1,1,188,0,0.784755," ","integrate(x^4*log(c*(b*x^2+a)^p),x, algorithm=""fricas"")","\left[\frac{15 \, b^{2} p x^{5} \log\left(b x^{2} + a\right) - 6 \, b^{2} p x^{5} + 15 \, b^{2} x^{5} \log\left(c\right) + 10 \, a b p x^{3} + 15 \, a^{2} p \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) - 30 \, a^{2} p x}{75 \, b^{2}}, \frac{15 \, b^{2} p x^{5} \log\left(b x^{2} + a\right) - 6 \, b^{2} p x^{5} + 15 \, b^{2} x^{5} \log\left(c\right) + 10 \, a b p x^{3} + 30 \, a^{2} p \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - 30 \, a^{2} p x}{75 \, b^{2}}\right]"," ",0,"[1/75*(15*b^2*p*x^5*log(b*x^2 + a) - 6*b^2*p*x^5 + 15*b^2*x^5*log(c) + 10*a*b*p*x^3 + 15*a^2*p*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) - 30*a^2*p*x)/b^2, 1/75*(15*b^2*p*x^5*log(b*x^2 + a) - 6*b^2*p*x^5 + 15*b^2*x^5*log(c) + 10*a*b*p*x^3 + 30*a^2*p*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - 30*a^2*p*x)/b^2]","A",0
2,1,57,0,0.782067," ","integrate(x^3*log(c*(b*x^2+a)^p),x, algorithm=""fricas"")","-\frac{b^{2} p x^{4} - 2 \, b^{2} x^{4} \log\left(c\right) - 2 \, a b p x^{2} - 2 \, {\left(b^{2} p x^{4} - a^{2} p\right)} \log\left(b x^{2} + a\right)}{8 \, b^{2}}"," ",0,"-1/8*(b^2*p*x^4 - 2*b^2*x^4*log(c) - 2*a*b*p*x^2 - 2*(b^2*p*x^4 - a^2*p)*log(b*x^2 + a))/b^2","A",0
3,1,152,0,0.992954," ","integrate(x^2*log(c*(b*x^2+a)^p),x, algorithm=""fricas"")","\left[\frac{3 \, b p x^{3} \log\left(b x^{2} + a\right) - 2 \, b p x^{3} + 3 \, b x^{3} \log\left(c\right) + 3 \, a p \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + 6 \, a p x}{9 \, b}, \frac{3 \, b p x^{3} \log\left(b x^{2} + a\right) - 2 \, b p x^{3} + 3 \, b x^{3} \log\left(c\right) - 6 \, a p \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) + 6 \, a p x}{9 \, b}\right]"," ",0,"[1/9*(3*b*p*x^3*log(b*x^2 + a) - 2*b*p*x^3 + 3*b*x^3*log(c) + 3*a*p*sqrt(-a/b)*log((b*x^2 - 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + 6*a*p*x)/b, 1/9*(3*b*p*x^3*log(b*x^2 + a) - 2*b*p*x^3 + 3*b*x^3*log(c) - 6*a*p*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) + 6*a*p*x)/b]","A",0
4,1,40,0,0.553880," ","integrate(x*log(c*(b*x^2+a)^p),x, algorithm=""fricas"")","-\frac{b p x^{2} - b x^{2} \log\left(c\right) - {\left(b p x^{2} + a p\right)} \log\left(b x^{2} + a\right)}{2 \, b}"," ",0,"-1/2*(b*p*x^2 - b*x^2*log(c) - (b*p*x^2 + a*p)*log(b*x^2 + a))/b","A",0
5,1,107,0,0.696292," ","integrate(log(c*(b*x^2+a)^p),x, algorithm=""fricas"")","\left[p x \log\left(b x^{2} + a\right) + p \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) - 2 \, p x + x \log\left(c\right), p x \log\left(b x^{2} + a\right) + 2 \, p \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - 2 \, p x + x \log\left(c\right)\right]"," ",0,"[p*x*log(b*x^2 + a) + p*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) - 2*p*x + x*log(c), p*x*log(b*x^2 + a) + 2*p*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - 2*p*x + x*log(c)]","A",0
6,0,0,0,0.876195," ","integrate(log(c*(b*x^2+a)^p)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)}{x}, x\right)"," ",0,"integral(log((b*x^2 + a)^p*c)/x, x)","F",0
7,1,105,0,1.002855," ","integrate(log(c*(b*x^2+a)^p)/x^2,x, algorithm=""fricas"")","\left[\frac{p x \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) - p \log\left(b x^{2} + a\right) - \log\left(c\right)}{x}, \frac{2 \, p x \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) - p \log\left(b x^{2} + a\right) - \log\left(c\right)}{x}\right]"," ",0,"[(p*x*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) - p*log(b*x^2 + a) - log(c))/x, (2*p*x*sqrt(b/a)*arctan(x*sqrt(b/a)) - p*log(b*x^2 + a) - log(c))/x]","A",0
8,1,43,0,0.879281," ","integrate(log(c*(b*x^2+a)^p)/x^3,x, algorithm=""fricas"")","\frac{2 \, b p x^{2} \log\left(x\right) - {\left(b p x^{2} + a p\right)} \log\left(b x^{2} + a\right) - a \log\left(c\right)}{2 \, a x^{2}}"," ",0,"1/2*(2*b*p*x^2*log(x) - (b*p*x^2 + a*p)*log(b*x^2 + a) - a*log(c))/(a*x^2)","A",0
9,1,135,0,1.025682," ","integrate(log(c*(b*x^2+a)^p)/x^4,x, algorithm=""fricas"")","\left[\frac{b p x^{3} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) - 2 \, b p x^{2} - a p \log\left(b x^{2} + a\right) - a \log\left(c\right)}{3 \, a x^{3}}, -\frac{2 \, b p x^{3} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + 2 \, b p x^{2} + a p \log\left(b x^{2} + a\right) + a \log\left(c\right)}{3 \, a x^{3}}\right]"," ",0,"[1/3*(b*p*x^3*sqrt(-b/a)*log((b*x^2 - 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) - 2*b*p*x^2 - a*p*log(b*x^2 + a) - a*log(c))/(a*x^3), -1/3*(2*b*p*x^3*sqrt(b/a)*arctan(x*sqrt(b/a)) + 2*b*p*x^2 + a*p*log(b*x^2 + a) + a*log(c))/(a*x^3)]","A",0
10,1,58,0,0.960737," ","integrate(log(c*(b*x^2+a)^p)/x^5,x, algorithm=""fricas"")","-\frac{2 \, b^{2} p x^{4} \log\left(x\right) + 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)}{4 \, a^{2} x^{4}}"," ",0,"-1/4*(2*b^2*p*x^4*log(x) + a*b*p*x^2 + a^2*log(c) - (b^2*p*x^4 - a^2*p)*log(b*x^2 + a))/(a^2*x^4)","A",0
11,1,170,0,1.024980," ","integrate(log(c*(b*x^2+a)^p)/x^6,x, algorithm=""fricas"")","\left[\frac{3 \, b^{2} p x^{5} \sqrt{-\frac{b}{a}} \log\left(\frac{b x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - a}{b x^{2} + a}\right) + 6 \, b^{2} p x^{4} - 2 \, a b p x^{2} - 3 \, a^{2} p \log\left(b x^{2} + a\right) - 3 \, a^{2} \log\left(c\right)}{15 \, a^{2} x^{5}}, \frac{6 \, b^{2} p x^{5} \sqrt{\frac{b}{a}} \arctan\left(x \sqrt{\frac{b}{a}}\right) + 6 \, b^{2} p x^{4} - 2 \, a b p x^{2} - 3 \, a^{2} p \log\left(b x^{2} + a\right) - 3 \, a^{2} \log\left(c\right)}{15 \, a^{2} x^{5}}\right]"," ",0,"[1/15*(3*b^2*p*x^5*sqrt(-b/a)*log((b*x^2 + 2*a*x*sqrt(-b/a) - a)/(b*x^2 + a)) + 6*b^2*p*x^4 - 2*a*b*p*x^2 - 3*a^2*p*log(b*x^2 + a) - 3*a^2*log(c))/(a^2*x^5), 1/15*(6*b^2*p*x^5*sqrt(b/a)*arctan(x*sqrt(b/a)) + 6*b^2*p*x^4 - 2*a*b*p*x^2 - 3*a^2*p*log(b*x^2 + a) - 3*a^2*log(c))/(a^2*x^5)]","A",0
12,1,71,0,0.922863," ","integrate(log(c*(b*x^2+a)^p)/x^7,x, algorithm=""fricas"")","\frac{4 \, b^{3} p x^{6} \log\left(x\right) + 2 \, a b^{2} p x^{4} - a^{2} b p x^{2} - 2 \, a^{3} \log\left(c\right) - 2 \, {\left(b^{3} p x^{6} + a^{3} p\right)} \log\left(b x^{2} + a\right)}{12 \, a^{3} x^{6}}"," ",0,"1/12*(4*b^3*p*x^6*log(x) + 2*a*b^2*p*x^4 - a^2*b*p*x^2 - 2*a^3*log(c) - 2*(b^3*p*x^6 + a^3*p)*log(b*x^2 + a))/(a^3*x^6)","A",0
13,1,57,0,0.731931," ","integrate(x^5*log(c*(b*x^3+a)^p),x, algorithm=""fricas"")","-\frac{b^{2} p x^{6} - 2 \, b^{2} x^{6} \log\left(c\right) - 2 \, a b p x^{3} - 2 \, {\left(b^{2} p x^{6} - a^{2} p\right)} \log\left(b x^{3} + a\right)}{12 \, b^{2}}"," ",0,"-1/12*(b^2*p*x^6 - 2*b^2*x^6*log(c) - 2*a*b*p*x^3 - 2*(b^2*p*x^6 - a^2*p)*log(b*x^3 + a))/b^2","A",0
14,1,161,0,0.777666," ","integrate(x^4*log(c*(b*x^3+a)^p),x, algorithm=""fricas"")","\frac{10 \, b p x^{5} \log\left(b x^{3} + a\right) - 6 \, b p x^{5} + 10 \, b x^{5} \log\left(c\right) + 15 \, a p x^{2} - 10 \, \sqrt{3} a p \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} - \sqrt{3} a}{3 \, a}\right) - 5 \, a p \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(a x^{2} - b x \left(\frac{a^{2}}{b^{2}}\right)^{\frac{2}{3}} + a \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}}\right) + 10 \, a p \left(\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(a x + b \left(\frac{a^{2}}{b^{2}}\right)^{\frac{2}{3}}\right)}{50 \, b}"," ",0,"1/50*(10*b*p*x^5*log(b*x^3 + a) - 6*b*p*x^5 + 10*b*x^5*log(c) + 15*a*p*x^2 - 10*sqrt(3)*a*p*(a^2/b^2)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x*(a^2/b^2)^(1/3) - sqrt(3)*a)/a) - 5*a*p*(a^2/b^2)^(1/3)*log(a*x^2 - b*x*(a^2/b^2)^(2/3) + a*(a^2/b^2)^(1/3)) + 10*a*p*(a^2/b^2)^(1/3)*log(a*x + b*(a^2/b^2)^(2/3)))/b","A",0
15,1,144,0,0.638434," ","integrate(x^3*log(c*(b*x^3+a)^p),x, algorithm=""fricas"")","\frac{4 \, b p x^{4} \log\left(b x^{3} + a\right) - 3 \, b p x^{4} + 4 \, b x^{4} \log\left(c\right) + 4 \, \sqrt{3} a p \left(-\frac{a}{b}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x \left(-\frac{a}{b}\right)^{\frac{2}{3}} - \sqrt{3} a}{3 \, a}\right) - 2 \, a p \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{a}{b}\right)^{\frac{1}{3}} + \left(-\frac{a}{b}\right)^{\frac{2}{3}}\right) + 4 \, a p \left(-\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x - \left(-\frac{a}{b}\right)^{\frac{1}{3}}\right) + 12 \, a p x}{16 \, b}"," ",0,"1/16*(4*b*p*x^4*log(b*x^3 + a) - 3*b*p*x^4 + 4*b*x^4*log(c) + 4*sqrt(3)*a*p*(-a/b)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x*(-a/b)^(2/3) - sqrt(3)*a)/a) - 2*a*p*(-a/b)^(1/3)*log(x^2 + x*(-a/b)^(1/3) + (-a/b)^(2/3)) + 4*a*p*(-a/b)^(1/3)*log(x - (-a/b)^(1/3)) + 12*a*p*x)/b","A",0
16,1,40,0,0.618239," ","integrate(x^2*log(c*(b*x^3+a)^p),x, algorithm=""fricas"")","-\frac{b p x^{3} - b x^{3} \log\left(c\right) - {\left(b p x^{3} + a p\right)} \log\left(b x^{3} + a\right)}{3 \, b}"," ",0,"-1/3*(b*p*x^3 - b*x^3*log(c) - (b*p*x^3 + a*p)*log(b*x^3 + a))/b","A",0
17,1,150,0,0.965563," ","integrate(x*log(c*(b*x^3+a)^p),x, algorithm=""fricas"")","\frac{1}{2} \, p x^{2} \log\left(b x^{3} + a\right) - \frac{3}{4} \, p x^{2} + \frac{1}{2} \, x^{2} \log\left(c\right) + \frac{1}{2} \, \sqrt{3} p \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} + \sqrt{3} a}{3 \, a}\right) - \frac{1}{4} \, p \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(a x^{2} - b x \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{2}{3}} - a \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}}\right) + \frac{1}{2} \, p \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{1}{3}} \log\left(a x + b \left(-\frac{a^{2}}{b^{2}}\right)^{\frac{2}{3}}\right)"," ",0,"1/2*p*x^2*log(b*x^3 + a) - 3/4*p*x^2 + 1/2*x^2*log(c) + 1/2*sqrt(3)*p*(-a^2/b^2)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x*(-a^2/b^2)^(1/3) + sqrt(3)*a)/a) - 1/4*p*(-a^2/b^2)^(1/3)*log(a*x^2 - b*x*(-a^2/b^2)^(2/3) - a*(-a^2/b^2)^(1/3)) + 1/2*p*(-a^2/b^2)^(1/3)*log(a*x + b*(-a^2/b^2)^(2/3))","A",0
18,1,110,0,0.720091," ","integrate(log(c*(b*x^3+a)^p),x, algorithm=""fricas"")","p x \log\left(b x^{3} + a\right) + \sqrt{3} p \left(\frac{a}{b}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x \left(\frac{a}{b}\right)^{\frac{2}{3}} - \sqrt{3} a}{3 \, a}\right) - \frac{1}{2} \, p \left(\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right) + p \left(\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right) - 3 \, p x + x \log\left(c\right)"," ",0,"p*x*log(b*x^3 + a) + sqrt(3)*p*(a/b)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x*(a/b)^(2/3) - sqrt(3)*a)/a) - 1/2*p*(a/b)^(1/3)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3)) + p*(a/b)^(1/3)*log(x + (a/b)^(1/3)) - 3*p*x + x*log(c)","A",0
19,0,0,0,1.029366," ","integrate(log(c*(b*x^3+a)^p)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{3} + a\right)}^{p} c\right)}{x}, x\right)"," ",0,"integral(log((b*x^3 + a)^p*c)/x, x)","F",0
20,1,126,0,1.127694," ","integrate(log(c*(b*x^3+a)^p)/x^2,x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} p x \left(-\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} x \left(-\frac{b}{a}\right)^{\frac{1}{3}} + \frac{1}{3} \, \sqrt{3}\right) - p x \left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x^{2} - a x \left(-\frac{b}{a}\right)^{\frac{2}{3}} - a \left(-\frac{b}{a}\right)^{\frac{1}{3}}\right) + 2 \, p x \left(-\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x + a \left(-\frac{b}{a}\right)^{\frac{2}{3}}\right) - 2 \, p \log\left(b x^{3} + a\right) - 2 \, \log\left(c\right)}{2 \, x}"," ",0,"1/2*(2*sqrt(3)*p*x*(-b/a)^(1/3)*arctan(2/3*sqrt(3)*x*(-b/a)^(1/3) + 1/3*sqrt(3)) - p*x*(-b/a)^(1/3)*log(b*x^2 - a*x*(-b/a)^(2/3) - a*(-b/a)^(1/3)) + 2*p*x*(-b/a)^(1/3)*log(b*x + a*(-b/a)^(2/3)) - 2*p*log(b*x^3 + a) - 2*log(c))/x","A",0
21,1,150,0,1.206236," ","integrate(log(c*(b*x^3+a)^p)/x^3,x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} p x^{2} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x \left(\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) - p x^{2} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b^{2} x^{2} - a b x \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} + a^{2} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}}\right) + 2 \, p x^{2} \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b x + a \left(\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) - 2 \, p \log\left(b x^{3} + a\right) - 2 \, \log\left(c\right)}{4 \, x^{2}}"," ",0,"1/4*(2*sqrt(3)*p*x^2*(b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x*(b^2/a^2)^(2/3) - sqrt(3)*b)/b) - p*x^2*(b^2/a^2)^(1/3)*log(b^2*x^2 - a*b*x*(b^2/a^2)^(1/3) + a^2*(b^2/a^2)^(2/3)) + 2*p*x^2*(b^2/a^2)^(1/3)*log(b*x + a*(b^2/a^2)^(1/3)) - 2*p*log(b*x^3 + a) - 2*log(c))/x^2","A",0
22,1,43,0,0.900012," ","integrate(log(c*(b*x^3+a)^p)/x^4,x, algorithm=""fricas"")","\frac{3 \, b p x^{3} \log\left(x\right) - {\left(b p x^{3} + a p\right)} \log\left(b x^{3} + a\right) - a \log\left(c\right)}{3 \, a x^{3}}"," ",0,"1/3*(3*b*p*x^3*log(x) - (b*p*x^3 + a*p)*log(b*x^3 + a) - a*log(c))/(a*x^3)","A",0
23,1,138,0,0.662941," ","integrate(log(c*(b*x^3+a)^p)/x^5,x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} b p x^{4} \left(\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(\frac{2}{3} \, \sqrt{3} x \left(\frac{b}{a}\right)^{\frac{1}{3}} - \frac{1}{3} \, \sqrt{3}\right) + b p x^{4} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x^{2} - a x \left(\frac{b}{a}\right)^{\frac{2}{3}} + a \left(\frac{b}{a}\right)^{\frac{1}{3}}\right) - 2 \, b p x^{4} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\left(b x + a \left(\frac{b}{a}\right)^{\frac{2}{3}}\right) + 6 \, b p x^{3} + 2 \, a p \log\left(b x^{3} + a\right) + 2 \, a \log\left(c\right)}{8 \, a x^{4}}"," ",0,"-1/8*(2*sqrt(3)*b*p*x^4*(b/a)^(1/3)*arctan(2/3*sqrt(3)*x*(b/a)^(1/3) - 1/3*sqrt(3)) + b*p*x^4*(b/a)^(1/3)*log(b*x^2 - a*x*(b/a)^(2/3) + a*(b/a)^(1/3)) - 2*b*p*x^4*(b/a)^(1/3)*log(b*x + a*(b/a)^(2/3)) + 6*b*p*x^3 + 2*a*p*log(b*x^3 + a) + 2*a*log(c))/(a*x^4)","A",0
24,1,172,0,0.969411," ","integrate(log(c*(b*x^3+a)^p)/x^6,x, algorithm=""fricas"")","\frac{2 \, \sqrt{3} b p x^{5} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} a x \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}} - \sqrt{3} b}{3 \, b}\right) - b p x^{5} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b^{2} x^{2} + a b x \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} + a^{2} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{2}{3}}\right) + 2 \, b p x^{5} \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}} \log\left(b x - a \left(-\frac{b^{2}}{a^{2}}\right)^{\frac{1}{3}}\right) - 3 \, b p x^{3} - 2 \, a p \log\left(b x^{3} + a\right) - 2 \, a \log\left(c\right)}{10 \, a x^{5}}"," ",0,"1/10*(2*sqrt(3)*b*p*x^5*(-b^2/a^2)^(1/3)*arctan(1/3*(2*sqrt(3)*a*x*(-b^2/a^2)^(2/3) - sqrt(3)*b)/b) - b*p*x^5*(-b^2/a^2)^(1/3)*log(b^2*x^2 + a*b*x*(-b^2/a^2)^(1/3) + a^2*(-b^2/a^2)^(2/3)) + 2*b*p*x^5*(-b^2/a^2)^(1/3)*log(b*x - a*(-b^2/a^2)^(1/3)) - 3*b*p*x^3 - 2*a*p*log(b*x^3 + a) - 2*a*log(c))/(a*x^5)","A",0
25,1,58,0,0.738092," ","integrate(log(c*(b*x^3+a)^p)/x^7,x, algorithm=""fricas"")","-\frac{3 \, b^{2} p x^{6} \log\left(x\right) + a b p x^{3} + a^{2} \log\left(c\right) - {\left(b^{2} p x^{6} - a^{2} p\right)} \log\left(b x^{3} + a\right)}{6 \, a^{2} x^{6}}"," ",0,"-1/6*(3*b^2*p*x^6*log(x) + a*b*p*x^3 + a^2*log(c) - (b^2*p*x^6 - a^2*p)*log(b*x^3 + a))/(a^2*x^6)","A",0
26,1,89,0,0.785518," ","integrate(x^4*log(c*(a+b/x)^p),x, algorithm=""fricas"")","\frac{12 \, a^{5} p x^{5} \log\left(\frac{a x + b}{x}\right) + 12 \, a^{5} x^{5} \log\left(c\right) + 3 \, a^{4} b p x^{4} - 4 \, a^{3} b^{2} p x^{3} + 6 \, a^{2} b^{3} p x^{2} - 12 \, a b^{4} p x + 12 \, b^{5} p \log\left(a x + b\right)}{60 \, a^{5}}"," ",0,"1/60*(12*a^5*p*x^5*log((a*x + b)/x) + 12*a^5*x^5*log(c) + 3*a^4*b*p*x^4 - 4*a^3*b^2*p*x^3 + 6*a^2*b^3*p*x^2 - 12*a*b^4*p*x + 12*b^5*p*log(a*x + b))/a^5","A",0
27,1,77,0,0.918626," ","integrate(x^3*log(c*(a+b/x)^p),x, algorithm=""fricas"")","\frac{6 \, a^{4} p x^{4} \log\left(\frac{a x + b}{x}\right) + 6 \, a^{4} x^{4} \log\left(c\right) + 2 \, a^{3} b p x^{3} - 3 \, a^{2} b^{2} p x^{2} + 6 \, a b^{3} p x - 6 \, b^{4} p \log\left(a x + b\right)}{24 \, a^{4}}"," ",0,"1/24*(6*a^4*p*x^4*log((a*x + b)/x) + 6*a^4*x^4*log(c) + 2*a^3*b*p*x^3 - 3*a^2*b^2*p*x^2 + 6*a*b^3*p*x - 6*b^4*p*log(a*x + b))/a^4","A",0
28,1,64,0,0.980356," ","integrate(x^2*log(c*(a+b/x)^p),x, algorithm=""fricas"")","\frac{2 \, a^{3} p x^{3} \log\left(\frac{a x + b}{x}\right) + 2 \, a^{3} x^{3} \log\left(c\right) + a^{2} b p x^{2} - 2 \, a b^{2} p x + 2 \, b^{3} p \log\left(a x + b\right)}{6 \, a^{3}}"," ",0,"1/6*(2*a^3*p*x^3*log((a*x + b)/x) + 2*a^3*x^3*log(c) + a^2*b*p*x^2 - 2*a*b^2*p*x + 2*b^3*p*log(a*x + b))/a^3","A",0
29,1,50,0,0.924983," ","integrate(x*log(c*(a+b/x)^p),x, algorithm=""fricas"")","\frac{a^{2} p x^{2} \log\left(\frac{a x + b}{x}\right) + a^{2} x^{2} \log\left(c\right) + a b p x - b^{2} p \log\left(a x + b\right)}{2 \, a^{2}}"," ",0,"1/2*(a^2*p*x^2*log((a*x + b)/x) + a^2*x^2*log(c) + a*b*p*x - b^2*p*log(a*x + b))/a^2","A",0
30,1,33,0,0.867145," ","integrate(log(c*(a+b/x)^p),x, algorithm=""fricas"")","\frac{a p x \log\left(\frac{a x + b}{x}\right) + b p \log\left(a x + b\right) + a x \log\left(c\right)}{a}"," ",0,"(a*p*x*log((a*x + b)/x) + b*p*log(a*x + b) + a*x*log(c))/a","A",0
31,0,0,0,0.749914," ","integrate(log(c*(a+b/x)^p)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(c \left(\frac{a x + b}{x}\right)^{p}\right)}{x}, x\right)"," ",0,"integral(log(c*((a*x + b)/x)^p)/x, x)","F",0
32,1,36,0,0.862690," ","integrate(log(c*(a+b/x)^p)/x^2,x, algorithm=""fricas"")","\frac{b p - b \log\left(c\right) - {\left(a p x + b p\right)} \log\left(\frac{a x + b}{x}\right)}{b x}"," ",0,"(b*p - b*log(c) - (a*p*x + b*p)*log((a*x + b)/x))/(b*x)","A",0
33,1,55,0,0.532239," ","integrate(log(c*(a+b/x)^p)/x^3,x, algorithm=""fricas"")","-\frac{2 \, a b p x - b^{2} p + 2 \, b^{2} \log\left(c\right) - 2 \, {\left(a^{2} p x^{2} - b^{2} p\right)} \log\left(\frac{a x + b}{x}\right)}{4 \, b^{2} x^{2}}"," ",0,"-1/4*(2*a*b*p*x - b^2*p + 2*b^2*log(c) - 2*(a^2*p*x^2 - b^2*p)*log((a*x + b)/x))/(b^2*x^2)","A",0
34,1,66,0,0.793405," ","integrate(log(c*(a+b/x)^p)/x^4,x, algorithm=""fricas"")","\frac{6 \, a^{2} b p x^{2} - 3 \, a b^{2} p x + 2 \, b^{3} p - 6 \, b^{3} \log\left(c\right) - 6 \, {\left(a^{3} p x^{3} + b^{3} p\right)} \log\left(\frac{a x + b}{x}\right)}{18 \, b^{3} x^{3}}"," ",0,"1/18*(6*a^2*b*p*x^2 - 3*a*b^2*p*x + 2*b^3*p - 6*b^3*log(c) - 6*(a^3*p*x^3 + b^3*p)*log((a*x + b)/x))/(b^3*x^3)","A",0
35,1,79,0,0.718837," ","integrate(log(c*(a+b/x)^p)/x^5,x, algorithm=""fricas"")","-\frac{12 \, a^{3} b p x^{3} - 6 \, a^{2} b^{2} p x^{2} + 4 \, a b^{3} p x - 3 \, b^{4} p + 12 \, b^{4} \log\left(c\right) - 12 \, {\left(a^{4} p x^{4} - b^{4} p\right)} \log\left(\frac{a x + b}{x}\right)}{48 \, b^{4} x^{4}}"," ",0,"-1/48*(12*a^3*b*p*x^3 - 6*a^2*b^2*p*x^2 + 4*a*b^3*p*x - 3*b^4*p + 12*b^4*log(c) - 12*(a^4*p*x^4 - b^4*p)*log((a*x + b)/x))/(b^4*x^4)","A",0
36,1,178,0,0.689715," ","integrate(x^4*log(c*(a+b/x^2)^p),x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} p x^{5} \log\left(\frac{a x^{2} + b}{x^{2}}\right) + 3 \, a^{2} x^{5} \log\left(c\right) + 2 \, a b p x^{3} + 3 \, b^{2} p \sqrt{-\frac{b}{a}} \log\left(\frac{a x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - b}{a x^{2} + b}\right) - 6 \, b^{2} p x}{15 \, a^{2}}, \frac{3 \, a^{2} p x^{5} \log\left(\frac{a x^{2} + b}{x^{2}}\right) + 3 \, a^{2} x^{5} \log\left(c\right) + 2 \, a b p x^{3} + 6 \, b^{2} p \sqrt{\frac{b}{a}} \arctan\left(\frac{a x \sqrt{\frac{b}{a}}}{b}\right) - 6 \, b^{2} p x}{15 \, a^{2}}\right]"," ",0,"[1/15*(3*a^2*p*x^5*log((a*x^2 + b)/x^2) + 3*a^2*x^5*log(c) + 2*a*b*p*x^3 + 3*b^2*p*sqrt(-b/a)*log((a*x^2 + 2*a*x*sqrt(-b/a) - b)/(a*x^2 + b)) - 6*b^2*p*x)/a^2, 1/15*(3*a^2*p*x^5*log((a*x^2 + b)/x^2) + 3*a^2*x^5*log(c) + 2*a*b*p*x^3 + 6*b^2*p*sqrt(b/a)*arctan(a*x*sqrt(b/a)/b) - 6*b^2*p*x)/a^2]","A",0
37,1,56,0,0.671776," ","integrate(x^3*log(c*(a+b/x^2)^p),x, algorithm=""fricas"")","\frac{a^{2} p x^{4} \log\left(\frac{a x^{2} + b}{x^{2}}\right) + a^{2} x^{4} \log\left(c\right) + a b p x^{2} - b^{2} p \log\left(a x^{2} + b\right)}{4 \, a^{2}}"," ",0,"1/4*(a^2*p*x^4*log((a*x^2 + b)/x^2) + a^2*x^4*log(c) + a*b*p*x^2 - b^2*p*log(a*x^2 + b))/a^2","A",0
38,1,141,0,0.796430," ","integrate(x^2*log(c*(a+b/x^2)^p),x, algorithm=""fricas"")","\left[\frac{a p x^{3} \log\left(\frac{a x^{2} + b}{x^{2}}\right) + a x^{3} \log\left(c\right) + b p \sqrt{-\frac{b}{a}} \log\left(\frac{a x^{2} - 2 \, a x \sqrt{-\frac{b}{a}} - b}{a x^{2} + b}\right) + 2 \, b p x}{3 \, a}, \frac{a p x^{3} \log\left(\frac{a x^{2} + b}{x^{2}}\right) + a x^{3} \log\left(c\right) - 2 \, b p \sqrt{\frac{b}{a}} \arctan\left(\frac{a x \sqrt{\frac{b}{a}}}{b}\right) + 2 \, b p x}{3 \, a}\right]"," ",0,"[1/3*(a*p*x^3*log((a*x^2 + b)/x^2) + a*x^3*log(c) + b*p*sqrt(-b/a)*log((a*x^2 - 2*a*x*sqrt(-b/a) - b)/(a*x^2 + b)) + 2*b*p*x)/a, 1/3*(a*p*x^3*log((a*x^2 + b)/x^2) + a*x^3*log(c) - 2*b*p*sqrt(b/a)*arctan(a*x*sqrt(b/a)/b) + 2*b*p*x)/a]","A",0
39,1,42,0,0.535612," ","integrate(x*log(c*(a+b/x^2)^p),x, algorithm=""fricas"")","\frac{a p x^{2} \log\left(\frac{a x^{2} + b}{x^{2}}\right) + a x^{2} \log\left(c\right) + b p \log\left(a x^{2} + b\right)}{2 \, a}"," ",0,"1/2*(a*p*x^2*log((a*x^2 + b)/x^2) + a*x^2*log(c) + b*p*log(a*x^2 + b))/a","A",0
40,1,107,0,0.493695," ","integrate(log(c*(a+b/x^2)^p),x, algorithm=""fricas"")","\left[p x \log\left(\frac{a x^{2} + b}{x^{2}}\right) + p \sqrt{-\frac{b}{a}} \log\left(\frac{a x^{2} + 2 \, a x \sqrt{-\frac{b}{a}} - b}{a x^{2} + b}\right) + x \log\left(c\right), p x \log\left(\frac{a x^{2} + b}{x^{2}}\right) + 2 \, p \sqrt{\frac{b}{a}} \arctan\left(\frac{a x \sqrt{\frac{b}{a}}}{b}\right) + x \log\left(c\right)\right]"," ",0,"[p*x*log((a*x^2 + b)/x^2) + p*sqrt(-b/a)*log((a*x^2 + 2*a*x*sqrt(-b/a) - b)/(a*x^2 + b)) + x*log(c), p*x*log((a*x^2 + b)/x^2) + 2*p*sqrt(b/a)*arctan(a*x*sqrt(b/a)/b) + x*log(c)]","A",0
41,0,0,0,0.603010," ","integrate(log(c*(a+b/x^2)^p)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(c \left(\frac{a x^{2} + b}{x^{2}}\right)^{p}\right)}{x}, x\right)"," ",0,"integral(log(c*((a*x^2 + b)/x^2)^p)/x, x)","F",0
42,1,119,0,0.643529," ","integrate(log(c*(a+b/x^2)^p)/x^2,x, algorithm=""fricas"")","\left[\frac{p x \sqrt{-\frac{a}{b}} \log\left(\frac{a x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - b}{a x^{2} + b}\right) - p \log\left(\frac{a x^{2} + b}{x^{2}}\right) + 2 \, p - \log\left(c\right)}{x}, \frac{2 \, p x \sqrt{\frac{a}{b}} \arctan\left(x \sqrt{\frac{a}{b}}\right) - p \log\left(\frac{a x^{2} + b}{x^{2}}\right) + 2 \, p - \log\left(c\right)}{x}\right]"," ",0,"[(p*x*sqrt(-a/b)*log((a*x^2 + 2*b*x*sqrt(-a/b) - b)/(a*x^2 + b)) - p*log((a*x^2 + b)/x^2) + 2*p - log(c))/x, (2*p*x*sqrt(a/b)*arctan(x*sqrt(a/b)) - p*log((a*x^2 + b)/x^2) + 2*p - log(c))/x]","A",0
43,1,41,0,0.627268," ","integrate(log(c*(a+b/x^2)^p)/x^3,x, algorithm=""fricas"")","\frac{b p - b \log\left(c\right) - {\left(a p x^{2} + b p\right)} \log\left(\frac{a x^{2} + b}{x^{2}}\right)}{2 \, b x^{2}}"," ",0,"1/2*(b*p - b*log(c) - (a*p*x^2 + b*p)*log((a*x^2 + b)/x^2))/(b*x^2)","A",0
44,1,154,0,0.877613," ","integrate(log(c*(a+b/x^2)^p)/x^4,x, algorithm=""fricas"")","\left[\frac{3 \, a p x^{3} \sqrt{-\frac{a}{b}} \log\left(\frac{a x^{2} - 2 \, b x \sqrt{-\frac{a}{b}} - b}{a x^{2} + b}\right) - 6 \, a p x^{2} - 3 \, b p \log\left(\frac{a x^{2} + b}{x^{2}}\right) + 2 \, b p - 3 \, b \log\left(c\right)}{9 \, b x^{3}}, -\frac{6 \, a p x^{3} \sqrt{\frac{a}{b}} \arctan\left(x \sqrt{\frac{a}{b}}\right) + 6 \, a p x^{2} + 3 \, b p \log\left(\frac{a x^{2} + b}{x^{2}}\right) - 2 \, b p + 3 \, b \log\left(c\right)}{9 \, b x^{3}}\right]"," ",0,"[1/9*(3*a*p*x^3*sqrt(-a/b)*log((a*x^2 - 2*b*x*sqrt(-a/b) - b)/(a*x^2 + b)) - 6*a*p*x^2 - 3*b*p*log((a*x^2 + b)/x^2) + 2*b*p - 3*b*log(c))/(b*x^3), -1/9*(6*a*p*x^3*sqrt(a/b)*arctan(x*sqrt(a/b)) + 6*a*p*x^2 + 3*b*p*log((a*x^2 + b)/x^2) - 2*b*p + 3*b*log(c))/(b*x^3)]","A",0
45,1,11,0,0.750663," ","integrate(log(1+b/x)/x,x, algorithm=""fricas"")","{\rm Li}_2\left(-\frac{b + x}{x} + 1\right)"," ",0,"dilog(-(b + x)/x + 1)","A",0
46,1,129,0,0.470541," ","integrate(x^3*log(c*(a+b*x^(1/2))^p),x, algorithm=""fricas"")","-\frac{105 \, b^{8} p x^{4} - 840 \, b^{8} x^{4} \log\left(c\right) + 140 \, a^{2} b^{6} p x^{3} + 210 \, a^{4} b^{4} p x^{2} + 420 \, a^{6} b^{2} p x - 840 \, {\left(b^{8} p x^{4} - a^{8} p\right)} \log\left(b \sqrt{x} + a\right) - 8 \, {\left(15 \, a b^{7} p x^{3} + 21 \, a^{3} b^{5} p x^{2} + 35 \, a^{5} b^{3} p x + 105 \, a^{7} b p\right)} \sqrt{x}}{3360 \, b^{8}}"," ",0,"-1/3360*(105*b^8*p*x^4 - 840*b^8*x^4*log(c) + 140*a^2*b^6*p*x^3 + 210*a^4*b^4*p*x^2 + 420*a^6*b^2*p*x - 840*(b^8*p*x^4 - a^8*p)*log(b*sqrt(x) + a) - 8*(15*a*b^7*p*x^3 + 21*a^3*b^5*p*x^2 + 35*a^5*b^3*p*x + 105*a^7*b*p)*sqrt(x))/b^8","A",0
47,1,105,0,0.672099," ","integrate(x^2*log(c*(a+b*x^(1/2))^p),x, algorithm=""fricas"")","-\frac{10 \, b^{6} p x^{3} - 60 \, b^{6} x^{3} \log\left(c\right) + 15 \, a^{2} b^{4} p x^{2} + 30 \, a^{4} b^{2} p x - 60 \, {\left(b^{6} p x^{3} - a^{6} p\right)} \log\left(b \sqrt{x} + a\right) - 4 \, {\left(3 \, a b^{5} p x^{2} + 5 \, a^{3} b^{3} p x + 15 \, a^{5} b p\right)} \sqrt{x}}{180 \, b^{6}}"," ",0,"-1/180*(10*b^6*p*x^3 - 60*b^6*x^3*log(c) + 15*a^2*b^4*p*x^2 + 30*a^4*b^2*p*x - 60*(b^6*p*x^3 - a^6*p)*log(b*sqrt(x) + a) - 4*(3*a*b^5*p*x^2 + 5*a^3*b^3*p*x + 15*a^5*b*p)*sqrt(x))/b^6","A",0
48,1,80,0,0.426449," ","integrate(x*log(c*(a+b*x^(1/2))^p),x, algorithm=""fricas"")","-\frac{3 \, b^{4} p x^{2} - 12 \, b^{4} x^{2} \log\left(c\right) + 6 \, a^{2} b^{2} p x - 12 \, {\left(b^{4} p x^{2} - a^{4} p\right)} \log\left(b \sqrt{x} + a\right) - 4 \, {\left(a b^{3} p x + 3 \, a^{3} b p\right)} \sqrt{x}}{24 \, b^{4}}"," ",0,"-1/24*(3*b^4*p*x^2 - 12*b^4*x^2*log(c) + 6*a^2*b^2*p*x - 12*(b^4*p*x^2 - a^4*p)*log(b*sqrt(x) + a) - 4*(a*b^3*p*x + 3*a^3*b*p)*sqrt(x))/b^4","A",0
49,1,51,0,0.707409," ","integrate(log(c*(a+b*x^(1/2))^p),x, algorithm=""fricas"")","-\frac{b^{2} p x - 2 \, b^{2} x \log\left(c\right) - 2 \, a b p \sqrt{x} - 2 \, {\left(b^{2} p x - a^{2} p\right)} \log\left(b \sqrt{x} + a\right)}{2 \, b^{2}}"," ",0,"-1/2*(b^2*p*x - 2*b^2*x*log(c) - 2*a*b*p*sqrt(x) - 2*(b^2*p*x - a^2*p)*log(b*sqrt(x) + a))/b^2","A",0
50,0,0,0,0.666297," ","integrate(log(c*(a+b*x^(1/2))^p)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b \sqrt{x} + a\right)}^{p} c\right)}{x}, x\right)"," ",0,"integral(log((b*sqrt(x) + a)^p*c)/x, x)","F",0
51,1,55,0,0.599059," ","integrate(log(c*(a+b*x^(1/2))^p)/x^2,x, algorithm=""fricas"")","-\frac{b^{2} p x \log\left(\sqrt{x}\right) + a b p \sqrt{x} + a^{2} \log\left(c\right) - {\left(b^{2} p x - a^{2} p\right)} \log\left(b \sqrt{x} + a\right)}{a^{2} x}"," ",0,"-(b^2*p*x*log(sqrt(x)) + a*b*p*sqrt(x) + a^2*log(c) - (b^2*p*x - a^2*p)*log(b*sqrt(x) + a))/(a^2*x)","A",0
52,1,84,0,0.704097," ","integrate(log(c*(a+b*x^(1/2))^p)/x^3,x, algorithm=""fricas"")","-\frac{6 \, b^{4} p x^{2} \log\left(\sqrt{x}\right) - 3 \, a^{2} b^{2} p x + 6 \, a^{4} \log\left(c\right) - 6 \, {\left(b^{4} p x^{2} - a^{4} p\right)} \log\left(b \sqrt{x} + a\right) + 2 \, {\left(3 \, a b^{3} p x + a^{3} b p\right)} \sqrt{x}}{12 \, a^{4} x^{2}}"," ",0,"-1/12*(6*b^4*p*x^2*log(sqrt(x)) - 3*a^2*b^2*p*x + 6*a^4*log(c) - 6*(b^4*p*x^2 - a^4*p)*log(b*sqrt(x) + a) + 2*(3*a*b^3*p*x + a^3*b*p)*sqrt(x))/(a^4*x^2)","A",0
53,1,109,0,0.931863," ","integrate(log(c*(a+b*x^(1/2))^p)/x^4,x, algorithm=""fricas"")","-\frac{60 \, b^{6} p x^{3} \log\left(\sqrt{x}\right) - 30 \, a^{2} b^{4} p x^{2} - 15 \, a^{4} b^{2} p x + 60 \, a^{6} \log\left(c\right) - 60 \, {\left(b^{6} p x^{3} - a^{6} p\right)} \log\left(b \sqrt{x} + a\right) + 4 \, {\left(15 \, a b^{5} p x^{2} + 5 \, a^{3} b^{3} p x + 3 \, a^{5} b p\right)} \sqrt{x}}{180 \, a^{6} x^{3}}"," ",0,"-1/180*(60*b^6*p*x^3*log(sqrt(x)) - 30*a^2*b^4*p*x^2 - 15*a^4*b^2*p*x + 60*a^6*log(c) - 60*(b^6*p*x^3 - a^6*p)*log(b*sqrt(x) + a) + 4*(15*a*b^5*p*x^2 + 5*a^3*b^3*p*x + 3*a^5*b*p)*sqrt(x))/(a^6*x^3)","A",0
54,1,28,0,0.743447," ","integrate(log(a+b*x^(1/2))/x^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(b \sqrt{x} + a\right)} \log\left(b \sqrt{x} + a\right) - b \sqrt{x}\right)}}{b}"," ",0,"2*((b*sqrt(x) + a)*log(b*sqrt(x) + a) - b*sqrt(x))/b","A",0
55,0,0,0,0.779096," ","integrate((f*x)^m*log(c*(e*x^3+d)^p),x, algorithm=""fricas"")","{\rm integral}\left(\left(f x\right)^{m} \log\left({\left(e x^{3} + d\right)}^{p} c\right), x\right)"," ",0,"integral((f*x)^m*log((e*x^3 + d)^p*c), x)","F",0
56,0,0,0,0.705453," ","integrate((f*x)^m*log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","{\rm integral}\left(\left(f x\right)^{m} \log\left({\left(e x^{2} + d\right)}^{p} c\right), x\right)"," ",0,"integral((f*x)^m*log((e*x^2 + d)^p*c), x)","F",0
57,0,0,0,0.744820," ","integrate((f*x)^m*log(c*(e*x+d)^p),x, algorithm=""fricas"")","{\rm integral}\left(\left(f x\right)^{m} \log\left({\left(e x + d\right)}^{p} c\right), x\right)"," ",0,"integral((f*x)^m*log((e*x + d)^p*c), x)","F",0
58,0,0,0,0.702878," ","integrate((f*x)^m*log(c*(d+e/x)^p),x, algorithm=""fricas"")","{\rm integral}\left(\left(f x\right)^{m} \log\left(c \left(\frac{d x + e}{x}\right)^{p}\right), x\right)"," ",0,"integral((f*x)^m*log(c*((d*x + e)/x)^p), x)","F",0
59,0,0,0,0.637987," ","integrate((f*x)^m*log(c*(d+e/x^2)^p),x, algorithm=""fricas"")","{\rm integral}\left(\left(f x\right)^{m} \log\left(c \left(\frac{d x^{2} + e}{x^{2}}\right)^{p}\right), x\right)"," ",0,"integral((f*x)^m*log(c*((d*x^2 + e)/x^2)^p), x)","F",0
60,0,0,0,0.692111," ","integrate((f*x)^m*log(c*(d+e/x^3)^p),x, algorithm=""fricas"")","{\rm integral}\left(\left(f x\right)^{m} \log\left(c \left(\frac{d x^{3} + e}{x^{3}}\right)^{p}\right), x\right)"," ",0,"integral((f*x)^m*log(c*((d*x^3 + e)/x^3)^p), x)","F",0
61,0,0,0,0.768223," ","integrate((f*x)^m*log(c*(d+e*x^(1/2))^p),x, algorithm=""fricas"")","{\rm integral}\left(\left(f x\right)^{m} \log\left({\left(e \sqrt{x} + d\right)}^{p} c\right), x\right)"," ",0,"integral((f*x)^m*log((e*sqrt(x) + d)^p*c), x)","F",0
62,0,0,0,0.782166," ","integrate((f*x)^m*log(c*(d+e/x^(1/2))^p),x, algorithm=""fricas"")","{\rm integral}\left(\left(f x\right)^{m} \log\left(c \left(\frac{d x + e \sqrt{x}}{x}\right)^{p}\right), x\right)"," ",0,"integral((f*x)^m*log(c*((d*x + e*sqrt(x))/x)^p), x)","F",0
63,0,0,0,0.679608," ","integrate((f*x)^m*log(c*(d+e*x^n)^p),x, algorithm=""fricas"")","{\rm integral}\left(\left(f x\right)^{m} \log\left({\left(e x^{n} + d\right)}^{p} c\right), x\right)"," ",0,"integral((f*x)^m*log((e*x^n + d)^p*c), x)","F",0
64,1,112,0,0.764560," ","integrate((f*x)^(-1+3*n)*log(c*(d+e*x^n)^p),x, algorithm=""fricas"")","\frac{3 \, d e^{2} f^{3 \, n - 1} p x^{2 \, n} - 6 \, d^{2} e f^{3 \, n - 1} p x^{n} - 2 \, {\left(e^{3} p - 3 \, e^{3} \log\left(c\right)\right)} f^{3 \, n - 1} x^{3 \, n} + 6 \, {\left(e^{3} f^{3 \, n - 1} p x^{3 \, n} + d^{3} f^{3 \, n - 1} p\right)} \log\left(e x^{n} + d\right)}{18 \, e^{3} n}"," ",0,"1/18*(3*d*e^2*f^(3*n - 1)*p*x^(2*n) - 6*d^2*e*f^(3*n - 1)*p*x^n - 2*(e^3*p - 3*e^3*log(c))*f^(3*n - 1)*x^(3*n) + 6*(e^3*f^(3*n - 1)*p*x^(3*n) + d^3*f^(3*n - 1)*p)*log(e*x^n + d))/(e^3*n)","A",0
65,1,92,0,0.681493," ","integrate((f*x)^(-1+2*n)*log(c*(d+e*x^n)^p),x, algorithm=""fricas"")","\frac{2 \, d e f^{2 \, n - 1} p x^{n} - {\left(e^{2} p - 2 \, e^{2} \log\left(c\right)\right)} f^{2 \, n - 1} x^{2 \, n} + 2 \, {\left(e^{2} f^{2 \, n - 1} p x^{2 \, n} - d^{2} f^{2 \, n - 1} p\right)} \log\left(e x^{n} + d\right)}{4 \, e^{2} n}"," ",0,"1/4*(2*d*e*f^(2*n - 1)*p*x^n - (e^2*p - 2*e^2*log(c))*f^(2*n - 1)*x^(2*n) + 2*(e^2*f^(2*n - 1)*p*x^(2*n) - d^2*f^(2*n - 1)*p)*log(e*x^n + d))/(e^2*n)","A",0
66,1,57,0,0.663722," ","integrate((f*x)^(-1+n)*log(c*(d+e*x^n)^p),x, algorithm=""fricas"")","-\frac{{\left(e p - e \log\left(c\right)\right)} f^{n - 1} x^{n} - {\left(e f^{n - 1} p x^{n} + d f^{n - 1} p\right)} \log\left(e x^{n} + d\right)}{e n}"," ",0,"-((e*p - e*log(c))*f^(n - 1)*x^n - (e*f^(n - 1)*p*x^n + d*f^(n - 1)*p)*log(e*x^n + d))/(e*n)","A",0
67,1,63,0,0.793174," ","integrate(log(c*(d+e*x^n)^p)/f/x,x, algorithm=""fricas"")","\frac{n p \log\left(e x^{n} + d\right) \log\left(x\right) - n p \log\left(x\right) \log\left(\frac{e x^{n} + d}{d}\right) + n \log\left(c\right) \log\left(x\right) - p {\rm Li}_2\left(-\frac{e x^{n} + d}{d} + 1\right)}{f n}"," ",0,"(n*p*log(e*x^n + d)*log(x) - n*p*log(x)*log((e*x^n + d)/d) + n*log(c)*log(x) - p*dilog(-(e*x^n + d)/d + 1))/(f*n)","A",0
68,1,75,0,0.657472," ","integrate((f*x)^(-1-n)*log(c*(d+e*x^n)^p),x, algorithm=""fricas"")","\frac{e f^{-n - 1} n p x^{n} \log\left(x\right) - d f^{-n - 1} \log\left(c\right) - {\left(e f^{-n - 1} p x^{n} + d f^{-n - 1} p\right)} \log\left(e x^{n} + d\right)}{d n x^{n}}"," ",0,"(e*f^(-n - 1)*n*p*x^n*log(x) - d*f^(-n - 1)*log(c) - (e*f^(-n - 1)*p*x^n + d*f^(-n - 1)*p)*log(e*x^n + d))/(d*n*x^n)","A",0
69,1,104,0,0.553441," ","integrate((f*x)^(-1-2*n)*log(c*(d+e*x^n)^p),x, algorithm=""fricas"")","-\frac{e^{2} f^{-2 \, n - 1} n p x^{2 \, n} \log\left(x\right) + d e f^{-2 \, n - 1} p x^{n} + d^{2} f^{-2 \, n - 1} \log\left(c\right) - {\left(e^{2} f^{-2 \, n - 1} p x^{2 \, n} - d^{2} f^{-2 \, n - 1} p\right)} \log\left(e x^{n} + d\right)}{2 \, d^{2} n x^{2 \, n}}"," ",0,"-1/2*(e^2*f^(-2*n - 1)*n*p*x^(2*n)*log(x) + d*e*f^(-2*n - 1)*p*x^n + d^2*f^(-2*n - 1)*log(c) - (e^2*f^(-2*n - 1)*p*x^(2*n) - d^2*f^(-2*n - 1)*p)*log(e*x^n + d))/(d^2*n*x^(2*n))","A",0
70,0,0,0,0.609957," ","integrate(x^2*log(c*(d+e*x^n)^p),x, algorithm=""fricas"")","{\rm integral}\left(x^{2} \log\left({\left(e x^{n} + d\right)}^{p} c\right), x\right)"," ",0,"integral(x^2*log((e*x^n + d)^p*c), x)","F",0
71,0,0,0,0.679080," ","integrate(x*log(c*(d+e*x^n)^p),x, algorithm=""fricas"")","{\rm integral}\left(x \log\left({\left(e x^{n} + d\right)}^{p} c\right), x\right)"," ",0,"integral(x*log((e*x^n + d)^p*c), x)","F",0
72,0,0,0,0.628599," ","integrate(log(c*(d+e*x^n)^p),x, algorithm=""fricas"")","{\rm integral}\left(\log\left({\left(e x^{n} + d\right)}^{p} c\right), x\right)"," ",0,"integral(log((e*x^n + d)^p*c), x)","F",0
73,1,60,0,0.622914," ","integrate(log(c*(d+e*x^n)^p)/x,x, algorithm=""fricas"")","\frac{n p \log\left(e x^{n} + d\right) \log\left(x\right) - n p \log\left(x\right) \log\left(\frac{e x^{n} + d}{d}\right) + n \log\left(c\right) \log\left(x\right) - p {\rm Li}_2\left(-\frac{e x^{n} + d}{d} + 1\right)}{n}"," ",0,"(n*p*log(e*x^n + d)*log(x) - n*p*log(x)*log((e*x^n + d)/d) + n*log(c)*log(x) - p*dilog(-(e*x^n + d)/d + 1))/n","A",0
74,0,0,0,0.919591," ","integrate(log(c*(d+e*x^n)^p)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{n} + d\right)}^{p} c\right)}{x^{2}}, x\right)"," ",0,"integral(log((e*x^n + d)^p*c)/x^2, x)","F",0
75,0,0,0,0.589211," ","integrate(log(c*(d+e*x^n)^p)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{n} + d\right)}^{p} c\right)}{x^{3}}, x\right)"," ",0,"integral(log((e*x^n + d)^p*c)/x^3, x)","F",0
76,0,0,0,0.873010," ","integrate(log(c*(d+e*x^n)^p)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{n} + d\right)}^{p} c\right)}{x^{4}}, x\right)"," ",0,"integral(log((e*x^n + d)^p*c)/x^4, x)","F",0
77,1,189,0,0.916926," ","integrate(x^5*log(c*(b*x^2+a)^p)^2,x, algorithm=""fricas"")","\frac{4 \, b^{3} p^{2} x^{6} + 18 \, b^{3} x^{6} \log\left(c\right)^{2} - 15 \, a b^{2} p^{2} x^{4} + 66 \, a^{2} b p^{2} x^{2} + 18 \, {\left(b^{3} p^{2} x^{6} + a^{3} p^{2}\right)} \log\left(b x^{2} + a\right)^{2} - 6 \, {\left(2 \, b^{3} p^{2} x^{6} - 3 \, a b^{2} p^{2} x^{4} + 6 \, a^{2} b p^{2} x^{2} + 11 \, a^{3} p^{2} - 6 \, {\left(b^{3} p x^{6} + a^{3} p\right)} \log\left(c\right)\right)} \log\left(b x^{2} + a\right) - 6 \, {\left(2 \, b^{3} p x^{6} - 3 \, a b^{2} p x^{4} + 6 \, a^{2} b p x^{2}\right)} \log\left(c\right)}{108 \, b^{3}}"," ",0,"1/108*(4*b^3*p^2*x^6 + 18*b^3*x^6*log(c)^2 - 15*a*b^2*p^2*x^4 + 66*a^2*b*p^2*x^2 + 18*(b^3*p^2*x^6 + a^3*p^2)*log(b*x^2 + a)^2 - 6*(2*b^3*p^2*x^6 - 3*a*b^2*p^2*x^4 + 6*a^2*b*p^2*x^2 + 11*a^3*p^2 - 6*(b^3*p*x^6 + a^3*p)*log(c))*log(b*x^2 + a) - 6*(2*b^3*p*x^6 - 3*a*b^2*p*x^4 + 6*a^2*b*p*x^2)*log(c))/b^3","A",0
78,1,148,0,0.633136," ","integrate(x^3*log(c*(b*x^2+a)^p)^2,x, algorithm=""fricas"")","\frac{b^{2} p^{2} x^{4} + 2 \, b^{2} x^{4} \log\left(c\right)^{2} - 6 \, a b p^{2} x^{2} + 2 \, {\left(b^{2} p^{2} x^{4} - a^{2} p^{2}\right)} \log\left(b x^{2} + a\right)^{2} - 2 \, {\left(b^{2} p^{2} x^{4} - 2 \, a b p^{2} x^{2} - 3 \, a^{2} p^{2} - 2 \, {\left(b^{2} p x^{4} - a^{2} p\right)} \log\left(c\right)\right)} \log\left(b x^{2} + a\right) - 2 \, {\left(b^{2} p x^{4} - 2 \, a b p x^{2}\right)} \log\left(c\right)}{8 \, b^{2}}"," ",0,"1/8*(b^2*p^2*x^4 + 2*b^2*x^4*log(c)^2 - 6*a*b*p^2*x^2 + 2*(b^2*p^2*x^4 - a^2*p^2)*log(b*x^2 + a)^2 - 2*(b^2*p^2*x^4 - 2*a*b*p^2*x^2 - 3*a^2*p^2 - 2*(b^2*p*x^4 - a^2*p)*log(c))*log(b*x^2 + a) - 2*(b^2*p*x^4 - 2*a*b*p*x^2)*log(c))/b^2","A",0
79,1,96,0,0.937887," ","integrate(x*log(c*(b*x^2+a)^p)^2,x, algorithm=""fricas"")","\frac{2 \, b p^{2} x^{2} - 2 \, b p x^{2} \log\left(c\right) + b x^{2} \log\left(c\right)^{2} + {\left(b p^{2} x^{2} + a p^{2}\right)} \log\left(b x^{2} + a\right)^{2} - 2 \, {\left(b p^{2} x^{2} + a p^{2} - {\left(b p x^{2} + a p\right)} \log\left(c\right)\right)} \log\left(b x^{2} + a\right)}{2 \, b}"," ",0,"1/2*(2*b*p^2*x^2 - 2*b*p*x^2*log(c) + b*x^2*log(c)^2 + (b*p^2*x^2 + a*p^2)*log(b*x^2 + a)^2 - 2*(b*p^2*x^2 + a*p^2 - (b*p*x^2 + a*p)*log(c))*log(b*x^2 + a))/b","A",0
80,0,0,0,0.937908," ","integrate(log(c*(b*x^2+a)^p)^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)^{2}}{x}, x\right)"," ",0,"integral(log((b*x^2 + a)^p*c)^2/x, x)","F",0
81,0,0,0,0.820328," ","integrate(log(c*(b*x^2+a)^p)^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)^{2}}{x^{3}}, x\right)"," ",0,"integral(log((b*x^2 + a)^p*c)^2/x^3, x)","F",0
82,0,0,0,0.791349," ","integrate(log(c*(b*x^2+a)^p)^2/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)^{2}}{x^{5}}, x\right)"," ",0,"integral(log((b*x^2 + a)^p*c)^2/x^5, x)","F",0
83,0,0,0,0.901425," ","integrate(log(c*(b*x^2+a)^p)^2/x^7,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)^{2}}{x^{7}}, x\right)"," ",0,"integral(log((b*x^2 + a)^p*c)^2/x^7, x)","F",0
84,0,0,0,0.836347," ","integrate(x^4*log(c*(b*x^2+a)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(x^{4} \log\left({\left(b x^{2} + a\right)}^{p} c\right)^{2}, x\right)"," ",0,"integral(x^4*log((b*x^2 + a)^p*c)^2, x)","F",0
85,0,0,0,0.800394," ","integrate(x^2*log(c*(b*x^2+a)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(x^{2} \log\left({\left(b x^{2} + a\right)}^{p} c\right)^{2}, x\right)"," ",0,"integral(x^2*log((b*x^2 + a)^p*c)^2, x)","F",0
86,0,0,0,0.879860," ","integrate(log(c*(b*x^2+a)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(\log\left({\left(b x^{2} + a\right)}^{p} c\right)^{2}, x\right)"," ",0,"integral(log((b*x^2 + a)^p*c)^2, x)","F",0
87,0,0,0,0.811902," ","integrate(log(c*(b*x^2+a)^p)^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)^{2}}{x^{2}}, x\right)"," ",0,"integral(log((b*x^2 + a)^p*c)^2/x^2, x)","F",0
88,0,0,0,0.640707," ","integrate(log(c*(b*x^2+a)^p)^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)^{2}}{x^{4}}, x\right)"," ",0,"integral(log((b*x^2 + a)^p*c)^2/x^4, x)","F",0
89,0,0,0,0.840593," ","integrate(log(c*(b*x^2+a)^p)^2/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)^{2}}{x^{6}}, x\right)"," ",0,"integral(log((b*x^2 + a)^p*c)^2/x^6, x)","F",0
90,0,0,0,0.859524," ","integrate(log(c*(b*x^2+a)^p)^2/x^8,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)^{2}}{x^{8}}, x\right)"," ",0,"integral(log((b*x^2 + a)^p*c)^2/x^8, x)","F",0
91,1,359,0,0.904359," ","integrate(x^5*log(c*(b*x^2+a)^p)^3,x, algorithm=""fricas"")","-\frac{8 \, b^{3} p^{3} x^{6} - 36 \, b^{3} x^{6} \log\left(c\right)^{3} - 57 \, a b^{2} p^{3} x^{4} + 510 \, a^{2} b p^{3} x^{2} - 36 \, {\left(b^{3} p^{3} x^{6} + a^{3} p^{3}\right)} \log\left(b x^{2} + a\right)^{3} + 18 \, {\left(2 \, b^{3} p^{3} x^{6} - 3 \, a b^{2} p^{3} x^{4} + 6 \, a^{2} b p^{3} x^{2} + 11 \, a^{3} p^{3} - 6 \, {\left(b^{3} p^{2} x^{6} + a^{3} p^{2}\right)} \log\left(c\right)\right)} \log\left(b x^{2} + a\right)^{2} + 18 \, {\left(2 \, b^{3} p x^{6} - 3 \, a b^{2} p x^{4} + 6 \, a^{2} b p x^{2}\right)} \log\left(c\right)^{2} - 6 \, {\left(4 \, b^{3} p^{3} x^{6} - 15 \, a b^{2} p^{3} x^{4} + 66 \, a^{2} b p^{3} x^{2} + 85 \, a^{3} p^{3} + 18 \, {\left(b^{3} p x^{6} + a^{3} p\right)} \log\left(c\right)^{2} - 6 \, {\left(2 \, b^{3} p^{2} x^{6} - 3 \, a b^{2} p^{2} x^{4} + 6 \, a^{2} b p^{2} x^{2} + 11 \, a^{3} p^{2}\right)} \log\left(c\right)\right)} \log\left(b x^{2} + a\right) - 6 \, {\left(4 \, b^{3} p^{2} x^{6} - 15 \, a b^{2} p^{2} x^{4} + 66 \, a^{2} b p^{2} x^{2}\right)} \log\left(c\right)}{216 \, b^{3}}"," ",0,"-1/216*(8*b^3*p^3*x^6 - 36*b^3*x^6*log(c)^3 - 57*a*b^2*p^3*x^4 + 510*a^2*b*p^3*x^2 - 36*(b^3*p^3*x^6 + a^3*p^3)*log(b*x^2 + a)^3 + 18*(2*b^3*p^3*x^6 - 3*a*b^2*p^3*x^4 + 6*a^2*b*p^3*x^2 + 11*a^3*p^3 - 6*(b^3*p^2*x^6 + a^3*p^2)*log(c))*log(b*x^2 + a)^2 + 18*(2*b^3*p*x^6 - 3*a*b^2*p*x^4 + 6*a^2*b*p*x^2)*log(c)^2 - 6*(4*b^3*p^3*x^6 - 15*a*b^2*p^3*x^4 + 66*a^2*b*p^3*x^2 + 85*a^3*p^3 + 18*(b^3*p*x^6 + a^3*p)*log(c)^2 - 6*(2*b^3*p^2*x^6 - 3*a*b^2*p^2*x^4 + 6*a^2*b*p^2*x^2 + 11*a^3*p^2)*log(c))*log(b*x^2 + a) - 6*(4*b^3*p^2*x^6 - 15*a*b^2*p^2*x^4 + 66*a^2*b*p^2*x^2)*log(c))/b^3","A",0
92,1,275,0,0.603219," ","integrate(x^3*log(c*(b*x^2+a)^p)^3,x, algorithm=""fricas"")","-\frac{3 \, b^{2} p^{3} x^{4} - 4 \, b^{2} x^{4} \log\left(c\right)^{3} - 42 \, a b p^{3} x^{2} - 4 \, {\left(b^{2} p^{3} x^{4} - a^{2} p^{3}\right)} \log\left(b x^{2} + a\right)^{3} + 6 \, {\left(b^{2} p^{3} x^{4} - 2 \, a b p^{3} x^{2} - 3 \, a^{2} p^{3} - 2 \, {\left(b^{2} p^{2} x^{4} - a^{2} p^{2}\right)} \log\left(c\right)\right)} \log\left(b x^{2} + a\right)^{2} + 6 \, {\left(b^{2} p x^{4} - 2 \, a b p x^{2}\right)} \log\left(c\right)^{2} - 6 \, {\left(b^{2} p^{3} x^{4} - 6 \, a b p^{3} x^{2} - 7 \, a^{2} p^{3} + 2 \, {\left(b^{2} p x^{4} - a^{2} p\right)} \log\left(c\right)^{2} - 2 \, {\left(b^{2} p^{2} x^{4} - 2 \, a b p^{2} x^{2} - 3 \, a^{2} p^{2}\right)} \log\left(c\right)\right)} \log\left(b x^{2} + a\right) - 6 \, {\left(b^{2} p^{2} x^{4} - 6 \, a b p^{2} x^{2}\right)} \log\left(c\right)}{16 \, b^{2}}"," ",0,"-1/16*(3*b^2*p^3*x^4 - 4*b^2*x^4*log(c)^3 - 42*a*b*p^3*x^2 - 4*(b^2*p^3*x^4 - a^2*p^3)*log(b*x^2 + a)^3 + 6*(b^2*p^3*x^4 - 2*a*b*p^3*x^2 - 3*a^2*p^3 - 2*(b^2*p^2*x^4 - a^2*p^2)*log(c))*log(b*x^2 + a)^2 + 6*(b^2*p*x^4 - 2*a*b*p*x^2)*log(c)^2 - 6*(b^2*p^3*x^4 - 6*a*b*p^3*x^2 - 7*a^2*p^3 + 2*(b^2*p*x^4 - a^2*p)*log(c)^2 - 2*(b^2*p^2*x^4 - 2*a*b*p^2*x^2 - 3*a^2*p^2)*log(c))*log(b*x^2 + a) - 6*(b^2*p^2*x^4 - 6*a*b*p^2*x^2)*log(c))/b^2","A",0
93,1,176,0,0.903293," ","integrate(x*log(c*(b*x^2+a)^p)^3,x, algorithm=""fricas"")","-\frac{6 \, b p^{3} x^{2} - 6 \, b p^{2} x^{2} \log\left(c\right) + 3 \, b p x^{2} \log\left(c\right)^{2} - b x^{2} \log\left(c\right)^{3} - {\left(b p^{3} x^{2} + a p^{3}\right)} \log\left(b x^{2} + a\right)^{3} + 3 \, {\left(b p^{3} x^{2} + a p^{3} - {\left(b p^{2} x^{2} + a p^{2}\right)} \log\left(c\right)\right)} \log\left(b x^{2} + a\right)^{2} - 3 \, {\left(2 \, b p^{3} x^{2} + 2 \, a p^{3} + {\left(b p x^{2} + a p\right)} \log\left(c\right)^{2} - 2 \, {\left(b p^{2} x^{2} + a p^{2}\right)} \log\left(c\right)\right)} \log\left(b x^{2} + a\right)}{2 \, b}"," ",0,"-1/2*(6*b*p^3*x^2 - 6*b*p^2*x^2*log(c) + 3*b*p*x^2*log(c)^2 - b*x^2*log(c)^3 - (b*p^3*x^2 + a*p^3)*log(b*x^2 + a)^3 + 3*(b*p^3*x^2 + a*p^3 - (b*p^2*x^2 + a*p^2)*log(c))*log(b*x^2 + a)^2 - 3*(2*b*p^3*x^2 + 2*a*p^3 + (b*p*x^2 + a*p)*log(c)^2 - 2*(b*p^2*x^2 + a*p^2)*log(c))*log(b*x^2 + a))/b","A",0
94,0,0,0,0.916587," ","integrate(log(c*(b*x^2+a)^p)^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)^{3}}{x}, x\right)"," ",0,"integral(log((b*x^2 + a)^p*c)^3/x, x)","F",0
95,0,0,0,0.965851," ","integrate(log(c*(b*x^2+a)^p)^3/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)^{3}}{x^{3}}, x\right)"," ",0,"integral(log((b*x^2 + a)^p*c)^3/x^3, x)","F",0
96,0,0,0,0.568027," ","integrate(log(c*(b*x^2+a)^p)^3/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)^{3}}{x^{5}}, x\right)"," ",0,"integral(log((b*x^2 + a)^p*c)^3/x^5, x)","F",0
97,0,0,0,0.797547," ","integrate(log(c*(b*x^2+a)^p)^3/x^7,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)^{3}}{x^{7}}, x\right)"," ",0,"integral(log((b*x^2 + a)^p*c)^3/x^7, x)","F",0
98,0,0,0,0.784797," ","integrate(x^2*log(c*(b*x^2+a)^p)^3,x, algorithm=""fricas"")","{\rm integral}\left(x^{2} \log\left({\left(b x^{2} + a\right)}^{p} c\right)^{3}, x\right)"," ",0,"integral(x^2*log((b*x^2 + a)^p*c)^3, x)","F",0
99,0,0,0,1.040615," ","integrate(log(c*(b*x^2+a)^p)^3,x, algorithm=""fricas"")","{\rm integral}\left(\log\left({\left(b x^{2} + a\right)}^{p} c\right)^{3}, x\right)"," ",0,"integral(log((b*x^2 + a)^p*c)^3, x)","F",0
100,0,0,0,0.675146," ","integrate(log(c*(b*x^2+a)^p)^3/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)^{3}}{x^{2}}, x\right)"," ",0,"integral(log((b*x^2 + a)^p*c)^3/x^2, x)","F",0
101,0,0,0,0.809944," ","integrate(log(c*(b*x^2+a)^p)^3/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)^{3}}{x^{4}}, x\right)"," ",0,"integral(log((b*x^2 + a)^p*c)^3/x^4, x)","F",0
102,1,68,0,0.883190," ","integrate(x^3/log(c*(b*x^2+a)^p),x, algorithm=""fricas"")","-\frac{a c^{\left(\frac{1}{p}\right)} \operatorname{log\_integral}\left({\left(b x^{2} + a\right)} c^{\left(\frac{1}{p}\right)}\right) - \operatorname{log\_integral}\left({\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} c^{\frac{2}{p}}\right)}{2 \, b^{2} c^{\frac{2}{p}} p}"," ",0,"-1/2*(a*c^(1/p)*log_integral((b*x^2 + a)*c^(1/p)) - log_integral((b^2*x^4 + 2*a*b*x^2 + a^2)*c^(2/p)))/(b^2*c^(2/p)*p)","A",0
103,1,29,0,0.817915," ","integrate(x/log(c*(b*x^2+a)^p),x, algorithm=""fricas"")","\frac{\operatorname{log\_integral}\left({\left(b x^{2} + a\right)} c^{\left(\frac{1}{p}\right)}\right)}{2 \, b c^{\left(\frac{1}{p}\right)} p}"," ",0,"1/2*log_integral((b*x^2 + a)*c^(1/p))/(b*c^(1/p)*p)","A",0
104,0,0,0,0.764566," ","integrate(1/x/log(c*(b*x^2+a)^p),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{x \log\left({\left(b x^{2} + a\right)}^{p} c\right)}, x\right)"," ",0,"integral(1/(x*log((b*x^2 + a)^p*c)), x)","F",0
105,0,0,0,0.676266," ","integrate(1/x^3/log(c*(b*x^2+a)^p),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{x^{3} \log\left({\left(b x^{2} + a\right)}^{p} c\right)}, x\right)"," ",0,"integral(1/(x^3*log((b*x^2 + a)^p*c)), x)","F",0
106,0,0,0,0.859112," ","integrate(x^2/log(c*(b*x^2+a)^p),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{\log\left({\left(b x^{2} + a\right)}^{p} c\right)}, x\right)"," ",0,"integral(x^2/log((b*x^2 + a)^p*c), x)","F",0
107,0,0,0,0.917579," ","integrate(1/log(c*(b*x^2+a)^p),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\log\left({\left(b x^{2} + a\right)}^{p} c\right)}, x\right)"," ",0,"integral(1/log((b*x^2 + a)^p*c), x)","F",0
108,0,0,0,0.785962," ","integrate(1/x^2/log(c*(b*x^2+a)^p),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{x^{2} \log\left({\left(b x^{2} + a\right)}^{p} c\right)}, x\right)"," ",0,"integral(1/(x^2*log((b*x^2 + a)^p*c)), x)","F",0
109,1,141,0,0.836951," ","integrate(x^3/log(c*(b*x^2+a)^p)^2,x, algorithm=""fricas"")","-\frac{{\left(a p \log\left(b x^{2} + a\right) + a \log\left(c\right)\right)} c^{\left(\frac{1}{p}\right)} \operatorname{log\_integral}\left({\left(b x^{2} + a\right)} c^{\left(\frac{1}{p}\right)}\right) + {\left(b^{2} p x^{4} + a b p x^{2}\right)} c^{\frac{2}{p}} - 2 \, {\left(p \log\left(b x^{2} + a\right) + \log\left(c\right)\right)} \operatorname{log\_integral}\left({\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} c^{\frac{2}{p}}\right)}{2 \, {\left(b^{2} p^{3} \log\left(b x^{2} + a\right) + b^{2} p^{2} \log\left(c\right)\right)} c^{\frac{2}{p}}}"," ",0,"-1/2*((a*p*log(b*x^2 + a) + a*log(c))*c^(1/p)*log_integral((b*x^2 + a)*c^(1/p)) + (b^2*p*x^4 + a*b*p*x^2)*c^(2/p) - 2*(p*log(b*x^2 + a) + log(c))*log_integral((b^2*x^4 + 2*a*b*x^2 + a^2)*c^(2/p)))/((b^2*p^3*log(b*x^2 + a) + b^2*p^2*log(c))*c^(2/p))","A",0
110,1,78,0,0.848135," ","integrate(x/log(c*(b*x^2+a)^p)^2,x, algorithm=""fricas"")","-\frac{{\left(b p x^{2} + a p\right)} c^{\left(\frac{1}{p}\right)} - {\left(p \log\left(b x^{2} + a\right) + \log\left(c\right)\right)} \operatorname{log\_integral}\left({\left(b x^{2} + a\right)} c^{\left(\frac{1}{p}\right)}\right)}{2 \, {\left(b p^{3} \log\left(b x^{2} + a\right) + b p^{2} \log\left(c\right)\right)} c^{\left(\frac{1}{p}\right)}}"," ",0,"-1/2*((b*p*x^2 + a*p)*c^(1/p) - (p*log(b*x^2 + a) + log(c))*log_integral((b*x^2 + a)*c^(1/p)))/((b*p^3*log(b*x^2 + a) + b*p^2*log(c))*c^(1/p))","A",0
111,0,0,0,0.853472," ","integrate(1/x/log(c*(b*x^2+a)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{x \log\left({\left(b x^{2} + a\right)}^{p} c\right)^{2}}, x\right)"," ",0,"integral(1/(x*log((b*x^2 + a)^p*c)^2), x)","F",0
112,0,0,0,0.629987," ","integrate(1/x^3/log(c*(b*x^2+a)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{x^{3} \log\left({\left(b x^{2} + a\right)}^{p} c\right)^{2}}, x\right)"," ",0,"integral(1/(x^3*log((b*x^2 + a)^p*c)^2), x)","F",0
113,0,0,0,0.667203," ","integrate(x^2/log(c*(b*x^2+a)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{\log\left({\left(b x^{2} + a\right)}^{p} c\right)^{2}}, x\right)"," ",0,"integral(x^2/log((b*x^2 + a)^p*c)^2, x)","F",0
114,0,0,0,0.877960," ","integrate(1/log(c*(b*x^2+a)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\log\left({\left(b x^{2} + a\right)}^{p} c\right)^{2}}, x\right)"," ",0,"integral(log((b*x^2 + a)^p*c)^(-2), x)","F",0
115,0,0,0,0.943703," ","integrate(1/x^2/log(c*(b*x^2+a)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{x^{2} \log\left({\left(b x^{2} + a\right)}^{p} c\right)^{2}}, x\right)"," ",0,"integral(1/(x^2*log((b*x^2 + a)^p*c)^2), x)","F",0
116,1,270,0,0.580913," ","integrate(x^3/log(c*(b*x^2+a)^p)^3,x, algorithm=""fricas"")","-\frac{{\left(a p^{2} \log\left(b x^{2} + a\right)^{2} + 2 \, a p \log\left(b x^{2} + a\right) \log\left(c\right) + a \log\left(c\right)^{2}\right)} c^{\left(\frac{1}{p}\right)} \operatorname{log\_integral}\left({\left(b x^{2} + a\right)} c^{\left(\frac{1}{p}\right)}\right) + {\left(b^{2} p^{2} x^{4} + a b p^{2} x^{2} + {\left(2 \, b^{2} p^{2} x^{4} + 3 \, a b p^{2} x^{2} + a^{2} p^{2}\right)} \log\left(b x^{2} + a\right) + {\left(2 \, b^{2} p x^{4} + 3 \, a b p x^{2} + a^{2} p\right)} \log\left(c\right)\right)} c^{\frac{2}{p}} - 4 \, {\left(p^{2} \log\left(b x^{2} + a\right)^{2} + 2 \, p \log\left(b x^{2} + a\right) \log\left(c\right) + \log\left(c\right)^{2}\right)} \operatorname{log\_integral}\left({\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} c^{\frac{2}{p}}\right)}{4 \, {\left(b^{2} p^{5} \log\left(b x^{2} + a\right)^{2} + 2 \, b^{2} p^{4} \log\left(b x^{2} + a\right) \log\left(c\right) + b^{2} p^{3} \log\left(c\right)^{2}\right)} c^{\frac{2}{p}}}"," ",0,"-1/4*((a*p^2*log(b*x^2 + a)^2 + 2*a*p*log(b*x^2 + a)*log(c) + a*log(c)^2)*c^(1/p)*log_integral((b*x^2 + a)*c^(1/p)) + (b^2*p^2*x^4 + a*b*p^2*x^2 + (2*b^2*p^2*x^4 + 3*a*b*p^2*x^2 + a^2*p^2)*log(b*x^2 + a) + (2*b^2*p*x^4 + 3*a*b*p*x^2 + a^2*p)*log(c))*c^(2/p) - 4*(p^2*log(b*x^2 + a)^2 + 2*p*log(b*x^2 + a)*log(c) + log(c)^2)*log_integral((b^2*x^4 + 2*a*b*x^2 + a^2)*c^(2/p)))/((b^2*p^5*log(b*x^2 + a)^2 + 2*b^2*p^4*log(b*x^2 + a)*log(c) + b^2*p^3*log(c)^2)*c^(2/p))","A",0
117,1,157,0,0.910285," ","integrate(x/log(c*(b*x^2+a)^p)^3,x, algorithm=""fricas"")","-\frac{{\left(b p^{2} x^{2} + a p^{2} + {\left(b p^{2} x^{2} + a p^{2}\right)} \log\left(b x^{2} + a\right) + {\left(b p x^{2} + a p\right)} \log\left(c\right)\right)} c^{\left(\frac{1}{p}\right)} - {\left(p^{2} \log\left(b x^{2} + a\right)^{2} + 2 \, p \log\left(b x^{2} + a\right) \log\left(c\right) + \log\left(c\right)^{2}\right)} \operatorname{log\_integral}\left({\left(b x^{2} + a\right)} c^{\left(\frac{1}{p}\right)}\right)}{4 \, {\left(b p^{5} \log\left(b x^{2} + a\right)^{2} + 2 \, b p^{4} \log\left(b x^{2} + a\right) \log\left(c\right) + b p^{3} \log\left(c\right)^{2}\right)} c^{\left(\frac{1}{p}\right)}}"," ",0,"-1/4*((b*p^2*x^2 + a*p^2 + (b*p^2*x^2 + a*p^2)*log(b*x^2 + a) + (b*p*x^2 + a*p)*log(c))*c^(1/p) - (p^2*log(b*x^2 + a)^2 + 2*p*log(b*x^2 + a)*log(c) + log(c)^2)*log_integral((b*x^2 + a)*c^(1/p)))/((b*p^5*log(b*x^2 + a)^2 + 2*b*p^4*log(b*x^2 + a)*log(c) + b*p^3*log(c)^2)*c^(1/p))","A",0
118,0,0,0,0.789638," ","integrate(1/x/log(c*(b*x^2+a)^p)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{x \log\left({\left(b x^{2} + a\right)}^{p} c\right)^{3}}, x\right)"," ",0,"integral(1/(x*log((b*x^2 + a)^p*c)^3), x)","F",0
119,0,0,0,0.851335," ","integrate(1/x^3/log(c*(b*x^2+a)^p)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{x^{3} \log\left({\left(b x^{2} + a\right)}^{p} c\right)^{3}}, x\right)"," ",0,"integral(1/(x^3*log((b*x^2 + a)^p*c)^3), x)","F",0
120,0,0,0,0.767730," ","integrate(x^2/log(c*(b*x^2+a)^p)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{\log\left({\left(b x^{2} + a\right)}^{p} c\right)^{3}}, x\right)"," ",0,"integral(x^2/log((b*x^2 + a)^p*c)^3, x)","F",0
121,0,0,0,0.834719," ","integrate(1/log(c*(b*x^2+a)^p)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\log\left({\left(b x^{2} + a\right)}^{p} c\right)^{3}}, x\right)"," ",0,"integral(log((b*x^2 + a)^p*c)^(-3), x)","F",0
122,0,0,0,0.829963," ","integrate(1/x^2/log(c*(b*x^2+a)^p)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{x^{2} \log\left({\left(b x^{2} + a\right)}^{p} c\right)^{3}}, x\right)"," ",0,"integral(1/(x^2*log((b*x^2 + a)^p*c)^3), x)","F",0
123,1,54,0,0.710416," ","integrate(x^3/log(c*(b*x^2+a)),x, algorithm=""fricas"")","-\frac{a c \operatorname{log\_integral}\left(b c x^{2} + a c\right) - \operatorname{log\_integral}\left(b^{2} c^{2} x^{4} + 2 \, a b c^{2} x^{2} + a^{2} c^{2}\right)}{2 \, b^{2} c^{2}}"," ",0,"-1/2*(a*c*log_integral(b*c*x^2 + a*c) - log_integral(b^2*c^2*x^4 + 2*a*b*c^2*x^2 + a^2*c^2))/(b^2*c^2)","A",0
124,1,19,0,0.846084," ","integrate(x/log(c*(b*x^2+a)),x, algorithm=""fricas"")","\frac{\operatorname{log\_integral}\left(b c x^{2} + a c\right)}{2 \, b c}"," ",0,"1/2*log_integral(b*c*x^2 + a*c)/(b*c)","A",0
125,1,99,0,0.762341," ","integrate(x^3/log(c*(b*x^2+a))^2,x, algorithm=""fricas"")","-\frac{b^{2} c^{2} x^{4} + a b c^{2} x^{2} + {\left(a c \operatorname{log\_integral}\left(b c x^{2} + a c\right) - 2 \, \operatorname{log\_integral}\left(b^{2} c^{2} x^{4} + 2 \, a b c^{2} x^{2} + a^{2} c^{2}\right)\right)} \log\left(b c x^{2} + a c\right)}{2 \, b^{2} c^{2} \log\left(b c x^{2} + a c\right)}"," ",0,"-1/2*(b^2*c^2*x^4 + a*b*c^2*x^2 + (a*c*log_integral(b*c*x^2 + a*c) - 2*log_integral(b^2*c^2*x^4 + 2*a*b*c^2*x^2 + a^2*c^2))*log(b*c*x^2 + a*c))/(b^2*c^2*log(b*c*x^2 + a*c))","A",0
126,1,55,0,0.623269," ","integrate(x/log(c*(b*x^2+a))^2,x, algorithm=""fricas"")","-\frac{b c x^{2} + a c - \log\left(b c x^{2} + a c\right) \operatorname{log\_integral}\left(b c x^{2} + a c\right)}{2 \, b c \log\left(b c x^{2} + a c\right)}"," ",0,"-1/2*(b*c*x^2 + a*c - log(b*c*x^2 + a*c)*log_integral(b*c*x^2 + a*c))/(b*c*log(b*c*x^2 + a*c))","A",0
127,1,142,0,0.839216," ","integrate(x^3/log(c*(b*x^2+a))^3,x, algorithm=""fricas"")","-\frac{b^{2} c^{2} x^{4} + a b c^{2} x^{2} + {\left(a c \operatorname{log\_integral}\left(b c x^{2} + a c\right) - 4 \, \operatorname{log\_integral}\left(b^{2} c^{2} x^{4} + 2 \, a b c^{2} x^{2} + a^{2} c^{2}\right)\right)} \log\left(b c x^{2} + a c\right)^{2} + {\left(2 \, b^{2} c^{2} x^{4} + 3 \, a b c^{2} x^{2} + a^{2} c^{2}\right)} \log\left(b c x^{2} + a c\right)}{4 \, b^{2} c^{2} \log\left(b c x^{2} + a c\right)^{2}}"," ",0,"-1/4*(b^2*c^2*x^4 + a*b*c^2*x^2 + (a*c*log_integral(b*c*x^2 + a*c) - 4*log_integral(b^2*c^2*x^4 + 2*a*b*c^2*x^2 + a^2*c^2))*log(b*c*x^2 + a*c)^2 + (2*b^2*c^2*x^4 + 3*a*b*c^2*x^2 + a^2*c^2)*log(b*c*x^2 + a*c))/(b^2*c^2*log(b*c*x^2 + a*c)^2)","A",0
128,1,79,0,0.736276," ","integrate(x/log(c*(b*x^2+a))^3,x, algorithm=""fricas"")","-\frac{b c x^{2} - \log\left(b c x^{2} + a c\right)^{2} \operatorname{log\_integral}\left(b c x^{2} + a c\right) + a c + {\left(b c x^{2} + a c\right)} \log\left(b c x^{2} + a c\right)}{4 \, b c \log\left(b c x^{2} + a c\right)^{2}}"," ",0,"-1/4*(b*c*x^2 - log(b*c*x^2 + a*c)^2*log_integral(b*c*x^2 + a*c) + a*c + (b*c*x^2 + a*c)*log(b*c*x^2 + a*c))/(b*c*log(b*c*x^2 + a*c)^2)","A",0
129,1,148,0,0.966022," ","integrate(x^5*log(c*(e*x^3+d)^p)^2,x, algorithm=""fricas"")","\frac{e^{2} p^{2} x^{6} + 2 \, e^{2} x^{6} \log\left(c\right)^{2} - 6 \, d e p^{2} x^{3} + 2 \, {\left(e^{2} p^{2} x^{6} - d^{2} p^{2}\right)} \log\left(e x^{3} + d\right)^{2} - 2 \, {\left(e^{2} p^{2} x^{6} - 2 \, d e p^{2} x^{3} - 3 \, d^{2} p^{2} - 2 \, {\left(e^{2} p x^{6} - d^{2} p\right)} \log\left(c\right)\right)} \log\left(e x^{3} + d\right) - 2 \, {\left(e^{2} p x^{6} - 2 \, d e p x^{3}\right)} \log\left(c\right)}{12 \, e^{2}}"," ",0,"1/12*(e^2*p^2*x^6 + 2*e^2*x^6*log(c)^2 - 6*d*e*p^2*x^3 + 2*(e^2*p^2*x^6 - d^2*p^2)*log(e*x^3 + d)^2 - 2*(e^2*p^2*x^6 - 2*d*e*p^2*x^3 - 3*d^2*p^2 - 2*(e^2*p*x^6 - d^2*p)*log(c))*log(e*x^3 + d) - 2*(e^2*p*x^6 - 2*d*e*p*x^3)*log(c))/e^2","A",0
