b^3*d*g*x + (d*f + e)*b^3)*log((g*x + f)^p)^3 + 3*((d*f + e)*b^3*log(c) + (d*f + e)*a*b^2 + (b^3*d*g*log(c) + a*b^2*d*g)*x)*log((g*x + f)^p)^2 + (b^3*d*g*log(c)^3 + 3*a*b^2*d*g*log(c)^2)*x + 3*(2*b^3*d*f*p^2*log(g*x + f) + (d*f + e)*b^3*log(c)^2 - 2*(d*f*p^2 + e*p^2)*b^3*log(d*g*x + d*f + e) + 2*(d*f + e)*a*b^2*log(c) + (b^3*d*g*x + (d*f + e)*b^3)*log((g*x + f)^p)^2 - (2*(d*g*p - d*g*log(c))*a*b^2 + (2*d*g*p*log(c) - d*g*log(c)^2)*b^3)*x - 2*((d*f + e)*b^3*log(c) + (d*f + e)*a*b^2 + (a*b^2*d*g - (d*g*p - d*g*log(c))*b^3)*x)*log((g*x + f)^p))*log((d*g*x + d*f + e)^p) - 3*((d*f + e)*b^3*log(c)^2 + 2*(d*f + e)*a*b^2*log(c) + (b^3*d*g*log(c)^2 + 2*a*b^2*d*g*log(c))*x)*log((g*x + f)^p))/(d*g*x + d*f + e), x)","F",0
638,0,0,0,0.000000," ","integrate((a+b*log(c*(d+e/(g*x+f))^p))^2,x, algorithm=""maxima"")","-2 \, a b e g p {\left(\frac{f \log\left(g x + f\right)}{e g^{2}} - \frac{{\left(d f + e\right)} \log\left(d g x + d f + e\right)}{d e g^{2}}\right)} + 2 \, a b x \log\left(c {\left(d + \frac{e}{g x + f}\right)}^{p}\right) + a^{2} x + b^{2} {\left(\frac{d g x \log\left({\left(d g x + d f + e\right)}^{p}\right)^{2} + d g x \log\left({\left(g x + f\right)}^{p}\right)^{2} - {\left(d f p^{2} + e p^{2}\right)} \log\left(d g x + d f + e\right)^{2} + 2 \, {\left(d f p^{2} + e p^{2}\right)} \log\left(d g x + d f + e\right) \log\left(g x + f\right) - 2 \, {\left(d f p \log\left(g x + f\right) + d g x \log\left({\left(g x + f\right)}^{p}\right) - d g x \log\left(c\right) - {\left(d f p + e p\right)} \log\left(d g x + d f + e\right)\right)} \log\left({\left(d g x + d f + e\right)}^{p}\right) + 2 \, {\left(d f p \log\left(g x + f\right) - d g x \log\left(c\right) - {\left(d f p + e p\right)} \log\left(d g x + d f + e\right)\right)} \log\left({\left(g x + f\right)}^{p}\right)}{d g} - \int -\frac{d g^{2} x^{2} \log\left(c\right)^{2} + {\left(d f^{2} + e f\right)} \log\left(c\right)^{2} + {\left(2 \, e g p \log\left(c\right) + {\left(2 \, d f g + e g\right)} \log\left(c\right)^{2}\right)} x - 2 \, {\left(d f^{2} p^{2} + 2 \, e f p^{2} + {\left(d f g p^{2} + e g p^{2}\right)} x\right)} \log\left(g x + f\right)}{d g^{2} x^{2} + d f^{2} + e f + {\left(2 \, d f g + e g\right)} x}\,{d x}\right)}"," ",0,"-2*a*b*e*g*p*(f*log(g*x + f)/(e*g^2) - (d*f + e)*log(d*g*x + d*f + e)/(d*e*g^2)) + 2*a*b*x*log(c*(d + e/(g*x + f))^p) + a^2*x + b^2*((d*g*x*log((d*g*x + d*f + e)^p)^2 + d*g*x*log((g*x + f)^p)^2 - (d*f*p^2 + e*p^2)*log(d*g*x + d*f + e)^2 + 2*(d*f*p^2 + e*p^2)*log(d*g*x + d*f + e)*log(g*x + f) - 2*(d*f*p*log(g*x + f) + d*g*x*log((g*x + f)^p) - d*g*x*log(c) - (d*f*p + e*p)*log(d*g*x + d*f + e))*log((d*g*x + d*f + e)^p) + 2*(d*f*p*log(g*x + f) - d*g*x*log(c) - (d*f*p + e*p)*log(d*g*x + d*f + e))*log((g*x + f)^p))/(d*g) - integrate(-(d*g^2*x^2*log(c)^2 + (d*f^2 + e*f)*log(c)^2 + (2*e*g*p*log(c) + (2*d*f*g + e*g)*log(c)^2)*x - 2*(d*f^2*p^2 + 2*e*f*p^2 + (d*f*g*p^2 + e*g*p^2)*x)*log(g*x + f))/(d*g^2*x^2 + d*f^2 + e*f + (2*d*f*g + e*g)*x), x))","F",0
639,1,70,0,0.674139," ","integrate(a+b*log(c*(d+e/(g*x+f))^p),x, algorithm=""maxima"")","-b e g p {\left(\frac{f \log\left(g x + f\right)}{e g^{2}} - \frac{{\left(d f + e\right)} \log\left(d g x + d f + e\right)}{d e g^{2}}\right)} + b x \log\left(c {\left(d + \frac{e}{g x + f}\right)}^{p}\right) + a x"," ",0,"-b*e*g*p*(f*log(g*x + f)/(e*g^2) - (d*f + e)*log(d*g*x + d*f + e)/(d*e*g^2)) + b*x*log(c*(d + e/(g*x + f))^p) + a*x","A",0
640,0,0,0,0.000000," ","integrate(1/(a+b*log(c*(d+e/(g*x+f))^p)),x, algorithm=""maxima"")","\int \frac{1}{b \log\left(c {\left(d + \frac{e}{g x + f}\right)}^{p}\right) + a}\,{d x}"," ",0,"integrate(1/(b*log(c*(d + e/(g*x + f))^p) + a), x)","F",0
641,0,0,0,0.000000," ","integrate(1/(a+b*log(c*(d+e/(g*x+f))^p))^2,x, algorithm=""maxima"")","\frac{d g^{2} x^{2} + d f^{2} + e f + {\left(2 \, d f g + e g\right)} x}{b^{2} e g p \log\left({\left(d g x + d f + e\right)}^{p}\right) - b^{2} e g p \log\left({\left(g x + f\right)}^{p}\right) + b^{2} e g p \log\left(c\right) + a b e g p} - \int \frac{2 \, d g x + 2 \, d f + e}{b^{2} e p \log\left({\left(d g x + d f + e\right)}^{p}\right) - b^{2} e p \log\left({\left(g x + f\right)}^{p}\right) + b^{2} e p \log\left(c\right) + a b e p}\,{d x}"," ",0,"(d*g^2*x^2 + d*f^2 + e*f + (2*d*f*g + e*g)*x)/(b^2*e*g*p*log((d*g*x + d*f + e)^p) - b^2*e*g*p*log((g*x + f)^p) + b^2*e*g*p*log(c) + a*b*e*g*p) - integrate((2*d*g*x + 2*d*f + e)/(b^2*e*p*log((d*g*x + d*f + e)^p) - b^2*e*p*log((g*x + f)^p) + b^2*e*p*log(c) + a*b*e*p), x)","F",0