130,1,96,0,0.867713," ","integrate(x^2*log(c*(e*x^3+d)^p)^2,x, algorithm=""fricas"")","\frac{2 \, e p^{2} x^{3} - 2 \, e p x^{3} \log\left(c\right) + e x^{3} \log\left(c\right)^{2} + {\left(e p^{2} x^{3} + d p^{2}\right)} \log\left(e x^{3} + d\right)^{2} - 2 \, {\left(e p^{2} x^{3} + d p^{2} - {\left(e p x^{3} + d p\right)} \log\left(c\right)\right)} \log\left(e x^{3} + d\right)}{3 \, e}"," ",0,"1/3*(2*e*p^2*x^3 - 2*e*p*x^3*log(c) + e*x^3*log(c)^2 + (e*p^2*x^3 + d*p^2)*log(e*x^3 + d)^2 - 2*(e*p^2*x^3 + d*p^2 - (e*p*x^3 + d*p)*log(c))*log(e*x^3 + d))/e","A",0
131,0,0,0,0.911164," ","integrate(log(c*(e*x^3+d)^p)^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{3} + d\right)}^{p} c\right)^{2}}{x}, x\right)"," ",0,"integral(log((e*x^3 + d)^p*c)^2/x, x)","F",0
132,0,0,0,0.785099," ","integrate(log(c*(e*x^3+d)^p)^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{3} + d\right)}^{p} c\right)^{2}}{x^{4}}, x\right)"," ",0,"integral(log((e*x^3 + d)^p*c)^2/x^4, x)","F",0
133,0,0,0,0.838797," ","integrate(x*log(c*(e*x^3+d)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(x \log\left({\left(e x^{3} + d\right)}^{p} c\right)^{2}, x\right)"," ",0,"integral(x*log((e*x^3 + d)^p*c)^2, x)","F",0
134,0,0,0,0.768738," ","integrate(log(c*(e*x^3+d)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(\log\left({\left(e x^{3} + d\right)}^{p} c\right)^{2}, x\right)"," ",0,"integral(log((e*x^3 + d)^p*c)^2, x)","F",0
135,0,0,0,0.958350," ","integrate(log(c*(e*x^3+d)^p)^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{3} + d\right)}^{p} c\right)^{2}}{x^{2}}, x\right)"," ",0,"integral(log((e*x^3 + d)^p*c)^2/x^2, x)","F",0
136,0,0,0,0.976360," ","integrate(log(c*(e*x^3+d)^p)^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{3} + d\right)}^{p} c\right)^{2}}{x^{3}}, x\right)"," ",0,"integral(log((e*x^3 + d)^p*c)^2/x^3, x)","F",0
137,0,0,0,0.799444," ","integrate(log(c*(e*x^3+d)^p)^2/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{3} + d\right)}^{p} c\right)^{2}}{x^{5}}, x\right)"," ",0,"integral(log((e*x^3 + d)^p*c)^2/x^5, x)","F",0
138,1,116,0,1.042807," ","integrate(x^8/log(c*(e*x^3+d)^p),x, algorithm=""fricas"")","\frac{c^{\frac{2}{p}} d^{2} \operatorname{log\_integral}\left({\left(e x^{3} + d\right)} c^{\left(\frac{1}{p}\right)}\right) - 2 \, c^{\left(\frac{1}{p}\right)} d \operatorname{log\_integral}\left({\left(e^{2} x^{6} + 2 \, d e x^{3} + d^{2}\right)} c^{\frac{2}{p}}\right) + \operatorname{log\_integral}\left({\left(e^{3} x^{9} + 3 \, d e^{2} x^{6} + 3 \, d^{2} e x^{3} + d^{3}\right)} c^{\frac{3}{p}}\right)}{3 \, c^{\frac{3}{p}} e^{3} p}"," ",0,"1/3*(c^(2/p)*d^2*log_integral((e*x^3 + d)*c^(1/p)) - 2*c^(1/p)*d*log_integral((e^2*x^6 + 2*d*e*x^3 + d^2)*c^(2/p)) + log_integral((e^3*x^9 + 3*d*e^2*x^6 + 3*d^2*e*x^3 + d^3)*c^(3/p)))/(c^(3/p)*e^3*p)","A",0
139,1,68,0,0.782865," ","integrate(x^5/log(c*(e*x^3+d)^p),x, algorithm=""fricas"")","-\frac{c^{\left(\frac{1}{p}\right)} d \operatorname{log\_integral}\left({\left(e x^{3} + d\right)} c^{\left(\frac{1}{p}\right)}\right) - \operatorname{log\_integral}\left({\left(e^{2} x^{6} + 2 \, d e x^{3} + d^{2}\right)} c^{\frac{2}{p}}\right)}{3 \, c^{\frac{2}{p}} e^{2} p}"," ",0,"-1/3*(c^(1/p)*d*log_integral((e*x^3 + d)*c^(1/p)) - log_integral((e^2*x^6 + 2*d*e*x^3 + d^2)*c^(2/p)))/(c^(2/p)*e^2*p)","A",0
140,1,29,0,0.708472," ","integrate(x^2/log(c*(e*x^3+d)^p),x, algorithm=""fricas"")","\frac{\operatorname{log\_integral}\left({\left(e x^{3} + d\right)} c^{\left(\frac{1}{p}\right)}\right)}{3 \, c^{\left(\frac{1}{p}\right)} e p}"," ",0,"1/3*log_integral((e*x^3 + d)*c^(1/p))/(c^(1/p)*e*p)","A",0
141,0,0,0,1.042342," ","integrate(1/x/log(c*(e*x^3+d)^p),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{x \log\left({\left(e x^{3} + d\right)}^{p} c\right)}, x\right)"," ",0,"integral(1/(x*log((e*x^3 + d)^p*c)), x)","F",0
142,0,0,0,0.834728," ","integrate(1/x^4/log(c*(e*x^3+d)^p),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{x^{4} \log\left({\left(e x^{3} + d\right)}^{p} c\right)}, x\right)"," ",0,"integral(1/(x^4*log((e*x^3 + d)^p*c)), x)","F",0
143,0,0,0,1.066823," ","integrate(x^3/log(c*(e*x^3+d)^p),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{\log\left({\left(e x^{3} + d\right)}^{p} c\right)}, x\right)"," ",0,"integral(x^3/log((e*x^3 + d)^p*c), x)","F",0
144,0,0,0,0.848629," ","integrate(x/log(c*(e*x^3+d)^p),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{\log\left({\left(e x^{3} + d\right)}^{p} c\right)}, x\right)"," ",0,"integral(x/log((e*x^3 + d)^p*c), x)","F",0
145,0,0,0,0.753893," ","integrate(1/log(c*(e*x^3+d)^p),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\log\left({\left(e x^{3} + d\right)}^{p} c\right)}, x\right)"," ",0,"integral(1/log((e*x^3 + d)^p*c), x)","F",0
146,0,0,0,0.889353," ","integrate(1/x^2/log(c*(e*x^3+d)^p),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{x^{2} \log\left({\left(e x^{3} + d\right)}^{p} c\right)}, x\right)"," ",0,"integral(1/(x^2*log((e*x^3 + d)^p*c)), x)","F",0
147,0,0,0,0.981512," ","integrate(1/x^3/log(c*(e*x^3+d)^p),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{x^{3} \log\left({\left(e x^{3} + d\right)}^{p} c\right)}, x\right)"," ",0,"integral(1/(x^3*log((e*x^3 + d)^p*c)), x)","F",0
148,1,211,0,0.981738," ","integrate(x^8/log(c*(e*x^3+d)^p)^2,x, algorithm=""fricas"")","-\frac{4 \, {\left(d p \log\left(e x^{3} + d\right) + d \log\left(c\right)\right)} c^{\left(\frac{1}{p}\right)} \operatorname{log\_integral}\left({\left(e^{2} x^{6} + 2 \, d e x^{3} + d^{2}\right)} c^{\frac{2}{p}}\right) - {\left(d^{2} p \log\left(e x^{3} + d\right) + d^{2} \log\left(c\right)\right)} c^{\frac{2}{p}} \operatorname{log\_integral}\left({\left(e x^{3} + d\right)} c^{\left(\frac{1}{p}\right)}\right) + {\left(e^{3} p x^{9} + d e^{2} p x^{6}\right)} c^{\frac{3}{p}} - 3 \, {\left(p \log\left(e x^{3} + d\right) + \log\left(c\right)\right)} \operatorname{log\_integral}\left({\left(e^{3} x^{9} + 3 \, d e^{2} x^{6} + 3 \, d^{2} e x^{3} + d^{3}\right)} c^{\frac{3}{p}}\right)}{3 \, {\left(e^{3} p^{3} \log\left(e x^{3} + d\right) + e^{3} p^{2} \log\left(c\right)\right)} c^{\frac{3}{p}}}"," ",0,"-1/3*(4*(d*p*log(e*x^3 + d) + d*log(c))*c^(1/p)*log_integral((e^2*x^6 + 2*d*e*x^3 + d^2)*c^(2/p)) - (d^2*p*log(e*x^3 + d) + d^2*log(c))*c^(2/p)*log_integral((e*x^3 + d)*c^(1/p)) + (e^3*p*x^9 + d*e^2*p*x^6)*c^(3/p) - 3*(p*log(e*x^3 + d) + log(c))*log_integral((e^3*x^9 + 3*d*e^2*x^6 + 3*d^2*e*x^3 + d^3)*c^(3/p)))/((e^3*p^3*log(e*x^3 + d) + e^3*p^2*log(c))*c^(3/p))","A",0
149,1,141,0,0.847915," ","integrate(x^5/log(c*(e*x^3+d)^p)^2,x, algorithm=""fricas"")","-\frac{{\left(d p \log\left(e x^{3} + d\right) + d \log\left(c\right)\right)} c^{\left(\frac{1}{p}\right)} \operatorname{log\_integral}\left({\left(e x^{3} + d\right)} c^{\left(\frac{1}{p}\right)}\right) + {\left(e^{2} p x^{6} + d e p x^{3}\right)} c^{\frac{2}{p}} - 2 \, {\left(p \log\left(e x^{3} + d\right) + \log\left(c\right)\right)} \operatorname{log\_integral}\left({\left(e^{2} x^{6} + 2 \, d e x^{3} + d^{2}\right)} c^{\frac{2}{p}}\right)}{3 \, {\left(e^{2} p^{3} \log\left(e x^{3} + d\right) + e^{2} p^{2} \log\left(c\right)\right)} c^{\frac{2}{p}}}"," ",0,"-1/3*((d*p*log(e*x^3 + d) + d*log(c))*c^(1/p)*log_integral((e*x^3 + d)*c^(1/p)) + (e^2*p*x^6 + d*e*p*x^3)*c^(2/p) - 2*(p*log(e*x^3 + d) + log(c))*log_integral((e^2*x^6 + 2*d*e*x^3 + d^2)*c^(2/p)))/((e^2*p^3*log(e*x^3 + d) + e^2*p^2*log(c))*c^(2/p))","A",0
150,1,78,0,1.125346," ","integrate(x^2/log(c*(e*x^3+d)^p)^2,x, algorithm=""fricas"")","-\frac{{\left(e p x^{3} + d p\right)} c^{\left(\frac{1}{p}\right)} - {\left(p \log\left(e x^{3} + d\right) + \log\left(c\right)\right)} \operatorname{log\_integral}\left({\left(e x^{3} + d\right)} c^{\left(\frac{1}{p}\right)}\right)}{3 \, {\left(e p^{3} \log\left(e x^{3} + d\right) + e p^{2} \log\left(c\right)\right)} c^{\left(\frac{1}{p}\right)}}"," ",0,"-1/3*((e*p*x^3 + d*p)*c^(1/p) - (p*log(e*x^3 + d) + log(c))*log_integral((e*x^3 + d)*c^(1/p)))/((e*p^3*log(e*x^3 + d) + e*p^2*log(c))*c^(1/p))","A",0
151,0,0,0,1.074916," ","integrate(1/x/log(c*(e*x^3+d)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{x \log\left({\left(e x^{3} + d\right)}^{p} c\right)^{2}}, x\right)"," ",0,"integral(1/(x*log((e*x^3 + d)^p*c)^2), x)","F",0
152,0,0,0,1.008063," ","integrate(1/x^4/log(c*(e*x^3+d)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{x^{4} \log\left({\left(e x^{3} + d\right)}^{p} c\right)^{2}}, x\right)"," ",0,"integral(1/(x^4*log((e*x^3 + d)^p*c)^2), x)","F",0
153,0,0,0,0.928272," ","integrate(x^3/log(c*(e*x^3+d)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{\log\left({\left(e x^{3} + d\right)}^{p} c\right)^{2}}, x\right)"," ",0,"integral(x^3/log((e*x^3 + d)^p*c)^2, x)","F",0
154,0,0,0,1.121708," ","integrate(x/log(c*(e*x^3+d)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{\log\left({\left(e x^{3} + d\right)}^{p} c\right)^{2}}, x\right)"," ",0,"integral(x/log((e*x^3 + d)^p*c)^2, x)","F",0
155,0,0,0,0.855473," ","integrate(1/log(c*(e*x^3+d)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\log\left({\left(e x^{3} + d\right)}^{p} c\right)^{2}}, x\right)"," ",0,"integral(log((e*x^3 + d)^p*c)^(-2), x)","F",0
156,0,0,0,0.749096," ","integrate(1/x^2/log(c*(e*x^3+d)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{x^{2} \log\left({\left(e x^{3} + d\right)}^{p} c\right)^{2}}, x\right)"," ",0,"integral(1/(x^2*log((e*x^3 + d)^p*c)^2), x)","F",0
157,0,0,0,1.037196," ","integrate(1/x^3/log(c*(e*x^3+d)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{x^{3} \log\left({\left(e x^{3} + d\right)}^{p} c\right)^{2}}, x\right)"," ",0,"integral(1/(x^3*log((e*x^3 + d)^p*c)^2), x)","F",0
158,0,0,0,1.029394," ","integrate((f*x)^m*log(c*(e*x^2+d)^p)^3,x, algorithm=""fricas"")","{\rm integral}\left(\left(f x\right)^{m} \log\left({\left(e x^{2} + d\right)}^{p} c\right)^{3}, x\right)"," ",0,"integral((f*x)^m*log((e*x^2 + d)^p*c)^3, x)","F",0
159,0,0,0,1.080066," ","integrate((f*x)^m*log(c*(e*x^2+d)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(\left(f x\right)^{m} \log\left({\left(e x^{2} + d\right)}^{p} c\right)^{2}, x\right)"," ",0,"integral((f*x)^m*log((e*x^2 + d)^p*c)^2, x)","F",0
160,0,0,0,1.258145," ","integrate((f*x)^m*log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","{\rm integral}\left(\left(f x\right)^{m} \log\left({\left(e x^{2} + d\right)}^{p} c\right), x\right)"," ",0,"integral((f*x)^m*log((e*x^2 + d)^p*c), x)","F",0
161,0,0,0,0.985180," ","integrate((f*x)^m/log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(f x\right)^{m}}{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}, x\right)"," ",0,"integral((f*x)^m/log((e*x^2 + d)^p*c), x)","F",0
162,0,0,0,0.972851," ","integrate((f*x)^m/log(c*(e*x^2+d)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(f x\right)^{m}}{\log\left({\left(e x^{2} + d\right)}^{p} c\right)^{2}}, x\right)"," ",0,"integral((f*x)^m/log((e*x^2 + d)^p*c)^2, x)","F",0
163,1,266,0,0.867959," ","integrate((f*x)^(-1+3*n)*log(c*(d+e*x^n)^p)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, e^{3} p^{2} - 6 \, e^{3} p \log\left(c\right) + 9 \, e^{3} \log\left(c\right)^{2}\right)} f^{3 \, n - 1} x^{3 \, n} - 3 \, {\left(5 \, d e^{2} p^{2} - 6 \, d e^{2} p \log\left(c\right)\right)} f^{3 \, n - 1} x^{2 \, n} + 6 \, {\left(11 \, d^{2} e p^{2} - 6 \, d^{2} e p \log\left(c\right)\right)} f^{3 \, n - 1} x^{n} + 18 \, {\left(e^{3} f^{3 \, n - 1} p^{2} x^{3 \, n} + d^{3} f^{3 \, n - 1} p^{2}\right)} \log\left(e x^{n} + d\right)^{2} + 6 \, {\left(3 \, d e^{2} f^{3 \, n - 1} p^{2} x^{2 \, n} - 6 \, d^{2} e f^{3 \, n - 1} p^{2} x^{n} - 2 \, {\left(e^{3} p^{2} - 3 \, e^{3} p \log\left(c\right)\right)} f^{3 \, n - 1} x^{3 \, n} - {\left(11 \, d^{3} p^{2} - 6 \, d^{3} p \log\left(c\right)\right)} f^{3 \, n - 1}\right)} \log\left(e x^{n} + d\right)}{54 \, e^{3} n}"," ",0,"1/54*(2*(2*e^3*p^2 - 6*e^3*p*log(c) + 9*e^3*log(c)^2)*f^(3*n - 1)*x^(3*n) - 3*(5*d*e^2*p^2 - 6*d*e^2*p*log(c))*f^(3*n - 1)*x^(2*n) + 6*(11*d^2*e*p^2 - 6*d^2*e*p*log(c))*f^(3*n - 1)*x^n + 18*(e^3*f^(3*n - 1)*p^2*x^(3*n) + d^3*f^(3*n - 1)*p^2)*log(e*x^n + d)^2 + 6*(3*d*e^2*f^(3*n - 1)*p^2*x^(2*n) - 6*d^2*e*f^(3*n - 1)*p^2*x^n - 2*(e^3*p^2 - 3*e^3*p*log(c))*f^(3*n - 1)*x^(3*n) - (11*d^3*p^2 - 6*d^3*p*log(c))*f^(3*n - 1))*log(e*x^n + d))/(e^3*n)","A",0
164,1,204,0,1.103765," ","integrate((f*x)^(-1+2*n)*log(c*(d+e*x^n)^p)^2,x, algorithm=""fricas"")","\frac{{\left(e^{2} p^{2} - 2 \, e^{2} p \log\left(c\right) + 2 \, e^{2} \log\left(c\right)^{2}\right)} f^{2 \, n - 1} x^{2 \, n} - 2 \, {\left(3 \, d e p^{2} - 2 \, d e p \log\left(c\right)\right)} f^{2 \, n - 1} x^{n} + 2 \, {\left(e^{2} f^{2 \, n - 1} p^{2} x^{2 \, n} - d^{2} f^{2 \, n - 1} p^{2}\right)} \log\left(e x^{n} + d\right)^{2} + 2 \, {\left(2 \, d e f^{2 \, n - 1} p^{2} x^{n} - {\left(e^{2} p^{2} - 2 \, e^{2} p \log\left(c\right)\right)} f^{2 \, n - 1} x^{2 \, n} + {\left(3 \, d^{2} p^{2} - 2 \, d^{2} p \log\left(c\right)\right)} f^{2 \, n - 1}\right)} \log\left(e x^{n} + d\right)}{4 \, e^{2} n}"," ",0,"1/4*((e^2*p^2 - 2*e^2*p*log(c) + 2*e^2*log(c)^2)*f^(2*n - 1)*x^(2*n) - 2*(3*d*e*p^2 - 2*d*e*p*log(c))*f^(2*n - 1)*x^n + 2*(e^2*f^(2*n - 1)*p^2*x^(2*n) - d^2*f^(2*n - 1)*p^2)*log(e*x^n + d)^2 + 2*(2*d*e*f^(2*n - 1)*p^2*x^n - (e^2*p^2 - 2*e^2*p*log(c))*f^(2*n - 1)*x^(2*n) + (3*d^2*p^2 - 2*d^2*p*log(c))*f^(2*n - 1))*log(e*x^n + d))/(e^2*n)","A",0
165,1,121,0,0.972599," ","integrate((f*x)^(-1+n)*log(c*(d+e*x^n)^p)^2,x, algorithm=""fricas"")","\frac{{\left(2 \, e p^{2} - 2 \, e p \log\left(c\right) + e \log\left(c\right)^{2}\right)} f^{n - 1} x^{n} + {\left(e f^{n - 1} p^{2} x^{n} + d f^{n - 1} p^{2}\right)} \log\left(e x^{n} + d\right)^{2} - 2 \, {\left({\left(e p^{2} - e p \log\left(c\right)\right)} f^{n - 1} x^{n} + {\left(d p^{2} - d p \log\left(c\right)\right)} f^{n - 1}\right)} \log\left(e x^{n} + d\right)}{e n}"," ",0,"((2*e*p^2 - 2*e*p*log(c) + e*log(c)^2)*f^(n - 1)*x^n + (e*f^(n - 1)*p^2*x^n + d*f^(n - 1)*p^2)*log(e*x^n + d)^2 - 2*((e*p^2 - e*p*log(c))*f^(n - 1)*x^n + (d*p^2 - d*p*log(c))*f^(n - 1))*log(e*x^n + d))/(e*n)","A",0
166,0,0,0,1.061813," ","integrate(log(c*(d+e*x^n)^p)^2/f/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{n} + d\right)}^{p} c\right)^{2}}{f x}, x\right)"," ",0,"integral(log((e*x^n + d)^p*c)^2/(f*x), x)","F",0
167,1,197,0,0.833680," ","integrate((f*x)^(-1-n)*log(c*(d+e*x^n)^p)^2,x, algorithm=""fricas"")","-\frac{2 \, e f^{-n - 1} n p^{2} x^{n} \log\left(x\right) \log\left(\frac{e x^{n} + d}{d}\right) - 2 \, e f^{-n - 1} n p x^{n} \log\left(c\right) \log\left(x\right) + 2 \, e f^{-n - 1} p^{2} x^{n} {\rm Li}_2\left(-\frac{e x^{n} + d}{d} + 1\right) + d f^{-n - 1} \log\left(c\right)^{2} + {\left(e f^{-n - 1} p^{2} x^{n} + d f^{-n - 1} p^{2}\right)} \log\left(e x^{n} + d\right)^{2} + 2 \, {\left(d f^{-n - 1} p \log\left(c\right) - {\left(e n p^{2} \log\left(x\right) - e p \log\left(c\right)\right)} f^{-n - 1} x^{n}\right)} \log\left(e x^{n} + d\right)}{d n x^{n}}"," ",0,"-(2*e*f^(-n - 1)*n*p^2*x^n*log(x)*log((e*x^n + d)/d) - 2*e*f^(-n - 1)*n*p*x^n*log(c)*log(x) + 2*e*f^(-n - 1)*p^2*x^n*dilog(-(e*x^n + d)/d + 1) + d*f^(-n - 1)*log(c)^2 + (e*f^(-n - 1)*p^2*x^n + d*f^(-n - 1)*p^2)*log(e*x^n + d)^2 + 2*(d*f^(-n - 1)*p*log(c) - (e*n*p^2*log(x) - e*p*log(c))*f^(-n - 1)*x^n)*log(e*x^n + d))/(d*n*x^n)","A",0
168,1,279,0,1.010233," ","integrate((f*x)^(-1-2*n)*log(c*(d+e*x^n)^p)^2,x, algorithm=""fricas"")","\frac{2 \, e^{2} f^{-2 \, n - 1} n p^{2} x^{2 \, n} \log\left(x\right) \log\left(\frac{e x^{n} + d}{d}\right) + 2 \, e^{2} f^{-2 \, n - 1} p^{2} x^{2 \, n} {\rm Li}_2\left(-\frac{e x^{n} + d}{d} + 1\right) - 2 \, d e f^{-2 \, n - 1} p x^{n} \log\left(c\right) - d^{2} f^{-2 \, n - 1} \log\left(c\right)^{2} + 2 \, {\left(e^{2} n p^{2} - e^{2} n p \log\left(c\right)\right)} f^{-2 \, n - 1} x^{2 \, n} \log\left(x\right) + {\left(e^{2} f^{-2 \, n - 1} p^{2} x^{2 \, n} - d^{2} f^{-2 \, n - 1} p^{2}\right)} \log\left(e x^{n} + d\right)^{2} - 2 \, {\left(d e f^{-2 \, n - 1} p^{2} x^{n} + d^{2} f^{-2 \, n - 1} p \log\left(c\right) + {\left(e^{2} n p^{2} \log\left(x\right) + e^{2} p^{2} - e^{2} p \log\left(c\right)\right)} f^{-2 \, n - 1} x^{2 \, n}\right)} \log\left(e x^{n} + d\right)}{2 \, d^{2} n x^{2 \, n}}"," ",0,"1/2*(2*e^2*f^(-2*n - 1)*n*p^2*x^(2*n)*log(x)*log((e*x^n + d)/d) + 2*e^2*f^(-2*n - 1)*p^2*x^(2*n)*dilog(-(e*x^n + d)/d + 1) - 2*d*e*f^(-2*n - 1)*p*x^n*log(c) - d^2*f^(-2*n - 1)*log(c)^2 + 2*(e^2*n*p^2 - e^2*n*p*log(c))*f^(-2*n - 1)*x^(2*n)*log(x) + (e^2*f^(-2*n - 1)*p^2*x^(2*n) - d^2*f^(-2*n - 1)*p^2)*log(e*x^n + d)^2 - 2*(d*e*f^(-2*n - 1)*p^2*x^n + d^2*f^(-2*n - 1)*p*log(c) + (e^2*n*p^2*log(x) + e^2*p^2 - e^2*p*log(c))*f^(-2*n - 1)*x^(2*n))*log(e*x^n + d))/(d^2*n*x^(2*n))","A",0
169,1,12,0,1.176028," ","integrate(log(1+e*x^n)/x,x, algorithm=""fricas"")","-\frac{{\rm Li}_2\left(-e x^{n}\right)}{n}"," ",0,"-dilog(-e*x^n)/n","A",0
170,1,40,0,0.850835," ","integrate(log(2+e*x^n)/x,x, algorithm=""fricas"")","\frac{n \log\left(e x^{n} + 2\right) \log\left(x\right) - n \log\left(\frac{1}{2} \, e x^{n} + 1\right) \log\left(x\right) - {\rm Li}_2\left(-\frac{1}{2} \, e x^{n}\right)}{n}"," ",0,"(n*log(e*x^n + 2)*log(x) - n*log(1/2*e*x^n + 1)*log(x) - dilog(-1/2*e*x^n))/n","B",0
171,1,41,0,1.161183," ","integrate(log(6+2*e*x^n)/x,x, algorithm=""fricas"")","\frac{n \log\left(2 \, e x^{n} + 6\right) \log\left(x\right) - n \log\left(\frac{1}{3} \, e x^{n} + 1\right) \log\left(x\right) - {\rm Li}_2\left(-\frac{1}{3} \, e x^{n}\right)}{n}"," ",0,"(n*log(2*e*x^n + 6)*log(x) - n*log(1/3*e*x^n + 1)*log(x) - dilog(-1/3*e*x^n))/n","B",0
172,1,54,0,0.766520," ","integrate(log(c*(d+e*x^n))/x,x, algorithm=""fricas"")","\frac{n \log\left(c e x^{n} + c d\right) \log\left(x\right) - n \log\left(x\right) \log\left(\frac{e x^{n} + d}{d}\right) - {\rm Li}_2\left(-\frac{e x^{n} + d}{d} + 1\right)}{n}"," ",0,"(n*log(c*e*x^n + c*d)*log(x) - n*log(x)*log((e*x^n + d)/d) - dilog(-(e*x^n + d)/d + 1))/n","A",0
173,1,60,0,1.107737," ","integrate(log(c*(d+e*x^n)^p)/x,x, algorithm=""fricas"")","\frac{n p \log\left(e x^{n} + d\right) \log\left(x\right) - n p \log\left(x\right) \log\left(\frac{e x^{n} + d}{d}\right) + n \log\left(c\right) \log\left(x\right) - p {\rm Li}_2\left(-\frac{e x^{n} + d}{d} + 1\right)}{n}"," ",0,"(n*p*log(e*x^n + d)*log(x) - n*p*log(x)*log((e*x^n + d)/d) + n*log(c)*log(x) - p*dilog(-(e*x^n + d)/d + 1))/n","A",0
174,0,0,0,1.186501," ","integrate(log(c*(d+e*x^n)^p)^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{n} + d\right)}^{p} c\right)^{2}}{x}, x\right)"," ",0,"integral(log((e*x^n + d)^p*c)^2/x, x)","F",0
175,0,0,0,1.527520," ","integrate(log(c*(d+e*x^n)^p)^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{n} + d\right)}^{p} c\right)^{3}}{x}, x\right)"," ",0,"integral(log((e*x^n + d)^p*c)^3/x, x)","F",0
176,1,269,0,1.022082," ","integrate((e*x+d)^3*log(c*(b*x+a)^p),x, algorithm=""fricas"")","-\frac{3 \, b^{4} e^{3} p x^{4} + 4 \, {\left(4 \, b^{4} d e^{2} - a b^{3} e^{3}\right)} p x^{3} + 6 \, {\left(6 \, b^{4} d^{2} e - 4 \, a b^{3} d e^{2} + a^{2} b^{2} e^{3}\right)} p x^{2} + 12 \, {\left(4 \, b^{4} d^{3} - 6 \, a b^{3} d^{2} e + 4 \, a^{2} b^{2} d e^{2} - a^{3} b e^{3}\right)} p x - 12 \, {\left(b^{4} e^{3} p x^{4} + 4 \, b^{4} d e^{2} p x^{3} + 6 \, b^{4} d^{2} e p x^{2} + 4 \, b^{4} d^{3} p x + {\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)} p\right)} \log\left(b x + a\right) - 12 \, {\left(b^{4} e^{3} x^{4} + 4 \, b^{4} d e^{2} x^{3} + 6 \, b^{4} d^{2} e x^{2} + 4 \, b^{4} d^{3} x\right)} \log\left(c\right)}{48 \, b^{4}}"," ",0,"-1/48*(3*b^4*e^3*p*x^4 + 4*(4*b^4*d*e^2 - a*b^3*e^3)*p*x^3 + 6*(6*b^4*d^2*e - 4*a*b^3*d*e^2 + a^2*b^2*e^3)*p*x^2 + 12*(4*b^4*d^3 - 6*a*b^3*d^2*e + 4*a^2*b^2*d*e^2 - a^3*b*e^3)*p*x - 12*(b^4*e^3*p*x^4 + 4*b^4*d*e^2*p*x^3 + 6*b^4*d^2*e*p*x^2 + 4*b^4*d^3*p*x + (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)*p)*log(b*x + a) - 12*(b^4*e^3*x^4 + 4*b^4*d*e^2*x^3 + 6*b^4*d^2*e*x^2 + 4*b^4*d^3*x)*log(c))/b^4","B",0
177,1,172,0,1.137131," ","integrate((e*x+d)^2*log(c*(b*x+a)^p),x, algorithm=""fricas"")","-\frac{2 \, b^{3} e^{2} p x^{3} + 3 \, {\left(3 \, b^{3} d e - a b^{2} e^{2}\right)} p x^{2} + 6 \, {\left(3 \, b^{3} d^{2} - 3 \, a b^{2} d e + a^{2} b e^{2}\right)} p x - 6 \, {\left(b^{3} e^{2} p x^{3} + 3 \, b^{3} d e p x^{2} + 3 \, b^{3} d^{2} p x + {\left(3 \, a b^{2} d^{2} - 3 \, a^{2} b d e + a^{3} e^{2}\right)} p\right)} \log\left(b x + a\right) - 6 \, {\left(b^{3} e^{2} x^{3} + 3 \, b^{3} d e x^{2} + 3 \, b^{3} d^{2} x\right)} \log\left(c\right)}{18 \, b^{3}}"," ",0,"-1/18*(2*b^3*e^2*p*x^3 + 3*(3*b^3*d*e - a*b^2*e^2)*p*x^2 + 6*(3*b^3*d^2 - 3*a*b^2*d*e + a^2*b*e^2)*p*x - 6*(b^3*e^2*p*x^3 + 3*b^3*d*e*p*x^2 + 3*b^3*d^2*p*x + (3*a*b^2*d^2 - 3*a^2*b*d*e + a^3*e^2)*p)*log(b*x + a) - 6*(b^3*e^2*x^3 + 3*b^3*d*e*x^2 + 3*b^3*d^2*x)*log(c))/b^3","A",0
178,1,91,0,1.047794," ","integrate((e*x+d)*log(c*(b*x+a)^p),x, algorithm=""fricas"")","-\frac{b^{2} e p x^{2} + 2 \, {\left(2 \, b^{2} d - a b e\right)} p x - 2 \, {\left(b^{2} e p x^{2} + 2 \, b^{2} d p x + {\left(2 \, a b d - a^{2} e\right)} p\right)} \log\left(b x + a\right) - 2 \, {\left(b^{2} e x^{2} + 2 \, b^{2} d x\right)} \log\left(c\right)}{4 \, b^{2}}"," ",0,"-1/4*(b^2*e*p*x^2 + 2*(2*b^2*d - a*b*e)*p*x - 2*(b^2*e*p*x^2 + 2*b^2*d*p*x + (2*a*b*d - a^2*e)*p)*log(b*x + a) - 2*(b^2*e*x^2 + 2*b^2*d*x)*log(c))/b^2","A",0
179,1,32,0,1.031575," ","integrate(log(c*(b*x+a)^p),x, algorithm=""fricas"")","-\frac{b p x - b x \log\left(c\right) - {\left(b p x + a p\right)} \log\left(b x + a\right)}{b}"," ",0,"-(b*p*x - b*x*log(c) - (b*p*x + a*p)*log(b*x + a))/b","A",0
180,0,0,0,1.178905," ","integrate(log(c*(b*x+a)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x + a\right)}^{p} c\right)}{e x + d}, x\right)"," ",0,"integral(log((b*x + a)^p*c)/(e*x + d), x)","F",0
181,1,80,0,1.239732," ","integrate(log(c*(b*x+a)^p)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{{\left(b e p x + a e p\right)} \log\left(b x + a\right) - {\left(b e p x + b d p\right)} \log\left(e x + d\right) - {\left(b d - a e\right)} \log\left(c\right)}{b d^{2} e - a d e^{2} + {\left(b d e^{2} - a e^{3}\right)} x}"," ",0,"((b*e*p*x + a*e*p)*log(b*x + a) - (b*e*p*x + b*d*p)*log(e*x + d) - (b*d - a*e)*log(c))/(b*d^2*e - a*d*e^2 + (b*d*e^2 - a*e^3)*x)","A",0
182,1,236,0,1.019635," ","integrate(log(c*(b*x+a)^p)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{{\left(b^{2} d e - a b e^{2}\right)} p x + {\left(b^{2} d^{2} - a b d e\right)} p + {\left(b^{2} e^{2} p x^{2} + 2 \, b^{2} d e p x + {\left(2 \, a b d e - a^{2} e^{2}\right)} p\right)} \log\left(b x + a\right) - {\left(b^{2} e^{2} p x^{2} + 2 \, b^{2} d e p x + b^{2} d^{2} p\right)} \log\left(e x + d\right) - {\left(b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}\right)} \log\left(c\right)}{2 \, {\left(b^{2} d^{4} e - 2 \, a b d^{3} e^{2} + a^{2} d^{2} e^{3} + {\left(b^{2} d^{2} e^{3} - 2 \, a b d e^{4} + a^{2} e^{5}\right)} x^{2} + 2 \, {\left(b^{2} d^{3} e^{2} - 2 \, a b d^{2} e^{3} + a^{2} d e^{4}\right)} x\right)}}"," ",0,"1/2*((b^2*d*e - a*b*e^2)*p*x + (b^2*d^2 - a*b*d*e)*p + (b^2*e^2*p*x^2 + 2*b^2*d*e*p*x + (2*a*b*d*e - a^2*e^2)*p)*log(b*x + a) - (b^2*e^2*p*x^2 + 2*b^2*d*e*p*x + b^2*d^2*p)*log(e*x + d) - (b^2*d^2 - 2*a*b*d*e + a^2*e^2)*log(c))/(b^2*d^4*e - 2*a*b*d^3*e^2 + a^2*d^2*e^3 + (b^2*d^2*e^3 - 2*a*b*d*e^4 + a^2*e^5)*x^2 + 2*(b^2*d^3*e^2 - 2*a*b*d^2*e^3 + a^2*d*e^4)*x)","B",0
183,1,443,0,1.087674," ","integrate(log(c*(b*x+a)^p)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{2 \, {\left(b^{3} d e^{2} - a b^{2} e^{3}\right)} p x^{2} + {\left(5 \, b^{3} d^{2} e - 6 \, a b^{2} d e^{2} + a^{2} b e^{3}\right)} p x + {\left(3 \, b^{3} d^{3} - 4 \, a b^{2} d^{2} e + a^{2} b d e^{2}\right)} p + 2 \, {\left(b^{3} e^{3} p x^{3} + 3 \, b^{3} d e^{2} p x^{2} + 3 \, b^{3} d^{2} e p x + {\left(3 \, a b^{2} d^{2} e - 3 \, a^{2} b d e^{2} + a^{3} e^{3}\right)} p\right)} \log\left(b x + a\right) - 2 \, {\left(b^{3} e^{3} p x^{3} + 3 \, b^{3} d e^{2} p x^{2} + 3 \, b^{3} d^{2} e p x + b^{3} d^{3} p\right)} \log\left(e x + d\right) - 2 \, {\left(b^{3} d^{3} - 3 \, a b^{2} d^{2} e + 3 \, a^{2} b d e^{2} - a^{3} e^{3}\right)} \log\left(c\right)}{6 \, {\left(b^{3} d^{6} e - 3 \, a b^{2} d^{5} e^{2} + 3 \, a^{2} b d^{4} e^{3} - a^{3} d^{3} e^{4} + {\left(b^{3} d^{3} e^{4} - 3 \, a b^{2} d^{2} e^{5} + 3 \, a^{2} b d e^{6} - a^{3} e^{7}\right)} x^{3} + 3 \, {\left(b^{3} d^{4} e^{3} - 3 \, a b^{2} d^{3} e^{4} + 3 \, a^{2} b d^{2} e^{5} - a^{3} d e^{6}\right)} x^{2} + 3 \, {\left(b^{3} d^{5} e^{2} - 3 \, a b^{2} d^{4} e^{3} + 3 \, a^{2} b d^{3} e^{4} - a^{3} d^{2} e^{5}\right)} x\right)}}"," ",0,"1/6*(2*(b^3*d*e^2 - a*b^2*e^3)*p*x^2 + (5*b^3*d^2*e - 6*a*b^2*d*e^2 + a^2*b*e^3)*p*x + (3*b^3*d^3 - 4*a*b^2*d^2*e + a^2*b*d*e^2)*p + 2*(b^3*e^3*p*x^3 + 3*b^3*d*e^2*p*x^2 + 3*b^3*d^2*e*p*x + (3*a*b^2*d^2*e - 3*a^2*b*d*e^2 + a^3*e^3)*p)*log(b*x + a) - 2*(b^3*e^3*p*x^3 + 3*b^3*d*e^2*p*x^2 + 3*b^3*d^2*e*p*x + b^3*d^3*p)*log(e*x + d) - 2*(b^3*d^3 - 3*a*b^2*d^2*e + 3*a^2*b*d*e^2 - a^3*e^3)*log(c))/(b^3*d^6*e - 3*a*b^2*d^5*e^2 + 3*a^2*b*d^4*e^3 - a^3*d^3*e^4 + (b^3*d^3*e^4 - 3*a*b^2*d^2*e^5 + 3*a^2*b*d*e^6 - a^3*e^7)*x^3 + 3*(b^3*d^4*e^3 - 3*a*b^2*d^3*e^4 + 3*a^2*b*d^2*e^5 - a^3*d*e^6)*x^2 + 3*(b^3*d^5*e^2 - 3*a*b^2*d^4*e^3 + 3*a^2*b*d^3*e^4 - a^3*d^2*e^5)*x)","B",0
184,1,498,0,0.941846," ","integrate((e*x+d)^3*log(c*(b*x^2+a)^p),x, algorithm=""fricas"")","\left[-\frac{3 \, b^{2} e^{3} p x^{4} + 16 \, b^{2} d e^{2} p x^{3} + 6 \, {\left(6 \, b^{2} d^{2} e - a b e^{3}\right)} p x^{2} - 24 \, {\left(b^{2} d^{3} - a b d e^{2}\right)} p \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + 48 \, {\left(b^{2} d^{3} - a b d e^{2}\right)} p x - 6 \, {\left(b^{2} e^{3} p x^{4} + 4 \, b^{2} d e^{2} p x^{3} + 6 \, b^{2} d^{2} e p x^{2} + 4 \, b^{2} d^{3} p x + {\left(6 \, a b d^{2} e - a^{2} e^{3}\right)} p\right)} \log\left(b x^{2} + a\right) - 6 \, {\left(b^{2} e^{3} x^{4} + 4 \, b^{2} d e^{2} x^{3} + 6 \, b^{2} d^{2} e x^{2} + 4 \, b^{2} d^{3} x\right)} \log\left(c\right)}{24 \, b^{2}}, -\frac{3 \, b^{2} e^{3} p x^{4} + 16 \, b^{2} d e^{2} p x^{3} + 6 \, {\left(6 \, b^{2} d^{2} e - a b e^{3}\right)} p x^{2} - 48 \, {\left(b^{2} d^{3} - a b d e^{2}\right)} p \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) + 48 \, {\left(b^{2} d^{3} - a b d e^{2}\right)} p x - 6 \, {\left(b^{2} e^{3} p x^{4} + 4 \, b^{2} d e^{2} p x^{3} + 6 \, b^{2} d^{2} e p x^{2} + 4 \, b^{2} d^{3} p x + {\left(6 \, a b d^{2} e - a^{2} e^{3}\right)} p\right)} \log\left(b x^{2} + a\right) - 6 \, {\left(b^{2} e^{3} x^{4} + 4 \, b^{2} d e^{2} x^{3} + 6 \, b^{2} d^{2} e x^{2} + 4 \, b^{2} d^{3} x\right)} \log\left(c\right)}{24 \, b^{2}}\right]"," ",0,"[-1/24*(3*b^2*e^3*p*x^4 + 16*b^2*d*e^2*p*x^3 + 6*(6*b^2*d^2*e - a*b*e^3)*p*x^2 - 24*(b^2*d^3 - a*b*d*e^2)*p*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + 48*(b^2*d^3 - a*b*d*e^2)*p*x - 6*(b^2*e^3*p*x^4 + 4*b^2*d*e^2*p*x^3 + 6*b^2*d^2*e*p*x^2 + 4*b^2*d^3*p*x + (6*a*b*d^2*e - a^2*e^3)*p)*log(b*x^2 + a) - 6*(b^2*e^3*x^4 + 4*b^2*d*e^2*x^3 + 6*b^2*d^2*e*x^2 + 4*b^2*d^3*x)*log(c))/b^2, -1/24*(3*b^2*e^3*p*x^4 + 16*b^2*d*e^2*p*x^3 + 6*(6*b^2*d^2*e - a*b*e^3)*p*x^2 - 48*(b^2*d^3 - a*b*d*e^2)*p*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) + 48*(b^2*d^3 - a*b*d*e^2)*p*x - 6*(b^2*e^3*p*x^4 + 4*b^2*d*e^2*p*x^3 + 6*b^2*d^2*e*p*x^2 + 4*b^2*d^3*p*x + (6*a*b*d^2*e - a^2*e^3)*p)*log(b*x^2 + a) - 6*(b^2*e^3*x^4 + 4*b^2*d*e^2*x^3 + 6*b^2*d^2*e*x^2 + 4*b^2*d^3*x)*log(c))/b^2]","A",0
185,1,320,0,0.952452," ","integrate((e*x+d)^2*log(c*(b*x^2+a)^p),x, algorithm=""fricas"")","\left[-\frac{2 \, b e^{2} p x^{3} + 9 \, b d e p x^{2} - 3 \, {\left(3 \, b d^{2} - a e^{2}\right)} p \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + 6 \, {\left(3 \, b d^{2} - a e^{2}\right)} p x - 3 \, {\left(b e^{2} p x^{3} + 3 \, b d e p x^{2} + 3 \, b d^{2} p x + 3 \, a d e p\right)} \log\left(b x^{2} + a\right) - 3 \, {\left(b e^{2} x^{3} + 3 \, b d e x^{2} + 3 \, b d^{2} x\right)} \log\left(c\right)}{9 \, b}, -\frac{2 \, b e^{2} p x^{3} + 9 \, b d e p x^{2} - 6 \, {\left(3 \, b d^{2} - a e^{2}\right)} p \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) + 6 \, {\left(3 \, b d^{2} - a e^{2}\right)} p x - 3 \, {\left(b e^{2} p x^{3} + 3 \, b d e p x^{2} + 3 \, b d^{2} p x + 3 \, a d e p\right)} \log\left(b x^{2} + a\right) - 3 \, {\left(b e^{2} x^{3} + 3 \, b d e x^{2} + 3 \, b d^{2} x\right)} \log\left(c\right)}{9 \, b}\right]"," ",0,"[-1/9*(2*b*e^2*p*x^3 + 9*b*d*e*p*x^2 - 3*(3*b*d^2 - a*e^2)*p*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + 6*(3*b*d^2 - a*e^2)*p*x - 3*(b*e^2*p*x^3 + 3*b*d*e*p*x^2 + 3*b*d^2*p*x + 3*a*d*e*p)*log(b*x^2 + a) - 3*(b*e^2*x^3 + 3*b*d*e*x^2 + 3*b*d^2*x)*log(c))/b, -1/9*(2*b*e^2*p*x^3 + 9*b*d*e*p*x^2 - 6*(3*b*d^2 - a*e^2)*p*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) + 6*(3*b*d^2 - a*e^2)*p*x - 3*(b*e^2*p*x^3 + 3*b*d*e*p*x^2 + 3*b*d^2*p*x + 3*a*d*e*p)*log(b*x^2 + a) - 3*(b*e^2*x^3 + 3*b*d*e*x^2 + 3*b*d^2*x)*log(c))/b]","A",0
186,1,198,0,0.947957," ","integrate((e*x+d)*log(c*(b*x^2+a)^p),x, algorithm=""fricas"")","\left[-\frac{b e p x^{2} - 2 \, b d p \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) + 4 \, b d p x - {\left(b e p x^{2} + 2 \, b d p x + a e p\right)} \log\left(b x^{2} + a\right) - {\left(b e x^{2} + 2 \, b d x\right)} \log\left(c\right)}{2 \, b}, -\frac{b e p x^{2} - 4 \, b d p \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) + 4 \, b d p x - {\left(b e p x^{2} + 2 \, b d p x + a e p\right)} \log\left(b x^{2} + a\right) - {\left(b e x^{2} + 2 \, b d x\right)} \log\left(c\right)}{2 \, b}\right]"," ",0,"[-1/2*(b*e*p*x^2 - 2*b*d*p*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) + 4*b*d*p*x - (b*e*p*x^2 + 2*b*d*p*x + a*e*p)*log(b*x^2 + a) - (b*e*x^2 + 2*b*d*x)*log(c))/b, -1/2*(b*e*p*x^2 - 4*b*d*p*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) + 4*b*d*p*x - (b*e*p*x^2 + 2*b*d*p*x + a*e*p)*log(b*x^2 + a) - (b*e*x^2 + 2*b*d*x)*log(c))/b]","A",0
187,1,107,0,0.763332," ","integrate(log(c*(b*x^2+a)^p),x, algorithm=""fricas"")","\left[p x \log\left(b x^{2} + a\right) + p \sqrt{-\frac{a}{b}} \log\left(\frac{b x^{2} + 2 \, b x \sqrt{-\frac{a}{b}} - a}{b x^{2} + a}\right) - 2 \, p x + x \log\left(c\right), p x \log\left(b x^{2} + a\right) + 2 \, p \sqrt{\frac{a}{b}} \arctan\left(\frac{b x \sqrt{\frac{a}{b}}}{a}\right) - 2 \, p x + x \log\left(c\right)\right]"," ",0,"[p*x*log(b*x^2 + a) + p*sqrt(-a/b)*log((b*x^2 + 2*b*x*sqrt(-a/b) - a)/(b*x^2 + a)) - 2*p*x + x*log(c), p*x*log(b*x^2 + a) + 2*p*sqrt(a/b)*arctan(b*x*sqrt(a/b)/a) - 2*p*x + x*log(c)]","A",0
188,0,0,0,0.751484," ","integrate(log(c*(b*x^2+a)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)}{e x + d}, x\right)"," ",0,"integral(log((b*x^2 + a)^p*c)/(e*x + d), x)","F",0
189,1,261,0,1.369004," ","integrate(log(c*(b*x^2+a)^p)/(e*x+d)^2,x, algorithm=""fricas"")","\left[\frac{{\left(e^{2} p x + d e p\right)} \sqrt{-a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + {\left(b d e p x - a e^{2} p\right)} \log\left(b x^{2} + a\right) - 2 \, {\left(b d e p x + b d^{2} p\right)} \log\left(e x + d\right) - {\left(b d^{2} + a e^{2}\right)} \log\left(c\right)}{b d^{3} e + a d e^{3} + {\left(b d^{2} e^{2} + a e^{4}\right)} x}, \frac{2 \, {\left(e^{2} p x + d e p\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + {\left(b d e p x - a e^{2} p\right)} \log\left(b x^{2} + a\right) - 2 \, {\left(b d e p x + b d^{2} p\right)} \log\left(e x + d\right) - {\left(b d^{2} + a e^{2}\right)} \log\left(c\right)}{b d^{3} e + a d e^{3} + {\left(b d^{2} e^{2} + a e^{4}\right)} x}\right]"," ",0,"[((e^2*p*x + d*e*p)*sqrt(-a*b)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + (b*d*e*p*x - a*e^2*p)*log(b*x^2 + a) - 2*(b*d*e*p*x + b*d^2*p)*log(e*x + d) - (b*d^2 + a*e^2)*log(c))/(b*d^3*e + a*d*e^3 + (b*d^2*e^2 + a*e^4)*x), (2*(e^2*p*x + d*e*p)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + (b*d*e*p*x - a*e^2*p)*log(b*x^2 + a) - 2*(b*d*e*p*x + b*d^2*p)*log(e*x + d) - (b*d^2 + a*e^2)*log(c))/(b*d^3*e + a*d*e^3 + (b*d^2*e^2 + a*e^4)*x)]","A",0
190,1,744,0,1.464839," ","integrate(log(c*(b*x^2+a)^p)/(e*x+d)^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b^{2} d^{3} e + a b d e^{3}\right)} p x + 2 \, {\left(b d e^{3} p x^{2} + 2 \, b d^{2} e^{2} p x + b d^{3} e p\right)} \sqrt{-a b} \log\left(\frac{b x^{2} + 2 \, \sqrt{-a b} x - a}{b x^{2} + a}\right) + 2 \, {\left(b^{2} d^{4} + a b d^{2} e^{2}\right)} p + {\left({\left(b^{2} d^{2} e^{2} - a b e^{4}\right)} p x^{2} + 2 \, {\left(b^{2} d^{3} e - a b d e^{3}\right)} p x - {\left(3 \, a b d^{2} e^{2} + a^{2} e^{4}\right)} p\right)} \log\left(b x^{2} + a\right) - 2 \, {\left({\left(b^{2} d^{2} e^{2} - a b e^{4}\right)} p x^{2} + 2 \, {\left(b^{2} d^{3} e - a b d e^{3}\right)} p x + {\left(b^{2} d^{4} - a b d^{2} e^{2}\right)} p\right)} \log\left(e x + d\right) - {\left(b^{2} d^{4} + 2 \, a b d^{2} e^{2} + a^{2} e^{4}\right)} \log\left(c\right)}{2 \, {\left(b^{2} d^{6} e + 2 \, a b d^{4} e^{3} + a^{2} d^{2} e^{5} + {\left(b^{2} d^{4} e^{3} + 2 \, a b d^{2} e^{5} + a^{2} e^{7}\right)} x^{2} + 2 \, {\left(b^{2} d^{5} e^{2} + 2 \, a b d^{3} e^{4} + a^{2} d e^{6}\right)} x\right)}}, \frac{2 \, {\left(b^{2} d^{3} e + a b d e^{3}\right)} p x + 4 \, {\left(b d e^{3} p x^{2} + 2 \, b d^{2} e^{2} p x + b d^{3} e p\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} x}{a}\right) + 2 \, {\left(b^{2} d^{4} + a b d^{2} e^{2}\right)} p + {\left({\left(b^{2} d^{2} e^{2} - a b e^{4}\right)} p x^{2} + 2 \, {\left(b^{2} d^{3} e - a b d e^{3}\right)} p x - {\left(3 \, a b d^{2} e^{2} + a^{2} e^{4}\right)} p\right)} \log\left(b x^{2} + a\right) - 2 \, {\left({\left(b^{2} d^{2} e^{2} - a b e^{4}\right)} p x^{2} + 2 \, {\left(b^{2} d^{3} e - a b d e^{3}\right)} p x + {\left(b^{2} d^{4} - a b d^{2} e^{2}\right)} p\right)} \log\left(e x + d\right) - {\left(b^{2} d^{4} + 2 \, a b d^{2} e^{2} + a^{2} e^{4}\right)} \log\left(c\right)}{2 \, {\left(b^{2} d^{6} e + 2 \, a b d^{4} e^{3} + a^{2} d^{2} e^{5} + {\left(b^{2} d^{4} e^{3} + 2 \, a b d^{2} e^{5} + a^{2} e^{7}\right)} x^{2} + 2 \, {\left(b^{2} d^{5} e^{2} + 2 \, a b d^{3} e^{4} + a^{2} d e^{6}\right)} x\right)}}\right]"," ",0,"[1/2*(2*(b^2*d^3*e + a*b*d*e^3)*p*x + 2*(b*d*e^3*p*x^2 + 2*b*d^2*e^2*p*x + b*d^3*e*p)*sqrt(-a*b)*log((b*x^2 + 2*sqrt(-a*b)*x - a)/(b*x^2 + a)) + 2*(b^2*d^4 + a*b*d^2*e^2)*p + ((b^2*d^2*e^2 - a*b*e^4)*p*x^2 + 2*(b^2*d^3*e - a*b*d*e^3)*p*x - (3*a*b*d^2*e^2 + a^2*e^4)*p)*log(b*x^2 + a) - 2*((b^2*d^2*e^2 - a*b*e^4)*p*x^2 + 2*(b^2*d^3*e - a*b*d*e^3)*p*x + (b^2*d^4 - a*b*d^2*e^2)*p)*log(e*x + d) - (b^2*d^4 + 2*a*b*d^2*e^2 + a^2*e^4)*log(c))/(b^2*d^6*e + 2*a*b*d^4*e^3 + a^2*d^2*e^5 + (b^2*d^4*e^3 + 2*a*b*d^2*e^5 + a^2*e^7)*x^2 + 2*(b^2*d^5*e^2 + 2*a*b*d^3*e^4 + a^2*d*e^6)*x), 1/2*(2*(b^2*d^3*e + a*b*d*e^3)*p*x + 4*(b*d*e^3*p*x^2 + 2*b*d^2*e^2*p*x + b*d^3*e*p)*sqrt(a*b)*arctan(sqrt(a*b)*x/a) + 2*(b^2*d^4 + a*b*d^2*e^2)*p + ((b^2*d^2*e^2 - a*b*e^4)*p*x^2 + 2*(b^2*d^3*e - a*b*d*e^3)*p*x - (3*a*b*d^2*e^2 + a^2*e^4)*p)*log(b*x^2 + a) - 2*((b^2*d^2*e^2 - a*b*e^4)*p*x^2 + 2*(b^2*d^3*e - a*b*d*e^3)*p*x + (b^2*d^4 - a*b*d^2*e^2)*p)*log(e*x + d) - (b^2*d^4 + 2*a*b*d^2*e^2 + a^2*e^4)*log(c))/(b^2*d^6*e + 2*a*b*d^4*e^3 + a^2*d^2*e^5 + (b^2*d^4*e^3 + 2*a*b*d^2*e^5 + a^2*e^7)*x^2 + 2*(b^2*d^5*e^2 + 2*a*b*d^3*e^4 + a^2*d*e^6)*x)]","B",0
191,1,8840,0,31.854298," ","integrate((e*x+d)^3*log(c*(b*x^3+a)^p),x, algorithm=""fricas"")","-\frac{3 \, b e^{3} p x^{4} + 16 \, b d e^{2} p x^{3} + 36 \, b d^{2} e p x^{2} + 12 \, {\left(4 \, b d^{3} - a e^{3}\right)} p x - 2 \, {\left(\frac{8 \, a d e^{2} p}{b} - \frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{8 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}} - \frac{12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} b \log\left(-\frac{3}{2} \, {\left(\frac{8 \, a d e^{2} p}{b} - \frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{8 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}} - \frac{12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} b^{3} d^{2} e - {\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} p^{2} x - \frac{1}{2} \, {\left(16 \, b^{3} d^{6} - 56 \, a b^{2} d^{3} e^{3} + a^{2} b e^{6}\right)} {\left(\frac{8 \, a d e^{2} p}{b} - \frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{8 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}} - \frac{12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} p - 4 \, {\left(56 \, a b^{2} d^{7} e^{2} + 14 \, a^{2} b d^{4} e^{5} - a^{3} d e^{8}\right)} p^{2}\right) - {\left(24 \, a d e^{2} p + 2 \, \sqrt{\frac{3}{2}} \sqrt{\frac{1}{2}} b \sqrt{\frac{16 \, {\left(\frac{8 \, a d e^{2} p}{b} - \frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{8 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}} - \frac{12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} a b d e^{2} p - {\left(\frac{8 \, a d e^{2} p}{b} - \frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{8 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}} - \frac{12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} b^{2} - 32 \, {\left(12 \, a b d^{5} e - a^{2} d^{2} e^{4}\right)} p^{2}}{b^{2}}} - {\left(\frac{8 \, a d e^{2} p}{b} - \frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{8 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}} - \frac{12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} b\right)} \log\left(\frac{3}{4} \, {\left(\frac{8 \, a d e^{2} p}{b} - \frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{8 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}} - \frac{12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} b^{3} d^{2} e - {\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} p^{2} x + \frac{1}{4} \, {\left(16 \, b^{3} d^{6} - 56 \, a b^{2} d^{3} e^{3} + a^{2} b e^{6}\right)} {\left(\frac{8 \, a d e^{2} p}{b} - \frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{8 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}} - \frac{12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} p + 2 \, {\left(56 \, a b^{2} d^{7} e^{2} + 14 \, a^{2} b d^{4} e^{5} - a^{3} d e^{8}\right)} p^{2} + \frac{1}{2} \, \sqrt{\frac{3}{2}} \sqrt{\frac{1}{2}} {\left(3 \, {\left(\frac{8 \, a d e^{2} p}{b} - \frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{8 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}} - \frac{12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} b^{3} d^{2} e - {\left(16 \, b^{3} d^{6} + 16 \, a b^{2} d^{3} e^{3} + a^{2} b e^{6}\right)} p\right)} \sqrt{\frac{16 \, {\left(\frac{8 \, a d e^{2} p}{b} - \frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{8 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}} - \frac{12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} a b d e^{2} p - {\left(\frac{8 \, a d e^{2} p}{b} - \frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{8 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}} - \frac{12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} b^{2} - 32 \, {\left(12 \, a b d^{5} e - a^{2} d^{2} e^{4}\right)} p^{2}}{b^{2}}}\right) - {\left(24 \, a d e^{2} p - 2 \, \sqrt{\frac{3}{2}} \sqrt{\frac{1}{2}} b \sqrt{\frac{16 \, {\left(\frac{8 \, a d e^{2} p}{b} - \frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{8 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}} - \frac{12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} a b d e^{2} p - {\left(\frac{8 \, a d e^{2} p}{b} - \frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{8 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}} - \frac{12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} b^{2} - 32 \, {\left(12 \, a b d^{5} e - a^{2} d^{2} e^{4}\right)} p^{2}}{b^{2}}} - {\left(\frac{8 \, a d e^{2} p}{b} - \frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{8 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}} - \frac{12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} b\right)} \log\left(\frac{3}{4} \, {\left(\frac{8 \, a d e^{2} p}{b} - \frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{8 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}} - \frac{12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} b^{3} d^{2} e - {\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} p^{2} x + \frac{1}{4} \, {\left(16 \, b^{3} d^{6} - 56 \, a b^{2} d^{3} e^{3} + a^{2} b e^{6}\right)} {\left(\frac{8 \, a d e^{2} p}{b} - \frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{8 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}} - \frac{12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} p + 2 \, {\left(56 \, a b^{2} d^{7} e^{2} + 14 \, a^{2} b d^{4} e^{5} - a^{3} d e^{8}\right)} p^{2} - \frac{1}{2} \, \sqrt{\frac{3}{2}} \sqrt{\frac{1}{2}} {\left(3 \, {\left(\frac{8 \, a d e^{2} p}{b} - \frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{8 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}} - \frac{12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} b^{3} d^{2} e - {\left(16 \, b^{3} d^{6} + 16 \, a b^{2} d^{3} e^{3} + a^{2} b e^{6}\right)} p\right)} \sqrt{\frac{16 \, {\left(\frac{8 \, a d e^{2} p}{b} - \frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{8 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}} - \frac{12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} a b d e^{2} p - {\left(\frac{8 \, a d e^{2} p}{b} - \frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{8 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}} - \frac{12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{128 \, a^{3} d^{3} e^{6} p^{3}}{b^{3}} - \frac{24 \, {\left(12 \, a b d^{5} e p^{2} + 5 \, a^{2} d^{2} e^{4} p^{2}\right)} a d e^{2} p}{b^{3}} - \frac{{\left(64 \, b^{3} d^{9} + 168 \, a b^{2} d^{6} e^{3} + 12 \, a^{2} b d^{3} e^{6} - a^{3} e^{9}\right)} a p^{3}}{b^{4}} + \frac{64 \, a b^{3} d^{9} p^{3} + 24 \, a^{2} b^{2} d^{6} e^{3} p^{3} + 4 \, a^{3} b d^{3} e^{6} p^{3} - a^{4} e^{9} p^{3}}{b^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} b^{2} - 32 \, {\left(12 \, a b d^{5} e - a^{2} d^{2} e^{4}\right)} p^{2}}{b^{2}}}\right) - 4 \, {\left(b e^{3} p x^{4} + 4 \, b d e^{2} p x^{3} + 6 \, b d^{2} e p x^{2} + 4 \, b d^{3} p x\right)} \log\left(b x^{3} + a\right) - 4 \, {\left(b e^{3} x^{4} + 4 \, b d e^{2} x^{3} + 6 \, b d^{2} e x^{2} + 4 \, b d^{3} x\right)} \log\left(c\right)}{16 \, b}"," ",0,"-1/16*(3*b*e^3*p*x^4 + 16*b*d*e^2*p*x^3 + 36*b*d^2*e*p*x^2 + 12*(4*b*d^3 - a*e^3)*p*x - 2*(8*a*d*e^2*p/b - 4*(1/2)^(2/3)*(8*a^2*d^2*e^4*p^2/b^2 - (12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3) - (1/2)^(1/3)*(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3)*(I*sqrt(3) + 1))*b*log(-3/2*(8*a*d*e^2*p/b - 4*(1/2)^(2/3)*(8*a^2*d^2*e^4*p^2/b^2 - (12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3) - (1/2)^(1/3)*(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3)*(I*sqrt(3) + 1))^2*b^3*d^2*e - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*p^2*x - 1/2*(16*b^3*d^6 - 56*a*b^2*d^3*e^3 + a^2*b*e^6)*(8*a*d*e^2*p/b - 4*(1/2)^(2/3)*(8*a^2*d^2*e^4*p^2/b^2 - (12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3) - (1/2)^(1/3)*(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3)*(I*sqrt(3) + 1))*p - 4*(56*a*b^2*d^7*e^2 + 14*a^2*b*d^4*e^5 - a^3*d*e^8)*p^2) - (24*a*d*e^2*p + 2*sqrt(3/2)*sqrt(1/2)*b*sqrt((16*(8*a*d*e^2*p/b - 4*(1/2)^(2/3)*(8*a^2*d^2*e^4*p^2/b^2 - (12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3) - (1/2)^(1/3)*(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3)*(I*sqrt(3) + 1))*a*b*d*e^2*p - (8*a*d*e^2*p/b - 4*(1/2)^(2/3)*(8*a^2*d^2*e^4*p^2/b^2 - (12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3) - (1/2)^(1/3)*(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3)*(I*sqrt(3) + 1))^2*b^2 - 32*(12*a*b*d^5*e - a^2*d^2*e^4)*p^2)/b^2) - (8*a*d*e^2*p/b - 4*(1/2)^(2/3)*(8*a^2*d^2*e^4*p^2/b^2 - (12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3) - (1/2)^(1/3)*(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3)*(I*sqrt(3) + 1))*b)*log(3/4*(8*a*d*e^2*p/b - 4*(1/2)^(2/3)*(8*a^2*d^2*e^4*p^2/b^2 - (12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3) - (1/2)^(1/3)*(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3)*(I*sqrt(3) + 1))^2*b^3*d^2*e - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*p^2*x + 1/4*(16*b^3*d^6 - 56*a*b^2*d^3*e^3 + a^2*b*e^6)*(8*a*d*e^2*p/b - 4*(1/2)^(2/3)*(8*a^2*d^2*e^4*p^2/b^2 - (12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3) - (1/2)^(1/3)*(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3)*(I*sqrt(3) + 1))*p + 2*(56*a*b^2*d^7*e^2 + 14*a^2*b*d^4*e^5 - a^3*d*e^8)*p^2 + 1/2*sqrt(3/2)*sqrt(1/2)*(3*(8*a*d*e^2*p/b - 4*(1/2)^(2/3)*(8*a^2*d^2*e^4*p^2/b^2 - (12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3) - (1/2)^(1/3)*(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3)*(I*sqrt(3) + 1))*b^3*d^2*e - (16*b^3*d^6 + 16*a*b^2*d^3*e^3 + a^2*b*e^6)*p)*sqrt((16*(8*a*d*e^2*p/b - 4*(1/2)^(2/3)*(8*a^2*d^2*e^4*p^2/b^2 - (12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3) - (1/2)^(1/3)*(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3)*(I*sqrt(3) + 1))*a*b*d*e^2*p - (8*a*d*e^2*p/b - 4*(1/2)^(2/3)*(8*a^2*d^2*e^4*p^2/b^2 - (12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3) - (1/2)^(1/3)*(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3)*(I*sqrt(3) + 1))^2*b^2 - 32*(12*a*b*d^5*e - a^2*d^2*e^4)*p^2)/b^2)) - (24*a*d*e^2*p - 2*sqrt(3/2)*sqrt(1/2)*b*sqrt((16*(8*a*d*e^2*p/b - 4*(1/2)^(2/3)*(8*a^2*d^2*e^4*p^2/b^2 - (12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3) - (1/2)^(1/3)*(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3)*(I*sqrt(3) + 1))*a*b*d*e^2*p - (8*a*d*e^2*p/b - 4*(1/2)^(2/3)*(8*a^2*d^2*e^4*p^2/b^2 - (12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3) - (1/2)^(1/3)*(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3)*(I*sqrt(3) + 1))^2*b^2 - 32*(12*a*b*d^5*e - a^2*d^2*e^4)*p^2)/b^2) - (8*a*d*e^2*p/b - 4*(1/2)^(2/3)*(8*a^2*d^2*e^4*p^2/b^2 - (12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3) - (1/2)^(1/3)*(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3)*(I*sqrt(3) + 1))*b)*log(3/4*(8*a*d*e^2*p/b - 4*(1/2)^(2/3)*(8*a^2*d^2*e^4*p^2/b^2 - (12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3) - (1/2)^(1/3)*(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3)*(I*sqrt(3) + 1))^2*b^3*d^2*e - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*p^2*x + 1/4*(16*b^3*d^6 - 56*a*b^2*d^3*e^3 + a^2*b*e^6)*(8*a*d*e^2*p/b - 4*(1/2)^(2/3)*(8*a^2*d^2*e^4*p^2/b^2 - (12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3) - (1/2)^(1/3)*(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3)*(I*sqrt(3) + 1))*p + 2*(56*a*b^2*d^7*e^2 + 14*a^2*b*d^4*e^5 - a^3*d*e^8)*p^2 - 1/2*sqrt(3/2)*sqrt(1/2)*(3*(8*a*d*e^2*p/b - 4*(1/2)^(2/3)*(8*a^2*d^2*e^4*p^2/b^2 - (12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3) - (1/2)^(1/3)*(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3)*(I*sqrt(3) + 1))*b^3*d^2*e - (16*b^3*d^6 + 16*a*b^2*d^3*e^3 + a^2*b*e^6)*p)*sqrt((16*(8*a*d*e^2*p/b - 4*(1/2)^(2/3)*(8*a^2*d^2*e^4*p^2/b^2 - (12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3) - (1/2)^(1/3)*(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3)*(I*sqrt(3) + 1))*a*b*d*e^2*p - (8*a*d*e^2*p/b - 4*(1/2)^(2/3)*(8*a^2*d^2*e^4*p^2/b^2 - (12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3) - (1/2)^(1/3)*(128*a^3*d^3*e^6*p^3/b^3 - 24*(12*a*b*d^5*e*p^2 + 5*a^2*d^2*e^4*p^2)*a*d*e^2*p/b^3 - (64*b^3*d^9 + 168*a*b^2*d^6*e^3 + 12*a^2*b*d^3*e^6 - a^3*e^9)*a*p^3/b^4 + (64*a*b^3*d^9*p^3 + 24*a^2*b^2*d^6*e^3*p^3 + 4*a^3*b*d^3*e^6*p^3 - a^4*e^9*p^3)/b^4)^(1/3)*(I*sqrt(3) + 1))^2*b^2 - 32*(12*a*b*d^5*e - a^2*d^2*e^4)*p^2)/b^2)) - 4*(b*e^3*p*x^4 + 4*b*d*e^2*p*x^3 + 6*b*d^2*e*p*x^2 + 4*b*d^3*p*x)*log(b*x^3 + a) - 4*(b*e^3*x^4 + 4*b*d*e^2*x^3 + 6*b*d^2*e*x^2 + 4*b*d^3*x)*log(c))/b","C",0
192,1,5799,0,7.626635," ","integrate((e*x+d)^2*log(c*(b*x^3+a)^p),x, algorithm=""fricas"")","-\frac{4 \, b e^{2} p x^{3} + 18 \, b d e p x^{2} + 36 \, b d^{2} p x - 2 \, {\left(\frac{2 \, a e^{2} p}{b} - \frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{a^{2} e^{4} p^{2}}{b^{2}} - \frac{9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} b \log\left(\frac{1}{4} \, {\left(\frac{2 \, a e^{2} p}{b} - \frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{a^{2} e^{4} p^{2}}{b^{2}} - \frac{9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} b^{2} e + 9 \, {\left(b^{2} d^{5} + a b d^{2} e^{3}\right)} p^{2} x + \frac{1}{2} \, {\left(3 \, b^{2} d^{3} - 2 \, a b e^{3}\right)} {\left(\frac{2 \, a e^{2} p}{b} - \frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{a^{2} e^{4} p^{2}}{b^{2}} - \frac{9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} p + {\left(15 \, a b d^{3} e^{2} + a^{2} e^{5}\right)} p^{2}\right) - {\left(6 \, a e^{2} p - {\left(\frac{2 \, a e^{2} p}{b} - \frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{a^{2} e^{4} p^{2}}{b^{2}} - \frac{9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} b - 3 \, \sqrt{\frac{1}{3}} b \sqrt{\frac{4 \, {\left(\frac{2 \, a e^{2} p}{b} - \frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{a^{2} e^{4} p^{2}}{b^{2}} - \frac{9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} a b e^{2} p - {\left(\frac{2 \, a e^{2} p}{b} - \frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{a^{2} e^{4} p^{2}}{b^{2}} - \frac{9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} b^{2} - 4 \, {\left(36 \, a b d^{3} e + a^{2} e^{4}\right)} p^{2}}{b^{2}}}\right)} \log\left(-\frac{1}{4} \, {\left(\frac{2 \, a e^{2} p}{b} - \frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{a^{2} e^{4} p^{2}}{b^{2}} - \frac{9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} b^{2} e + 18 \, {\left(b^{2} d^{5} + a b d^{2} e^{3}\right)} p^{2} x - \frac{1}{2} \, {\left(3 \, b^{2} d^{3} - 2 \, a b e^{3}\right)} {\left(\frac{2 \, a e^{2} p}{b} - \frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{a^{2} e^{4} p^{2}}{b^{2}} - \frac{9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} p - {\left(15 \, a b d^{3} e^{2} + a^{2} e^{5}\right)} p^{2} + \frac{3}{4} \, \sqrt{\frac{1}{3}} {\left({\left(\frac{2 \, a e^{2} p}{b} - \frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{a^{2} e^{4} p^{2}}{b^{2}} - \frac{9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} b^{2} e - 2 \, {\left(3 \, b^{2} d^{3} + a b e^{3}\right)} p\right)} \sqrt{\frac{4 \, {\left(\frac{2 \, a e^{2} p}{b} - \frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{a^{2} e^{4} p^{2}}{b^{2}} - \frac{9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} a b e^{2} p - {\left(\frac{2 \, a e^{2} p}{b} - \frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{a^{2} e^{4} p^{2}}{b^{2}} - \frac{9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} b^{2} - 4 \, {\left(36 \, a b d^{3} e + a^{2} e^{4}\right)} p^{2}}{b^{2}}}\right) - {\left(6 \, a e^{2} p - {\left(\frac{2 \, a e^{2} p}{b} - \frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{a^{2} e^{4} p^{2}}{b^{2}} - \frac{9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} b + 3 \, \sqrt{\frac{1}{3}} b \sqrt{\frac{4 \, {\left(\frac{2 \, a e^{2} p}{b} - \frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{a^{2} e^{4} p^{2}}{b^{2}} - \frac{9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} a b e^{2} p - {\left(\frac{2 \, a e^{2} p}{b} - \frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{a^{2} e^{4} p^{2}}{b^{2}} - \frac{9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} b^{2} - 4 \, {\left(36 \, a b d^{3} e + a^{2} e^{4}\right)} p^{2}}{b^{2}}}\right)} \log\left(-\frac{1}{4} \, {\left(\frac{2 \, a e^{2} p}{b} - \frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{a^{2} e^{4} p^{2}}{b^{2}} - \frac{9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} b^{2} e + 18 \, {\left(b^{2} d^{5} + a b d^{2} e^{3}\right)} p^{2} x - \frac{1}{2} \, {\left(3 \, b^{2} d^{3} - 2 \, a b e^{3}\right)} {\left(\frac{2 \, a e^{2} p}{b} - \frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{a^{2} e^{4} p^{2}}{b^{2}} - \frac{9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} p - {\left(15 \, a b d^{3} e^{2} + a^{2} e^{5}\right)} p^{2} - \frac{3}{4} \, \sqrt{\frac{1}{3}} {\left({\left(\frac{2 \, a e^{2} p}{b} - \frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{a^{2} e^{4} p^{2}}{b^{2}} - \frac{9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} b^{2} e - 2 \, {\left(3 \, b^{2} d^{3} + a b e^{3}\right)} p\right)} \sqrt{\frac{4 \, {\left(\frac{2 \, a e^{2} p}{b} - \frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{a^{2} e^{4} p^{2}}{b^{2}} - \frac{9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} a b e^{2} p - {\left(\frac{2 \, a e^{2} p}{b} - \frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\frac{a^{2} e^{4} p^{2}}{b^{2}} - \frac{9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}}{b^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{2 \, a^{3} e^{6} p^{3}}{b^{3}} + \frac{27 \, {\left(b d^{3} + a e^{3}\right)} a d^{3} p^{3}}{b^{2}} - \frac{3 \, {\left(9 \, a b d^{3} e p^{2} + a^{2} e^{4} p^{2}\right)} a e^{2} p}{b^{3}} + \frac{27 \, a b^{2} d^{6} p^{3} + a^{3} e^{6} p^{3}}{b^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} b^{2} - 4 \, {\left(36 \, a b d^{3} e + a^{2} e^{4}\right)} p^{2}}{b^{2}}}\right) - 4 \, {\left(b e^{2} p x^{3} + 3 \, b d e p x^{2} + 3 \, b d^{2} p x\right)} \log\left(b x^{3} + a\right) - 4 \, {\left(b e^{2} x^{3} + 3 \, b d e x^{2} + 3 \, b d^{2} x\right)} \log\left(c\right)}{12 \, b}"," ",0,"-1/12*(4*b*e^2*p*x^3 + 18*b*d*e*p*x^2 + 36*b*d^2*p*x - 2*(2*a*e^2*p/b - 2*(1/2)^(2/3)*(a^2*e^4*p^2/b^2 - (9*a*b*d^3*e*p^2 + a^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3) - (1/2)^(1/3)*(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3)*(I*sqrt(3) + 1))*b*log(1/4*(2*a*e^2*p/b - 2*(1/2)^(2/3)*(a^2*e^4*p^2/b^2 - (9*a*b*d^3*e*p^2 + a^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3) - (1/2)^(1/3)*(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3)*(I*sqrt(3) + 1))^2*b^2*e + 9*(b^2*d^5 + a*b*d^2*e^3)*p^2*x + 1/2*(3*b^2*d^3 - 2*a*b*e^3)*(2*a*e^2*p/b - 2*(1/2)^(2/3)*(a^2*e^4*p^2/b^2 - (9*a*b*d^3*e*p^2 + a^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3) - (1/2)^(1/3)*(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3)*(I*sqrt(3) + 1))*p + (15*a*b*d^3*e^2 + a^2*e^5)*p^2) - (6*a*e^2*p - (2*a*e^2*p/b - 2*(1/2)^(2/3)*(a^2*e^4*p^2/b^2 - (9*a*b*d^3*e*p^2 + a^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3) - (1/2)^(1/3)*(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3)*(I*sqrt(3) + 1))*b - 3*sqrt(1/3)*b*sqrt((4*(2*a*e^2*p/b - 2*(1/2)^(2/3)*(a^2*e^4*p^2/b^2 - (9*a*b*d^3*e*p^2 + a^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3) - (1/2)^(1/3)*(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3)*(I*sqrt(3) + 1))*a*b*e^2*p - (2*a*e^2*p/b - 2*(1/2)^(2/3)*(a^2*e^4*p^2/b^2 - (9*a*b*d^3*e*p^2 + a^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3) - (1/2)^(1/3)*(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3)*(I*sqrt(3) + 1))^2*b^2 - 4*(36*a*b*d^3*e + a^2*e^4)*p^2)/b^2))*log(-1/4*(2*a*e^2*p/b - 2*(1/2)^(2/3)*(a^2*e^4*p^2/b^2 - (9*a*b*d^3*e*p^2 + a^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3) - (1/2)^(1/3)*(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3)*(I*sqrt(3) + 1))^2*b^2*e + 18*(b^2*d^5 + a*b*d^2*e^3)*p^2*x - 1/2*(3*b^2*d^3 - 2*a*b*e^3)*(2*a*e^2*p/b - 2*(1/2)^(2/3)*(a^2*e^4*p^2/b^2 - (9*a*b*d^3*e*p^2 + a^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3) - (1/2)^(1/3)*(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3)*(I*sqrt(3) + 1))*p - (15*a*b*d^3*e^2 + a^2*e^5)*p^2 + 3/4*sqrt(1/3)*((2*a*e^2*p/b - 2*(1/2)^(2/3)*(a^2*e^4*p^2/b^2 - (9*a*b*d^3*e*p^2 + a^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3) - (1/2)^(1/3)*(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3)*(I*sqrt(3) + 1))*b^2*e - 2*(3*b^2*d^3 + a*b*e^3)*p)*sqrt((4*(2*a*e^2*p/b - 2*(1/2)^(2/3)*(a^2*e^4*p^2/b^2 - (9*a*b*d^3*e*p^2 + a^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3) - (1/2)^(1/3)*(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3)*(I*sqrt(3) + 1))*a*b*e^2*p - (2*a*e^2*p/b - 2*(1/2)^(2/3)*(a^2*e^4*p^2/b^2 - (9*a*b*d^3*e*p^2 + a^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3) - (1/2)^(1/3)*(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3)*(I*sqrt(3) + 1))^2*b^2 - 4*(36*a*b*d^3*e + a^2*e^4)*p^2)/b^2)) - (6*a*e^2*p - (2*a*e^2*p/b - 2*(1/2)^(2/3)*(a^2*e^4*p^2/b^2 - (9*a*b*d^3*e*p^2 + a^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3) - (1/2)^(1/3)*(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3)*(I*sqrt(3) + 1))*b + 3*sqrt(1/3)*b*sqrt((4*(2*a*e^2*p/b - 2*(1/2)^(2/3)*(a^2*e^4*p^2/b^2 - (9*a*b*d^3*e*p^2 + a^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3) - (1/2)^(1/3)*(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3)*(I*sqrt(3) + 1))*a*b*e^2*p - (2*a*e^2*p/b - 2*(1/2)^(2/3)*(a^2*e^4*p^2/b^2 - (9*a*b*d^3*e*p^2 + a^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3) - (1/2)^(1/3)*(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3)*(I*sqrt(3) + 1))^2*b^2 - 4*(36*a*b*d^3*e + a^2*e^4)*p^2)/b^2))*log(-1/4*(2*a*e^2*p/b - 2*(1/2)^(2/3)*(a^2*e^4*p^2/b^2 - (9*a*b*d^3*e*p^2 + a^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3) - (1/2)^(1/3)*(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3)*(I*sqrt(3) + 1))^2*b^2*e + 18*(b^2*d^5 + a*b*d^2*e^3)*p^2*x - 1/2*(3*b^2*d^3 - 2*a*b*e^3)*(2*a*e^2*p/b - 2*(1/2)^(2/3)*(a^2*e^4*p^2/b^2 - (9*a*b*d^3*e*p^2 + a^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3) - (1/2)^(1/3)*(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3)*(I*sqrt(3) + 1))*p - (15*a*b*d^3*e^2 + a^2*e^5)*p^2 - 3/4*sqrt(1/3)*((2*a*e^2*p/b - 2*(1/2)^(2/3)*(a^2*e^4*p^2/b^2 - (9*a*b*d^3*e*p^2 + a^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3) - (1/2)^(1/3)*(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3)*(I*sqrt(3) + 1))*b^2*e - 2*(3*b^2*d^3 + a*b*e^3)*p)*sqrt((4*(2*a*e^2*p/b - 2*(1/2)^(2/3)*(a^2*e^4*p^2/b^2 - (9*a*b*d^3*e*p^2 + a^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3) - (1/2)^(1/3)*(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3)*(I*sqrt(3) + 1))*a*b*e^2*p - (2*a*e^2*p/b - 2*(1/2)^(2/3)*(a^2*e^4*p^2/b^2 - (9*a*b*d^3*e*p^2 + a^2*e^4*p^2)/b^2)*(-I*sqrt(3) + 1)/(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3) - (1/2)^(1/3)*(2*a^3*e^6*p^3/b^3 + 27*(b*d^3 + a*e^3)*a*d^3*p^3/b^2 - 3*(9*a*b*d^3*e*p^2 + a^2*e^4*p^2)*a*e^2*p/b^3 + (27*a*b^2*d^6*p^3 + a^3*e^6*p^3)/b^3)^(1/3)*(I*sqrt(3) + 1))^2*b^2 - 4*(36*a*b*d^3*e + a^2*e^4)*p^2)/b^2)) - 4*(b*e^2*p*x^3 + 3*b*d*e*p*x^2 + 3*b*d^2*p*x)*log(b*x^3 + a) - 4*(b*e^2*x^3 + 3*b*d*e*x^2 + 3*b*d^2*x)*log(c))/b","C",0
193,1,2284,0,3.465910," ","integrate((e*x+d)*log(c*(b*x^3+a)^p),x, algorithm=""fricas"")","-\frac{3}{4} \, e p x^{2} - 3 \, d p x + \frac{1}{4} \, {\left(\frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} a d e p^{2} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} b} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} \log\left(4 \, a d e^{2} p^{2} + 2 \, {\left(\frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} a d e p^{2} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} b} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} b d^{2} p + \frac{1}{4} \, {\left(\frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} a d e p^{2} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} b} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} b e + {\left(8 \, b d^{3} + a e^{3}\right)} p^{2} x\right) - \frac{1}{8} \, {\left(\frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} a d e p^{2} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} b} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \sqrt{3} \sqrt{-\frac{32 \, a d e p^{2} + {\left(\frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} a d e p^{2} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} b} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} b}{b}}\right)} \log\left(-2 \, a d e^{2} p^{2} - {\left(\frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} a d e p^{2} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} b} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} b d^{2} p - \frac{1}{8} \, {\left(\frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} a d e p^{2} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} b} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} b e + {\left(8 \, b d^{3} + a e^{3}\right)} p^{2} x + \frac{1}{8} \, \sqrt{3} {\left(8 \, b d^{2} p - {\left(\frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} a d e p^{2} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} b} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} b e\right)} \sqrt{-\frac{32 \, a d e p^{2} + {\left(\frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} a d e p^{2} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} b} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} b}{b}}\right) - \frac{1}{8} \, {\left(\frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} a d e p^{2} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} b} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \sqrt{3} \sqrt{-\frac{32 \, a d e p^{2} + {\left(\frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} a d e p^{2} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} b} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} b}{b}}\right)} \log\left(-2 \, a d e^{2} p^{2} - {\left(\frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} a d e p^{2} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} b} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} b d^{2} p - \frac{1}{8} \, {\left(\frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} a d e p^{2} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} b} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} b e + {\left(8 \, b d^{3} + a e^{3}\right)} p^{2} x - \frac{1}{8} \, \sqrt{3} {\left(8 \, b d^{2} p - {\left(\frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} a d e p^{2} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} b} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} b e\right)} \sqrt{-\frac{32 \, a d e p^{2} + {\left(\frac{4 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} a d e p^{2} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} b} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\frac{{\left(8 \, b d^{3} + a e^{3}\right)} a p^{3}}{b^{2}} + \frac{8 \, a b d^{3} p^{3} - a^{2} e^{3} p^{3}}{b^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} b}{b}}\right) + \frac{1}{2} \, {\left(e p x^{2} + 2 \, d p x\right)} \log\left(b x^{3} + a\right) + \frac{1}{2} \, {\left(e x^{2} + 2 \, d x\right)} \log\left(c\right)"," ",0,"-3/4*e*p*x^2 - 3*d*p*x + 1/4*(4*(1/2)^(2/3)*a*d*e*p^2*(-I*sqrt(3) + 1)/(((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*b) - (1/2)^(1/3)*((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*(I*sqrt(3) + 1))*log(4*a*d*e^2*p^2 + 2*(4*(1/2)^(2/3)*a*d*e*p^2*(-I*sqrt(3) + 1)/(((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*b) - (1/2)^(1/3)*((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*(I*sqrt(3) + 1))*b*d^2*p + 1/4*(4*(1/2)^(2/3)*a*d*e*p^2*(-I*sqrt(3) + 1)/(((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*b) - (1/2)^(1/3)*((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*(I*sqrt(3) + 1))^2*b*e + (8*b*d^3 + a*e^3)*p^2*x) - 1/8*(4*(1/2)^(2/3)*a*d*e*p^2*(-I*sqrt(3) + 1)/(((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*b) - (1/2)^(1/3)*((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*(I*sqrt(3) + 1) - sqrt(3)*sqrt(-(32*a*d*e*p^2 + (4*(1/2)^(2/3)*a*d*e*p^2*(-I*sqrt(3) + 1)/(((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*b) - (1/2)^(1/3)*((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*(I*sqrt(3) + 1))^2*b)/b))*log(-2*a*d*e^2*p^2 - (4*(1/2)^(2/3)*a*d*e*p^2*(-I*sqrt(3) + 1)/(((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*b) - (1/2)^(1/3)*((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*(I*sqrt(3) + 1))*b*d^2*p - 1/8*(4*(1/2)^(2/3)*a*d*e*p^2*(-I*sqrt(3) + 1)/(((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*b) - (1/2)^(1/3)*((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*(I*sqrt(3) + 1))^2*b*e + (8*b*d^3 + a*e^3)*p^2*x + 1/8*sqrt(3)*(8*b*d^2*p - (4*(1/2)^(2/3)*a*d*e*p^2*(-I*sqrt(3) + 1)/(((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*b) - (1/2)^(1/3)*((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*(I*sqrt(3) + 1))*b*e)*sqrt(-(32*a*d*e*p^2 + (4*(1/2)^(2/3)*a*d*e*p^2*(-I*sqrt(3) + 1)/(((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*b) - (1/2)^(1/3)*((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*(I*sqrt(3) + 1))^2*b)/b)) - 1/8*(4*(1/2)^(2/3)*a*d*e*p^2*(-I*sqrt(3) + 1)/(((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*b) - (1/2)^(1/3)*((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*(I*sqrt(3) + 1) + sqrt(3)*sqrt(-(32*a*d*e*p^2 + (4*(1/2)^(2/3)*a*d*e*p^2*(-I*sqrt(3) + 1)/(((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*b) - (1/2)^(1/3)*((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*(I*sqrt(3) + 1))^2*b)/b))*log(-2*a*d*e^2*p^2 - (4*(1/2)^(2/3)*a*d*e*p^2*(-I*sqrt(3) + 1)/(((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*b) - (1/2)^(1/3)*((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*(I*sqrt(3) + 1))*b*d^2*p - 1/8*(4*(1/2)^(2/3)*a*d*e*p^2*(-I*sqrt(3) + 1)/(((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*b) - (1/2)^(1/3)*((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*(I*sqrt(3) + 1))^2*b*e + (8*b*d^3 + a*e^3)*p^2*x - 1/8*sqrt(3)*(8*b*d^2*p - (4*(1/2)^(2/3)*a*d*e*p^2*(-I*sqrt(3) + 1)/(((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*b) - (1/2)^(1/3)*((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*(I*sqrt(3) + 1))*b*e)*sqrt(-(32*a*d*e*p^2 + (4*(1/2)^(2/3)*a*d*e*p^2*(-I*sqrt(3) + 1)/(((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*b) - (1/2)^(1/3)*((8*b*d^3 + a*e^3)*a*p^3/b^2 + (8*a*b*d^3*p^3 - a^2*e^3*p^3)/b^2)^(1/3)*(I*sqrt(3) + 1))^2*b)/b)) + 1/2*(e*p*x^2 + 2*d*p*x)*log(b*x^3 + a) + 1/2*(e*x^2 + 2*d*x)*log(c)","C",0
194,1,110,0,1.051975," ","integrate(log(c*(b*x^3+a)^p),x, algorithm=""fricas"")","p x \log\left(b x^{3} + a\right) + \sqrt{3} p \left(\frac{a}{b}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, \sqrt{3} b x \left(\frac{a}{b}\right)^{\frac{2}{3}} - \sqrt{3} a}{3 \, a}\right) - \frac{1}{2} \, p \left(\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x^{2} - x \left(\frac{a}{b}\right)^{\frac{1}{3}} + \left(\frac{a}{b}\right)^{\frac{2}{3}}\right) + p \left(\frac{a}{b}\right)^{\frac{1}{3}} \log\left(x + \left(\frac{a}{b}\right)^{\frac{1}{3}}\right) - 3 \, p x + x \log\left(c\right)"," ",0,"p*x*log(b*x^3 + a) + sqrt(3)*p*(a/b)^(1/3)*arctan(1/3*(2*sqrt(3)*b*x*(a/b)^(2/3) - sqrt(3)*a)/a) - 1/2*p*(a/b)^(1/3)*log(x^2 - x*(a/b)^(1/3) + (a/b)^(2/3)) + p*(a/b)^(1/3)*log(x + (a/b)^(1/3)) - 3*p*x + x*log(c)","A",0
195,0,0,0,0.702367," ","integrate(log(c*(b*x^3+a)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{3} + a\right)}^{p} c\right)}{e x + d}, x\right)"," ",0,"integral(log((b*x^3 + a)^p*c)/(e*x + d), x)","F",0
196,1,7010,0,3.943006," ","integrate(log(c*(b*x^3+a)^p)/(e*x+d)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(b d^{4} e - a d e^{4} + {\left(b d^{3} e^{2} - a e^{5}\right)} x\right)} {\left(\frac{2 \, b d^{2} p}{b d^{3} e - a e^{4}} - \frac{{\left(\frac{b^{2} d^{4} p^{2}}{{\left(b d^{3} e - a e^{4}\right)}^{2}} - \frac{b d p^{2}}{b d^{3} e^{2} - a e^{5}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}}} - {\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} \log\left(\frac{3}{2} \, {\left(\frac{2 \, b d^{2} p}{b d^{3} e - a e^{4}} - \frac{{\left(\frac{b^{2} d^{4} p^{2}}{{\left(b d^{3} e - a e^{4}\right)}^{2}} - \frac{b d p^{2}}{b d^{3} e^{2} - a e^{5}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}}} - {\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} b d^{2} e p + b e p^{2} x - 2 \, b d p^{2} - \frac{1}{4} \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(\frac{2 \, b d^{2} p}{b d^{3} e - a e^{4}} - \frac{{\left(\frac{b^{2} d^{4} p^{2}}{{\left(b d^{3} e - a e^{4}\right)}^{2}} - \frac{b d p^{2}}{b d^{3} e^{2} - a e^{5}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}}} - {\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2}\right) - 4 \, {\left(b d^{3} - a e^{3}\right)} p \log\left(b x^{3} + a\right) + {\left(6 \, b d^{2} e p x + 6 \, b d^{3} p - {\left(b d^{4} e - a d e^{4} + {\left(b d^{3} e^{2} - a e^{5}\right)} x\right)} {\left(\frac{2 \, b d^{2} p}{b d^{3} e - a e^{4}} - \frac{{\left(\frac{b^{2} d^{4} p^{2}}{{\left(b d^{3} e - a e^{4}\right)}^{2}} - \frac{b d p^{2}}{b d^{3} e^{2} - a e^{5}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}}} - {\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} + \sqrt{3} {\left(b d^{4} e - a d e^{4} + {\left(b d^{3} e^{2} - a e^{5}\right)} x\right)} \sqrt{-\frac{{\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(\frac{2 \, b d^{2} p}{b d^{3} e - a e^{4}} - \frac{{\left(\frac{b^{2} d^{4} p^{2}}{{\left(b d^{3} e - a e^{4}\right)}^{2}} - \frac{b d p^{2}}{b d^{3} e^{2} - a e^{5}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}}} - {\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} - 4 \, {\left(b^{2} d^{5} e - a b d^{2} e^{4}\right)} {\left(\frac{2 \, b d^{2} p}{b d^{3} e - a e^{4}} - \frac{{\left(\frac{b^{2} d^{4} p^{2}}{{\left(b d^{3} e - a e^{4}\right)}^{2}} - \frac{b d p^{2}}{b d^{3} e^{2} - a e^{5}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}}} - {\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} p + 4 \, {\left(b^{2} d^{4} - 4 \, a b d e^{3}\right)} p^{2}}{b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}}}\right)} \log\left(-\frac{3}{2} \, {\left(\frac{2 \, b d^{2} p}{b d^{3} e - a e^{4}} - \frac{{\left(\frac{b^{2} d^{4} p^{2}}{{\left(b d^{3} e - a e^{4}\right)}^{2}} - \frac{b d p^{2}}{b d^{3} e^{2} - a e^{5}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}}} - {\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} b d^{2} e p + 2 \, b e p^{2} x + 2 \, b d p^{2} + \frac{1}{4} \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(\frac{2 \, b d^{2} p}{b d^{3} e - a e^{4}} - \frac{{\left(\frac{b^{2} d^{4} p^{2}}{{\left(b d^{3} e - a e^{4}\right)}^{2}} - \frac{b d p^{2}}{b d^{3} e^{2} - a e^{5}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}}} - {\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} + \frac{1}{4} \, \sqrt{3} {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(\frac{2 \, b d^{2} p}{b d^{3} e - a e^{4}} - \frac{{\left(\frac{b^{2} d^{4} p^{2}}{{\left(b d^{3} e - a e^{4}\right)}^{2}} - \frac{b d p^{2}}{b d^{3} e^{2} - a e^{5}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}}} - {\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} \sqrt{-\frac{{\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(\frac{2 \, b d^{2} p}{b d^{3} e - a e^{4}} - \frac{{\left(\frac{b^{2} d^{4} p^{2}}{{\left(b d^{3} e - a e^{4}\right)}^{2}} - \frac{b d p^{2}}{b d^{3} e^{2} - a e^{5}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}}} - {\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} - 4 \, {\left(b^{2} d^{5} e - a b d^{2} e^{4}\right)} {\left(\frac{2 \, b d^{2} p}{b d^{3} e - a e^{4}} - \frac{{\left(\frac{b^{2} d^{4} p^{2}}{{\left(b d^{3} e - a e^{4}\right)}^{2}} - \frac{b d p^{2}}{b d^{3} e^{2} - a e^{5}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}}} - {\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} p + 4 \, {\left(b^{2} d^{4} - 4 \, a b d e^{3}\right)} p^{2}}{b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}}}\right) + {\left(6 \, b d^{2} e p x + 6 \, b d^{3} p - {\left(b d^{4} e - a d e^{4} + {\left(b d^{3} e^{2} - a e^{5}\right)} x\right)} {\left(\frac{2 \, b d^{2} p}{b d^{3} e - a e^{4}} - \frac{{\left(\frac{b^{2} d^{4} p^{2}}{{\left(b d^{3} e - a e^{4}\right)}^{2}} - \frac{b d p^{2}}{b d^{3} e^{2} - a e^{5}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}}} - {\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} - \sqrt{3} {\left(b d^{4} e - a d e^{4} + {\left(b d^{3} e^{2} - a e^{5}\right)} x\right)} \sqrt{-\frac{{\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(\frac{2 \, b d^{2} p}{b d^{3} e - a e^{4}} - \frac{{\left(\frac{b^{2} d^{4} p^{2}}{{\left(b d^{3} e - a e^{4}\right)}^{2}} - \frac{b d p^{2}}{b d^{3} e^{2} - a e^{5}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}}} - {\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} - 4 \, {\left(b^{2} d^{5} e - a b d^{2} e^{4}\right)} {\left(\frac{2 \, b d^{2} p}{b d^{3} e - a e^{4}} - \frac{{\left(\frac{b^{2} d^{4} p^{2}}{{\left(b d^{3} e - a e^{4}\right)}^{2}} - \frac{b d p^{2}}{b d^{3} e^{2} - a e^{5}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}}} - {\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} p + 4 \, {\left(b^{2} d^{4} - 4 \, a b d e^{3}\right)} p^{2}}{b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}}}\right)} \log\left(-\frac{3}{2} \, {\left(\frac{2 \, b d^{2} p}{b d^{3} e - a e^{4}} - \frac{{\left(\frac{b^{2} d^{4} p^{2}}{{\left(b d^{3} e - a e^{4}\right)}^{2}} - \frac{b d p^{2}}{b d^{3} e^{2} - a e^{5}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}}} - {\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} b d^{2} e p + 2 \, b e p^{2} x + 2 \, b d p^{2} + \frac{1}{4} \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(\frac{2 \, b d^{2} p}{b d^{3} e - a e^{4}} - \frac{{\left(\frac{b^{2} d^{4} p^{2}}{{\left(b d^{3} e - a e^{4}\right)}^{2}} - \frac{b d p^{2}}{b d^{3} e^{2} - a e^{5}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}}} - {\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} - \frac{1}{4} \, \sqrt{3} {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(\frac{2 \, b d^{2} p}{b d^{3} e - a e^{4}} - \frac{{\left(\frac{b^{2} d^{4} p^{2}}{{\left(b d^{3} e - a e^{4}\right)}^{2}} - \frac{b d p^{2}}{b d^{3} e^{2} - a e^{5}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}}} - {\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} \sqrt{-\frac{{\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(\frac{2 \, b d^{2} p}{b d^{3} e - a e^{4}} - \frac{{\left(\frac{b^{2} d^{4} p^{2}}{{\left(b d^{3} e - a e^{4}\right)}^{2}} - \frac{b d p^{2}}{b d^{3} e^{2} - a e^{5}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}}} - {\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)}^{2} - 4 \, {\left(b^{2} d^{5} e - a b d^{2} e^{4}\right)} {\left(\frac{2 \, b d^{2} p}{b d^{3} e - a e^{4}} - \frac{{\left(\frac{b^{2} d^{4} p^{2}}{{\left(b d^{3} e - a e^{4}\right)}^{2}} - \frac{b d p^{2}}{b d^{3} e^{2} - a e^{5}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}}} - {\left(\frac{b^{3} d^{6} p^{3}}{{\left(b d^{3} e - a e^{4}\right)}^{3}} - \frac{3 \, b^{2} d^{3} p^{3}}{2 \, {\left(b d^{3} e^{2} - a e^{5}\right)} {\left(b d^{3} e - a e^{4}\right)}} + \frac{b p^{3}}{2 \, {\left(b d^{3} e^{3} - a e^{6}\right)}} + \frac{a b p^{3}}{2 \, {\left(b d^{3} - a e^{3}\right)}^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)}\right)} p + 4 \, {\left(b^{2} d^{4} - 4 \, a b d e^{3}\right)} p^{2}}{b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}}}\right) - 12 \, {\left(b d^{2} e p x + b d^{3} p\right)} \log\left(e x + d\right) - 4 \, {\left(b d^{3} - a e^{3}\right)} \log\left(c\right)}{4 \, {\left(b d^{4} e - a d e^{4} + {\left(b d^{3} e^{2} - a e^{5}\right)} x\right)}}"," ",0,"1/4*(2*(b*d^4*e - a*d*e^4 + (b*d^3*e^2 - a*e^5)*x)*(2*b*d^2*p/(b*d^3*e - a*e^4) - (b^2*d^4*p^2/(b*d^3*e - a*e^4)^2 - b*d*p^2/(b*d^3*e^2 - a*e^5))*(-I*sqrt(3) + 1)/(b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3) - (b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3)*(I*sqrt(3) + 1))*log(3/2*(2*b*d^2*p/(b*d^3*e - a*e^4) - (b^2*d^4*p^2/(b*d^3*e - a*e^4)^2 - b*d*p^2/(b*d^3*e^2 - a*e^5))*(-I*sqrt(3) + 1)/(b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3) - (b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3)*(I*sqrt(3) + 1))*b*d^2*e*p + b*e*p^2*x - 2*b*d*p^2 - 1/4*(b*d^3*e^2 - a*e^5)*(2*b*d^2*p/(b*d^3*e - a*e^4) - (b^2*d^4*p^2/(b*d^3*e - a*e^4)^2 - b*d*p^2/(b*d^3*e^2 - a*e^5))*(-I*sqrt(3) + 1)/(b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3) - (b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3)*(I*sqrt(3) + 1))^2) - 4*(b*d^3 - a*e^3)*p*log(b*x^3 + a) + (6*b*d^2*e*p*x + 6*b*d^3*p - (b*d^4*e - a*d*e^4 + (b*d^3*e^2 - a*e^5)*x)*(2*b*d^2*p/(b*d^3*e - a*e^4) - (b^2*d^4*p^2/(b*d^3*e - a*e^4)^2 - b*d*p^2/(b*d^3*e^2 - a*e^5))*(-I*sqrt(3) + 1)/(b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3) - (b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3)*(I*sqrt(3) + 1)) + sqrt(3)*(b*d^4*e - a*d*e^4 + (b*d^3*e^2 - a*e^5)*x)*sqrt(-((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(2*b*d^2*p/(b*d^3*e - a*e^4) - (b^2*d^4*p^2/(b*d^3*e - a*e^4)^2 - b*d*p^2/(b*d^3*e^2 - a*e^5))*(-I*sqrt(3) + 1)/(b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3) - (b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3)*(I*sqrt(3) + 1))^2 - 4*(b^2*d^5*e - a*b*d^2*e^4)*(2*b*d^2*p/(b*d^3*e - a*e^4) - (b^2*d^4*p^2/(b*d^3*e - a*e^4)^2 - b*d*p^2/(b*d^3*e^2 - a*e^5))*(-I*sqrt(3) + 1)/(b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3) - (b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3)*(I*sqrt(3) + 1))*p + 4*(b^2*d^4 - 4*a*b*d*e^3)*p^2)/(b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)))*log(-3/2*(2*b*d^2*p/(b*d^3*e - a*e^4) - (b^2*d^4*p^2/(b*d^3*e - a*e^4)^2 - b*d*p^2/(b*d^3*e^2 - a*e^5))*(-I*sqrt(3) + 1)/(b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3) - (b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3)*(I*sqrt(3) + 1))*b*d^2*e*p + 2*b*e*p^2*x + 2*b*d*p^2 + 1/4*(b*d^3*e^2 - a*e^5)*(2*b*d^2*p/(b*d^3*e - a*e^4) - (b^2*d^4*p^2/(b*d^3*e - a*e^4)^2 - b*d*p^2/(b*d^3*e^2 - a*e^5))*(-I*sqrt(3) + 1)/(b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3) - (b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3)*(I*sqrt(3) + 1))^2 + 1/4*sqrt(3)*(b*d^3*e^2 - a*e^5)*(2*b*d^2*p/(b*d^3*e - a*e^4) - (b^2*d^4*p^2/(b*d^3*e - a*e^4)^2 - b*d*p^2/(b*d^3*e^2 - a*e^5))*(-I*sqrt(3) + 1)/(b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3) - (b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3)*(I*sqrt(3) + 1))*sqrt(-((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(2*b*d^2*p/(b*d^3*e - a*e^4) - (b^2*d^4*p^2/(b*d^3*e - a*e^4)^2 - b*d*p^2/(b*d^3*e^2 - a*e^5))*(-I*sqrt(3) + 1)/(b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3) - (b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3)*(I*sqrt(3) + 1))^2 - 4*(b^2*d^5*e - a*b*d^2*e^4)*(2*b*d^2*p/(b*d^3*e - a*e^4) - (b^2*d^4*p^2/(b*d^3*e - a*e^4)^2 - b*d*p^2/(b*d^3*e^2 - a*e^5))*(-I*sqrt(3) + 1)/(b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3) - (b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3)*(I*sqrt(3) + 1))*p + 4*(b^2*d^4 - 4*a*b*d*e^3)*p^2)/(b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8))) + (6*b*d^2*e*p*x + 6*b*d^3*p - (b*d^4*e - a*d*e^4 + (b*d^3*e^2 - a*e^5)*x)*(2*b*d^2*p/(b*d^3*e - a*e^4) - (b^2*d^4*p^2/(b*d^3*e - a*e^4)^2 - b*d*p^2/(b*d^3*e^2 - a*e^5))*(-I*sqrt(3) + 1)/(b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3) - (b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3)*(I*sqrt(3) + 1)) - sqrt(3)*(b*d^4*e - a*d*e^4 + (b*d^3*e^2 - a*e^5)*x)*sqrt(-((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(2*b*d^2*p/(b*d^3*e - a*e^4) - (b^2*d^4*p^2/(b*d^3*e - a*e^4)^2 - b*d*p^2/(b*d^3*e^2 - a*e^5))*(-I*sqrt(3) + 1)/(b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3) - (b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3)*(I*sqrt(3) + 1))^2 - 4*(b^2*d^5*e - a*b*d^2*e^4)*(2*b*d^2*p/(b*d^3*e - a*e^4) - (b^2*d^4*p^2/(b*d^3*e - a*e^4)^2 - b*d*p^2/(b*d^3*e^2 - a*e^5))*(-I*sqrt(3) + 1)/(b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3) - (b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3)*(I*sqrt(3) + 1))*p + 4*(b^2*d^4 - 4*a*b*d*e^3)*p^2)/(b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)))*log(-3/2*(2*b*d^2*p/(b*d^3*e - a*e^4) - (b^2*d^4*p^2/(b*d^3*e - a*e^4)^2 - b*d*p^2/(b*d^3*e^2 - a*e^5))*(-I*sqrt(3) + 1)/(b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3) - (b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3)*(I*sqrt(3) + 1))*b*d^2*e*p + 2*b*e*p^2*x + 2*b*d*p^2 + 1/4*(b*d^3*e^2 - a*e^5)*(2*b*d^2*p/(b*d^3*e - a*e^4) - (b^2*d^4*p^2/(b*d^3*e - a*e^4)^2 - b*d*p^2/(b*d^3*e^2 - a*e^5))*(-I*sqrt(3) + 1)/(b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3) - (b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3)*(I*sqrt(3) + 1))^2 - 1/4*sqrt(3)*(b*d^3*e^2 - a*e^5)*(2*b*d^2*p/(b*d^3*e - a*e^4) - (b^2*d^4*p^2/(b*d^3*e - a*e^4)^2 - b*d*p^2/(b*d^3*e^2 - a*e^5))*(-I*sqrt(3) + 1)/(b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3) - (b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3)*(I*sqrt(3) + 1))*sqrt(-((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(2*b*d^2*p/(b*d^3*e - a*e^4) - (b^2*d^4*p^2/(b*d^3*e - a*e^4)^2 - b*d*p^2/(b*d^3*e^2 - a*e^5))*(-I*sqrt(3) + 1)/(b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3) - (b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3)*(I*sqrt(3) + 1))^2 - 4*(b^2*d^5*e - a*b*d^2*e^4)*(2*b*d^2*p/(b*d^3*e - a*e^4) - (b^2*d^4*p^2/(b*d^3*e - a*e^4)^2 - b*d*p^2/(b*d^3*e^2 - a*e^5))*(-I*sqrt(3) + 1)/(b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3) - (b^3*d^6*p^3/(b*d^3*e - a*e^4)^3 - 3/2*b^2*d^3*p^3/((b*d^3*e^2 - a*e^5)*(b*d^3*e - a*e^4)) + 1/2*b*p^3/(b*d^3*e^3 - a*e^6) + 1/2*a*b*p^3/(b*d^3 - a*e^3)^2)^(1/3)*(I*sqrt(3) + 1))*p + 4*(b^2*d^4 - 4*a*b*d*e^3)*p^2)/(b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8))) - 12*(b*d^2*e*p*x + b*d^3*p)*log(e*x + d) - 4*(b*d^3 - a*e^3)*log(c))/(b*d^4*e - a*d*e^4 + (b*d^3*e^2 - a*e^5)*x)","C",0
197,1,13236,0,14.981869," ","integrate(log(c*(b*x^3+a)^p)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{24 \, {\left(b^{2} d^{5} e - a b d^{2} e^{4}\right)} p x + 2 \, {\left(b^{2} d^{8} e - 2 \, a b d^{5} e^{4} + a^{2} d^{2} e^{7} + {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)} x^{2} + 2 \, {\left(b^{2} d^{7} e^{2} - 2 \, a b d^{4} e^{5} + a^{2} d e^{8}\right)} x\right)} {\left(\frac{{\left(\frac{b^{2} d^{2} p^{2}}{b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}} - \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{2}}{{\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}}} - 4 \, {\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{4 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}}{b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}}\right)} \log\left({\left(8 \, b^{2} d^{3} e + a b e^{4}\right)} p^{2} x - \frac{3}{16} \, {\left(b^{2} d^{8} e^{2} - 2 \, a b d^{5} e^{5} + a^{2} d^{2} e^{8}\right)} {\left(\frac{{\left(\frac{b^{2} d^{2} p^{2}}{b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}} - \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{2}}{{\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}}} - 4 \, {\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{4 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}}{b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}}\right)}^{2} + \frac{1}{4} \, {\left(10 \, b^{2} d^{6} e + 16 \, a b d^{3} e^{4} + a^{2} e^{7}\right)} {\left(\frac{{\left(\frac{b^{2} d^{2} p^{2}}{b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}} - \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{2}}{{\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}}} - 4 \, {\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{4 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}}{b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}}\right)} p - {\left(7 \, b^{2} d^{4} + 2 \, a b d e^{3}\right)} p^{2}\right) - 8 \, {\left(b^{2} d^{6} - 2 \, a b d^{3} e^{3} + a^{2} e^{6}\right)} p \log\left(b x^{3} + a\right) + 24 \, {\left(b^{2} d^{6} - a b d^{3} e^{3}\right)} p + {\left(12 \, {\left(b^{2} d^{4} e^{2} + 2 \, a b d e^{5}\right)} p x^{2} + 24 \, {\left(b^{2} d^{5} e + 2 \, a b d^{2} e^{4}\right)} p x - {\left(b^{2} d^{8} e - 2 \, a b d^{5} e^{4} + a^{2} d^{2} e^{7} + {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)} x^{2} + 2 \, {\left(b^{2} d^{7} e^{2} - 2 \, a b d^{4} e^{5} + a^{2} d e^{8}\right)} x\right)} {\left(\frac{{\left(\frac{b^{2} d^{2} p^{2}}{b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}} - \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{2}}{{\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}}} - 4 \, {\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{4 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}}{b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}}\right)} + 12 \, {\left(b^{2} d^{6} + 2 \, a b d^{3} e^{3}\right)} p + \sqrt{3} {\left(b^{2} d^{8} e - 2 \, a b d^{5} e^{4} + a^{2} d^{2} e^{7} + {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)} x^{2} + 2 \, {\left(b^{2} d^{7} e^{2} - 2 \, a b d^{4} e^{5} + a^{2} d e^{8}\right)} x\right)} \sqrt{-\frac{{\left(b^{4} d^{12} e^{2} - 4 \, a b^{3} d^{9} e^{5} + 6 \, a^{2} b^{2} d^{6} e^{8} - 4 \, a^{3} b d^{3} e^{11} + a^{4} e^{14}\right)} {\left(\frac{{\left(\frac{b^{2} d^{2} p^{2}}{b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}} - \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{2}}{{\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}}} - 4 \, {\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{4 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}}{b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}}\right)}^{2} - 8 \, {\left(b^{4} d^{10} e - 3 \, a^{2} b^{2} d^{4} e^{7} + 2 \, a^{3} b d e^{10}\right)} {\left(\frac{{\left(\frac{b^{2} d^{2} p^{2}}{b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}} - \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{2}}{{\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}}} - 4 \, {\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{4 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}}{b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}}\right)} p + 16 \, {\left(b^{4} d^{8} - 20 \, a b^{3} d^{5} e^{3} - 8 \, a^{2} b^{2} d^{2} e^{6}\right)} p^{2}}{b^{4} d^{12} e^{2} - 4 \, a b^{3} d^{9} e^{5} + 6 \, a^{2} b^{2} d^{6} e^{8} - 4 \, a^{3} b d^{3} e^{11} + a^{4} e^{14}}}\right)} \log\left(2 \, {\left(8 \, b^{2} d^{3} e + a b e^{4}\right)} p^{2} x + \frac{3}{16} \, {\left(b^{2} d^{8} e^{2} - 2 \, a b d^{5} e^{5} + a^{2} d^{2} e^{8}\right)} {\left(\frac{{\left(\frac{b^{2} d^{2} p^{2}}{b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}} - \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{2}}{{\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}}} - 4 \, {\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{4 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}}{b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}}\right)}^{2} - \frac{1}{4} \, {\left(10 \, b^{2} d^{6} e + 16 \, a b d^{3} e^{4} + a^{2} e^{7}\right)} {\left(\frac{{\left(\frac{b^{2} d^{2} p^{2}}{b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}} - \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{2}}{{\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}}} - 4 \, {\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{4 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}}{b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}}\right)} p + {\left(7 \, b^{2} d^{4} + 2 \, a b d e^{3}\right)} p^{2} + \frac{1}{16} \, \sqrt{3} {\left(3 \, {\left(b^{2} d^{8} e^{2} - 2 \, a b d^{5} e^{5} + a^{2} d^{2} e^{8}\right)} {\left(\frac{{\left(\frac{b^{2} d^{2} p^{2}}{b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}} - \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{2}}{{\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}}} - 4 \, {\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{4 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}}{b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}}\right)} + 4 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)} p\right)} \sqrt{-\frac{{\left(b^{4} d^{12} e^{2} - 4 \, a b^{3} d^{9} e^{5} + 6 \, a^{2} b^{2} d^{6} e^{8} - 4 \, a^{3} b d^{3} e^{11} + a^{4} e^{14}\right)} {\left(\frac{{\left(\frac{b^{2} d^{2} p^{2}}{b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}} - \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{2}}{{\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}}} - 4 \, {\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{4 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}}{b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}}\right)}^{2} - 8 \, {\left(b^{4} d^{10} e - 3 \, a^{2} b^{2} d^{4} e^{7} + 2 \, a^{3} b d e^{10}\right)} {\left(\frac{{\left(\frac{b^{2} d^{2} p^{2}}{b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}} - \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{2}}{{\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}}} - 4 \, {\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{4 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}}{b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}}\right)} p + 16 \, {\left(b^{4} d^{8} - 20 \, a b^{3} d^{5} e^{3} - 8 \, a^{2} b^{2} d^{2} e^{6}\right)} p^{2}}{b^{4} d^{12} e^{2} - 4 \, a b^{3} d^{9} e^{5} + 6 \, a^{2} b^{2} d^{6} e^{8} - 4 \, a^{3} b d^{3} e^{11} + a^{4} e^{14}}}\right) + {\left(12 \, {\left(b^{2} d^{4} e^{2} + 2 \, a b d e^{5}\right)} p x^{2} + 24 \, {\left(b^{2} d^{5} e + 2 \, a b d^{2} e^{4}\right)} p x - {\left(b^{2} d^{8} e - 2 \, a b d^{5} e^{4} + a^{2} d^{2} e^{7} + {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)} x^{2} + 2 \, {\left(b^{2} d^{7} e^{2} - 2 \, a b d^{4} e^{5} + a^{2} d e^{8}\right)} x\right)} {\left(\frac{{\left(\frac{b^{2} d^{2} p^{2}}{b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}} - \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{2}}{{\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}}} - 4 \, {\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{4 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}}{b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}}\right)} + 12 \, {\left(b^{2} d^{6} + 2 \, a b d^{3} e^{3}\right)} p - \sqrt{3} {\left(b^{2} d^{8} e - 2 \, a b d^{5} e^{4} + a^{2} d^{2} e^{7} + {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)} x^{2} + 2 \, {\left(b^{2} d^{7} e^{2} - 2 \, a b d^{4} e^{5} + a^{2} d e^{8}\right)} x\right)} \sqrt{-\frac{{\left(b^{4} d^{12} e^{2} - 4 \, a b^{3} d^{9} e^{5} + 6 \, a^{2} b^{2} d^{6} e^{8} - 4 \, a^{3} b d^{3} e^{11} + a^{4} e^{14}\right)} {\left(\frac{{\left(\frac{b^{2} d^{2} p^{2}}{b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}} - \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{2}}{{\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}}} - 4 \, {\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{4 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}}{b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}}\right)}^{2} - 8 \, {\left(b^{4} d^{10} e - 3 \, a^{2} b^{2} d^{4} e^{7} + 2 \, a^{3} b d e^{10}\right)} {\left(\frac{{\left(\frac{b^{2} d^{2} p^{2}}{b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}} - \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{2}}{{\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}}} - 4 \, {\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{4 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}}{b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}}\right)} p + 16 \, {\left(b^{4} d^{8} - 20 \, a b^{3} d^{5} e^{3} - 8 \, a^{2} b^{2} d^{2} e^{6}\right)} p^{2}}{b^{4} d^{12} e^{2} - 4 \, a b^{3} d^{9} e^{5} + 6 \, a^{2} b^{2} d^{6} e^{8} - 4 \, a^{3} b d^{3} e^{11} + a^{4} e^{14}}}\right)} \log\left(2 \, {\left(8 \, b^{2} d^{3} e + a b e^{4}\right)} p^{2} x + \frac{3}{16} \, {\left(b^{2} d^{8} e^{2} - 2 \, a b d^{5} e^{5} + a^{2} d^{2} e^{8}\right)} {\left(\frac{{\left(\frac{b^{2} d^{2} p^{2}}{b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}} - \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{2}}{{\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}}} - 4 \, {\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{4 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}}{b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}}\right)}^{2} - \frac{1}{4} \, {\left(10 \, b^{2} d^{6} e + 16 \, a b d^{3} e^{4} + a^{2} e^{7}\right)} {\left(\frac{{\left(\frac{b^{2} d^{2} p^{2}}{b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}} - \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{2}}{{\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}}} - 4 \, {\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{4 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}}{b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}}\right)} p + {\left(7 \, b^{2} d^{4} + 2 \, a b d e^{3}\right)} p^{2} - \frac{1}{16} \, \sqrt{3} {\left(3 \, {\left(b^{2} d^{8} e^{2} - 2 \, a b d^{5} e^{5} + a^{2} d^{2} e^{8}\right)} {\left(\frac{{\left(\frac{b^{2} d^{2} p^{2}}{b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}} - \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{2}}{{\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}}} - 4 \, {\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{4 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}}{b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}}\right)} + 4 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)} p\right)} \sqrt{-\frac{{\left(b^{4} d^{12} e^{2} - 4 \, a b^{3} d^{9} e^{5} + 6 \, a^{2} b^{2} d^{6} e^{8} - 4 \, a^{3} b d^{3} e^{11} + a^{4} e^{14}\right)} {\left(\frac{{\left(\frac{b^{2} d^{2} p^{2}}{b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}} - \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{2}}{{\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}}} - 4 \, {\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{4 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}}{b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}}\right)}^{2} - 8 \, {\left(b^{4} d^{10} e - 3 \, a^{2} b^{2} d^{4} e^{7} + 2 \, a^{3} b d e^{10}\right)} {\left(\frac{{\left(\frac{b^{2} d^{2} p^{2}}{b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}} - \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{2}}{{\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}}} - 4 \, {\left(-\frac{3 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)} b^{2} d^{2} p^{2}}{16 \, {\left(b^{2} d^{6} e^{2} - 2 \, a b d^{3} e^{5} + a^{2} e^{8}\right)} {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}} + \frac{b^{2} p^{3}}{16 \, {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)}} + \frac{{\left(8 \, b d^{3} + a e^{3}\right)} a b^{2} p^{3}}{16 \, {\left(b d^{3} - a e^{3}\right)}^{4}} + \frac{{\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}^{3}}{8 \, {\left(b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}\right)}^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{4 \, {\left(b^{2} d^{4} p + 2 \, a b d e^{3} p\right)}}{b^{2} d^{6} e - 2 \, a b d^{3} e^{4} + a^{2} e^{7}}\right)} p + 16 \, {\left(b^{4} d^{8} - 20 \, a b^{3} d^{5} e^{3} - 8 \, a^{2} b^{2} d^{2} e^{6}\right)} p^{2}}{b^{4} d^{12} e^{2} - 4 \, a b^{3} d^{9} e^{5} + 6 \, a^{2} b^{2} d^{6} e^{8} - 4 \, a^{3} b d^{3} e^{11} + a^{4} e^{14}}}\right) - 24 \, {\left({\left(b^{2} d^{4} e^{2} + 2 \, a b d e^{5}\right)} p x^{2} + 2 \, {\left(b^{2} d^{5} e + 2 \, a b d^{2} e^{4}\right)} p x + {\left(b^{2} d^{6} + 2 \, a b d^{3} e^{3}\right)} p\right)} \log\left(e x + d\right) - 8 \, {\left(b^{2} d^{6} - 2 \, a b d^{3} e^{3} + a^{2} e^{6}\right)} \log\left(c\right)}{16 \, {\left(b^{2} d^{8} e - 2 \, a b d^{5} e^{4} + a^{2} d^{2} e^{7} + {\left(b^{2} d^{6} e^{3} - 2 \, a b d^{3} e^{6} + a^{2} e^{9}\right)} x^{2} + 2 \, {\left(b^{2} d^{7} e^{2} - 2 \, a b d^{4} e^{5} + a^{2} d e^{8}\right)} x\right)}}"," ",0,"1/16*(24*(b^2*d^5*e - a*b*d^2*e^4)*p*x + 2*(b^2*d^8*e - 2*a*b*d^5*e^4 + a^2*d^2*e^7 + (b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9)*x^2 + 2*(b^2*d^7*e^2 - 2*a*b*d^4*e^5 + a^2*d*e^8)*x)*((b^2*d^2*p^2/(b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8) - (b^2*d^4*p + 2*a*b*d*e^3*p)^2/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^2)*(-I*sqrt(3) + 1)/(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3) - 4*(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3)*(I*sqrt(3) + 1) + 4*(b^2*d^4*p + 2*a*b*d*e^3*p)/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7))*log((8*b^2*d^3*e + a*b*e^4)*p^2*x - 3/16*(b^2*d^8*e^2 - 2*a*b*d^5*e^5 + a^2*d^2*e^8)*((b^2*d^2*p^2/(b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8) - (b^2*d^4*p + 2*a*b*d*e^3*p)^2/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^2)*(-I*sqrt(3) + 1)/(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3) - 4*(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3)*(I*sqrt(3) + 1) + 4*(b^2*d^4*p + 2*a*b*d*e^3*p)/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7))^2 + 1/4*(10*b^2*d^6*e + 16*a*b*d^3*e^4 + a^2*e^7)*((b^2*d^2*p^2/(b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8) - (b^2*d^4*p + 2*a*b*d*e^3*p)^2/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^2)*(-I*sqrt(3) + 1)/(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3) - 4*(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3)*(I*sqrt(3) + 1) + 4*(b^2*d^4*p + 2*a*b*d*e^3*p)/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7))*p - (7*b^2*d^4 + 2*a*b*d*e^3)*p^2) - 8*(b^2*d^6 - 2*a*b*d^3*e^3 + a^2*e^6)*p*log(b*x^3 + a) + 24*(b^2*d^6 - a*b*d^3*e^3)*p + (12*(b^2*d^4*e^2 + 2*a*b*d*e^5)*p*x^2 + 24*(b^2*d^5*e + 2*a*b*d^2*e^4)*p*x - (b^2*d^8*e - 2*a*b*d^5*e^4 + a^2*d^2*e^7 + (b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9)*x^2 + 2*(b^2*d^7*e^2 - 2*a*b*d^4*e^5 + a^2*d*e^8)*x)*((b^2*d^2*p^2/(b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8) - (b^2*d^4*p + 2*a*b*d*e^3*p)^2/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^2)*(-I*sqrt(3) + 1)/(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3) - 4*(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3)*(I*sqrt(3) + 1) + 4*(b^2*d^4*p + 2*a*b*d*e^3*p)/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 12*(b^2*d^6 + 2*a*b*d^3*e^3)*p + sqrt(3)*(b^2*d^8*e - 2*a*b*d^5*e^4 + a^2*d^2*e^7 + (b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9)*x^2 + 2*(b^2*d^7*e^2 - 2*a*b*d^4*e^5 + a^2*d*e^8)*x)*sqrt(-((b^4*d^12*e^2 - 4*a*b^3*d^9*e^5 + 6*a^2*b^2*d^6*e^8 - 4*a^3*b*d^3*e^11 + a^4*e^14)*((b^2*d^2*p^2/(b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8) - (b^2*d^4*p + 2*a*b*d*e^3*p)^2/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^2)*(-I*sqrt(3) + 1)/(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3) - 4*(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3)*(I*sqrt(3) + 1) + 4*(b^2*d^4*p + 2*a*b*d*e^3*p)/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7))^2 - 8*(b^4*d^10*e - 3*a^2*b^2*d^4*e^7 + 2*a^3*b*d*e^10)*((b^2*d^2*p^2/(b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8) - (b^2*d^4*p + 2*a*b*d*e^3*p)^2/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^2)*(-I*sqrt(3) + 1)/(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3) - 4*(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3)*(I*sqrt(3) + 1) + 4*(b^2*d^4*p + 2*a*b*d*e^3*p)/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7))*p + 16*(b^4*d^8 - 20*a*b^3*d^5*e^3 - 8*a^2*b^2*d^2*e^6)*p^2)/(b^4*d^12*e^2 - 4*a*b^3*d^9*e^5 + 6*a^2*b^2*d^6*e^8 - 4*a^3*b*d^3*e^11 + a^4*e^14)))*log(2*(8*b^2*d^3*e + a*b*e^4)*p^2*x + 3/16*(b^2*d^8*e^2 - 2*a*b*d^5*e^5 + a^2*d^2*e^8)*((b^2*d^2*p^2/(b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8) - (b^2*d^4*p + 2*a*b*d*e^3*p)^2/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^2)*(-I*sqrt(3) + 1)/(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3) - 4*(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3)*(I*sqrt(3) + 1) + 4*(b^2*d^4*p + 2*a*b*d*e^3*p)/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7))^2 - 1/4*(10*b^2*d^6*e + 16*a*b*d^3*e^4 + a^2*e^7)*((b^2*d^2*p^2/(b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8) - (b^2*d^4*p + 2*a*b*d*e^3*p)^2/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^2)*(-I*sqrt(3) + 1)/(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3) - 4*(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3)*(I*sqrt(3) + 1) + 4*(b^2*d^4*p + 2*a*b*d*e^3*p)/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7))*p + (7*b^2*d^4 + 2*a*b*d*e^3)*p^2 + 1/16*sqrt(3)*(3*(b^2*d^8*e^2 - 2*a*b*d^5*e^5 + a^2*d^2*e^8)*((b^2*d^2*p^2/(b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8) - (b^2*d^4*p + 2*a*b*d*e^3*p)^2/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^2)*(-I*sqrt(3) + 1)/(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3) - 4*(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3)*(I*sqrt(3) + 1) + 4*(b^2*d^4*p + 2*a*b*d*e^3*p)/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 4*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)*p)*sqrt(-((b^4*d^12*e^2 - 4*a*b^3*d^9*e^5 + 6*a^2*b^2*d^6*e^8 - 4*a^3*b*d^3*e^11 + a^4*e^14)*((b^2*d^2*p^2/(b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8) - (b^2*d^4*p + 2*a*b*d*e^3*p)^2/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^2)*(-I*sqrt(3) + 1)/(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3) - 4*(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3)*(I*sqrt(3) + 1) + 4*(b^2*d^4*p + 2*a*b*d*e^3*p)/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7))^2 - 8*(b^4*d^10*e - 3*a^2*b^2*d^4*e^7 + 2*a^3*b*d*e^10)*((b^2*d^2*p^2/(b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8) - (b^2*d^4*p + 2*a*b*d*e^3*p)^2/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^2)*(-I*sqrt(3) + 1)/(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3) - 4*(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3)*(I*sqrt(3) + 1) + 4*(b^2*d^4*p + 2*a*b*d*e^3*p)/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7))*p + 16*(b^4*d^8 - 20*a*b^3*d^5*e^3 - 8*a^2*b^2*d^2*e^6)*p^2)/(b^4*d^12*e^2 - 4*a*b^3*d^9*e^5 + 6*a^2*b^2*d^6*e^8 - 4*a^3*b*d^3*e^11 + a^4*e^14))) + (12*(b^2*d^4*e^2 + 2*a*b*d*e^5)*p*x^2 + 24*(b^2*d^5*e + 2*a*b*d^2*e^4)*p*x - (b^2*d^8*e - 2*a*b*d^5*e^4 + a^2*d^2*e^7 + (b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9)*x^2 + 2*(b^2*d^7*e^2 - 2*a*b*d^4*e^5 + a^2*d*e^8)*x)*((b^2*d^2*p^2/(b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8) - (b^2*d^4*p + 2*a*b*d*e^3*p)^2/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^2)*(-I*sqrt(3) + 1)/(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3) - 4*(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3)*(I*sqrt(3) + 1) + 4*(b^2*d^4*p + 2*a*b*d*e^3*p)/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 12*(b^2*d^6 + 2*a*b*d^3*e^3)*p - sqrt(3)*(b^2*d^8*e - 2*a*b*d^5*e^4 + a^2*d^2*e^7 + (b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9)*x^2 + 2*(b^2*d^7*e^2 - 2*a*b*d^4*e^5 + a^2*d*e^8)*x)*sqrt(-((b^4*d^12*e^2 - 4*a*b^3*d^9*e^5 + 6*a^2*b^2*d^6*e^8 - 4*a^3*b*d^3*e^11 + a^4*e^14)*((b^2*d^2*p^2/(b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8) - (b^2*d^4*p + 2*a*b*d*e^3*p)^2/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^2)*(-I*sqrt(3) + 1)/(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3) - 4*(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3)*(I*sqrt(3) + 1) + 4*(b^2*d^4*p + 2*a*b*d*e^3*p)/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7))^2 - 8*(b^4*d^10*e - 3*a^2*b^2*d^4*e^7 + 2*a^3*b*d*e^10)*((b^2*d^2*p^2/(b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8) - (b^2*d^4*p + 2*a*b*d*e^3*p)^2/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^2)*(-I*sqrt(3) + 1)/(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3) - 4*(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3)*(I*sqrt(3) + 1) + 4*(b^2*d^4*p + 2*a*b*d*e^3*p)/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7))*p + 16*(b^4*d^8 - 20*a*b^3*d^5*e^3 - 8*a^2*b^2*d^2*e^6)*p^2)/(b^4*d^12*e^2 - 4*a*b^3*d^9*e^5 + 6*a^2*b^2*d^6*e^8 - 4*a^3*b*d^3*e^11 + a^4*e^14)))*log(2*(8*b^2*d^3*e + a*b*e^4)*p^2*x + 3/16*(b^2*d^8*e^2 - 2*a*b*d^5*e^5 + a^2*d^2*e^8)*((b^2*d^2*p^2/(b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8) - (b^2*d^4*p + 2*a*b*d*e^3*p)^2/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^2)*(-I*sqrt(3) + 1)/(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3) - 4*(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3)*(I*sqrt(3) + 1) + 4*(b^2*d^4*p + 2*a*b*d*e^3*p)/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7))^2 - 1/4*(10*b^2*d^6*e + 16*a*b*d^3*e^4 + a^2*e^7)*((b^2*d^2*p^2/(b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8) - (b^2*d^4*p + 2*a*b*d*e^3*p)^2/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^2)*(-I*sqrt(3) + 1)/(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3) - 4*(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3)*(I*sqrt(3) + 1) + 4*(b^2*d^4*p + 2*a*b*d*e^3*p)/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7))*p + (7*b^2*d^4 + 2*a*b*d*e^3)*p^2 - 1/16*sqrt(3)*(3*(b^2*d^8*e^2 - 2*a*b*d^5*e^5 + a^2*d^2*e^8)*((b^2*d^2*p^2/(b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8) - (b^2*d^4*p + 2*a*b*d*e^3*p)^2/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^2)*(-I*sqrt(3) + 1)/(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3) - 4*(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3)*(I*sqrt(3) + 1) + 4*(b^2*d^4*p + 2*a*b*d*e^3*p)/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 4*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)*p)*sqrt(-((b^4*d^12*e^2 - 4*a*b^3*d^9*e^5 + 6*a^2*b^2*d^6*e^8 - 4*a^3*b*d^3*e^11 + a^4*e^14)*((b^2*d^2*p^2/(b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8) - (b^2*d^4*p + 2*a*b*d*e^3*p)^2/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^2)*(-I*sqrt(3) + 1)/(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3) - 4*(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3)*(I*sqrt(3) + 1) + 4*(b^2*d^4*p + 2*a*b*d*e^3*p)/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7))^2 - 8*(b^4*d^10*e - 3*a^2*b^2*d^4*e^7 + 2*a^3*b*d*e^10)*((b^2*d^2*p^2/(b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8) - (b^2*d^4*p + 2*a*b*d*e^3*p)^2/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^2)*(-I*sqrt(3) + 1)/(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3) - 4*(-3/16*(b^2*d^4*p + 2*a*b*d*e^3*p)*b^2*d^2*p^2/((b^2*d^6*e^2 - 2*a*b*d^3*e^5 + a^2*e^8)*(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)) + 1/16*b^2*p^3/(b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9) + 1/16*(8*b*d^3 + a*e^3)*a*b^2*p^3/(b*d^3 - a*e^3)^4 + 1/8*(b^2*d^4*p + 2*a*b*d*e^3*p)^3/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7)^3)^(1/3)*(I*sqrt(3) + 1) + 4*(b^2*d^4*p + 2*a*b*d*e^3*p)/(b^2*d^6*e - 2*a*b*d^3*e^4 + a^2*e^7))*p + 16*(b^4*d^8 - 20*a*b^3*d^5*e^3 - 8*a^2*b^2*d^2*e^6)*p^2)/(b^4*d^12*e^2 - 4*a*b^3*d^9*e^5 + 6*a^2*b^2*d^6*e^8 - 4*a^3*b*d^3*e^11 + a^4*e^14))) - 24*((b^2*d^4*e^2 + 2*a*b*d*e^5)*p*x^2 + 2*(b^2*d^5*e + 2*a*b*d^2*e^4)*p*x + (b^2*d^6 + 2*a*b*d^3*e^3)*p)*log(e*x + d) - 8*(b^2*d^6 - 2*a*b*d^3*e^3 + a^2*e^6)*log(c))/(b^2*d^8*e - 2*a*b*d^5*e^4 + a^2*d^2*e^7 + (b^2*d^6*e^3 - 2*a*b*d^3*e^6 + a^2*e^9)*x^2 + 2*(b^2*d^7*e^2 - 2*a*b*d^4*e^5 + a^2*d*e^8)*x)","C",0
198,1,239,0,0.907049," ","integrate((e*x+d)^3*log(c*(a+b/x)^p),x, algorithm=""fricas"")","\frac{2 \, a^{3} b e^{3} p x^{3} + 3 \, {\left(4 \, a^{3} b d e^{2} - a^{2} b^{2} e^{3}\right)} p x^{2} + 6 \, {\left(6 \, a^{3} b d^{2} e - 4 \, a^{2} b^{2} d e^{2} + a b^{3} e^{3}\right)} p x + 6 \, {\left(4 \, a^{3} b d^{3} - 6 \, a^{2} b^{2} d^{2} e + 4 \, a b^{3} d e^{2} - b^{4} e^{3}\right)} p \log\left(a x + b\right) + 6 \, {\left(a^{4} e^{3} x^{4} + 4 \, a^{4} d e^{2} x^{3} + 6 \, a^{4} d^{2} e x^{2} + 4 \, a^{4} d^{3} x\right)} \log\left(c\right) + 6 \, {\left(a^{4} e^{3} p x^{4} + 4 \, a^{4} d e^{2} p x^{3} + 6 \, a^{4} d^{2} e p x^{2} + 4 \, a^{4} d^{3} p x\right)} \log\left(\frac{a x + b}{x}\right)}{24 \, a^{4}}"," ",0,"1/24*(2*a^3*b*e^3*p*x^3 + 3*(4*a^3*b*d*e^2 - a^2*b^2*e^3)*p*x^2 + 6*(6*a^3*b*d^2*e - 4*a^2*b^2*d*e^2 + a*b^3*e^3)*p*x + 6*(4*a^3*b*d^3 - 6*a^2*b^2*d^2*e + 4*a*b^3*d*e^2 - b^4*e^3)*p*log(a*x + b) + 6*(a^4*e^3*x^4 + 4*a^4*d*e^2*x^3 + 6*a^4*d^2*e*x^2 + 4*a^4*d^3*x)*log(c) + 6*(a^4*e^3*p*x^4 + 4*a^4*d*e^2*p*x^3 + 6*a^4*d^2*e*p*x^2 + 4*a^4*d^3*p*x)*log((a*x + b)/x))/a^4","A",0
199,1,153,0,0.825452," ","integrate((e*x+d)^2*log(c*(a+b/x)^p),x, algorithm=""fricas"")","\frac{a^{2} b e^{2} p x^{2} + 2 \, {\left(3 \, a^{2} b d e - a b^{2} e^{2}\right)} p x + 2 \, {\left(3 \, a^{2} b d^{2} - 3 \, a b^{2} d e + b^{3} e^{2}\right)} p \log\left(a x + b\right) + 2 \, {\left(a^{3} e^{2} x^{3} + 3 \, a^{3} d e x^{2} + 3 \, a^{3} d^{2} x\right)} \log\left(c\right) + 2 \, {\left(a^{3} e^{2} p x^{3} + 3 \, a^{3} d e p x^{2} + 3 \, a^{3} d^{2} p x\right)} \log\left(\frac{a x + b}{x}\right)}{6 \, a^{3}}"," ",0,"1/6*(a^2*b*e^2*p*x^2 + 2*(3*a^2*b*d*e - a*b^2*e^2)*p*x + 2*(3*a^2*b*d^2 - 3*a*b^2*d*e + b^3*e^2)*p*log(a*x + b) + 2*(a^3*e^2*x^3 + 3*a^3*d*e*x^2 + 3*a^3*d^2*x)*log(c) + 2*(a^3*e^2*p*x^3 + 3*a^3*d*e*p*x^2 + 3*a^3*d^2*p*x)*log((a*x + b)/x))/a^3","A",0
200,1,80,0,0.926338," ","integrate((e*x+d)*log(c*(a+b/x)^p),x, algorithm=""fricas"")","\frac{a b e p x + {\left(2 \, a b d - b^{2} e\right)} p \log\left(a x + b\right) + {\left(a^{2} e x^{2} + 2 \, a^{2} d x\right)} \log\left(c\right) + {\left(a^{2} e p x^{2} + 2 \, a^{2} d p x\right)} \log\left(\frac{a x + b}{x}\right)}{2 \, a^{2}}"," ",0,"1/2*(a*b*e*p*x + (2*a*b*d - b^2*e)*p*log(a*x + b) + (a^2*e*x^2 + 2*a^2*d*x)*log(c) + (a^2*e*p*x^2 + 2*a^2*d*p*x)*log((a*x + b)/x))/a^2","A",0
201,0,0,0,0.952840," ","integrate(log(c*(a+b/x)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(c \left(\frac{a x + b}{x}\right)^{p}\right)}{e x + d}, x\right)"," ",0,"integral(log(c*((a*x + b)/x)^p)/(e*x + d), x)","F",0
202,1,148,0,1.112904," ","integrate(log(c*(a+b/x)^p)/(e*x+d)^2,x, algorithm=""fricas"")","-\frac{{\left(a d^{2} - b d e\right)} p \log\left(\frac{a x + b}{x}\right) - {\left(a d e p x + a d^{2} p\right)} \log\left(a x + b\right) + {\left(b e^{2} p x + b d e p\right)} \log\left(e x + d\right) + {\left(a d^{2} - b d e\right)} \log\left(c\right) + {\left({\left(a d e - b e^{2}\right)} p x + {\left(a d^{2} - b d e\right)} p\right)} \log\left(x\right)}{a d^{3} e - b d^{2} e^{2} + {\left(a d^{2} e^{2} - b d e^{3}\right)} x}"," ",0,"-((a*d^2 - b*d*e)*p*log((a*x + b)/x) - (a*d*e*p*x + a*d^2*p)*log(a*x + b) + (b*e^2*p*x + b*d*e*p)*log(e*x + d) + (a*d^2 - b*d*e)*log(c) + ((a*d*e - b*e^2)*p*x + (a*d^2 - b*d*e)*p)*log(x))/(a*d^3*e - b*d^2*e^2 + (a*d^2*e^2 - b*d*e^3)*x)","A",0
203,1,428,0,2.382691," ","integrate(log(c*(a+b/x)^p)/(e*x+d)^3,x, algorithm=""fricas"")","\frac{{\left(a b d^{2} e^{2} - b^{2} d e^{3}\right)} p x - {\left(a^{2} d^{4} - 2 \, a b d^{3} e + b^{2} d^{2} e^{2}\right)} p \log\left(\frac{a x + b}{x}\right) + {\left(a b d^{3} e - b^{2} d^{2} e^{2}\right)} p + {\left(a^{2} d^{2} e^{2} p x^{2} + 2 \, a^{2} d^{3} e p x + a^{2} d^{4} p\right)} \log\left(a x + b\right) - {\left({\left(2 \, a b d e^{3} - b^{2} e^{4}\right)} p x^{2} + 2 \, {\left(2 \, a b d^{2} e^{2} - b^{2} d e^{3}\right)} p x + {\left(2 \, a b d^{3} e - b^{2} d^{2} e^{2}\right)} p\right)} \log\left(e x + d\right) - {\left(a^{2} d^{4} - 2 \, a b d^{3} e + b^{2} d^{2} e^{2}\right)} \log\left(c\right) - {\left({\left(a^{2} d^{2} e^{2} - 2 \, a b d e^{3} + b^{2} e^{4}\right)} p x^{2} + 2 \, {\left(a^{2} d^{3} e - 2 \, a b d^{2} e^{2} + b^{2} d e^{3}\right)} p x + {\left(a^{2} d^{4} - 2 \, a b d^{3} e + b^{2} d^{2} e^{2}\right)} p\right)} \log\left(x\right)}{2 \, {\left(a^{2} d^{6} e - 2 \, a b d^{5} e^{2} + b^{2} d^{4} e^{3} + {\left(a^{2} d^{4} e^{3} - 2 \, a b d^{3} e^{4} + b^{2} d^{2} e^{5}\right)} x^{2} + 2 \, {\left(a^{2} d^{5} e^{2} - 2 \, a b d^{4} e^{3} + b^{2} d^{3} e^{4}\right)} x\right)}}"," ",0,"1/2*((a*b*d^2*e^2 - b^2*d*e^3)*p*x - (a^2*d^4 - 2*a*b*d^3*e + b^2*d^2*e^2)*p*log((a*x + b)/x) + (a*b*d^3*e - b^2*d^2*e^2)*p + (a^2*d^2*e^2*p*x^2 + 2*a^2*d^3*e*p*x + a^2*d^4*p)*log(a*x + b) - ((2*a*b*d*e^3 - b^2*e^4)*p*x^2 + 2*(2*a*b*d^2*e^2 - b^2*d*e^3)*p*x + (2*a*b*d^3*e - b^2*d^2*e^2)*p)*log(e*x + d) - (a^2*d^4 - 2*a*b*d^3*e + b^2*d^2*e^2)*log(c) - ((a^2*d^2*e^2 - 2*a*b*d*e^3 + b^2*e^4)*p*x^2 + 2*(a^2*d^3*e - 2*a*b*d^2*e^2 + b^2*d*e^3)*p*x + (a^2*d^4 - 2*a*b*d^3*e + b^2*d^2*e^2)*p)*log(x))/(a^2*d^6*e - 2*a*b*d^5*e^2 + b^2*d^4*e^3 + (a^2*d^4*e^3 - 2*a*b*d^3*e^4 + b^2*d^2*e^5)*x^2 + 2*(a^2*d^5*e^2 - 2*a*b*d^4*e^3 + b^2*d^3*e^4)*x)","B",0
204,1,818,0,12.905056," ","integrate(log(c*(a+b/x)^p)/(e*x+d)^4,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a^{2} b d^{3} e^{3} - 3 \, a b^{2} d^{2} e^{4} + b^{3} d e^{5}\right)} p x^{2} + {\left(9 \, a^{2} b d^{4} e^{2} - 14 \, a b^{2} d^{3} e^{3} + 5 \, b^{3} d^{2} e^{4}\right)} p x - 2 \, {\left(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}\right)} p \log\left(\frac{a x + b}{x}\right) + {\left(5 \, a^{2} b d^{5} e - 8 \, a b^{2} d^{4} e^{2} + 3 \, b^{3} d^{3} e^{3}\right)} p + 2 \, {\left(a^{3} d^{3} e^{3} p x^{3} + 3 \, a^{3} d^{4} e^{2} p x^{2} + 3 \, a^{3} d^{5} e p x + a^{3} d^{6} p\right)} \log\left(a x + b\right) - 2 \, {\left({\left(3 \, a^{2} b d^{2} e^{4} - 3 \, a b^{2} d e^{5} + b^{3} e^{6}\right)} p x^{3} + 3 \, {\left(3 \, a^{2} b d^{3} e^{3} - 3 \, a b^{2} d^{2} e^{4} + b^{3} d e^{5}\right)} p x^{2} + 3 \, {\left(3 \, a^{2} b d^{4} e^{2} - 3 \, a b^{2} d^{3} e^{3} + b^{3} d^{2} e^{4}\right)} p x + {\left(3 \, a^{2} b d^{5} e - 3 \, a b^{2} d^{4} e^{2} + b^{3} d^{3} e^{3}\right)} p\right)} \log\left(e x + d\right) - 2 \, {\left(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}\right)} \log\left(c\right) - 2 \, {\left({\left(a^{3} d^{3} e^{3} - 3 \, a^{2} b d^{2} e^{4} + 3 \, a b^{2} d e^{5} - b^{3} e^{6}\right)} p x^{3} + 3 \, {\left(a^{3} d^{4} e^{2} - 3 \, a^{2} b d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{4} - b^{3} d e^{5}\right)} p x^{2} + 3 \, {\left(a^{3} d^{5} e - 3 \, a^{2} b d^{4} e^{2} + 3 \, a b^{2} d^{3} e^{3} - b^{3} d^{2} e^{4}\right)} p x + {\left(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}\right)} p\right)} \log\left(x\right)}{6 \, {\left(a^{3} d^{9} e - 3 \, a^{2} b d^{8} e^{2} + 3 \, a b^{2} d^{7} e^{3} - b^{3} d^{6} e^{4} + {\left(a^{3} d^{6} e^{4} - 3 \, a^{2} b d^{5} e^{5} + 3 \, a b^{2} d^{4} e^{6} - b^{3} d^{3} e^{7}\right)} x^{3} + 3 \, {\left(a^{3} d^{7} e^{3} - 3 \, a^{2} b d^{6} e^{4} + 3 \, a b^{2} d^{5} e^{5} - b^{3} d^{4} e^{6}\right)} x^{2} + 3 \, {\left(a^{3} d^{8} e^{2} - 3 \, a^{2} b d^{7} e^{3} + 3 \, a b^{2} d^{6} e^{4} - b^{3} d^{5} e^{5}\right)} x\right)}}"," ",0,"1/6*(2*(2*a^2*b*d^3*e^3 - 3*a*b^2*d^2*e^4 + b^3*d*e^5)*p*x^2 + (9*a^2*b*d^4*e^2 - 14*a*b^2*d^3*e^3 + 5*b^3*d^2*e^4)*p*x - 2*(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)*p*log((a*x + b)/x) + (5*a^2*b*d^5*e - 8*a*b^2*d^4*e^2 + 3*b^3*d^3*e^3)*p + 2*(a^3*d^3*e^3*p*x^3 + 3*a^3*d^4*e^2*p*x^2 + 3*a^3*d^5*e*p*x + a^3*d^6*p)*log(a*x + b) - 2*((3*a^2*b*d^2*e^4 - 3*a*b^2*d*e^5 + b^3*e^6)*p*x^3 + 3*(3*a^2*b*d^3*e^3 - 3*a*b^2*d^2*e^4 + b^3*d*e^5)*p*x^2 + 3*(3*a^2*b*d^4*e^2 - 3*a*b^2*d^3*e^3 + b^3*d^2*e^4)*p*x + (3*a^2*b*d^5*e - 3*a*b^2*d^4*e^2 + b^3*d^3*e^3)*p)*log(e*x + d) - 2*(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)*log(c) - 2*((a^3*d^3*e^3 - 3*a^2*b*d^2*e^4 + 3*a*b^2*d*e^5 - b^3*e^6)*p*x^3 + 3*(a^3*d^4*e^2 - 3*a^2*b*d^3*e^3 + 3*a*b^2*d^2*e^4 - b^3*d*e^5)*p*x^2 + 3*(a^3*d^5*e - 3*a^2*b*d^4*e^2 + 3*a*b^2*d^3*e^3 - b^3*d^2*e^4)*p*x + (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)*p)*log(x))/(a^3*d^9*e - 3*a^2*b*d^8*e^2 + 3*a*b^2*d^7*e^3 - b^3*d^6*e^4 + (a^3*d^6*e^4 - 3*a^2*b*d^5*e^5 + 3*a*b^2*d^4*e^6 - b^3*d^3*e^7)*x^3 + 3*(a^3*d^7*e^3 - 3*a^2*b*d^6*e^4 + 3*a*b^2*d^5*e^5 - b^3*d^4*e^6)*x^2 + 3*(a^3*d^8*e^2 - 3*a^2*b*d^7*e^3 + 3*a*b^2*d^6*e^4 - b^3*d^5*e^5)*x)","B",0
205,0,0,0,0.860073," ","integrate(log(a+b/x)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(\frac{a x + b}{x}\right)}{d x + c}, x\right)"," ",0,"integral(log((a*x + b)/x)/(d*x + c), x)","F",0
206,0,0,0,0.953556," ","integrate((e*x+d)^m*log(c*(b*x^3+a)^p),x, algorithm=""fricas"")","{\rm integral}\left({\left(e x + d\right)}^{m} \log\left({\left(b x^{3} + a\right)}^{p} c\right), x\right)"," ",0,"integral((e*x + d)^m*log((b*x^3 + a)^p*c), x)","F",0
207,0,0,0,0.686041," ","integrate((e*x+d)^m*log(c*(b*x^2+a)^p),x, algorithm=""fricas"")","{\rm integral}\left({\left(e x + d\right)}^{m} \log\left({\left(b x^{2} + a\right)}^{p} c\right), x\right)"," ",0,"integral((e*x + d)^m*log((b*x^2 + a)^p*c), x)","F",0
208,0,0,0,0.770113," ","integrate((e*x+d)^m*log(c*(b*x+a)^p),x, algorithm=""fricas"")","{\rm integral}\left({\left(e x + d\right)}^{m} \log\left({\left(b x + a\right)}^{p} c\right), x\right)"," ",0,"integral((e*x + d)^m*log((b*x + a)^p*c), x)","F",0
209,0,0,0,0.935734," ","integrate((e*x+d)^m*log(c*(a+b/x)^p),x, algorithm=""fricas"")","{\rm integral}\left({\left(e x + d\right)}^{m} \log\left(c \left(\frac{a x + b}{x}\right)^{p}\right), x\right)"," ",0,"integral((e*x + d)^m*log(c*((a*x + b)/x)^p), x)","F",0
210,0,0,0,0.595007," ","integrate((e*x+d)^m*log(c*(a+b/x^2)^p),x, algorithm=""fricas"")","{\rm integral}\left({\left(e x + d\right)}^{m} \log\left(c \left(\frac{a x^{2} + b}{x^{2}}\right)^{p}\right), x\right)"," ",0,"integral((e*x + d)^m*log(c*((a*x^2 + b)/x^2)^p), x)","F",0
211,0,0,0,0.924935," ","integrate((g*x+f)^m*log(c*(d+e*x^n)^p),x, algorithm=""fricas"")","{\rm integral}\left({\left(g x + f\right)}^{m} \log\left({\left(e x^{n} + d\right)}^{p} c\right), x\right)"," ",0,"integral((g*x + f)^m*log((e*x^n + d)^p*c), x)","F",0
212,0,0,0,0.878953," ","integrate((g*x+f)^3*log(c*(d+e*x^n)^p),x, algorithm=""fricas"")","{\rm integral}\left({\left(g^{3} x^{3} + 3 \, f g^{2} x^{2} + 3 \, f^{2} g x + f^{3}\right)} \log\left({\left(e x^{n} + d\right)}^{p} c\right), x\right)"," ",0,"integral((g^3*x^3 + 3*f*g^2*x^2 + 3*f^2*g*x + f^3)*log((e*x^n + d)^p*c), x)","F",0
213,0,0,0,0.895051," ","integrate((g*x+f)^2*log(c*(d+e*x^n)^p),x, algorithm=""fricas"")","{\rm integral}\left({\left(g^{2} x^{2} + 2 \, f g x + f^{2}\right)} \log\left({\left(e x^{n} + d\right)}^{p} c\right), x\right)"," ",0,"integral((g^2*x^2 + 2*f*g*x + f^2)*log((e*x^n + d)^p*c), x)","F",0
214,0,0,0,0.825603," ","integrate((g*x+f)*log(c*(d+e*x^n)^p),x, algorithm=""fricas"")","{\rm integral}\left({\left(g x + f\right)} \log\left({\left(e x^{n} + d\right)}^{p} c\right), x\right)"," ",0,"integral((g*x + f)*log((e*x^n + d)^p*c), x)","F",0
215,0,0,0,0.963409," ","integrate(log(c*(d+e*x^n)^p),x, algorithm=""fricas"")","{\rm integral}\left(\log\left({\left(e x^{n} + d\right)}^{p} c\right), x\right)"," ",0,"integral(log((e*x^n + d)^p*c), x)","F",0
216,0,0,0,0.985297," ","integrate(log(c*(d+e*x^n)^p)/(g*x+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{n} + d\right)}^{p} c\right)}{g x + f}, x\right)"," ",0,"integral(log((e*x^n + d)^p*c)/(g*x + f), x)","F",0
217,0,0,0,0.858218," ","integrate(log(c*(d+e*x^n)^p)/(g*x+f)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{n} + d\right)}^{p} c\right)}{g^{2} x^{2} + 2 \, f g x + f^{2}}, x\right)"," ",0,"integral(log((e*x^n + d)^p*c)/(g^2*x^2 + 2*f*g*x + f^2), x)","F",0
218,0,0,0,0.720755," ","integrate(log(c*(d+e*x^n)^p)/(g*x+f)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{n} + d\right)}^{p} c\right)}{g^{3} x^{3} + 3 \, f g^{2} x^{2} + 3 \, f^{2} g x + f^{3}}, x\right)"," ",0,"integral(log((e*x^n + d)^p*c)/(g^3*x^3 + 3*f*g^2*x^2 + 3*f^2*g*x + f^3), x)","F",0
219,0,0,0,0.656621," ","integrate(x^3*log(c*(b*x+a)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} \log\left({\left(b x + a\right)}^{p} c\right)}{e x + d}, x\right)"," ",0,"integral(x^3*log((b*x + a)^p*c)/(e*x + d), x)","F",0
220,0,0,0,1.133751," ","integrate(x^2*log(c*(b*x+a)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} \log\left({\left(b x + a\right)}^{p} c\right)}{e x + d}, x\right)"," ",0,"integral(x^2*log((b*x + a)^p*c)/(e*x + d), x)","F",0
221,0,0,0,0.986711," ","integrate(x*log(c*(b*x+a)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x \log\left({\left(b x + a\right)}^{p} c\right)}{e x + d}, x\right)"," ",0,"integral(x*log((b*x + a)^p*c)/(e*x + d), x)","F",0
222,0,0,0,0.799086," ","integrate(log(c*(b*x+a)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x + a\right)}^{p} c\right)}{e x + d}, x\right)"," ",0,"integral(log((b*x + a)^p*c)/(e*x + d), x)","F",0
223,0,0,0,0.934078," ","integrate(log(c*(b*x+a)^p)/x/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x + a\right)}^{p} c\right)}{e x^{2} + d x}, x\right)"," ",0,"integral(log((b*x + a)^p*c)/(e*x^2 + d*x), x)","F",0
224,0,0,0,0.840012," ","integrate(log(c*(b*x+a)^p)/x^2/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x + a\right)}^{p} c\right)}{e x^{3} + d x^{2}}, x\right)"," ",0,"integral(log((b*x + a)^p*c)/(e*x^3 + d*x^2), x)","F",0
225,0,0,0,0.792635," ","integrate(log(c*(b*x+a)^p)/x^3/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x + a\right)}^{p} c\right)}{e x^{4} + d x^{3}}, x\right)"," ",0,"integral(log((b*x + a)^p*c)/(e*x^4 + d*x^3), x)","F",0
226,0,0,0,0.721061," ","integrate(x^3*log(c*(b*x^2+a)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} \log\left({\left(b x^{2} + a\right)}^{p} c\right)}{e x + d}, x\right)"," ",0,"integral(x^3*log((b*x^2 + a)^p*c)/(e*x + d), x)","F",0
227,0,0,0,0.896506," ","integrate(x^2*log(c*(b*x^2+a)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} \log\left({\left(b x^{2} + a\right)}^{p} c\right)}{e x + d}, x\right)"," ",0,"integral(x^2*log((b*x^2 + a)^p*c)/(e*x + d), x)","F",0
228,0,0,0,0.812826," ","integrate(x*log(c*(b*x^2+a)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x \log\left({\left(b x^{2} + a\right)}^{p} c\right)}{e x + d}, x\right)"," ",0,"integral(x*log((b*x^2 + a)^p*c)/(e*x + d), x)","F",0
229,0,0,0,0.937618," ","integrate(log(c*(b*x^2+a)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)}{e x + d}, x\right)"," ",0,"integral(log((b*x^2 + a)^p*c)/(e*x + d), x)","F",0
230,0,0,0,0.929622," ","integrate(log(c*(b*x^2+a)^p)/x/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)}{e x^{2} + d x}, x\right)"," ",0,"integral(log((b*x^2 + a)^p*c)/(e*x^2 + d*x), x)","F",0
231,0,0,0,0.672573," ","integrate(log(c*(b*x^2+a)^p)/x^2/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)}{e x^{3} + d x^{2}}, x\right)"," ",0,"integral(log((b*x^2 + a)^p*c)/(e*x^3 + d*x^2), x)","F",0
232,0,0,0,1.206264," ","integrate(log(c*(b*x^2+a)^p)/x^3/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{2} + a\right)}^{p} c\right)}{e x^{4} + d x^{3}}, x\right)"," ",0,"integral(log((b*x^2 + a)^p*c)/(e*x^4 + d*x^3), x)","F",0
233,0,0,0,1.024626," ","integrate(x^3*log(c*(b*x^3+a)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} \log\left({\left(b x^{3} + a\right)}^{p} c\right)}{e x + d}, x\right)"," ",0,"integral(x^3*log((b*x^3 + a)^p*c)/(e*x + d), x)","F",0
234,0,0,0,0.915246," ","integrate(x^2*log(c*(b*x^3+a)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} \log\left({\left(b x^{3} + a\right)}^{p} c\right)}{e x + d}, x\right)"," ",0,"integral(x^2*log((b*x^3 + a)^p*c)/(e*x + d), x)","F",0
235,0,0,0,0.955027," ","integrate(x*log(c*(b*x^3+a)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x \log\left({\left(b x^{3} + a\right)}^{p} c\right)}{e x + d}, x\right)"," ",0,"integral(x*log((b*x^3 + a)^p*c)/(e*x + d), x)","F",0
236,0,0,0,0.870152," ","integrate(log(c*(b*x^3+a)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{3} + a\right)}^{p} c\right)}{e x + d}, x\right)"," ",0,"integral(log((b*x^3 + a)^p*c)/(e*x + d), x)","F",0
237,0,0,0,0.989855," ","integrate(log(c*(b*x^3+a)^p)/x/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{3} + a\right)}^{p} c\right)}{e x^{2} + d x}, x\right)"," ",0,"integral(log((b*x^3 + a)^p*c)/(e*x^2 + d*x), x)","F",0
238,0,0,0,1.181275," ","integrate(log(c*(b*x^3+a)^p)/x^2/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{3} + a\right)}^{p} c\right)}{e x^{3} + d x^{2}}, x\right)"," ",0,"integral(log((b*x^3 + a)^p*c)/(e*x^3 + d*x^2), x)","F",0
239,0,0,0,1.115148," ","integrate(log(c*(b*x^3+a)^p)/x^3/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{3} + a\right)}^{p} c\right)}{e x^{4} + d x^{3}}, x\right)"," ",0,"integral(log((b*x^3 + a)^p*c)/(e*x^4 + d*x^3), x)","F",0
240,0,0,0,1.049270," ","integrate(x^3*log(c*(a+b/x)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} \log\left(c \left(\frac{a x + b}{x}\right)^{p}\right)}{e x + d}, x\right)"," ",0,"integral(x^3*log(c*((a*x + b)/x)^p)/(e*x + d), x)","F",0
241,0,0,0,0.909742," ","integrate(x^2*log(c*(a+b/x)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} \log\left(c \left(\frac{a x + b}{x}\right)^{p}\right)}{e x + d}, x\right)"," ",0,"integral(x^2*log(c*((a*x + b)/x)^p)/(e*x + d), x)","F",0
242,0,0,0,0.925292," ","integrate(x*log(c*(a+b/x)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x \log\left(c \left(\frac{a x + b}{x}\right)^{p}\right)}{e x + d}, x\right)"," ",0,"integral(x*log(c*((a*x + b)/x)^p)/(e*x + d), x)","F",0
243,0,0,0,1.050994," ","integrate(log(c*(a+b/x)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(c \left(\frac{a x + b}{x}\right)^{p}\right)}{e x + d}, x\right)"," ",0,"integral(log(c*((a*x + b)/x)^p)/(e*x + d), x)","F",0
244,0,0,0,0.982528," ","integrate(log(c*(a+b/x)^p)/x/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(c \left(\frac{a x + b}{x}\right)^{p}\right)}{e x^{2} + d x}, x\right)"," ",0,"integral(log(c*((a*x + b)/x)^p)/(e*x^2 + d*x), x)","F",0
245,0,0,0,0.995635," ","integrate(log(c*(a+b/x)^p)/x^2/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(c \left(\frac{a x + b}{x}\right)^{p}\right)}{e x^{3} + d x^{2}}, x\right)"," ",0,"integral(log(c*((a*x + b)/x)^p)/(e*x^3 + d*x^2), x)","F",0
246,0,0,0,1.060212," ","integrate(log(c*(a+b/x)^p)/x^3/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(c \left(\frac{a x + b}{x}\right)^{p}\right)}{e x^{4} + d x^{3}}, x\right)"," ",0,"integral(log(c*((a*x + b)/x)^p)/(e*x^4 + d*x^3), x)","F",0
247,0,0,0,1.174549," ","integrate(x^3*log(c*(a+b/x^2)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} \log\left(c \left(\frac{a x^{2} + b}{x^{2}}\right)^{p}\right)}{e x + d}, x\right)"," ",0,"integral(x^3*log(c*((a*x^2 + b)/x^2)^p)/(e*x + d), x)","F",0
248,0,0,0,0.893938," ","integrate(x^2*log(c*(a+b/x^2)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} \log\left(c \left(\frac{a x^{2} + b}{x^{2}}\right)^{p}\right)}{e x + d}, x\right)"," ",0,"integral(x^2*log(c*((a*x^2 + b)/x^2)^p)/(e*x + d), x)","F",0
249,0,0,0,0.697425," ","integrate(x*log(c*(a+b/x^2)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x \log\left(c \left(\frac{a x^{2} + b}{x^{2}}\right)^{p}\right)}{e x + d}, x\right)"," ",0,"integral(x*log(c*((a*x^2 + b)/x^2)^p)/(e*x + d), x)","F",0
250,0,0,0,0.983986," ","integrate(log(c*(a+b/x^2)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(c \left(\frac{a x^{2} + b}{x^{2}}\right)^{p}\right)}{e x + d}, x\right)"," ",0,"integral(log(c*((a*x^2 + b)/x^2)^p)/(e*x + d), x)","F",0
251,0,0,0,1.014364," ","integrate(log(c*(a+b/x^2)^p)/x/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(c \left(\frac{a x^{2} + b}{x^{2}}\right)^{p}\right)}{e x^{2} + d x}, x\right)"," ",0,"integral(log(c*((a*x^2 + b)/x^2)^p)/(e*x^2 + d*x), x)","F",0
252,0,0,0,1.052508," ","integrate(log(c*(a+b/x^2)^p)/x^2/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(c \left(\frac{a x^{2} + b}{x^{2}}\right)^{p}\right)}{e x^{3} + d x^{2}}, x\right)"," ",0,"integral(log(c*((a*x^2 + b)/x^2)^p)/(e*x^3 + d*x^2), x)","F",0
253,0,0,0,0.921859," ","integrate(log(c*(a+b/x^2)^p)/x^3/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(c \left(\frac{a x^{2} + b}{x^{2}}\right)^{p}\right)}{e x^{4} + d x^{3}}, x\right)"," ",0,"integral(log(c*((a*x^2 + b)/x^2)^p)/(e*x^4 + d*x^3), x)","F",0
254,0,0,0,1.223184," ","integrate(x^3*log(c*(a+b/x^3)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} \log\left(c \left(\frac{a x^{3} + b}{x^{3}}\right)^{p}\right)}{e x + d}, x\right)"," ",0,"integral(x^3*log(c*((a*x^3 + b)/x^3)^p)/(e*x + d), x)","F",0
255,0,0,0,0.793007," ","integrate(x^2*log(c*(a+b/x^3)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} \log\left(c \left(\frac{a x^{3} + b}{x^{3}}\right)^{p}\right)}{e x + d}, x\right)"," ",0,"integral(x^2*log(c*((a*x^3 + b)/x^3)^p)/(e*x + d), x)","F",0
256,0,0,0,0.679564," ","integrate(x*log(c*(a+b/x^3)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x \log\left(c \left(\frac{a x^{3} + b}{x^{3}}\right)^{p}\right)}{e x + d}, x\right)"," ",0,"integral(x*log(c*((a*x^3 + b)/x^3)^p)/(e*x + d), x)","F",0
257,0,0,0,0.860243," ","integrate(log(c*(a+b/x^3)^p)/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(c \left(\frac{a x^{3} + b}{x^{3}}\right)^{p}\right)}{e x + d}, x\right)"," ",0,"integral(log(c*((a*x^3 + b)/x^3)^p)/(e*x + d), x)","F",0
258,0,0,0,1.013244," ","integrate(log(c*(a+b/x^3)^p)/x/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(c \left(\frac{a x^{3} + b}{x^{3}}\right)^{p}\right)}{e x^{2} + d x}, x\right)"," ",0,"integral(log(c*((a*x^3 + b)/x^3)^p)/(e*x^2 + d*x), x)","F",0
259,0,0,0,0.965843," ","integrate(log(c*(a+b/x^3)^p)/x^2/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(c \left(\frac{a x^{3} + b}{x^{3}}\right)^{p}\right)}{e x^{3} + d x^{2}}, x\right)"," ",0,"integral(log(c*((a*x^3 + b)/x^3)^p)/(e*x^3 + d*x^2), x)","F",0
260,0,0,0,0.900188," ","integrate(log(c*(a+b/x^3)^p)/x^3/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(c \left(\frac{a x^{3} + b}{x^{3}}\right)^{p}\right)}{e x^{4} + d x^{3}}, x\right)"," ",0,"integral(log(c*((a*x^3 + b)/x^3)^p)/(e*x^4 + d*x^3), x)","F",0
261,0,0,0,0.758055," ","integrate(log(c*(e*x^3+d)^p)/(g*x^2+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{3} + d\right)}^{p} c\right)}{g x^{2} + f}, x\right)"," ",0,"integral(log((e*x^3 + d)^p*c)/(g*x^2 + f), x)","F",0
262,0,0,0,0.935172," ","integrate(log(c*(e*x^2+d)^p)/(g*x^2+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g x^{2} + f}, x\right)"," ",0,"integral(log((e*x^2 + d)^p*c)/(g*x^2 + f), x)","F",0
263,0,0,0,1.156606," ","integrate(log(c*(e*x+d)^p)/(g*x^2+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x + d\right)}^{p} c\right)}{g x^{2} + f}, x\right)"," ",0,"integral(log((e*x + d)^p*c)/(g*x^2 + f), x)","F",0
264,0,0,0,0.882682," ","integrate(log(c*(d+e/x)^p)/(g*x^2+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(c \left(\frac{d x + e}{x}\right)^{p}\right)}{g x^{2} + f}, x\right)"," ",0,"integral(log(c*((d*x + e)/x)^p)/(g*x^2 + f), x)","F",0
265,0,0,0,1.014664," ","integrate(log(c*(d+e/x^2)^p)/(g*x^2+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(c \left(\frac{d x^{2} + e}{x^{2}}\right)^{p}\right)}{g x^{2} + f}, x\right)"," ",0,"integral(log(c*((d*x^2 + e)/x^2)^p)/(g*x^2 + f), x)","F",0
266,0,0,0,1.266953," ","integrate(log(c*(d+e*x^(1/2))^p)/(g*x^2+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e \sqrt{x} + d\right)}^{p} c\right)}{g x^{2} + f}, x\right)"," ",0,"integral(log((e*sqrt(x) + d)^p*c)/(g*x^2 + f), x)","F",0
267,0,0,0,0.921865," ","integrate(log(c*(d+e/x^(1/2))^p)/(g*x^2+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(c \left(\frac{d x + e \sqrt{x}}{x}\right)^{p}\right)}{g x^{2} + f}, x\right)"," ",0,"integral(log(c*((d*x + e*sqrt(x))/x)^p)/(g*x^2 + f), x)","F",0
268,1,596,0,1.026387," ","integrate((g*x^2+f)^3*log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","\left[-\frac{150 \, e^{3} g^{3} p x^{7} + 42 \, {\left(21 \, e^{3} f g^{2} - 5 \, d e^{2} g^{3}\right)} p x^{5} + 70 \, {\left(35 \, e^{3} f^{2} g - 21 \, d e^{2} f g^{2} + 5 \, d^{2} e g^{3}\right)} p 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)} p \sqrt{-\frac{d}{e}} \log\left(\frac{e x^{2} - 2 \, e x \sqrt{-\frac{d}{e}} - d}{e x^{2} + d}\right) + 210 \, {\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)} p x - 105 \, {\left(5 \, e^{3} g^{3} p x^{7} + 21 \, e^{3} f g^{2} p x^{5} + 35 \, e^{3} f^{2} g p x^{3} + 35 \, e^{3} f^{3} p x\right)} \log\left(e x^{2} + d\right) - 105 \, {\left(5 \, e^{3} g^{3} x^{7} + 21 \, e^{3} f g^{2} x^{5} + 35 \, e^{3} f^{2} g x^{3} + 35 \, e^{3} f^{3} x\right)} \log\left(c\right)}{3675 \, e^{3}}, -\frac{150 \, e^{3} g^{3} p x^{7} + 42 \, {\left(21 \, e^{3} f g^{2} - 5 \, d e^{2} g^{3}\right)} p x^{5} + 70 \, {\left(35 \, e^{3} f^{2} g - 21 \, d e^{2} f g^{2} + 5 \, d^{2} e g^{3}\right)} p x^{3} - 210 \, {\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)} p \sqrt{\frac{d}{e}} \arctan\left(\frac{e x \sqrt{\frac{d}{e}}}{d}\right) + 210 \, {\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)} p x - 105 \, {\left(5 \, e^{3} g^{3} p x^{7} + 21 \, e^{3} f g^{2} p x^{5} + 35 \, e^{3} f^{2} g p x^{3} + 35 \, e^{3} f^{3} p x\right)} \log\left(e x^{2} + d\right) - 105 \, {\left(5 \, e^{3} g^{3} x^{7} + 21 \, e^{3} f g^{2} x^{5} + 35 \, e^{3} f^{2} g x^{3} + 35 \, e^{3} f^{3} x\right)} \log\left(c\right)}{3675 \, e^{3}}\right]"," ",0,"[-1/3675*(150*e^3*g^3*p*x^7 + 42*(21*e^3*f*g^2 - 5*d*e^2*g^3)*p*x^5 + 70*(35*e^3*f^2*g - 21*d*e^2*f*g^2 + 5*d^2*e*g^3)*p*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)*p*sqrt(-d/e)*log((e*x^2 - 2*e*x*sqrt(-d/e) - d)/(e*x^2 + d)) + 210*(35*e^3*f^3 - 35*d*e^2*f^2*g + 21*d^2*e*f*g^2 - 5*d^3*g^3)*p*x - 105*(5*e^3*g^3*p*x^7 + 21*e^3*f*g^2*p*x^5 + 35*e^3*f^2*g*p*x^3 + 35*e^3*f^3*p*x)*log(e*x^2 + d) - 105*(5*e^3*g^3*x^7 + 21*e^3*f*g^2*x^5 + 35*e^3*f^2*g*x^3 + 35*e^3*f^3*x)*log(c))/e^3, -1/3675*(150*e^3*g^3*p*x^7 + 42*(21*e^3*f*g^2 - 5*d*e^2*g^3)*p*x^5 + 70*(35*e^3*f^2*g - 21*d*e^2*f*g^2 + 5*d^2*e*g^3)*p*x^3 - 210*(35*e^3*f^3 - 35*d*e^2*f^2*g + 21*d^2*e*f*g^2 - 5*d^3*g^3)*p*sqrt(d/e)*arctan(e*x*sqrt(d/e)/d) + 210*(35*e^3*f^3 - 35*d*e^2*f^2*g + 21*d^2*e*f*g^2 - 5*d^3*g^3)*p*x - 105*(5*e^3*g^3*p*x^7 + 21*e^3*f*g^2*p*x^5 + 35*e^3*f^2*g*p*x^3 + 35*e^3*f^3*p*x)*log(e*x^2 + d) - 105*(5*e^3*g^3*x^7 + 21*e^3*f*g^2*x^5 + 35*e^3*f^2*g*x^3 + 35*e^3*f^3*x)*log(c))/e^3]","A",0
269,1,404,0,1.098366," ","integrate((g*x^2+f)^2*log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","\left[-\frac{18 \, e^{2} g^{2} p x^{5} + 10 \, {\left(10 \, e^{2} f g - 3 \, d e g^{2}\right)} p x^{3} - 15 \, {\left(15 \, e^{2} f^{2} - 10 \, d e f g + 3 \, d^{2} g^{2}\right)} p \sqrt{-\frac{d}{e}} \log\left(\frac{e x^{2} + 2 \, e x \sqrt{-\frac{d}{e}} - d}{e x^{2} + d}\right) + 30 \, {\left(15 \, e^{2} f^{2} - 10 \, d e f g + 3 \, d^{2} g^{2}\right)} p x - 15 \, {\left(3 \, e^{2} g^{2} p x^{5} + 10 \, e^{2} f g p x^{3} + 15 \, e^{2} f^{2} p x\right)} \log\left(e x^{2} + d\right) - 15 \, {\left(3 \, e^{2} g^{2} x^{5} + 10 \, e^{2} f g x^{3} + 15 \, e^{2} f^{2} x\right)} \log\left(c\right)}{225 \, e^{2}}, -\frac{18 \, e^{2} g^{2} p x^{5} + 10 \, {\left(10 \, e^{2} f g - 3 \, d e g^{2}\right)} p x^{3} - 30 \, {\left(15 \, e^{2} f^{2} - 10 \, d e f g + 3 \, d^{2} g^{2}\right)} p \sqrt{\frac{d}{e}} \arctan\left(\frac{e x \sqrt{\frac{d}{e}}}{d}\right) + 30 \, {\left(15 \, e^{2} f^{2} - 10 \, d e f g + 3 \, d^{2} g^{2}\right)} p x - 15 \, {\left(3 \, e^{2} g^{2} p x^{5} + 10 \, e^{2} f g p x^{3} + 15 \, e^{2} f^{2} p x\right)} \log\left(e x^{2} + d\right) - 15 \, {\left(3 \, e^{2} g^{2} x^{5} + 10 \, e^{2} f g x^{3} + 15 \, e^{2} f^{2} x\right)} \log\left(c\right)}{225 \, e^{2}}\right]"," ",0,"[-1/225*(18*e^2*g^2*p*x^5 + 10*(10*e^2*f*g - 3*d*e*g^2)*p*x^3 - 15*(15*e^2*f^2 - 10*d*e*f*g + 3*d^2*g^2)*p*sqrt(-d/e)*log((e*x^2 + 2*e*x*sqrt(-d/e) - d)/(e*x^2 + d)) + 30*(15*e^2*f^2 - 10*d*e*f*g + 3*d^2*g^2)*p*x - 15*(3*e^2*g^2*p*x^5 + 10*e^2*f*g*p*x^3 + 15*e^2*f^2*p*x)*log(e*x^2 + d) - 15*(3*e^2*g^2*x^5 + 10*e^2*f*g*x^3 + 15*e^2*f^2*x)*log(c))/e^2, -1/225*(18*e^2*g^2*p*x^5 + 10*(10*e^2*f*g - 3*d*e*g^2)*p*x^3 - 30*(15*e^2*f^2 - 10*d*e*f*g + 3*d^2*g^2)*p*sqrt(d/e)*arctan(e*x*sqrt(d/e)/d) + 30*(15*e^2*f^2 - 10*d*e*f*g + 3*d^2*g^2)*p*x - 15*(3*e^2*g^2*p*x^5 + 10*e^2*f*g*p*x^3 + 15*e^2*f^2*p*x)*log(e*x^2 + d) - 15*(3*e^2*g^2*x^5 + 10*e^2*f*g*x^3 + 15*e^2*f^2*x)*log(c))/e^2]","A",0
270,1,220,0,1.133966," ","integrate((g*x^2+f)*log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","\left[-\frac{2 \, e g p x^{3} + 3 \, {\left(3 \, e f - d g\right)} p \sqrt{-\frac{d}{e}} \log\left(\frac{e x^{2} - 2 \, e x \sqrt{-\frac{d}{e}} - d}{e x^{2} + d}\right) + 6 \, {\left(3 \, e f - d g\right)} p x - 3 \, {\left(e g p x^{3} + 3 \, e f p x\right)} \log\left(e x^{2} + d\right) - 3 \, {\left(e g x^{3} + 3 \, e f x\right)} \log\left(c\right)}{9 \, e}, -\frac{2 \, e g p x^{3} - 6 \, {\left(3 \, e f - d g\right)} p \sqrt{\frac{d}{e}} \arctan\left(\frac{e x \sqrt{\frac{d}{e}}}{d}\right) + 6 \, {\left(3 \, e f - d g\right)} p x - 3 \, {\left(e g p x^{3} + 3 \, e f p x\right)} \log\left(e x^{2} + d\right) - 3 \, {\left(e g x^{3} + 3 \, e f x\right)} \log\left(c\right)}{9 \, e}\right]"," ",0,"[-1/9*(2*e*g*p*x^3 + 3*(3*e*f - d*g)*p*sqrt(-d/e)*log((e*x^2 - 2*e*x*sqrt(-d/e) - d)/(e*x^2 + d)) + 6*(3*e*f - d*g)*p*x - 3*(e*g*p*x^3 + 3*e*f*p*x)*log(e*x^2 + d) - 3*(e*g*x^3 + 3*e*f*x)*log(c))/e, -1/9*(2*e*g*p*x^3 - 6*(3*e*f - d*g)*p*sqrt(d/e)*arctan(e*x*sqrt(d/e)/d) + 6*(3*e*f - d*g)*p*x - 3*(e*g*p*x^3 + 3*e*f*p*x)*log(e*x^2 + d) - 3*(e*g*x^3 + 3*e*f*x)*log(c))/e]","A",0
271,0,0,0,0.767816," ","integrate(log(c*(e*x^2+d)^p)/(g*x^2+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g x^{2} + f}, x\right)"," ",0,"integral(log((e*x^2 + d)^p*c)/(g*x^2 + f), x)","F",0
272,0,0,0,0.892877," ","integrate(log(c*(e*x^2+d)^p)/(g*x^2+f)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g^{2} x^{4} + 2 \, f g x^{2} + f^{2}}, x\right)"," ",0,"integral(log((e*x^2 + d)^p*c)/(g^2*x^4 + 2*f*g*x^2 + f^2), x)","F",0
273,0,0,0,0.809141," ","integrate((g*x^2+f)^2*log(c*(e*x^2+d)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(g^{2} x^{4} + 2 \, f g x^{2} + f^{2}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)^{2}, x\right)"," ",0,"integral((g^2*x^4 + 2*f*g*x^2 + f^2)*log((e*x^2 + d)^p*c)^2, x)","F",0
274,0,0,0,0.987041," ","integrate((g*x^2+f)*log(c*(e*x^2+d)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(g x^{2} + f\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)^{2}, x\right)"," ",0,"integral((g*x^2 + f)*log((e*x^2 + d)^p*c)^2, x)","F",0
275,0,0,0,0.912945," ","integrate(log(c*(e*x^2+d)^p)^2/(g*x^2+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)^{2}}{g x^{2} + f}, x\right)"," ",0,"integral(log((e*x^2 + d)^p*c)^2/(g*x^2 + f), x)","F",0
276,0,0,0,0.915315," ","integrate(log(c*(e*x^2+d)^p)^2/(g*x^2+f)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)^{2}}{g^{2} x^{4} + 2 \, f g x^{2} + f^{2}}, x\right)"," ",0,"integral(log((e*x^2 + d)^p*c)^2/(g^2*x^4 + 2*f*g*x^2 + f^2), x)","F",0
277,0,0,0,1.006616," ","integrate((g*x^2+f)*log(c*(e*x^2+d)^p)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(g x^{2} + f\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)^{3}, x\right)"," ",0,"integral((g*x^2 + f)*log((e*x^2 + d)^p*c)^3, x)","F",0
278,0,0,0,0.761919," ","integrate(log(c*(e*x^2+d)^p)^3/(g*x^2+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)^{3}}{g x^{2} + f}, x\right)"," ",0,"integral(log((e*x^2 + d)^p*c)^3/(g*x^2 + f), x)","F",0
279,0,0,0,0.839173," ","integrate(log(c*(e*x^2+d)^p)^3/(g*x^2+f)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)^{3}}{g^{2} x^{4} + 2 \, f g x^{2} + f^{2}}, x\right)"," ",0,"integral(log((e*x^2 + d)^p*c)^3/(g^2*x^4 + 2*f*g*x^2 + f^2), x)","F",0
280,0,0,0,0.669623," ","integrate((g*x^2+f)^2/log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","{\rm integral}\left(\frac{g^{2} x^{4} + 2 \, f g x^{2} + f^{2}}{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}, x\right)"," ",0,"integral((g^2*x^4 + 2*f*g*x^2 + f^2)/log((e*x^2 + d)^p*c), x)","F",0
281,0,0,0,0.626066," ","integrate((g*x^2+f)/log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","{\rm integral}\left(\frac{g x^{2} + f}{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}, x\right)"," ",0,"integral((g*x^2 + f)/log((e*x^2 + d)^p*c), x)","F",0
282,0,0,0,0.864193," ","integrate(1/(g*x^2+f)/log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(g x^{2} + f\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}, x\right)"," ",0,"integral(1/((g*x^2 + f)*log((e*x^2 + d)^p*c)), x)","F",0
283,0,0,0,0.827420," ","integrate(1/(g*x^2+f)^2/log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(g^{2} x^{4} + 2 \, f g x^{2} + f^{2}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}, x\right)"," ",0,"integral(1/((g^2*x^4 + 2*f*g*x^2 + f^2)*log((e*x^2 + d)^p*c)), x)","F",0
284,0,0,0,0.950358," ","integrate((g*x^2+f)^2/log(c*(e*x^2+d)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{g^{2} x^{4} + 2 \, f g x^{2} + f^{2}}{\log\left({\left(e x^{2} + d\right)}^{p} c\right)^{2}}, x\right)"," ",0,"integral((g^2*x^4 + 2*f*g*x^2 + f^2)/log((e*x^2 + d)^p*c)^2, x)","F",0
285,0,0,0,0.829661," ","integrate((g*x^2+f)/log(c*(e*x^2+d)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{g x^{2} + f}{\log\left({\left(e x^{2} + d\right)}^{p} c\right)^{2}}, x\right)"," ",0,"integral((g*x^2 + f)/log((e*x^2 + d)^p*c)^2, x)","F",0
286,0,0,0,0.899531," ","integrate(1/(g*x^2+f)/log(c*(e*x^2+d)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(g x^{2} + f\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)^{2}}, x\right)"," ",0,"integral(1/((g*x^2 + f)*log((e*x^2 + d)^p*c)^2), x)","F",0
287,0,0,0,0.869290," ","integrate(1/(g*x^2+f)^2/log(c*(e*x^2+d)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(g^{2} x^{4} + 2 \, f g x^{2} + f^{2}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)^{2}}, x\right)"," ",0,"integral(1/((g^2*x^4 + 2*f*g*x^2 + f^2)*log((e*x^2 + d)^p*c)^2), x)","F",0
288,1,708,0,1.003597," ","integrate((g*x^3+f)^3*log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","\left[-\frac{588 \, e^{5} g^{3} p x^{10} - 735 \, d e^{4} g^{3} p x^{8} + 3600 \, e^{5} f g^{2} p x^{7} + 980 \, d^{2} e^{3} g^{3} p x^{6} - 5040 \, d e^{4} f g^{2} p x^{5} + 8400 \, d^{2} e^{3} f g^{2} p x^{3} + 735 \, {\left(15 \, e^{5} f^{2} g - 2 \, d^{3} e^{2} g^{3}\right)} p x^{4} - 1470 \, {\left(15 \, d e^{4} f^{2} g - 2 \, d^{4} e g^{3}\right)} p x^{2} + 4200 \, {\left(7 \, e^{5} f^{3} - 3 \, d^{3} e^{2} f g^{2}\right)} p \sqrt{-\frac{d}{e}} \log\left(\frac{e x^{2} - 2 \, e x \sqrt{-\frac{d}{e}} - d}{e x^{2} + d}\right) + 8400 \, {\left(7 \, e^{5} f^{3} - 3 \, d^{3} e^{2} f g^{2}\right)} p x - 210 \, {\left(14 \, e^{5} g^{3} p x^{10} + 60 \, e^{5} f g^{2} p x^{7} + 105 \, e^{5} f^{2} g p x^{4} + 140 \, e^{5} f^{3} p x - 7 \, {\left(15 \, d^{2} e^{3} f^{2} g - 2 \, d^{5} g^{3}\right)} p\right)} \log\left(e x^{2} + d\right) - 210 \, {\left(14 \, e^{5} g^{3} x^{10} + 60 \, e^{5} f g^{2} x^{7} + 105 \, e^{5} f^{2} g x^{4} + 140 \, e^{5} f^{3} x\right)} \log\left(c\right)}{29400 \, e^{5}}, -\frac{588 \, e^{5} g^{3} p x^{10} - 735 \, d e^{4} g^{3} p x^{8} + 3600 \, e^{5} f g^{2} p x^{7} + 980 \, d^{2} e^{3} g^{3} p x^{6} - 5040 \, d e^{4} f g^{2} p x^{5} + 8400 \, d^{2} e^{3} f g^{2} p x^{3} + 735 \, {\left(15 \, e^{5} f^{2} g - 2 \, d^{3} e^{2} g^{3}\right)} p x^{4} - 1470 \, {\left(15 \, d e^{4} f^{2} g - 2 \, d^{4} e g^{3}\right)} p x^{2} - 8400 \, {\left(7 \, e^{5} f^{3} - 3 \, d^{3} e^{2} f g^{2}\right)} p \sqrt{\frac{d}{e}} \arctan\left(\frac{e x \sqrt{\frac{d}{e}}}{d}\right) + 8400 \, {\left(7 \, e^{5} f^{3} - 3 \, d^{3} e^{2} f g^{2}\right)} p x - 210 \, {\left(14 \, e^{5} g^{3} p x^{10} + 60 \, e^{5} f g^{2} p x^{7} + 105 \, e^{5} f^{2} g p x^{4} + 140 \, e^{5} f^{3} p x - 7 \, {\left(15 \, d^{2} e^{3} f^{2} g - 2 \, d^{5} g^{3}\right)} p\right)} \log\left(e x^{2} + d\right) - 210 \, {\left(14 \, e^{5} g^{3} x^{10} + 60 \, e^{5} f g^{2} x^{7} + 105 \, e^{5} f^{2} g x^{4} + 140 \, e^{5} f^{3} x\right)} \log\left(c\right)}{29400 \, e^{5}}\right]"," ",0,"[-1/29400*(588*e^5*g^3*p*x^10 - 735*d*e^4*g^3*p*x^8 + 3600*e^5*f*g^2*p*x^7 + 980*d^2*e^3*g^3*p*x^6 - 5040*d*e^4*f*g^2*p*x^5 + 8400*d^2*e^3*f*g^2*p*x^3 + 735*(15*e^5*f^2*g - 2*d^3*e^2*g^3)*p*x^4 - 1470*(15*d*e^4*f^2*g - 2*d^4*e*g^3)*p*x^2 + 4200*(7*e^5*f^3 - 3*d^3*e^2*f*g^2)*p*sqrt(-d/e)*log((e*x^2 - 2*e*x*sqrt(-d/e) - d)/(e*x^2 + d)) + 8400*(7*e^5*f^3 - 3*d^3*e^2*f*g^2)*p*x - 210*(14*e^5*g^3*p*x^10 + 60*e^5*f*g^2*p*x^7 + 105*e^5*f^2*g*p*x^4 + 140*e^5*f^3*p*x - 7*(15*d^2*e^3*f^2*g - 2*d^5*g^3)*p)*log(e*x^2 + d) - 210*(14*e^5*g^3*x^10 + 60*e^5*f*g^2*x^7 + 105*e^5*f^2*g*x^4 + 140*e^5*f^3*x)*log(c))/e^5, -1/29400*(588*e^5*g^3*p*x^10 - 735*d*e^4*g^3*p*x^8 + 3600*e^5*f*g^2*p*x^7 + 980*d^2*e^3*g^3*p*x^6 - 5040*d*e^4*f*g^2*p*x^5 + 8400*d^2*e^3*f*g^2*p*x^3 + 735*(15*e^5*f^2*g - 2*d^3*e^2*g^3)*p*x^4 - 1470*(15*d*e^4*f^2*g - 2*d^4*e*g^3)*p*x^2 - 8400*(7*e^5*f^3 - 3*d^3*e^2*f*g^2)*p*sqrt(d/e)*arctan(e*x*sqrt(d/e)/d) + 8400*(7*e^5*f^3 - 3*d^3*e^2*f*g^2)*p*x - 210*(14*e^5*g^3*p*x^10 + 60*e^5*f*g^2*p*x^7 + 105*e^5*f^2*g*p*x^4 + 140*e^5*f^3*p*x - 7*(15*d^2*e^3*f^2*g - 2*d^5*g^3)*p)*log(e*x^2 + d) - 210*(14*e^5*g^3*x^10 + 60*e^5*f*g^2*x^7 + 105*e^5*f^2*g*x^4 + 140*e^5*f^3*x)*log(c))/e^5]","A",0
289,1,454,0,0.965088," ","integrate((g*x^3+f)^2*log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","\left[-\frac{120 \, e^{3} g^{2} p x^{7} - 168 \, d e^{2} g^{2} p x^{5} + 735 \, e^{3} f g p x^{4} + 280 \, d^{2} e g^{2} p x^{3} - 1470 \, d e^{2} f g p x^{2} + 420 \, {\left(7 \, e^{3} f^{2} - d^{3} g^{2}\right)} p \sqrt{-\frac{d}{e}} \log\left(\frac{e x^{2} - 2 \, e x \sqrt{-\frac{d}{e}} - d}{e x^{2} + d}\right) + 840 \, {\left(7 \, e^{3} f^{2} - d^{3} g^{2}\right)} p x - 210 \, {\left(2 \, e^{3} g^{2} p x^{7} + 7 \, e^{3} f g p x^{4} + 14 \, e^{3} f^{2} p x - 7 \, d^{2} e f g p\right)} \log\left(e x^{2} + d\right) - 210 \, {\left(2 \, e^{3} g^{2} x^{7} + 7 \, e^{3} f g x^{4} + 14 \, e^{3} f^{2} x\right)} \log\left(c\right)}{2940 \, e^{3}}, -\frac{120 \, e^{3} g^{2} p x^{7} - 168 \, d e^{2} g^{2} p x^{5} + 735 \, e^{3} f g p x^{4} + 280 \, d^{2} e g^{2} p x^{3} - 1470 \, d e^{2} f g p x^{2} - 840 \, {\left(7 \, e^{3} f^{2} - d^{3} g^{2}\right)} p \sqrt{\frac{d}{e}} \arctan\left(\frac{e x \sqrt{\frac{d}{e}}}{d}\right) + 840 \, {\left(7 \, e^{3} f^{2} - d^{3} g^{2}\right)} p x - 210 \, {\left(2 \, e^{3} g^{2} p x^{7} + 7 \, e^{3} f g p x^{4} + 14 \, e^{3} f^{2} p x - 7 \, d^{2} e f g p\right)} \log\left(e x^{2} + d\right) - 210 \, {\left(2 \, e^{3} g^{2} x^{7} + 7 \, e^{3} f g x^{4} + 14 \, e^{3} f^{2} x\right)} \log\left(c\right)}{2940 \, e^{3}}\right]"," ",0,"[-1/2940*(120*e^3*g^2*p*x^7 - 168*d*e^2*g^2*p*x^5 + 735*e^3*f*g*p*x^4 + 280*d^2*e*g^2*p*x^3 - 1470*d*e^2*f*g*p*x^2 + 420*(7*e^3*f^2 - d^3*g^2)*p*sqrt(-d/e)*log((e*x^2 - 2*e*x*sqrt(-d/e) - d)/(e*x^2 + d)) + 840*(7*e^3*f^2 - d^3*g^2)*p*x - 210*(2*e^3*g^2*p*x^7 + 7*e^3*f*g*p*x^4 + 14*e^3*f^2*p*x - 7*d^2*e*f*g*p)*log(e*x^2 + d) - 210*(2*e^3*g^2*x^7 + 7*e^3*f*g*x^4 + 14*e^3*f^2*x)*log(c))/e^3, -1/2940*(120*e^3*g^2*p*x^7 - 168*d*e^2*g^2*p*x^5 + 735*e^3*f*g*p*x^4 + 280*d^2*e*g^2*p*x^3 - 1470*d*e^2*f*g*p*x^2 - 840*(7*e^3*f^2 - d^3*g^2)*p*sqrt(d/e)*arctan(e*x*sqrt(d/e)/d) + 840*(7*e^3*f^2 - d^3*g^2)*p*x - 210*(2*e^3*g^2*p*x^7 + 7*e^3*f*g*p*x^4 + 14*e^3*f^2*p*x - 7*d^2*e*f*g*p)*log(e*x^2 + d) - 210*(2*e^3*g^2*x^7 + 7*e^3*f*g*x^4 + 14*e^3*f^2*x)*log(c))/e^3]","A",0
290,1,250,0,0.886067," ","integrate((g*x^3+f)*log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","\left[-\frac{e^{2} g p x^{4} - 2 \, d e g p x^{2} - 8 \, e^{2} f p \sqrt{-\frac{d}{e}} \log\left(\frac{e x^{2} + 2 \, e x \sqrt{-\frac{d}{e}} - d}{e x^{2} + d}\right) + 16 \, e^{2} f p x - 2 \, {\left(e^{2} g p x^{4} + 4 \, e^{2} f p x - d^{2} g p\right)} \log\left(e x^{2} + d\right) - 2 \, {\left(e^{2} g x^{4} + 4 \, e^{2} f x\right)} \log\left(c\right)}{8 \, e^{2}}, -\frac{e^{2} g p x^{4} - 2 \, d e g p x^{2} - 16 \, e^{2} f p \sqrt{\frac{d}{e}} \arctan\left(\frac{e x \sqrt{\frac{d}{e}}}{d}\right) + 16 \, e^{2} f p x - 2 \, {\left(e^{2} g p x^{4} + 4 \, e^{2} f p x - d^{2} g p\right)} \log\left(e x^{2} + d\right) - 2 \, {\left(e^{2} g x^{4} + 4 \, e^{2} f x\right)} \log\left(c\right)}{8 \, e^{2}}\right]"," ",0,"[-1/8*(e^2*g*p*x^4 - 2*d*e*g*p*x^2 - 8*e^2*f*p*sqrt(-d/e)*log((e*x^2 + 2*e*x*sqrt(-d/e) - d)/(e*x^2 + d)) + 16*e^2*f*p*x - 2*(e^2*g*p*x^4 + 4*e^2*f*p*x - d^2*g*p)*log(e*x^2 + d) - 2*(e^2*g*x^4 + 4*e^2*f*x)*log(c))/e^2, -1/8*(e^2*g*p*x^4 - 2*d*e*g*p*x^2 - 16*e^2*f*p*sqrt(d/e)*arctan(e*x*sqrt(d/e)/d) + 16*e^2*f*p*x - 2*(e^2*g*p*x^4 + 4*e^2*f*p*x - d^2*g*p)*log(e*x^2 + d) - 2*(e^2*g*x^4 + 4*e^2*f*x)*log(c))/e^2]","A",0
291,0,0,0,0.617683," ","integrate(log(c*(e*x^2+d)^p)/(g*x^3+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g x^{3} + f}, x\right)"," ",0,"integral(log((e*x^2 + d)^p*c)/(g*x^3 + f), x)","F",0
292,0,0,0,0.638092," ","integrate(log(c*(e*x^2+d)^p)/(g*x^3+f)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g^{2} x^{6} + 2 \, f g x^{3} + f^{2}}, x\right)"," ",0,"integral(log((e*x^2 + d)^p*c)/(g^2*x^6 + 2*f*g*x^3 + f^2), x)","F",0
293,0,0,0,0.923363," ","integrate((g*x^3+f)^3*log(c*(e*x^2+d)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(g^{3} x^{9} + 3 \, f g^{2} x^{6} + 3 \, f^{2} g x^{3} + f^{3}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)^{2}, x\right)"," ",0,"integral((g^3*x^9 + 3*f*g^2*x^6 + 3*f^2*g*x^3 + f^3)*log((e*x^2 + d)^p*c)^2, x)","F",0
294,0,0,0,0.781869," ","integrate((g*x^3+f)^2*log(c*(e*x^2+d)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(g^{2} x^{6} + 2 \, f g x^{3} + f^{2}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)^{2}, x\right)"," ",0,"integral((g^2*x^6 + 2*f*g*x^3 + f^2)*log((e*x^2 + d)^p*c)^2, x)","F",0
295,0,0,0,0.730667," ","integrate((g*x^3+f)*log(c*(e*x^2+d)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(g x^{3} + f\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)^{2}, x\right)"," ",0,"integral((g*x^3 + f)*log((e*x^2 + d)^p*c)^2, x)","F",0
296,0,0,0,0.857023," ","integrate(log(c*(e*x^2+d)^p)^2/(g*x^3+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)^{2}}{g x^{3} + f}, x\right)"," ",0,"integral(log((e*x^2 + d)^p*c)^2/(g*x^3 + f), x)","F",0
297,0,0,0,0.977674," ","integrate(log(c*(e*x^2+d)^p)^2/(g*x^3+f)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)^{2}}{g^{2} x^{6} + 2 \, f g x^{3} + f^{2}}, x\right)"," ",0,"integral(log((e*x^2 + d)^p*c)^2/(g^2*x^6 + 2*f*g*x^3 + f^2), x)","F",0
298,0,0,0,0.922781," ","integrate((g*x^3+f)^2*log(c*(e*x^2+d)^p)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(g^{2} x^{6} + 2 \, f g x^{3} + f^{2}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)^{3}, x\right)"," ",0,"integral((g^2*x^6 + 2*f*g*x^3 + f^2)*log((e*x^2 + d)^p*c)^3, x)","F",0
299,0,0,0,0.530360," ","integrate((g*x^3+f)*log(c*(e*x^2+d)^p)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(g x^{3} + f\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)^{3}, x\right)"," ",0,"integral((g*x^3 + f)*log((e*x^2 + d)^p*c)^3, x)","F",0
300,0,0,0,0.904865," ","integrate(log(c*(e*x^2+d)^p)^3/(g*x^3+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)^{3}}{g x^{3} + f}, x\right)"," ",0,"integral(log((e*x^2 + d)^p*c)^3/(g*x^3 + f), x)","F",0
301,0,0,0,0.783026," ","integrate(log(c*(e*x^2+d)^p)^3/(g*x^3+f)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)^{3}}{g^{2} x^{6} + 2 \, f g x^{3} + f^{2}}, x\right)"," ",0,"integral(log((e*x^2 + d)^p*c)^3/(g^2*x^6 + 2*f*g*x^3 + f^2), x)","F",0
302,0,0,0,0.757380," ","integrate((g*x^3+f)^2/log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","{\rm integral}\left(\frac{g^{2} x^{6} + 2 \, f g x^{3} + f^{2}}{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}, x\right)"," ",0,"integral((g^2*x^6 + 2*f*g*x^3 + f^2)/log((e*x^2 + d)^p*c), x)","F",0
303,0,0,0,0.805029," ","integrate((g*x^3+f)/log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","{\rm integral}\left(\frac{g x^{3} + f}{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}, x\right)"," ",0,"integral((g*x^3 + f)/log((e*x^2 + d)^p*c), x)","F",0
304,0,0,0,0.638851," ","integrate(1/(g*x^3+f)/log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(g x^{3} + f\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}, x\right)"," ",0,"integral(1/((g*x^3 + f)*log((e*x^2 + d)^p*c)), x)","F",0
305,0,0,0,0.707014," ","integrate(1/(g*x^3+f)^2/log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(g^{2} x^{6} + 2 \, f g x^{3} + f^{2}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}, x\right)"," ",0,"integral(1/((g^2*x^6 + 2*f*g*x^3 + f^2)*log((e*x^2 + d)^p*c)), x)","F",0
306,0,0,0,0.842002," ","integrate((g*x^3+f)^2/log(c*(e*x^2+d)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{g^{2} x^{6} + 2 \, f g x^{3} + f^{2}}{\log\left({\left(e x^{2} + d\right)}^{p} c\right)^{2}}, x\right)"," ",0,"integral((g^2*x^6 + 2*f*g*x^3 + f^2)/log((e*x^2 + d)^p*c)^2, x)","F",0
307,0,0,0,0.951713," ","integrate((g*x^3+f)/log(c*(e*x^2+d)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{g x^{3} + f}{\log\left({\left(e x^{2} + d\right)}^{p} c\right)^{2}}, x\right)"," ",0,"integral((g*x^3 + f)/log((e*x^2 + d)^p*c)^2, x)","F",0
308,0,0,0,0.832822," ","integrate(1/(g*x^3+f)/log(c*(e*x^2+d)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(g x^{3} + f\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)^{2}}, x\right)"," ",0,"integral(1/((g*x^3 + f)*log((e*x^2 + d)^p*c)^2), x)","F",0
309,0,0,0,0.914333," ","integrate(1/(g*x^3+f)^2/log(c*(e*x^2+d)^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(g^{2} x^{6} + 2 \, f g x^{3} + f^{2}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)^{2}}, x\right)"," ",0,"integral(1/((g^2*x^6 + 2*f*g*x^3 + f^2)*log((e*x^2 + d)^p*c)^2), x)","F",0
310,1,152,0,1.073992," ","integrate(x^5*(g*x^2+f)*log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","-\frac{9 \, e^{4} g p x^{8} + 4 \, {\left(4 \, e^{4} f - 3 \, d e^{3} g\right)} p x^{6} - 6 \, {\left(4 \, d e^{3} f - 3 \, d^{2} e^{2} g\right)} p x^{4} + 12 \, {\left(4 \, d^{2} e^{2} f - 3 \, d^{3} e g\right)} p x^{2} - 12 \, {\left(3 \, e^{4} g p x^{8} + 4 \, e^{4} f p x^{6} + {\left(4 \, d^{3} e f - 3 \, d^{4} g\right)} p\right)} \log\left(e x^{2} + d\right) - 12 \, {\left(3 \, e^{4} g x^{8} + 4 \, e^{4} f x^{6}\right)} \log\left(c\right)}{288 \, e^{4}}"," ",0,"-1/288*(9*e^4*g*p*x^8 + 4*(4*e^4*f - 3*d*e^3*g)*p*x^6 - 6*(4*d*e^3*f - 3*d^2*e^2*g)*p*x^4 + 12*(4*d^2*e^2*f - 3*d^3*e*g)*p*x^2 - 12*(3*e^4*g*p*x^8 + 4*e^4*f*p*x^6 + (4*d^3*e*f - 3*d^4*g)*p)*log(e*x^2 + d) - 12*(3*e^4*g*x^8 + 4*e^4*f*x^6)*log(c))/e^4","A",0
311,1,128,0,0.916250," ","integrate(x^3*(g*x^2+f)*log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","-\frac{4 \, e^{3} g p x^{6} + 3 \, {\left(3 \, e^{3} f - 2 \, d e^{2} g\right)} p x^{4} - 6 \, {\left(3 \, d e^{2} f - 2 \, d^{2} e g\right)} p x^{2} - 6 \, {\left(2 \, e^{3} g p x^{6} + 3 \, e^{3} f p x^{4} - {\left(3 \, d^{2} e f - 2 \, d^{3} g\right)} p\right)} \log\left(e x^{2} + d\right) - 6 \, {\left(2 \, e^{3} g x^{6} + 3 \, e^{3} f x^{4}\right)} \log\left(c\right)}{72 \, e^{3}}"," ",0,"-1/72*(4*e^3*g*p*x^6 + 3*(3*e^3*f - 2*d*e^2*g)*p*x^4 - 6*(3*d*e^2*f - 2*d^2*e*g)*p*x^2 - 6*(2*e^3*g*p*x^6 + 3*e^3*f*p*x^4 - (3*d^2*e*f - 2*d^3*g)*p)*log(e*x^2 + d) - 6*(2*e^3*g*x^6 + 3*e^3*f*x^4)*log(c))/e^3","A",0
312,1,99,0,0.602545," ","integrate(x*(g*x^2+f)*log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","-\frac{e^{2} g p x^{4} + 2 \, {\left(2 \, e^{2} f - d e g\right)} p x^{2} - 2 \, {\left(e^{2} g p x^{4} + 2 \, e^{2} f p x^{2} + {\left(2 \, d e f - d^{2} g\right)} p\right)} \log\left(e x^{2} + d\right) - 2 \, {\left(e^{2} g x^{4} + 2 \, e^{2} f x^{2}\right)} \log\left(c\right)}{8 \, e^{2}}"," ",0,"-1/8*(e^2*g*p*x^4 + 2*(2*e^2*f - d*e*g)*p*x^2 - 2*(e^2*g*p*x^4 + 2*e^2*f*p*x^2 + (2*d*e*f - d^2*g)*p)*log(e*x^2 + d) - 2*(e^2*g*x^4 + 2*e^2*f*x^2)*log(c))/e^2","A",0
313,0,0,0,0.869862," ","integrate((g*x^2+f)*log(c*(e*x^2+d)^p)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(g x^{2} + f\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{x}, x\right)"," ",0,"integral((g*x^2 + f)*log((e*x^2 + d)^p*c)/x, x)","F",0
314,0,0,0,1.028061," ","integrate((g*x^2+f)*log(c*(e*x^2+d)^p)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(g x^{2} + f\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{x^{3}}, x\right)"," ",0,"integral((g*x^2 + f)*log((e*x^2 + d)^p*c)/x^3, x)","F",0
315,1,97,0,0.966179," ","integrate((g*x^2+f)*log(c*(e*x^2+d)^p)/x^5,x, algorithm=""fricas"")","-\frac{2 \, {\left(e^{2} f - 2 \, d e g\right)} p x^{4} \log\left(x\right) + d e f p x^{2} + {\left(2 \, d^{2} g p x^{2} - {\left(e^{2} f - 2 \, d e g\right)} p x^{4} + d^{2} f p\right)} \log\left(e x^{2} + d\right) + {\left(2 \, d^{2} g x^{2} + d^{2} f\right)} \log\left(c\right)}{4 \, d^{2} x^{4}}"," ",0,"-1/4*(2*(e^2*f - 2*d*e*g)*p*x^4*log(x) + d*e*f*p*x^2 + (2*d^2*g*p*x^2 - (e^2*f - 2*d*e*g)*p*x^4 + d^2*f*p)*log(e*x^2 + d) + (2*d^2*g*x^2 + d^2*f)*log(c))/(d^2*x^4)","A",0
316,1,129,0,0.995893," ","integrate((g*x^2+f)*log(c*(e*x^2+d)^p)/x^7,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, e^{3} f - 3 \, d e^{2} g\right)} p x^{6} \log\left(x\right) - d^{2} e f p x^{2} + {\left(2 \, d e^{2} f - 3 \, d^{2} e g\right)} p x^{4} - {\left({\left(2 \, e^{3} f - 3 \, d e^{2} g\right)} p x^{6} + 3 \, d^{3} g p x^{2} + 2 \, d^{3} f p\right)} \log\left(e x^{2} + d\right) - {\left(3 \, d^{3} g x^{2} + 2 \, d^{3} f\right)} \log\left(c\right)}{12 \, d^{3} x^{6}}"," ",0,"1/12*(2*(2*e^3*f - 3*d*e^2*g)*p*x^6*log(x) - d^2*e*f*p*x^2 + (2*d*e^2*f - 3*d^2*e*g)*p*x^4 - ((2*e^3*f - 3*d*e^2*g)*p*x^6 + 3*d^3*g*p*x^2 + 2*d^3*f*p)*log(e*x^2 + d) - (3*d^3*g*x^2 + 2*d^3*f)*log(c))/(d^3*x^6)","A",0
317,1,155,0,0.950986," ","integrate((g*x^2+f)*log(c*(e*x^2+d)^p)/x^9,x, algorithm=""fricas"")","-\frac{4 \, {\left(3 \, e^{4} f - 4 \, d e^{3} g\right)} p x^{8} \log\left(x\right) + 2 \, d^{3} e f p x^{2} + 2 \, {\left(3 \, d e^{3} f - 4 \, d^{2} e^{2} g\right)} p x^{6} - {\left(3 \, d^{2} e^{2} f - 4 \, d^{3} e g\right)} p x^{4} - 2 \, {\left({\left(3 \, e^{4} f - 4 \, d e^{3} g\right)} p x^{8} - 4 \, d^{4} g p x^{2} - 3 \, d^{4} f p\right)} \log\left(e x^{2} + d\right) + 2 \, {\left(4 \, d^{4} g x^{2} + 3 \, d^{4} f\right)} \log\left(c\right)}{48 \, d^{4} x^{8}}"," ",0,"-1/48*(4*(3*e^4*f - 4*d*e^3*g)*p*x^8*log(x) + 2*d^3*e*f*p*x^2 + 2*(3*d*e^3*f - 4*d^2*e^2*g)*p*x^6 - (3*d^2*e^2*f - 4*d^3*e*g)*p*x^4 - 2*((3*e^4*f - 4*d*e^3*g)*p*x^8 - 4*d^4*g*p*x^2 - 3*d^4*f*p)*log(e*x^2 + d) + 2*(4*d^4*g*x^2 + 3*d^4*f)*log(c))/(d^4*x^8)","A",0
318,1,300,0,0.915401," ","integrate(x^2*(g*x^2+f)*log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","\left[-\frac{18 \, e^{2} g p x^{5} + 10 \, {\left(5 \, e^{2} f - 3 \, d e g\right)} p x^{3} + 15 \, {\left(5 \, d e f - 3 \, d^{2} g\right)} p \sqrt{-\frac{d}{e}} \log\left(\frac{e x^{2} + 2 \, e x \sqrt{-\frac{d}{e}} - d}{e x^{2} + d}\right) - 30 \, {\left(5 \, d e f - 3 \, d^{2} g\right)} p x - 15 \, {\left(3 \, e^{2} g p x^{5} + 5 \, e^{2} f p x^{3}\right)} \log\left(e x^{2} + d\right) - 15 \, {\left(3 \, e^{2} g x^{5} + 5 \, e^{2} f x^{3}\right)} \log\left(c\right)}{225 \, e^{2}}, -\frac{18 \, e^{2} g p x^{5} + 10 \, {\left(5 \, e^{2} f - 3 \, d e g\right)} p x^{3} + 30 \, {\left(5 \, d e f - 3 \, d^{2} g\right)} p \sqrt{\frac{d}{e}} \arctan\left(\frac{e x \sqrt{\frac{d}{e}}}{d}\right) - 30 \, {\left(5 \, d e f - 3 \, d^{2} g\right)} p x - 15 \, {\left(3 \, e^{2} g p x^{5} + 5 \, e^{2} f p x^{3}\right)} \log\left(e x^{2} + d\right) - 15 \, {\left(3 \, e^{2} g x^{5} + 5 \, e^{2} f x^{3}\right)} \log\left(c\right)}{225 \, e^{2}}\right]"," ",0,"[-1/225*(18*e^2*g*p*x^5 + 10*(5*e^2*f - 3*d*e*g)*p*x^3 + 15*(5*d*e*f - 3*d^2*g)*p*sqrt(-d/e)*log((e*x^2 + 2*e*x*sqrt(-d/e) - d)/(e*x^2 + d)) - 30*(5*d*e*f - 3*d^2*g)*p*x - 15*(3*e^2*g*p*x^5 + 5*e^2*f*p*x^3)*log(e*x^2 + d) - 15*(3*e^2*g*x^5 + 5*e^2*f*x^3)*log(c))/e^2, -1/225*(18*e^2*g*p*x^5 + 10*(5*e^2*f - 3*d*e*g)*p*x^3 + 30*(5*d*e*f - 3*d^2*g)*p*sqrt(d/e)*arctan(e*x*sqrt(d/e)/d) - 30*(5*d*e*f - 3*d^2*g)*p*x - 15*(3*e^2*g*p*x^5 + 5*e^2*f*p*x^3)*log(e*x^2 + d) - 15*(3*e^2*g*x^5 + 5*e^2*f*x^3)*log(c))/e^2]","A",0
319,1,220,0,0.772503," ","integrate((g*x^2+f)*log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","\left[-\frac{2 \, e g p x^{3} + 3 \, {\left(3 \, e f - d g\right)} p \sqrt{-\frac{d}{e}} \log\left(\frac{e x^{2} - 2 \, e x \sqrt{-\frac{d}{e}} - d}{e x^{2} + d}\right) + 6 \, {\left(3 \, e f - d g\right)} p x - 3 \, {\left(e g p x^{3} + 3 \, e f p x\right)} \log\left(e x^{2} + d\right) - 3 \, {\left(e g x^{3} + 3 \, e f x\right)} \log\left(c\right)}{9 \, e}, -\frac{2 \, e g p x^{3} - 6 \, {\left(3 \, e f - d g\right)} p \sqrt{\frac{d}{e}} \arctan\left(\frac{e x \sqrt{\frac{d}{e}}}{d}\right) + 6 \, {\left(3 \, e f - d g\right)} p x - 3 \, {\left(e g p x^{3} + 3 \, e f p x\right)} \log\left(e x^{2} + d\right) - 3 \, {\left(e g x^{3} + 3 \, e f x\right)} \log\left(c\right)}{9 \, e}\right]"," ",0,"[-1/9*(2*e*g*p*x^3 + 3*(3*e*f - d*g)*p*sqrt(-d/e)*log((e*x^2 - 2*e*x*sqrt(-d/e) - d)/(e*x^2 + d)) + 6*(3*e*f - d*g)*p*x - 3*(e*g*p*x^3 + 3*e*f*p*x)*log(e*x^2 + d) - 3*(e*g*x^3 + 3*e*f*x)*log(c))/e, -1/9*(2*e*g*p*x^3 - 6*(3*e*f - d*g)*p*sqrt(d/e)*arctan(e*x*sqrt(d/e)/d) + 6*(3*e*f - d*g)*p*x - 3*(e*g*p*x^3 + 3*e*f*p*x)*log(e*x^2 + d) - 3*(e*g*x^3 + 3*e*f*x)*log(c))/e]","A",0
320,1,199,0,0.814663," ","integrate((g*x^2+f)*log(c*(e*x^2+d)^p)/x^2,x, algorithm=""fricas"")","\left[-\frac{2 \, d e g p x^{2} + \sqrt{-d e} {\left(e f + d g\right)} p x \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) - {\left(d e g p x^{2} - d e f p\right)} \log\left(e x^{2} + d\right) - {\left(d e g x^{2} - d e f\right)} \log\left(c\right)}{d e x}, -\frac{2 \, d e g p x^{2} - 2 \, \sqrt{d e} {\left(e f + d g\right)} p x \arctan\left(\frac{\sqrt{d e} x}{d}\right) - {\left(d e g p x^{2} - d e f p\right)} \log\left(e x^{2} + d\right) - {\left(d e g x^{2} - d e f\right)} \log\left(c\right)}{d e x}\right]"," ",0,"[-(2*d*e*g*p*x^2 + sqrt(-d*e)*(e*f + d*g)*p*x*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) - (d*e*g*p*x^2 - d*e*f*p)*log(e*x^2 + d) - (d*e*g*x^2 - d*e*f)*log(c))/(d*e*x), -(2*d*e*g*p*x^2 - 2*sqrt(d*e)*(e*f + d*g)*p*x*arctan(sqrt(d*e)*x/d) - (d*e*g*p*x^2 - d*e*f*p)*log(e*x^2 + d) - (d*e*g*x^2 - d*e*f)*log(c))/(d*e*x)]","A",0
321,1,191,0,1.080755," ","integrate((g*x^2+f)*log(c*(e*x^2+d)^p)/x^4,x, algorithm=""fricas"")","\left[-\frac{{\left(e f - 3 \, d g\right)} p x^{3} \sqrt{-\frac{e}{d}} \log\left(\frac{e x^{2} + 2 \, d x \sqrt{-\frac{e}{d}} - d}{e x^{2} + d}\right) + 2 \, e f p x^{2} + {\left(3 \, d g p x^{2} + d f p\right)} \log\left(e x^{2} + d\right) + {\left(3 \, d g x^{2} + d f\right)} \log\left(c\right)}{3 \, d x^{3}}, -\frac{2 \, {\left(e f - 3 \, d g\right)} p x^{3} \sqrt{\frac{e}{d}} \arctan\left(x \sqrt{\frac{e}{d}}\right) + 2 \, e f p x^{2} + {\left(3 \, d g p x^{2} + d f p\right)} \log\left(e x^{2} + d\right) + {\left(3 \, d g x^{2} + d f\right)} \log\left(c\right)}{3 \, d x^{3}}\right]"," ",0,"[-1/3*((e*f - 3*d*g)*p*x^3*sqrt(-e/d)*log((e*x^2 + 2*d*x*sqrt(-e/d) - d)/(e*x^2 + d)) + 2*e*f*p*x^2 + (3*d*g*p*x^2 + d*f*p)*log(e*x^2 + d) + (3*d*g*x^2 + d*f)*log(c))/(d*x^3), -1/3*(2*(e*f - 3*d*g)*p*x^3*sqrt(e/d)*arctan(x*sqrt(e/d)) + 2*e*f*p*x^2 + (3*d*g*p*x^2 + d*f*p)*log(e*x^2 + d) + (3*d*g*x^2 + d*f)*log(c))/(d*x^3)]","A",0
322,1,259,0,0.697548," ","integrate((g*x^2+f)*log(c*(e*x^2+d)^p)/x^6,x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, e^{2} f - 5 \, d e g\right)} p x^{5} \sqrt{-\frac{e}{d}} \log\left(\frac{e x^{2} - 2 \, d x \sqrt{-\frac{e}{d}} - d}{e x^{2} + d}\right) + 2 \, d e f p x^{2} - 2 \, {\left(3 \, e^{2} f - 5 \, d e g\right)} p x^{4} + {\left(5 \, d^{2} g p x^{2} + 3 \, d^{2} f p\right)} \log\left(e x^{2} + d\right) + {\left(5 \, d^{2} g x^{2} + 3 \, d^{2} f\right)} \log\left(c\right)}{15 \, d^{2} x^{5}}, \frac{2 \, {\left(3 \, e^{2} f - 5 \, d e g\right)} p x^{5} \sqrt{\frac{e}{d}} \arctan\left(x \sqrt{\frac{e}{d}}\right) - 2 \, d e f p x^{2} + 2 \, {\left(3 \, e^{2} f - 5 \, d e g\right)} p x^{4} - {\left(5 \, d^{2} g p x^{2} + 3 \, d^{2} f p\right)} \log\left(e x^{2} + d\right) - {\left(5 \, d^{2} g x^{2} + 3 \, d^{2} f\right)} \log\left(c\right)}{15 \, d^{2} x^{5}}\right]"," ",0,"[-1/15*((3*e^2*f - 5*d*e*g)*p*x^5*sqrt(-e/d)*log((e*x^2 - 2*d*x*sqrt(-e/d) - d)/(e*x^2 + d)) + 2*d*e*f*p*x^2 - 2*(3*e^2*f - 5*d*e*g)*p*x^4 + (5*d^2*g*p*x^2 + 3*d^2*f*p)*log(e*x^2 + d) + (5*d^2*g*x^2 + 3*d^2*f)*log(c))/(d^2*x^5), 1/15*(2*(3*e^2*f - 5*d*e*g)*p*x^5*sqrt(e/d)*arctan(x*sqrt(e/d)) - 2*d*e*f*p*x^2 + 2*(3*e^2*f - 5*d*e*g)*p*x^4 - (5*d^2*g*p*x^2 + 3*d^2*f*p)*log(e*x^2 + d) - (5*d^2*g*x^2 + 3*d^2*f)*log(c))/(d^2*x^5)]","A",0
323,1,262,0,0.899743," ","integrate(x^5*(g*x^2+f)^2*log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","-\frac{72 \, e^{5} g^{2} p x^{10} + 45 \, {\left(5 \, e^{5} f g - 2 \, d e^{4} g^{2}\right)} p x^{8} + 20 \, {\left(10 \, e^{5} f^{2} - 15 \, d e^{4} f g + 6 \, d^{2} e^{3} g^{2}\right)} p x^{6} - 30 \, {\left(10 \, d e^{4} f^{2} - 15 \, d^{2} e^{3} f g + 6 \, d^{3} e^{2} g^{2}\right)} p x^{4} + 60 \, {\left(10 \, d^{2} e^{3} f^{2} - 15 \, d^{3} e^{2} f g + 6 \, d^{4} e g^{2}\right)} p x^{2} - 60 \, {\left(6 \, e^{5} g^{2} p x^{10} + 15 \, e^{5} f g p x^{8} + 10 \, e^{5} f^{2} p x^{6} + {\left(10 \, d^{3} e^{2} f^{2} - 15 \, d^{4} e f g + 6 \, d^{5} g^{2}\right)} p\right)} \log\left(e x^{2} + d\right) - 60 \, {\left(6 \, e^{5} g^{2} x^{10} + 15 \, e^{5} f g x^{8} + 10 \, e^{5} f^{2} x^{6}\right)} \log\left(c\right)}{3600 \, e^{5}}"," ",0,"-1/3600*(72*e^5*g^2*p*x^10 + 45*(5*e^5*f*g - 2*d*e^4*g^2)*p*x^8 + 20*(10*e^5*f^2 - 15*d*e^4*f*g + 6*d^2*e^3*g^2)*p*x^6 - 30*(10*d*e^4*f^2 - 15*d^2*e^3*f*g + 6*d^3*e^2*g^2)*p*x^4 + 60*(10*d^2*e^3*f^2 - 15*d^3*e^2*f*g + 6*d^4*e*g^2)*p*x^2 - 60*(6*e^5*g^2*p*x^10 + 15*e^5*f*g*p*x^8 + 10*e^5*f^2*p*x^6 + (10*d^3*e^2*f^2 - 15*d^4*e*f*g + 6*d^5*g^2)*p)*log(e*x^2 + d) - 60*(6*e^5*g^2*x^10 + 15*e^5*f*g*x^8 + 10*e^5*f^2*x^6)*log(c))/e^5","A",0
324,1,224,0,0.653167," ","integrate(x^3*(g*x^2+f)^2*log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","-\frac{9 \, e^{4} g^{2} p x^{8} + 4 \, {\left(8 \, e^{4} f g - 3 \, d e^{3} g^{2}\right)} p x^{6} + 6 \, {\left(6 \, e^{4} f^{2} - 8 \, d e^{3} f g + 3 \, d^{2} e^{2} g^{2}\right)} p x^{4} - 12 \, {\left(6 \, d e^{3} f^{2} - 8 \, d^{2} e^{2} f g + 3 \, d^{3} e g^{2}\right)} p x^{2} - 12 \, {\left(3 \, e^{4} g^{2} p x^{8} + 8 \, e^{4} f g p x^{6} + 6 \, e^{4} f^{2} p x^{4} - {\left(6 \, d^{2} e^{2} f^{2} - 8 \, d^{3} e f g + 3 \, d^{4} g^{2}\right)} p\right)} \log\left(e x^{2} + d\right) - 12 \, {\left(3 \, e^{4} g^{2} x^{8} + 8 \, e^{4} f g x^{6} + 6 \, e^{4} f^{2} x^{4}\right)} \log\left(c\right)}{288 \, e^{4}}"," ",0,"-1/288*(9*e^4*g^2*p*x^8 + 4*(8*e^4*f*g - 3*d*e^3*g^2)*p*x^6 + 6*(6*e^4*f^2 - 8*d*e^3*f*g + 3*d^2*e^2*g^2)*p*x^4 - 12*(6*d*e^3*f^2 - 8*d^2*e^2*f*g + 3*d^3*e*g^2)*p*x^2 - 12*(3*e^4*g^2*p*x^8 + 8*e^4*f*g*p*x^6 + 6*e^4*f^2*p*x^4 - (6*d^2*e^2*f^2 - 8*d^3*e*f*g + 3*d^4*g^2)*p)*log(e*x^2 + d) - 12*(3*e^4*g^2*x^8 + 8*e^4*f*g*x^6 + 6*e^4*f^2*x^4)*log(c))/e^4","A",0
325,1,180,0,0.664192," ","integrate(x*(g*x^2+f)^2*log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","-\frac{2 \, e^{3} g^{2} p x^{6} + 3 \, {\left(3 \, e^{3} f g - d e^{2} g^{2}\right)} p x^{4} + 6 \, {\left(3 \, e^{3} f^{2} - 3 \, d e^{2} f g + d^{2} e g^{2}\right)} p x^{2} - 6 \, {\left(e^{3} g^{2} p x^{6} + 3 \, e^{3} f g p x^{4} + 3 \, e^{3} f^{2} p x^{2} + {\left(3 \, d e^{2} f^{2} - 3 \, d^{2} e f g + d^{3} g^{2}\right)} p\right)} \log\left(e x^{2} + d\right) - 6 \, {\left(e^{3} g^{2} x^{6} + 3 \, e^{3} f g x^{4} + 3 \, e^{3} f^{2} x^{2}\right)} \log\left(c\right)}{36 \, e^{3}}"," ",0,"-1/36*(2*e^3*g^2*p*x^6 + 3*(3*e^3*f*g - d*e^2*g^2)*p*x^4 + 6*(3*e^3*f^2 - 3*d*e^2*f*g + d^2*e*g^2)*p*x^2 - 6*(e^3*g^2*p*x^6 + 3*e^3*f*g*p*x^4 + 3*e^3*f^2*p*x^2 + (3*d*e^2*f^2 - 3*d^2*e*f*g + d^3*g^2)*p)*log(e*x^2 + d) - 6*(e^3*g^2*x^6 + 3*e^3*f*g*x^4 + 3*e^3*f^2*x^2)*log(c))/e^3","A",0
326,0,0,0,0.836780," ","integrate((g*x^2+f)^2*log(c*(e*x^2+d)^p)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(g^{2} x^{4} + 2 \, f g x^{2} + f^{2}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{x}, x\right)"," ",0,"integral((g^2*x^4 + 2*f*g*x^2 + f^2)*log((e*x^2 + d)^p*c)/x, x)","F",0
327,0,0,0,0.907500," ","integrate((g*x^2+f)^2*log(c*(e*x^2+d)^p)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(g^{2} x^{4} + 2 \, f g x^{2} + f^{2}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{x^{3}}, x\right)"," ",0,"integral((g^2*x^4 + 2*f*g*x^2 + f^2)*log((e*x^2 + d)^p*c)/x^3, x)","F",0
328,0,0,0,0.900352," ","integrate((g*x^2+f)^2*log(c*(e*x^2+d)^p)/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(g^{2} x^{4} + 2 \, f g x^{2} + f^{2}\right)} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{x^{5}}, x\right)"," ",0,"integral((g^2*x^4 + 2*f*g*x^2 + f^2)*log((e*x^2 + d)^p*c)/x^5, x)","F",0
329,1,183,0,0.930586," ","integrate((g*x^2+f)^2*log(c*(e*x^2+d)^p)/x^7,x, algorithm=""fricas"")","\frac{4 \, {\left(e^{3} f^{2} - 3 \, d e^{2} f g + 3 \, d^{2} e g^{2}\right)} p x^{6} \log\left(x\right) - d^{2} e f^{2} p x^{2} + 2 \, {\left(d e^{2} f^{2} - 3 \, d^{2} e f g\right)} p x^{4} - 2 \, {\left(3 \, d^{3} g^{2} p x^{4} + 3 \, d^{3} f g p x^{2} + {\left(e^{3} f^{2} - 3 \, d e^{2} f g + 3 \, d^{2} e g^{2}\right)} p x^{6} + d^{3} f^{2} p\right)} \log\left(e x^{2} + d\right) - 2 \, {\left(3 \, d^{3} g^{2} x^{4} + 3 \, d^{3} f g x^{2} + d^{3} f^{2}\right)} \log\left(c\right)}{12 \, d^{3} x^{6}}"," ",0,"1/12*(4*(e^3*f^2 - 3*d*e^2*f*g + 3*d^2*e*g^2)*p*x^6*log(x) - d^2*e*f^2*p*x^2 + 2*(d*e^2*f^2 - 3*d^2*e*f*g)*p*x^4 - 2*(3*d^3*g^2*p*x^4 + 3*d^3*f*g*p*x^2 + (e^3*f^2 - 3*d*e^2*f*g + 3*d^2*e*g^2)*p*x^6 + d^3*f^2*p)*log(e*x^2 + d) - 2*(3*d^3*g^2*x^4 + 3*d^3*f*g*x^2 + d^3*f^2)*log(c))/(d^3*x^6)","A",0
330,1,230,0,0.714418," ","integrate((g*x^2+f)^2*log(c*(e*x^2+d)^p)/x^9,x, algorithm=""fricas"")","-\frac{4 \, {\left(3 \, e^{4} f^{2} - 8 \, d e^{3} f g + 6 \, d^{2} e^{2} g^{2}\right)} p x^{8} \log\left(x\right) + 2 \, d^{3} e f^{2} p x^{2} + 2 \, {\left(3 \, d e^{3} f^{2} - 8 \, d^{2} e^{2} f g + 6 \, d^{3} e g^{2}\right)} p x^{6} - {\left(3 \, d^{2} e^{2} f^{2} - 8 \, d^{3} e f g\right)} p x^{4} + 2 \, {\left(6 \, d^{4} g^{2} p x^{4} - {\left(3 \, e^{4} f^{2} - 8 \, d e^{3} f g + 6 \, d^{2} e^{2} g^{2}\right)} p x^{8} + 8 \, d^{4} f g p x^{2} + 3 \, d^{4} f^{2} p\right)} \log\left(e x^{2} + d\right) + 2 \, {\left(6 \, d^{4} g^{2} x^{4} + 8 \, d^{4} f g x^{2} + 3 \, d^{4} f^{2}\right)} \log\left(c\right)}{48 \, d^{4} x^{8}}"," ",0,"-1/48*(4*(3*e^4*f^2 - 8*d*e^3*f*g + 6*d^2*e^2*g^2)*p*x^8*log(x) + 2*d^3*e*f^2*p*x^2 + 2*(3*d*e^3*f^2 - 8*d^2*e^2*f*g + 6*d^3*e*g^2)*p*x^6 - (3*d^2*e^2*f^2 - 8*d^3*e*f*g)*p*x^4 + 2*(6*d^4*g^2*p*x^4 - (3*e^4*f^2 - 8*d*e^3*f*g + 6*d^2*e^2*g^2)*p*x^8 + 8*d^4*f*g*p*x^2 + 3*d^4*f^2*p)*log(e*x^2 + d) + 2*(6*d^4*g^2*x^4 + 8*d^4*f*g*x^2 + 3*d^4*f^2)*log(c))/(d^4*x^8)","A",0
331,1,268,0,0.922718," ","integrate((g*x^2+f)^2*log(c*(e*x^2+d)^p)/x^11,x, algorithm=""fricas"")","\frac{4 \, {\left(6 \, e^{5} f^{2} - 15 \, d e^{4} f g + 10 \, d^{2} e^{3} g^{2}\right)} p x^{10} \log\left(x\right) - 3 \, d^{4} e f^{2} p x^{2} + 2 \, {\left(6 \, d e^{4} f^{2} - 15 \, d^{2} e^{3} f g + 10 \, d^{3} e^{2} g^{2}\right)} p x^{8} - {\left(6 \, d^{2} e^{3} f^{2} - 15 \, d^{3} e^{2} f g + 10 \, d^{4} e g^{2}\right)} p x^{6} + 2 \, {\left(2 \, d^{3} e^{2} f^{2} - 5 \, d^{4} e f g\right)} p x^{4} - 2 \, {\left(10 \, d^{5} g^{2} p x^{4} + {\left(6 \, e^{5} f^{2} - 15 \, d e^{4} f g + 10 \, d^{2} e^{3} g^{2}\right)} p x^{10} + 15 \, d^{5} f g p x^{2} + 6 \, d^{5} f^{2} p\right)} \log\left(e x^{2} + d\right) - 2 \, {\left(10 \, d^{5} g^{2} x^{4} + 15 \, d^{5} f g x^{2} + 6 \, d^{5} f^{2}\right)} \log\left(c\right)}{120 \, d^{5} x^{10}}"," ",0,"1/120*(4*(6*e^5*f^2 - 15*d*e^4*f*g + 10*d^2*e^3*g^2)*p*x^10*log(x) - 3*d^4*e*f^2*p*x^2 + 2*(6*d*e^4*f^2 - 15*d^2*e^3*f*g + 10*d^3*e^2*g^2)*p*x^8 - (6*d^2*e^3*f^2 - 15*d^3*e^2*f*g + 10*d^4*e*g^2)*p*x^6 + 2*(2*d^3*e^2*f^2 - 5*d^4*e*f*g)*p*x^4 - 2*(10*d^5*g^2*p*x^4 + (6*e^5*f^2 - 15*d*e^4*f*g + 10*d^2*e^3*g^2)*p*x^10 + 15*d^5*f*g*p*x^2 + 6*d^5*f^2*p)*log(e*x^2 + d) - 2*(10*d^5*g^2*x^4 + 15*d^5*f*g*x^2 + 6*d^5*f^2)*log(c))/(d^5*x^10)","A",0
332,1,492,0,0.799244," ","integrate(x^2*(g*x^2+f)^2*log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","\left[-\frac{450 \, e^{3} g^{2} p x^{7} + 126 \, {\left(14 \, e^{3} f g - 5 \, d e^{2} g^{2}\right)} p x^{5} + 70 \, {\left(35 \, e^{3} f^{2} - 42 \, d e^{2} f g + 15 \, d^{2} e g^{2}\right)} p x^{3} - 105 \, {\left(35 \, d e^{2} f^{2} - 42 \, d^{2} e f g + 15 \, d^{3} g^{2}\right)} p \sqrt{-\frac{d}{e}} \log\left(\frac{e x^{2} - 2 \, e x \sqrt{-\frac{d}{e}} - d}{e x^{2} + d}\right) - 210 \, {\left(35 \, d e^{2} f^{2} - 42 \, d^{2} e f g + 15 \, d^{3} g^{2}\right)} p x - 105 \, {\left(15 \, e^{3} g^{2} p x^{7} + 42 \, e^{3} f g p x^{5} + 35 \, e^{3} f^{2} p x^{3}\right)} \log\left(e x^{2} + d\right) - 105 \, {\left(15 \, e^{3} g^{2} x^{7} + 42 \, e^{3} f g x^{5} + 35 \, e^{3} f^{2} x^{3}\right)} \log\left(c\right)}{11025 \, e^{3}}, -\frac{450 \, e^{3} g^{2} p x^{7} + 126 \, {\left(14 \, e^{3} f g - 5 \, d e^{2} g^{2}\right)} p x^{5} + 70 \, {\left(35 \, e^{3} f^{2} - 42 \, d e^{2} f g + 15 \, d^{2} e g^{2}\right)} p x^{3} + 210 \, {\left(35 \, d e^{2} f^{2} - 42 \, d^{2} e f g + 15 \, d^{3} g^{2}\right)} p \sqrt{\frac{d}{e}} \arctan\left(\frac{e x \sqrt{\frac{d}{e}}}{d}\right) - 210 \, {\left(35 \, d e^{2} f^{2} - 42 \, d^{2} e f g + 15 \, d^{3} g^{2}\right)} p x - 105 \, {\left(15 \, e^{3} g^{2} p x^{7} + 42 \, e^{3} f g p x^{5} + 35 \, e^{3} f^{2} p x^{3}\right)} \log\left(e x^{2} + d\right) - 105 \, {\left(15 \, e^{3} g^{2} x^{7} + 42 \, e^{3} f g x^{5} + 35 \, e^{3} f^{2} x^{3}\right)} \log\left(c\right)}{11025 \, e^{3}}\right]"," ",0,"[-1/11025*(450*e^3*g^2*p*x^7 + 126*(14*e^3*f*g - 5*d*e^2*g^2)*p*x^5 + 70*(35*e^3*f^2 - 42*d*e^2*f*g + 15*d^2*e*g^2)*p*x^3 - 105*(35*d*e^2*f^2 - 42*d^2*e*f*g + 15*d^3*g^2)*p*sqrt(-d/e)*log((e*x^2 - 2*e*x*sqrt(-d/e) - d)/(e*x^2 + d)) - 210*(35*d*e^2*f^2 - 42*d^2*e*f*g + 15*d^3*g^2)*p*x - 105*(15*e^3*g^2*p*x^7 + 42*e^3*f*g*p*x^5 + 35*e^3*f^2*p*x^3)*log(e*x^2 + d) - 105*(15*e^3*g^2*x^7 + 42*e^3*f*g*x^5 + 35*e^3*f^2*x^3)*log(c))/e^3, -1/11025*(450*e^3*g^2*p*x^7 + 126*(14*e^3*f*g - 5*d*e^2*g^2)*p*x^5 + 70*(35*e^3*f^2 - 42*d*e^2*f*g + 15*d^2*e*g^2)*p*x^3 + 210*(35*d*e^2*f^2 - 42*d^2*e*f*g + 15*d^3*g^2)*p*sqrt(d/e)*arctan(e*x*sqrt(d/e)/d) - 210*(35*d*e^2*f^2 - 42*d^2*e*f*g + 15*d^3*g^2)*p*x - 105*(15*e^3*g^2*p*x^7 + 42*e^3*f*g*p*x^5 + 35*e^3*f^2*p*x^3)*log(e*x^2 + d) - 105*(15*e^3*g^2*x^7 + 42*e^3*f*g*x^5 + 35*e^3*f^2*x^3)*log(c))/e^3]","A",0
333,1,404,0,0.781201," ","integrate((g*x^2+f)^2*log(c*(e*x^2+d)^p),x, algorithm=""fricas"")","\left[-\frac{18 \, e^{2} g^{2} p x^{5} + 10 \, {\left(10 \, e^{2} f g - 3 \, d e g^{2}\right)} p x^{3} - 15 \, {\left(15 \, e^{2} f^{2} - 10 \, d e f g + 3 \, d^{2} g^{2}\right)} p \sqrt{-\frac{d}{e}} \log\left(\frac{e x^{2} + 2 \, e x \sqrt{-\frac{d}{e}} - d}{e x^{2} + d}\right) + 30 \, {\left(15 \, e^{2} f^{2} - 10 \, d e f g + 3 \, d^{2} g^{2}\right)} p x - 15 \, {\left(3 \, e^{2} g^{2} p x^{5} + 10 \, e^{2} f g p x^{3} + 15 \, e^{2} f^{2} p x\right)} \log\left(e x^{2} + d\right) - 15 \, {\left(3 \, e^{2} g^{2} x^{5} + 10 \, e^{2} f g x^{3} + 15 \, e^{2} f^{2} x\right)} \log\left(c\right)}{225 \, e^{2}}, -\frac{18 \, e^{2} g^{2} p x^{5} + 10 \, {\left(10 \, e^{2} f g - 3 \, d e g^{2}\right)} p x^{3} - 30 \, {\left(15 \, e^{2} f^{2} - 10 \, d e f g + 3 \, d^{2} g^{2}\right)} p \sqrt{\frac{d}{e}} \arctan\left(\frac{e x \sqrt{\frac{d}{e}}}{d}\right) + 30 \, {\left(15 \, e^{2} f^{2} - 10 \, d e f g + 3 \, d^{2} g^{2}\right)} p x - 15 \, {\left(3 \, e^{2} g^{2} p x^{5} + 10 \, e^{2} f g p x^{3} + 15 \, e^{2} f^{2} p x\right)} \log\left(e x^{2} + d\right) - 15 \, {\left(3 \, e^{2} g^{2} x^{5} + 10 \, e^{2} f g x^{3} + 15 \, e^{2} f^{2} x\right)} \log\left(c\right)}{225 \, e^{2}}\right]"," ",0,"[-1/225*(18*e^2*g^2*p*x^5 + 10*(10*e^2*f*g - 3*d*e*g^2)*p*x^3 - 15*(15*e^2*f^2 - 10*d*e*f*g + 3*d^2*g^2)*p*sqrt(-d/e)*log((e*x^2 + 2*e*x*sqrt(-d/e) - d)/(e*x^2 + d)) + 30*(15*e^2*f^2 - 10*d*e*f*g + 3*d^2*g^2)*p*x - 15*(3*e^2*g^2*p*x^5 + 10*e^2*f*g*p*x^3 + 15*e^2*f^2*p*x)*log(e*x^2 + d) - 15*(3*e^2*g^2*x^5 + 10*e^2*f*g*x^3 + 15*e^2*f^2*x)*log(c))/e^2, -1/225*(18*e^2*g^2*p*x^5 + 10*(10*e^2*f*g - 3*d*e*g^2)*p*x^3 - 30*(15*e^2*f^2 - 10*d*e*f*g + 3*d^2*g^2)*p*sqrt(d/e)*arctan(e*x*sqrt(d/e)/d) + 30*(15*e^2*f^2 - 10*d*e*f*g + 3*d^2*g^2)*p*x - 15*(3*e^2*g^2*p*x^5 + 10*e^2*f*g*p*x^3 + 15*e^2*f^2*p*x)*log(e*x^2 + d) - 15*(3*e^2*g^2*x^5 + 10*e^2*f*g*x^3 + 15*e^2*f^2*x)*log(c))/e^2]","A",0
334,1,366,0,0.955741," ","integrate((g*x^2+f)^2*log(c*(e*x^2+d)^p)/x^2,x, algorithm=""fricas"")","\left[-\frac{2 \, d e^{2} g^{2} p x^{4} - 3 \, {\left(3 \, e^{2} f^{2} + 6 \, d e f g - d^{2} g^{2}\right)} \sqrt{-d e} p x \log\left(\frac{e x^{2} + 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) + 6 \, {\left(6 \, d e^{2} f g - d^{2} e g^{2}\right)} p x^{2} - 3 \, {\left(d e^{2} g^{2} p x^{4} + 6 \, d e^{2} f g p x^{2} - 3 \, d e^{2} f^{2} p\right)} \log\left(e x^{2} + d\right) - 3 \, {\left(d e^{2} g^{2} x^{4} + 6 \, d e^{2} f g x^{2} - 3 \, d e^{2} f^{2}\right)} \log\left(c\right)}{9 \, d e^{2} x}, -\frac{2 \, d e^{2} g^{2} p x^{4} - 6 \, {\left(3 \, e^{2} f^{2} + 6 \, d e f g - d^{2} g^{2}\right)} \sqrt{d e} p x \arctan\left(\frac{\sqrt{d e} x}{d}\right) + 6 \, {\left(6 \, d e^{2} f g - d^{2} e g^{2}\right)} p x^{2} - 3 \, {\left(d e^{2} g^{2} p x^{4} + 6 \, d e^{2} f g p x^{2} - 3 \, d e^{2} f^{2} p\right)} \log\left(e x^{2} + d\right) - 3 \, {\left(d e^{2} g^{2} x^{4} + 6 \, d e^{2} f g x^{2} - 3 \, d e^{2} f^{2}\right)} \log\left(c\right)}{9 \, d e^{2} x}\right]"," ",0,"[-1/9*(2*d*e^2*g^2*p*x^4 - 3*(3*e^2*f^2 + 6*d*e*f*g - d^2*g^2)*sqrt(-d*e)*p*x*log((e*x^2 + 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) + 6*(6*d*e^2*f*g - d^2*e*g^2)*p*x^2 - 3*(d*e^2*g^2*p*x^4 + 6*d*e^2*f*g*p*x^2 - 3*d*e^2*f^2*p)*log(e*x^2 + d) - 3*(d*e^2*g^2*x^4 + 6*d*e^2*f*g*x^2 - 3*d*e^2*f^2)*log(c))/(d*e^2*x), -1/9*(2*d*e^2*g^2*p*x^4 - 6*(3*e^2*f^2 + 6*d*e*f*g - d^2*g^2)*sqrt(d*e)*p*x*arctan(sqrt(d*e)*x/d) + 6*(6*d*e^2*f*g - d^2*e*g^2)*p*x^2 - 3*(d*e^2*g^2*p*x^4 + 6*d*e^2*f*g*p*x^2 - 3*d*e^2*f^2*p)*log(e*x^2 + d) - 3*(d*e^2*g^2*x^4 + 6*d*e^2*f*g*x^2 - 3*d*e^2*f^2)*log(c))/(d*e^2*x)]","A",0
335,1,350,0,0.670021," ","integrate((g*x^2+f)^2*log(c*(e*x^2+d)^p)/x^4,x, algorithm=""fricas"")","\left[-\frac{6 \, d^{2} e g^{2} p x^{4} + 2 \, d e^{2} f^{2} p x^{2} - {\left(e^{2} f^{2} - 6 \, d e f g - 3 \, d^{2} g^{2}\right)} \sqrt{-d e} p x^{3} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) - {\left(3 \, d^{2} e g^{2} p x^{4} - 6 \, d^{2} e f g p x^{2} - d^{2} e f^{2} p\right)} \log\left(e x^{2} + d\right) - {\left(3 \, d^{2} e g^{2} x^{4} - 6 \, d^{2} e f g x^{2} - d^{2} e f^{2}\right)} \log\left(c\right)}{3 \, d^{2} e x^{3}}, -\frac{6 \, d^{2} e g^{2} p x^{4} + 2 \, d e^{2} f^{2} p x^{2} + 2 \, {\left(e^{2} f^{2} - 6 \, d e f g - 3 \, d^{2} g^{2}\right)} \sqrt{d e} p x^{3} \arctan\left(\frac{\sqrt{d e} x}{d}\right) - {\left(3 \, d^{2} e g^{2} p x^{4} - 6 \, d^{2} e f g p x^{2} - d^{2} e f^{2} p\right)} \log\left(e x^{2} + d\right) - {\left(3 \, d^{2} e g^{2} x^{4} - 6 \, d^{2} e f g x^{2} - d^{2} e f^{2}\right)} \log\left(c\right)}{3 \, d^{2} e x^{3}}\right]"," ",0,"[-1/3*(6*d^2*e*g^2*p*x^4 + 2*d*e^2*f^2*p*x^2 - (e^2*f^2 - 6*d*e*f*g - 3*d^2*g^2)*sqrt(-d*e)*p*x^3*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) - (3*d^2*e*g^2*p*x^4 - 6*d^2*e*f*g*p*x^2 - d^2*e*f^2*p)*log(e*x^2 + d) - (3*d^2*e*g^2*x^4 - 6*d^2*e*f*g*x^2 - d^2*e*f^2)*log(c))/(d^2*e*x^3), -1/3*(6*d^2*e*g^2*p*x^4 + 2*d*e^2*f^2*p*x^2 + 2*(e^2*f^2 - 6*d*e*f*g - 3*d^2*g^2)*sqrt(d*e)*p*x^3*arctan(sqrt(d*e)*x/d) - (3*d^2*e*g^2*p*x^4 - 6*d^2*e*f*g*p*x^2 - d^2*e*f^2*p)*log(e*x^2 + d) - (3*d^2*e*g^2*x^4 - 6*d^2*e*f*g*x^2 - d^2*e*f^2)*log(c))/(d^2*e*x^3)]","A",0
336,1,351,0,0.948230," ","integrate((g*x^2+f)^2*log(c*(e*x^2+d)^p)/x^6,x, algorithm=""fricas"")","\left[\frac{{\left(3 \, e^{2} f^{2} - 10 \, d e f g + 15 \, d^{2} g^{2}\right)} p x^{5} \sqrt{-\frac{e}{d}} \log\left(\frac{e x^{2} + 2 \, d x \sqrt{-\frac{e}{d}} - d}{e x^{2} + d}\right) - 2 \, d e f^{2} p x^{2} + 2 \, {\left(3 \, e^{2} f^{2} - 10 \, d e f g\right)} p x^{4} - {\left(15 \, d^{2} g^{2} p x^{4} + 10 \, d^{2} f g p x^{2} + 3 \, d^{2} f^{2} p\right)} \log\left(e x^{2} + d\right) - {\left(15 \, d^{2} g^{2} x^{4} + 10 \, d^{2} f g x^{2} + 3 \, d^{2} f^{2}\right)} \log\left(c\right)}{15 \, d^{2} x^{5}}, \frac{2 \, {\left(3 \, e^{2} f^{2} - 10 \, d e f g + 15 \, d^{2} g^{2}\right)} p x^{5} \sqrt{\frac{e}{d}} \arctan\left(x \sqrt{\frac{e}{d}}\right) - 2 \, d e f^{2} p x^{2} + 2 \, {\left(3 \, e^{2} f^{2} - 10 \, d e f g\right)} p x^{4} - {\left(15 \, d^{2} g^{2} p x^{4} + 10 \, d^{2} f g p x^{2} + 3 \, d^{2} f^{2} p\right)} \log\left(e x^{2} + d\right) - {\left(15 \, d^{2} g^{2} x^{4} + 10 \, d^{2} f g x^{2} + 3 \, d^{2} f^{2}\right)} \log\left(c\right)}{15 \, d^{2} x^{5}}\right]"," ",0,"[1/15*((3*e^2*f^2 - 10*d*e*f*g + 15*d^2*g^2)*p*x^5*sqrt(-e/d)*log((e*x^2 + 2*d*x*sqrt(-e/d) - d)/(e*x^2 + d)) - 2*d*e*f^2*p*x^2 + 2*(3*e^2*f^2 - 10*d*e*f*g)*p*x^4 - (15*d^2*g^2*p*x^4 + 10*d^2*f*g*p*x^2 + 3*d^2*f^2*p)*log(e*x^2 + d) - (15*d^2*g^2*x^4 + 10*d^2*f*g*x^2 + 3*d^2*f^2)*log(c))/(d^2*x^5), 1/15*(2*(3*e^2*f^2 - 10*d*e*f*g + 15*d^2*g^2)*p*x^5*sqrt(e/d)*arctan(x*sqrt(e/d)) - 2*d*e*f^2*p*x^2 + 2*(3*e^2*f^2 - 10*d*e*f*g)*p*x^4 - (15*d^2*g^2*p*x^4 + 10*d^2*f*g*p*x^2 + 3*d^2*f^2*p)*log(e*x^2 + d) - (15*d^2*g^2*x^4 + 10*d^2*f*g*x^2 + 3*d^2*f^2)*log(c))/(d^2*x^5)]","A",0
337,1,429,0,1.041788," ","integrate((g*x^2+f)^2*log(c*(e*x^2+d)^p)/x^8,x, algorithm=""fricas"")","\left[\frac{{\left(15 \, e^{3} f^{2} - 42 \, d e^{2} f g + 35 \, d^{2} e g^{2}\right)} p x^{7} \sqrt{-\frac{e}{d}} \log\left(\frac{e x^{2} - 2 \, d x \sqrt{-\frac{e}{d}} - d}{e x^{2} + d}\right) - 6 \, d^{2} e f^{2} p x^{2} - 2 \, {\left(15 \, e^{3} f^{2} - 42 \, d e^{2} f g + 35 \, d^{2} e g^{2}\right)} p x^{6} + 2 \, {\left(5 \, d e^{2} f^{2} - 14 \, d^{2} e f g\right)} p x^{4} - {\left(35 \, d^{3} g^{2} p x^{4} + 42 \, d^{3} f g p x^{2} + 15 \, d^{3} f^{2} p\right)} \log\left(e x^{2} + d\right) - {\left(35 \, d^{3} g^{2} x^{4} + 42 \, d^{3} f g x^{2} + 15 \, d^{3} f^{2}\right)} \log\left(c\right)}{105 \, d^{3} x^{7}}, -\frac{2 \, {\left(15 \, e^{3} f^{2} - 42 \, d e^{2} f g + 35 \, d^{2} e g^{2}\right)} p x^{7} \sqrt{\frac{e}{d}} \arctan\left(x \sqrt{\frac{e}{d}}\right) + 6 \, d^{2} e f^{2} p x^{2} + 2 \, {\left(15 \, e^{3} f^{2} - 42 \, d e^{2} f g + 35 \, d^{2} e g^{2}\right)} p x^{6} - 2 \, {\left(5 \, d e^{2} f^{2} - 14 \, d^{2} e f g\right)} p x^{4} + {\left(35 \, d^{3} g^{2} p x^{4} + 42 \, d^{3} f g p x^{2} + 15 \, d^{3} f^{2} p\right)} \log\left(e x^{2} + d\right) + {\left(35 \, d^{3} g^{2} x^{4} + 42 \, d^{3} f g x^{2} + 15 \, d^{3} f^{2}\right)} \log\left(c\right)}{105 \, d^{3} x^{7}}\right]"," ",0,"[1/105*((15*e^3*f^2 - 42*d*e^2*f*g + 35*d^2*e*g^2)*p*x^7*sqrt(-e/d)*log((e*x^2 - 2*d*x*sqrt(-e/d) - d)/(e*x^2 + d)) - 6*d^2*e*f^2*p*x^2 - 2*(15*e^3*f^2 - 42*d*e^2*f*g + 35*d^2*e*g^2)*p*x^6 + 2*(5*d*e^2*f^2 - 14*d^2*e*f*g)*p*x^4 - (35*d^3*g^2*p*x^4 + 42*d^3*f*g*p*x^2 + 15*d^3*f^2*p)*log(e*x^2 + d) - (35*d^3*g^2*x^4 + 42*d^3*f*g*x^2 + 15*d^3*f^2)*log(c))/(d^3*x^7), -1/105*(2*(15*e^3*f^2 - 42*d*e^2*f*g + 35*d^2*e*g^2)*p*x^7*sqrt(e/d)*arctan(x*sqrt(e/d)) + 6*d^2*e*f^2*p*x^2 + 2*(15*e^3*f^2 - 42*d*e^2*f*g + 35*d^2*e*g^2)*p*x^6 - 2*(5*d*e^2*f^2 - 14*d^2*e*f*g)*p*x^4 + (35*d^3*g^2*p*x^4 + 42*d^3*f*g*p*x^2 + 15*d^3*f^2*p)*log(e*x^2 + d) + (35*d^3*g^2*x^4 + 42*d^3*f*g*x^2 + 15*d^3*f^2)*log(c))/(d^3*x^7)]","A",0
338,0,0,0,0.815154," ","integrate(x^5*log(c*(e*x^2+d)^p)/(g*x^2+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{5} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g x^{2} + f}, x\right)"," ",0,"integral(x^5*log((e*x^2 + d)^p*c)/(g*x^2 + f), x)","F",0
339,0,0,0,0.664882," ","integrate(x^3*log(c*(e*x^2+d)^p)/(g*x^2+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g x^{2} + f}, x\right)"," ",0,"integral(x^3*log((e*x^2 + d)^p*c)/(g*x^2 + f), x)","F",0
340,0,0,0,0.899788," ","integrate(x*log(c*(e*x^2+d)^p)/(g*x^2+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g x^{2} + f}, x\right)"," ",0,"integral(x*log((e*x^2 + d)^p*c)/(g*x^2 + f), x)","F",0
341,0,0,0,0.730974," ","integrate(log(c*(e*x^2+d)^p)/x/(g*x^2+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g x^{3} + f x}, x\right)"," ",0,"integral(log((e*x^2 + d)^p*c)/(g*x^3 + f*x), x)","F",0
342,0,0,0,0.883302," ","integrate(log(c*(e*x^2+d)^p)/x^3/(g*x^2+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g x^{5} + f x^{3}}, x\right)"," ",0,"integral(log((e*x^2 + d)^p*c)/(g*x^5 + f*x^3), x)","F",0
343,0,0,0,0.918982," ","integrate(x^4*log(c*(e*x^2+d)^p)/(g*x^2+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g x^{2} + f}, x\right)"," ",0,"integral(x^4*log((e*x^2 + d)^p*c)/(g*x^2 + f), x)","F",0
344,0,0,0,1.019501," ","integrate(x^2*log(c*(e*x^2+d)^p)/(g*x^2+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g x^{2} + f}, x\right)"," ",0,"integral(x^2*log((e*x^2 + d)^p*c)/(g*x^2 + f), x)","F",0
345,0,0,0,0.837282," ","integrate(log(c*(e*x^2+d)^p)/(g*x^2+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g x^{2} + f}, x\right)"," ",0,"integral(log((e*x^2 + d)^p*c)/(g*x^2 + f), x)","F",0
346,0,0,0,1.074747," ","integrate(log(c*(e*x^2+d)^p)/x^2/(g*x^2+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g x^{4} + f x^{2}}, x\right)"," ",0,"integral(log((e*x^2 + d)^p*c)/(g*x^4 + f*x^2), x)","F",0
347,0,0,0,1.060321," ","integrate(log(c*(e*x^2+d)^p)/x^4/(g*x^2+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g x^{6} + f x^{4}}, x\right)"," ",0,"integral(log((e*x^2 + d)^p*c)/(g*x^6 + f*x^4), x)","F",0
348,0,0,0,1.011465," ","integrate(x^5*log(c*(e*x^2+d)^p)/(g*x^2+f)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{5} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g^{2} x^{4} + 2 \, f g x^{2} + f^{2}}, x\right)"," ",0,"integral(x^5*log((e*x^2 + d)^p*c)/(g^2*x^4 + 2*f*g*x^2 + f^2), x)","F",0
349,0,0,0,0.818193," ","integrate(x^3*log(c*(e*x^2+d)^p)/(g*x^2+f)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g^{2} x^{4} + 2 \, f g x^{2} + f^{2}}, x\right)"," ",0,"integral(x^3*log((e*x^2 + d)^p*c)/(g^2*x^4 + 2*f*g*x^2 + f^2), x)","F",0
350,1,91,0,0.773743," ","integrate(x*log(c*(e*x^2+d)^p)/(g*x^2+f)^2,x, algorithm=""fricas"")","\frac{{\left(e g p x^{2} + d g p\right)} \log\left(e x^{2} + d\right) - {\left(e g p x^{2} + e f p\right)} \log\left(g x^{2} + f\right) - {\left(e f - d g\right)} \log\left(c\right)}{2 \, {\left(e f^{2} g - d f g^{2} + {\left(e f g^{2} - d g^{3}\right)} x^{2}\right)}}"," ",0,"1/2*((e*g*p*x^2 + d*g*p)*log(e*x^2 + d) - (e*g*p*x^2 + e*f*p)*log(g*x^2 + f) - (e*f - d*g)*log(c))/(e*f^2*g - d*f*g^2 + (e*f*g^2 - d*g^3)*x^2)","A",0
351,0,0,0,0.693717," ","integrate(log(c*(e*x^2+d)^p)/x/(g*x^2+f)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g^{2} x^{5} + 2 \, f g x^{3} + f^{2} x}, x\right)"," ",0,"integral(log((e*x^2 + d)^p*c)/(g^2*x^5 + 2*f*g*x^3 + f^2*x), x)","F",0
352,0,0,0,0.666447," ","integrate(log(c*(e*x^2+d)^p)/x^3/(g*x^2+f)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g^{2} x^{7} + 2 \, f g x^{5} + f^{2} x^{3}}, x\right)"," ",0,"integral(log((e*x^2 + d)^p*c)/(g^2*x^7 + 2*f*g*x^5 + f^2*x^3), x)","F",0
353,0,0,0,1.143466," ","integrate(x^4*log(c*(e*x^2+d)^p)/(g*x^2+f)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g^{2} x^{4} + 2 \, f g x^{2} + f^{2}}, x\right)"," ",0,"integral(x^4*log((e*x^2 + d)^p*c)/(g^2*x^4 + 2*f*g*x^2 + f^2), x)","F",0
354,0,0,0,0.794085," ","integrate(x^2*log(c*(e*x^2+d)^p)/(g*x^2+f)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} \log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g^{2} x^{4} + 2 \, f g x^{2} + f^{2}}, x\right)"," ",0,"integral(x^2*log((e*x^2 + d)^p*c)/(g^2*x^4 + 2*f*g*x^2 + f^2), x)","F",0
355,0,0,0,0.872449," ","integrate(log(c*(e*x^2+d)^p)/(g*x^2+f)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g^{2} x^{4} + 2 \, f g x^{2} + f^{2}}, x\right)"," ",0,"integral(log((e*x^2 + d)^p*c)/(g^2*x^4 + 2*f*g*x^2 + f^2), x)","F",0
356,0,0,0,0.657390," ","integrate(log(c*(e*x^2+d)^p)/x^2/(g*x^2+f)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{2} + d\right)}^{p} c\right)}{g^{2} x^{6} + 2 \, f g x^{4} + f^{2} x^{2}}, x\right)"," ",0,"integral(log((e*x^2 + d)^p*c)/(g^2*x^6 + 2*f*g*x^4 + f^2*x^2), x)","F",0
357,0,0,0,0.756088," ","integrate(log(c*(b*x^2+a)^n)/(b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(b x^{2} + a\right)}^{n} c\right)}{b x^{2} + a}, x\right)"," ",0,"integral(log((b*x^2 + a)^n*c)/(b*x^2 + a), x)","F",0
358,0,0,0,0.642297," ","integrate(log(-x^2+1)/(-x^2+2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\log\left(-x^{2} + 1\right)}{x^{2} - 2}, x\right)"," ",0,"integral(-log(-x^2 + 1)/(x^2 - 2), x)","F",0
359,0,0,0,0.884959," ","integrate(log(e*x^2+d)/(-x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\log\left(e x^{2} + d\right)}{x^{2} - 1}, x\right)"," ",0,"integral(-log(e*x^2 + d)/(x^2 - 1), x)","F",0
360,1,148,0,0.975621," ","integrate((f+g*x^(3*n))*log(c*(d+e*x^n)^p)/x,x, algorithm=""fricas"")","-\frac{18 \, e^{3} f n p \log\left(x\right) \log\left(\frac{e x^{n} + d}{d}\right) - 18 \, e^{3} f n \log\left(c\right) \log\left(x\right) - 3 \, d e^{2} g p x^{2 \, n} + 6 \, d^{2} e g p x^{n} + 18 \, e^{3} f p {\rm Li}_2\left(-\frac{e x^{n} + d}{d} + 1\right) + 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 p \log\left(x\right) + e^{3} g p x^{3 \, n} + d^{3} g p\right)} \log\left(e x^{n} + d\right)}{18 \, e^{3} n}"," ",0,"-1/18*(18*e^3*f*n*p*log(x)*log((e*x^n + d)/d) - 18*e^3*f*n*log(c)*log(x) - 3*d*e^2*g*p*x^(2*n) + 6*d^2*e*g*p*x^n + 18*e^3*f*p*dilog(-(e*x^n + d)/d + 1) + 2*(e^3*g*p - 3*e^3*g*log(c))*x^(3*n) - 6*(3*e^3*f*n*p*log(x) + e^3*g*p*x^(3*n) + d^3*g*p)*log(e*x^n + d))/(e^3*n)","A",0
361,1,133,0,0.957497," ","integrate((f+g*x^(2*n))*log(c*(d+e*x^n)^p)/x,x, algorithm=""fricas"")","-\frac{4 \, e^{2} f n p \log\left(x\right) \log\left(\frac{e x^{n} + d}{d}\right) - 4 \, e^{2} f n \log\left(c\right) \log\left(x\right) - 2 \, d e g p x^{n} + 4 \, e^{2} f p {\rm Li}_2\left(-\frac{e x^{n} + d}{d} + 1\right) + {\left(e^{2} g p - 2 \, e^{2} g \log\left(c\right)\right)} x^{2 \, n} - 2 \, {\left(2 \, e^{2} f n p \log\left(x\right) + e^{2} g p x^{2 \, n} - d^{2} g p\right)} \log\left(e x^{n} + d\right)}{4 \, e^{2} n}"," ",0,"-1/4*(4*e^2*f*n*p*log(x)*log((e*x^n + d)/d) - 4*e^2*f*n*log(c)*log(x) - 2*d*e*g*p*x^n + 4*e^2*f*p*dilog(-(e*x^n + d)/d + 1) + (e^2*g*p - 2*e^2*g*log(c))*x^(2*n) - 2*(2*e^2*f*n*p*log(x) + e^2*g*p*x^(2*n) - d^2*g*p)*log(e*x^n + d))/(e^2*n)","A",0
362,1,100,0,0.989319," ","integrate((f+g*x^n)*log(c*(d+e*x^n)^p)/x,x, algorithm=""fricas"")","-\frac{e f n p \log\left(x\right) \log\left(\frac{e x^{n} + d}{d}\right) - e f n \log\left(c\right) \log\left(x\right) + e f p {\rm Li}_2\left(-\frac{e x^{n} + d}{d} + 1\right) + {\left(e g p - e g \log\left(c\right)\right)} x^{n} - {\left(e f n p \log\left(x\right) + e g p x^{n} + d g p\right)} \log\left(e x^{n} + d\right)}{e n}"," ",0,"-(e*f*n*p*log(x)*log((e*x^n + d)/d) - e*f*n*log(c)*log(x) + e*f*p*dilog(-(e*x^n + d)/d + 1) + (e*g*p - e*g*log(c))*x^n - (e*f*n*p*log(x) + e*g*p*x^n + d*g*p)*log(e*x^n + d))/(e*n)","A",0
363,1,114,0,1.020844," ","integrate((f+g/(x^n))*log(c*(d+e*x^n)^p)/x,x, algorithm=""fricas"")","-\frac{d f n p x^{n} \log\left(x\right) \log\left(\frac{e x^{n} + d}{d}\right) + d f p x^{n} {\rm Li}_2\left(-\frac{e x^{n} + d}{d} + 1\right) + d g \log\left(c\right) - {\left(e g n p + d f n \log\left(c\right)\right)} x^{n} \log\left(x\right) + {\left(d g p - {\left(d f n p \log\left(x\right) - e g p\right)} x^{n}\right)} \log\left(e x^{n} + d\right)}{d n x^{n}}"," ",0,"-(d*f*n*p*x^n*log(x)*log((e*x^n + d)/d) + d*f*p*x^n*dilog(-(e*x^n + d)/d + 1) + d*g*log(c) - (e*g*n*p + d*f*n*log(c))*x^n*log(x) + (d*g*p - (d*f*n*p*log(x) - e*g*p)*x^n)*log(e*x^n + d))/(d*n*x^n)","A",0
364,1,150,0,0.839787," ","integrate((f+g/(x^(2*n)))*log(c*(d+e*x^n)^p)/x,x, algorithm=""fricas"")","-\frac{2 \, d^{2} f n p x^{2 \, n} \log\left(x\right) \log\left(\frac{e x^{n} + d}{d}\right) + 2 \, d^{2} f p x^{2 \, n} {\rm Li}_2\left(-\frac{e x^{n} + d}{d} + 1\right) + d e g p x^{n} + d^{2} g \log\left(c\right) + {\left(e^{2} g n p - 2 \, d^{2} f n \log\left(c\right)\right)} x^{2 \, n} \log\left(x\right) + {\left(d^{2} g p - {\left(2 \, d^{2} f n p \log\left(x\right) + e^{2} g p\right)} x^{2 \, n}\right)} \log\left(e x^{n} + d\right)}{2 \, d^{2} n x^{2 \, n}}"," ",0,"-1/2*(2*d^2*f*n*p*x^(2*n)*log(x)*log((e*x^n + d)/d) + 2*d^2*f*p*x^(2*n)*dilog(-(e*x^n + d)/d + 1) + d*e*g*p*x^n + d^2*g*log(c) + (e^2*g*n*p - 2*d^2*f*n*log(c))*x^(2*n)*log(x) + (d^2*g*p - (2*d^2*f*n*p*log(x) + e^2*g*p)*x^(2*n))*log(e*x^n + d))/(d^2*n*x^(2*n))","A",0
365,1,291,0,0.726507," ","integrate((f+g*x^(3*n))^2*log(c*(d+e*x^n)^p)/x,x, algorithm=""fricas"")","-\frac{360 \, e^{6} f^{2} n p \log\left(x\right) \log\left(\frac{e x^{n} + d}{d}\right) - 360 \, e^{6} f^{2} n \log\left(c\right) \log\left(x\right) - 12 \, d e^{5} g^{2} p x^{5 \, n} + 15 \, d^{2} e^{4} g^{2} p x^{4 \, n} + 360 \, e^{6} f^{2} p {\rm Li}_2\left(-\frac{e x^{n} + d}{d} + 1\right) - 30 \, {\left(4 \, d e^{5} f g - d^{4} e^{2} g^{2}\right)} p x^{2 \, n} + 60 \, {\left(4 \, d^{2} e^{4} f g - d^{5} e g^{2}\right)} p x^{n} + 10 \, {\left(e^{6} g^{2} p - 6 \, e^{6} g^{2} \log\left(c\right)\right)} x^{6 \, n} - 20 \, {\left(12 \, e^{6} f g \log\left(c\right) - {\left(4 \, e^{6} f g - d^{3} e^{3} g^{2}\right)} p\right)} x^{3 \, n} - 60 \, {\left(6 \, e^{6} f^{2} n p \log\left(x\right) + e^{6} g^{2} p x^{6 \, n} + 4 \, e^{6} f g p x^{3 \, n} + {\left(4 \, d^{3} e^{3} f g - d^{6} g^{2}\right)} p\right)} \log\left(e x^{n} + d\right)}{360 \, e^{6} n}"," ",0,"-1/360*(360*e^6*f^2*n*p*log(x)*log((e*x^n + d)/d) - 360*e^6*f^2*n*log(c)*log(x) - 12*d*e^5*g^2*p*x^(5*n) + 15*d^2*e^4*g^2*p*x^(4*n) + 360*e^6*f^2*p*dilog(-(e*x^n + d)/d + 1) - 30*(4*d*e^5*f*g - d^4*e^2*g^2)*p*x^(2*n) + 60*(4*d^2*e^4*f*g - d^5*e*g^2)*p*x^n + 10*(e^6*g^2*p - 6*e^6*g^2*log(c))*x^(6*n) - 20*(12*e^6*f*g*log(c) - (4*e^6*f*g - d^3*e^3*g^2)*p)*x^(3*n) - 60*(6*e^6*f^2*n*p*log(x) + e^6*g^2*p*x^(6*n) + 4*e^6*f*g*p*x^(3*n) + (4*d^3*e^3*f*g - d^6*g^2)*p)*log(e*x^n + d))/(e^6*n)","A",0
366,1,242,0,0.880224," ","integrate((f+g*x^(2*n))^2*log(c*(d+e*x^n)^p)/x,x, algorithm=""fricas"")","-\frac{48 \, e^{4} f^{2} n p \log\left(x\right) \log\left(\frac{e x^{n} + d}{d}\right) - 48 \, e^{4} f^{2} n \log\left(c\right) \log\left(x\right) - 4 \, d e^{3} g^{2} p x^{3 \, n} + 48 \, e^{4} f^{2} p {\rm Li}_2\left(-\frac{e x^{n} + d}{d} + 1\right) - 12 \, {\left(4 \, d e^{3} f g + d^{3} e g^{2}\right)} p x^{n} + 3 \, {\left(e^{4} g^{2} p - 4 \, e^{4} g^{2} \log\left(c\right)\right)} x^{4 \, n} - 6 \, {\left(8 \, e^{4} f g \log\left(c\right) - {\left(4 \, e^{4} f g + d^{2} e^{2} g^{2}\right)} p\right)} x^{2 \, n} - 12 \, {\left(4 \, e^{4} f^{2} n p \log\left(x\right) + e^{4} g^{2} p x^{4 \, n} + 4 \, e^{4} f g p x^{2 \, n} - {\left(4 \, d^{2} e^{2} f g + d^{4} g^{2}\right)} p\right)} \log\left(e x^{n} + d\right)}{48 \, e^{4} n}"," ",0,"-1/48*(48*e^4*f^2*n*p*log(x)*log((e*x^n + d)/d) - 48*e^4*f^2*n*log(c)*log(x) - 4*d*e^3*g^2*p*x^(3*n) + 48*e^4*f^2*p*dilog(-(e*x^n + d)/d + 1) - 12*(4*d*e^3*f*g + d^3*e*g^2)*p*x^n + 3*(e^4*g^2*p - 4*e^4*g^2*log(c))*x^(4*n) - 6*(8*e^4*f*g*log(c) - (4*e^4*f*g + d^2*e^2*g^2)*p)*x^(2*n) - 12*(4*e^4*f^2*n*p*log(x) + e^4*g^2*p*x^(4*n) + 4*e^4*f*g*p*x^(2*n) - (4*d^2*e^2*f*g + d^4*g^2)*p)*log(e*x^n + d))/(e^4*n)","A",0
367,1,192,0,0.901201," ","integrate((f+g*x^n)^2*log(c*(d+e*x^n)^p)/x,x, algorithm=""fricas"")","-\frac{4 \, e^{2} f^{2} n p \log\left(x\right) \log\left(\frac{e x^{n} + d}{d}\right) - 4 \, e^{2} f^{2} n \log\left(c\right) \log\left(x\right) + 4 \, e^{2} f^{2} p {\rm Li}_2\left(-\frac{e x^{n} + d}{d} + 1\right) + {\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 \log\left(c\right) - {\left(4 \, e^{2} f g - d e g^{2}\right)} p\right)} x^{n} - 2 \, {\left(2 \, e^{2} f^{2} n p \log\left(x\right) + e^{2} g^{2} p x^{2 \, n} + 4 \, e^{2} f g p x^{n} + {\left(4 \, d e f g - d^{2} g^{2}\right)} p\right)} \log\left(e x^{n} + d\right)}{4 \, e^{2} n}"," ",0,"-1/4*(4*e^2*f^2*n*p*log(x)*log((e*x^n + d)/d) - 4*e^2*f^2*n*log(c)*log(x) + 4*e^2*f^2*p*dilog(-(e*x^n + d)/d + 1) + (e^2*g^2*p - 2*e^2*g^2*log(c))*x^(2*n) - 2*(4*e^2*f*g*log(c) - (4*e^2*f*g - d*e*g^2)*p)*x^n - 2*(2*e^2*f^2*n*p*log(x) + e^2*g^2*p*x^(2*n) + 4*e^2*f*g*p*x^n + (4*d*e*f*g - d^2*g^2)*p)*log(e*x^n + d))/(e^2*n)","A",0
368,1,210,0,0.954734," ","integrate((f+g/(x^n))^2*log(c*(d+e*x^n)^p)/x,x, algorithm=""fricas"")","-\frac{2 \, d^{2} f^{2} n p x^{2 \, n} \log\left(x\right) \log\left(\frac{e x^{n} + d}{d}\right) + 2 \, d^{2} f^{2} p x^{2 \, n} {\rm Li}_2\left(-\frac{e x^{n} + d}{d} + 1\right) + d^{2} g^{2} \log\left(c\right) - {\left(2 \, d^{2} f^{2} n \log\left(c\right) + {\left(4 \, d e f g - e^{2} g^{2}\right)} n p\right)} x^{2 \, n} \log\left(x\right) + {\left(d e g^{2} p + 4 \, d^{2} f g \log\left(c\right)\right)} x^{n} + {\left(4 \, d^{2} f g p x^{n} + d^{2} g^{2} p - {\left(2 \, d^{2} f^{2} n p \log\left(x\right) - {\left(4 \, d e f g - e^{2} g^{2}\right)} p\right)} x^{2 \, n}\right)} \log\left(e x^{n} + d\right)}{2 \, d^{2} n x^{2 \, n}}"," ",0,"-1/2*(2*d^2*f^2*n*p*x^(2*n)*log(x)*log((e*x^n + d)/d) + 2*d^2*f^2*p*x^(2*n)*dilog(-(e*x^n + d)/d + 1) + d^2*g^2*log(c) - (2*d^2*f^2*n*log(c) + (4*d*e*f*g - e^2*g^2)*n*p)*x^(2*n)*log(x) + (d*e*g^2*p + 4*d^2*f*g*log(c))*x^n + (4*d^2*f*g*p*x^n + d^2*g^2*p - (2*d^2*f^2*n*p*log(x) - (4*d*e*f*g - e^2*g^2)*p)*x^(2*n))*log(e*x^n + d))/(d^2*n*x^(2*n))","A",0
369,1,265,0,1.014311," ","integrate((f+g/(x^(2*n)))^2*log(c*(d+e*x^n)^p)/x,x, algorithm=""fricas"")","-\frac{24 \, d^{4} f^{2} n p x^{4 \, n} \log\left(x\right) \log\left(\frac{e x^{n} + d}{d}\right) + 24 \, d^{4} f^{2} p x^{4 \, n} {\rm Li}_2\left(-\frac{e x^{n} + d}{d} + 1\right) + 2 \, d^{3} e g^{2} p x^{n} + 6 \, d^{4} g^{2} \log\left(c\right) + 6 \, {\left(4 \, d^{3} e f g + d e^{3} g^{2}\right)} p x^{3 \, n} - 6 \, {\left(4 \, d^{4} f^{2} n \log\left(c\right) - {\left(4 \, d^{2} e^{2} f g + e^{4} g^{2}\right)} n p\right)} x^{4 \, n} \log\left(x\right) - 3 \, {\left(d^{2} e^{2} g^{2} p - 8 \, d^{4} f g \log\left(c\right)\right)} x^{2 \, n} + 6 \, {\left(4 \, d^{4} f g p x^{2 \, n} + d^{4} g^{2} p - {\left(4 \, d^{4} f^{2} n p \log\left(x\right) + {\left(4 \, d^{2} e^{2} f g + e^{4} g^{2}\right)} p\right)} x^{4 \, n}\right)} \log\left(e x^{n} + d\right)}{24 \, d^{4} n x^{4 \, n}}"," ",0,"-1/24*(24*d^4*f^2*n*p*x^(4*n)*log(x)*log((e*x^n + d)/d) + 24*d^4*f^2*p*x^(4*n)*dilog(-(e*x^n + d)/d + 1) + 2*d^3*e*g^2*p*x^n + 6*d^4*g^2*log(c) + 6*(4*d^3*e*f*g + d*e^3*g^2)*p*x^(3*n) - 6*(4*d^4*f^2*n*log(c) - (4*d^2*e^2*f*g + e^4*g^2)*n*p)*x^(4*n)*log(x) - 3*(d^2*e^2*g^2*p - 8*d^4*f*g*log(c))*x^(2*n) + 6*(4*d^4*f*g*p*x^(2*n) + d^4*g^2*p - (4*d^4*f^2*n*p*log(x) + (4*d^2*e^2*f*g + e^4*g^2)*p)*x^(4*n))*log(e*x^n + d))/(d^4*n*x^(4*n))","A",0
370,0,0,0,0.777596," ","integrate(log(c*(d+e*x^n)^p)/x/(f+g*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{n} + d\right)}^{p} c\right)}{g x x^{2 \, n} + f x}, x\right)"," ",0,"integral(log((e*x^n + d)^p*c)/(g*x*x^(2*n) + f*x), x)","F",0
371,0,0,0,0.934810," ","integrate(log(c*(d+e*x^n)^p)/x/(f+g*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{n} + d\right)}^{p} c\right)}{g x x^{n} + f x}, x\right)"," ",0,"integral(log((e*x^n + d)^p*c)/(g*x*x^n + f*x), x)","F",0
372,0,0,0,0.688102," ","integrate(log(c*(d+e*x^n)^p)/x/(f+g/(x^n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{n} \log\left({\left(e x^{n} + d\right)}^{p} c\right)}{f x x^{n} + g x}, x\right)"," ",0,"integral(x^n*log((e*x^n + d)^p*c)/(f*x*x^n + g*x), x)","F",0
373,0,0,0,0.875678," ","integrate(log(c*(d+e*x^n)^p)/x/(f+g/(x^(2*n))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2 \, n} \log\left({\left(e x^{n} + d\right)}^{p} c\right)}{f x x^{2 \, n} + g x}, x\right)"," ",0,"integral(x^(2*n)*log((e*x^n + d)^p*c)/(f*x*x^(2*n) + g*x), x)","F",0
374,0,0,0,0.864021," ","integrate(log(c*(d+e*x^n)^p)/x/(f+g*x^(2*n))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{n} + d\right)}^{p} c\right)}{g^{2} x x^{4 \, n} + 2 \, f g x x^{2 \, n} + f^{2} x}, x\right)"," ",0,"integral(log((e*x^n + d)^p*c)/(g^2*x*x^(4*n) + 2*f*g*x*x^(2*n) + f^2*x), x)","F",0
375,0,0,0,0.900074," ","integrate(log(c*(d+e*x^n)^p)/x/(f+g*x^n)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{n} + d\right)}^{p} c\right)}{g^{2} x x^{2 \, n} + 2 \, f g x x^{n} + f^{2} x}, x\right)"," ",0,"integral(log((e*x^n + d)^p*c)/(g^2*x*x^(2*n) + 2*f*g*x*x^n + f^2*x), x)","F",0
376,0,0,0,0.786091," ","integrate(log(c*(d+e*x^n)^p)/x/(f+g/(x^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{n} + d\right)}^{p} c\right)}{f^{2} x + \frac{2 \, f g x x^{n}}{x^{2 \, n}} + \frac{g^{2} x}{x^{2 \, n}}}, x\right)"," ",0,"integral(log((e*x^n + d)^p*c)/(f^2*x + 2*f*g*x*x^n/x^(2*n) + g^2*x/x^(2*n)), x)","F",0
377,0,0,0,0.812608," ","integrate(log(c*(d+e*x^n)^p)/x/(f+g/(x^(2*n)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{n} + d\right)}^{p} c\right)}{f^{2} x + \frac{2 \, f g x x^{2 \, n}}{x^{4 \, n}} + \frac{g^{2} x}{x^{4 \, n}}}, x\right)"," ",0,"integral(log((e*x^n + d)^p*c)/(f^2*x + 2*f*g*x*x^(2*n)/x^(4*n) + g^2*x/x^(4*n)), x)","F",0
378,1,25,0,0.941899," ","integrate(log(c*(d+e*x^n))/x/(c*e+(c*d-1)/(x^n)),x, algorithm=""fricas"")","-\frac{{\rm Li}_2\left(-c e x^{n} - c d + 1\right)}{c e n}"," ",0,"-dilog(-c*e*x^n - c*d + 1)/(c*e*n)","A",0
379,1,25,0,0.636205," ","integrate(x^(-1+n)*log(c*(d+e*x^n))/(-1+c*d+c*e*x^n),x, algorithm=""fricas"")","-\frac{{\rm Li}_2\left(-c e x^{n} - c d + 1\right)}{c e n}"," ",0,"-dilog(-c*e*x^n - c*d + 1)/(c*e*n)","A",0
380,1,30,0,0.915596," ","integrate(log(c*(d+e/(x^n)))/x/(c*e-(-c*d+1)*x^n),x, algorithm=""fricas"")","\frac{{\rm Li}_2\left(-\frac{c d x^{n} + c e}{x^{n}} + 1\right)}{c e n}"," ",0,"dilog(-(c*d*x^n + c*e)/x^n + 1)/(c*e*n)","A",0
381,0,0,0,0.891709," ","integrate((f+g*x^(2*n))^2*log(c*(d+e*x^n)^p)^q/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(g^{2} x^{4 \, n} + 2 \, f g x^{2 \, n} + f^{2}\right)} \log\left({\left(e x^{n} + d\right)}^{p} c\right)^{q}}{x}, x\right)"," ",0,"integral((g^2*x^(4*n) + 2*f*g*x^(2*n) + f^2)*log((e*x^n + d)^p*c)^q/x, x)","F",0
382,0,0,0,0.518167," ","integrate((f+g*x^n)^2*log(c*(d+e*x^n)^p)^q/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(g^{2} x^{2 \, n} + 2 \, f g x^{n} + f^{2}\right)} \log\left({\left(e x^{n} + d\right)}^{p} c\right)^{q}}{x}, x\right)"," ",0,"integral((g^2*x^(2*n) + 2*f*g*x^n + f^2)*log((e*x^n + d)^p*c)^q/x, x)","F",0
383,0,0,0,0.853457," ","integrate((f+g/(x^n))^2*log(c*(d+e*x^n)^p)^q/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f^{2} x^{2 \, n} + 2 \, f g x^{n} + g^{2}\right)} \log\left({\left(e x^{n} + d\right)}^{p} c\right)^{q}}{x x^{2 \, n}}, x\right)"," ",0,"integral((f^2*x^(2*n) + 2*f*g*x^n + g^2)*log((e*x^n + d)^p*c)^q/(x*x^(2*n)), x)","F",0
384,0,0,0,0.632735," ","integrate((f+g/(x^(2*n)))^2*log(c*(d+e*x^n)^p)^q/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f^{2} x^{4 \, n} + 2 \, f g x^{2 \, n} + g^{2}\right)} \log\left({\left(e x^{n} + d\right)}^{p} c\right)^{q}}{x x^{4 \, n}}, x\right)"," ",0,"integral((f^2*x^(4*n) + 2*f*g*x^(2*n) + g^2)*log((e*x^n + d)^p*c)^q/(x*x^(4*n)), x)","F",0
385,0,0,0,0.970235," ","integrate(log(c*(d+e*x^n)^p)^q/x/(f+g*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{n} + d\right)}^{p} c\right)^{q}}{g x x^{2 \, n} + f x}, x\right)"," ",0,"integral(log((e*x^n + d)^p*c)^q/(g*x*x^(2*n) + f*x), x)","F",0
386,0,0,0,1.015099," ","integrate(log(c*(d+e*x^n)^p)^q/x/(f+g*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left({\left(e x^{n} + d\right)}^{p} c\right)^{q}}{g x x^{n} + f x}, x\right)"," ",0,"integral(log((e*x^n + d)^p*c)^q/(g*x*x^n + f*x), x)","F",0
387,0,0,0,0.908099," ","integrate(log(c*(d+e*x^n)^p)^q/x/(f+g/(x^n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{n} \log\left({\left(e x^{n} + d\right)}^{p} c\right)^{q}}{f x x^{n} + g x}, x\right)"," ",0,"integral(x^n*log((e*x^n + d)^p*c)^q/(f*x*x^n + g*x), x)","F",0
388,0,0,0,0.698746," ","integrate(log(c*(d+e*x^n)^p)^q/x/(f+g/(x^(2*n))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2 \, n} \log\left({\left(e x^{n} + d\right)}^{p} c\right)^{q}}{f x x^{2 \, n} + g x}, x\right)"," ",0,"integral(x^(2*n)*log((e*x^n + d)^p*c)^q/(f*x*x^(2*n) + g*x), x)","F",0
389,1,76,0,0.898310," ","integrate(log(x)*log(d+e*x^m)/x,x, algorithm=""fricas"")","\frac{m^{2} \log\left(e x^{m} + d\right) \log\left(x\right)^{2} - m^{2} \log\left(x\right)^{2} \log\left(\frac{e x^{m} + d}{d}\right) - 2 \, m {\rm Li}_2\left(-\frac{e x^{m} + d}{d} + 1\right) \log\left(x\right) + 2 \, {\rm polylog}\left(3, -\frac{e x^{m}}{d}\right)}{2 \, m^{2}}"," ",0,"1/2*(m^2*log(e*x^m + d)*log(x)^2 - m^2*log(x)^2*log((e*x^m + d)/d) - 2*m*dilog(-(e*x^m + d)/d + 1)*log(x) + 2*polylog(3, -e*x^m/d))/m^2","C",0
390,1,11,0,0.860253," ","integrate(log((a+x)/x)/x,x, algorithm=""fricas"")","{\rm Li}_2\left(-\frac{a + x}{x} + 1\right)"," ",0,"dilog(-(a + x)/x + 1)","A",0
391,1,15,0,0.927353," ","integrate(log((x^2+a)/x^2)/x,x, algorithm=""fricas"")","\frac{1}{2} \, {\rm Li}_2\left(-\frac{x^{2} + a}{x^{2}} + 1\right)"," ",0,"1/2*dilog(-(x^2 + a)/x^2 + 1)","A",0
392,1,61,0,0.735376," ","integrate(log((a+x^n)/(x^n))/x,x, algorithm=""fricas"")","\frac{n^{2} \log\left(x\right)^{2} - 2 \, n \log\left(x\right) \log\left(\frac{a + x^{n}}{a}\right) + 2 \, n \log\left(x\right) \log\left(\frac{a + x^{n}}{x^{n}}\right) - 2 \, {\rm Li}_2\left(-\frac{a + x^{n}}{a} + 1\right)}{2 \, n}"," ",0,"1/2*(n^2*log(x)^2 - 2*n*log(x)*log((a + x^n)/a) + 2*n*log(x)*log((a + x^n)/x^n) - 2*dilog(-(a + x^n)/a + 1))/n","B",0
393,0,0,0,0.881833," ","integrate(log((b*x+a)/x)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(\frac{b x + a}{x}\right)}{x}, x\right)"," ",0,"integral(log((b*x + a)/x)/x, x)","F",0
394,0,0,0,0.841776," ","integrate(log((b*x^2+a)/x^2)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(\frac{b x^{2} + a}{x^{2}}\right)}{x}, x\right)"," ",0,"integral(log((b*x^2 + a)/x^2)/x, x)","F",0
395,1,67,0,0.869325," ","integrate(log((a+b*x^n)/(x^n))/x,x, algorithm=""fricas"")","\frac{n^{2} \log\left(x\right)^{2} - 2 \, n \log\left(x\right) \log\left(\frac{b x^{n} + a}{a}\right) + 2 \, n \log\left(x\right) \log\left(\frac{b x^{n} + a}{x^{n}}\right) - 2 \, {\rm Li}_2\left(-\frac{b x^{n} + a}{a} + 1\right)}{2 \, n}"," ",0,"1/2*(n^2*log(x)^2 - 2*n*log(x)*log((b*x^n + a)/a) + 2*n*log(x)*log((b*x^n + a)/x^n) - 2*dilog(-(b*x^n + a)/a + 1))/n","A",0
396,0,0,0,0.666556," ","integrate(log((b*x+a)/x)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(\frac{b x + a}{x}\right)}{d x + c}, x\right)"," ",0,"integral(log((b*x + a)/x)/(d*x + c), x)","F",0
397,0,0,0,0.931855," ","integrate(log((b*x^2+a)/x^2)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(\frac{b x^{2} + a}{x^{2}}\right)}{d x + c}, x\right)"," ",0,"integral(log((b*x^2 + a)/x^2)/(d*x + c), x)","F",0
398,0,0,0,0.828485," ","integrate(log((a+b*x^n)/(x^n))/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(\frac{b x^{n} + a}{x^{n}}\right)}{d x + c}, x\right)"," ",0,"integral(log((b*x^n + a)/x^n)/(d*x + c), x)","F",0
399,0,0,0,0.956482," ","integrate((f*x)^q*(a+b*log(c*(d+e*x^m)^n)),x, algorithm=""fricas"")","{\rm integral}\left(\left(f x\right)^{q} b \log\left({\left(e x^{m} + d\right)}^{n} c\right) + \left(f x\right)^{q} a, x\right)"," ",0,"integral((f*x)^q*b*log((e*x^m + d)^n*c) + (f*x)^q*a, x)","F",0
400,1,148,0,0.879726," ","integrate(x^3*(a+b*log(c*(d+e*x^(1/2))^n)),x, algorithm=""fricas"")","\frac{840 \, b e^{8} x^{4} \log\left(c\right) - 140 \, b d^{2} e^{6} n x^{3} - 210 \, b d^{4} e^{4} n x^{2} - 420 \, b d^{6} e^{2} n x - 105 \, {\left(b e^{8} n - 8 \, a e^{8}\right)} x^{4} + 840 \, {\left(b e^{8} n x^{4} - b d^{8} n\right)} \log\left(e \sqrt{x} + d\right) + 8 \, {\left(15 \, b d e^{7} n x^{3} + 21 \, b d^{3} e^{5} n x^{2} + 35 \, b d^{5} e^{3} n x + 105 \, b d^{7} e n\right)} \sqrt{x}}{3360 \, e^{8}}"," ",0,"1/3360*(840*b*e^8*x^4*log(c) - 140*b*d^2*e^6*n*x^3 - 210*b*d^4*e^4*n*x^2 - 420*b*d^6*e^2*n*x - 105*(b*e^8*n - 8*a*e^8)*x^4 + 840*(b*e^8*n*x^4 - b*d^8*n)*log(e*sqrt(x) + d) + 8*(15*b*d*e^7*n*x^3 + 21*b*d^3*e^5*n*x^2 + 35*b*d^5*e^3*n*x + 105*b*d^7*e*n)*sqrt(x))/e^8","A",0
401,1,122,0,0.846323," ","integrate(x^2*(a+b*log(c*(d+e*x^(1/2))^n)),x, algorithm=""fricas"")","\frac{60 \, b e^{6} x^{3} \log\left(c\right) - 15 \, b d^{2} e^{4} n x^{2} - 30 \, b d^{4} e^{2} n x - 10 \, {\left(b e^{6} n - 6 \, a e^{6}\right)} x^{3} + 60 \, {\left(b e^{6} n x^{3} - b d^{6} n\right)} \log\left(e \sqrt{x} + d\right) + 4 \, {\left(3 \, b d e^{5} n x^{2} + 5 \, b d^{3} e^{3} n x + 15 \, b d^{5} e n\right)} \sqrt{x}}{180 \, e^{6}}"," ",0,"1/180*(60*b*e^6*x^3*log(c) - 15*b*d^2*e^4*n*x^2 - 30*b*d^4*e^2*n*x - 10*(b*e^6*n - 6*a*e^6)*x^3 + 60*(b*e^6*n*x^3 - b*d^6*n)*log(e*sqrt(x) + d) + 4*(3*b*d*e^5*n*x^2 + 5*b*d^3*e^3*n*x + 15*b*d^5*e*n)*sqrt(x))/e^6","A",0
402,1,95,0,0.697504," ","integrate(x*(a+b*log(c*(d+e*x^(1/2))^n)),x, algorithm=""fricas"")","\frac{12 \, b e^{4} x^{2} \log\left(c\right) - 6 \, b d^{2} e^{2} n x - 3 \, {\left(b e^{4} n - 4 \, a e^{4}\right)} x^{2} + 12 \, {\left(b e^{4} n x^{2} - b d^{4} n\right)} \log\left(e \sqrt{x} + d\right) + 4 \, {\left(b d e^{3} n x + 3 \, b d^{3} e n\right)} \sqrt{x}}{24 \, e^{4}}"," ",0,"1/24*(12*b*e^4*x^2*log(c) - 6*b*d^2*e^2*n*x - 3*(b*e^4*n - 4*a*e^4)*x^2 + 12*(b*e^4*n*x^2 - b*d^4*n)*log(e*sqrt(x) + d) + 4*(b*d*e^3*n*x + 3*b*d^3*e*n)*sqrt(x))/e^4","A",0
403,1,65,0,0.830831," ","integrate(a+b*log(c*(d+e*x^(1/2))^n),x, algorithm=""fricas"")","\frac{2 \, b e^{2} x \log\left(c\right) + 2 \, b d e n \sqrt{x} - {\left(b e^{2} n - 2 \, a e^{2}\right)} x + 2 \, {\left(b e^{2} n x - b d^{2} n\right)} \log\left(e \sqrt{x} + d\right)}{2 \, e^{2}}"," ",0,"1/2*(2*b*e^2*x*log(c) + 2*b*d*e*n*sqrt(x) - (b*e^2*n - 2*a*e^2)*x + 2*(b*e^2*n*x - b*d^2*n)*log(e*sqrt(x) + d))/e^2","A",0
404,0,0,0,0.540511," ","integrate((a+b*log(c*(d+e*x^(1/2))^n))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right) + a}{x}, x\right)"," ",0,"integral((b*log((e*sqrt(x) + d)^n*c) + a)/x, x)","F",0
405,1,65,0,0.969135," ","integrate((a+b*log(c*(d+e*x^(1/2))^n))/x^2,x, algorithm=""fricas"")","-\frac{b e^{2} n x \log\left(\sqrt{x}\right) + b d e n \sqrt{x} + b d^{2} \log\left(c\right) + a d^{2} - {\left(b e^{2} n x - b d^{2} n\right)} \log\left(e \sqrt{x} + d\right)}{d^{2} x}"," ",0,"-(b*e^2*n*x*log(sqrt(x)) + b*d*e*n*sqrt(x) + b*d^2*log(c) + a*d^2 - (b*e^2*n*x - b*d^2*n)*log(e*sqrt(x) + d))/(d^2*x)","A",0
406,1,97,0,0.976944," ","integrate((a+b*log(c*(d+e*x^(1/2))^n))/x^3,x, algorithm=""fricas"")","-\frac{6 \, b e^{4} n x^{2} \log\left(\sqrt{x}\right) - 3 \, b d^{2} e^{2} n x + 6 \, b d^{4} \log\left(c\right) + 6 \, a d^{4} - 6 \, {\left(b e^{4} n x^{2} - b d^{4} n\right)} \log\left(e \sqrt{x} + d\right) + 2 \, {\left(3 \, b d e^{3} n x + b d^{3} e n\right)} \sqrt{x}}{12 \, d^{4} x^{2}}"," ",0,"-1/12*(6*b*e^4*n*x^2*log(sqrt(x)) - 3*b*d^2*e^2*n*x + 6*b*d^4*log(c) + 6*a*d^4 - 6*(b*e^4*n*x^2 - b*d^4*n)*log(e*sqrt(x) + d) + 2*(3*b*d*e^3*n*x + b*d^3*e*n)*sqrt(x))/(d^4*x^2)","A",0
407,1,124,0,0.944752," ","integrate((a+b*log(c*(d+e*x^(1/2))^n))/x^4,x, algorithm=""fricas"")","-\frac{60 \, b e^{6} n x^{3} \log\left(\sqrt{x}\right) - 30 \, b d^{2} e^{4} n x^{2} - 15 \, b d^{4} e^{2} n x + 60 \, b d^{6} \log\left(c\right) + 60 \, a d^{6} - 60 \, {\left(b e^{6} n x^{3} - b d^{6} n\right)} \log\left(e \sqrt{x} + d\right) + 4 \, {\left(15 \, b d e^{5} n x^{2} + 5 \, b d^{3} e^{3} n x + 3 \, b d^{5} e n\right)} \sqrt{x}}{180 \, d^{6} x^{3}}"," ",0,"-1/180*(60*b*e^6*n*x^3*log(sqrt(x)) - 30*b*d^2*e^4*n*x^2 - 15*b*d^4*e^2*n*x + 60*b*d^6*log(c) + 60*a*d^6 - 60*(b*e^6*n*x^3 - b*d^6*n)*log(e*sqrt(x) + d) + 4*(15*b*d*e^5*n*x^2 + 5*b*d^3*e^3*n*x + 3*b*d^5*e*n)*sqrt(x))/(d^6*x^3)","A",0
408,1,487,0,0.900089," ","integrate(x^2*(a+b*log(c*(d+e*x^(1/2))^n))^2,x, algorithm=""fricas"")","\frac{1800 \, b^{2} e^{6} x^{3} \log\left(c\right)^{2} + 100 \, {\left(b^{2} e^{6} n^{2} - 6 \, a b e^{6} n + 18 \, a^{2} e^{6}\right)} x^{3} + 15 \, {\left(37 \, b^{2} d^{2} e^{4} n^{2} - 60 \, a b d^{2} e^{4} n\right)} x^{2} + 1800 \, {\left(b^{2} e^{6} n^{2} x^{3} - b^{2} d^{6} n^{2}\right)} \log\left(e \sqrt{x} + d\right)^{2} + 90 \, {\left(29 \, b^{2} d^{4} e^{2} n^{2} - 20 \, a b d^{4} e^{2} n\right)} x - 60 \, {\left(15 \, b^{2} d^{2} e^{4} n^{2} x^{2} + 30 \, b^{2} d^{4} e^{2} n^{2} x - 147 \, b^{2} d^{6} n^{2} + 60 \, a b d^{6} n + 10 \, {\left(b^{2} e^{6} n^{2} - 6 \, a b e^{6} n\right)} x^{3} - 60 \, {\left(b^{2} e^{6} n x^{3} - b^{2} d^{6} n\right)} \log\left(c\right) - 4 \, {\left(3 \, b^{2} d e^{5} n^{2} x^{2} + 5 \, b^{2} d^{3} e^{3} n^{2} x + 15 \, b^{2} d^{5} e n^{2}\right)} \sqrt{x}\right)} \log\left(e \sqrt{x} + d\right) - 300 \, {\left(3 \, b^{2} d^{2} e^{4} n x^{2} + 6 \, b^{2} d^{4} e^{2} n x + 2 \, {\left(b^{2} e^{6} n - 6 \, a b e^{6}\right)} x^{3}\right)} \log\left(c\right) - 12 \, {\left(735 \, b^{2} d^{5} e n^{2} - 300 \, a b d^{5} e n + 2 \, {\left(11 \, b^{2} d e^{5} n^{2} - 30 \, a b d e^{5} n\right)} x^{2} + 5 \, {\left(19 \, b^{2} d^{3} e^{3} n^{2} - 20 \, a b d^{3} e^{3} n\right)} x - 20 \, {\left(3 \, b^{2} d e^{5} n x^{2} + 5 \, b^{2} d^{3} e^{3} n x + 15 \, b^{2} d^{5} e n\right)} \log\left(c\right)\right)} \sqrt{x}}{5400 \, e^{6}}"," ",0,"1/5400*(1800*b^2*e^6*x^3*log(c)^2 + 100*(b^2*e^6*n^2 - 6*a*b*e^6*n + 18*a^2*e^6)*x^3 + 15*(37*b^2*d^2*e^4*n^2 - 60*a*b*d^2*e^4*n)*x^2 + 1800*(b^2*e^6*n^2*x^3 - b^2*d^6*n^2)*log(e*sqrt(x) + d)^2 + 90*(29*b^2*d^4*e^2*n^2 - 20*a*b*d^4*e^2*n)*x - 60*(15*b^2*d^2*e^4*n^2*x^2 + 30*b^2*d^4*e^2*n^2*x - 147*b^2*d^6*n^2 + 60*a*b*d^6*n + 10*(b^2*e^6*n^2 - 6*a*b*e^6*n)*x^3 - 60*(b^2*e^6*n*x^3 - b^2*d^6*n)*log(c) - 4*(3*b^2*d*e^5*n^2*x^2 + 5*b^2*d^3*e^3*n^2*x + 15*b^2*d^5*e*n^2)*sqrt(x))*log(e*sqrt(x) + d) - 300*(3*b^2*d^2*e^4*n*x^2 + 6*b^2*d^4*e^2*n*x + 2*(b^2*e^6*n - 6*a*b*e^6)*x^3)*log(c) - 12*(735*b^2*d^5*e*n^2 - 300*a*b*d^5*e*n + 2*(11*b^2*d*e^5*n^2 - 30*a*b*d*e^5*n)*x^2 + 5*(19*b^2*d^3*e^3*n^2 - 20*a*b*d^3*e^3*n)*x - 20*(3*b^2*d*e^5*n*x^2 + 5*b^2*d^3*e^3*n*x + 15*b^2*d^5*e*n)*log(c))*sqrt(x))/e^6","A",0
409,1,357,0,0.792179," ","integrate(x*(a+b*log(c*(d+e*x^(1/2))^n))^2,x, algorithm=""fricas"")","\frac{72 \, b^{2} e^{4} x^{2} \log\left(c\right)^{2} + 9 \, {\left(b^{2} e^{4} n^{2} - 4 \, a b e^{4} n + 8 \, a^{2} e^{4}\right)} x^{2} + 72 \, {\left(b^{2} e^{4} n^{2} x^{2} - b^{2} d^{4} n^{2}\right)} \log\left(e \sqrt{x} + d\right)^{2} + 6 \, {\left(13 \, b^{2} d^{2} e^{2} n^{2} - 12 \, a b d^{2} e^{2} n\right)} x - 12 \, {\left(6 \, b^{2} d^{2} e^{2} n^{2} x - 25 \, b^{2} d^{4} n^{2} + 12 \, a b d^{4} n + 3 \, {\left(b^{2} e^{4} n^{2} - 4 \, a b e^{4} n\right)} x^{2} - 12 \, {\left(b^{2} e^{4} n x^{2} - b^{2} d^{4} n\right)} \log\left(c\right) - 4 \, {\left(b^{2} d e^{3} n^{2} x + 3 \, b^{2} d^{3} e n^{2}\right)} \sqrt{x}\right)} \log\left(e \sqrt{x} + d\right) - 36 \, {\left(2 \, b^{2} d^{2} e^{2} n x + {\left(b^{2} e^{4} n - 4 \, a b e^{4}\right)} x^{2}\right)} \log\left(c\right) - 4 \, {\left(75 \, b^{2} d^{3} e n^{2} - 36 \, a b d^{3} e n + {\left(7 \, b^{2} d e^{3} n^{2} - 12 \, a b d e^{3} n\right)} x - 12 \, {\left(b^{2} d e^{3} n x + 3 \, b^{2} d^{3} e n\right)} \log\left(c\right)\right)} \sqrt{x}}{144 \, e^{4}}"," ",0,"1/144*(72*b^2*e^4*x^2*log(c)^2 + 9*(b^2*e^4*n^2 - 4*a*b*e^4*n + 8*a^2*e^4)*x^2 + 72*(b^2*e^4*n^2*x^2 - b^2*d^4*n^2)*log(e*sqrt(x) + d)^2 + 6*(13*b^2*d^2*e^2*n^2 - 12*a*b*d^2*e^2*n)*x - 12*(6*b^2*d^2*e^2*n^2*x - 25*b^2*d^4*n^2 + 12*a*b*d^4*n + 3*(b^2*e^4*n^2 - 4*a*b*e^4*n)*x^2 - 12*(b^2*e^4*n*x^2 - b^2*d^4*n)*log(c) - 4*(b^2*d*e^3*n^2*x + 3*b^2*d^3*e*n^2)*sqrt(x))*log(e*sqrt(x) + d) - 36*(2*b^2*d^2*e^2*n*x + (b^2*e^4*n - 4*a*b*e^4)*x^2)*log(c) - 4*(75*b^2*d^3*e*n^2 - 36*a*b*d^3*e*n + (7*b^2*d*e^3*n^2 - 12*a*b*d*e^3*n)*x - 12*(b^2*d*e^3*n*x + 3*b^2*d^3*e*n)*log(c))*sqrt(x))/e^4","A",0
410,1,225,0,0.931927," ","integrate((a+b*log(c*(d+e*x^(1/2))^n))^2,x, algorithm=""fricas"")","\frac{2 \, b^{2} e^{2} x \log\left(c\right)^{2} + 2 \, {\left(b^{2} e^{2} n^{2} x - b^{2} d^{2} n^{2}\right)} \log\left(e \sqrt{x} + d\right)^{2} - 2 \, {\left(b^{2} e^{2} n - 2 \, a b e^{2}\right)} x \log\left(c\right) + {\left(b^{2} e^{2} n^{2} - 2 \, a b e^{2} n + 2 \, a^{2} e^{2}\right)} x + 2 \, {\left(2 \, b^{2} d e n^{2} \sqrt{x} + 3 \, b^{2} d^{2} n^{2} - 2 \, a b d^{2} n - {\left(b^{2} e^{2} n^{2} - 2 \, a b e^{2} n\right)} x + 2 \, {\left(b^{2} e^{2} n x - b^{2} d^{2} n\right)} \log\left(c\right)\right)} \log\left(e \sqrt{x} + d\right) - 2 \, {\left(3 \, b^{2} d e n^{2} - 2 \, b^{2} d e n \log\left(c\right) - 2 \, a b d e n\right)} \sqrt{x}}{2 \, e^{2}}"," ",0,"1/2*(2*b^2*e^2*x*log(c)^2 + 2*(b^2*e^2*n^2*x - b^2*d^2*n^2)*log(e*sqrt(x) + d)^2 - 2*(b^2*e^2*n - 2*a*b*e^2)*x*log(c) + (b^2*e^2*n^2 - 2*a*b*e^2*n + 2*a^2*e^2)*x + 2*(2*b^2*d*e*n^2*sqrt(x) + 3*b^2*d^2*n^2 - 2*a*b*d^2*n - (b^2*e^2*n^2 - 2*a*b*e^2*n)*x + 2*(b^2*e^2*n*x - b^2*d^2*n)*log(c))*log(e*sqrt(x) + d) - 2*(3*b^2*d*e*n^2 - 2*b^2*d*e*n*log(c) - 2*a*b*d*e*n)*sqrt(x))/e^2","A",0
411,0,0,0,1.030554," ","integrate((a+b*log(c*(d+e*x^(1/2))^n))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)^{2} + 2 \, a b \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*log((e*sqrt(x) + d)^n*c)^2 + 2*a*b*log((e*sqrt(x) + d)^n*c) + a^2)/x, x)","F",0
412,0,0,0,1.200994," ","integrate((a+b*log(c*(d+e*x^(1/2))^n))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)^{2} + 2 \, a b \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right) + a^{2}}{x^{2}}, x\right)"," ",0,"integral((b^2*log((e*sqrt(x) + d)^n*c)^2 + 2*a*b*log((e*sqrt(x) + d)^n*c) + a^2)/x^2, x)","F",0
413,0,0,0,1.093874," ","integrate((a+b*log(c*(d+e*x^(1/2))^n))^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)^{2} + 2 \, a b \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right) + a^{2}}{x^{3}}, x\right)"," ",0,"integral((b^2*log((e*sqrt(x) + d)^n*c)^2 + 2*a*b*log((e*sqrt(x) + d)^n*c) + a^2)/x^3, x)","F",0
414,0,0,0,1.168213," ","integrate((a+b*log(c*(d+e*x^(1/2))^n))^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)^{2} + 2 \, a b \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right) + a^{2}}{x^{4}}, x\right)"," ",0,"integral((b^2*log((e*sqrt(x) + d)^n*c)^2 + 2*a*b*log((e*sqrt(x) + d)^n*c) + a^2)/x^4, x)","F",0
415,1,1197,0,1.368316," ","integrate(x^2*(a+b*log(c*(d+e*x^(1/2))^n))^3,x, algorithm=""fricas"")","\frac{36000 \, b^{3} e^{6} x^{3} \log\left(c\right)^{3} - 1000 \, {\left(b^{3} e^{6} n^{3} - 6 \, a b^{2} e^{6} n^{2} + 18 \, a^{2} b e^{6} n - 36 \, a^{3} e^{6}\right)} x^{3} + 36000 \, {\left(b^{3} e^{6} n^{3} x^{3} - b^{3} d^{6} n^{3}\right)} \log\left(e \sqrt{x} + d\right)^{3} - 15 \, {\left(919 \, b^{3} d^{2} e^{4} n^{3} - 2220 \, a b^{2} d^{2} e^{4} n^{2} + 1800 \, a^{2} b d^{2} e^{4} n\right)} x^{2} - 1800 \, {\left(15 \, b^{3} d^{2} e^{4} n^{3} x^{2} + 30 \, b^{3} d^{4} e^{2} n^{3} x - 147 \, b^{3} d^{6} n^{3} + 60 \, a b^{2} d^{6} n^{2} + 10 \, {\left(b^{3} e^{6} n^{3} - 6 \, a b^{2} e^{6} n^{2}\right)} x^{3} - 60 \, {\left(b^{3} e^{6} n^{2} x^{3} - b^{3} d^{6} n^{2}\right)} \log\left(c\right) - 4 \, {\left(3 \, b^{3} d e^{5} n^{3} x^{2} + 5 \, b^{3} d^{3} e^{3} n^{3} x + 15 \, b^{3} d^{5} e n^{3}\right)} \sqrt{x}\right)} \log\left(e \sqrt{x} + d\right)^{2} - 9000 \, {\left(3 \, b^{3} d^{2} e^{4} n x^{2} + 6 \, b^{3} d^{4} e^{2} n x + 2 \, {\left(b^{3} e^{6} n - 6 \, a b^{2} e^{6}\right)} x^{3}\right)} \log\left(c\right)^{2} - 30 \, {\left(4669 \, b^{3} d^{4} e^{2} n^{3} - 5220 \, a b^{2} d^{4} e^{2} n^{2} + 1800 \, a^{2} b d^{4} e^{2} n\right)} x - 60 \, {\left(13489 \, b^{3} d^{6} n^{3} - 8820 \, a b^{2} d^{6} n^{2} + 1800 \, a^{2} b d^{6} n - 100 \, {\left(b^{3} e^{6} n^{3} - 6 \, a b^{2} e^{6} n^{2} + 18 \, a^{2} b e^{6} n\right)} x^{3} - 15 \, {\left(37 \, b^{3} d^{2} e^{4} n^{3} - 60 \, a b^{2} d^{2} e^{4} n^{2}\right)} x^{2} - 1800 \, {\left(b^{3} e^{6} n x^{3} - b^{3} d^{6} n\right)} \log\left(c\right)^{2} - 90 \, {\left(29 \, b^{3} d^{4} e^{2} n^{3} - 20 \, a b^{2} d^{4} e^{2} n^{2}\right)} x + 60 \, {\left(15 \, b^{3} d^{2} e^{4} n^{2} x^{2} + 30 \, b^{3} d^{4} e^{2} n^{2} x - 147 \, b^{3} d^{6} n^{2} + 60 \, a b^{2} d^{6} n + 10 \, {\left(b^{3} e^{6} n^{2} - 6 \, a b^{2} e^{6} n\right)} x^{3}\right)} \log\left(c\right) + 12 \, {\left(735 \, b^{3} d^{5} e n^{3} - 300 \, a b^{2} d^{5} e n^{2} + 2 \, {\left(11 \, b^{3} d e^{5} n^{3} - 30 \, a b^{2} d e^{5} n^{2}\right)} x^{2} + 5 \, {\left(19 \, b^{3} d^{3} e^{3} n^{3} - 20 \, a b^{2} d^{3} e^{3} n^{2}\right)} x - 20 \, {\left(3 \, b^{3} d e^{5} n^{2} x^{2} + 5 \, b^{3} d^{3} e^{3} n^{2} x + 15 \, b^{3} d^{5} e n^{2}\right)} \log\left(c\right)\right)} \sqrt{x}\right)} \log\left(e \sqrt{x} + d\right) + 300 \, {\left(20 \, {\left(b^{3} e^{6} n^{2} - 6 \, a b^{2} e^{6} n + 18 \, a^{2} b e^{6}\right)} x^{3} + 3 \, {\left(37 \, b^{3} d^{2} e^{4} n^{2} - 60 \, a b^{2} d^{2} e^{4} n\right)} x^{2} + 18 \, {\left(29 \, b^{3} d^{4} e^{2} n^{2} - 20 \, a b^{2} d^{4} e^{2} n\right)} x\right)} \log\left(c\right) + 4 \, {\left(202335 \, b^{3} d^{5} e n^{3} - 132300 \, a b^{2} d^{5} e n^{2} + 27000 \, a^{2} b d^{5} e n + 12 \, {\left(91 \, b^{3} d e^{5} n^{3} - 330 \, a b^{2} d e^{5} n^{2} + 450 \, a^{2} b d e^{5} n\right)} x^{2} + 1800 \, {\left(3 \, b^{3} d e^{5} n x^{2} + 5 \, b^{3} d^{3} e^{3} n x + 15 \, b^{3} d^{5} e n\right)} \log\left(c\right)^{2} + 5 \, {\left(2059 \, b^{3} d^{3} e^{3} n^{3} - 3420 \, a b^{2} d^{3} e^{3} n^{2} + 1800 \, a^{2} b d^{3} e^{3} n\right)} x - 180 \, {\left(735 \, b^{3} d^{5} e n^{2} - 300 \, a b^{2} d^{5} e n + 2 \, {\left(11 \, b^{3} d e^{5} n^{2} - 30 \, a b^{2} d e^{5} n\right)} x^{2} + 5 \, {\left(19 \, b^{3} d^{3} e^{3} n^{2} - 20 \, a b^{2} d^{3} e^{3} n\right)} x\right)} \log\left(c\right)\right)} \sqrt{x}}{108000 \, e^{6}}"," ",0,"1/108000*(36000*b^3*e^6*x^3*log(c)^3 - 1000*(b^3*e^6*n^3 - 6*a*b^2*e^6*n^2 + 18*a^2*b*e^6*n - 36*a^3*e^6)*x^3 + 36000*(b^3*e^6*n^3*x^3 - b^3*d^6*n^3)*log(e*sqrt(x) + d)^3 - 15*(919*b^3*d^2*e^4*n^3 - 2220*a*b^2*d^2*e^4*n^2 + 1800*a^2*b*d^2*e^4*n)*x^2 - 1800*(15*b^3*d^2*e^4*n^3*x^2 + 30*b^3*d^4*e^2*n^3*x - 147*b^3*d^6*n^3 + 60*a*b^2*d^6*n^2 + 10*(b^3*e^6*n^3 - 6*a*b^2*e^6*n^2)*x^3 - 60*(b^3*e^6*n^2*x^3 - b^3*d^6*n^2)*log(c) - 4*(3*b^3*d*e^5*n^3*x^2 + 5*b^3*d^3*e^3*n^3*x + 15*b^3*d^5*e*n^3)*sqrt(x))*log(e*sqrt(x) + d)^2 - 9000*(3*b^3*d^2*e^4*n*x^2 + 6*b^3*d^4*e^2*n*x + 2*(b^3*e^6*n - 6*a*b^2*e^6)*x^3)*log(c)^2 - 30*(4669*b^3*d^4*e^2*n^3 - 5220*a*b^2*d^4*e^2*n^2 + 1800*a^2*b*d^4*e^2*n)*x - 60*(13489*b^3*d^6*n^3 - 8820*a*b^2*d^6*n^2 + 1800*a^2*b*d^6*n - 100*(b^3*e^6*n^3 - 6*a*b^2*e^6*n^2 + 18*a^2*b*e^6*n)*x^3 - 15*(37*b^3*d^2*e^4*n^3 - 60*a*b^2*d^2*e^4*n^2)*x^2 - 1800*(b^3*e^6*n*x^3 - b^3*d^6*n)*log(c)^2 - 90*(29*b^3*d^4*e^2*n^3 - 20*a*b^2*d^4*e^2*n^2)*x + 60*(15*b^3*d^2*e^4*n^2*x^2 + 30*b^3*d^4*e^2*n^2*x - 147*b^3*d^6*n^2 + 60*a*b^2*d^6*n + 10*(b^3*e^6*n^2 - 6*a*b^2*e^6*n)*x^3)*log(c) + 12*(735*b^3*d^5*e*n^3 - 300*a*b^2*d^5*e*n^2 + 2*(11*b^3*d*e^5*n^3 - 30*a*b^2*d*e^5*n^2)*x^2 + 5*(19*b^3*d^3*e^3*n^3 - 20*a*b^2*d^3*e^3*n^2)*x - 20*(3*b^3*d*e^5*n^2*x^2 + 5*b^3*d^3*e^3*n^2*x + 15*b^3*d^5*e*n^2)*log(c))*sqrt(x))*log(e*sqrt(x) + d) + 300*(20*(b^3*e^6*n^2 - 6*a*b^2*e^6*n + 18*a^2*b*e^6)*x^3 + 3*(37*b^3*d^2*e^4*n^2 - 60*a*b^2*d^2*e^4*n)*x^2 + 18*(29*b^3*d^4*e^2*n^2 - 20*a*b^2*d^4*e^2*n)*x)*log(c) + 4*(202335*b^3*d^5*e*n^3 - 132300*a*b^2*d^5*e*n^2 + 27000*a^2*b*d^5*e*n + 12*(91*b^3*d*e^5*n^3 - 330*a*b^2*d*e^5*n^2 + 450*a^2*b*d*e^5*n)*x^2 + 1800*(3*b^3*d*e^5*n*x^2 + 5*b^3*d^3*e^3*n*x + 15*b^3*d^5*e*n)*log(c)^2 + 5*(2059*b^3*d^3*e^3*n^3 - 3420*a*b^2*d^3*e^3*n^2 + 1800*a^2*b*d^3*e^3*n)*x - 180*(735*b^3*d^5*e*n^2 - 300*a*b^2*d^5*e*n + 2*(11*b^3*d*e^5*n^2 - 30*a*b^2*d*e^5*n)*x^2 + 5*(19*b^3*d^3*e^3*n^2 - 20*a*b^2*d^3*e^3*n)*x)*log(c))*sqrt(x))/e^6","A",0
416,1,861,0,1.113627," ","integrate(x*(a+b*log(c*(d+e*x^(1/2))^n))^3,x, algorithm=""fricas"")","\frac{288 \, b^{3} e^{4} x^{2} \log\left(c\right)^{3} + 288 \, {\left(b^{3} e^{4} n^{3} x^{2} - b^{3} d^{4} n^{3}\right)} \log\left(e \sqrt{x} + d\right)^{3} - 9 \, {\left(3 \, b^{3} e^{4} n^{3} - 12 \, a b^{2} e^{4} n^{2} + 24 \, a^{2} b e^{4} n - 32 \, a^{3} e^{4}\right)} x^{2} - 72 \, {\left(6 \, b^{3} d^{2} e^{2} n^{3} x - 25 \, b^{3} d^{4} n^{3} + 12 \, a b^{2} d^{4} n^{2} + 3 \, {\left(b^{3} e^{4} n^{3} - 4 \, a b^{2} e^{4} n^{2}\right)} x^{2} - 12 \, {\left(b^{3} e^{4} n^{2} x^{2} - b^{3} d^{4} n^{2}\right)} \log\left(c\right) - 4 \, {\left(b^{3} d e^{3} n^{3} x + 3 \, b^{3} d^{3} e n^{3}\right)} \sqrt{x}\right)} \log\left(e \sqrt{x} + d\right)^{2} - 216 \, {\left(2 \, b^{3} d^{2} e^{2} n x + {\left(b^{3} e^{4} n - 4 \, a b^{2} e^{4}\right)} x^{2}\right)} \log\left(c\right)^{2} - 6 \, {\left(115 \, b^{3} d^{2} e^{2} n^{3} - 156 \, a b^{2} d^{2} e^{2} n^{2} + 72 \, a^{2} b d^{2} e^{2} n\right)} x - 12 \, {\left(415 \, b^{3} d^{4} n^{3} - 300 \, a b^{2} d^{4} n^{2} + 72 \, a^{2} b d^{4} n - 9 \, {\left(b^{3} e^{4} n^{3} - 4 \, a b^{2} e^{4} n^{2} + 8 \, a^{2} b e^{4} n\right)} x^{2} - 72 \, {\left(b^{3} e^{4} n x^{2} - b^{3} d^{4} n\right)} \log\left(c\right)^{2} - 6 \, {\left(13 \, b^{3} d^{2} e^{2} n^{3} - 12 \, a b^{2} d^{2} e^{2} n^{2}\right)} x + 12 \, {\left(6 \, b^{3} d^{2} e^{2} n^{2} x - 25 \, b^{3} d^{4} n^{2} + 12 \, a b^{2} d^{4} n + 3 \, {\left(b^{3} e^{4} n^{2} - 4 \, a b^{2} e^{4} n\right)} x^{2}\right)} \log\left(c\right) + 4 \, {\left(75 \, b^{3} d^{3} e n^{3} - 36 \, a b^{2} d^{3} e n^{2} + {\left(7 \, b^{3} d e^{3} n^{3} - 12 \, a b^{2} d e^{3} n^{2}\right)} x - 12 \, {\left(b^{3} d e^{3} n^{2} x + 3 \, b^{3} d^{3} e n^{2}\right)} \log\left(c\right)\right)} \sqrt{x}\right)} \log\left(e \sqrt{x} + d\right) + 36 \, {\left(3 \, {\left(b^{3} e^{4} n^{2} - 4 \, a b^{2} e^{4} n + 8 \, a^{2} b e^{4}\right)} x^{2} + 2 \, {\left(13 \, b^{3} d^{2} e^{2} n^{2} - 12 \, a b^{2} d^{2} e^{2} n\right)} x\right)} \log\left(c\right) + 4 \, {\left(1245 \, b^{3} d^{3} e n^{3} - 900 \, a b^{2} d^{3} e n^{2} + 216 \, a^{2} b d^{3} e n + 72 \, {\left(b^{3} d e^{3} n x + 3 \, b^{3} d^{3} e n\right)} \log\left(c\right)^{2} + {\left(37 \, b^{3} d e^{3} n^{3} - 84 \, a b^{2} d e^{3} n^{2} + 72 \, a^{2} b d e^{3} n\right)} x - 12 \, {\left(75 \, b^{3} d^{3} e n^{2} - 36 \, a b^{2} d^{3} e n + {\left(7 \, b^{3} d e^{3} n^{2} - 12 \, a b^{2} d e^{3} n\right)} x\right)} \log\left(c\right)\right)} \sqrt{x}}{576 \, e^{4}}"," ",0,"1/576*(288*b^3*e^4*x^2*log(c)^3 + 288*(b^3*e^4*n^3*x^2 - b^3*d^4*n^3)*log(e*sqrt(x) + d)^3 - 9*(3*b^3*e^4*n^3 - 12*a*b^2*e^4*n^2 + 24*a^2*b*e^4*n - 32*a^3*e^4)*x^2 - 72*(6*b^3*d^2*e^2*n^3*x - 25*b^3*d^4*n^3 + 12*a*b^2*d^4*n^2 + 3*(b^3*e^4*n^3 - 4*a*b^2*e^4*n^2)*x^2 - 12*(b^3*e^4*n^2*x^2 - b^3*d^4*n^2)*log(c) - 4*(b^3*d*e^3*n^3*x + 3*b^3*d^3*e*n^3)*sqrt(x))*log(e*sqrt(x) + d)^2 - 216*(2*b^3*d^2*e^2*n*x + (b^3*e^4*n - 4*a*b^2*e^4)*x^2)*log(c)^2 - 6*(115*b^3*d^2*e^2*n^3 - 156*a*b^2*d^2*e^2*n^2 + 72*a^2*b*d^2*e^2*n)*x - 12*(415*b^3*d^4*n^3 - 300*a*b^2*d^4*n^2 + 72*a^2*b*d^4*n - 9*(b^3*e^4*n^3 - 4*a*b^2*e^4*n^2 + 8*a^2*b*e^4*n)*x^2 - 72*(b^3*e^4*n*x^2 - b^3*d^4*n)*log(c)^2 - 6*(13*b^3*d^2*e^2*n^3 - 12*a*b^2*d^2*e^2*n^2)*x + 12*(6*b^3*d^2*e^2*n^2*x - 25*b^3*d^4*n^2 + 12*a*b^2*d^4*n + 3*(b^3*e^4*n^2 - 4*a*b^2*e^4*n)*x^2)*log(c) + 4*(75*b^3*d^3*e*n^3 - 36*a*b^2*d^3*e*n^2 + (7*b^3*d*e^3*n^3 - 12*a*b^2*d*e^3*n^2)*x - 12*(b^3*d*e^3*n^2*x + 3*b^3*d^3*e*n^2)*log(c))*sqrt(x))*log(e*sqrt(x) + d) + 36*(3*(b^3*e^4*n^2 - 4*a*b^2*e^4*n + 8*a^2*b*e^4)*x^2 + 2*(13*b^3*d^2*e^2*n^2 - 12*a*b^2*d^2*e^2*n)*x)*log(c) + 4*(1245*b^3*d^3*e*n^3 - 900*a*b^2*d^3*e*n^2 + 216*a^2*b*d^3*e*n + 72*(b^3*d*e^3*n*x + 3*b^3*d^3*e*n)*log(c)^2 + (37*b^3*d*e^3*n^3 - 84*a*b^2*d*e^3*n^2 + 72*a^2*b*d*e^3*n)*x - 12*(75*b^3*d^3*e*n^2 - 36*a*b^2*d^3*e*n + (7*b^3*d*e^3*n^2 - 12*a*b^2*d*e^3*n)*x)*log(c))*sqrt(x))/e^4","A",0
417,1,527,0,1.070842," ","integrate((a+b*log(c*(d+e*x^(1/2))^n))^3,x, algorithm=""fricas"")","\frac{4 \, b^{3} e^{2} x \log\left(c\right)^{3} + 4 \, {\left(b^{3} e^{2} n^{3} x - b^{3} d^{2} n^{3}\right)} \log\left(e \sqrt{x} + d\right)^{3} - 6 \, {\left(b^{3} e^{2} n - 2 \, a b^{2} e^{2}\right)} x \log\left(c\right)^{2} + 6 \, {\left(2 \, b^{3} d e n^{3} \sqrt{x} + 3 \, b^{3} d^{2} n^{3} - 2 \, a b^{2} d^{2} n^{2} - {\left(b^{3} e^{2} n^{3} - 2 \, a b^{2} e^{2} n^{2}\right)} x + 2 \, {\left(b^{3} e^{2} n^{2} x - b^{3} d^{2} n^{2}\right)} \log\left(c\right)\right)} \log\left(e \sqrt{x} + d\right)^{2} + 6 \, {\left(b^{3} e^{2} n^{2} - 2 \, a b^{2} e^{2} n + 2 \, a^{2} b e^{2}\right)} x \log\left(c\right) - {\left(3 \, b^{3} e^{2} n^{3} - 6 \, a b^{2} e^{2} n^{2} + 6 \, a^{2} b e^{2} n - 4 \, a^{3} e^{2}\right)} x - 6 \, {\left(7 \, b^{3} d^{2} n^{3} - 6 \, a b^{2} d^{2} n^{2} + 2 \, a^{2} b d^{2} n - 2 \, {\left(b^{3} e^{2} n x - b^{3} d^{2} n\right)} \log\left(c\right)^{2} - {\left(b^{3} e^{2} n^{3} - 2 \, a b^{2} e^{2} n^{2} + 2 \, a^{2} b e^{2} n\right)} x - 2 \, {\left(3 \, b^{3} d^{2} n^{2} - 2 \, a b^{2} d^{2} n - {\left(b^{3} e^{2} n^{2} - 2 \, a b^{2} e^{2} n\right)} x\right)} \log\left(c\right) + 2 \, {\left(3 \, b^{3} d e n^{3} - 2 \, b^{3} d e n^{2} \log\left(c\right) - 2 \, a b^{2} d e n^{2}\right)} \sqrt{x}\right)} \log\left(e \sqrt{x} + d\right) + 6 \, {\left(7 \, b^{3} d e n^{3} + 2 \, b^{3} d e n \log\left(c\right)^{2} - 6 \, a b^{2} d e n^{2} + 2 \, a^{2} b d e n - 2 \, {\left(3 \, b^{3} d e n^{2} - 2 \, a b^{2} d e n\right)} \log\left(c\right)\right)} \sqrt{x}}{4 \, e^{2}}"," ",0,"1/4*(4*b^3*e^2*x*log(c)^3 + 4*(b^3*e^2*n^3*x - b^3*d^2*n^3)*log(e*sqrt(x) + d)^3 - 6*(b^3*e^2*n - 2*a*b^2*e^2)*x*log(c)^2 + 6*(2*b^3*d*e*n^3*sqrt(x) + 3*b^3*d^2*n^3 - 2*a*b^2*d^2*n^2 - (b^3*e^2*n^3 - 2*a*b^2*e^2*n^2)*x + 2*(b^3*e^2*n^2*x - b^3*d^2*n^2)*log(c))*log(e*sqrt(x) + d)^2 + 6*(b^3*e^2*n^2 - 2*a*b^2*e^2*n + 2*a^2*b*e^2)*x*log(c) - (3*b^3*e^2*n^3 - 6*a*b^2*e^2*n^2 + 6*a^2*b*e^2*n - 4*a^3*e^2)*x - 6*(7*b^3*d^2*n^3 - 6*a*b^2*d^2*n^2 + 2*a^2*b*d^2*n - 2*(b^3*e^2*n*x - b^3*d^2*n)*log(c)^2 - (b^3*e^2*n^3 - 2*a*b^2*e^2*n^2 + 2*a^2*b*e^2*n)*x - 2*(3*b^3*d^2*n^2 - 2*a*b^2*d^2*n - (b^3*e^2*n^2 - 2*a*b^2*e^2*n)*x)*log(c) + 2*(3*b^3*d*e*n^3 - 2*b^3*d*e*n^2*log(c) - 2*a*b^2*d*e*n^2)*sqrt(x))*log(e*sqrt(x) + d) + 6*(7*b^3*d*e*n^3 + 2*b^3*d*e*n*log(c)^2 - 6*a*b^2*d*e*n^2 + 2*a^2*b*d*e*n - 2*(3*b^3*d*e*n^2 - 2*a*b^2*d*e*n)*log(c))*sqrt(x))/e^2","B",0
418,0,0,0,0.936729," ","integrate((a+b*log(c*(d+e*x^(1/2))^n))^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)^{3} + 3 \, a b^{2} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)^{2} + 3 \, a^{2} b \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right) + a^{3}}{x}, x\right)"," ",0,"integral((b^3*log((e*sqrt(x) + d)^n*c)^3 + 3*a*b^2*log((e*sqrt(x) + d)^n*c)^2 + 3*a^2*b*log((e*sqrt(x) + d)^n*c) + a^3)/x, x)","F",0
419,0,0,0,1.279346," ","integrate((a+b*log(c*(d+e*x^(1/2))^n))^3/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)^{3} + 3 \, a b^{2} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)^{2} + 3 \, a^{2} b \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right) + a^{3}}{x^{2}}, x\right)"," ",0,"integral((b^3*log((e*sqrt(x) + d)^n*c)^3 + 3*a*b^2*log((e*sqrt(x) + d)^n*c)^2 + 3*a^2*b*log((e*sqrt(x) + d)^n*c) + a^3)/x^2, x)","F",0
420,0,0,0,1.114963," ","integrate((a+b*log(c*(d+e*x^(1/2))^n))^3/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)^{3} + 3 \, a b^{2} \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right)^{2} + 3 \, a^{2} b \log\left({\left(e \sqrt{x} + d\right)}^{n} c\right) + a^{3}}{x^{3}}, x\right)"," ",0,"integral((b^3*log((e*sqrt(x) + d)^n*c)^3 + 3*a*b^2*log((e*sqrt(x) + d)^n*c)^2 + 3*a^2*b*log((e*sqrt(x) + d)^n*c) + a^3)/x^3, x)","F",0
421,1,179,0,1.230512," ","integrate(x^3*(a+b*log(c*(d+e/x^(1/2))^n)),x, algorithm=""fricas"")","\frac{420 \, b d^{8} x^{4} \log\left(c\right) - 70 \, b d^{6} e^{2} n x^{3} + 420 \, a d^{8} x^{4} - 105 \, b d^{4} e^{4} n x^{2} - 210 \, b d^{2} e^{6} n x - 420 \, b d^{8} n \log\left(\sqrt{x}\right) + 420 \, {\left(b d^{8} - b e^{8}\right)} n \log\left(d \sqrt{x} + e\right) + 420 \, {\left(b d^{8} n x^{4} - b d^{8} n\right)} \log\left(\frac{d x + e \sqrt{x}}{x}\right) + 4 \, {\left(15 \, b d^{7} e n x^{3} + 21 \, b d^{5} e^{3} n x^{2} + 35 \, b d^{3} e^{5} n x + 105 \, b d e^{7} n\right)} \sqrt{x}}{1680 \, d^{8}}"," ",0,"1/1680*(420*b*d^8*x^4*log(c) - 70*b*d^6*e^2*n*x^3 + 420*a*d^8*x^4 - 105*b*d^4*e^4*n*x^2 - 210*b*d^2*e^6*n*x - 420*b*d^8*n*log(sqrt(x)) + 420*(b*d^8 - b*e^8)*n*log(d*sqrt(x) + e) + 420*(b*d^8*n*x^4 - b*d^8*n)*log((d*x + e*sqrt(x))/x) + 4*(15*b*d^7*e*n*x^3 + 21*b*d^5*e^3*n*x^2 + 35*b*d^3*e^5*n*x + 105*b*d*e^7*n)*sqrt(x))/d^8","A",0
422,1,153,0,1.036566," ","integrate(x^2*(a+b*log(c*(d+e/x^(1/2))^n)),x, algorithm=""fricas"")","\frac{60 \, b d^{6} x^{3} \log\left(c\right) - 15 \, b d^{4} e^{2} n x^{2} + 60 \, a d^{6} x^{3} - 30 \, b d^{2} e^{4} n x - 60 \, b d^{6} n \log\left(\sqrt{x}\right) + 60 \, {\left(b d^{6} - b e^{6}\right)} n \log\left(d \sqrt{x} + e\right) + 60 \, {\left(b d^{6} n x^{3} - b d^{6} n\right)} \log\left(\frac{d x + e \sqrt{x}}{x}\right) + 4 \, {\left(3 \, b d^{5} e n x^{2} + 5 \, b d^{3} e^{3} n x + 15 \, b d e^{5} n\right)} \sqrt{x}}{180 \, d^{6}}"," ",0,"1/180*(60*b*d^6*x^3*log(c) - 15*b*d^4*e^2*n*x^2 + 60*a*d^6*x^3 - 30*b*d^2*e^4*n*x - 60*b*d^6*n*log(sqrt(x)) + 60*(b*d^6 - b*e^6)*n*log(d*sqrt(x) + e) + 60*(b*d^6*n*x^3 - b*d^6*n)*log((d*x + e*sqrt(x))/x) + 4*(3*b*d^5*e*n*x^2 + 5*b*d^3*e^3*n*x + 15*b*d*e^5*n)*sqrt(x))/d^6","A",0
423,1,126,0,0.940807," ","integrate(x*(a+b*log(c*(d+e/x^(1/2))^n)),x, algorithm=""fricas"")","\frac{6 \, b d^{4} x^{2} \log\left(c\right) - 3 \, b d^{2} e^{2} n x + 6 \, a d^{4} x^{2} - 6 \, b d^{4} n \log\left(\sqrt{x}\right) + 6 \, {\left(b d^{4} - b e^{4}\right)} n \log\left(d \sqrt{x} + e\right) + 6 \, {\left(b d^{4} n x^{2} - b d^{4} n\right)} \log\left(\frac{d x + e \sqrt{x}}{x}\right) + 2 \, {\left(b d^{3} e n x + 3 \, b d e^{3} n\right)} \sqrt{x}}{12 \, d^{4}}"," ",0,"1/12*(6*b*d^4*x^2*log(c) - 3*b*d^2*e^2*n*x + 6*a*d^4*x^2 - 6*b*d^4*n*log(sqrt(x)) + 6*(b*d^4 - b*e^4)*n*log(d*sqrt(x) + e) + 6*(b*d^4*n*x^2 - b*d^4*n)*log((d*x + e*sqrt(x))/x) + 2*(b*d^3*e*n*x + 3*b*d*e^3*n)*sqrt(x))/d^4","A",0
424,1,90,0,1.135519," ","integrate(a+b*log(c*(d+e/x^(1/2))^n),x, algorithm=""fricas"")","\frac{b d^{2} x \log\left(c\right) - b d^{2} n \log\left(\sqrt{x}\right) + b d e n \sqrt{x} + a d^{2} x + {\left(b d^{2} - b e^{2}\right)} n \log\left(d \sqrt{x} + e\right) + {\left(b d^{2} n x - b d^{2} n\right)} \log\left(\frac{d x + e \sqrt{x}}{x}\right)}{d^{2}}"," ",0,"(b*d^2*x*log(c) - b*d^2*n*log(sqrt(x)) + b*d*e*n*sqrt(x) + a*d^2*x + (b*d^2 - b*e^2)*n*log(d*sqrt(x) + e) + (b*d^2*n*x - b*d^2*n)*log((d*x + e*sqrt(x))/x))/d^2","A",0
425,0,0,0,1.107634," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \log\left(c \left(\frac{d x + e \sqrt{x}}{x}\right)^{n}\right) + a}{x}, x\right)"," ",0,"integral((b*log(c*((d*x + e*sqrt(x))/x)^n) + a)/x, x)","F",0
426,1,70,0,1.146257," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))/x^2,x, algorithm=""fricas"")","-\frac{2 \, b d e n \sqrt{x} - b e^{2} n + 2 \, b e^{2} \log\left(c\right) + 2 \, a e^{2} - 2 \, {\left(b d^{2} n x - b e^{2} n\right)} \log\left(\frac{d x + e \sqrt{x}}{x}\right)}{2 \, e^{2} x}"," ",0,"-1/2*(2*b*d*e*n*sqrt(x) - b*e^2*n + 2*b*e^2*log(c) + 2*a*e^2 - 2*(b*d^2*n*x - b*e^2*n)*log((d*x + e*sqrt(x))/x))/(e^2*x)","A",0
427,1,96,0,1.137439," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))/x^3,x, algorithm=""fricas"")","\frac{6 \, b d^{2} e^{2} n x + 3 \, b e^{4} n - 12 \, b e^{4} \log\left(c\right) - 12 \, a e^{4} + 12 \, {\left(b d^{4} n x^{2} - b e^{4} n\right)} \log\left(\frac{d x + e \sqrt{x}}{x}\right) - 4 \, {\left(3 \, b d^{3} e n x + b d e^{3} n\right)} \sqrt{x}}{24 \, e^{4} x^{2}}"," ",0,"1/24*(6*b*d^2*e^2*n*x + 3*b*e^4*n - 12*b*e^4*log(c) - 12*a*e^4 + 12*(b*d^4*n*x^2 - b*e^4*n)*log((d*x + e*sqrt(x))/x) - 4*(3*b*d^3*e*n*x + b*d*e^3*n)*sqrt(x))/(e^4*x^2)","A",0
428,1,123,0,1.085662," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))/x^4,x, algorithm=""fricas"")","\frac{30 \, b d^{4} e^{2} n x^{2} + 15 \, b d^{2} e^{4} n x + 10 \, b e^{6} n - 60 \, b e^{6} \log\left(c\right) - 60 \, a e^{6} + 60 \, {\left(b d^{6} n x^{3} - b e^{6} n\right)} \log\left(\frac{d x + e \sqrt{x}}{x}\right) - 4 \, {\left(15 \, b d^{5} e n x^{2} + 5 \, b d^{3} e^{3} n x + 3 \, b d e^{5} n\right)} \sqrt{x}}{180 \, e^{6} x^{3}}"," ",0,"1/180*(30*b*d^4*e^2*n*x^2 + 15*b*d^2*e^4*n*x + 10*b*e^6*n - 60*b*e^6*log(c) - 60*a*e^6 + 60*(b*d^6*n*x^3 - b*e^6*n)*log((d*x + e*sqrt(x))/x) - 4*(15*b*d^5*e*n*x^2 + 5*b*d^3*e^3*n*x + 3*b*d*e^5*n)*sqrt(x))/(e^6*x^3)","A",0
429,0,0,0,1.217438," ","integrate(x^2*(a+b*log(c*(d+e/x^(1/2))^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{2} \log\left(c \left(\frac{d x + e \sqrt{x}}{x}\right)^{n}\right)^{2} + 2 \, a b x^{2} \log\left(c \left(\frac{d x + e \sqrt{x}}{x}\right)^{n}\right) + a^{2} x^{2}, x\right)"," ",0,"integral(b^2*x^2*log(c*((d*x + e*sqrt(x))/x)^n)^2 + 2*a*b*x^2*log(c*((d*x + e*sqrt(x))/x)^n) + a^2*x^2, x)","F",0
430,0,0,0,1.354011," ","integrate(x*(a+b*log(c*(d+e/x^(1/2))^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x \log\left(c \left(\frac{d x + e \sqrt{x}}{x}\right)^{n}\right)^{2} + 2 \, a b x \log\left(c \left(\frac{d x + e \sqrt{x}}{x}\right)^{n}\right) + a^{2} x, x\right)"," ",0,"integral(b^2*x*log(c*((d*x + e*sqrt(x))/x)^n)^2 + 2*a*b*x*log(c*((d*x + e*sqrt(x))/x)^n) + a^2*x, x)","F",0
431,0,0,0,0.811917," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} \log\left(c \left(\frac{d x + e \sqrt{x}}{x}\right)^{n}\right)^{2} + 2 \, a b \log\left(c \left(\frac{d x + e \sqrt{x}}{x}\right)^{n}\right) + a^{2}, x\right)"," ",0,"integral(b^2*log(c*((d*x + e*sqrt(x))/x)^n)^2 + 2*a*b*log(c*((d*x + e*sqrt(x))/x)^n) + a^2, x)","F",0
432,0,0,0,0.741541," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \log\left(c \left(\frac{d x + e \sqrt{x}}{x}\right)^{n}\right)^{2} + 2 \, a b \log\left(c \left(\frac{d x + e \sqrt{x}}{x}\right)^{n}\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*log(c*((d*x + e*sqrt(x))/x)^n)^2 + 2*a*b*log(c*((d*x + e*sqrt(x))/x)^n) + a^2)/x, x)","F",0
433,1,235,0,1.007554," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))^2/x^2,x, algorithm=""fricas"")","-\frac{b^{2} e^{2} n^{2} + 2 \, b^{2} e^{2} \log\left(c\right)^{2} - 2 \, a b e^{2} n + 2 \, a^{2} e^{2} - 2 \, {\left(b^{2} d^{2} n^{2} x - b^{2} e^{2} n^{2}\right)} \log\left(\frac{d x + e \sqrt{x}}{x}\right)^{2} - 2 \, {\left(b^{2} e^{2} n - 2 \, a b e^{2}\right)} \log\left(c\right) + 2 \, {\left(2 \, b^{2} d e n^{2} \sqrt{x} - b^{2} e^{2} n^{2} + 2 \, a b e^{2} n + {\left(3 \, b^{2} d^{2} n^{2} - 2 \, a b d^{2} n\right)} x - 2 \, {\left(b^{2} d^{2} n x - b^{2} e^{2} n\right)} \log\left(c\right)\right)} \log\left(\frac{d x + e \sqrt{x}}{x}\right) - 2 \, {\left(3 \, b^{2} d e n^{2} - 2 \, b^{2} d e n \log\left(c\right) - 2 \, a b d e n\right)} \sqrt{x}}{2 \, e^{2} x}"," ",0,"-1/2*(b^2*e^2*n^2 + 2*b^2*e^2*log(c)^2 - 2*a*b*e^2*n + 2*a^2*e^2 - 2*(b^2*d^2*n^2*x - b^2*e^2*n^2)*log((d*x + e*sqrt(x))/x)^2 - 2*(b^2*e^2*n - 2*a*b*e^2)*log(c) + 2*(2*b^2*d*e*n^2*sqrt(x) - b^2*e^2*n^2 + 2*a*b*e^2*n + (3*b^2*d^2*n^2 - 2*a*b*d^2*n)*x - 2*(b^2*d^2*n*x - b^2*e^2*n)*log(c))*log((d*x + e*sqrt(x))/x) - 2*(3*b^2*d*e*n^2 - 2*b^2*d*e*n*log(c) - 2*a*b*d*e*n)*sqrt(x))/(e^2*x)","A",0
434,1,361,0,1.031441," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))^2/x^3,x, algorithm=""fricas"")","-\frac{9 \, b^{2} e^{4} n^{2} + 72 \, b^{2} e^{4} \log\left(c\right)^{2} - 36 \, a b e^{4} n + 72 \, a^{2} e^{4} - 72 \, {\left(b^{2} d^{4} n^{2} x^{2} - b^{2} e^{4} n^{2}\right)} \log\left(\frac{d x + e \sqrt{x}}{x}\right)^{2} + 6 \, {\left(13 \, b^{2} d^{2} e^{2} n^{2} - 12 \, a b d^{2} e^{2} n\right)} x - 36 \, {\left(2 \, b^{2} d^{2} e^{2} n x + b^{2} e^{4} n - 4 \, a b e^{4}\right)} \log\left(c\right) - 12 \, {\left(6 \, b^{2} d^{2} e^{2} n^{2} x + 3 \, b^{2} e^{4} n^{2} - 12 \, a b e^{4} n - {\left(25 \, b^{2} d^{4} n^{2} - 12 \, a b d^{4} n\right)} x^{2} + 12 \, {\left(b^{2} d^{4} n x^{2} - b^{2} e^{4} n\right)} \log\left(c\right) - 4 \, {\left(3 \, b^{2} d^{3} e n^{2} x + b^{2} d e^{3} n^{2}\right)} \sqrt{x}\right)} \log\left(\frac{d x + e \sqrt{x}}{x}\right) - 4 \, {\left(7 \, b^{2} d e^{3} n^{2} - 12 \, a b d e^{3} n + 3 \, {\left(25 \, b^{2} d^{3} e n^{2} - 12 \, a b d^{3} e n\right)} x - 12 \, {\left(3 \, b^{2} d^{3} e n x + b^{2} d e^{3} n\right)} \log\left(c\right)\right)} \sqrt{x}}{144 \, e^{4} x^{2}}"," ",0,"-1/144*(9*b^2*e^4*n^2 + 72*b^2*e^4*log(c)^2 - 36*a*b*e^4*n + 72*a^2*e^4 - 72*(b^2*d^4*n^2*x^2 - b^2*e^4*n^2)*log((d*x + e*sqrt(x))/x)^2 + 6*(13*b^2*d^2*e^2*n^2 - 12*a*b*d^2*e^2*n)*x - 36*(2*b^2*d^2*e^2*n*x + b^2*e^4*n - 4*a*b*e^4)*log(c) - 12*(6*b^2*d^2*e^2*n^2*x + 3*b^2*e^4*n^2 - 12*a*b*e^4*n - (25*b^2*d^4*n^2 - 12*a*b*d^4*n)*x^2 + 12*(b^2*d^4*n*x^2 - b^2*e^4*n)*log(c) - 4*(3*b^2*d^3*e*n^2*x + b^2*d*e^3*n^2)*sqrt(x))*log((d*x + e*sqrt(x))/x) - 4*(7*b^2*d*e^3*n^2 - 12*a*b*d*e^3*n + 3*(25*b^2*d^3*e*n^2 - 12*a*b*d^3*e*n)*x - 12*(3*b^2*d^3*e*n*x + b^2*d*e^3*n)*log(c))*sqrt(x))/(e^4*x^2)","A",0
435,1,490,0,1.276844," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))^2/x^4,x, algorithm=""fricas"")","-\frac{100 \, b^{2} e^{6} n^{2} + 1800 \, b^{2} e^{6} \log\left(c\right)^{2} - 600 \, a b e^{6} n + 1800 \, a^{2} e^{6} + 90 \, {\left(29 \, b^{2} d^{4} e^{2} n^{2} - 20 \, a b d^{4} e^{2} n\right)} x^{2} - 1800 \, {\left(b^{2} d^{6} n^{2} x^{3} - b^{2} e^{6} n^{2}\right)} \log\left(\frac{d x + e \sqrt{x}}{x}\right)^{2} + 15 \, {\left(37 \, b^{2} d^{2} e^{4} n^{2} - 60 \, a b d^{2} e^{4} n\right)} x - 300 \, {\left(6 \, b^{2} d^{4} e^{2} n x^{2} + 3 \, b^{2} d^{2} e^{4} n x + 2 \, b^{2} e^{6} n - 12 \, a b e^{6}\right)} \log\left(c\right) - 60 \, {\left(30 \, b^{2} d^{4} e^{2} n^{2} x^{2} + 15 \, b^{2} d^{2} e^{4} n^{2} x + 10 \, b^{2} e^{6} n^{2} - 60 \, a b e^{6} n - 3 \, {\left(49 \, b^{2} d^{6} n^{2} - 20 \, a b d^{6} n\right)} x^{3} + 60 \, {\left(b^{2} d^{6} n x^{3} - b^{2} e^{6} n\right)} \log\left(c\right) - 4 \, {\left(15 \, b^{2} d^{5} e n^{2} x^{2} + 5 \, b^{2} d^{3} e^{3} n^{2} x + 3 \, b^{2} d e^{5} n^{2}\right)} \sqrt{x}\right)} \log\left(\frac{d x + e \sqrt{x}}{x}\right) - 12 \, {\left(22 \, b^{2} d e^{5} n^{2} - 60 \, a b d e^{5} n + 15 \, {\left(49 \, b^{2} d^{5} e n^{2} - 20 \, a b d^{5} e n\right)} x^{2} + 5 \, {\left(19 \, b^{2} d^{3} e^{3} n^{2} - 20 \, a b d^{3} e^{3} n\right)} x - 20 \, {\left(15 \, b^{2} d^{5} e n x^{2} + 5 \, b^{2} d^{3} e^{3} n x + 3 \, b^{2} d e^{5} n\right)} \log\left(c\right)\right)} \sqrt{x}}{5400 \, e^{6} x^{3}}"," ",0,"-1/5400*(100*b^2*e^6*n^2 + 1800*b^2*e^6*log(c)^2 - 600*a*b*e^6*n + 1800*a^2*e^6 + 90*(29*b^2*d^4*e^2*n^2 - 20*a*b*d^4*e^2*n)*x^2 - 1800*(b^2*d^6*n^2*x^3 - b^2*e^6*n^2)*log((d*x + e*sqrt(x))/x)^2 + 15*(37*b^2*d^2*e^4*n^2 - 60*a*b*d^2*e^4*n)*x - 300*(6*b^2*d^4*e^2*n*x^2 + 3*b^2*d^2*e^4*n*x + 2*b^2*e^6*n - 12*a*b*e^6)*log(c) - 60*(30*b^2*d^4*e^2*n^2*x^2 + 15*b^2*d^2*e^4*n^2*x + 10*b^2*e^6*n^2 - 60*a*b*e^6*n - 3*(49*b^2*d^6*n^2 - 20*a*b*d^6*n)*x^3 + 60*(b^2*d^6*n*x^3 - b^2*e^6*n)*log(c) - 4*(15*b^2*d^5*e*n^2*x^2 + 5*b^2*d^3*e^3*n^2*x + 3*b^2*d*e^5*n^2)*sqrt(x))*log((d*x + e*sqrt(x))/x) - 12*(22*b^2*d*e^5*n^2 - 60*a*b*d*e^5*n + 15*(49*b^2*d^5*e*n^2 - 20*a*b*d^5*e*n)*x^2 + 5*(19*b^2*d^3*e^3*n^2 - 20*a*b*d^3*e^3*n)*x - 20*(15*b^2*d^5*e*n*x^2 + 5*b^2*d^3*e^3*n*x + 3*b^2*d*e^5*n)*log(c))*sqrt(x))/(e^6*x^3)","A",0
436,0,0,0,1.350049," ","integrate(x*(a+b*log(c*(d+e/x^(1/2))^n))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x \log\left(c \left(\frac{d x + e \sqrt{x}}{x}\right)^{n}\right)^{3} + 3 \, a b^{2} x \log\left(c \left(\frac{d x + e \sqrt{x}}{x}\right)^{n}\right)^{2} + 3 \, a^{2} b x \log\left(c \left(\frac{d x + e \sqrt{x}}{x}\right)^{n}\right) + a^{3} x, x\right)"," ",0,"integral(b^3*x*log(c*((d*x + e*sqrt(x))/x)^n)^3 + 3*a*b^2*x*log(c*((d*x + e*sqrt(x))/x)^n)^2 + 3*a^2*b*x*log(c*((d*x + e*sqrt(x))/x)^n) + a^3*x, x)","F",0
437,0,0,0,1.301584," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} \log\left(c \left(\frac{d x + e \sqrt{x}}{x}\right)^{n}\right)^{3} + 3 \, a b^{2} \log\left(c \left(\frac{d x + e \sqrt{x}}{x}\right)^{n}\right)^{2} + 3 \, a^{2} b \log\left(c \left(\frac{d x + e \sqrt{x}}{x}\right)^{n}\right) + a^{3}, x\right)"," ",0,"integral(b^3*log(c*((d*x + e*sqrt(x))/x)^n)^3 + 3*a*b^2*log(c*((d*x + e*sqrt(x))/x)^n)^2 + 3*a^2*b*log(c*((d*x + e*sqrt(x))/x)^n) + a^3, x)","F",0
438,0,0,0,0.661735," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \log\left(c \left(\frac{d x + e \sqrt{x}}{x}\right)^{n}\right)^{3} + 3 \, a b^{2} \log\left(c \left(\frac{d x + e \sqrt{x}}{x}\right)^{n}\right)^{2} + 3 \, a^{2} b \log\left(c \left(\frac{d x + e \sqrt{x}}{x}\right)^{n}\right) + a^{3}}{x}, x\right)"," ",0,"integral((b^3*log(c*((d*x + e*sqrt(x))/x)^n)^3 + 3*a*b^2*log(c*((d*x + e*sqrt(x))/x)^n)^2 + 3*a^2*b*log(c*((d*x + e*sqrt(x))/x)^n) + a^3)/x, x)","F",0
439,1,541,0,0.882042," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))^3/x^2,x, algorithm=""fricas"")","\frac{3 \, b^{3} e^{2} n^{3} - 4 \, b^{3} e^{2} \log\left(c\right)^{3} - 6 \, a b^{2} e^{2} n^{2} + 6 \, a^{2} b e^{2} n - 4 \, a^{3} e^{2} + 4 \, {\left(b^{3} d^{2} n^{3} x - b^{3} e^{2} n^{3}\right)} \log\left(\frac{d x + e \sqrt{x}}{x}\right)^{3} + 6 \, {\left(b^{3} e^{2} n - 2 \, a b^{2} e^{2}\right)} \log\left(c\right)^{2} - 6 \, {\left(2 \, b^{3} d e n^{3} \sqrt{x} - b^{3} e^{2} n^{3} + 2 \, a b^{2} e^{2} n^{2} + {\left(3 \, b^{3} d^{2} n^{3} - 2 \, a b^{2} d^{2} n^{2}\right)} x - 2 \, {\left(b^{3} d^{2} n^{2} x - b^{3} e^{2} n^{2}\right)} \log\left(c\right)\right)} \log\left(\frac{d x + e \sqrt{x}}{x}\right)^{2} - 6 \, {\left(b^{3} e^{2} n^{2} - 2 \, a b^{2} e^{2} n + 2 \, a^{2} b e^{2}\right)} \log\left(c\right) - 6 \, {\left(b^{3} e^{2} n^{3} - 2 \, a b^{2} e^{2} n^{2} + 2 \, a^{2} b e^{2} n - 2 \, {\left(b^{3} d^{2} n x - b^{3} e^{2} n\right)} \log\left(c\right)^{2} - {\left(7 \, b^{3} d^{2} n^{3} - 6 \, a b^{2} d^{2} n^{2} + 2 \, a^{2} b d^{2} n\right)} x - 2 \, {\left(b^{3} e^{2} n^{2} - 2 \, a b^{2} e^{2} n - {\left(3 \, b^{3} d^{2} n^{2} - 2 \, a b^{2} d^{2} n\right)} x\right)} \log\left(c\right) - 2 \, {\left(3 \, b^{3} d e n^{3} - 2 \, b^{3} d e n^{2} \log\left(c\right) - 2 \, a b^{2} d e n^{2}\right)} \sqrt{x}\right)} \log\left(\frac{d x + e \sqrt{x}}{x}\right) - 6 \, {\left(7 \, b^{3} d e n^{3} + 2 \, b^{3} d e n \log\left(c\right)^{2} - 6 \, a b^{2} d e n^{2} + 2 \, a^{2} b d e n - 2 \, {\left(3 \, b^{3} d e n^{2} - 2 \, a b^{2} d e n\right)} \log\left(c\right)\right)} \sqrt{x}}{4 \, e^{2} x}"," ",0,"1/4*(3*b^3*e^2*n^3 - 4*b^3*e^2*log(c)^3 - 6*a*b^2*e^2*n^2 + 6*a^2*b*e^2*n - 4*a^3*e^2 + 4*(b^3*d^2*n^3*x - b^3*e^2*n^3)*log((d*x + e*sqrt(x))/x)^3 + 6*(b^3*e^2*n - 2*a*b^2*e^2)*log(c)^2 - 6*(2*b^3*d*e*n^3*sqrt(x) - b^3*e^2*n^3 + 2*a*b^2*e^2*n^2 + (3*b^3*d^2*n^3 - 2*a*b^2*d^2*n^2)*x - 2*(b^3*d^2*n^2*x - b^3*e^2*n^2)*log(c))*log((d*x + e*sqrt(x))/x)^2 - 6*(b^3*e^2*n^2 - 2*a*b^2*e^2*n + 2*a^2*b*e^2)*log(c) - 6*(b^3*e^2*n^3 - 2*a*b^2*e^2*n^2 + 2*a^2*b*e^2*n - 2*(b^3*d^2*n*x - b^3*e^2*n)*log(c)^2 - (7*b^3*d^2*n^3 - 6*a*b^2*d^2*n^2 + 2*a^2*b*d^2*n)*x - 2*(b^3*e^2*n^2 - 2*a*b^2*e^2*n - (3*b^3*d^2*n^2 - 2*a*b^2*d^2*n)*x)*log(c) - 2*(3*b^3*d*e*n^3 - 2*b^3*d*e*n^2*log(c) - 2*a*b^2*d*e*n^2)*sqrt(x))*log((d*x + e*sqrt(x))/x) - 6*(7*b^3*d*e*n^3 + 2*b^3*d*e*n*log(c)^2 - 6*a*b^2*d*e*n^2 + 2*a^2*b*d*e*n - 2*(3*b^3*d*e*n^2 - 2*a*b^2*d*e*n)*log(c))*sqrt(x))/(e^2*x)","B",0
440,1,869,0,0.907835," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))^3/x^3,x, algorithm=""fricas"")","\frac{27 \, b^{3} e^{4} n^{3} - 288 \, b^{3} e^{4} \log\left(c\right)^{3} - 108 \, a b^{2} e^{4} n^{2} + 216 \, a^{2} b e^{4} n - 288 \, a^{3} e^{4} + 288 \, {\left(b^{3} d^{4} n^{3} x^{2} - b^{3} e^{4} n^{3}\right)} \log\left(\frac{d x + e \sqrt{x}}{x}\right)^{3} + 216 \, {\left(2 \, b^{3} d^{2} e^{2} n x + b^{3} e^{4} n - 4 \, a b^{2} e^{4}\right)} \log\left(c\right)^{2} + 72 \, {\left(6 \, b^{3} d^{2} e^{2} n^{3} x + 3 \, b^{3} e^{4} n^{3} - 12 \, a b^{2} e^{4} n^{2} - {\left(25 \, b^{3} d^{4} n^{3} - 12 \, a b^{2} d^{4} n^{2}\right)} x^{2} + 12 \, {\left(b^{3} d^{4} n^{2} x^{2} - b^{3} e^{4} n^{2}\right)} \log\left(c\right) - 4 \, {\left(3 \, b^{3} d^{3} e n^{3} x + b^{3} d e^{3} n^{3}\right)} \sqrt{x}\right)} \log\left(\frac{d x + e \sqrt{x}}{x}\right)^{2} + 6 \, {\left(115 \, b^{3} d^{2} e^{2} n^{3} - 156 \, a b^{2} d^{2} e^{2} n^{2} + 72 \, a^{2} b d^{2} e^{2} n\right)} x - 36 \, {\left(3 \, b^{3} e^{4} n^{2} - 12 \, a b^{2} e^{4} n + 24 \, a^{2} b e^{4} + 2 \, {\left(13 \, b^{3} d^{2} e^{2} n^{2} - 12 \, a b^{2} d^{2} e^{2} n\right)} x\right)} \log\left(c\right) - 12 \, {\left(9 \, b^{3} e^{4} n^{3} - 36 \, a b^{2} e^{4} n^{2} + 72 \, a^{2} b e^{4} n - {\left(415 \, b^{3} d^{4} n^{3} - 300 \, a b^{2} d^{4} n^{2} + 72 \, a^{2} b d^{4} n\right)} x^{2} - 72 \, {\left(b^{3} d^{4} n x^{2} - b^{3} e^{4} n\right)} \log\left(c\right)^{2} + 6 \, {\left(13 \, b^{3} d^{2} e^{2} n^{3} - 12 \, a b^{2} d^{2} e^{2} n^{2}\right)} x - 12 \, {\left(6 \, b^{3} d^{2} e^{2} n^{2} x + 3 \, b^{3} e^{4} n^{2} - 12 \, a b^{2} e^{4} n - {\left(25 \, b^{3} d^{4} n^{2} - 12 \, a b^{2} d^{4} n\right)} x^{2}\right)} \log\left(c\right) - 4 \, {\left(7 \, b^{3} d e^{3} n^{3} - 12 \, a b^{2} d e^{3} n^{2} + 3 \, {\left(25 \, b^{3} d^{3} e n^{3} - 12 \, a b^{2} d^{3} e n^{2}\right)} x - 12 \, {\left(3 \, b^{3} d^{3} e n^{2} x + b^{3} d e^{3} n^{2}\right)} \log\left(c\right)\right)} \sqrt{x}\right)} \log\left(\frac{d x + e \sqrt{x}}{x}\right) - 4 \, {\left(37 \, b^{3} d e^{3} n^{3} - 84 \, a b^{2} d e^{3} n^{2} + 72 \, a^{2} b d e^{3} n + 72 \, {\left(3 \, b^{3} d^{3} e n x + b^{3} d e^{3} n\right)} \log\left(c\right)^{2} + 3 \, {\left(415 \, b^{3} d^{3} e n^{3} - 300 \, a b^{2} d^{3} e n^{2} + 72 \, a^{2} b d^{3} e n\right)} x - 12 \, {\left(7 \, b^{3} d e^{3} n^{2} - 12 \, a b^{2} d e^{3} n + 3 \, {\left(25 \, b^{3} d^{3} e n^{2} - 12 \, a b^{2} d^{3} e n\right)} x\right)} \log\left(c\right)\right)} \sqrt{x}}{576 \, e^{4} x^{2}}"," ",0,"1/576*(27*b^3*e^4*n^3 - 288*b^3*e^4*log(c)^3 - 108*a*b^2*e^4*n^2 + 216*a^2*b*e^4*n - 288*a^3*e^4 + 288*(b^3*d^4*n^3*x^2 - b^3*e^4*n^3)*log((d*x + e*sqrt(x))/x)^3 + 216*(2*b^3*d^2*e^2*n*x + b^3*e^4*n - 4*a*b^2*e^4)*log(c)^2 + 72*(6*b^3*d^2*e^2*n^3*x + 3*b^3*e^4*n^3 - 12*a*b^2*e^4*n^2 - (25*b^3*d^4*n^3 - 12*a*b^2*d^4*n^2)*x^2 + 12*(b^3*d^4*n^2*x^2 - b^3*e^4*n^2)*log(c) - 4*(3*b^3*d^3*e*n^3*x + b^3*d*e^3*n^3)*sqrt(x))*log((d*x + e*sqrt(x))/x)^2 + 6*(115*b^3*d^2*e^2*n^3 - 156*a*b^2*d^2*e^2*n^2 + 72*a^2*b*d^2*e^2*n)*x - 36*(3*b^3*e^4*n^2 - 12*a*b^2*e^4*n + 24*a^2*b*e^4 + 2*(13*b^3*d^2*e^2*n^2 - 12*a*b^2*d^2*e^2*n)*x)*log(c) - 12*(9*b^3*e^4*n^3 - 36*a*b^2*e^4*n^2 + 72*a^2*b*e^4*n - (415*b^3*d^4*n^3 - 300*a*b^2*d^4*n^2 + 72*a^2*b*d^4*n)*x^2 - 72*(b^3*d^4*n*x^2 - b^3*e^4*n)*log(c)^2 + 6*(13*b^3*d^2*e^2*n^3 - 12*a*b^2*d^2*e^2*n^2)*x - 12*(6*b^3*d^2*e^2*n^2*x + 3*b^3*e^4*n^2 - 12*a*b^2*e^4*n - (25*b^3*d^4*n^2 - 12*a*b^2*d^4*n)*x^2)*log(c) - 4*(7*b^3*d*e^3*n^3 - 12*a*b^2*d*e^3*n^2 + 3*(25*b^3*d^3*e*n^3 - 12*a*b^2*d^3*e*n^2)*x - 12*(3*b^3*d^3*e*n^2*x + b^3*d*e^3*n^2)*log(c))*sqrt(x))*log((d*x + e*sqrt(x))/x) - 4*(37*b^3*d*e^3*n^3 - 84*a*b^2*d*e^3*n^2 + 72*a^2*b*d*e^3*n + 72*(3*b^3*d^3*e*n*x + b^3*d*e^3*n)*log(c)^2 + 3*(415*b^3*d^3*e*n^3 - 300*a*b^2*d^3*e*n^2 + 72*a^2*b*d^3*e*n)*x - 12*(7*b^3*d*e^3*n^2 - 12*a*b^2*d*e^3*n + 3*(25*b^3*d^3*e*n^2 - 12*a*b^2*d^3*e*n)*x)*log(c))*sqrt(x))/(e^4*x^2)","A",0
441,1,1203,0,1.217632," ","integrate((a+b*log(c*(d+e/x^(1/2))^n))^3/x^4,x, algorithm=""fricas"")","\frac{1000 \, b^{3} e^{6} n^{3} - 36000 \, b^{3} e^{6} \log\left(c\right)^{3} - 6000 \, a b^{2} e^{6} n^{2} + 18000 \, a^{2} b e^{6} n - 36000 \, a^{3} e^{6} + 36000 \, {\left(b^{3} d^{6} n^{3} x^{3} - b^{3} e^{6} n^{3}\right)} \log\left(\frac{d x + e \sqrt{x}}{x}\right)^{3} + 30 \, {\left(4669 \, b^{3} d^{4} e^{2} n^{3} - 5220 \, a b^{2} d^{4} e^{2} n^{2} + 1800 \, a^{2} b d^{4} e^{2} n\right)} x^{2} + 9000 \, {\left(6 \, b^{3} d^{4} e^{2} n x^{2} + 3 \, b^{3} d^{2} e^{4} n x + 2 \, b^{3} e^{6} n - 12 \, a b^{2} e^{6}\right)} \log\left(c\right)^{2} + 1800 \, {\left(30 \, b^{3} d^{4} e^{2} n^{3} x^{2} + 15 \, b^{3} d^{2} e^{4} n^{3} x + 10 \, b^{3} e^{6} n^{3} - 60 \, a b^{2} e^{6} n^{2} - 3 \, {\left(49 \, b^{3} d^{6} n^{3} - 20 \, a b^{2} d^{6} n^{2}\right)} x^{3} + 60 \, {\left(b^{3} d^{6} n^{2} x^{3} - b^{3} e^{6} n^{2}\right)} \log\left(c\right) - 4 \, {\left(15 \, b^{3} d^{5} e n^{3} x^{2} + 5 \, b^{3} d^{3} e^{3} n^{3} x + 3 \, b^{3} d e^{5} n^{3}\right)} \sqrt{x}\right)} \log\left(\frac{d x + e \sqrt{x}}{x}\right)^{2} + 15 \, {\left(919 \, b^{3} d^{2} e^{4} n^{3} - 2220 \, a b^{2} d^{2} e^{4} n^{2} + 1800 \, a^{2} b d^{2} e^{4} n\right)} x - 300 \, {\left(20 \, b^{3} e^{6} n^{2} - 120 \, a b^{2} e^{6} n + 360 \, a^{2} b e^{6} + 18 \, {\left(29 \, b^{3} d^{4} e^{2} n^{2} - 20 \, a b^{2} d^{4} e^{2} n\right)} x^{2} + 3 \, {\left(37 \, b^{3} d^{2} e^{4} n^{2} - 60 \, a b^{2} d^{2} e^{4} n\right)} x\right)} \log\left(c\right) - 60 \, {\left(100 \, b^{3} e^{6} n^{3} - 600 \, a b^{2} e^{6} n^{2} + 1800 \, a^{2} b e^{6} n - {\left(13489 \, b^{3} d^{6} n^{3} - 8820 \, a b^{2} d^{6} n^{2} + 1800 \, a^{2} b d^{6} n\right)} x^{3} + 90 \, {\left(29 \, b^{3} d^{4} e^{2} n^{3} - 20 \, a b^{2} d^{4} e^{2} n^{2}\right)} x^{2} - 1800 \, {\left(b^{3} d^{6} n x^{3} - b^{3} e^{6} n\right)} \log\left(c\right)^{2} + 15 \, {\left(37 \, b^{3} d^{2} e^{4} n^{3} - 60 \, a b^{2} d^{2} e^{4} n^{2}\right)} x - 60 \, {\left(30 \, b^{3} d^{4} e^{2} n^{2} x^{2} + 15 \, b^{3} d^{2} e^{4} n^{2} x + 10 \, b^{3} e^{6} n^{2} - 60 \, a b^{2} e^{6} n - 3 \, {\left(49 \, b^{3} d^{6} n^{2} - 20 \, a b^{2} d^{6} n\right)} x^{3}\right)} \log\left(c\right) - 12 \, {\left(22 \, b^{3} d e^{5} n^{3} - 60 \, a b^{2} d e^{5} n^{2} + 15 \, {\left(49 \, b^{3} d^{5} e n^{3} - 20 \, a b^{2} d^{5} e n^{2}\right)} x^{2} + 5 \, {\left(19 \, b^{3} d^{3} e^{3} n^{3} - 20 \, a b^{2} d^{3} e^{3} n^{2}\right)} x - 20 \, {\left(15 \, b^{3} d^{5} e n^{2} x^{2} + 5 \, b^{3} d^{3} e^{3} n^{2} x + 3 \, b^{3} d e^{5} n^{2}\right)} \log\left(c\right)\right)} \sqrt{x}\right)} \log\left(\frac{d x + e \sqrt{x}}{x}\right) - 4 \, {\left(1092 \, b^{3} d e^{5} n^{3} - 3960 \, a b^{2} d e^{5} n^{2} + 5400 \, a^{2} b d e^{5} n + 15 \, {\left(13489 \, b^{3} d^{5} e n^{3} - 8820 \, a b^{2} d^{5} e n^{2} + 1800 \, a^{2} b d^{5} e n\right)} x^{2} + 1800 \, {\left(15 \, b^{3} d^{5} e n x^{2} + 5 \, b^{3} d^{3} e^{3} n x + 3 \, b^{3} d e^{5} n\right)} \log\left(c\right)^{2} + 5 \, {\left(2059 \, b^{3} d^{3} e^{3} n^{3} - 3420 \, a b^{2} d^{3} e^{3} n^{2} + 1800 \, a^{2} b d^{3} e^{3} n\right)} x - 180 \, {\left(22 \, b^{3} d e^{5} n^{2} - 60 \, a b^{2} d e^{5} n + 15 \, {\left(49 \, b^{3} d^{5} e n^{2} - 20 \, a b^{2} d^{5} e n\right)} x^{2} + 5 \, {\left(19 \, b^{3} d^{3} e^{3} n^{2} - 20 \, a b^{2} d^{3} e^{3} n\right)} x\right)} \log\left(c\right)\right)} \sqrt{x}}{108000 \, e^{6} x^{3}}"," ",0,"1/108000*(1000*b^3*e^6*n^3 - 36000*b^3*e^6*log(c)^3 - 6000*a*b^2*e^6*n^2 + 18000*a^2*b*e^6*n - 36000*a^3*e^6 + 36000*(b^3*d^6*n^3*x^3 - b^3*e^6*n^3)*log((d*x + e*sqrt(x))/x)^3 + 30*(4669*b^3*d^4*e^2*n^3 - 5220*a*b^2*d^4*e^2*n^2 + 1800*a^2*b*d^4*e^2*n)*x^2 + 9000*(6*b^3*d^4*e^2*n*x^2 + 3*b^3*d^2*e^4*n*x + 2*b^3*e^6*n - 12*a*b^2*e^6)*log(c)^2 + 1800*(30*b^3*d^4*e^2*n^3*x^2 + 15*b^3*d^2*e^4*n^3*x + 10*b^3*e^6*n^3 - 60*a*b^2*e^6*n^2 - 3*(49*b^3*d^6*n^3 - 20*a*b^2*d^6*n^2)*x^3 + 60*(b^3*d^6*n^2*x^3 - b^3*e^6*n^2)*log(c) - 4*(15*b^3*d^5*e*n^3*x^2 + 5*b^3*d^3*e^3*n^3*x + 3*b^3*d*e^5*n^3)*sqrt(x))*log((d*x + e*sqrt(x))/x)^2 + 15*(919*b^3*d^2*e^4*n^3 - 2220*a*b^2*d^2*e^4*n^2 + 1800*a^2*b*d^2*e^4*n)*x - 300*(20*b^3*e^6*n^2 - 120*a*b^2*e^6*n + 360*a^2*b*e^6 + 18*(29*b^3*d^4*e^2*n^2 - 20*a*b^2*d^4*e^2*n)*x^2 + 3*(37*b^3*d^2*e^4*n^2 - 60*a*b^2*d^2*e^4*n)*x)*log(c) - 60*(100*b^3*e^6*n^3 - 600*a*b^2*e^6*n^2 + 1800*a^2*b*e^6*n - (13489*b^3*d^6*n^3 - 8820*a*b^2*d^6*n^2 + 1800*a^2*b*d^6*n)*x^3 + 90*(29*b^3*d^4*e^2*n^3 - 20*a*b^2*d^4*e^2*n^2)*x^2 - 1800*(b^3*d^6*n*x^3 - b^3*e^6*n)*log(c)^2 + 15*(37*b^3*d^2*e^4*n^3 - 60*a*b^2*d^2*e^4*n^2)*x - 60*(30*b^3*d^4*e^2*n^2*x^2 + 15*b^3*d^2*e^4*n^2*x + 10*b^3*e^6*n^2 - 60*a*b^2*e^6*n - 3*(49*b^3*d^6*n^2 - 20*a*b^2*d^6*n)*x^3)*log(c) - 12*(22*b^3*d*e^5*n^3 - 60*a*b^2*d*e^5*n^2 + 15*(49*b^3*d^5*e*n^3 - 20*a*b^2*d^5*e*n^2)*x^2 + 5*(19*b^3*d^3*e^3*n^3 - 20*a*b^2*d^3*e^3*n^2)*x - 20*(15*b^3*d^5*e*n^2*x^2 + 5*b^3*d^3*e^3*n^2*x + 3*b^3*d*e^5*n^2)*log(c))*sqrt(x))*log((d*x + e*sqrt(x))/x) - 4*(1092*b^3*d*e^5*n^3 - 3960*a*b^2*d*e^5*n^2 + 5400*a^2*b*d*e^5*n + 15*(13489*b^3*d^5*e*n^3 - 8820*a*b^2*d^5*e*n^2 + 1800*a^2*b*d^5*e*n)*x^2 + 1800*(15*b^3*d^5*e*n*x^2 + 5*b^3*d^3*e^3*n*x + 3*b^3*d*e^5*n)*log(c)^2 + 5*(2059*b^3*d^3*e^3*n^3 - 3420*a*b^2*d^3*e^3*n^2 + 1800*a^2*b*d^3*e^3*n)*x - 180*(22*b^3*d*e^5*n^2 - 60*a*b^2*d*e^5*n + 15*(49*b^3*d^5*e*n^2 - 20*a*b^2*d^5*e*n)*x^2 + 5*(19*b^3*d^3*e^3*n^2 - 20*a*b^2*d^3*e^3*n)*x)*log(c))*sqrt(x))/(e^6*x^3)","A",0
442,1,201,0,1.075407," ","integrate(x^3*(a+b*log(c*(d+e*x^(1/3))^n)),x, algorithm=""fricas"")","\frac{27720 \, b e^{12} x^{4} \log\left(c\right) + 3080 \, b d^{3} e^{9} n x^{3} - 4620 \, b d^{6} e^{6} n x^{2} + 9240 \, b d^{9} e^{3} n x - 2310 \, {\left(b e^{12} n - 12 \, a e^{12}\right)} x^{4} + 27720 \, {\left(b e^{12} n x^{4} - b d^{12} n\right)} \log\left(e x^{\frac{1}{3}} + d\right) + 63 \, {\left(40 \, b d e^{11} n x^{3} - 55 \, b d^{4} e^{8} n x^{2} + 88 \, b d^{7} e^{5} n x - 220 \, b d^{10} e^{2} n\right)} x^{\frac{2}{3}} - 198 \, {\left(14 \, b d^{2} e^{10} n x^{3} - 20 \, b d^{5} e^{7} n x^{2} + 35 \, b d^{8} e^{4} n x - 140 \, b d^{11} e n\right)} x^{\frac{1}{3}}}{110880 \, e^{12}}"," ",0,"1/110880*(27720*b*e^12*x^4*log(c) + 3080*b*d^3*e^9*n*x^3 - 4620*b*d^6*e^6*n*x^2 + 9240*b*d^9*e^3*n*x - 2310*(b*e^12*n - 12*a*e^12)*x^4 + 27720*(b*e^12*n*x^4 - b*d^12*n)*log(e*x^(1/3) + d) + 63*(40*b*d*e^11*n*x^3 - 55*b*d^4*e^8*n*x^2 + 88*b*d^7*e^5*n*x - 220*b*d^10*e^2*n)*x^(2/3) - 198*(14*b*d^2*e^10*n*x^3 - 20*b*d^5*e^7*n*x^2 + 35*b*d^8*e^4*n*x - 140*b*d^11*e*n)*x^(1/3))/e^12","A",0
443,1,161,0,1.122936," ","integrate(x^2*(a+b*log(c*(d+e*x^(1/3))^n)),x, algorithm=""fricas"")","\frac{2520 \, b e^{9} x^{3} \log\left(c\right) + 420 \, b d^{3} e^{6} n x^{2} - 840 \, b d^{6} e^{3} n x - 280 \, {\left(b e^{9} n - 9 \, a e^{9}\right)} x^{3} + 2520 \, {\left(b e^{9} n x^{3} + b d^{9} n\right)} \log\left(e x^{\frac{1}{3}} + d\right) + 63 \, {\left(5 \, b d e^{8} n x^{2} - 8 \, b d^{4} e^{5} n x + 20 \, b d^{7} e^{2} n\right)} x^{\frac{2}{3}} - 90 \, {\left(4 \, b d^{2} e^{7} n x^{2} - 7 \, b d^{5} e^{4} n x + 28 \, b d^{8} e n\right)} x^{\frac{1}{3}}}{7560 \, e^{9}}"," ",0,"1/7560*(2520*b*e^9*x^3*log(c) + 420*b*d^3*e^6*n*x^2 - 840*b*d^6*e^3*n*x - 280*(b*e^9*n - 9*a*e^9)*x^3 + 2520*(b*e^9*n*x^3 + b*d^9*n)*log(e*x^(1/3) + d) + 63*(5*b*d*e^8*n*x^2 - 8*b*d^4*e^5*n*x + 20*b*d^7*e^2*n)*x^(2/3) - 90*(4*b*d^2*e^7*n*x^2 - 7*b*d^5*e^4*n*x + 28*b*d^8*e*n)*x^(1/3))/e^9","A",0
444,1,122,0,1.200259," ","integrate(x*(a+b*log(c*(d+e*x^(1/3))^n)),x, algorithm=""fricas"")","\frac{60 \, b e^{6} x^{2} \log\left(c\right) + 20 \, b d^{3} e^{3} n x - 10 \, {\left(b e^{6} n - 6 \, a e^{6}\right)} x^{2} + 60 \, {\left(b e^{6} n x^{2} - b d^{6} n\right)} \log\left(e x^{\frac{1}{3}} + d\right) + 6 \, {\left(2 \, b d e^{5} n x - 5 \, b d^{4} e^{2} n\right)} x^{\frac{2}{3}} - 15 \, {\left(b d^{2} e^{4} n x - 4 \, b d^{5} e n\right)} x^{\frac{1}{3}}}{120 \, e^{6}}"," ",0,"1/120*(60*b*e^6*x^2*log(c) + 20*b*d^3*e^3*n*x - 10*(b*e^6*n - 6*a*e^6)*x^2 + 60*(b*e^6*n*x^2 - b*d^6*n)*log(e*x^(1/3) + d) + 6*(2*b*d*e^5*n*x - 5*b*d^4*e^2*n)*x^(2/3) - 15*(b*d^2*e^4*n*x - 4*b*d^5*e*n)*x^(1/3))/e^6","A",0
445,1,77,0,0.928311," ","integrate(a+b*log(c*(d+e*x^(1/3))^n),x, algorithm=""fricas"")","\frac{6 \, b e^{3} x \log\left(c\right) + 3 \, b d e^{2} n x^{\frac{2}{3}} - 6 \, b d^{2} e n x^{\frac{1}{3}} - 2 \, {\left(b e^{3} n - 3 \, a e^{3}\right)} x + 6 \, {\left(b e^{3} n x + b d^{3} n\right)} \log\left(e x^{\frac{1}{3}} + d\right)}{6 \, e^{3}}"," ",0,"1/6*(6*b*e^3*x*log(c) + 3*b*d*e^2*n*x^(2/3) - 6*b*d^2*e*n*x^(1/3) - 2*(b*e^3*n - 3*a*e^3)*x + 6*(b*e^3*n*x + b*d^3*n)*log(e*x^(1/3) + d))/e^3","A",0
446,0,0,0,0.811934," ","integrate((a+b*log(c*(d+e*x^(1/3))^n))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right) + a}{x}, x\right)"," ",0,"integral((b*log((e*x^(1/3) + d)^n*c) + a)/x, x)","F",0
447,1,81,0,1.100726," ","integrate((a+b*log(c*(d+e*x^(1/3))^n))/x^2,x, algorithm=""fricas"")","\frac{2 \, b e^{3} n x \log\left(x^{\frac{1}{3}}\right) + 2 \, b d e^{2} n x^{\frac{2}{3}} - b d^{2} e n x^{\frac{1}{3}} - 2 \, b d^{3} \log\left(c\right) - 2 \, a d^{3} - 2 \, {\left(b e^{3} n x + b d^{3} n\right)} \log\left(e x^{\frac{1}{3}} + d\right)}{2 \, d^{3} x}"," ",0,"1/2*(2*b*e^3*n*x*log(x^(1/3)) + 2*b*d*e^2*n*x^(2/3) - b*d^2*e*n*x^(1/3) - 2*b*d^3*log(c) - 2*a*d^3 - 2*(b*e^3*n*x + b*d^3*n)*log(e*x^(1/3) + d))/(d^3*x)","A",0
448,1,125,0,0.800479," ","integrate((a+b*log(c*(d+e*x^(1/3))^n))/x^3,x, algorithm=""fricas"")","-\frac{60 \, b e^{6} n x^{2} \log\left(x^{\frac{1}{3}}\right) + 20 \, b d^{3} e^{3} n x + 60 \, b d^{6} \log\left(c\right) + 60 \, a d^{6} - 60 \, {\left(b e^{6} n x^{2} - b d^{6} n\right)} \log\left(e x^{\frac{1}{3}} + d\right) + 15 \, {\left(4 \, b d e^{5} n x - b d^{4} e^{2} n\right)} x^{\frac{2}{3}} - 6 \, {\left(5 \, b d^{2} e^{4} n x - 2 \, b d^{5} e n\right)} x^{\frac{1}{3}}}{120 \, d^{6} x^{2}}"," ",0,"-1/120*(60*b*e^6*n*x^2*log(x^(1/3)) + 20*b*d^3*e^3*n*x + 60*b*d^6*log(c) + 60*a*d^6 - 60*(b*e^6*n*x^2 - b*d^6*n)*log(e*x^(1/3) + d) + 15*(4*b*d*e^5*n*x - b*d^4*e^2*n)*x^(2/3) - 6*(5*b*d^2*e^4*n*x - 2*b*d^5*e*n)*x^(1/3))/(d^6*x^2)","A",0
449,1,163,0,1.081079," ","integrate((a+b*log(c*(d+e*x^(1/3))^n))/x^4,x, algorithm=""fricas"")","\frac{840 \, b e^{9} n x^{3} \log\left(x^{\frac{1}{3}}\right) + 280 \, b d^{3} e^{6} n x^{2} - 140 \, b d^{6} e^{3} n x - 840 \, b d^{9} \log\left(c\right) - 840 \, a d^{9} - 840 \, {\left(b e^{9} n x^{3} + b d^{9} n\right)} \log\left(e x^{\frac{1}{3}} + d\right) + 30 \, {\left(28 \, b d e^{8} n x^{2} - 7 \, b d^{4} e^{5} n x + 4 \, b d^{7} e^{2} n\right)} x^{\frac{2}{3}} - 21 \, {\left(20 \, b d^{2} e^{7} n x^{2} - 8 \, b d^{5} e^{4} n x + 5 \, b d^{8} e n\right)} x^{\frac{1}{3}}}{2520 \, d^{9} x^{3}}"," ",0,"1/2520*(840*b*e^9*n*x^3*log(x^(1/3)) + 280*b*d^3*e^6*n*x^2 - 140*b*d^6*e^3*n*x - 840*b*d^9*log(c) - 840*a*d^9 - 840*(b*e^9*n*x^3 + b*d^9*n)*log(e*x^(1/3) + d) + 30*(28*b*d*e^8*n*x^2 - 7*b*d^4*e^5*n*x + 4*b*d^7*e^2*n)*x^(2/3) - 21*(20*b*d^2*e^7*n*x^2 - 8*b*d^5*e^4*n*x + 5*b*d^8*e*n)*x^(1/3))/(d^9*x^3)","A",0
450,1,674,0,1.362323," ","integrate(x^2*(a+b*log(c*(d+e*x^(1/3))^n))^2,x, algorithm=""fricas"")","\frac{3175200 \, b^{2} e^{9} x^{3} \log\left(c\right)^{2} + 39200 \, {\left(2 \, b^{2} e^{9} n^{2} - 18 \, a b e^{9} n + 81 \, a^{2} e^{9}\right)} x^{3} - 2100 \, {\left(275 \, b^{2} d^{3} e^{6} n^{2} - 504 \, a b d^{3} e^{6} n\right)} x^{2} + 3175200 \, {\left(b^{2} e^{9} n^{2} x^{3} + b^{2} d^{9} n^{2}\right)} \log\left(e x^{\frac{1}{3}} + d\right)^{2} + 840 \, {\left(3349 \, b^{2} d^{6} e^{3} n^{2} - 2520 \, a b d^{6} e^{3} n\right)} x + 2520 \, {\left(420 \, b^{2} d^{3} e^{6} n^{2} x^{2} - 840 \, b^{2} d^{6} e^{3} n^{2} x - 7129 \, b^{2} d^{9} n^{2} + 2520 \, a b d^{9} n - 280 \, {\left(b^{2} e^{9} n^{2} - 9 \, a b e^{9} n\right)} x^{3} + 2520 \, {\left(b^{2} e^{9} n x^{3} + b^{2} d^{9} n\right)} \log\left(c\right) + 63 \, {\left(5 \, b^{2} d e^{8} n^{2} x^{2} - 8 \, b^{2} d^{4} e^{5} n^{2} x + 20 \, b^{2} d^{7} e^{2} n^{2}\right)} x^{\frac{2}{3}} - 90 \, {\left(4 \, b^{2} d^{2} e^{7} n^{2} x^{2} - 7 \, b^{2} d^{5} e^{4} n^{2} x + 28 \, b^{2} d^{8} e n^{2}\right)} x^{\frac{1}{3}}\right)} \log\left(e x^{\frac{1}{3}} + d\right) + 352800 \, {\left(3 \, b^{2} d^{3} e^{6} n x^{2} - 6 \, b^{2} d^{6} e^{3} n x - 2 \, {\left(b^{2} e^{9} n - 9 \, a b e^{9}\right)} x^{3}\right)} \log\left(c\right) - 63 \, {\left(92180 \, b^{2} d^{7} e^{2} n^{2} - 50400 \, a b d^{7} e^{2} n + 175 \, {\left(17 \, b^{2} d e^{8} n^{2} - 72 \, a b d e^{8} n\right)} x^{2} - 8 \, {\left(1879 \, b^{2} d^{4} e^{5} n^{2} - 2520 \, a b d^{4} e^{5} n\right)} x - 2520 \, {\left(5 \, b^{2} d e^{8} n x^{2} - 8 \, b^{2} d^{4} e^{5} n x + 20 \, b^{2} d^{7} e^{2} n\right)} \log\left(c\right)\right)} x^{\frac{2}{3}} + 90 \, {\left(199612 \, b^{2} d^{8} e n^{2} - 70560 \, a b d^{8} e n + 20 \, {\left(191 \, b^{2} d^{2} e^{7} n^{2} - 504 \, a b d^{2} e^{7} n\right)} x^{2} - 7 \, {\left(2509 \, b^{2} d^{5} e^{4} n^{2} - 2520 \, a b d^{5} e^{4} n\right)} x - 2520 \, {\left(4 \, b^{2} d^{2} e^{7} n x^{2} - 7 \, b^{2} d^{5} e^{4} n x + 28 \, b^{2} d^{8} e n\right)} \log\left(c\right)\right)} x^{\frac{1}{3}}}{9525600 \, e^{9}}"," ",0,"1/9525600*(3175200*b^2*e^9*x^3*log(c)^2 + 39200*(2*b^2*e^9*n^2 - 18*a*b*e^9*n + 81*a^2*e^9)*x^3 - 2100*(275*b^2*d^3*e^6*n^2 - 504*a*b*d^3*e^6*n)*x^2 + 3175200*(b^2*e^9*n^2*x^3 + b^2*d^9*n^2)*log(e*x^(1/3) + d)^2 + 840*(3349*b^2*d^6*e^3*n^2 - 2520*a*b*d^6*e^3*n)*x + 2520*(420*b^2*d^3*e^6*n^2*x^2 - 840*b^2*d^6*e^3*n^2*x - 7129*b^2*d^9*n^2 + 2520*a*b*d^9*n - 280*(b^2*e^9*n^2 - 9*a*b*e^9*n)*x^3 + 2520*(b^2*e^9*n*x^3 + b^2*d^9*n)*log(c) + 63*(5*b^2*d*e^8*n^2*x^2 - 8*b^2*d^4*e^5*n^2*x + 20*b^2*d^7*e^2*n^2)*x^(2/3) - 90*(4*b^2*d^2*e^7*n^2*x^2 - 7*b^2*d^5*e^4*n^2*x + 28*b^2*d^8*e*n^2)*x^(1/3))*log(e*x^(1/3) + d) + 352800*(3*b^2*d^3*e^6*n*x^2 - 6*b^2*d^6*e^3*n*x - 2*(b^2*e^9*n - 9*a*b*e^9)*x^3)*log(c) - 63*(92180*b^2*d^7*e^2*n^2 - 50400*a*b*d^7*e^2*n + 175*(17*b^2*d*e^8*n^2 - 72*a*b*d*e^8*n)*x^2 - 8*(1879*b^2*d^4*e^5*n^2 - 2520*a*b*d^4*e^5*n)*x - 2520*(5*b^2*d*e^8*n*x^2 - 8*b^2*d^4*e^5*n*x + 20*b^2*d^7*e^2*n)*log(c))*x^(2/3) + 90*(199612*b^2*d^8*e*n^2 - 70560*a*b*d^8*e*n + 20*(191*b^2*d^2*e^7*n^2 - 504*a*b*d^2*e^7*n)*x^2 - 7*(2509*b^2*d^5*e^4*n^2 - 2520*a*b*d^5*e^4*n)*x - 2520*(4*b^2*d^2*e^7*n*x^2 - 7*b^2*d^5*e^4*n*x + 28*b^2*d^8*e*n)*log(c))*x^(1/3))/e^9","A",0
451,1,484,0,1.153430," ","integrate(x*(a+b*log(c*(d+e*x^(1/3))^n))^2,x, algorithm=""fricas"")","\frac{1800 \, b^{2} e^{6} x^{2} \log\left(c\right)^{2} + 100 \, {\left(b^{2} e^{6} n^{2} - 6 \, a b e^{6} n + 18 \, a^{2} e^{6}\right)} x^{2} + 1800 \, {\left(b^{2} e^{6} n^{2} x^{2} - b^{2} d^{6} n^{2}\right)} \log\left(e x^{\frac{1}{3}} + d\right)^{2} - 60 \, {\left(19 \, b^{2} d^{3} e^{3} n^{2} - 20 \, a b d^{3} e^{3} n\right)} x + 60 \, {\left(20 \, b^{2} d^{3} e^{3} n^{2} x + 147 \, b^{2} d^{6} n^{2} - 60 \, a b d^{6} n - 10 \, {\left(b^{2} e^{6} n^{2} - 6 \, a b e^{6} n\right)} x^{2} + 60 \, {\left(b^{2} e^{6} n x^{2} - b^{2} d^{6} n\right)} \log\left(c\right) + 6 \, {\left(2 \, b^{2} d e^{5} n^{2} x - 5 \, b^{2} d^{4} e^{2} n^{2}\right)} x^{\frac{2}{3}} - 15 \, {\left(b^{2} d^{2} e^{4} n^{2} x - 4 \, b^{2} d^{5} e n^{2}\right)} x^{\frac{1}{3}}\right)} \log\left(e x^{\frac{1}{3}} + d\right) + 600 \, {\left(2 \, b^{2} d^{3} e^{3} n x - {\left(b^{2} e^{6} n - 6 \, a b e^{6}\right)} x^{2}\right)} \log\left(c\right) + 6 \, {\left(435 \, b^{2} d^{4} e^{2} n^{2} - 300 \, a b d^{4} e^{2} n - 4 \, {\left(11 \, b^{2} d e^{5} n^{2} - 30 \, a b d e^{5} n\right)} x + 60 \, {\left(2 \, b^{2} d e^{5} n x - 5 \, b^{2} d^{4} e^{2} n\right)} \log\left(c\right)\right)} x^{\frac{2}{3}} - 15 \, {\left(588 \, b^{2} d^{5} e n^{2} - 240 \, a b d^{5} e n - {\left(37 \, b^{2} d^{2} e^{4} n^{2} - 60 \, a b d^{2} e^{4} n\right)} x + 60 \, {\left(b^{2} d^{2} e^{4} n x - 4 \, b^{2} d^{5} e n\right)} \log\left(c\right)\right)} x^{\frac{1}{3}}}{3600 \, e^{6}}"," ",0,"1/3600*(1800*b^2*e^6*x^2*log(c)^2 + 100*(b^2*e^6*n^2 - 6*a*b*e^6*n + 18*a^2*e^6)*x^2 + 1800*(b^2*e^6*n^2*x^2 - b^2*d^6*n^2)*log(e*x^(1/3) + d)^2 - 60*(19*b^2*d^3*e^3*n^2 - 20*a*b*d^3*e^3*n)*x + 60*(20*b^2*d^3*e^3*n^2*x + 147*b^2*d^6*n^2 - 60*a*b*d^6*n - 10*(b^2*e^6*n^2 - 6*a*b*e^6*n)*x^2 + 60*(b^2*e^6*n*x^2 - b^2*d^6*n)*log(c) + 6*(2*b^2*d*e^5*n^2*x - 5*b^2*d^4*e^2*n^2)*x^(2/3) - 15*(b^2*d^2*e^4*n^2*x - 4*b^2*d^5*e*n^2)*x^(1/3))*log(e*x^(1/3) + d) + 600*(2*b^2*d^3*e^3*n*x - (b^2*e^6*n - 6*a*b*e^6)*x^2)*log(c) + 6*(435*b^2*d^4*e^2*n^2 - 300*a*b*d^4*e^2*n - 4*(11*b^2*d*e^5*n^2 - 30*a*b*d*e^5*n)*x + 60*(2*b^2*d*e^5*n*x - 5*b^2*d^4*e^2*n)*log(c))*x^(2/3) - 15*(588*b^2*d^5*e*n^2 - 240*a*b*d^5*e*n - (37*b^2*d^2*e^4*n^2 - 60*a*b*d^2*e^4*n)*x + 60*(b^2*d^2*e^4*n*x - 4*b^2*d^5*e*n)*log(c))*x^(1/3))/e^6","A",0
452,1,287,0,1.243820," ","integrate((a+b*log(c*(d+e*x^(1/3))^n))^2,x, algorithm=""fricas"")","\frac{18 \, b^{2} e^{3} x \log\left(c\right)^{2} + 18 \, {\left(b^{2} e^{3} n^{2} x + b^{2} d^{3} n^{2}\right)} \log\left(e x^{\frac{1}{3}} + d\right)^{2} - 12 \, {\left(b^{2} e^{3} n - 3 \, a b e^{3}\right)} x \log\left(c\right) + 2 \, {\left(2 \, b^{2} e^{3} n^{2} - 6 \, a b e^{3} n + 9 \, a^{2} e^{3}\right)} x + 6 \, {\left(3 \, b^{2} d e^{2} n^{2} x^{\frac{2}{3}} - 6 \, b^{2} d^{2} e n^{2} x^{\frac{1}{3}} - 11 \, b^{2} d^{3} n^{2} + 6 \, a b d^{3} n - 2 \, {\left(b^{2} e^{3} n^{2} - 3 \, a b e^{3} n\right)} x + 6 \, {\left(b^{2} e^{3} n x + b^{2} d^{3} n\right)} \log\left(c\right)\right)} \log\left(e x^{\frac{1}{3}} + d\right) - 3 \, {\left(5 \, b^{2} d e^{2} n^{2} - 6 \, b^{2} d e^{2} n \log\left(c\right) - 6 \, a b d e^{2} n\right)} x^{\frac{2}{3}} + 6 \, {\left(11 \, b^{2} d^{2} e n^{2} - 6 \, b^{2} d^{2} e n \log\left(c\right) - 6 \, a b d^{2} e n\right)} x^{\frac{1}{3}}}{18 \, e^{3}}"," ",0,"1/18*(18*b^2*e^3*x*log(c)^2 + 18*(b^2*e^3*n^2*x + b^2*d^3*n^2)*log(e*x^(1/3) + d)^2 - 12*(b^2*e^3*n - 3*a*b*e^3)*x*log(c) + 2*(2*b^2*e^3*n^2 - 6*a*b*e^3*n + 9*a^2*e^3)*x + 6*(3*b^2*d*e^2*n^2*x^(2/3) - 6*b^2*d^2*e*n^2*x^(1/3) - 11*b^2*d^3*n^2 + 6*a*b*d^3*n - 2*(b^2*e^3*n^2 - 3*a*b*e^3*n)*x + 6*(b^2*e^3*n*x + b^2*d^3*n)*log(c))*log(e*x^(1/3) + d) - 3*(5*b^2*d*e^2*n^2 - 6*b^2*d*e^2*n*log(c) - 6*a*b*d*e^2*n)*x^(2/3) + 6*(11*b^2*d^2*e*n^2 - 6*b^2*d^2*e*n*log(c) - 6*a*b*d^2*e*n)*x^(1/3))/e^3","A",0
453,0,0,0,0.883133," ","integrate((a+b*log(c*(d+e*x^(1/3))^n))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)^{2} + 2 \, a b \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*log((e*x^(1/3) + d)^n*c)^2 + 2*a*b*log((e*x^(1/3) + d)^n*c) + a^2)/x, x)","F",0
454,0,0,0,1.174133," ","integrate((a+b*log(c*(d+e*x^(1/3))^n))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)^{2} + 2 \, a b \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right) + a^{2}}{x^{2}}, x\right)"," ",0,"integral((b^2*log((e*x^(1/3) + d)^n*c)^2 + 2*a*b*log((e*x^(1/3) + d)^n*c) + a^2)/x^2, x)","F",0
455,0,0,0,1.174757," ","integrate((a+b*log(c*(d+e*x^(1/3))^n))^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)^{2} + 2 \, a b \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right) + a^{2}}{x^{3}}, x\right)"," ",0,"integral((b^2*log((e*x^(1/3) + d)^n*c)^2 + 2*a*b*log((e*x^(1/3) + d)^n*c) + a^2)/x^3, x)","F",0
456,1,2183,0,1.991013," ","integrate(x^3*(a+b*log(c*(d+e*x^(1/3))^n))^3,x, algorithm=""fricas"")","\frac{3550000608000 \, b^{3} e^{12} x^{4} \log\left(c\right)^{3} - 12326391000 \, {\left(b^{3} e^{12} n^{3} - 12 \, a b^{2} e^{12} n^{2} + 72 \, a^{2} b e^{12} n - 288 \, a^{3} e^{12}\right)} x^{4} + 603680 \, {\left(364699 \, b^{3} d^{3} e^{9} n^{3} - 1510740 \, a b^{2} d^{3} e^{9} n^{2} + 1960200 \, a^{2} b d^{3} e^{9} n\right)} x^{3} + 3550000608000 \, {\left(b^{3} e^{12} n^{3} x^{4} - b^{3} d^{12} n^{3}\right)} \log\left(e x^{\frac{1}{3}} + d\right)^{3} - 4620 \, {\left(297202819 \, b^{3} d^{6} e^{6} n^{3} - 629992440 \, a b^{2} d^{6} e^{6} n^{2} + 384199200 \, a^{2} b d^{6} e^{6} n\right)} x^{2} + 384199200 \, {\left(3080 \, b^{3} d^{3} e^{9} n^{3} x^{3} - 4620 \, b^{3} d^{6} e^{6} n^{3} x^{2} + 9240 \, b^{3} d^{9} e^{3} n^{3} x + 86021 \, b^{3} d^{12} n^{3} - 27720 \, a b^{2} d^{12} n^{2} - 2310 \, {\left(b^{3} e^{12} n^{3} - 12 \, a b^{2} e^{12} n^{2}\right)} x^{4} + 27720 \, {\left(b^{3} e^{12} n^{2} x^{4} - b^{3} d^{12} n^{2}\right)} \log\left(c\right) + 63 \, {\left(40 \, b^{3} d e^{11} n^{3} x^{3} - 55 \, b^{3} d^{4} e^{8} n^{3} x^{2} + 88 \, b^{3} d^{7} e^{5} n^{3} x - 220 \, b^{3} d^{10} e^{2} n^{3}\right)} x^{\frac{2}{3}} - 198 \, {\left(14 \, b^{3} d^{2} e^{10} n^{3} x^{3} - 20 \, b^{3} d^{5} e^{7} n^{3} x^{2} + 35 \, b^{3} d^{8} e^{4} n^{3} x - 140 \, b^{3} d^{11} e n^{3}\right)} x^{\frac{1}{3}}\right)} \log\left(e x^{\frac{1}{3}} + d\right)^{2} + 295833384000 \, {\left(4 \, b^{3} d^{3} e^{9} n x^{3} - 6 \, b^{3} d^{6} e^{6} n x^{2} + 12 \, b^{3} d^{9} e^{3} n x - 3 \, {\left(b^{3} e^{12} n - 12 \, a b^{2} e^{12}\right)} x^{4}\right)} \log\left(c\right)^{2} + 9240 \, {\left(1108515013 \, b^{3} d^{9} e^{3} n^{3} - 1231904520 \, a b^{2} d^{9} e^{3} n^{2} + 384199200 \, a^{2} b d^{9} e^{3} n\right)} x - 27720 \, {\left(4301068993 \, b^{3} d^{12} n^{3} - 2384502120 \, a b^{2} d^{12} n^{2} + 384199200 \, a^{2} b d^{12} n - 5336100 \, {\left(b^{3} e^{12} n^{3} - 12 \, a b^{2} e^{12} n^{2} + 72 \, a^{2} b e^{12} n\right)} x^{4} + 43120 \, {\left(763 \, b^{3} d^{3} e^{9} n^{3} - 1980 \, a b^{2} d^{3} e^{9} n^{2}\right)} x^{3} - 4620 \, {\left(22727 \, b^{3} d^{6} e^{6} n^{3} - 27720 \, a b^{2} d^{6} e^{6} n^{2}\right)} x^{2} - 384199200 \, {\left(b^{3} e^{12} n x^{4} - b^{3} d^{12} n\right)} \log\left(c\right)^{2} + 9240 \, {\left(44441 \, b^{3} d^{9} e^{3} n^{3} - 27720 \, a b^{2} d^{9} e^{3} n^{2}\right)} x - 27720 \, {\left(3080 \, b^{3} d^{3} e^{9} n^{2} x^{3} - 4620 \, b^{3} d^{6} e^{6} n^{2} x^{2} + 9240 \, b^{3} d^{9} e^{3} n^{2} x + 86021 \, b^{3} d^{12} n^{2} - 27720 \, a b^{2} d^{12} n - 2310 \, {\left(b^{3} e^{12} n^{2} - 12 \, a b^{2} e^{12} n\right)} x^{4}\right)} \log\left(c\right) - 63 \, {\left(12826220 \, b^{3} d^{10} e^{2} n^{3} - 6098400 \, a b^{2} d^{10} e^{2} n^{2} - 8400 \, {\left(23 \, b^{3} d e^{11} n^{3} - 132 \, a b^{2} d e^{11} n^{2}\right)} x^{3} + 385 \, {\left(2021 \, b^{3} d^{4} e^{8} n^{3} - 3960 \, a b^{2} d^{4} e^{8} n^{2}\right)} x^{2} - 88 \, {\left(28271 \, b^{3} d^{7} e^{5} n^{3} - 27720 \, a b^{2} d^{7} e^{5} n^{2}\right)} x + 27720 \, {\left(40 \, b^{3} d e^{11} n^{2} x^{3} - 55 \, b^{3} d^{4} e^{8} n^{2} x^{2} + 88 \, b^{3} d^{7} e^{5} n^{2} x - 220 \, b^{3} d^{10} e^{2} n^{2}\right)} \log\left(c\right)\right)} x^{\frac{2}{3}} + 198 \, {\left(12042940 \, b^{3} d^{11} e n^{3} - 3880800 \, a b^{2} d^{11} e n^{2} - 588 \, {\left(181 \, b^{3} d^{2} e^{10} n^{3} - 660 \, a b^{2} d^{2} e^{10} n^{2}\right)} x^{3} + 20 \, {\left(18107 \, b^{3} d^{5} e^{7} n^{3} - 27720 \, a b^{2} d^{5} e^{7} n^{2}\right)} x^{2} - 35 \, {\left(35201 \, b^{3} d^{8} e^{4} n^{3} - 27720 \, a b^{2} d^{8} e^{4} n^{2}\right)} x + 27720 \, {\left(14 \, b^{3} d^{2} e^{10} n^{2} x^{3} - 20 \, b^{3} d^{5} e^{7} n^{2} x^{2} + 35 \, b^{3} d^{8} e^{4} n^{2} x - 140 \, b^{3} d^{11} e n^{2}\right)} \log\left(c\right)\right)} x^{\frac{1}{3}}\right)} \log\left(e x^{\frac{1}{3}} + d\right) + 42688800 \, {\left(3465 \, {\left(b^{3} e^{12} n^{2} - 12 \, a b^{2} e^{12} n + 72 \, a^{2} b e^{12}\right)} x^{4} - 28 \, {\left(763 \, b^{3} d^{3} e^{9} n^{2} - 1980 \, a b^{2} d^{3} e^{9} n\right)} x^{3} + 3 \, {\left(22727 \, b^{3} d^{6} e^{6} n^{2} - 27720 \, a b^{2} d^{6} e^{6} n\right)} x^{2} - 6 \, {\left(44441 \, b^{3} d^{9} e^{3} n^{2} - 27720 \, a b^{2} d^{9} e^{3} n\right)} x\right)} \log\left(c\right) - 63 \, {\left(421644712060 \, b^{3} d^{10} e^{2} n^{3} - 355542818400 \, a b^{2} d^{10} e^{2} n^{2} + 84523824000 \, a^{2} b d^{10} e^{2} n - 1764000 \, {\left(397 \, b^{3} d e^{11} n^{3} - 3036 \, a b^{2} d e^{11} n^{2} + 8712 \, a^{2} b d e^{11} n\right)} x^{3} + 2695 \, {\left(2459191 \, b^{3} d^{4} e^{8} n^{3} - 8003160 \, a b^{2} d^{4} e^{8} n^{2} + 7840800 \, a^{2} b d^{4} e^{8} n\right)} x^{2} - 384199200 \, {\left(40 \, b^{3} d e^{11} n x^{3} - 55 \, b^{3} d^{4} e^{8} n x^{2} + 88 \, b^{3} d^{7} e^{5} n x - 220 \, b^{3} d^{10} e^{2} n\right)} \log\left(c\right)^{2} - 88 \, {\left(453937243 \, b^{3} d^{7} e^{5} n^{3} - 783672120 \, a b^{2} d^{7} e^{5} n^{2} + 384199200 \, a^{2} b d^{7} e^{5} n\right)} x - 27720 \, {\left(12826220 \, b^{3} d^{10} e^{2} n^{2} - 6098400 \, a b^{2} d^{10} e^{2} n - 8400 \, {\left(23 \, b^{3} d e^{11} n^{2} - 132 \, a b^{2} d e^{11} n\right)} x^{3} + 385 \, {\left(2021 \, b^{3} d^{4} e^{8} n^{2} - 3960 \, a b^{2} d^{4} e^{8} n\right)} x^{2} - 88 \, {\left(28271 \, b^{3} d^{7} e^{5} n^{2} - 27720 \, a b^{2} d^{7} e^{5} n\right)} x\right)} \log\left(c\right)\right)} x^{\frac{2}{3}} + 198 \, {\left(602149659020 \, b^{3} d^{11} e n^{3} - 333830296800 \, a b^{2} d^{11} e n^{2} + 53787888000 \, a^{2} b d^{11} e n - 24696 \, {\left(21871 \, b^{3} d^{2} e^{10} n^{3} - 119460 \, a b^{2} d^{2} e^{10} n^{2} + 217800 \, a^{2} b d^{2} e^{10} n\right)} x^{3} + 20 \, {\left(192204079 \, b^{3} d^{5} e^{7} n^{3} - 501926040 \, a b^{2} d^{5} e^{7} n^{2} + 384199200 \, a^{2} b d^{5} e^{7} n\right)} x^{2} - 384199200 \, {\left(14 \, b^{3} d^{2} e^{10} n x^{3} - 20 \, b^{3} d^{5} e^{7} n x^{2} + 35 \, b^{3} d^{8} e^{4} n x - 140 \, b^{3} d^{11} e n\right)} \log\left(c\right)^{2} - 35 \, {\left(697880173 \, b^{3} d^{8} e^{4} n^{3} - 975771720 \, a b^{2} d^{8} e^{4} n^{2} + 384199200 \, a^{2} b d^{8} e^{4} n\right)} x - 27720 \, {\left(12042940 \, b^{3} d^{11} e n^{2} - 3880800 \, a b^{2} d^{11} e n - 588 \, {\left(181 \, b^{3} d^{2} e^{10} n^{2} - 660 \, a b^{2} d^{2} e^{10} n\right)} x^{3} + 20 \, {\left(18107 \, b^{3} d^{5} e^{7} n^{2} - 27720 \, a b^{2} d^{5} e^{7} n\right)} x^{2} - 35 \, {\left(35201 \, b^{3} d^{8} e^{4} n^{2} - 27720 \, a b^{2} d^{8} e^{4} n\right)} x\right)} \log\left(c\right)\right)} x^{\frac{1}{3}}}{14200002432000 \, e^{12}}"," ",0,"1/14200002432000*(3550000608000*b^3*e^12*x^4*log(c)^3 - 12326391000*(b^3*e^12*n^3 - 12*a*b^2*e^12*n^2 + 72*a^2*b*e^12*n - 288*a^3*e^12)*x^4 + 603680*(364699*b^3*d^3*e^9*n^3 - 1510740*a*b^2*d^3*e^9*n^2 + 1960200*a^2*b*d^3*e^9*n)*x^3 + 3550000608000*(b^3*e^12*n^3*x^4 - b^3*d^12*n^3)*log(e*x^(1/3) + d)^3 - 4620*(297202819*b^3*d^6*e^6*n^3 - 629992440*a*b^2*d^6*e^6*n^2 + 384199200*a^2*b*d^6*e^6*n)*x^2 + 384199200*(3080*b^3*d^3*e^9*n^3*x^3 - 4620*b^3*d^6*e^6*n^3*x^2 + 9240*b^3*d^9*e^3*n^3*x + 86021*b^3*d^12*n^3 - 27720*a*b^2*d^12*n^2 - 2310*(b^3*e^12*n^3 - 12*a*b^2*e^12*n^2)*x^4 + 27720*(b^3*e^12*n^2*x^4 - b^3*d^12*n^2)*log(c) + 63*(40*b^3*d*e^11*n^3*x^3 - 55*b^3*d^4*e^8*n^3*x^2 + 88*b^3*d^7*e^5*n^3*x - 220*b^3*d^10*e^2*n^3)*x^(2/3) - 198*(14*b^3*d^2*e^10*n^3*x^3 - 20*b^3*d^5*e^7*n^3*x^2 + 35*b^3*d^8*e^4*n^3*x - 140*b^3*d^11*e*n^3)*x^(1/3))*log(e*x^(1/3) + d)^2 + 295833384000*(4*b^3*d^3*e^9*n*x^3 - 6*b^3*d^6*e^6*n*x^2 + 12*b^3*d^9*e^3*n*x - 3*(b^3*e^12*n - 12*a*b^2*e^12)*x^4)*log(c)^2 + 9240*(1108515013*b^3*d^9*e^3*n^3 - 1231904520*a*b^2*d^9*e^3*n^2 + 384199200*a^2*b*d^9*e^3*n)*x - 27720*(4301068993*b^3*d^12*n^3 - 2384502120*a*b^2*d^12*n^2 + 384199200*a^2*b*d^12*n - 5336100*(b^3*e^12*n^3 - 12*a*b^2*e^12*n^2 + 72*a^2*b*e^12*n)*x^4 + 43120*(763*b^3*d^3*e^9*n^3 - 1980*a*b^2*d^3*e^9*n^2)*x^3 - 4620*(22727*b^3*d^6*e^6*n^3 - 27720*a*b^2*d^6*e^6*n^2)*x^2 - 384199200*(b^3*e^12*n*x^4 - b^3*d^12*n)*log(c)^2 + 9240*(44441*b^3*d^9*e^3*n^3 - 27720*a*b^2*d^9*e^3*n^2)*x - 27720*(3080*b^3*d^3*e^9*n^2*x^3 - 4620*b^3*d^6*e^6*n^2*x^2 + 9240*b^3*d^9*e^3*n^2*x + 86021*b^3*d^12*n^2 - 27720*a*b^2*d^12*n - 2310*(b^3*e^12*n^2 - 12*a*b^2*e^12*n)*x^4)*log(c) - 63*(12826220*b^3*d^10*e^2*n^3 - 6098400*a*b^2*d^10*e^2*n^2 - 8400*(23*b^3*d*e^11*n^3 - 132*a*b^2*d*e^11*n^2)*x^3 + 385*(2021*b^3*d^4*e^8*n^3 - 3960*a*b^2*d^4*e^8*n^2)*x^2 - 88*(28271*b^3*d^7*e^5*n^3 - 27720*a*b^2*d^7*e^5*n^2)*x + 27720*(40*b^3*d*e^11*n^2*x^3 - 55*b^3*d^4*e^8*n^2*x^2 + 88*b^3*d^7*e^5*n^2*x - 220*b^3*d^10*e^2*n^2)*log(c))*x^(2/3) + 198*(12042940*b^3*d^11*e*n^3 - 3880800*a*b^2*d^11*e*n^2 - 588*(181*b^3*d^2*e^10*n^3 - 660*a*b^2*d^2*e^10*n^2)*x^3 + 20*(18107*b^3*d^5*e^7*n^3 - 27720*a*b^2*d^5*e^7*n^2)*x^2 - 35*(35201*b^3*d^8*e^4*n^3 - 27720*a*b^2*d^8*e^4*n^2)*x + 27720*(14*b^3*d^2*e^10*n^2*x^3 - 20*b^3*d^5*e^7*n^2*x^2 + 35*b^3*d^8*e^4*n^2*x - 140*b^3*d^11*e*n^2)*log(c))*x^(1/3))*log(e*x^(1/3) + d) + 42688800*(3465*(b^3*e^12*n^2 - 12*a*b^2*e^12*n + 72*a^2*b*e^12)*x^4 - 28*(763*b^3*d^3*e^9*n^2 - 1980*a*b^2*d^3*e^9*n)*x^3 + 3*(22727*b^3*d^6*e^6*n^2 - 27720*a*b^2*d^6*e^6*n)*x^2 - 6*(44441*b^3*d^9*e^3*n^2 - 27720*a*b^2*d^9*e^3*n)*x)*log(c) - 63*(421644712060*b^3*d^10*e^2*n^3 - 355542818400*a*b^2*d^10*e^2*n^2 + 84523824000*a^2*b*d^10*e^2*n - 1764000*(397*b^3*d*e^11*n^3 - 3036*a*b^2*d*e^11*n^2 + 8712*a^2*b*d*e^11*n)*x^3 + 2695*(2459191*b^3*d^4*e^8*n^3 - 8003160*a*b^2*d^4*e^8*n^2 + 7840800*a^2*b*d^4*e^8*n)*x^2 - 384199200*(40*b^3*d*e^11*n*x^3 - 55*b^3*d^4*e^8*n*x^2 + 88*b^3*d^7*e^5*n*x - 220*b^3*d^10*e^2*n)*log(c)^2 - 88*(453937243*b^3*d^7*e^5*n^3 - 783672120*a*b^2*d^7*e^5*n^2 + 384199200*a^2*b*d^7*e^5*n)*x - 27720*(12826220*b^3*d^10*e^2*n^2 - 6098400*a*b^2*d^10*e^2*n - 8400*(23*b^3*d*e^11*n^2 - 132*a*b^2*d*e^11*n)*x^3 + 385*(2021*b^3*d^4*e^8*n^2 - 3960*a*b^2*d^4*e^8*n)*x^2 - 88*(28271*b^3*d^7*e^5*n^2 - 27720*a*b^2*d^7*e^5*n)*x)*log(c))*x^(2/3) + 198*(602149659020*b^3*d^11*e*n^3 - 333830296800*a*b^2*d^11*e*n^2 + 53787888000*a^2*b*d^11*e*n - 24696*(21871*b^3*d^2*e^10*n^3 - 119460*a*b^2*d^2*e^10*n^2 + 217800*a^2*b*d^2*e^10*n)*x^3 + 20*(192204079*b^3*d^5*e^7*n^3 - 501926040*a*b^2*d^5*e^7*n^2 + 384199200*a^2*b*d^5*e^7*n)*x^2 - 384199200*(14*b^3*d^2*e^10*n*x^3 - 20*b^3*d^5*e^7*n*x^2 + 35*b^3*d^8*e^4*n*x - 140*b^3*d^11*e*n)*log(c)^2 - 35*(697880173*b^3*d^8*e^4*n^3 - 975771720*a*b^2*d^8*e^4*n^2 + 384199200*a^2*b*d^8*e^4*n)*x - 27720*(12042940*b^3*d^11*e*n^2 - 3880800*a*b^2*d^11*e*n - 588*(181*b^3*d^2*e^10*n^2 - 660*a*b^2*d^2*e^10*n)*x^3 + 20*(18107*b^3*d^5*e^7*n^2 - 27720*a*b^2*d^5*e^7*n)*x^2 - 35*(35201*b^3*d^8*e^4*n^2 - 27720*a*b^2*d^8*e^4*n)*x)*log(c))*x^(1/3))/e^12","A",0
457,1,1688,0,1.709637," ","integrate(x^2*(a+b*log(c*(d+e*x^(1/3))^n))^3,x, algorithm=""fricas"")","\frac{2667168000 \, b^{3} e^{9} x^{3} \log\left(c\right)^{3} - 10976000 \, {\left(2 \, b^{3} e^{9} n^{3} - 18 \, a b^{2} e^{9} n^{2} + 81 \, a^{2} b e^{9} n - 243 \, a^{3} e^{9}\right)} x^{3} + 2667168000 \, {\left(b^{3} e^{9} n^{3} x^{3} + b^{3} d^{9} n^{3}\right)} \log\left(e x^{\frac{1}{3}} + d\right)^{3} + 10500 \, {\left(47485 \, b^{3} d^{3} e^{6} n^{3} - 138600 \, a b^{2} d^{3} e^{6} n^{2} + 127008 \, a^{2} b d^{3} e^{6} n\right)} x^{2} + 3175200 \, {\left(420 \, b^{3} d^{3} e^{6} n^{3} x^{2} - 840 \, b^{3} d^{6} e^{3} n^{3} x - 7129 \, b^{3} d^{9} n^{3} + 2520 \, a b^{2} d^{9} n^{2} - 280 \, {\left(b^{3} e^{9} n^{3} - 9 \, a b^{2} e^{9} n^{2}\right)} x^{3} + 2520 \, {\left(b^{3} e^{9} n^{2} x^{3} + b^{3} d^{9} n^{2}\right)} \log\left(c\right) + 63 \, {\left(5 \, b^{3} d e^{8} n^{3} x^{2} - 8 \, b^{3} d^{4} e^{5} n^{3} x + 20 \, b^{3} d^{7} e^{2} n^{3}\right)} x^{\frac{2}{3}} - 90 \, {\left(4 \, b^{3} d^{2} e^{7} n^{3} x^{2} - 7 \, b^{3} d^{5} e^{4} n^{3} x + 28 \, b^{3} d^{8} e n^{3}\right)} x^{\frac{1}{3}}\right)} \log\left(e x^{\frac{1}{3}} + d\right)^{2} + 444528000 \, {\left(3 \, b^{3} d^{3} e^{6} n x^{2} - 6 \, b^{3} d^{6} e^{3} n x - 2 \, {\left(b^{3} e^{9} n - 9 \, a b^{2} e^{9}\right)} x^{3}\right)} \log\left(c\right)^{2} - 840 \, {\left(6527971 \, b^{3} d^{6} e^{3} n^{3} - 8439480 \, a b^{2} d^{6} e^{3} n^{2} + 3175200 \, a^{2} b d^{6} e^{3} n\right)} x + 2520 \, {\left(30300391 \, b^{3} d^{9} n^{3} - 17965080 \, a b^{2} d^{9} n^{2} + 3175200 \, a^{2} b d^{9} n + 39200 \, {\left(2 \, b^{3} e^{9} n^{3} - 18 \, a b^{2} e^{9} n^{2} + 81 \, a^{2} b e^{9} n\right)} x^{3} - 2100 \, {\left(275 \, b^{3} d^{3} e^{6} n^{3} - 504 \, a b^{2} d^{3} e^{6} n^{2}\right)} x^{2} + 3175200 \, {\left(b^{3} e^{9} n x^{3} + b^{3} d^{9} n\right)} \log\left(c\right)^{2} + 840 \, {\left(3349 \, b^{3} d^{6} e^{3} n^{3} - 2520 \, a b^{2} d^{6} e^{3} n^{2}\right)} x + 2520 \, {\left(420 \, b^{3} d^{3} e^{6} n^{2} x^{2} - 840 \, b^{3} d^{6} e^{3} n^{2} x - 7129 \, b^{3} d^{9} n^{2} + 2520 \, a b^{2} d^{9} n - 280 \, {\left(b^{3} e^{9} n^{2} - 9 \, a b^{2} e^{9} n\right)} x^{3}\right)} \log\left(c\right) - 63 \, {\left(92180 \, b^{3} d^{7} e^{2} n^{3} - 50400 \, a b^{2} d^{7} e^{2} n^{2} + 175 \, {\left(17 \, b^{3} d e^{8} n^{3} - 72 \, a b^{2} d e^{8} n^{2}\right)} x^{2} - 8 \, {\left(1879 \, b^{3} d^{4} e^{5} n^{3} - 2520 \, a b^{2} d^{4} e^{5} n^{2}\right)} x - 2520 \, {\left(5 \, b^{3} d e^{8} n^{2} x^{2} - 8 \, b^{3} d^{4} e^{5} n^{2} x + 20 \, b^{3} d^{7} e^{2} n^{2}\right)} \log\left(c\right)\right)} x^{\frac{2}{3}} + 90 \, {\left(199612 \, b^{3} d^{8} e n^{3} - 70560 \, a b^{2} d^{8} e n^{2} + 20 \, {\left(191 \, b^{3} d^{2} e^{7} n^{3} - 504 \, a b^{2} d^{2} e^{7} n^{2}\right)} x^{2} - 7 \, {\left(2509 \, b^{3} d^{5} e^{4} n^{3} - 2520 \, a b^{2} d^{5} e^{4} n^{2}\right)} x - 2520 \, {\left(4 \, b^{3} d^{2} e^{7} n^{2} x^{2} - 7 \, b^{3} d^{5} e^{4} n^{2} x + 28 \, b^{3} d^{8} e n^{2}\right)} \log\left(c\right)\right)} x^{\frac{1}{3}}\right)} \log\left(e x^{\frac{1}{3}} + d\right) + 352800 \, {\left(280 \, {\left(2 \, b^{3} e^{9} n^{2} - 18 \, a b^{2} e^{9} n + 81 \, a^{2} b e^{9}\right)} x^{3} - 15 \, {\left(275 \, b^{3} d^{3} e^{6} n^{2} - 504 \, a b^{2} d^{3} e^{6} n\right)} x^{2} + 6 \, {\left(3349 \, b^{3} d^{6} e^{3} n^{2} - 2520 \, a b^{2} d^{6} e^{3} n\right)} x\right)} \log\left(c\right) + 63 \, {\left(246706220 \, b^{3} d^{7} e^{2} n^{3} - 232293600 \, a b^{2} d^{7} e^{2} n^{2} + 63504000 \, a^{2} b d^{7} e^{2} n + 6125 \, {\left(217 \, b^{3} d e^{8} n^{3} - 1224 \, a b^{2} d e^{8} n^{2} + 2592 \, a^{2} b d e^{8} n\right)} x^{2} + 3175200 \, {\left(5 \, b^{3} d e^{8} n x^{2} - 8 \, b^{3} d^{4} e^{5} n x + 20 \, b^{3} d^{7} e^{2} n\right)} \log\left(c\right)^{2} - 8 \, {\left(2134141 \, b^{3} d^{4} e^{5} n^{3} - 4735080 \, a b^{2} d^{4} e^{5} n^{2} + 3175200 \, a^{2} b d^{4} e^{5} n\right)} x - 2520 \, {\left(92180 \, b^{3} d^{7} e^{2} n^{2} - 50400 \, a b^{2} d^{7} e^{2} n + 175 \, {\left(17 \, b^{3} d e^{8} n^{2} - 72 \, a b^{2} d e^{8} n\right)} x^{2} - 8 \, {\left(1879 \, b^{3} d^{4} e^{5} n^{2} - 2520 \, a b^{2} d^{4} e^{5} n\right)} x\right)} \log\left(c\right)\right)} x^{\frac{2}{3}} - 90 \, {\left(848410948 \, b^{3} d^{8} e n^{3} - 503022240 \, a b^{2} d^{8} e n^{2} + 88905600 \, a^{2} b d^{8} e n + 100 \, {\left(24385 \, b^{3} d^{2} e^{7} n^{3} - 96264 \, a b^{2} d^{2} e^{7} n^{2} + 127008 \, a^{2} b d^{2} e^{7} n\right)} x^{2} + 3175200 \, {\left(4 \, b^{3} d^{2} e^{7} n x^{2} - 7 \, b^{3} d^{5} e^{4} n x + 28 \, b^{3} d^{8} e n\right)} \log\left(c\right)^{2} - 7 \, {\left(3714811 \, b^{3} d^{5} e^{4} n^{3} - 6322680 \, a b^{2} d^{5} e^{4} n^{2} + 3175200 \, a^{2} b d^{5} e^{4} n\right)} x - 2520 \, {\left(199612 \, b^{3} d^{8} e n^{2} - 70560 \, a b^{2} d^{8} e n + 20 \, {\left(191 \, b^{3} d^{2} e^{7} n^{2} - 504 \, a b^{2} d^{2} e^{7} n\right)} x^{2} - 7 \, {\left(2509 \, b^{3} d^{5} e^{4} n^{2} - 2520 \, a b^{2} d^{5} e^{4} n\right)} x\right)} \log\left(c\right)\right)} x^{\frac{1}{3}}}{8001504000 \, e^{9}}"," ",0,"1/8001504000*(2667168000*b^3*e^9*x^3*log(c)^3 - 10976000*(2*b^3*e^9*n^3 - 18*a*b^2*e^9*n^2 + 81*a^2*b*e^9*n - 243*a^3*e^9)*x^3 + 2667168000*(b^3*e^9*n^3*x^3 + b^3*d^9*n^3)*log(e*x^(1/3) + d)^3 + 10500*(47485*b^3*d^3*e^6*n^3 - 138600*a*b^2*d^3*e^6*n^2 + 127008*a^2*b*d^3*e^6*n)*x^2 + 3175200*(420*b^3*d^3*e^6*n^3*x^2 - 840*b^3*d^6*e^3*n^3*x - 7129*b^3*d^9*n^3 + 2520*a*b^2*d^9*n^2 - 280*(b^3*e^9*n^3 - 9*a*b^2*e^9*n^2)*x^3 + 2520*(b^3*e^9*n^2*x^3 + b^3*d^9*n^2)*log(c) + 63*(5*b^3*d*e^8*n^3*x^2 - 8*b^3*d^4*e^5*n^3*x + 20*b^3*d^7*e^2*n^3)*x^(2/3) - 90*(4*b^3*d^2*e^7*n^3*x^2 - 7*b^3*d^5*e^4*n^3*x + 28*b^3*d^8*e*n^3)*x^(1/3))*log(e*x^(1/3) + d)^2 + 444528000*(3*b^3*d^3*e^6*n*x^2 - 6*b^3*d^6*e^3*n*x - 2*(b^3*e^9*n - 9*a*b^2*e^9)*x^3)*log(c)^2 - 840*(6527971*b^3*d^6*e^3*n^3 - 8439480*a*b^2*d^6*e^3*n^2 + 3175200*a^2*b*d^6*e^3*n)*x + 2520*(30300391*b^3*d^9*n^3 - 17965080*a*b^2*d^9*n^2 + 3175200*a^2*b*d^9*n + 39200*(2*b^3*e^9*n^3 - 18*a*b^2*e^9*n^2 + 81*a^2*b*e^9*n)*x^3 - 2100*(275*b^3*d^3*e^6*n^3 - 504*a*b^2*d^3*e^6*n^2)*x^2 + 3175200*(b^3*e^9*n*x^3 + b^3*d^9*n)*log(c)^2 + 840*(3349*b^3*d^6*e^3*n^3 - 2520*a*b^2*d^6*e^3*n^2)*x + 2520*(420*b^3*d^3*e^6*n^2*x^2 - 840*b^3*d^6*e^3*n^2*x - 7129*b^3*d^9*n^2 + 2520*a*b^2*d^9*n - 280*(b^3*e^9*n^2 - 9*a*b^2*e^9*n)*x^3)*log(c) - 63*(92180*b^3*d^7*e^2*n^3 - 50400*a*b^2*d^7*e^2*n^2 + 175*(17*b^3*d*e^8*n^3 - 72*a*b^2*d*e^8*n^2)*x^2 - 8*(1879*b^3*d^4*e^5*n^3 - 2520*a*b^2*d^4*e^5*n^2)*x - 2520*(5*b^3*d*e^8*n^2*x^2 - 8*b^3*d^4*e^5*n^2*x + 20*b^3*d^7*e^2*n^2)*log(c))*x^(2/3) + 90*(199612*b^3*d^8*e*n^3 - 70560*a*b^2*d^8*e*n^2 + 20*(191*b^3*d^2*e^7*n^3 - 504*a*b^2*d^2*e^7*n^2)*x^2 - 7*(2509*b^3*d^5*e^4*n^3 - 2520*a*b^2*d^5*e^4*n^2)*x - 2520*(4*b^3*d^2*e^7*n^2*x^2 - 7*b^3*d^5*e^4*n^2*x + 28*b^3*d^8*e*n^2)*log(c))*x^(1/3))*log(e*x^(1/3) + d) + 352800*(280*(2*b^3*e^9*n^2 - 18*a*b^2*e^9*n + 81*a^2*b*e^9)*x^3 - 15*(275*b^3*d^3*e^6*n^2 - 504*a*b^2*d^3*e^6*n)*x^2 + 6*(3349*b^3*d^6*e^3*n^2 - 2520*a*b^2*d^6*e^3*n)*x)*log(c) + 63*(246706220*b^3*d^7*e^2*n^3 - 232293600*a*b^2*d^7*e^2*n^2 + 63504000*a^2*b*d^7*e^2*n + 6125*(217*b^3*d*e^8*n^3 - 1224*a*b^2*d*e^8*n^2 + 2592*a^2*b*d*e^8*n)*x^2 + 3175200*(5*b^3*d*e^8*n*x^2 - 8*b^3*d^4*e^5*n*x + 20*b^3*d^7*e^2*n)*log(c)^2 - 8*(2134141*b^3*d^4*e^5*n^3 - 4735080*a*b^2*d^4*e^5*n^2 + 3175200*a^2*b*d^4*e^5*n)*x - 2520*(92180*b^3*d^7*e^2*n^2 - 50400*a*b^2*d^7*e^2*n + 175*(17*b^3*d*e^8*n^2 - 72*a*b^2*d*e^8*n)*x^2 - 8*(1879*b^3*d^4*e^5*n^2 - 2520*a*b^2*d^4*e^5*n)*x)*log(c))*x^(2/3) - 90*(848410948*b^3*d^8*e*n^3 - 503022240*a*b^2*d^8*e*n^2 + 88905600*a^2*b*d^8*e*n + 100*(24385*b^3*d^2*e^7*n^3 - 96264*a*b^2*d^2*e^7*n^2 + 127008*a^2*b*d^2*e^7*n)*x^2 + 3175200*(4*b^3*d^2*e^7*n*x^2 - 7*b^3*d^5*e^4*n*x + 28*b^3*d^8*e*n)*log(c)^2 - 7*(3714811*b^3*d^5*e^4*n^3 - 6322680*a*b^2*d^5*e^4*n^2 + 3175200*a^2*b*d^5*e^4*n)*x - 2520*(199612*b^3*d^8*e*n^2 - 70560*a*b^2*d^8*e*n + 20*(191*b^3*d^2*e^7*n^2 - 504*a*b^2*d^2*e^7*n)*x^2 - 7*(2509*b^3*d^5*e^4*n^2 - 2520*a*b^2*d^5*e^4*n)*x)*log(c))*x^(1/3))/e^9","A",0
458,1,1190,0,1.153004," ","integrate(x*(a+b*log(c*(d+e*x^(1/3))^n))^3,x, algorithm=""fricas"")","\frac{36000 \, b^{3} e^{6} x^{2} \log\left(c\right)^{3} + 36000 \, {\left(b^{3} e^{6} n^{3} x^{2} - b^{3} d^{6} n^{3}\right)} \log\left(e x^{\frac{1}{3}} + d\right)^{3} - 1000 \, {\left(b^{3} e^{6} n^{3} - 6 \, a b^{2} e^{6} n^{2} + 18 \, a^{2} b e^{6} n - 36 \, a^{3} e^{6}\right)} x^{2} + 1800 \, {\left(20 \, b^{3} d^{3} e^{3} n^{3} x + 147 \, b^{3} d^{6} n^{3} - 60 \, a b^{2} d^{6} n^{2} - 10 \, {\left(b^{3} e^{6} n^{3} - 6 \, a b^{2} e^{6} n^{2}\right)} x^{2} + 60 \, {\left(b^{3} e^{6} n^{2} x^{2} - b^{3} d^{6} n^{2}\right)} \log\left(c\right) + 6 \, {\left(2 \, b^{3} d e^{5} n^{3} x - 5 \, b^{3} d^{4} e^{2} n^{3}\right)} x^{\frac{2}{3}} - 15 \, {\left(b^{3} d^{2} e^{4} n^{3} x - 4 \, b^{3} d^{5} e n^{3}\right)} x^{\frac{1}{3}}\right)} \log\left(e x^{\frac{1}{3}} + d\right)^{2} + 18000 \, {\left(2 \, b^{3} d^{3} e^{3} n x - {\left(b^{3} e^{6} n - 6 \, a b^{2} e^{6}\right)} x^{2}\right)} \log\left(c\right)^{2} + 20 \, {\left(2059 \, b^{3} d^{3} e^{3} n^{3} - 3420 \, a b^{2} d^{3} e^{3} n^{2} + 1800 \, a^{2} b d^{3} e^{3} n\right)} x - 60 \, {\left(13489 \, b^{3} d^{6} n^{3} - 8820 \, a b^{2} d^{6} n^{2} + 1800 \, a^{2} b d^{6} n - 100 \, {\left(b^{3} e^{6} n^{3} - 6 \, a b^{2} e^{6} n^{2} + 18 \, a^{2} b e^{6} n\right)} x^{2} - 1800 \, {\left(b^{3} e^{6} n x^{2} - b^{3} d^{6} n\right)} \log\left(c\right)^{2} + 60 \, {\left(19 \, b^{3} d^{3} e^{3} n^{3} - 20 \, a b^{2} d^{3} e^{3} n^{2}\right)} x - 60 \, {\left(20 \, b^{3} d^{3} e^{3} n^{2} x + 147 \, b^{3} d^{6} n^{2} - 60 \, a b^{2} d^{6} n - 10 \, {\left(b^{3} e^{6} n^{2} - 6 \, a b^{2} e^{6} n\right)} x^{2}\right)} \log\left(c\right) - 6 \, {\left(435 \, b^{3} d^{4} e^{2} n^{3} - 300 \, a b^{2} d^{4} e^{2} n^{2} - 4 \, {\left(11 \, b^{3} d e^{5} n^{3} - 30 \, a b^{2} d e^{5} n^{2}\right)} x + 60 \, {\left(2 \, b^{3} d e^{5} n^{2} x - 5 \, b^{3} d^{4} e^{2} n^{2}\right)} \log\left(c\right)\right)} x^{\frac{2}{3}} + 15 \, {\left(588 \, b^{3} d^{5} e n^{3} - 240 \, a b^{2} d^{5} e n^{2} - {\left(37 \, b^{3} d^{2} e^{4} n^{3} - 60 \, a b^{2} d^{2} e^{4} n^{2}\right)} x + 60 \, {\left(b^{3} d^{2} e^{4} n^{2} x - 4 \, b^{3} d^{5} e n^{2}\right)} \log\left(c\right)\right)} x^{\frac{1}{3}}\right)} \log\left(e x^{\frac{1}{3}} + d\right) + 1200 \, {\left(5 \, {\left(b^{3} e^{6} n^{2} - 6 \, a b^{2} e^{6} n + 18 \, a^{2} b e^{6}\right)} x^{2} - 3 \, {\left(19 \, b^{3} d^{3} e^{3} n^{2} - 20 \, a b^{2} d^{3} e^{3} n\right)} x\right)} \log\left(c\right) - 6 \, {\left(23345 \, b^{3} d^{4} e^{2} n^{3} - 26100 \, a b^{2} d^{4} e^{2} n^{2} + 9000 \, a^{2} b d^{4} e^{2} n - 1800 \, {\left(2 \, b^{3} d e^{5} n x - 5 \, b^{3} d^{4} e^{2} n\right)} \log\left(c\right)^{2} - 8 \, {\left(91 \, b^{3} d e^{5} n^{3} - 330 \, a b^{2} d e^{5} n^{2} + 450 \, a^{2} b d e^{5} n\right)} x - 60 \, {\left(435 \, b^{3} d^{4} e^{2} n^{2} - 300 \, a b^{2} d^{4} e^{2} n - 4 \, {\left(11 \, b^{3} d e^{5} n^{2} - 30 \, a b^{2} d e^{5} n\right)} x\right)} \log\left(c\right)\right)} x^{\frac{2}{3}} + 15 \, {\left(53956 \, b^{3} d^{5} e n^{3} - 35280 \, a b^{2} d^{5} e n^{2} + 7200 \, a^{2} b d^{5} e n - 1800 \, {\left(b^{3} d^{2} e^{4} n x - 4 \, b^{3} d^{5} e n\right)} \log\left(c\right)^{2} - {\left(919 \, b^{3} d^{2} e^{4} n^{3} - 2220 \, a b^{2} d^{2} e^{4} n^{2} + 1800 \, a^{2} b d^{2} e^{4} n\right)} x - 60 \, {\left(588 \, b^{3} d^{5} e n^{2} - 240 \, a b^{2} d^{5} e n - {\left(37 \, b^{3} d^{2} e^{4} n^{2} - 60 \, a b^{2} d^{2} e^{4} n\right)} x\right)} \log\left(c\right)\right)} x^{\frac{1}{3}}}{72000 \, e^{6}}"," ",0,"1/72000*(36000*b^3*e^6*x^2*log(c)^3 + 36000*(b^3*e^6*n^3*x^2 - b^3*d^6*n^3)*log(e*x^(1/3) + d)^3 - 1000*(b^3*e^6*n^3 - 6*a*b^2*e^6*n^2 + 18*a^2*b*e^6*n - 36*a^3*e^6)*x^2 + 1800*(20*b^3*d^3*e^3*n^3*x + 147*b^3*d^6*n^3 - 60*a*b^2*d^6*n^2 - 10*(b^3*e^6*n^3 - 6*a*b^2*e^6*n^2)*x^2 + 60*(b^3*e^6*n^2*x^2 - b^3*d^6*n^2)*log(c) + 6*(2*b^3*d*e^5*n^3*x - 5*b^3*d^4*e^2*n^3)*x^(2/3) - 15*(b^3*d^2*e^4*n^3*x - 4*b^3*d^5*e*n^3)*x^(1/3))*log(e*x^(1/3) + d)^2 + 18000*(2*b^3*d^3*e^3*n*x - (b^3*e^6*n - 6*a*b^2*e^6)*x^2)*log(c)^2 + 20*(2059*b^3*d^3*e^3*n^3 - 3420*a*b^2*d^3*e^3*n^2 + 1800*a^2*b*d^3*e^3*n)*x - 60*(13489*b^3*d^6*n^3 - 8820*a*b^2*d^6*n^2 + 1800*a^2*b*d^6*n - 100*(b^3*e^6*n^3 - 6*a*b^2*e^6*n^2 + 18*a^2*b*e^6*n)*x^2 - 1800*(b^3*e^6*n*x^2 - b^3*d^6*n)*log(c)^2 + 60*(19*b^3*d^3*e^3*n^3 - 20*a*b^2*d^3*e^3*n^2)*x - 60*(20*b^3*d^3*e^3*n^2*x + 147*b^3*d^6*n^2 - 60*a*b^2*d^6*n - 10*(b^3*e^6*n^2 - 6*a*b^2*e^6*n)*x^2)*log(c) - 6*(435*b^3*d^4*e^2*n^3 - 300*a*b^2*d^4*e^2*n^2 - 4*(11*b^3*d*e^5*n^3 - 30*a*b^2*d*e^5*n^2)*x + 60*(2*b^3*d*e^5*n^2*x - 5*b^3*d^4*e^2*n^2)*log(c))*x^(2/3) + 15*(588*b^3*d^5*e*n^3 - 240*a*b^2*d^5*e*n^2 - (37*b^3*d^2*e^4*n^3 - 60*a*b^2*d^2*e^4*n^2)*x + 60*(b^3*d^2*e^4*n^2*x - 4*b^3*d^5*e*n^2)*log(c))*x^(1/3))*log(e*x^(1/3) + d) + 1200*(5*(b^3*e^6*n^2 - 6*a*b^2*e^6*n + 18*a^2*b*e^6)*x^2 - 3*(19*b^3*d^3*e^3*n^2 - 20*a*b^2*d^3*e^3*n)*x)*log(c) - 6*(23345*b^3*d^4*e^2*n^3 - 26100*a*b^2*d^4*e^2*n^2 + 9000*a^2*b*d^4*e^2*n - 1800*(2*b^3*d*e^5*n*x - 5*b^3*d^4*e^2*n)*log(c)^2 - 8*(91*b^3*d*e^5*n^3 - 330*a*b^2*d*e^5*n^2 + 450*a^2*b*d*e^5*n)*x - 60*(435*b^3*d^4*e^2*n^2 - 300*a*b^2*d^4*e^2*n - 4*(11*b^3*d*e^5*n^2 - 30*a*b^2*d*e^5*n)*x)*log(c))*x^(2/3) + 15*(53956*b^3*d^5*e*n^3 - 35280*a*b^2*d^5*e*n^2 + 7200*a^2*b*d^5*e*n - 1800*(b^3*d^2*e^4*n*x - 4*b^3*d^5*e*n)*log(c)^2 - (919*b^3*d^2*e^4*n^3 - 2220*a*b^2*d^2*e^4*n^2 + 1800*a^2*b*d^2*e^4*n)*x - 60*(588*b^3*d^5*e*n^2 - 240*a*b^2*d^5*e*n - (37*b^3*d^2*e^4*n^2 - 60*a*b^2*d^2*e^4*n)*x)*log(c))*x^(1/3))/e^6","A",0
459,1,690,0,1.154625," ","integrate((a+b*log(c*(d+e*x^(1/3))^n))^3,x, algorithm=""fricas"")","\frac{36 \, b^{3} e^{3} x \log\left(c\right)^{3} + 36 \, {\left(b^{3} e^{3} n^{3} x + b^{3} d^{3} n^{3}\right)} \log\left(e x^{\frac{1}{3}} + d\right)^{3} - 36 \, {\left(b^{3} e^{3} n - 3 \, a b^{2} e^{3}\right)} x \log\left(c\right)^{2} + 18 \, {\left(3 \, b^{3} d e^{2} n^{3} x^{\frac{2}{3}} - 6 \, b^{3} d^{2} e n^{3} x^{\frac{1}{3}} - 11 \, b^{3} d^{3} n^{3} + 6 \, a b^{2} d^{3} n^{2} - 2 \, {\left(b^{3} e^{3} n^{3} - 3 \, a b^{2} e^{3} n^{2}\right)} x + 6 \, {\left(b^{3} e^{3} n^{2} x + b^{3} d^{3} n^{2}\right)} \log\left(c\right)\right)} \log\left(e x^{\frac{1}{3}} + d\right)^{2} + 12 \, {\left(2 \, b^{3} e^{3} n^{2} - 6 \, a b^{2} e^{3} n + 9 \, a^{2} b e^{3}\right)} x \log\left(c\right) - 4 \, {\left(2 \, b^{3} e^{3} n^{3} - 6 \, a b^{2} e^{3} n^{2} + 9 \, a^{2} b e^{3} n - 9 \, a^{3} e^{3}\right)} x + 6 \, {\left(85 \, b^{3} d^{3} n^{3} - 66 \, a b^{2} d^{3} n^{2} + 18 \, a^{2} b d^{3} n + 18 \, {\left(b^{3} e^{3} n x + b^{3} d^{3} n\right)} \log\left(c\right)^{2} + 2 \, {\left(2 \, b^{3} e^{3} n^{3} - 6 \, a b^{2} e^{3} n^{2} + 9 \, a^{2} b e^{3} n\right)} x - 6 \, {\left(11 \, b^{3} d^{3} n^{2} - 6 \, a b^{2} d^{3} n + 2 \, {\left(b^{3} e^{3} n^{2} - 3 \, a b^{2} e^{3} n\right)} x\right)} \log\left(c\right) - 3 \, {\left(5 \, b^{3} d e^{2} n^{3} - 6 \, b^{3} d e^{2} n^{2} \log\left(c\right) - 6 \, a b^{2} d e^{2} n^{2}\right)} x^{\frac{2}{3}} + 6 \, {\left(11 \, b^{3} d^{2} e n^{3} - 6 \, b^{3} d^{2} e n^{2} \log\left(c\right) - 6 \, a b^{2} d^{2} e n^{2}\right)} x^{\frac{1}{3}}\right)} \log\left(e x^{\frac{1}{3}} + d\right) + 3 \, {\left(19 \, b^{3} d e^{2} n^{3} + 18 \, b^{3} d e^{2} n \log\left(c\right)^{2} - 30 \, a b^{2} d e^{2} n^{2} + 18 \, a^{2} b d e^{2} n - 6 \, {\left(5 \, b^{3} d e^{2} n^{2} - 6 \, a b^{2} d e^{2} n\right)} \log\left(c\right)\right)} x^{\frac{2}{3}} - 6 \, {\left(85 \, b^{3} d^{2} e n^{3} + 18 \, b^{3} d^{2} e n \log\left(c\right)^{2} - 66 \, a b^{2} d^{2} e n^{2} + 18 \, a^{2} b d^{2} e n - 6 \, {\left(11 \, b^{3} d^{2} e n^{2} - 6 \, a b^{2} d^{2} e n\right)} \log\left(c\right)\right)} x^{\frac{1}{3}}}{36 \, e^{3}}"," ",0,"1/36*(36*b^3*e^3*x*log(c)^3 + 36*(b^3*e^3*n^3*x + b^3*d^3*n^3)*log(e*x^(1/3) + d)^3 - 36*(b^3*e^3*n - 3*a*b^2*e^3)*x*log(c)^2 + 18*(3*b^3*d*e^2*n^3*x^(2/3) - 6*b^3*d^2*e*n^3*x^(1/3) - 11*b^3*d^3*n^3 + 6*a*b^2*d^3*n^2 - 2*(b^3*e^3*n^3 - 3*a*b^2*e^3*n^2)*x + 6*(b^3*e^3*n^2*x + b^3*d^3*n^2)*log(c))*log(e*x^(1/3) + d)^2 + 12*(2*b^3*e^3*n^2 - 6*a*b^2*e^3*n + 9*a^2*b*e^3)*x*log(c) - 4*(2*b^3*e^3*n^3 - 6*a*b^2*e^3*n^2 + 9*a^2*b*e^3*n - 9*a^3*e^3)*x + 6*(85*b^3*d^3*n^3 - 66*a*b^2*d^3*n^2 + 18*a^2*b*d^3*n + 18*(b^3*e^3*n*x + b^3*d^3*n)*log(c)^2 + 2*(2*b^3*e^3*n^3 - 6*a*b^2*e^3*n^2 + 9*a^2*b*e^3*n)*x - 6*(11*b^3*d^3*n^2 - 6*a*b^2*d^3*n + 2*(b^3*e^3*n^2 - 3*a*b^2*e^3*n)*x)*log(c) - 3*(5*b^3*d*e^2*n^3 - 6*b^3*d*e^2*n^2*log(c) - 6*a*b^2*d*e^2*n^2)*x^(2/3) + 6*(11*b^3*d^2*e*n^3 - 6*b^3*d^2*e*n^2*log(c) - 6*a*b^2*d^2*e*n^2)*x^(1/3))*log(e*x^(1/3) + d) + 3*(19*b^3*d*e^2*n^3 + 18*b^3*d*e^2*n*log(c)^2 - 30*a*b^2*d*e^2*n^2 + 18*a^2*b*d*e^2*n - 6*(5*b^3*d*e^2*n^2 - 6*a*b^2*d*e^2*n)*log(c))*x^(2/3) - 6*(85*b^3*d^2*e*n^3 + 18*b^3*d^2*e*n*log(c)^2 - 66*a*b^2*d^2*e*n^2 + 18*a^2*b*d^2*e*n - 6*(11*b^3*d^2*e*n^2 - 6*a*b^2*d^2*e*n)*log(c))*x^(1/3))/e^3","A",0
460,0,0,0,1.099050," ","integrate((a+b*log(c*(d+e*x^(1/3))^n))^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)^{3} + 3 \, a b^{2} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)^{2} + 3 \, a^{2} b \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right) + a^{3}}{x}, x\right)"," ",0,"integral((b^3*log((e*x^(1/3) + d)^n*c)^3 + 3*a*b^2*log((e*x^(1/3) + d)^n*c)^2 + 3*a^2*b*log((e*x^(1/3) + d)^n*c) + a^3)/x, x)","F",0
461,0,0,0,1.167488," ","integrate((a+b*log(c*(d+e*x^(1/3))^n))^3/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)^{3} + 3 \, a b^{2} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)^{2} + 3 \, a^{2} b \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right) + a^{3}}{x^{2}}, x\right)"," ",0,"integral((b^3*log((e*x^(1/3) + d)^n*c)^3 + 3*a*b^2*log((e*x^(1/3) + d)^n*c)^2 + 3*a^2*b*log((e*x^(1/3) + d)^n*c) + a^3)/x^2, x)","F",0
462,0,0,0,0.862345," ","integrate((a+b*log(c*(d+e*x^(1/3))^n))^3/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)^{3} + 3 \, a b^{2} \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right)^{2} + 3 \, a^{2} b \log\left({\left(e x^{\frac{1}{3}} + d\right)}^{n} c\right) + a^{3}}{x^{3}}, x\right)"," ",0,"integral((b^3*log((e*x^(1/3) + d)^n*c)^3 + 3*a*b^2*log((e*x^(1/3) + d)^n*c)^2 + 3*a^2*b*log((e*x^(1/3) + d)^n*c) + a^3)/x^3, x)","F",0
463,1,129,0,0.982954," ","integrate(x^3*(a+b*log(c*(d+e*x^(2/3))^n)),x, algorithm=""fricas"")","\frac{60 \, b e^{6} x^{4} \log\left(c\right) + 20 \, b d^{3} e^{3} n x^{2} - 10 \, {\left(b e^{6} n - 6 \, a e^{6}\right)} x^{4} + 60 \, {\left(b e^{6} n x^{4} - b d^{6} n\right)} \log\left(e x^{\frac{2}{3}} + d\right) - 15 \, {\left(b d^{2} e^{4} n x^{2} - 4 \, b d^{5} e n\right)} x^{\frac{2}{3}} + 6 \, {\left(2 \, b d e^{5} n x^{3} - 5 \, b d^{4} e^{2} n x\right)} x^{\frac{1}{3}}}{240 \, e^{6}}"," ",0,"1/240*(60*b*e^6*x^4*log(c) + 20*b*d^3*e^3*n*x^2 - 10*(b*e^6*n - 6*a*e^6)*x^4 + 60*(b*e^6*n*x^4 - b*d^6*n)*log(e*x^(2/3) + d) - 15*(b*d^2*e^4*n*x^2 - 4*b*d^5*e*n)*x^(2/3) + 6*(2*b*d*e^5*n*x^3 - 5*b*d^4*e^2*n*x)*x^(1/3))/e^6","A",0
464,1,337,0,0.945609," ","integrate(x^2*(a+b*log(c*(d+e*x^(2/3))^n)),x, algorithm=""fricas"")","\left[\frac{315 \, b e^{4} n x^{3} \log\left(e x^{\frac{2}{3}} + d\right) + 315 \, b e^{4} x^{3} \log\left(c\right) - 126 \, b d^{2} e^{2} n x^{\frac{5}{3}} + 315 \, b d^{4} n \sqrt{-\frac{d}{e}} \log\left(\frac{e^{3} x^{2} - 2 \, d e^{2} x \sqrt{-\frac{d}{e}} - d^{3} + 2 \, {\left(e^{3} x \sqrt{-\frac{d}{e}} + d^{2} e\right)} x^{\frac{2}{3}} - 2 \, {\left(d e^{2} x - d^{2} e \sqrt{-\frac{d}{e}}\right)} x^{\frac{1}{3}}}{e^{3} x^{2} + d^{3}}\right) + 210 \, b d^{3} e n x - 35 \, {\left(2 \, b e^{4} n - 9 \, a e^{4}\right)} x^{3} + 90 \, {\left(b d e^{3} n x^{2} - 7 \, b d^{4} n\right)} x^{\frac{1}{3}}}{945 \, e^{4}}, \frac{315 \, b e^{4} n x^{3} \log\left(e x^{\frac{2}{3}} + d\right) + 315 \, b e^{4} x^{3} \log\left(c\right) - 126 \, b d^{2} e^{2} n x^{\frac{5}{3}} + 630 \, b d^{4} n \sqrt{\frac{d}{e}} \arctan\left(\frac{e x^{\frac{1}{3}} \sqrt{\frac{d}{e}}}{d}\right) + 210 \, b d^{3} e n x - 35 \, {\left(2 \, b e^{4} n - 9 \, a e^{4}\right)} x^{3} + 90 \, {\left(b d e^{3} n x^{2} - 7 \, b d^{4} n\right)} x^{\frac{1}{3}}}{945 \, e^{4}}\right]"," ",0,"[1/945*(315*b*e^4*n*x^3*log(e*x^(2/3) + d) + 315*b*e^4*x^3*log(c) - 126*b*d^2*e^2*n*x^(5/3) + 315*b*d^4*n*sqrt(-d/e)*log((e^3*x^2 - 2*d*e^2*x*sqrt(-d/e) - d^3 + 2*(e^3*x*sqrt(-d/e) + d^2*e)*x^(2/3) - 2*(d*e^2*x - d^2*e*sqrt(-d/e))*x^(1/3))/(e^3*x^2 + d^3)) + 210*b*d^3*e*n*x - 35*(2*b*e^4*n - 9*a*e^4)*x^3 + 90*(b*d*e^3*n*x^2 - 7*b*d^4*n)*x^(1/3))/e^4, 1/945*(315*b*e^4*n*x^3*log(e*x^(2/3) + d) + 315*b*e^4*x^3*log(c) - 126*b*d^2*e^2*n*x^(5/3) + 630*b*d^4*n*sqrt(d/e)*arctan(e*x^(1/3)*sqrt(d/e)/d) + 210*b*d^3*e*n*x - 35*(2*b*e^4*n - 9*a*e^4)*x^3 + 90*(b*d*e^3*n*x^2 - 7*b*d^4*n)*x^(1/3))/e^4]","A",0
465,1,83,0,1.123640," ","integrate(x*(a+b*log(c*(d+e*x^(2/3))^n)),x, algorithm=""fricas"")","\frac{6 \, b e^{3} x^{2} \log\left(c\right) + 3 \, b d e^{2} n x^{\frac{4}{3}} - 6 \, b d^{2} e n x^{\frac{2}{3}} - 2 \, {\left(b e^{3} n - 3 \, a e^{3}\right)} x^{2} + 6 \, {\left(b e^{3} n x^{2} + b d^{3} n\right)} \log\left(e x^{\frac{2}{3}} + d\right)}{12 \, e^{3}}"," ",0,"1/12*(6*b*e^3*x^2*log(c) + 3*b*d*e^2*n*x^(4/3) - 6*b*d^2*e*n*x^(2/3) - 2*(b*e^3*n - 3*a*e^3)*x^2 + 6*(b*e^3*n*x^2 + b*d^3*n)*log(e*x^(2/3) + d))/e^3","A",0
466,1,231,0,1.146687," ","integrate(a+b*log(c*(d+e*x^(2/3))^n),x, algorithm=""fricas"")","\left[\frac{3 \, b e n x \log\left(e x^{\frac{2}{3}} + d\right) + 3 \, b d n \sqrt{-\frac{d}{e}} \log\left(\frac{e^{3} x^{2} + 2 \, d e^{2} x \sqrt{-\frac{d}{e}} - d^{3} - 2 \, {\left(e^{3} x \sqrt{-\frac{d}{e}} - d^{2} e\right)} x^{\frac{2}{3}} - 2 \, {\left(d e^{2} x + d^{2} e \sqrt{-\frac{d}{e}}\right)} x^{\frac{1}{3}}}{e^{3} x^{2} + d^{3}}\right) + 3 \, b e x \log\left(c\right) + 6 \, b d n x^{\frac{1}{3}} - {\left(2 \, b e n - 3 \, a e\right)} x}{3 \, e}, \frac{3 \, b e n x \log\left(e x^{\frac{2}{3}} + d\right) - 6 \, b d n \sqrt{\frac{d}{e}} \arctan\left(\frac{e x^{\frac{1}{3}} \sqrt{\frac{d}{e}}}{d}\right) + 3 \, b e x \log\left(c\right) + 6 \, b d n x^{\frac{1}{3}} - {\left(2 \, b e n - 3 \, a e\right)} x}{3 \, e}\right]"," ",0,"[1/3*(3*b*e*n*x*log(e*x^(2/3) + d) + 3*b*d*n*sqrt(-d/e)*log((e^3*x^2 + 2*d*e^2*x*sqrt(-d/e) - d^3 - 2*(e^3*x*sqrt(-d/e) - d^2*e)*x^(2/3) - 2*(d*e^2*x + d^2*e*sqrt(-d/e))*x^(1/3))/(e^3*x^2 + d^3)) + 3*b*e*x*log(c) + 6*b*d*n*x^(1/3) - (2*b*e*n - 3*a*e)*x)/e, 1/3*(3*b*e*n*x*log(e*x^(2/3) + d) - 6*b*d*n*sqrt(d/e)*arctan(e*x^(1/3)*sqrt(d/e)/d) + 3*b*e*x*log(c) + 6*b*d*n*x^(1/3) - (2*b*e*n - 3*a*e)*x)/e]","A",0
467,0,0,0,0.798178," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right) + a}{x}, x\right)"," ",0,"integral((b*log((e*x^(2/3) + d)^n*c) + a)/x, x)","F",0
468,1,208,0,1.335891," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))/x^2,x, algorithm=""fricas"")","\left[\frac{b e n x \sqrt{-\frac{e}{d}} \log\left(\frac{e^{3} x^{2} + 2 \, d^{2} e x \sqrt{-\frac{e}{d}} - d^{3} - 2 \, {\left(d e^{2} x \sqrt{-\frac{e}{d}} - d^{2} e\right)} x^{\frac{2}{3}} - 2 \, {\left(d e^{2} x + d^{3} \sqrt{-\frac{e}{d}}\right)} x^{\frac{1}{3}}}{e^{3} x^{2} + d^{3}}\right) - b d n \log\left(e x^{\frac{2}{3}} + d\right) - 2 \, b e n x^{\frac{2}{3}} - b d \log\left(c\right) - a d}{d x}, -\frac{2 \, b e n x \sqrt{\frac{e}{d}} \arctan\left(x^{\frac{1}{3}} \sqrt{\frac{e}{d}}\right) + b d n \log\left(e x^{\frac{2}{3}} + d\right) + 2 \, b e n x^{\frac{2}{3}} + b d \log\left(c\right) + a d}{d x}\right]"," ",0,"[(b*e*n*x*sqrt(-e/d)*log((e^3*x^2 + 2*d^2*e*x*sqrt(-e/d) - d^3 - 2*(d*e^2*x*sqrt(-e/d) - d^2*e)*x^(2/3) - 2*(d*e^2*x + d^3*sqrt(-e/d))*x^(1/3))/(e^3*x^2 + d^3)) - b*d*n*log(e*x^(2/3) + d) - 2*b*e*n*x^(2/3) - b*d*log(c) - a*d)/(d*x), -(2*b*e*n*x*sqrt(e/d)*arctan(x^(1/3)*sqrt(e/d)) + b*d*n*log(e*x^(2/3) + d) + 2*b*e*n*x^(2/3) + b*d*log(c) + a*d)/(d*x)]","A",0
469,1,85,0,1.031124," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))/x^3,x, algorithm=""fricas"")","\frac{4 \, b e^{3} n x^{2} \log\left(x^{\frac{1}{3}}\right) + 2 \, b d e^{2} n x^{\frac{4}{3}} - b d^{2} e n x^{\frac{2}{3}} - 2 \, b d^{3} \log\left(c\right) - 2 \, a d^{3} - 2 \, {\left(b e^{3} n x^{2} + b d^{3} n\right)} \log\left(e x^{\frac{2}{3}} + d\right)}{4 \, d^{3} x^{2}}"," ",0,"1/4*(4*b*e^3*n*x^2*log(x^(1/3)) + 2*b*d*e^2*n*x^(4/3) - b*d^2*e*n*x^(2/3) - 2*b*d^3*log(c) - 2*a*d^3 - 2*(b*e^3*n*x^2 + b*d^3*n)*log(e*x^(2/3) + d))/(d^3*x^2)","A",0
470,1,313,0,1.010916," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))/x^4,x, algorithm=""fricas"")","\left[\frac{105 \, b e^{4} n x^{3} \sqrt{-\frac{e}{d}} \log\left(\frac{e^{3} x^{2} - 2 \, d^{2} e x \sqrt{-\frac{e}{d}} - d^{3} + 2 \, {\left(d e^{2} x \sqrt{-\frac{e}{d}} + d^{2} e\right)} x^{\frac{2}{3}} - 2 \, {\left(d e^{2} x - d^{3} \sqrt{-\frac{e}{d}}\right)} x^{\frac{1}{3}}}{e^{3} x^{2} + d^{3}}\right) - 70 \, b d e^{3} n x^{2} + 42 \, b d^{2} e^{2} n x^{\frac{4}{3}} - 105 \, b d^{4} n \log\left(e x^{\frac{2}{3}} + d\right) - 105 \, b d^{4} \log\left(c\right) - 105 \, a d^{4} + 30 \, {\left(7 \, b e^{4} n x^{2} - b d^{3} e n\right)} x^{\frac{2}{3}}}{315 \, d^{4} x^{3}}, \frac{210 \, b e^{4} n x^{3} \sqrt{\frac{e}{d}} \arctan\left(x^{\frac{1}{3}} \sqrt{\frac{e}{d}}\right) - 70 \, b d e^{3} n x^{2} + 42 \, b d^{2} e^{2} n x^{\frac{4}{3}} - 105 \, b d^{4} n \log\left(e x^{\frac{2}{3}} + d\right) - 105 \, b d^{4} \log\left(c\right) - 105 \, a d^{4} + 30 \, {\left(7 \, b e^{4} n x^{2} - b d^{3} e n\right)} x^{\frac{2}{3}}}{315 \, d^{4} x^{3}}\right]"," ",0,"[1/315*(105*b*e^4*n*x^3*sqrt(-e/d)*log((e^3*x^2 - 2*d^2*e*x*sqrt(-e/d) - d^3 + 2*(d*e^2*x*sqrt(-e/d) + d^2*e)*x^(2/3) - 2*(d*e^2*x - d^3*sqrt(-e/d))*x^(1/3))/(e^3*x^2 + d^3)) - 70*b*d*e^3*n*x^2 + 42*b*d^2*e^2*n*x^(4/3) - 105*b*d^4*n*log(e*x^(2/3) + d) - 105*b*d^4*log(c) - 105*a*d^4 + 30*(7*b*e^4*n*x^2 - b*d^3*e*n)*x^(2/3))/(d^4*x^3), 1/315*(210*b*e^4*n*x^3*sqrt(e/d)*arctan(x^(1/3)*sqrt(e/d)) - 70*b*d*e^3*n*x^2 + 42*b*d^2*e^2*n*x^(4/3) - 105*b*d^4*n*log(e*x^(2/3) + d) - 105*b*d^4*log(c) - 105*a*d^4 + 30*(7*b*e^4*n*x^2 - b*d^3*e*n)*x^(2/3))/(d^4*x^3)]","A",0
471,1,508,0,1.287869," ","integrate(x^3*(a+b*log(c*(d+e*x^(2/3))^n))^2,x, algorithm=""fricas"")","\frac{1800 \, b^{2} e^{6} x^{4} \log\left(c\right)^{2} + 100 \, {\left(b^{2} e^{6} n^{2} - 6 \, a b e^{6} n + 18 \, a^{2} e^{6}\right)} x^{4} - 60 \, {\left(19 \, b^{2} d^{3} e^{3} n^{2} - 20 \, a b d^{3} e^{3} n\right)} x^{2} + 1800 \, {\left(b^{2} e^{6} n^{2} x^{4} - b^{2} d^{6} n^{2}\right)} \log\left(e x^{\frac{2}{3}} + d\right)^{2} + 60 \, {\left(20 \, b^{2} d^{3} e^{3} n^{2} x^{2} + 147 \, b^{2} d^{6} n^{2} - 60 \, a b d^{6} n - 10 \, {\left(b^{2} e^{6} n^{2} - 6 \, a b e^{6} n\right)} x^{4} + 60 \, {\left(b^{2} e^{6} n x^{4} - b^{2} d^{6} n\right)} \log\left(c\right) - 15 \, {\left(b^{2} d^{2} e^{4} n^{2} x^{2} - 4 \, b^{2} d^{5} e n^{2}\right)} x^{\frac{2}{3}} + 6 \, {\left(2 \, b^{2} d e^{5} n^{2} x^{3} - 5 \, b^{2} d^{4} e^{2} n^{2} x\right)} x^{\frac{1}{3}}\right)} \log\left(e x^{\frac{2}{3}} + d\right) + 600 \, {\left(2 \, b^{2} d^{3} e^{3} n x^{2} - {\left(b^{2} e^{6} n - 6 \, a b e^{6}\right)} x^{4}\right)} \log\left(c\right) - 15 \, {\left(588 \, b^{2} d^{5} e n^{2} - 240 \, a b d^{5} e n - {\left(37 \, b^{2} d^{2} e^{4} n^{2} - 60 \, a b d^{2} e^{4} n\right)} x^{2} + 60 \, {\left(b^{2} d^{2} e^{4} n x^{2} - 4 \, b^{2} d^{5} e n\right)} \log\left(c\right)\right)} x^{\frac{2}{3}} - 6 \, {\left(4 \, {\left(11 \, b^{2} d e^{5} n^{2} - 30 \, a b d e^{5} n\right)} x^{3} - 15 \, {\left(29 \, b^{2} d^{4} e^{2} n^{2} - 20 \, a b d^{4} e^{2} n\right)} x - 60 \, {\left(2 \, b^{2} d e^{5} n x^{3} - 5 \, b^{2} d^{4} e^{2} n x\right)} \log\left(c\right)\right)} x^{\frac{1}{3}}}{7200 \, e^{6}}"," ",0,"1/7200*(1800*b^2*e^6*x^4*log(c)^2 + 100*(b^2*e^6*n^2 - 6*a*b*e^6*n + 18*a^2*e^6)*x^4 - 60*(19*b^2*d^3*e^3*n^2 - 20*a*b*d^3*e^3*n)*x^2 + 1800*(b^2*e^6*n^2*x^4 - b^2*d^6*n^2)*log(e*x^(2/3) + d)^2 + 60*(20*b^2*d^3*e^3*n^2*x^2 + 147*b^2*d^6*n^2 - 60*a*b*d^6*n - 10*(b^2*e^6*n^2 - 6*a*b*e^6*n)*x^4 + 60*(b^2*e^6*n*x^4 - b^2*d^6*n)*log(c) - 15*(b^2*d^2*e^4*n^2*x^2 - 4*b^2*d^5*e*n^2)*x^(2/3) + 6*(2*b^2*d*e^5*n^2*x^3 - 5*b^2*d^4*e^2*n^2*x)*x^(1/3))*log(e*x^(2/3) + d) + 600*(2*b^2*d^3*e^3*n*x^2 - (b^2*e^6*n - 6*a*b*e^6)*x^4)*log(c) - 15*(588*b^2*d^5*e*n^2 - 240*a*b*d^5*e*n - (37*b^2*d^2*e^4*n^2 - 60*a*b*d^2*e^4*n)*x^2 + 60*(b^2*d^2*e^4*n*x^2 - 4*b^2*d^5*e*n)*log(c))*x^(2/3) - 6*(4*(11*b^2*d*e^5*n^2 - 30*a*b*d*e^5*n)*x^3 - 15*(29*b^2*d^4*e^2*n^2 - 20*a*b*d^4*e^2*n)*x - 60*(2*b^2*d*e^5*n*x^3 - 5*b^2*d^4*e^2*n*x)*log(c))*x^(1/3))/e^6","A",0
472,1,304,0,1.232546," ","integrate(x*(a+b*log(c*(d+e*x^(2/3))^n))^2,x, algorithm=""fricas"")","\frac{18 \, b^{2} e^{3} x^{2} \log\left(c\right)^{2} - 12 \, {\left(b^{2} e^{3} n - 3 \, a b e^{3}\right)} x^{2} \log\left(c\right) + 2 \, {\left(2 \, b^{2} e^{3} n^{2} - 6 \, a b e^{3} n + 9 \, a^{2} e^{3}\right)} x^{2} + 18 \, {\left(b^{2} e^{3} n^{2} x^{2} + b^{2} d^{3} n^{2}\right)} \log\left(e x^{\frac{2}{3}} + d\right)^{2} + 6 \, {\left(3 \, b^{2} d e^{2} n^{2} x^{\frac{4}{3}} - 6 \, b^{2} d^{2} e n^{2} x^{\frac{2}{3}} - 11 \, b^{2} d^{3} n^{2} + 6 \, a b d^{3} n - 2 \, {\left(b^{2} e^{3} n^{2} - 3 \, a b e^{3} n\right)} x^{2} + 6 \, {\left(b^{2} e^{3} n x^{2} + b^{2} d^{3} n\right)} \log\left(c\right)\right)} \log\left(e x^{\frac{2}{3}} + d\right) + 6 \, {\left(11 \, b^{2} d^{2} e n^{2} - 6 \, b^{2} d^{2} e n \log\left(c\right) - 6 \, a b d^{2} e n\right)} x^{\frac{2}{3}} + 3 \, {\left(6 \, b^{2} d e^{2} n x \log\left(c\right) - {\left(5 \, b^{2} d e^{2} n^{2} - 6 \, a b d e^{2} n\right)} x\right)} x^{\frac{1}{3}}}{36 \, e^{3}}"," ",0,"1/36*(18*b^2*e^3*x^2*log(c)^2 - 12*(b^2*e^3*n - 3*a*b*e^3)*x^2*log(c) + 2*(2*b^2*e^3*n^2 - 6*a*b*e^3*n + 9*a^2*e^3)*x^2 + 18*(b^2*e^3*n^2*x^2 + b^2*d^3*n^2)*log(e*x^(2/3) + d)^2 + 6*(3*b^2*d*e^2*n^2*x^(4/3) - 6*b^2*d^2*e*n^2*x^(2/3) - 11*b^2*d^3*n^2 + 6*a*b*d^3*n - 2*(b^2*e^3*n^2 - 3*a*b*e^3*n)*x^2 + 6*(b^2*e^3*n*x^2 + b^2*d^3*n)*log(c))*log(e*x^(2/3) + d) + 6*(11*b^2*d^2*e*n^2 - 6*b^2*d^2*e*n*log(c) - 6*a*b*d^2*e*n)*x^(2/3) + 3*(6*b^2*d*e^2*n*x*log(c) - (5*b^2*d*e^2*n^2 - 6*a*b*d*e^2*n)*x)*x^(1/3))/e^3","A",0
473,0,0,0,1.201890," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{2} + 2 \, a b \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*log((e*x^(2/3) + d)^n*c)^2 + 2*a*b*log((e*x^(2/3) + d)^n*c) + a^2)/x, x)","F",0
474,0,0,0,1.137222," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{2} + 2 \, a b \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right) + a^{2}}{x^{3}}, x\right)"," ",0,"integral((b^2*log((e*x^(2/3) + d)^n*c)^2 + 2*a*b*log((e*x^(2/3) + d)^n*c) + a^2)/x^3, x)","F",0
475,0,0,0,1.228323," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))^2/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{2} + 2 \, a b \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right) + a^{2}}{x^{5}}, x\right)"," ",0,"integral((b^2*log((e*x^(2/3) + d)^n*c)^2 + 2*a*b*log((e*x^(2/3) + d)^n*c) + a^2)/x^5, x)","F",0
476,0,0,0,1.275329," ","integrate(x^2*(a+b*log(c*(d+e*x^(2/3))^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{2} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{2} + 2 \, a b x^{2} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right) + a^{2} x^{2}, x\right)"," ",0,"integral(b^2*x^2*log((e*x^(2/3) + d)^n*c)^2 + 2*a*b*x^2*log((e*x^(2/3) + d)^n*c) + a^2*x^2, x)","F",0
477,0,0,0,1.125149," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{2} + 2 \, a b \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right) + a^{2}, x\right)"," ",0,"integral(b^2*log((e*x^(2/3) + d)^n*c)^2 + 2*a*b*log((e*x^(2/3) + d)^n*c) + a^2, x)","F",0
478,0,0,0,0.966970," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{2} + 2 \, a b \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right) + a^{2}}{x^{2}}, x\right)"," ",0,"integral((b^2*log((e*x^(2/3) + d)^n*c)^2 + 2*a*b*log((e*x^(2/3) + d)^n*c) + a^2)/x^2, x)","F",0
479,0,0,0,1.197768," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{2} + 2 \, a b \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right) + a^{2}}{x^{4}}, x\right)"," ",0,"integral((b^2*log((e*x^(2/3) + d)^n*c)^2 + 2*a*b*log((e*x^(2/3) + d)^n*c) + a^2)/x^4, x)","F",0
480,0,0,0,1.157399," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))^2/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{2} + 2 \, a b \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right) + a^{2}}{x^{6}}, x\right)"," ",0,"integral((b^2*log((e*x^(2/3) + d)^n*c)^2 + 2*a*b*log((e*x^(2/3) + d)^n*c) + a^2)/x^6, x)","F",0
481,1,1241,0,1.709557," ","integrate(x^3*(a+b*log(c*(d+e*x^(2/3))^n))^3,x, algorithm=""fricas"")","\frac{36000 \, b^{3} e^{6} x^{4} \log\left(c\right)^{3} - 1000 \, {\left(b^{3} e^{6} n^{3} - 6 \, a b^{2} e^{6} n^{2} + 18 \, a^{2} b e^{6} n - 36 \, a^{3} e^{6}\right)} x^{4} + 36000 \, {\left(b^{3} e^{6} n^{3} x^{4} - b^{3} d^{6} n^{3}\right)} \log\left(e x^{\frac{2}{3}} + d\right)^{3} + 20 \, {\left(2059 \, b^{3} d^{3} e^{3} n^{3} - 3420 \, a b^{2} d^{3} e^{3} n^{2} + 1800 \, a^{2} b d^{3} e^{3} n\right)} x^{2} + 1800 \, {\left(20 \, b^{3} d^{3} e^{3} n^{3} x^{2} + 147 \, b^{3} d^{6} n^{3} - 60 \, a b^{2} d^{6} n^{2} - 10 \, {\left(b^{3} e^{6} n^{3} - 6 \, a b^{2} e^{6} n^{2}\right)} x^{4} + 60 \, {\left(b^{3} e^{6} n^{2} x^{4} - b^{3} d^{6} n^{2}\right)} \log\left(c\right) - 15 \, {\left(b^{3} d^{2} e^{4} n^{3} x^{2} - 4 \, b^{3} d^{5} e n^{3}\right)} x^{\frac{2}{3}} + 6 \, {\left(2 \, b^{3} d e^{5} n^{3} x^{3} - 5 \, b^{3} d^{4} e^{2} n^{3} x\right)} x^{\frac{1}{3}}\right)} \log\left(e x^{\frac{2}{3}} + d\right)^{2} + 18000 \, {\left(2 \, b^{3} d^{3} e^{3} n x^{2} - {\left(b^{3} e^{6} n - 6 \, a b^{2} e^{6}\right)} x^{4}\right)} \log\left(c\right)^{2} - 60 \, {\left(13489 \, b^{3} d^{6} n^{3} - 8820 \, a b^{2} d^{6} n^{2} + 1800 \, a^{2} b d^{6} n - 100 \, {\left(b^{3} e^{6} n^{3} - 6 \, a b^{2} e^{6} n^{2} + 18 \, a^{2} b e^{6} n\right)} x^{4} + 60 \, {\left(19 \, b^{3} d^{3} e^{3} n^{3} - 20 \, a b^{2} d^{3} e^{3} n^{2}\right)} x^{2} - 1800 \, {\left(b^{3} e^{6} n x^{4} - b^{3} d^{6} n\right)} \log\left(c\right)^{2} - 60 \, {\left(20 \, b^{3} d^{3} e^{3} n^{2} x^{2} + 147 \, b^{3} d^{6} n^{2} - 60 \, a b^{2} d^{6} n - 10 \, {\left(b^{3} e^{6} n^{2} - 6 \, a b^{2} e^{6} n\right)} x^{4}\right)} \log\left(c\right) + 15 \, {\left(588 \, b^{3} d^{5} e n^{3} - 240 \, a b^{2} d^{5} e n^{2} - {\left(37 \, b^{3} d^{2} e^{4} n^{3} - 60 \, a b^{2} d^{2} e^{4} n^{2}\right)} x^{2} + 60 \, {\left(b^{3} d^{2} e^{4} n^{2} x^{2} - 4 \, b^{3} d^{5} e n^{2}\right)} \log\left(c\right)\right)} x^{\frac{2}{3}} + 6 \, {\left(4 \, {\left(11 \, b^{3} d e^{5} n^{3} - 30 \, a b^{2} d e^{5} n^{2}\right)} x^{3} - 15 \, {\left(29 \, b^{3} d^{4} e^{2} n^{3} - 20 \, a b^{2} d^{4} e^{2} n^{2}\right)} x - 60 \, {\left(2 \, b^{3} d e^{5} n^{2} x^{3} - 5 \, b^{3} d^{4} e^{2} n^{2} x\right)} \log\left(c\right)\right)} x^{\frac{1}{3}}\right)} \log\left(e x^{\frac{2}{3}} + d\right) + 1200 \, {\left(5 \, {\left(b^{3} e^{6} n^{2} - 6 \, a b^{2} e^{6} n + 18 \, a^{2} b e^{6}\right)} x^{4} - 3 \, {\left(19 \, b^{3} d^{3} e^{3} n^{2} - 20 \, a b^{2} d^{3} e^{3} n\right)} x^{2}\right)} \log\left(c\right) + 15 \, {\left(53956 \, b^{3} d^{5} e n^{3} - 35280 \, a b^{2} d^{5} e n^{2} + 7200 \, a^{2} b d^{5} e n - {\left(919 \, b^{3} d^{2} e^{4} n^{3} - 2220 \, a b^{2} d^{2} e^{4} n^{2} + 1800 \, a^{2} b d^{2} e^{4} n\right)} x^{2} - 1800 \, {\left(b^{3} d^{2} e^{4} n x^{2} - 4 \, b^{3} d^{5} e n\right)} \log\left(c\right)^{2} - 60 \, {\left(588 \, b^{3} d^{5} e n^{2} - 240 \, a b^{2} d^{5} e n - {\left(37 \, b^{3} d^{2} e^{4} n^{2} - 60 \, a b^{2} d^{2} e^{4} n\right)} x^{2}\right)} \log\left(c\right)\right)} x^{\frac{2}{3}} + 6 \, {\left(8 \, {\left(91 \, b^{3} d e^{5} n^{3} - 330 \, a b^{2} d e^{5} n^{2} + 450 \, a^{2} b d e^{5} n\right)} x^{3} + 1800 \, {\left(2 \, b^{3} d e^{5} n x^{3} - 5 \, b^{3} d^{4} e^{2} n x\right)} \log\left(c\right)^{2} - 5 \, {\left(4669 \, b^{3} d^{4} e^{2} n^{3} - 5220 \, a b^{2} d^{4} e^{2} n^{2} + 1800 \, a^{2} b d^{4} e^{2} n\right)} x - 60 \, {\left(4 \, {\left(11 \, b^{3} d e^{5} n^{2} - 30 \, a b^{2} d e^{5} n\right)} x^{3} - 15 \, {\left(29 \, b^{3} d^{4} e^{2} n^{2} - 20 \, a b^{2} d^{4} e^{2} n\right)} x\right)} \log\left(c\right)\right)} x^{\frac{1}{3}}}{144000 \, e^{6}}"," ",0,"1/144000*(36000*b^3*e^6*x^4*log(c)^3 - 1000*(b^3*e^6*n^3 - 6*a*b^2*e^6*n^2 + 18*a^2*b*e^6*n - 36*a^3*e^6)*x^4 + 36000*(b^3*e^6*n^3*x^4 - b^3*d^6*n^3)*log(e*x^(2/3) + d)^3 + 20*(2059*b^3*d^3*e^3*n^3 - 3420*a*b^2*d^3*e^3*n^2 + 1800*a^2*b*d^3*e^3*n)*x^2 + 1800*(20*b^3*d^3*e^3*n^3*x^2 + 147*b^3*d^6*n^3 - 60*a*b^2*d^6*n^2 - 10*(b^3*e^6*n^3 - 6*a*b^2*e^6*n^2)*x^4 + 60*(b^3*e^6*n^2*x^4 - b^3*d^6*n^2)*log(c) - 15*(b^3*d^2*e^4*n^3*x^2 - 4*b^3*d^5*e*n^3)*x^(2/3) + 6*(2*b^3*d*e^5*n^3*x^3 - 5*b^3*d^4*e^2*n^3*x)*x^(1/3))*log(e*x^(2/3) + d)^2 + 18000*(2*b^3*d^3*e^3*n*x^2 - (b^3*e^6*n - 6*a*b^2*e^6)*x^4)*log(c)^2 - 60*(13489*b^3*d^6*n^3 - 8820*a*b^2*d^6*n^2 + 1800*a^2*b*d^6*n - 100*(b^3*e^6*n^3 - 6*a*b^2*e^6*n^2 + 18*a^2*b*e^6*n)*x^4 + 60*(19*b^3*d^3*e^3*n^3 - 20*a*b^2*d^3*e^3*n^2)*x^2 - 1800*(b^3*e^6*n*x^4 - b^3*d^6*n)*log(c)^2 - 60*(20*b^3*d^3*e^3*n^2*x^2 + 147*b^3*d^6*n^2 - 60*a*b^2*d^6*n - 10*(b^3*e^6*n^2 - 6*a*b^2*e^6*n)*x^4)*log(c) + 15*(588*b^3*d^5*e*n^3 - 240*a*b^2*d^5*e*n^2 - (37*b^3*d^2*e^4*n^3 - 60*a*b^2*d^2*e^4*n^2)*x^2 + 60*(b^3*d^2*e^4*n^2*x^2 - 4*b^3*d^5*e*n^2)*log(c))*x^(2/3) + 6*(4*(11*b^3*d*e^5*n^3 - 30*a*b^2*d*e^5*n^2)*x^3 - 15*(29*b^3*d^4*e^2*n^3 - 20*a*b^2*d^4*e^2*n^2)*x - 60*(2*b^3*d*e^5*n^2*x^3 - 5*b^3*d^4*e^2*n^2*x)*log(c))*x^(1/3))*log(e*x^(2/3) + d) + 1200*(5*(b^3*e^6*n^2 - 6*a*b^2*e^6*n + 18*a^2*b*e^6)*x^4 - 3*(19*b^3*d^3*e^3*n^2 - 20*a*b^2*d^3*e^3*n)*x^2)*log(c) + 15*(53956*b^3*d^5*e*n^3 - 35280*a*b^2*d^5*e*n^2 + 7200*a^2*b*d^5*e*n - (919*b^3*d^2*e^4*n^3 - 2220*a*b^2*d^2*e^4*n^2 + 1800*a^2*b*d^2*e^4*n)*x^2 - 1800*(b^3*d^2*e^4*n*x^2 - 4*b^3*d^5*e*n)*log(c)^2 - 60*(588*b^3*d^5*e*n^2 - 240*a*b^2*d^5*e*n - (37*b^3*d^2*e^4*n^2 - 60*a*b^2*d^2*e^4*n)*x^2)*log(c))*x^(2/3) + 6*(8*(91*b^3*d*e^5*n^3 - 330*a*b^2*d*e^5*n^2 + 450*a^2*b*d*e^5*n)*x^3 + 1800*(2*b^3*d*e^5*n*x^3 - 5*b^3*d^4*e^2*n*x)*log(c)^2 - 5*(4669*b^3*d^4*e^2*n^3 - 5220*a*b^2*d^4*e^2*n^2 + 1800*a^2*b*d^4*e^2*n)*x - 60*(4*(11*b^3*d*e^5*n^2 - 30*a*b^2*d*e^5*n)*x^3 - 15*(29*b^3*d^4*e^2*n^2 - 20*a*b^2*d^4*e^2*n)*x)*log(c))*x^(1/3))/e^6","A",0
482,1,720,0,1.189221," ","integrate(x*(a+b*log(c*(d+e*x^(2/3))^n))^3,x, algorithm=""fricas"")","\frac{36 \, b^{3} e^{3} x^{2} \log\left(c\right)^{3} - 36 \, {\left(b^{3} e^{3} n - 3 \, a b^{2} e^{3}\right)} x^{2} \log\left(c\right)^{2} + 36 \, {\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} + 12 \, {\left(2 \, b^{3} e^{3} n^{2} - 6 \, a b^{2} e^{3} n + 9 \, a^{2} b e^{3}\right)} x^{2} \log\left(c\right) - 4 \, {\left(2 \, b^{3} e^{3} n^{3} - 6 \, a b^{2} e^{3} n^{2} + 9 \, a^{2} b e^{3} n - 9 \, a^{3} e^{3}\right)} x^{2} + 18 \, {\left(3 \, b^{3} d e^{2} n^{3} x^{\frac{4}{3}} - 6 \, b^{3} d^{2} e n^{3} x^{\frac{2}{3}} - 11 \, b^{3} d^{3} n^{3} + 6 \, a b^{2} d^{3} n^{2} - 2 \, {\left(b^{3} e^{3} n^{3} - 3 \, a b^{2} e^{3} n^{2}\right)} x^{2} + 6 \, {\left(b^{3} e^{3} n^{2} x^{2} + b^{3} d^{3} n^{2}\right)} \log\left(c\right)\right)} \log\left(e x^{\frac{2}{3}} + d\right)^{2} + 6 \, {\left(85 \, b^{3} d^{3} n^{3} - 66 \, a b^{2} d^{3} n^{2} + 18 \, a^{2} b d^{3} n + 2 \, {\left(2 \, b^{3} e^{3} n^{3} - 6 \, a b^{2} e^{3} n^{2} + 9 \, a^{2} b e^{3} n\right)} x^{2} + 18 \, {\left(b^{3} e^{3} n x^{2} + b^{3} d^{3} n\right)} \log\left(c\right)^{2} - 6 \, {\left(11 \, b^{3} d^{3} n^{2} - 6 \, a b^{2} d^{3} n + 2 \, {\left(b^{3} e^{3} n^{2} - 3 \, a b^{2} e^{3} n\right)} x^{2}\right)} \log\left(c\right) + 6 \, {\left(11 \, b^{3} d^{2} e n^{3} - 6 \, b^{3} d^{2} e n^{2} \log\left(c\right) - 6 \, a b^{2} d^{2} e n^{2}\right)} x^{\frac{2}{3}} + 3 \, {\left(6 \, b^{3} d e^{2} n^{2} x \log\left(c\right) - {\left(5 \, b^{3} d e^{2} n^{3} - 6 \, a b^{2} d e^{2} n^{2}\right)} x\right)} x^{\frac{1}{3}}\right)} \log\left(e x^{\frac{2}{3}} + d\right) - 6 \, {\left(85 \, b^{3} d^{2} e n^{3} + 18 \, b^{3} d^{2} e n \log\left(c\right)^{2} - 66 \, a b^{2} d^{2} e n^{2} + 18 \, a^{2} b d^{2} e n - 6 \, {\left(11 \, b^{3} d^{2} e n^{2} - 6 \, a b^{2} d^{2} e n\right)} \log\left(c\right)\right)} x^{\frac{2}{3}} + 3 \, {\left(18 \, b^{3} d e^{2} n x \log\left(c\right)^{2} - 6 \, {\left(5 \, b^{3} d e^{2} n^{2} - 6 \, a b^{2} d e^{2} n\right)} x \log\left(c\right) + {\left(19 \, b^{3} d e^{2} n^{3} - 30 \, a b^{2} d e^{2} n^{2} + 18 \, a^{2} b d e^{2} n\right)} x\right)} x^{\frac{1}{3}}}{72 \, e^{3}}"," ",0,"1/72*(36*b^3*e^3*x^2*log(c)^3 - 36*(b^3*e^3*n - 3*a*b^2*e^3)*x^2*log(c)^2 + 36*(b^3*e^3*n^3*x^2 + b^3*d^3*n^3)*log(e*x^(2/3) + d)^3 + 12*(2*b^3*e^3*n^2 - 6*a*b^2*e^3*n + 9*a^2*b*e^3)*x^2*log(c) - 4*(2*b^3*e^3*n^3 - 6*a*b^2*e^3*n^2 + 9*a^2*b*e^3*n - 9*a^3*e^3)*x^2 + 18*(3*b^3*d*e^2*n^3*x^(4/3) - 6*b^3*d^2*e*n^3*x^(2/3) - 11*b^3*d^3*n^3 + 6*a*b^2*d^3*n^2 - 2*(b^3*e^3*n^3 - 3*a*b^2*e^3*n^2)*x^2 + 6*(b^3*e^3*n^2*x^2 + b^3*d^3*n^2)*log(c))*log(e*x^(2/3) + d)^2 + 6*(85*b^3*d^3*n^3 - 66*a*b^2*d^3*n^2 + 18*a^2*b*d^3*n + 2*(2*b^3*e^3*n^3 - 6*a*b^2*e^3*n^2 + 9*a^2*b*e^3*n)*x^2 + 18*(b^3*e^3*n*x^2 + b^3*d^3*n)*log(c)^2 - 6*(11*b^3*d^3*n^2 - 6*a*b^2*d^3*n + 2*(b^3*e^3*n^2 - 3*a*b^2*e^3*n)*x^2)*log(c) + 6*(11*b^3*d^2*e*n^3 - 6*b^3*d^2*e*n^2*log(c) - 6*a*b^2*d^2*e*n^2)*x^(2/3) + 3*(6*b^3*d*e^2*n^2*x*log(c) - (5*b^3*d*e^2*n^3 - 6*a*b^2*d*e^2*n^2)*x)*x^(1/3))*log(e*x^(2/3) + d) - 6*(85*b^3*d^2*e*n^3 + 18*b^3*d^2*e*n*log(c)^2 - 66*a*b^2*d^2*e*n^2 + 18*a^2*b*d^2*e*n - 6*(11*b^3*d^2*e*n^2 - 6*a*b^2*d^2*e*n)*log(c))*x^(2/3) + 3*(18*b^3*d*e^2*n*x*log(c)^2 - 6*(5*b^3*d*e^2*n^2 - 6*a*b^2*d*e^2*n)*x*log(c) + (19*b^3*d*e^2*n^3 - 30*a*b^2*d*e^2*n^2 + 18*a^2*b*d*e^2*n)*x)*x^(1/3))/e^3","A",0
483,0,0,0,1.053496," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{3} + 3 \, a b^{2} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{2} + 3 \, a^{2} b \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right) + a^{3}}{x}, x\right)"," ",0,"integral((b^3*log((e*x^(2/3) + d)^n*c)^3 + 3*a*b^2*log((e*x^(2/3) + d)^n*c)^2 + 3*a^2*b*log((e*x^(2/3) + d)^n*c) + a^3)/x, x)","F",0
484,0,0,0,0.901502," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))^3/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{3} + 3 \, a b^{2} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{2} + 3 \, a^{2} b \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right) + a^{3}}{x^{3}}, x\right)"," ",0,"integral((b^3*log((e*x^(2/3) + d)^n*c)^3 + 3*a*b^2*log((e*x^(2/3) + d)^n*c)^2 + 3*a^2*b*log((e*x^(2/3) + d)^n*c) + a^3)/x^3, x)","F",0
485,0,0,0,1.193407," ","integrate(x^2*(a+b*log(c*(d+e*x^(2/3))^n))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{2} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{3} + 3 \, a b^{2} x^{2} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{2} + 3 \, a^{2} b x^{2} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right) + a^{3} x^{2}, x\right)"," ",0,"integral(b^3*x^2*log((e*x^(2/3) + d)^n*c)^3 + 3*a*b^2*x^2*log((e*x^(2/3) + d)^n*c)^2 + 3*a^2*b*x^2*log((e*x^(2/3) + d)^n*c) + a^3*x^2, x)","F",0
486,0,0,0,1.252969," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{3} + 3 \, a b^{2} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{2} + 3 \, a^{2} b \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right) + a^{3}, x\right)"," ",0,"integral(b^3*log((e*x^(2/3) + d)^n*c)^3 + 3*a*b^2*log((e*x^(2/3) + d)^n*c)^2 + 3*a^2*b*log((e*x^(2/3) + d)^n*c) + a^3, x)","F",0
487,0,0,0,1.040189," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))^3/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{3} + 3 \, a b^{2} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{2} + 3 \, a^{2} b \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right) + a^{3}}{x^{2}}, x\right)"," ",0,"integral((b^3*log((e*x^(2/3) + d)^n*c)^3 + 3*a*b^2*log((e*x^(2/3) + d)^n*c)^2 + 3*a^2*b*log((e*x^(2/3) + d)^n*c) + a^3)/x^2, x)","F",0
488,0,0,0,1.221967," ","integrate((a+b*log(c*(d+e*x^(2/3))^n))^3/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{3} + 3 \, a b^{2} \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right)^{2} + 3 \, a^{2} b \log\left({\left(e x^{\frac{2}{3}} + d\right)}^{n} c\right) + a^{3}}{x^{4}}, x\right)"," ",0,"integral((b^3*log((e*x^(2/3) + d)^n*c)^3 + 3*a*b^2*log((e*x^(2/3) + d)^n*c)^2 + 3*a^2*b*log((e*x^(2/3) + d)^n*c) + a^3)/x^4, x)","F",0
489,1,232,0,0.937218," ","integrate(x^3*(a+b*log(c*(d+e/x^(1/3))^n)),x, algorithm=""fricas"")","\frac{27720 \, b d^{12} x^{4} \log\left(c\right) + 3080 \, b d^{9} e^{3} n x^{3} + 27720 \, a d^{12} x^{4} - 4620 \, b d^{6} e^{6} n x^{2} + 9240 \, b d^{3} e^{9} n x - 27720 \, b d^{12} n \log\left(x^{\frac{1}{3}}\right) + 27720 \, {\left(b d^{12} - b e^{12}\right)} n \log\left(d x^{\frac{1}{3}} + e\right) + 27720 \, {\left(b d^{12} n x^{4} - b d^{12} n\right)} \log\left(\frac{d x + e x^{\frac{2}{3}}}{x}\right) + 63 \, {\left(40 \, b d^{11} e n x^{3} - 55 \, b d^{8} e^{4} n x^{2} + 88 \, b d^{5} e^{7} n x - 220 \, b d^{2} e^{10} n\right)} x^{\frac{2}{3}} - 198 \, {\left(14 \, b d^{10} e^{2} n x^{3} - 20 \, b d^{7} e^{5} n x^{2} + 35 \, b d^{4} e^{8} n x - 140 \, b d e^{11} n\right)} x^{\frac{1}{3}}}{110880 \, d^{12}}"," ",0,"1/110880*(27720*b*d^12*x^4*log(c) + 3080*b*d^9*e^3*n*x^3 + 27720*a*d^12*x^4 - 4620*b*d^6*e^6*n*x^2 + 9240*b*d^3*e^9*n*x - 27720*b*d^12*n*log(x^(1/3)) + 27720*(b*d^12 - b*e^12)*n*log(d*x^(1/3) + e) + 27720*(b*d^12*n*x^4 - b*d^12*n)*log((d*x + e*x^(2/3))/x) + 63*(40*b*d^11*e*n*x^3 - 55*b*d^8*e^4*n*x^2 + 88*b*d^5*e^7*n*x - 220*b*d^2*e^10*n)*x^(2/3) - 198*(14*b*d^10*e^2*n*x^3 - 20*b*d^7*e^5*n*x^2 + 35*b*d^4*e^8*n*x - 140*b*d*e^11*n)*x^(1/3))/d^12","A",0
490,1,192,0,0.807632," ","integrate(x^2*(a+b*log(c*(d+e/x^(1/3))^n)),x, algorithm=""fricas"")","\frac{840 \, b d^{9} x^{3} \log\left(c\right) + 140 \, b d^{6} e^{3} n x^{2} + 840 \, a d^{9} x^{3} - 280 \, b d^{3} e^{6} n x - 840 \, b d^{9} n \log\left(x^{\frac{1}{3}}\right) + 840 \, {\left(b d^{9} + b e^{9}\right)} n \log\left(d x^{\frac{1}{3}} + e\right) + 840 \, {\left(b d^{9} n x^{3} - b d^{9} n\right)} \log\left(\frac{d x + e x^{\frac{2}{3}}}{x}\right) + 21 \, {\left(5 \, b d^{8} e n x^{2} - 8 \, b d^{5} e^{4} n x + 20 \, b d^{2} e^{7} n\right)} x^{\frac{2}{3}} - 30 \, {\left(4 \, b d^{7} e^{2} n x^{2} - 7 \, b d^{4} e^{5} n x + 28 \, b d e^{8} n\right)} x^{\frac{1}{3}}}{2520 \, d^{9}}"," ",0,"1/2520*(840*b*d^9*x^3*log(c) + 140*b*d^6*e^3*n*x^2 + 840*a*d^9*x^3 - 280*b*d^3*e^6*n*x - 840*b*d^9*n*log(x^(1/3)) + 840*(b*d^9 + b*e^9)*n*log(d*x^(1/3) + e) + 840*(b*d^9*n*x^3 - b*d^9*n)*log((d*x + e*x^(2/3))/x) + 21*(5*b*d^8*e*n*x^2 - 8*b*d^5*e^4*n*x + 20*b*d^2*e^7*n)*x^(2/3) - 30*(4*b*d^7*e^2*n*x^2 - 7*b*d^4*e^5*n*x + 28*b*d*e^8*n)*x^(1/3))/d^9","A",0
491,1,153,0,0.858282," ","integrate(x*(a+b*log(c*(d+e/x^(1/3))^n)),x, algorithm=""fricas"")","\frac{60 \, b d^{6} x^{2} \log\left(c\right) + 20 \, b d^{3} e^{3} n x + 60 \, a d^{6} x^{2} - 60 \, b d^{6} n \log\left(x^{\frac{1}{3}}\right) + 60 \, {\left(b d^{6} - b e^{6}\right)} n \log\left(d x^{\frac{1}{3}} + e\right) + 60 \, {\left(b d^{6} n x^{2} - b d^{6} n\right)} \log\left(\frac{d x + e x^{\frac{2}{3}}}{x}\right) + 6 \, {\left(2 \, b d^{5} e n x - 5 \, b d^{2} e^{4} n\right)} x^{\frac{2}{3}} - 15 \, {\left(b d^{4} e^{2} n x - 4 \, b d e^{5} n\right)} x^{\frac{1}{3}}}{120 \, d^{6}}"," ",0,"1/120*(60*b*d^6*x^2*log(c) + 20*b*d^3*e^3*n*x + 60*a*d^6*x^2 - 60*b*d^6*n*log(x^(1/3)) + 60*(b*d^6 - b*e^6)*n*log(d*x^(1/3) + e) + 60*(b*d^6*n*x^2 - b*d^6*n)*log((d*x + e*x^(2/3))/x) + 6*(2*b*d^5*e*n*x - 5*b*d^2*e^4*n)*x^(2/3) - 15*(b*d^4*e^2*n*x - 4*b*d*e^5*n)*x^(1/3))/d^6","A",0
492,1,107,0,1.029138," ","integrate(a+b*log(c*(d+e/x^(1/3))^n),x, algorithm=""fricas"")","\frac{2 \, b d^{3} x \log\left(c\right) - 2 \, b d^{3} n \log\left(x^{\frac{1}{3}}\right) + b d^{2} e n x^{\frac{2}{3}} - 2 \, b d e^{2} n x^{\frac{1}{3}} + 2 \, a d^{3} x + 2 \, {\left(b d^{3} + b e^{3}\right)} n \log\left(d x^{\frac{1}{3}} + e\right) + 2 \, {\left(b d^{3} n x - b d^{3} n\right)} \log\left(\frac{d x + e x^{\frac{2}{3}}}{x}\right)}{2 \, d^{3}}"," ",0,"1/2*(2*b*d^3*x*log(c) - 2*b*d^3*n*log(x^(1/3)) + b*d^2*e*n*x^(2/3) - 2*b*d*e^2*n*x^(1/3) + 2*a*d^3*x + 2*(b*d^3 + b*e^3)*n*log(d*x^(1/3) + e) + 2*(b*d^3*n*x - b*d^3*n)*log((d*x + e*x^(2/3))/x))/d^3","A",0
493,0,0,0,0.999118," ","integrate((a+b*log(c*(d+e/x^(1/3))^n))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \log\left(c \left(\frac{d x + e x^{\frac{2}{3}}}{x}\right)^{n}\right) + a}{x}, x\right)"," ",0,"integral((b*log(c*((d*x + e*x^(2/3))/x)^n) + a)/x, x)","F",0
494,1,107,0,0.919741," ","integrate((a+b*log(c*(d+e/x^(1/3))^n))/x^2,x, algorithm=""fricas"")","\frac{6 \, b d^{2} e n x^{\frac{2}{3}} - 3 \, b d e^{2} n x^{\frac{1}{3}} + 2 \, b e^{3} n - 6 \, a e^{3} - 2 \, {\left(b e^{3} n - 3 \, a e^{3}\right)} x + 6 \, {\left(b e^{3} x - b e^{3}\right)} \log\left(c\right) - 6 \, {\left(b d^{3} n x + b e^{3} n\right)} \log\left(\frac{d x + e x^{\frac{2}{3}}}{x}\right)}{6 \, e^{3} x}"," ",0,"1/6*(6*b*d^2*e*n*x^(2/3) - 3*b*d*e^2*n*x^(1/3) + 2*b*e^3*n - 6*a*e^3 - 2*(b*e^3*n - 3*a*e^3)*x + 6*(b*e^3*x - b*e^3)*log(c) - 6*(b*d^3*n*x + b*e^3*n)*log((d*x + e*x^(2/3))/x))/(e^3*x)","A",0
495,1,165,0,0.977357," ","integrate((a+b*log(c*(d+e/x^(1/3))^n))/x^3,x, algorithm=""fricas"")","-\frac{20 \, b d^{3} e^{3} n x - 10 \, b e^{6} n + 60 \, a e^{6} - 10 \, {\left(6 \, a e^{6} + {\left(2 \, b d^{3} e^{3} - b e^{6}\right)} n\right)} x^{2} - 60 \, {\left(b e^{6} x^{2} - b e^{6}\right)} \log\left(c\right) - 60 \, {\left(b d^{6} n x^{2} - b e^{6} n\right)} \log\left(\frac{d x + e x^{\frac{2}{3}}}{x}\right) + 15 \, {\left(4 \, b d^{5} e n x - b d^{2} e^{4} n\right)} x^{\frac{2}{3}} - 6 \, {\left(5 \, b d^{4} e^{2} n x - 2 \, b d e^{5} n\right)} x^{\frac{1}{3}}}{120 \, e^{6} x^{2}}"," ",0,"-1/120*(20*b*d^3*e^3*n*x - 10*b*e^6*n + 60*a*e^6 - 10*(6*a*e^6 + (2*b*d^3*e^3 - b*e^6)*n)*x^2 - 60*(b*e^6*x^2 - b*e^6)*log(c) - 60*(b*d^6*n*x^2 - b*e^6*n)*log((d*x + e*x^(2/3))/x) + 15*(4*b*d^5*e*n*x - b*d^2*e^4*n)*x^(2/3) - 6*(5*b*d^4*e^2*n*x - 2*b*d*e^5*n)*x^(1/3))/(e^6*x^2)","A",0
496,1,213,0,1.319567," ","integrate((a+b*log(c*(d+e/x^(1/3))^n))/x^4,x, algorithm=""fricas"")","\frac{840 \, b d^{6} e^{3} n x^{2} - 420 \, b d^{3} e^{6} n x + 280 \, b e^{9} n - 2520 \, a e^{9} + 140 \, {\left(18 \, a e^{9} - {\left(6 \, b d^{6} e^{3} - 3 \, b d^{3} e^{6} + 2 \, b e^{9}\right)} n\right)} x^{3} + 2520 \, {\left(b e^{9} x^{3} - b e^{9}\right)} \log\left(c\right) - 2520 \, {\left(b d^{9} n x^{3} + b e^{9} n\right)} \log\left(\frac{d x + e x^{\frac{2}{3}}}{x}\right) + 90 \, {\left(28 \, b d^{8} e n x^{2} - 7 \, b d^{5} e^{4} n x + 4 \, b d^{2} e^{7} n\right)} x^{\frac{2}{3}} - 63 \, {\left(20 \, b d^{7} e^{2} n x^{2} - 8 \, b d^{4} e^{5} n x + 5 \, b d e^{8} n\right)} x^{\frac{1}{3}}}{7560 \, e^{9} x^{3}}"," ",0,"1/7560*(840*b*d^6*e^3*n*x^2 - 420*b*d^3*e^6*n*x + 280*b*e^9*n - 2520*a*e^9 + 140*(18*a*e^9 - (6*b*d^6*e^3 - 3*b*d^3*e^6 + 2*b*e^9)*n)*x^3 + 2520*(b*e^9*x^3 - b*e^9)*log(c) - 2520*(b*d^9*n*x^3 + b*e^9*n)*log((d*x + e*x^(2/3))/x) + 90*(28*b*d^8*e*n*x^2 - 7*b*d^5*e^4*n*x + 4*b*d^2*e^7*n)*x^(2/3) - 63*(20*b*d^7*e^2*n*x^2 - 8*b*d^4*e^5*n*x + 5*b*d*e^8*n)*x^(1/3))/(e^9*x^3)","A",0
497,0,0,0,1.338112," ","integrate(x^2*(a+b*log(c*(d+e/x^(1/3))^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{2} \log\left(c \left(\frac{d x + e x^{\frac{2}{3}}}{x}\right)^{n}\right)^{2} + 2 \, a b x^{2} \log\left(c \left(\frac{d x + e x^{\frac{2}{3}}}{x}\right)^{n}\right) + a^{2} x^{2}, x\right)"," ",0,"integral(b^2*x^2*log(c*((d*x + e*x^(2/3))/x)^n)^2 + 2*a*b*x^2*log(c*((d*x + e*x^(2/3))/x)^n) + a^2*x^2, x)","F",0
498,0,0,0,0.834397," ","integrate(x*(a+b*log(c*(d+e/x^(1/3))^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x \log\left(c \left(\frac{d x + e x^{\frac{2}{3}}}{x}\right)^{n}\right)^{2} + 2 \, a b x \log\left(c \left(\frac{d x + e x^{\frac{2}{3}}}{x}\right)^{n}\right) + a^{2} x, x\right)"," ",0,"integral(b^2*x*log(c*((d*x + e*x^(2/3))/x)^n)^2 + 2*a*b*x*log(c*((d*x + e*x^(2/3))/x)^n) + a^2*x, x)","F",0
499,0,0,0,0.940817," ","integrate((a+b*log(c*(d+e/x^(1/3))^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} \log\left(c \left(\frac{d x + e x^{\frac{2}{3}}}{x}\right)^{n}\right)^{2} + 2 \, a b \log\left(c \left(\frac{d x + e x^{\frac{2}{3}}}{x}\right)^{n}\right) + a^{2}, x\right)"," ",0,"integral(b^2*log(c*((d*x + e*x^(2/3))/x)^n)^2 + 2*a*b*log(c*((d*x + e*x^(2/3))/x)^n) + a^2, x)","F",0
500,0,0,0,1.195769," ","integrate((a+b*log(c*(d+e/x^(1/3))^n))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \log\left(c \left(\frac{d x + e x^{\frac{2}{3}}}{x}\right)^{n}\right)^{2} + 2 \, a b \log\left(c \left(\frac{d x + e x^{\frac{2}{3}}}{x}\right)^{n}\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*log(c*((d*x + e*x^(2/3))/x)^n)^2 + 2*a*b*log(c*((d*x + e*x^(2/3))/x)^n) + a^2)/x, x)","F",0
501,1,357,0,1.150095," ","integrate((a+b*log(c*(d+e/x^(1/3))^n))^2/x^2,x, algorithm=""fricas"")","-\frac{4 \, b^{2} e^{3} n^{2} - 12 \, a b e^{3} n + 18 \, a^{2} e^{3} - 18 \, {\left(b^{2} e^{3} x - b^{2} e^{3}\right)} \log\left(c\right)^{2} + 18 \, {\left(b^{2} d^{3} n^{2} x + b^{2} e^{3} n^{2}\right)} \log\left(\frac{d x + e x^{\frac{2}{3}}}{x}\right)^{2} - 2 \, {\left(2 \, b^{2} e^{3} n^{2} - 6 \, a b e^{3} n + 9 \, a^{2} e^{3}\right)} x - 12 \, {\left(b^{2} e^{3} n - 3 \, a b e^{3} - {\left(b^{2} e^{3} n - 3 \, a b e^{3}\right)} x\right)} \log\left(c\right) - 6 \, {\left(6 \, b^{2} d^{2} e n^{2} x^{\frac{2}{3}} - 3 \, b^{2} d e^{2} n^{2} x^{\frac{1}{3}} + 2 \, b^{2} e^{3} n^{2} - 6 \, a b e^{3} n + {\left(11 \, b^{2} d^{3} n^{2} - 6 \, a b d^{3} n\right)} x - 6 \, {\left(b^{2} d^{3} n x + b^{2} e^{3} n\right)} \log\left(c\right)\right)} \log\left(\frac{d x + e x^{\frac{2}{3}}}{x}\right) + 6 \, {\left(11 \, b^{2} d^{2} e n^{2} - 6 \, b^{2} d^{2} e n \log\left(c\right) - 6 \, a b d^{2} e n\right)} x^{\frac{2}{3}} - 3 \, {\left(5 \, b^{2} d e^{2} n^{2} - 6 \, b^{2} d e^{2} n \log\left(c\right) - 6 \, a b d e^{2} n\right)} x^{\frac{1}{3}}}{18 \, e^{3} x}"," ",0,"-1/18*(4*b^2*e^3*n^2 - 12*a*b*e^3*n + 18*a^2*e^3 - 18*(b^2*e^3*x - b^2*e^3)*log(c)^2 + 18*(b^2*d^3*n^2*x + b^2*e^3*n^2)*log((d*x + e*x^(2/3))/x)^2 - 2*(2*b^2*e^3*n^2 - 6*a*b*e^3*n + 9*a^2*e^3)*x - 12*(b^2*e^3*n - 3*a*b*e^3 - (b^2*e^3*n - 3*a*b*e^3)*x)*log(c) - 6*(6*b^2*d^2*e*n^2*x^(2/3) - 3*b^2*d*e^2*n^2*x^(1/3) + 2*b^2*e^3*n^2 - 6*a*b*e^3*n + (11*b^2*d^3*n^2 - 6*a*b*d^3*n)*x - 6*(b^2*d^3*n*x + b^2*e^3*n)*log(c))*log((d*x + e*x^(2/3))/x) + 6*(11*b^2*d^2*e*n^2 - 6*b^2*d^2*e*n*log(c) - 6*a*b*d^2*e*n)*x^(2/3) - 3*(5*b^2*d*e^2*n^2 - 6*b^2*d*e^2*n*log(c) - 6*a*b*d*e^2*n)*x^(1/3))/(e^3*x)","A",0
502,1,597,0,1.534502," ","integrate((a+b*log(c*(d+e/x^(1/3))^n))^2/x^3,x, algorithm=""fricas"")","-\frac{100 \, b^{2} e^{6} n^{2} - 600 \, a b e^{6} n + 1800 \, a^{2} e^{6} - 20 \, {\left(90 \, a^{2} e^{6} - {\left(57 \, b^{2} d^{3} e^{3} - 5 \, b^{2} e^{6}\right)} n^{2} + 30 \, {\left(2 \, a b d^{3} e^{3} - a b e^{6}\right)} n\right)} x^{2} - 1800 \, {\left(b^{2} e^{6} x^{2} - b^{2} e^{6}\right)} \log\left(c\right)^{2} - 1800 \, {\left(b^{2} d^{6} n^{2} x^{2} - b^{2} e^{6} n^{2}\right)} \log\left(\frac{d x + e x^{\frac{2}{3}}}{x}\right)^{2} - 60 \, {\left(19 \, b^{2} d^{3} e^{3} n^{2} - 20 \, a b d^{3} e^{3} n\right)} x + 600 \, {\left(2 \, b^{2} d^{3} e^{3} n x - b^{2} e^{6} n + 6 \, a b e^{6} - {\left(6 \, a b e^{6} + {\left(2 \, b^{2} d^{3} e^{3} - b^{2} e^{6}\right)} n\right)} x^{2}\right)} \log\left(c\right) + 60 \, {\left(20 \, b^{2} d^{3} e^{3} n^{2} x - 10 \, b^{2} e^{6} n^{2} + 60 \, a b e^{6} n + 3 \, {\left(49 \, b^{2} d^{6} n^{2} - 20 \, a b d^{6} n\right)} x^{2} - 60 \, {\left(b^{2} d^{6} n x^{2} - b^{2} e^{6} n\right)} \log\left(c\right) + 15 \, {\left(4 \, b^{2} d^{5} e n^{2} x - b^{2} d^{2} e^{4} n^{2}\right)} x^{\frac{2}{3}} - 6 \, {\left(5 \, b^{2} d^{4} e^{2} n^{2} x - 2 \, b^{2} d e^{5} n^{2}\right)} x^{\frac{1}{3}}\right)} \log\left(\frac{d x + e x^{\frac{2}{3}}}{x}\right) + 15 \, {\left(37 \, b^{2} d^{2} e^{4} n^{2} - 60 \, a b d^{2} e^{4} n - 12 \, {\left(49 \, b^{2} d^{5} e n^{2} - 20 \, a b d^{5} e n\right)} x + 60 \, {\left(4 \, b^{2} d^{5} e n x - b^{2} d^{2} e^{4} n\right)} \log\left(c\right)\right)} x^{\frac{2}{3}} - 6 \, {\left(44 \, b^{2} d e^{5} n^{2} - 120 \, a b d e^{5} n - 15 \, {\left(29 \, b^{2} d^{4} e^{2} n^{2} - 20 \, a b d^{4} e^{2} n\right)} x + 60 \, {\left(5 \, b^{2} d^{4} e^{2} n x - 2 \, b^{2} d e^{5} n\right)} \log\left(c\right)\right)} x^{\frac{1}{3}}}{3600 \, e^{6} x^{2}}"," ",0,"-1/3600*(100*b^2*e^6*n^2 - 600*a*b*e^6*n + 1800*a^2*e^6 - 20*(90*a^2*e^6 - (57*b^2*d^3*e^3 - 5*b^2*e^6)*n^2 + 30*(2*a*b*d^3*e^3 - a*b*e^6)*n)*x^2 - 1800*(b^2*e^6*x^2 - b^2*e^6)*log(c)^2 - 1800*(b^2*d^6*n^2*x^2 - b^2*e^6*n^2)*log((d*x + e*x^(2/3))/x)^2 - 60*(19*b^2*d^3*e^3*n^2 - 20*a*b*d^3*e^3*n)*x + 600*(2*b^2*d^3*e^3*n*x - b^2*e^6*n + 6*a*b*e^6 - (6*a*b*e^6 + (2*b^2*d^3*e^3 - b^2*e^6)*n)*x^2)*log(c) + 60*(20*b^2*d^3*e^3*n^2*x - 10*b^2*e^6*n^2 + 60*a*b*e^6*n + 3*(49*b^2*d^6*n^2 - 20*a*b*d^6*n)*x^2 - 60*(b^2*d^6*n*x^2 - b^2*e^6*n)*log(c) + 15*(4*b^2*d^5*e*n^2*x - b^2*d^2*e^4*n^2)*x^(2/3) - 6*(5*b^2*d^4*e^2*n^2*x - 2*b^2*d*e^5*n^2)*x^(1/3))*log((d*x + e*x^(2/3))/x) + 15*(37*b^2*d^2*e^4*n^2 - 60*a*b*d^2*e^4*n - 12*(49*b^2*d^5*e*n^2 - 20*a*b*d^5*e*n)*x + 60*(4*b^2*d^5*e*n*x - b^2*d^2*e^4*n)*log(c))*x^(2/3) - 6*(44*b^2*d*e^5*n^2 - 120*a*b*d*e^5*n - 15*(29*b^2*d^4*e^2*n^2 - 20*a*b*d^4*e^2*n)*x + 60*(5*b^2*d^4*e^2*n*x - 2*b^2*d*e^5*n)*log(c))*x^(1/3))/(e^6*x^2)","A",0
503,0,0,0,1.364404," ","integrate(x*(a+b*log(c*(d+e/x^(1/3))^n))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x \log\left(c \left(\frac{d x + e x^{\frac{2}{3}}}{x}\right)^{n}\right)^{3} + 3 \, a b^{2} x \log\left(c \left(\frac{d x + e x^{\frac{2}{3}}}{x}\right)^{n}\right)^{2} + 3 \, a^{2} b x \log\left(c \left(\frac{d x + e x^{\frac{2}{3}}}{x}\right)^{n}\right) + a^{3} x, x\right)"," ",0,"integral(b^3*x*log(c*((d*x + e*x^(2/3))/x)^n)^3 + 3*a*b^2*x*log(c*((d*x + e*x^(2/3))/x)^n)^2 + 3*a^2*b*x*log(c*((d*x + e*x^(2/3))/x)^n) + a^3*x, x)","F",0
504,0,0,0,1.161759," ","integrate((a+b*log(c*(d+e/x^(1/3))^n))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} \log\left(c \left(\frac{d x + e x^{\frac{2}{3}}}{x}\right)^{n}\right)^{3} + 3 \, a b^{2} \log\left(c \left(\frac{d x + e x^{\frac{2}{3}}}{x}\right)^{n}\right)^{2} + 3 \, a^{2} b \log\left(c \left(\frac{d x + e x^{\frac{2}{3}}}{x}\right)^{n}\right) + a^{3}, x\right)"," ",0,"integral(b^3*log(c*((d*x + e*x^(2/3))/x)^n)^3 + 3*a*b^2*log(c*((d*x + e*x^(2/3))/x)^n)^2 + 3*a^2*b*log(c*((d*x + e*x^(2/3))/x)^n) + a^3, x)","F",0
505,0,0,0,0.977229," ","integrate((a+b*log(c*(d+e/x^(1/3))^n))^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \log\left(c \left(\frac{d x + e x^{\frac{2}{3}}}{x}\right)^{n}\right)^{3} + 3 \, a b^{2} \log\left(c \left(\frac{d x + e x^{\frac{2}{3}}}{x}\right)^{n}\right)^{2} + 3 \, a^{2} b \log\left(c \left(\frac{d x + e x^{\frac{2}{3}}}{x}\right)^{n}\right) + a^{3}}{x}, x\right)"," ",0,"integral((b^3*log(c*((d*x + e*x^(2/3))/x)^n)^3 + 3*a*b^2*log(c*((d*x + e*x^(2/3))/x)^n)^2 + 3*a^2*b*log(c*((d*x + e*x^(2/3))/x)^n) + a^3)/x, x)","F",0
506,1,814,0,1.073689," ","integrate((a+b*log(c*(d+e/x^(1/3))^n))^3/x^2,x, algorithm=""fricas"")","\frac{8 \, b^{3} e^{3} n^{3} - 24 \, a b^{2} e^{3} n^{2} + 36 \, a^{2} b e^{3} n - 36 \, a^{3} e^{3} + 36 \, {\left(b^{3} e^{3} x - b^{3} e^{3}\right)} \log\left(c\right)^{3} - 36 \, {\left(b^{3} d^{3} n^{3} x + b^{3} e^{3} n^{3}\right)} \log\left(\frac{d x + e x^{\frac{2}{3}}}{x}\right)^{3} + 36 \, {\left(b^{3} e^{3} n - 3 \, a b^{2} e^{3} - {\left(b^{3} e^{3} n - 3 \, a b^{2} e^{3}\right)} x\right)} \log\left(c\right)^{2} + 18 \, {\left(6 \, b^{3} d^{2} e n^{3} x^{\frac{2}{3}} - 3 \, b^{3} d e^{2} n^{3} x^{\frac{1}{3}} + 2 \, b^{3} e^{3} n^{3} - 6 \, a b^{2} e^{3} n^{2} + {\left(11 \, b^{3} d^{3} n^{3} - 6 \, a b^{2} d^{3} n^{2}\right)} x - 6 \, {\left(b^{3} d^{3} n^{2} x + b^{3} e^{3} n^{2}\right)} \log\left(c\right)\right)} \log\left(\frac{d x + e x^{\frac{2}{3}}}{x}\right)^{2} - 4 \, {\left(2 \, b^{3} e^{3} n^{3} - 6 \, a b^{2} e^{3} n^{2} + 9 \, a^{2} b e^{3} n - 9 \, a^{3} e^{3}\right)} x - 12 \, {\left(2 \, b^{3} e^{3} n^{2} - 6 \, a b^{2} e^{3} n + 9 \, a^{2} b e^{3} - {\left(2 \, b^{3} e^{3} n^{2} - 6 \, a b^{2} e^{3} n + 9 \, a^{2} b e^{3}\right)} x\right)} \log\left(c\right) - 6 \, {\left(4 \, b^{3} e^{3} n^{3} - 12 \, a b^{2} e^{3} n^{2} + 18 \, a^{2} b e^{3} n + 18 \, {\left(b^{3} d^{3} n x + b^{3} e^{3} n\right)} \log\left(c\right)^{2} + {\left(85 \, b^{3} d^{3} n^{3} - 66 \, a b^{2} d^{3} n^{2} + 18 \, a^{2} b d^{3} n\right)} x - 6 \, {\left(2 \, b^{3} e^{3} n^{2} - 6 \, a b^{2} e^{3} n + {\left(11 \, b^{3} d^{3} n^{2} - 6 \, a b^{2} d^{3} n\right)} x\right)} \log\left(c\right) + 6 \, {\left(11 \, b^{3} d^{2} e n^{3} - 6 \, b^{3} d^{2} e n^{2} \log\left(c\right) - 6 \, a b^{2} d^{2} e n^{2}\right)} x^{\frac{2}{3}} - 3 \, {\left(5 \, b^{3} d e^{2} n^{3} - 6 \, b^{3} d e^{2} n^{2} \log\left(c\right) - 6 \, a b^{2} d e^{2} n^{2}\right)} x^{\frac{1}{3}}\right)} \log\left(\frac{d x + e x^{\frac{2}{3}}}{x}\right) + 6 \, {\left(85 \, b^{3} d^{2} e n^{3} + 18 \, b^{3} d^{2} e n \log\left(c\right)^{2} - 66 \, a b^{2} d^{2} e n^{2} + 18 \, a^{2} b d^{2} e n - 6 \, {\left(11 \, b^{3} d^{2} e n^{2} - 6 \, a b^{2} d^{2} e n\right)} \log\left(c\right)\right)} x^{\frac{2}{3}} - 3 \, {\left(19 \, b^{3} d e^{2} n^{3} + 18 \, b^{3} d e^{2} n \log\left(c\right)^{2} - 30 \, a b^{2} d e^{2} n^{2} + 18 \, a^{2} b d e^{2} n - 6 \, {\left(5 \, b^{3} d e^{2} n^{2} - 6 \, a b^{2} d e^{2} n\right)} \log\left(c\right)\right)} x^{\frac{1}{3}}}{36 \, e^{3} x}"," ",0,"1/36*(8*b^3*e^3*n^3 - 24*a*b^2*e^3*n^2 + 36*a^2*b*e^3*n - 36*a^3*e^3 + 36*(b^3*e^3*x - b^3*e^3)*log(c)^3 - 36*(b^3*d^3*n^3*x + b^3*e^3*n^3)*log((d*x + e*x^(2/3))/x)^3 + 36*(b^3*e^3*n - 3*a*b^2*e^3 - (b^3*e^3*n - 3*a*b^2*e^3)*x)*log(c)^2 + 18*(6*b^3*d^2*e*n^3*x^(2/3) - 3*b^3*d*e^2*n^3*x^(1/3) + 2*b^3*e^3*n^3 - 6*a*b^2*e^3*n^2 + (11*b^3*d^3*n^3 - 6*a*b^2*d^3*n^2)*x - 6*(b^3*d^3*n^2*x + b^3*e^3*n^2)*log(c))*log((d*x + e*x^(2/3))/x)^2 - 4*(2*b^3*e^3*n^3 - 6*a*b^2*e^3*n^2 + 9*a^2*b*e^3*n - 9*a^3*e^3)*x - 12*(2*b^3*e^3*n^2 - 6*a*b^2*e^3*n + 9*a^2*b*e^3 - (2*b^3*e^3*n^2 - 6*a*b^2*e^3*n + 9*a^2*b*e^3)*x)*log(c) - 6*(4*b^3*e^3*n^3 - 12*a*b^2*e^3*n^2 + 18*a^2*b*e^3*n + 18*(b^3*d^3*n*x + b^3*e^3*n)*log(c)^2 + (85*b^3*d^3*n^3 - 66*a*b^2*d^3*n^2 + 18*a^2*b*d^3*n)*x - 6*(2*b^3*e^3*n^2 - 6*a*b^2*e^3*n + (11*b^3*d^3*n^2 - 6*a*b^2*d^3*n)*x)*log(c) + 6*(11*b^3*d^2*e*n^3 - 6*b^3*d^2*e*n^2*log(c) - 6*a*b^2*d^2*e*n^2)*x^(2/3) - 3*(5*b^3*d*e^2*n^3 - 6*b^3*d*e^2*n^2*log(c) - 6*a*b^2*d*e^2*n^2)*x^(1/3))*log((d*x + e*x^(2/3))/x) + 6*(85*b^3*d^2*e*n^3 + 18*b^3*d^2*e*n*log(c)^2 - 66*a*b^2*d^2*e*n^2 + 18*a^2*b*d^2*e*n - 6*(11*b^3*d^2*e*n^2 - 6*a*b^2*d^2*e*n)*log(c))*x^(2/3) - 3*(19*b^3*d*e^2*n^3 + 18*b^3*d*e^2*n*log(c)^2 - 30*a*b^2*d*e^2*n^2 + 18*a^2*b*d*e^2*n - 6*(5*b^3*d*e^2*n^2 - 6*a*b^2*d*e^2*n)*log(c))*x^(1/3))/(e^3*x)","B",0
507,1,1404,0,0.864752," ","integrate((a+b*log(c*(d+e/x^(1/3))^n))^3/x^3,x, algorithm=""fricas"")","\frac{1000 \, b^{3} e^{6} n^{3} - 6000 \, a b^{2} e^{6} n^{2} + 18000 \, a^{2} b e^{6} n - 36000 \, a^{3} e^{6} + 36000 \, {\left(b^{3} e^{6} x^{2} - b^{3} e^{6}\right)} \log\left(c\right)^{3} + 36000 \, {\left(b^{3} d^{6} n^{3} x^{2} - b^{3} e^{6} n^{3}\right)} \log\left(\frac{d x + e x^{\frac{2}{3}}}{x}\right)^{3} + 20 \, {\left(1800 \, a^{3} e^{6} + {\left(2059 \, b^{3} d^{3} e^{3} - 50 \, b^{3} e^{6}\right)} n^{3} - 60 \, {\left(57 \, a b^{2} d^{3} e^{3} - 5 \, a b^{2} e^{6}\right)} n^{2} + 900 \, {\left(2 \, a^{2} b d^{3} e^{3} - a^{2} b e^{6}\right)} n\right)} x^{2} - 18000 \, {\left(2 \, b^{3} d^{3} e^{3} n x - b^{3} e^{6} n + 6 \, a b^{2} e^{6} - {\left(6 \, a b^{2} e^{6} + {\left(2 \, b^{3} d^{3} e^{3} - b^{3} e^{6}\right)} n\right)} x^{2}\right)} \log\left(c\right)^{2} - 1800 \, {\left(20 \, b^{3} d^{3} e^{3} n^{3} x - 10 \, b^{3} e^{6} n^{3} + 60 \, a b^{2} e^{6} n^{2} + 3 \, {\left(49 \, b^{3} d^{6} n^{3} - 20 \, a b^{2} d^{6} n^{2}\right)} x^{2} - 60 \, {\left(b^{3} d^{6} n^{2} x^{2} - b^{3} e^{6} n^{2}\right)} \log\left(c\right) + 15 \, {\left(4 \, b^{3} d^{5} e n^{3} x - b^{3} d^{2} e^{4} n^{3}\right)} x^{\frac{2}{3}} - 6 \, {\left(5 \, b^{3} d^{4} e^{2} n^{3} x - 2 \, b^{3} d e^{5} n^{3}\right)} x^{\frac{1}{3}}\right)} \log\left(\frac{d x + e x^{\frac{2}{3}}}{x}\right)^{2} - 20 \, {\left(2059 \, b^{3} d^{3} e^{3} n^{3} - 3420 \, a b^{2} d^{3} e^{3} n^{2} + 1800 \, a^{2} b d^{3} e^{3} n\right)} x - 1200 \, {\left(5 \, b^{3} e^{6} n^{2} - 30 \, a b^{2} e^{6} n + 90 \, a^{2} b e^{6} - {\left(90 \, a^{2} b e^{6} - {\left(57 \, b^{3} d^{3} e^{3} - 5 \, b^{3} e^{6}\right)} n^{2} + 30 \, {\left(2 \, a b^{2} d^{3} e^{3} - a b^{2} e^{6}\right)} n\right)} x^{2} - 3 \, {\left(19 \, b^{3} d^{3} e^{3} n^{2} - 20 \, a b^{2} d^{3} e^{3} n\right)} x\right)} \log\left(c\right) - 60 \, {\left(100 \, b^{3} e^{6} n^{3} - 600 \, a b^{2} e^{6} n^{2} + 1800 \, a^{2} b e^{6} n - {\left(13489 \, b^{3} d^{6} n^{3} - 8820 \, a b^{2} d^{6} n^{2} + 1800 \, a^{2} b d^{6} n\right)} x^{2} - 1800 \, {\left(b^{3} d^{6} n x^{2} - b^{3} e^{6} n\right)} \log\left(c\right)^{2} - 60 \, {\left(19 \, b^{3} d^{3} e^{3} n^{3} - 20 \, a b^{2} d^{3} e^{3} n^{2}\right)} x + 60 \, {\left(20 \, b^{3} d^{3} e^{3} n^{2} x - 10 \, b^{3} e^{6} n^{2} + 60 \, a b^{2} e^{6} n + 3 \, {\left(49 \, b^{3} d^{6} n^{2} - 20 \, a b^{2} d^{6} n\right)} x^{2}\right)} \log\left(c\right) + 15 \, {\left(37 \, b^{3} d^{2} e^{4} n^{3} - 60 \, a b^{2} d^{2} e^{4} n^{2} - 12 \, {\left(49 \, b^{3} d^{5} e n^{3} - 20 \, a b^{2} d^{5} e n^{2}\right)} x + 60 \, {\left(4 \, b^{3} d^{5} e n^{2} x - b^{3} d^{2} e^{4} n^{2}\right)} \log\left(c\right)\right)} x^{\frac{2}{3}} - 6 \, {\left(44 \, b^{3} d e^{5} n^{3} - 120 \, a b^{2} d e^{5} n^{2} - 15 \, {\left(29 \, b^{3} d^{4} e^{2} n^{3} - 20 \, a b^{2} d^{4} e^{2} n^{2}\right)} x + 60 \, {\left(5 \, b^{3} d^{4} e^{2} n^{2} x - 2 \, b^{3} d e^{5} n^{2}\right)} \log\left(c\right)\right)} x^{\frac{1}{3}}\right)} \log\left(\frac{d x + e x^{\frac{2}{3}}}{x}\right) + 15 \, {\left(919 \, b^{3} d^{2} e^{4} n^{3} - 2220 \, a b^{2} d^{2} e^{4} n^{2} + 1800 \, a^{2} b d^{2} e^{4} n - 1800 \, {\left(4 \, b^{3} d^{5} e n x - b^{3} d^{2} e^{4} n\right)} \log\left(c\right)^{2} - 4 \, {\left(13489 \, b^{3} d^{5} e n^{3} - 8820 \, a b^{2} d^{5} e n^{2} + 1800 \, a^{2} b d^{5} e n\right)} x - 60 \, {\left(37 \, b^{3} d^{2} e^{4} n^{2} - 60 \, a b^{2} d^{2} e^{4} n - 12 \, {\left(49 \, b^{3} d^{5} e n^{2} - 20 \, a b^{2} d^{5} e n\right)} x\right)} \log\left(c\right)\right)} x^{\frac{2}{3}} - 6 \, {\left(728 \, b^{3} d e^{5} n^{3} - 2640 \, a b^{2} d e^{5} n^{2} + 3600 \, a^{2} b d e^{5} n - 1800 \, {\left(5 \, b^{3} d^{4} e^{2} n x - 2 \, b^{3} d e^{5} n\right)} \log\left(c\right)^{2} - 5 \, {\left(4669 \, b^{3} d^{4} e^{2} n^{3} - 5220 \, a b^{2} d^{4} e^{2} n^{2} + 1800 \, a^{2} b d^{4} e^{2} n\right)} x - 60 \, {\left(44 \, b^{3} d e^{5} n^{2} - 120 \, a b^{2} d e^{5} n - 15 \, {\left(29 \, b^{3} d^{4} e^{2} n^{2} - 20 \, a b^{2} d^{4} e^{2} n\right)} x\right)} \log\left(c\right)\right)} x^{\frac{1}{3}}}{72000 \, e^{6} x^{2}}"," ",0,"1/72000*(1000*b^3*e^6*n^3 - 6000*a*b^2*e^6*n^2 + 18000*a^2*b*e^6*n - 36000*a^3*e^6 + 36000*(b^3*e^6*x^2 - b^3*e^6)*log(c)^3 + 36000*(b^3*d^6*n^3*x^2 - b^3*e^6*n^3)*log((d*x + e*x^(2/3))/x)^3 + 20*(1800*a^3*e^6 + (2059*b^3*d^3*e^3 - 50*b^3*e^6)*n^3 - 60*(57*a*b^2*d^3*e^3 - 5*a*b^2*e^6)*n^2 + 900*(2*a^2*b*d^3*e^3 - a^2*b*e^6)*n)*x^2 - 18000*(2*b^3*d^3*e^3*n*x - b^3*e^6*n + 6*a*b^2*e^6 - (6*a*b^2*e^6 + (2*b^3*d^3*e^3 - b^3*e^6)*n)*x^2)*log(c)^2 - 1800*(20*b^3*d^3*e^3*n^3*x - 10*b^3*e^6*n^3 + 60*a*b^2*e^6*n^2 + 3*(49*b^3*d^6*n^3 - 20*a*b^2*d^6*n^2)*x^2 - 60*(b^3*d^6*n^2*x^2 - b^3*e^6*n^2)*log(c) + 15*(4*b^3*d^5*e*n^3*x - b^3*d^2*e^4*n^3)*x^(2/3) - 6*(5*b^3*d^4*e^2*n^3*x - 2*b^3*d*e^5*n^3)*x^(1/3))*log((d*x + e*x^(2/3))/x)^2 - 20*(2059*b^3*d^3*e^3*n^3 - 3420*a*b^2*d^3*e^3*n^2 + 1800*a^2*b*d^3*e^3*n)*x - 1200*(5*b^3*e^6*n^2 - 30*a*b^2*e^6*n + 90*a^2*b*e^6 - (90*a^2*b*e^6 - (57*b^3*d^3*e^3 - 5*b^3*e^6)*n^2 + 30*(2*a*b^2*d^3*e^3 - a*b^2*e^6)*n)*x^2 - 3*(19*b^3*d^3*e^3*n^2 - 20*a*b^2*d^3*e^3*n)*x)*log(c) - 60*(100*b^3*e^6*n^3 - 600*a*b^2*e^6*n^2 + 1800*a^2*b*e^6*n - (13489*b^3*d^6*n^3 - 8820*a*b^2*d^6*n^2 + 1800*a^2*b*d^6*n)*x^2 - 1800*(b^3*d^6*n*x^2 - b^3*e^6*n)*log(c)^2 - 60*(19*b^3*d^3*e^3*n^3 - 20*a*b^2*d^3*e^3*n^2)*x + 60*(20*b^3*d^3*e^3*n^2*x - 10*b^3*e^6*n^2 + 60*a*b^2*e^6*n + 3*(49*b^3*d^6*n^2 - 20*a*b^2*d^6*n)*x^2)*log(c) + 15*(37*b^3*d^2*e^4*n^3 - 60*a*b^2*d^2*e^4*n^2 - 12*(49*b^3*d^5*e*n^3 - 20*a*b^2*d^5*e*n^2)*x + 60*(4*b^3*d^5*e*n^2*x - b^3*d^2*e^4*n^2)*log(c))*x^(2/3) - 6*(44*b^3*d*e^5*n^3 - 120*a*b^2*d*e^5*n^2 - 15*(29*b^3*d^4*e^2*n^3 - 20*a*b^2*d^4*e^2*n^2)*x + 60*(5*b^3*d^4*e^2*n^2*x - 2*b^3*d*e^5*n^2)*log(c))*x^(1/3))*log((d*x + e*x^(2/3))/x) + 15*(919*b^3*d^2*e^4*n^3 - 2220*a*b^2*d^2*e^4*n^2 + 1800*a^2*b*d^2*e^4*n - 1800*(4*b^3*d^5*e*n*x - b^3*d^2*e^4*n)*log(c)^2 - 4*(13489*b^3*d^5*e*n^3 - 8820*a*b^2*d^5*e*n^2 + 1800*a^2*b*d^5*e*n)*x - 60*(37*b^3*d^2*e^4*n^2 - 60*a*b^2*d^2*e^4*n - 12*(49*b^3*d^5*e*n^2 - 20*a*b^2*d^5*e*n)*x)*log(c))*x^(2/3) - 6*(728*b^3*d*e^5*n^3 - 2640*a*b^2*d*e^5*n^2 + 3600*a^2*b*d*e^5*n - 1800*(5*b^3*d^4*e^2*n*x - 2*b^3*d*e^5*n)*log(c)^2 - 5*(4669*b^3*d^4*e^2*n^3 - 5220*a*b^2*d^4*e^2*n^2 + 1800*a^2*b*d^4*e^2*n)*x - 60*(44*b^3*d*e^5*n^2 - 120*a*b^2*d*e^5*n - 15*(29*b^3*d^4*e^2*n^2 - 20*a*b^2*d^4*e^2*n)*x)*log(c))*x^(1/3))/(e^6*x^2)","A",0
508,1,160,0,0.964691," ","integrate(x^3*(a+b*log(c*(d+e/x^(2/3))^n)),x, algorithm=""fricas"")","\frac{60 \, b d^{6} x^{4} \log\left(c\right) + 60 \, a d^{6} x^{4} + 20 \, b d^{3} e^{3} n x^{2} - 120 \, b d^{6} n \log\left(x^{\frac{1}{3}}\right) + 60 \, {\left(b d^{6} - b e^{6}\right)} n \log\left(d x^{\frac{2}{3}} + e\right) + 60 \, {\left(b d^{6} n x^{4} - b d^{6} n\right)} \log\left(\frac{d x + e x^{\frac{1}{3}}}{x}\right) - 15 \, {\left(b d^{4} e^{2} n x^{2} - 4 \, b d e^{5} n\right)} x^{\frac{2}{3}} + 6 \, {\left(2 \, b d^{5} e n x^{3} - 5 \, b d^{2} e^{4} n x\right)} x^{\frac{1}{3}}}{240 \, d^{6}}"," ",0,"1/240*(60*b*d^6*x^4*log(c) + 60*a*d^6*x^4 + 20*b*d^3*e^3*n*x^2 - 120*b*d^6*n*log(x^(1/3)) + 60*(b*d^6 - b*e^6)*n*log(d*x^(2/3) + e) + 60*(b*d^6*n*x^4 - b*d^6*n)*log((d*x + e*x^(1/3))/x) - 15*(b*d^4*e^2*n*x^2 - 4*b*d*e^5*n)*x^(2/3) + 6*(2*b*d^5*e*n*x^3 - 5*b*d^2*e^4*n*x)*x^(1/3))/d^6","A",0
509,1,399,0,0.704941," ","integrate(x^2*(a+b*log(c*(d+e/x^(2/3))^n)),x, algorithm=""fricas"")","\left[\frac{105 \, b d^{4} x^{3} \log\left(c\right) + 105 \, a d^{4} x^{3} - 42 \, b d^{2} e^{2} n x^{\frac{5}{3}} + 105 \, b e^{4} n \sqrt{-\frac{e}{d}} \log\left(\frac{d^{3} x^{2} - 2 \, d^{2} e x \sqrt{-\frac{e}{d}} - e^{3} + 2 \, {\left(d^{3} x \sqrt{-\frac{e}{d}} + d e^{2}\right)} x^{\frac{2}{3}} - 2 \, {\left(d^{2} e x - d e^{2} \sqrt{-\frac{e}{d}}\right)} x^{\frac{1}{3}}}{d^{3} x^{2} + e^{3}}\right) + 70 \, b d e^{3} n x + 105 \, b d^{4} n \log\left(d x^{\frac{2}{3}} + e\right) - 210 \, b d^{4} n \log\left(x^{\frac{1}{3}}\right) + 105 \, {\left(b d^{4} n x^{3} - b d^{4} n\right)} \log\left(\frac{d x + e x^{\frac{1}{3}}}{x}\right) + 30 \, {\left(b d^{3} e n x^{2} - 7 \, b e^{4} n\right)} x^{\frac{1}{3}}}{315 \, d^{4}}, \frac{105 \, b d^{4} x^{3} \log\left(c\right) + 105 \, a d^{4} x^{3} - 42 \, b d^{2} e^{2} n x^{\frac{5}{3}} + 210 \, b e^{4} n \sqrt{\frac{e}{d}} \arctan\left(\frac{d x^{\frac{1}{3}} \sqrt{\frac{e}{d}}}{e}\right) + 70 \, b d e^{3} n x + 105 \, b d^{4} n \log\left(d x^{\frac{2}{3}} + e\right) - 210 \, b d^{4} n \log\left(x^{\frac{1}{3}}\right) + 105 \, {\left(b d^{4} n x^{3} - b d^{4} n\right)} \log\left(\frac{d x + e x^{\frac{1}{3}}}{x}\right) + 30 \, {\left(b d^{3} e n x^{2} - 7 \, b e^{4} n\right)} x^{\frac{1}{3}}}{315 \, d^{4}}\right]"," ",0,"[1/315*(105*b*d^4*x^3*log(c) + 105*a*d^4*x^3 - 42*b*d^2*e^2*n*x^(5/3) + 105*b*e^4*n*sqrt(-e/d)*log((d^3*x^2 - 2*d^2*e*x*sqrt(-e/d) - e^3 + 2*(d^3*x*sqrt(-e/d) + d*e^2)*x^(2/3) - 2*(d^2*e*x - d*e^2*sqrt(-e/d))*x^(1/3))/(d^3*x^2 + e^3)) + 70*b*d*e^3*n*x + 105*b*d^4*n*log(d*x^(2/3) + e) - 210*b*d^4*n*log(x^(1/3)) + 105*(b*d^4*n*x^3 - b*d^4*n)*log((d*x + e*x^(1/3))/x) + 30*(b*d^3*e*n*x^2 - 7*b*e^4*n)*x^(1/3))/d^4, 1/315*(105*b*d^4*x^3*log(c) + 105*a*d^4*x^3 - 42*b*d^2*e^2*n*x^(5/3) + 210*b*e^4*n*sqrt(e/d)*arctan(d*x^(1/3)*sqrt(e/d)/e) + 70*b*d*e^3*n*x + 105*b*d^4*n*log(d*x^(2/3) + e) - 210*b*d^4*n*log(x^(1/3)) + 105*(b*d^4*n*x^3 - b*d^4*n)*log((d*x + e*x^(1/3))/x) + 30*(b*d^3*e*n*x^2 - 7*b*e^4*n)*x^(1/3))/d^4]","A",0
510,1,113,0,0.870457," ","integrate(x*(a+b*log(c*(d+e/x^(2/3))^n)),x, algorithm=""fricas"")","\frac{2 \, b d^{3} x^{2} \log\left(c\right) + b d^{2} e n x^{\frac{4}{3}} + 2 \, a d^{3} x^{2} - 4 \, b d^{3} n \log\left(x^{\frac{1}{3}}\right) - 2 \, b d e^{2} n x^{\frac{2}{3}} + 2 \, {\left(b d^{3} + b e^{3}\right)} n \log\left(d x^{\frac{2}{3}} + e\right) + 2 \, {\left(b d^{3} n x^{2} - b d^{3} n\right)} \log\left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)}{4 \, d^{3}}"," ",0,"1/4*(2*b*d^3*x^2*log(c) + b*d^2*e*n*x^(4/3) + 2*a*d^3*x^2 - 4*b*d^3*n*log(x^(1/3)) - 2*b*d*e^2*n*x^(2/3) + 2*(b*d^3 + b*e^3)*n*log(d*x^(2/3) + e) + 2*(b*d^3*n*x^2 - b*d^3*n)*log((d*x + e*x^(1/3))/x))/d^3","A",0
511,1,279,0,0.948232," ","integrate(a+b*log(c*(d+e/x^(2/3))^n),x, algorithm=""fricas"")","\left[\frac{b e n \sqrt{-\frac{e}{d}} \log\left(\frac{d^{3} x^{2} + 2 \, d^{2} e x \sqrt{-\frac{e}{d}} - e^{3} - 2 \, {\left(d^{3} x \sqrt{-\frac{e}{d}} - d e^{2}\right)} x^{\frac{2}{3}} - 2 \, {\left(d^{2} e x + d e^{2} \sqrt{-\frac{e}{d}}\right)} x^{\frac{1}{3}}}{d^{3} x^{2} + e^{3}}\right) + b d n \log\left(d x^{\frac{2}{3}} + e\right) + b d x \log\left(c\right) - 2 \, b d n \log\left(x^{\frac{1}{3}}\right) + 2 \, b e n x^{\frac{1}{3}} + a d x + {\left(b d n x - b d n\right)} \log\left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)}{d}, -\frac{2 \, b e n \sqrt{\frac{e}{d}} \arctan\left(\frac{d x^{\frac{1}{3}} \sqrt{\frac{e}{d}}}{e}\right) - b d n \log\left(d x^{\frac{2}{3}} + e\right) - b d x \log\left(c\right) + 2 \, b d n \log\left(x^{\frac{1}{3}}\right) - 2 \, b e n x^{\frac{1}{3}} - a d x - {\left(b d n x - b d n\right)} \log\left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)}{d}\right]"," ",0,"[(b*e*n*sqrt(-e/d)*log((d^3*x^2 + 2*d^2*e*x*sqrt(-e/d) - e^3 - 2*(d^3*x*sqrt(-e/d) - d*e^2)*x^(2/3) - 2*(d^2*e*x + d*e^2*sqrt(-e/d))*x^(1/3))/(d^3*x^2 + e^3)) + b*d*n*log(d*x^(2/3) + e) + b*d*x*log(c) - 2*b*d*n*log(x^(1/3)) + 2*b*e*n*x^(1/3) + a*d*x + (b*d*n*x - b*d*n)*log((d*x + e*x^(1/3))/x))/d, -(2*b*e*n*sqrt(e/d)*arctan(d*x^(1/3)*sqrt(e/d)/e) - b*d*n*log(d*x^(2/3) + e) - b*d*x*log(c) + 2*b*d*n*log(x^(1/3)) - 2*b*e*n*x^(1/3) - a*d*x - (b*d*n*x - b*d*n)*log((d*x + e*x^(1/3))/x))/d]","B",0
512,0,0,0,0.884532," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right) + a}{x}, x\right)"," ",0,"integral((b*log(c*((d*x + e*x^(1/3))/x)^n) + a)/x, x)","F",0
513,1,235,0,0.984275," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))/x^2,x, algorithm=""fricas"")","\left[\frac{3 \, b d n x \sqrt{-\frac{d}{e}} \log\left(\frac{d^{3} x^{2} + 2 \, d e^{2} x \sqrt{-\frac{d}{e}} - e^{3} - 2 \, {\left(d^{2} e x \sqrt{-\frac{d}{e}} - d e^{2}\right)} x^{\frac{2}{3}} - 2 \, {\left(d^{2} e x + e^{3} \sqrt{-\frac{d}{e}}\right)} x^{\frac{1}{3}}}{d^{3} x^{2} + e^{3}}\right) - 3 \, b e n \log\left(\frac{d x + e x^{\frac{1}{3}}}{x}\right) - 6 \, b d n x^{\frac{2}{3}} + 2 \, b e n - 3 \, b e \log\left(c\right) - 3 \, a e}{3 \, e x}, -\frac{6 \, b d n x \sqrt{\frac{d}{e}} \arctan\left(x^{\frac{1}{3}} \sqrt{\frac{d}{e}}\right) + 3 \, b e n \log\left(\frac{d x + e x^{\frac{1}{3}}}{x}\right) + 6 \, b d n x^{\frac{2}{3}} - 2 \, b e n + 3 \, b e \log\left(c\right) + 3 \, a e}{3 \, e x}\right]"," ",0,"[1/3*(3*b*d*n*x*sqrt(-d/e)*log((d^3*x^2 + 2*d*e^2*x*sqrt(-d/e) - e^3 - 2*(d^2*e*x*sqrt(-d/e) - d*e^2)*x^(2/3) - 2*(d^2*e*x + e^3*sqrt(-d/e))*x^(1/3))/(d^3*x^2 + e^3)) - 3*b*e*n*log((d*x + e*x^(1/3))/x) - 6*b*d*n*x^(2/3) + 2*b*e*n - 3*b*e*log(c) - 3*a*e)/(e*x), -1/3*(6*b*d*n*x*sqrt(d/e)*arctan(x^(1/3)*sqrt(d/e)) + 3*b*e*n*log((d*x + e*x^(1/3))/x) + 6*b*d*n*x^(2/3) - 2*b*e*n + 3*b*e*log(c) + 3*a*e)/(e*x)]","A",0
514,1,84,0,0.958554," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))/x^3,x, algorithm=""fricas"")","\frac{6 \, b d^{2} e n x^{\frac{4}{3}} - 3 \, b d e^{2} n x^{\frac{2}{3}} + 2 \, b e^{3} n - 6 \, b e^{3} \log\left(c\right) - 6 \, a e^{3} - 6 \, {\left(b d^{3} n x^{2} + b e^{3} n\right)} \log\left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)}{12 \, e^{3} x^{2}}"," ",0,"1/12*(6*b*d^2*e*n*x^(4/3) - 3*b*d*e^2*n*x^(2/3) + 2*b*e^3*n - 6*b*e^3*log(c) - 6*a*e^3 - 6*(b*d^3*n*x^2 + b*e^3*n)*log((d*x + e*x^(1/3))/x))/(e^3*x^2)","A",0
515,1,339,0,0.884731," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))/x^4,x, algorithm=""fricas"")","\left[\frac{315 \, b d^{4} n x^{3} \sqrt{-\frac{d}{e}} \log\left(\frac{d^{3} x^{2} - 2 \, d e^{2} x \sqrt{-\frac{d}{e}} - e^{3} + 2 \, {\left(d^{2} e x \sqrt{-\frac{d}{e}} + d e^{2}\right)} x^{\frac{2}{3}} - 2 \, {\left(d^{2} e x - e^{3} \sqrt{-\frac{d}{e}}\right)} x^{\frac{1}{3}}}{d^{3} x^{2} + e^{3}}\right) - 210 \, b d^{3} e n x^{2} + 126 \, b d^{2} e^{2} n x^{\frac{4}{3}} - 315 \, b e^{4} n \log\left(\frac{d x + e x^{\frac{1}{3}}}{x}\right) + 70 \, b e^{4} n - 315 \, b e^{4} \log\left(c\right) - 315 \, a e^{4} + 90 \, {\left(7 \, b d^{4} n x^{2} - b d e^{3} n\right)} x^{\frac{2}{3}}}{945 \, e^{4} x^{3}}, \frac{630 \, b d^{4} n x^{3} \sqrt{\frac{d}{e}} \arctan\left(x^{\frac{1}{3}} \sqrt{\frac{d}{e}}\right) - 210 \, b d^{3} e n x^{2} + 126 \, b d^{2} e^{2} n x^{\frac{4}{3}} - 315 \, b e^{4} n \log\left(\frac{d x + e x^{\frac{1}{3}}}{x}\right) + 70 \, b e^{4} n - 315 \, b e^{4} \log\left(c\right) - 315 \, a e^{4} + 90 \, {\left(7 \, b d^{4} n x^{2} - b d e^{3} n\right)} x^{\frac{2}{3}}}{945 \, e^{4} x^{3}}\right]"," ",0,"[1/945*(315*b*d^4*n*x^3*sqrt(-d/e)*log((d^3*x^2 - 2*d*e^2*x*sqrt(-d/e) - e^3 + 2*(d^2*e*x*sqrt(-d/e) + d*e^2)*x^(2/3) - 2*(d^2*e*x - e^3*sqrt(-d/e))*x^(1/3))/(d^3*x^2 + e^3)) - 210*b*d^3*e*n*x^2 + 126*b*d^2*e^2*n*x^(4/3) - 315*b*e^4*n*log((d*x + e*x^(1/3))/x) + 70*b*e^4*n - 315*b*e^4*log(c) - 315*a*e^4 + 90*(7*b*d^4*n*x^2 - b*d*e^3*n)*x^(2/3))/(e^4*x^3), 1/945*(630*b*d^4*n*x^3*sqrt(d/e)*arctan(x^(1/3)*sqrt(d/e)) - 210*b*d^3*e*n*x^2 + 126*b*d^2*e^2*n*x^(4/3) - 315*b*e^4*n*log((d*x + e*x^(1/3))/x) + 70*b*e^4*n - 315*b*e^4*log(c) - 315*a*e^4 + 90*(7*b*d^4*n*x^2 - b*d*e^3*n)*x^(2/3))/(e^4*x^3)]","A",0
516,0,0,0,0.784038," ","integrate(x^3*(a+b*log(c*(d+e/x^(2/3))^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{3} \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right)^{2} + 2 \, a b x^{3} \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right) + a^{2} x^{3}, x\right)"," ",0,"integral(b^2*x^3*log(c*((d*x + e*x^(1/3))/x)^n)^2 + 2*a*b*x^3*log(c*((d*x + e*x^(1/3))/x)^n) + a^2*x^3, x)","F",0
517,0,0,0,0.708288," ","integrate(x*(a+b*log(c*(d+e/x^(2/3))^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right)^{2} + 2 \, a b x \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right) + a^{2} x, x\right)"," ",0,"integral(b^2*x*log(c*((d*x + e*x^(1/3))/x)^n)^2 + 2*a*b*x*log(c*((d*x + e*x^(1/3))/x)^n) + a^2*x, x)","F",0
518,0,0,0,0.924785," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right)^{2} + 2 \, a b \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*log(c*((d*x + e*x^(1/3))/x)^n)^2 + 2*a*b*log(c*((d*x + e*x^(1/3))/x)^n) + a^2)/x, x)","F",0
519,1,307,0,0.811764," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))^2/x^3,x, algorithm=""fricas"")","-\frac{4 \, b^{2} e^{3} n^{2} + 18 \, b^{2} e^{3} \log\left(c\right)^{2} - 12 \, a b e^{3} n + 18 \, a^{2} e^{3} + 18 \, {\left(b^{2} d^{3} n^{2} x^{2} + b^{2} e^{3} n^{2}\right)} \log\left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{2} - 12 \, {\left(b^{2} e^{3} n - 3 \, a b e^{3}\right)} \log\left(c\right) - 6 \, {\left(6 \, b^{2} d^{2} e n^{2} x^{\frac{4}{3}} - 3 \, b^{2} d e^{2} n^{2} x^{\frac{2}{3}} + 2 \, b^{2} e^{3} n^{2} - 6 \, a b e^{3} n + {\left(11 \, b^{2} d^{3} n^{2} - 6 \, a b d^{3} n\right)} x^{2} - 6 \, {\left(b^{2} d^{3} n x^{2} + b^{2} e^{3} n\right)} \log\left(c\right)\right)} \log\left(\frac{d x + e x^{\frac{1}{3}}}{x}\right) - 3 \, {\left(5 \, b^{2} d e^{2} n^{2} - 6 \, b^{2} d e^{2} n \log\left(c\right) - 6 \, a b d e^{2} n\right)} x^{\frac{2}{3}} - 6 \, {\left(6 \, b^{2} d^{2} e n x \log\left(c\right) - {\left(11 \, b^{2} d^{2} e n^{2} - 6 \, a b d^{2} e n\right)} x\right)} x^{\frac{1}{3}}}{36 \, e^{3} x^{2}}"," ",0,"-1/36*(4*b^2*e^3*n^2 + 18*b^2*e^3*log(c)^2 - 12*a*b*e^3*n + 18*a^2*e^3 + 18*(b^2*d^3*n^2*x^2 + b^2*e^3*n^2)*log((d*x + e*x^(1/3))/x)^2 - 12*(b^2*e^3*n - 3*a*b*e^3)*log(c) - 6*(6*b^2*d^2*e*n^2*x^(4/3) - 3*b^2*d*e^2*n^2*x^(2/3) + 2*b^2*e^3*n^2 - 6*a*b*e^3*n + (11*b^2*d^3*n^2 - 6*a*b*d^3*n)*x^2 - 6*(b^2*d^3*n*x^2 + b^2*e^3*n)*log(c))*log((d*x + e*x^(1/3))/x) - 3*(5*b^2*d*e^2*n^2 - 6*b^2*d*e^2*n*log(c) - 6*a*b*d*e^2*n)*x^(2/3) - 6*(6*b^2*d^2*e*n*x*log(c) - (11*b^2*d^2*e*n^2 - 6*a*b*d^2*e*n)*x)*x^(1/3))/(e^3*x^2)","A",0
520,1,513,0,0.666209," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))^2/x^5,x, algorithm=""fricas"")","-\frac{100 \, b^{2} e^{6} n^{2} + 1800 \, b^{2} e^{6} \log\left(c\right)^{2} - 600 \, a b e^{6} n + 1800 \, a^{2} e^{6} - 60 \, {\left(19 \, b^{2} d^{3} e^{3} n^{2} - 20 \, a b d^{3} e^{3} n\right)} x^{2} - 1800 \, {\left(b^{2} d^{6} n^{2} x^{4} - b^{2} e^{6} n^{2}\right)} \log\left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{2} + 600 \, {\left(2 \, b^{2} d^{3} e^{3} n x^{2} - b^{2} e^{6} n + 6 \, a b e^{6}\right)} \log\left(c\right) + 60 \, {\left(20 \, b^{2} d^{3} e^{3} n^{2} x^{2} - 10 \, b^{2} e^{6} n^{2} + 60 \, a b e^{6} n + 3 \, {\left(49 \, b^{2} d^{6} n^{2} - 20 \, a b d^{6} n\right)} x^{4} - 60 \, {\left(b^{2} d^{6} n x^{4} - b^{2} e^{6} n\right)} \log\left(c\right) - 6 \, {\left(5 \, b^{2} d^{4} e^{2} n^{2} x^{2} - 2 \, b^{2} d e^{5} n^{2}\right)} x^{\frac{2}{3}} + 15 \, {\left(4 \, b^{2} d^{5} e n^{2} x^{3} - b^{2} d^{2} e^{4} n^{2} x\right)} x^{\frac{1}{3}}\right)} \log\left(\frac{d x + e x^{\frac{1}{3}}}{x}\right) - 6 \, {\left(44 \, b^{2} d e^{5} n^{2} - 120 \, a b d e^{5} n - 15 \, {\left(29 \, b^{2} d^{4} e^{2} n^{2} - 20 \, a b d^{4} e^{2} n\right)} x^{2} + 60 \, {\left(5 \, b^{2} d^{4} e^{2} n x^{2} - 2 \, b^{2} d e^{5} n\right)} \log\left(c\right)\right)} x^{\frac{2}{3}} - 15 \, {\left(12 \, {\left(49 \, b^{2} d^{5} e n^{2} - 20 \, a b d^{5} e n\right)} x^{3} - {\left(37 \, b^{2} d^{2} e^{4} n^{2} - 60 \, a b d^{2} e^{4} n\right)} x - 60 \, {\left(4 \, b^{2} d^{5} e n x^{3} - b^{2} d^{2} e^{4} n x\right)} \log\left(c\right)\right)} x^{\frac{1}{3}}}{7200 \, e^{6} x^{4}}"," ",0,"-1/7200*(100*b^2*e^6*n^2 + 1800*b^2*e^6*log(c)^2 - 600*a*b*e^6*n + 1800*a^2*e^6 - 60*(19*b^2*d^3*e^3*n^2 - 20*a*b*d^3*e^3*n)*x^2 - 1800*(b^2*d^6*n^2*x^4 - b^2*e^6*n^2)*log((d*x + e*x^(1/3))/x)^2 + 600*(2*b^2*d^3*e^3*n*x^2 - b^2*e^6*n + 6*a*b*e^6)*log(c) + 60*(20*b^2*d^3*e^3*n^2*x^2 - 10*b^2*e^6*n^2 + 60*a*b*e^6*n + 3*(49*b^2*d^6*n^2 - 20*a*b*d^6*n)*x^4 - 60*(b^2*d^6*n*x^4 - b^2*e^6*n)*log(c) - 6*(5*b^2*d^4*e^2*n^2*x^2 - 2*b^2*d*e^5*n^2)*x^(2/3) + 15*(4*b^2*d^5*e*n^2*x^3 - b^2*d^2*e^4*n^2*x)*x^(1/3))*log((d*x + e*x^(1/3))/x) - 6*(44*b^2*d*e^5*n^2 - 120*a*b*d*e^5*n - 15*(29*b^2*d^4*e^2*n^2 - 20*a*b*d^4*e^2*n)*x^2 + 60*(5*b^2*d^4*e^2*n*x^2 - 2*b^2*d*e^5*n)*log(c))*x^(2/3) - 15*(12*(49*b^2*d^5*e*n^2 - 20*a*b*d^5*e*n)*x^3 - (37*b^2*d^2*e^4*n^2 - 60*a*b*d^2*e^4*n)*x - 60*(4*b^2*d^5*e*n*x^3 - b^2*d^2*e^4*n*x)*log(c))*x^(1/3))/(e^6*x^4)","A",0
521,0,0,0,1.011449," ","integrate(x^2*(a+b*log(c*(d+e/x^(2/3))^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{2} \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right)^{2} + 2 \, a b x^{2} \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right) + a^{2} x^{2}, x\right)"," ",0,"integral(b^2*x^2*log(c*((d*x + e*x^(1/3))/x)^n)^2 + 2*a*b*x^2*log(c*((d*x + e*x^(1/3))/x)^n) + a^2*x^2, x)","F",0
522,0,0,0,0.955101," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right)^{2} + 2 \, a b \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right) + a^{2}, x\right)"," ",0,"integral(b^2*log(c*((d*x + e*x^(1/3))/x)^n)^2 + 2*a*b*log(c*((d*x + e*x^(1/3))/x)^n) + a^2, x)","F",0
523,0,0,0,0.977147," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right)^{2} + 2 \, a b \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right) + a^{2}}{x^{2}}, x\right)"," ",0,"integral((b^2*log(c*((d*x + e*x^(1/3))/x)^n)^2 + 2*a*b*log(c*((d*x + e*x^(1/3))/x)^n) + a^2)/x^2, x)","F",0
524,0,0,0,1.018842," ","integrate(x^3*(a+b*log(c*(d+e/x^(2/3))^n))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{3} \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right)^{3} + 3 \, a b^{2} x^{3} \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right)^{2} + 3 \, a^{2} b x^{3} \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right) + a^{3} x^{3}, x\right)"," ",0,"integral(b^3*x^3*log(c*((d*x + e*x^(1/3))/x)^n)^3 + 3*a*b^2*x^3*log(c*((d*x + e*x^(1/3))/x)^n)^2 + 3*a^2*b*x^3*log(c*((d*x + e*x^(1/3))/x)^n) + a^3*x^3, x)","F",0
525,0,0,0,0.876993," ","integrate(x*(a+b*log(c*(d+e/x^(2/3))^n))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right)^{3} + 3 \, a b^{2} x \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right)^{2} + 3 \, a^{2} b x \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right) + a^{3} x, x\right)"," ",0,"integral(b^3*x*log(c*((d*x + e*x^(1/3))/x)^n)^3 + 3*a*b^2*x*log(c*((d*x + e*x^(1/3))/x)^n)^2 + 3*a^2*b*x*log(c*((d*x + e*x^(1/3))/x)^n) + a^3*x, x)","F",0
526,0,0,0,0.687804," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right)^{3} + 3 \, a b^{2} \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right)^{2} + 3 \, a^{2} b \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right) + a^{3}}{x}, x\right)"," ",0,"integral((b^3*log(c*((d*x + e*x^(1/3))/x)^n)^3 + 3*a*b^2*log(c*((d*x + e*x^(1/3))/x)^n)^2 + 3*a^2*b*log(c*((d*x + e*x^(1/3))/x)^n) + a^3)/x, x)","F",0
527,1,725,0,0.984849," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))^3/x^3,x, algorithm=""fricas"")","\frac{8 \, b^{3} e^{3} n^{3} - 36 \, b^{3} e^{3} \log\left(c\right)^{3} - 24 \, a b^{2} e^{3} n^{2} + 36 \, a^{2} b e^{3} n - 36 \, a^{3} e^{3} - 36 \, {\left(b^{3} d^{3} n^{3} x^{2} + b^{3} e^{3} n^{3}\right)} \log\left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{3} + 36 \, {\left(b^{3} e^{3} n - 3 \, a b^{2} e^{3}\right)} \log\left(c\right)^{2} + 18 \, {\left(6 \, b^{3} d^{2} e n^{3} x^{\frac{4}{3}} - 3 \, b^{3} d e^{2} n^{3} x^{\frac{2}{3}} + 2 \, b^{3} e^{3} n^{3} - 6 \, a b^{2} e^{3} n^{2} + {\left(11 \, b^{3} d^{3} n^{3} - 6 \, a b^{2} d^{3} n^{2}\right)} x^{2} - 6 \, {\left(b^{3} d^{3} n^{2} x^{2} + b^{3} e^{3} n^{2}\right)} \log\left(c\right)\right)} \log\left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{2} - 12 \, {\left(2 \, b^{3} e^{3} n^{2} - 6 \, a b^{2} e^{3} n + 9 \, a^{2} b e^{3}\right)} \log\left(c\right) - 6 \, {\left(4 \, b^{3} e^{3} n^{3} - 12 \, a b^{2} e^{3} n^{2} + 18 \, a^{2} b e^{3} n + {\left(85 \, b^{3} d^{3} n^{3} - 66 \, a b^{2} d^{3} n^{2} + 18 \, a^{2} b d^{3} n\right)} x^{2} + 18 \, {\left(b^{3} d^{3} n x^{2} + b^{3} e^{3} n\right)} \log\left(c\right)^{2} - 6 \, {\left(2 \, b^{3} e^{3} n^{2} - 6 \, a b^{2} e^{3} n + {\left(11 \, b^{3} d^{3} n^{2} - 6 \, a b^{2} d^{3} n\right)} x^{2}\right)} \log\left(c\right) - 3 \, {\left(5 \, b^{3} d e^{2} n^{3} - 6 \, b^{3} d e^{2} n^{2} \log\left(c\right) - 6 \, a b^{2} d e^{2} n^{2}\right)} x^{\frac{2}{3}} - 6 \, {\left(6 \, b^{3} d^{2} e n^{2} x \log\left(c\right) - {\left(11 \, b^{3} d^{2} e n^{3} - 6 \, a b^{2} d^{2} e n^{2}\right)} x\right)} x^{\frac{1}{3}}\right)} \log\left(\frac{d x + e x^{\frac{1}{3}}}{x}\right) - 3 \, {\left(19 \, b^{3} d e^{2} n^{3} + 18 \, b^{3} d e^{2} n \log\left(c\right)^{2} - 30 \, a b^{2} d e^{2} n^{2} + 18 \, a^{2} b d e^{2} n - 6 \, {\left(5 \, b^{3} d e^{2} n^{2} - 6 \, a b^{2} d e^{2} n\right)} \log\left(c\right)\right)} x^{\frac{2}{3}} + 6 \, {\left(18 \, b^{3} d^{2} e n x \log\left(c\right)^{2} - 6 \, {\left(11 \, b^{3} d^{2} e n^{2} - 6 \, a b^{2} d^{2} e n\right)} x \log\left(c\right) + {\left(85 \, b^{3} d^{2} e n^{3} - 66 \, a b^{2} d^{2} e n^{2} + 18 \, a^{2} b d^{2} e n\right)} x\right)} x^{\frac{1}{3}}}{72 \, e^{3} x^{2}}"," ",0,"1/72*(8*b^3*e^3*n^3 - 36*b^3*e^3*log(c)^3 - 24*a*b^2*e^3*n^2 + 36*a^2*b*e^3*n - 36*a^3*e^3 - 36*(b^3*d^3*n^3*x^2 + b^3*e^3*n^3)*log((d*x + e*x^(1/3))/x)^3 + 36*(b^3*e^3*n - 3*a*b^2*e^3)*log(c)^2 + 18*(6*b^3*d^2*e*n^3*x^(4/3) - 3*b^3*d*e^2*n^3*x^(2/3) + 2*b^3*e^3*n^3 - 6*a*b^2*e^3*n^2 + (11*b^3*d^3*n^3 - 6*a*b^2*d^3*n^2)*x^2 - 6*(b^3*d^3*n^2*x^2 + b^3*e^3*n^2)*log(c))*log((d*x + e*x^(1/3))/x)^2 - 12*(2*b^3*e^3*n^2 - 6*a*b^2*e^3*n + 9*a^2*b*e^3)*log(c) - 6*(4*b^3*e^3*n^3 - 12*a*b^2*e^3*n^2 + 18*a^2*b*e^3*n + (85*b^3*d^3*n^3 - 66*a*b^2*d^3*n^2 + 18*a^2*b*d^3*n)*x^2 + 18*(b^3*d^3*n*x^2 + b^3*e^3*n)*log(c)^2 - 6*(2*b^3*e^3*n^2 - 6*a*b^2*e^3*n + (11*b^3*d^3*n^2 - 6*a*b^2*d^3*n)*x^2)*log(c) - 3*(5*b^3*d*e^2*n^3 - 6*b^3*d*e^2*n^2*log(c) - 6*a*b^2*d*e^2*n^2)*x^(2/3) - 6*(6*b^3*d^2*e*n^2*x*log(c) - (11*b^3*d^2*e*n^3 - 6*a*b^2*d^2*e*n^2)*x)*x^(1/3))*log((d*x + e*x^(1/3))/x) - 3*(19*b^3*d*e^2*n^3 + 18*b^3*d*e^2*n*log(c)^2 - 30*a*b^2*d*e^2*n^2 + 18*a^2*b*d*e^2*n - 6*(5*b^3*d*e^2*n^2 - 6*a*b^2*d*e^2*n)*log(c))*x^(2/3) + 6*(18*b^3*d^2*e*n*x*log(c)^2 - 6*(11*b^3*d^2*e*n^2 - 6*a*b^2*d^2*e*n)*x*log(c) + (85*b^3*d^2*e*n^3 - 66*a*b^2*d^2*e*n^2 + 18*a^2*b*d^2*e*n)*x)*x^(1/3))/(e^3*x^2)","A",0
528,0,0,0,0.911817," ","integrate(x^2*(a+b*log(c*(d+e/x^(2/3))^n))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{2} \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right)^{3} + 3 \, a b^{2} x^{2} \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right)^{2} + 3 \, a^{2} b x^{2} \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right) + a^{3} x^{2}, x\right)"," ",0,"integral(b^3*x^2*log(c*((d*x + e*x^(1/3))/x)^n)^3 + 3*a*b^2*x^2*log(c*((d*x + e*x^(1/3))/x)^n)^2 + 3*a^2*b*x^2*log(c*((d*x + e*x^(1/3))/x)^n) + a^3*x^2, x)","F",0
529,0,0,0,0.918997," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right)^{3} + 3 \, a b^{2} \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right)^{2} + 3 \, a^{2} b \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right) + a^{3}, x\right)"," ",0,"integral(b^3*log(c*((d*x + e*x^(1/3))/x)^n)^3 + 3*a*b^2*log(c*((d*x + e*x^(1/3))/x)^n)^2 + 3*a^2*b*log(c*((d*x + e*x^(1/3))/x)^n) + a^3, x)","F",0
530,0,0,0,0.915141," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))^3/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right)^{3} + 3 \, a b^{2} \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right)^{2} + 3 \, a^{2} b \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right) + a^{3}}{x^{2}}, x\right)"," ",0,"integral((b^3*log(c*((d*x + e*x^(1/3))/x)^n)^3 + 3*a*b^2*log(c*((d*x + e*x^(1/3))/x)^n)^2 + 3*a^2*b*log(c*((d*x + e*x^(1/3))/x)^n) + a^3)/x^2, x)","F",0
531,0,0,0,0.715465," ","integrate((a+b*log(c*(d+e/x^(2/3))^n))^3/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right)^{3} + 3 \, a b^{2} \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right)^{2} + 3 \, a^{2} b \log\left(c \left(\frac{d x + e x^{\frac{1}{3}}}{x}\right)^{n}\right) + a^{3}}{x^{4}}, x\right)"," ",0,"integral((b^3*log(c*((d*x + e*x^(1/3))/x)^n)^3 + 3*a*b^2*log(c*((d*x + e*x^(1/3))/x)^n)^2 + 3*a^2*b*log(c*((d*x + e*x^(1/3))/x)^n) + a^3)/x^4, x)","F",0
532,0,0,0,1.025071," ","integrate(x^3*(a+b*log(c*(d+e*x^(1/2))))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(c e \sqrt{x} + c d\right) + a\right)}^{p} x^{3}, x\right)"," ",0,"integral((b*log(c*e*sqrt(x) + c*d) + a)^p*x^3, x)","F",0
533,0,0,0,1.018527," ","integrate(x^2*(a+b*log(c*(d+e*x^(1/2))))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(c e \sqrt{x} + c d\right) + a\right)}^{p} x^{2}, x\right)"," ",0,"integral((b*log(c*e*sqrt(x) + c*d) + a)^p*x^2, x)","F",0
534,0,0,0,1.028275," ","integrate(x*(a+b*log(c*(d+e*x^(1/2))))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(c e \sqrt{x} + c d\right) + a\right)}^{p} x, x\right)"," ",0,"integral((b*log(c*e*sqrt(x) + c*d) + a)^p*x, x)","F",0
535,0,0,0,0.973758," ","integrate((a+b*log(c*(d+e*x^(1/2))))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(c e \sqrt{x} + c d\right) + a\right)}^{p}, x\right)"," ",0,"integral((b*log(c*e*sqrt(x) + c*d) + a)^p, x)","F",0
536,0,0,0,0.932606," ","integrate((a+b*log(c*(d+e*x^(1/2))))^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(c e \sqrt{x} + c d\right) + a\right)}^{p}}{x}, x\right)"," ",0,"integral((b*log(c*e*sqrt(x) + c*d) + a)^p/x, x)","F",0
537,0,0,0,1.003408," ","integrate((a+b*log(c*(d+e*x^(1/2))))^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(c e \sqrt{x} + c d\right) + a\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((b*log(c*e*sqrt(x) + c*d) + a)^p/x^2, x)","F",0
538,0,0,0,0.970011," ","integrate(x^3*(a+b*log(c*(d+e*x^(1/2))^2))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(c e^{2} x + 2 \, c d e \sqrt{x} + c d^{2}\right) + a\right)}^{p} x^{3}, x\right)"," ",0,"integral((b*log(c*e^2*x + 2*c*d*e*sqrt(x) + c*d^2) + a)^p*x^3, x)","F",0
539,0,0,0,0.728668," ","integrate(x^2*(a+b*log(c*(d+e*x^(1/2))^2))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(c e^{2} x + 2 \, c d e \sqrt{x} + c d^{2}\right) + a\right)}^{p} x^{2}, x\right)"," ",0,"integral((b*log(c*e^2*x + 2*c*d*e*sqrt(x) + c*d^2) + a)^p*x^2, x)","F",0
540,0,0,0,0.967390," ","integrate(x*(a+b*log(c*(d+e*x^(1/2))^2))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(c e^{2} x + 2 \, c d e \sqrt{x} + c d^{2}\right) + a\right)}^{p} x, x\right)"," ",0,"integral((b*log(c*e^2*x + 2*c*d*e*sqrt(x) + c*d^2) + a)^p*x, x)","F",0
541,0,0,0,0.976755," ","integrate((a+b*log(c*(d+e*x^(1/2))^2))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(c e^{2} x + 2 \, c d e \sqrt{x} + c d^{2}\right) + a\right)}^{p}, x\right)"," ",0,"integral((b*log(c*e^2*x + 2*c*d*e*sqrt(x) + c*d^2) + a)^p, x)","F",0
542,0,0,0,0.959893," ","integrate((a+b*log(c*(d+e*x^(1/2))^2))^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(c e^{2} x + 2 \, c d e \sqrt{x} + c d^{2}\right) + a\right)}^{p}}{x}, x\right)"," ",0,"integral((b*log(c*e^2*x + 2*c*d*e*sqrt(x) + c*d^2) + a)^p/x, x)","F",0
543,0,0,0,0.920928," ","integrate((a+b*log(c*(d+e*x^(1/2))^2))^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(c e^{2} x + 2 \, c d e \sqrt{x} + c d^{2}\right) + a\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((b*log(c*e^2*x + 2*c*d*e*sqrt(x) + c*d^2) + a)^p/x^2, x)","F",0
544,0,0,0,0.803680," ","integrate(x*(a+b*log(c*(d+e/x^(1/2))))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(\frac{c d x + c e \sqrt{x}}{x}\right) + a\right)}^{p} x, x\right)"," ",0,"integral((b*log((c*d*x + c*e*sqrt(x))/x) + a)^p*x, x)","F",0
545,0,0,0,0.954277," ","integrate((a+b*log(c*(d+e/x^(1/2))))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(\frac{c d x + c e \sqrt{x}}{x}\right) + a\right)}^{p}, x\right)"," ",0,"integral((b*log((c*d*x + c*e*sqrt(x))/x) + a)^p, x)","F",0
546,0,0,0,0.951406," ","integrate((a+b*log(c*(d+e/x^(1/2))))^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(\frac{c d x + c e \sqrt{x}}{x}\right) + a\right)}^{p}}{x}, x\right)"," ",0,"integral((b*log((c*d*x + c*e*sqrt(x))/x) + a)^p/x, x)","F",0
547,0,0,0,0.924888," ","integrate((a+b*log(c*(d+e/x^(1/2))))^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(\frac{c d x + c e \sqrt{x}}{x}\right) + a\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((b*log((c*d*x + c*e*sqrt(x))/x) + a)^p/x^2, x)","F",0
548,0,0,0,0.791603," ","integrate((a+b*log(c*(d+e/x^(1/2))))^p/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(\frac{c d x + c e \sqrt{x}}{x}\right) + a\right)}^{p}}{x^{4}}, x\right)"," ",0,"integral((b*log((c*d*x + c*e*sqrt(x))/x) + a)^p/x^4, x)","F",0
549,0,0,0,0.903054," ","integrate((a+b*log(c*(d+e/x^(1/2))))^p/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(\frac{c d x + c e \sqrt{x}}{x}\right) + a\right)}^{p}}{x^{6}}, x\right)"," ",0,"integral((b*log((c*d*x + c*e*sqrt(x))/x) + a)^p/x^6, x)","F",0
550,0,0,0,0.798190," ","integrate(x*(a+b*log(c*(d+e/x^(1/2))^2))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(\frac{c d^{2} x + 2 \, c d e \sqrt{x} + c e^{2}}{x}\right) + a\right)}^{p} x, x\right)"," ",0,"integral((b*log((c*d^2*x + 2*c*d*e*sqrt(x) + c*e^2)/x) + a)^p*x, x)","F",0
551,0,0,0,0.652183," ","integrate((a+b*log(c*(d+e/x^(1/2))^2))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(\frac{c d^{2} x + 2 \, c d e \sqrt{x} + c e^{2}}{x}\right) + a\right)}^{p}, x\right)"," ",0,"integral((b*log((c*d^2*x + 2*c*d*e*sqrt(x) + c*e^2)/x) + a)^p, x)","F",0
552,0,0,0,0.726407," ","integrate((a+b*log(c*(d+e/x^(1/2))^2))^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(\frac{c d^{2} x + 2 \, c d e \sqrt{x} + c e^{2}}{x}\right) + a\right)}^{p}}{x}, x\right)"," ",0,"integral((b*log((c*d^2*x + 2*c*d*e*sqrt(x) + c*e^2)/x) + a)^p/x, x)","F",0
553,0,0,0,1.033647," ","integrate((a+b*log(c*(d+e/x^(1/2))^2))^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(\frac{c d^{2} x + 2 \, c d e \sqrt{x} + c e^{2}}{x}\right) + a\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((b*log((c*d^2*x + 2*c*d*e*sqrt(x) + c*e^2)/x) + a)^p/x^2, x)","F",0
554,0,0,0,0.957402," ","integrate((a+b*log(c*(d+e/x^(1/2))^2))^p/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(\frac{c d^{2} x + 2 \, c d e \sqrt{x} + c e^{2}}{x}\right) + a\right)}^{p}}{x^{4}}, x\right)"," ",0,"integral((b*log((c*d^2*x + 2*c*d*e*sqrt(x) + c*e^2)/x) + a)^p/x^4, x)","F",0
555,0,0,0,0.807210," ","integrate((a+b*log(c*(d+e/x^(1/2))^2))^p/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(\frac{c d^{2} x + 2 \, c d e \sqrt{x} + c e^{2}}{x}\right) + a\right)}^{p}}{x^{6}}, x\right)"," ",0,"integral((b*log((c*d^2*x + 2*c*d*e*sqrt(x) + c*e^2)/x) + a)^p/x^6, x)","F",0
556,0,0,0,0.987727," ","integrate(x^3*(a+b*log(c*(d+e*x^(1/3))))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(c e x^{\frac{1}{3}} + c d\right) + a\right)}^{p} x^{3}, x\right)"," ",0,"integral((b*log(c*e*x^(1/3) + c*d) + a)^p*x^3, x)","F",0
557,0,0,0,0.894092," ","integrate(x^2*(a+b*log(c*(d+e*x^(1/3))))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(c e x^{\frac{1}{3}} + c d\right) + a\right)}^{p} x^{2}, x\right)"," ",0,"integral((b*log(c*e*x^(1/3) + c*d) + a)^p*x^2, x)","F",0
558,0,0,0,0.984464," ","integrate(x*(a+b*log(c*(d+e*x^(1/3))))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(c e x^{\frac{1}{3}} + c d\right) + a\right)}^{p} x, x\right)"," ",0,"integral((b*log(c*e*x^(1/3) + c*d) + a)^p*x, x)","F",0
559,0,0,0,0.960169," ","integrate((a+b*log(c*(d+e*x^(1/3))))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(c e x^{\frac{1}{3}} + c d\right) + a\right)}^{p}, x\right)"," ",0,"integral((b*log(c*e*x^(1/3) + c*d) + a)^p, x)","F",0
560,0,0,0,0.941913," ","integrate((a+b*log(c*(d+e*x^(1/3))))^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(c e x^{\frac{1}{3}} + c d\right) + a\right)}^{p}}{x}, x\right)"," ",0,"integral((b*log(c*e*x^(1/3) + c*d) + a)^p/x, x)","F",0
561,0,0,0,1.010740," ","integrate((a+b*log(c*(d+e*x^(1/3))))^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(c e x^{\frac{1}{3}} + c d\right) + a\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((b*log(c*e*x^(1/3) + c*d) + a)^p/x^2, x)","F",0
562,0,0,0,0.728731," ","integrate(x^3*(a+b*log(c*(d+e*x^(1/3))^2))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(c e^{2} x^{\frac{2}{3}} + 2 \, c d e x^{\frac{1}{3}} + c d^{2}\right) + a\right)}^{p} x^{3}, x\right)"," ",0,"integral((b*log(c*e^2*x^(2/3) + 2*c*d*e*x^(1/3) + c*d^2) + a)^p*x^3, x)","F",0
563,0,0,0,0.998753," ","integrate(x^2*(a+b*log(c*(d+e*x^(1/3))^2))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(c e^{2} x^{\frac{2}{3}} + 2 \, c d e x^{\frac{1}{3}} + c d^{2}\right) + a\right)}^{p} x^{2}, x\right)"," ",0,"integral((b*log(c*e^2*x^(2/3) + 2*c*d*e*x^(1/3) + c*d^2) + a)^p*x^2, x)","F",0
564,0,0,0,1.030681," ","integrate(x*(a+b*log(c*(d+e*x^(1/3))^2))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(c e^{2} x^{\frac{2}{3}} + 2 \, c d e x^{\frac{1}{3}} + c d^{2}\right) + a\right)}^{p} x, x\right)"," ",0,"integral((b*log(c*e^2*x^(2/3) + 2*c*d*e*x^(1/3) + c*d^2) + a)^p*x, x)","F",0
565,0,0,0,0.678039," ","integrate((a+b*log(c*(d+e*x^(1/3))^2))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(c e^{2} x^{\frac{2}{3}} + 2 \, c d e x^{\frac{1}{3}} + c d^{2}\right) + a\right)}^{p}, x\right)"," ",0,"integral((b*log(c*e^2*x^(2/3) + 2*c*d*e*x^(1/3) + c*d^2) + a)^p, x)","F",0
566,0,0,0,1.009601," ","integrate((a+b*log(c*(d+e*x^(1/3))^2))^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(c e^{2} x^{\frac{2}{3}} + 2 \, c d e x^{\frac{1}{3}} + c d^{2}\right) + a\right)}^{p}}{x}, x\right)"," ",0,"integral((b*log(c*e^2*x^(2/3) + 2*c*d*e*x^(1/3) + c*d^2) + a)^p/x, x)","F",0
567,0,0,0,1.002221," ","integrate((a+b*log(c*(d+e*x^(1/3))^2))^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(c e^{2} x^{\frac{2}{3}} + 2 \, c d e x^{\frac{1}{3}} + c d^{2}\right) + a\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((b*log(c*e^2*x^(2/3) + 2*c*d*e*x^(1/3) + c*d^2) + a)^p/x^2, x)","F",0
568,0,0,0,0.801102," ","integrate(x^3*(a+b*log(c*(d+e*x^(2/3))))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(c e x^{\frac{2}{3}} + c d\right) + a\right)}^{p} x^{3}, x\right)"," ",0,"integral((b*log(c*e*x^(2/3) + c*d) + a)^p*x^3, x)","F",0
569,0,0,0,0.910415," ","integrate(x*(a+b*log(c*(d+e*x^(2/3))))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(c e x^{\frac{2}{3}} + c d\right) + a\right)}^{p} x, x\right)"," ",0,"integral((b*log(c*e*x^(2/3) + c*d) + a)^p*x, x)","F",0
570,0,0,0,1.029502," ","integrate((a+b*log(c*(d+e*x^(2/3))))^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(c e x^{\frac{2}{3}} + c d\right) + a\right)}^{p}}{x}, x\right)"," ",0,"integral((b*log(c*e*x^(2/3) + c*d) + a)^p/x, x)","F",0
571,0,0,0,1.026417," ","integrate((a+b*log(c*(d+e*x^(2/3))))^p/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(c e x^{\frac{2}{3}} + c d\right) + a\right)}^{p}}{x^{3}}, x\right)"," ",0,"integral((b*log(c*e*x^(2/3) + c*d) + a)^p/x^3, x)","F",0
572,0,0,0,0.922954," ","integrate(x^2*(a+b*log(c*(d+e*x^(2/3))))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(c e x^{\frac{2}{3}} + c d\right) + a\right)}^{p} x^{2}, x\right)"," ",0,"integral((b*log(c*e*x^(2/3) + c*d) + a)^p*x^2, x)","F",0
573,0,0,0,1.038693," ","integrate((a+b*log(c*(d+e*x^(2/3))))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(c e x^{\frac{2}{3}} + c d\right) + a\right)}^{p}, x\right)"," ",0,"integral((b*log(c*e*x^(2/3) + c*d) + a)^p, x)","F",0
574,0,0,0,0.735340," ","integrate((a+b*log(c*(d+e*x^(2/3))))^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(c e x^{\frac{2}{3}} + c d\right) + a\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((b*log(c*e*x^(2/3) + c*d) + a)^p/x^2, x)","F",0
575,0,0,0,1.008426," ","integrate(x^3*(a+b*log(c*(d+e*x^(2/3))^2))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(c e^{2} x^{\frac{4}{3}} + 2 \, c d e x^{\frac{2}{3}} + c d^{2}\right) + a\right)}^{p} x^{3}, x\right)"," ",0,"integral((b*log(c*e^2*x^(4/3) + 2*c*d*e*x^(2/3) + c*d^2) + a)^p*x^3, x)","F",0
576,0,0,0,1.060174," ","integrate(x*(a+b*log(c*(d+e*x^(2/3))^2))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(c e^{2} x^{\frac{4}{3}} + 2 \, c d e x^{\frac{2}{3}} + c d^{2}\right) + a\right)}^{p} x, x\right)"," ",0,"integral((b*log(c*e^2*x^(4/3) + 2*c*d*e*x^(2/3) + c*d^2) + a)^p*x, x)","F",0
577,0,0,0,1.018356," ","integrate((a+b*log(c*(d+e*x^(2/3))^2))^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(c e^{2} x^{\frac{4}{3}} + 2 \, c d e x^{\frac{2}{3}} + c d^{2}\right) + a\right)}^{p}}{x}, x\right)"," ",0,"integral((b*log(c*e^2*x^(4/3) + 2*c*d*e*x^(2/3) + c*d^2) + a)^p/x, x)","F",0
578,0,0,0,1.049602," ","integrate((a+b*log(c*(d+e*x^(2/3))^2))^p/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(c e^{2} x^{\frac{4}{3}} + 2 \, c d e x^{\frac{2}{3}} + c d^{2}\right) + a\right)}^{p}}{x^{3}}, x\right)"," ",0,"integral((b*log(c*e^2*x^(4/3) + 2*c*d*e*x^(2/3) + c*d^2) + a)^p/x^3, x)","F",0
579,0,0,0,0.832034," ","integrate(x^2*(a+b*log(c*(d+e*x^(2/3))^2))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(c e^{2} x^{\frac{4}{3}} + 2 \, c d e x^{\frac{2}{3}} + c d^{2}\right) + a\right)}^{p} x^{2}, x\right)"," ",0,"integral((b*log(c*e^2*x^(4/3) + 2*c*d*e*x^(2/3) + c*d^2) + a)^p*x^2, x)","F",0
580,0,0,0,1.035732," ","integrate((a+b*log(c*(d+e*x^(2/3))^2))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(c e^{2} x^{\frac{4}{3}} + 2 \, c d e x^{\frac{2}{3}} + c d^{2}\right) + a\right)}^{p}, x\right)"," ",0,"integral((b*log(c*e^2*x^(4/3) + 2*c*d*e*x^(2/3) + c*d^2) + a)^p, x)","F",0
581,0,0,0,1.237616," ","integrate((a+b*log(c*(d+e*x^(2/3))^2))^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(c e^{2} x^{\frac{4}{3}} + 2 \, c d e x^{\frac{2}{3}} + c d^{2}\right) + a\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((b*log(c*e^2*x^(4/3) + 2*c*d*e*x^(2/3) + c*d^2) + a)^p/x^2, x)","F",0
582,0,0,0,1.106344," ","integrate(x*(a+b*log(c*(d+e/x^(1/3))))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(\frac{c d x + c e x^{\frac{2}{3}}}{x}\right) + a\right)}^{p} x, x\right)"," ",0,"integral((b*log((c*d*x + c*e*x^(2/3))/x) + a)^p*x, x)","F",0
583,0,0,0,0.657094," ","integrate((a+b*log(c*(d+e/x^(1/3))))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(\frac{c d x + c e x^{\frac{2}{3}}}{x}\right) + a\right)}^{p}, x\right)"," ",0,"integral((b*log((c*d*x + c*e*x^(2/3))/x) + a)^p, x)","F",0
584,0,0,0,0.680631," ","integrate((a+b*log(c*(d+e/x^(1/3))))^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(\frac{c d x + c e x^{\frac{2}{3}}}{x}\right) + a\right)}^{p}}{x}, x\right)"," ",0,"integral((b*log((c*d*x + c*e*x^(2/3))/x) + a)^p/x, x)","F",0
585,0,0,0,1.025110," ","integrate((a+b*log(c*(d+e/x^(1/3))))^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(\frac{c d x + c e x^{\frac{2}{3}}}{x}\right) + a\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((b*log((c*d*x + c*e*x^(2/3))/x) + a)^p/x^2, x)","F",0
586,0,0,0,0.626719," ","integrate((a+b*log(c*(d+e/x^(1/3))))^p/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(\frac{c d x + c e x^{\frac{2}{3}}}{x}\right) + a\right)}^{p}}{x^{3}}, x\right)"," ",0,"integral((b*log((c*d*x + c*e*x^(2/3))/x) + a)^p/x^3, x)","F",0
587,0,0,0,0.786197," ","integrate((a+b*log(c*(d+e/x^(1/3))))^p/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(\frac{c d x + c e x^{\frac{2}{3}}}{x}\right) + a\right)}^{p}}{x^{4}}, x\right)"," ",0,"integral((b*log((c*d*x + c*e*x^(2/3))/x) + a)^p/x^4, x)","F",0
588,0,0,0,1.020679," ","integrate(x*(a+b*log(c*(d+e/x^(1/3))^2))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(\frac{c d^{2} x + 2 \, c d e x^{\frac{2}{3}} + c e^{2} x^{\frac{1}{3}}}{x}\right) + a\right)}^{p} x, x\right)"," ",0,"integral((b*log((c*d^2*x + 2*c*d*e*x^(2/3) + c*e^2*x^(1/3))/x) + a)^p*x, x)","F",0
589,0,0,0,0.995672," ","integrate((a+b*log(c*(d+e/x^(1/3))^2))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(\frac{c d^{2} x + 2 \, c d e x^{\frac{2}{3}} + c e^{2} x^{\frac{1}{3}}}{x}\right) + a\right)}^{p}, x\right)"," ",0,"integral((b*log((c*d^2*x + 2*c*d*e*x^(2/3) + c*e^2*x^(1/3))/x) + a)^p, x)","F",0
590,0,0,0,0.791920," ","integrate((a+b*log(c*(d+e/x^(1/3))^2))^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(\frac{c d^{2} x + 2 \, c d e x^{\frac{2}{3}} + c e^{2} x^{\frac{1}{3}}}{x}\right) + a\right)}^{p}}{x}, x\right)"," ",0,"integral((b*log((c*d^2*x + 2*c*d*e*x^(2/3) + c*e^2*x^(1/3))/x) + a)^p/x, x)","F",0
591,0,0,0,1.010053," ","integrate((a+b*log(c*(d+e/x^(1/3))^2))^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(\frac{c d^{2} x + 2 \, c d e x^{\frac{2}{3}} + c e^{2} x^{\frac{1}{3}}}{x}\right) + a\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((b*log((c*d^2*x + 2*c*d*e*x^(2/3) + c*e^2*x^(1/3))/x) + a)^p/x^2, x)","F",0
592,0,0,0,0.884987," ","integrate((a+b*log(c*(d+e/x^(1/3))^2))^p/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(\frac{c d^{2} x + 2 \, c d e x^{\frac{2}{3}} + c e^{2} x^{\frac{1}{3}}}{x}\right) + a\right)}^{p}}{x^{3}}, x\right)"," ",0,"integral((b*log((c*d^2*x + 2*c*d*e*x^(2/3) + c*e^2*x^(1/3))/x) + a)^p/x^3, x)","F",0
593,0,0,0,0.884566," ","integrate((a+b*log(c*(d+e/x^(1/3))^2))^p/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(\frac{c d^{2} x + 2 \, c d e x^{\frac{2}{3}} + c e^{2} x^{\frac{1}{3}}}{x}\right) + a\right)}^{p}}{x^{4}}, x\right)"," ",0,"integral((b*log((c*d^2*x + 2*c*d*e*x^(2/3) + c*e^2*x^(1/3))/x) + a)^p/x^4, x)","F",0
594,0,0,0,0.938279," ","integrate(x^3*(a+b*log(c*(d+e/x^(2/3))))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(\frac{c d x + c e x^{\frac{1}{3}}}{x}\right) + a\right)}^{p} x^{3}, x\right)"," ",0,"integral((b*log((c*d*x + c*e*x^(1/3))/x) + a)^p*x^3, x)","F",0
595,0,0,0,0.926491," ","integrate(x^2*(a+b*log(c*(d+e/x^(2/3))))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(\frac{c d x + c e x^{\frac{1}{3}}}{x}\right) + a\right)}^{p} x^{2}, x\right)"," ",0,"integral((b*log((c*d*x + c*e*x^(1/3))/x) + a)^p*x^2, x)","F",0
596,0,0,0,1.085506," ","integrate(x*(a+b*log(c*(d+e/x^(2/3))))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(\frac{c d x + c e x^{\frac{1}{3}}}{x}\right) + a\right)}^{p} x, x\right)"," ",0,"integral((b*log((c*d*x + c*e*x^(1/3))/x) + a)^p*x, x)","F",0
597,0,0,0,1.022694," ","integrate((a+b*log(c*(d+e/x^(2/3))))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(\frac{c d x + c e x^{\frac{1}{3}}}{x}\right) + a\right)}^{p}, x\right)"," ",0,"integral((b*log((c*d*x + c*e*x^(1/3))/x) + a)^p, x)","F",0
598,0,0,0,0.995452," ","integrate((a+b*log(c*(d+e/x^(2/3))))^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(\frac{c d x + c e x^{\frac{1}{3}}}{x}\right) + a\right)}^{p}}{x}, x\right)"," ",0,"integral((b*log((c*d*x + c*e*x^(1/3))/x) + a)^p/x, x)","F",0
599,0,0,0,1.056807," ","integrate((a+b*log(c*(d+e/x^(2/3))))^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(\frac{c d x + c e x^{\frac{1}{3}}}{x}\right) + a\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((b*log((c*d*x + c*e*x^(1/3))/x) + a)^p/x^2, x)","F",0
600,0,0,0,0.902156," ","integrate(x^3*(a+b*log(c*(d+e/x^(2/3))^2))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(\frac{c d^{2} x^{2} + 2 \, c d e x^{\frac{4}{3}} + c e^{2} x^{\frac{2}{3}}}{x^{2}}\right) + a\right)}^{p} x^{3}, x\right)"," ",0,"integral((b*log((c*d^2*x^2 + 2*c*d*e*x^(4/3) + c*e^2*x^(2/3))/x^2) + a)^p*x^3, x)","F",0
601,0,0,0,0.828194," ","integrate(x^2*(a+b*log(c*(d+e/x^(2/3))^2))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(\frac{c d^{2} x^{2} + 2 \, c d e x^{\frac{4}{3}} + c e^{2} x^{\frac{2}{3}}}{x^{2}}\right) + a\right)}^{p} x^{2}, x\right)"," ",0,"integral((b*log((c*d^2*x^2 + 2*c*d*e*x^(4/3) + c*e^2*x^(2/3))/x^2) + a)^p*x^2, x)","F",0
602,0,0,0,0.675128," ","integrate(x*(a+b*log(c*(d+e/x^(2/3))^2))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(\frac{c d^{2} x^{2} + 2 \, c d e x^{\frac{4}{3}} + c e^{2} x^{\frac{2}{3}}}{x^{2}}\right) + a\right)}^{p} x, x\right)"," ",0,"integral((b*log((c*d^2*x^2 + 2*c*d*e*x^(4/3) + c*e^2*x^(2/3))/x^2) + a)^p*x, x)","F",0
603,0,0,0,0.984766," ","integrate((a+b*log(c*(d+e/x^(2/3))^2))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(\frac{c d^{2} x^{2} + 2 \, c d e x^{\frac{4}{3}} + c e^{2} x^{\frac{2}{3}}}{x^{2}}\right) + a\right)}^{p}, x\right)"," ",0,"integral((b*log((c*d^2*x^2 + 2*c*d*e*x^(4/3) + c*e^2*x^(2/3))/x^2) + a)^p, x)","F",0
604,0,0,0,1.033311," ","integrate((a+b*log(c*(d+e/x^(2/3))^2))^p/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(\frac{c d^{2} x^{2} + 2 \, c d e x^{\frac{4}{3}} + c e^{2} x^{\frac{2}{3}}}{x^{2}}\right) + a\right)}^{p}}{x}, x\right)"," ",0,"integral((b*log((c*d^2*x^2 + 2*c*d*e*x^(4/3) + c*e^2*x^(2/3))/x^2) + a)^p/x, x)","F",0
605,0,0,0,0.835527," ","integrate((a+b*log(c*(d+e/x^(2/3))^2))^p/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \log\left(\frac{c d^{2} x^{2} + 2 \, c d e x^{\frac{4}{3}} + c e^{2} x^{\frac{2}{3}}}{x^{2}}\right) + a\right)}^{p}}{x^{2}}, x\right)"," ",0,"integral((b*log((c*d^2*x^2 + 2*c*d*e*x^(4/3) + c*e^2*x^(2/3))/x^2) + a)^p/x^2, x)","F",0
606,1,1196,0,0.991217," ","integrate((g*x+f)*(a+b*log(c*(e*x^2+d)^p))/(h*x)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, h \sqrt{-\frac{6 \, b^{2} d f g p^{2} + e h \sqrt{-\frac{{\left(81 \, b^{4} d e^{2} f^{4} - 18 \, b^{4} d^{2} e f^{2} g^{2} + b^{4} d^{3} g^{4}\right)} p^{4}}{e^{3} h^{2}}}}{e h}} \log\left(-32 \, {\left(81 \, b^{3} e^{2} f^{4} - b^{3} d^{2} g^{4}\right)} \sqrt{h x} p^{3} + 32 \, {\left(e^{2} g h^{2} \sqrt{-\frac{{\left(81 \, b^{4} d e^{2} f^{4} - 18 \, b^{4} d^{2} e f^{2} g^{2} + b^{4} d^{3} g^{4}\right)} p^{4}}{e^{3} h^{2}}} + 3 \, {\left(9 \, b^{2} e^{2} f^{3} - b^{2} d e f g^{2}\right)} h p^{2}\right)} \sqrt{-\frac{6 \, b^{2} d f g p^{2} + e h \sqrt{-\frac{{\left(81 \, b^{4} d e^{2} f^{4} - 18 \, b^{4} d^{2} e f^{2} g^{2} + b^{4} d^{3} g^{4}\right)} p^{4}}{e^{3} h^{2}}}}{e h}}\right) - 3 \, h \sqrt{-\frac{6 \, b^{2} d f g p^{2} + e h \sqrt{-\frac{{\left(81 \, b^{4} d e^{2} f^{4} - 18 \, b^{4} d^{2} e f^{2} g^{2} + b^{4} d^{3} g^{4}\right)} p^{4}}{e^{3} h^{2}}}}{e h}} \log\left(-32 \, {\left(81 \, b^{3} e^{2} f^{4} - b^{3} d^{2} g^{4}\right)} \sqrt{h x} p^{3} - 32 \, {\left(e^{2} g h^{2} \sqrt{-\frac{{\left(81 \, b^{4} d e^{2} f^{4} - 18 \, b^{4} d^{2} e f^{2} g^{2} + b^{4} d^{3} g^{4}\right)} p^{4}}{e^{3} h^{2}}} + 3 \, {\left(9 \, b^{2} e^{2} f^{3} - b^{2} d e f g^{2}\right)} h p^{2}\right)} \sqrt{-\frac{6 \, b^{2} d f g p^{2} + e h \sqrt{-\frac{{\left(81 \, b^{4} d e^{2} f^{4} - 18 \, b^{4} d^{2} e f^{2} g^{2} + b^{4} d^{3} g^{4}\right)} p^{4}}{e^{3} h^{2}}}}{e h}}\right) - 3 \, h \sqrt{-\frac{6 \, b^{2} d f g p^{2} - e h \sqrt{-\frac{{\left(81 \, b^{4} d e^{2} f^{4} - 18 \, b^{4} d^{2} e f^{2} g^{2} + b^{4} d^{3} g^{4}\right)} p^{4}}{e^{3} h^{2}}}}{e h}} \log\left(-32 \, {\left(81 \, b^{3} e^{2} f^{4} - b^{3} d^{2} g^{4}\right)} \sqrt{h x} p^{3} + 32 \, {\left(e^{2} g h^{2} \sqrt{-\frac{{\left(81 \, b^{4} d e^{2} f^{4} - 18 \, b^{4} d^{2} e f^{2} g^{2} + b^{4} d^{3} g^{4}\right)} p^{4}}{e^{3} h^{2}}} - 3 \, {\left(9 \, b^{2} e^{2} f^{3} - b^{2} d e f g^{2}\right)} h p^{2}\right)} \sqrt{-\frac{6 \, b^{2} d f g p^{2} - e h \sqrt{-\frac{{\left(81 \, b^{4} d e^{2} f^{4} - 18 \, b^{4} d^{2} e f^{2} g^{2} + b^{4} d^{3} g^{4}\right)} p^{4}}{e^{3} h^{2}}}}{e h}}\right) + 3 \, h \sqrt{-\frac{6 \, b^{2} d f g p^{2} - e h \sqrt{-\frac{{\left(81 \, b^{4} d e^{2} f^{4} - 18 \, b^{4} d^{2} e f^{2} g^{2} + b^{4} d^{3} g^{4}\right)} p^{4}}{e^{3} h^{2}}}}{e h}} \log\left(-32 \, {\left(81 \, b^{3} e^{2} f^{4} - b^{3} d^{2} g^{4}\right)} \sqrt{h x} p^{3} - 32 \, {\left(e^{2} g h^{2} \sqrt{-\frac{{\left(81 \, b^{4} d e^{2} f^{4} - 18 \, b^{4} d^{2} e f^{2} g^{2} + b^{4} d^{3} g^{4}\right)} p^{4}}{e^{3} h^{2}}} - 3 \, {\left(9 \, b^{2} e^{2} f^{3} - b^{2} d e f g^{2}\right)} h p^{2}\right)} \sqrt{-\frac{6 \, b^{2} d f g p^{2} - e h \sqrt{-\frac{{\left(81 \, b^{4} d e^{2} f^{4} - 18 \, b^{4} d^{2} e f^{2} g^{2} + b^{4} d^{3} g^{4}\right)} p^{4}}{e^{3} h^{2}}}}{e h}}\right) + {\left(36 \, b f p - 9 \, a f + {\left(4 \, b g p - 3 \, a g\right)} x - 3 \, {\left(b g p x + 3 \, b f p\right)} \log\left(e x^{2} + d\right) - 3 \, {\left(b g x + 3 \, b f\right)} \log\left(c\right)\right)} \sqrt{h x}\right)}}{9 \, h}"," ",0,"-2/9*(3*h*sqrt(-(6*b^2*d*f*g*p^2 + e*h*sqrt(-(81*b^4*d*e^2*f^4 - 18*b^4*d^2*e*f^2*g^2 + b^4*d^3*g^4)*p^4/(e^3*h^2)))/(e*h))*log(-32*(81*b^3*e^2*f^4 - b^3*d^2*g^4)*sqrt(h*x)*p^3 + 32*(e^2*g*h^2*sqrt(-(81*b^4*d*e^2*f^4 - 18*b^4*d^2*e*f^2*g^2 + b^4*d^3*g^4)*p^4/(e^3*h^2)) + 3*(9*b^2*e^2*f^3 - b^2*d*e*f*g^2)*h*p^2)*sqrt(-(6*b^2*d*f*g*p^2 + e*h*sqrt(-(81*b^4*d*e^2*f^4 - 18*b^4*d^2*e*f^2*g^2 + b^4*d^3*g^4)*p^4/(e^3*h^2)))/(e*h))) - 3*h*sqrt(-(6*b^2*d*f*g*p^2 + e*h*sqrt(-(81*b^4*d*e^2*f^4 - 18*b^4*d^2*e*f^2*g^2 + b^4*d^3*g^4)*p^4/(e^3*h^2)))/(e*h))*log(-32*(81*b^3*e^2*f^4 - b^3*d^2*g^4)*sqrt(h*x)*p^3 - 32*(e^2*g*h^2*sqrt(-(81*b^4*d*e^2*f^4 - 18*b^4*d^2*e*f^2*g^2 + b^4*d^3*g^4)*p^4/(e^3*h^2)) + 3*(9*b^2*e^2*f^3 - b^2*d*e*f*g^2)*h*p^2)*sqrt(-(6*b^2*d*f*g*p^2 + e*h*sqrt(-(81*b^4*d*e^2*f^4 - 18*b^4*d^2*e*f^2*g^2 + b^4*d^3*g^4)*p^4/(e^3*h^2)))/(e*h))) - 3*h*sqrt(-(6*b^2*d*f*g*p^2 - e*h*sqrt(-(81*b^4*d*e^2*f^4 - 18*b^4*d^2*e*f^2*g^2 + b^4*d^3*g^4)*p^4/(e^3*h^2)))/(e*h))*log(-32*(81*b^3*e^2*f^4 - b^3*d^2*g^4)*sqrt(h*x)*p^3 + 32*(e^2*g*h^2*sqrt(-(81*b^4*d*e^2*f^4 - 18*b^4*d^2*e*f^2*g^2 + b^4*d^3*g^4)*p^4/(e^3*h^2)) - 3*(9*b^2*e^2*f^3 - b^2*d*e*f*g^2)*h*p^2)*sqrt(-(6*b^2*d*f*g*p^2 - e*h*sqrt(-(81*b^4*d*e^2*f^4 - 18*b^4*d^2*e*f^2*g^2 + b^4*d^3*g^4)*p^4/(e^3*h^2)))/(e*h))) + 3*h*sqrt(-(6*b^2*d*f*g*p^2 - e*h*sqrt(-(81*b^4*d*e^2*f^4 - 18*b^4*d^2*e*f^2*g^2 + b^4*d^3*g^4)*p^4/(e^3*h^2)))/(e*h))*log(-32*(81*b^3*e^2*f^4 - b^3*d^2*g^4)*sqrt(h*x)*p^3 - 32*(e^2*g*h^2*sqrt(-(81*b^4*d*e^2*f^4 - 18*b^4*d^2*e*f^2*g^2 + b^4*d^3*g^4)*p^4/(e^3*h^2)) - 3*(9*b^2*e^2*f^3 - b^2*d*e*f*g^2)*h*p^2)*sqrt(-(6*b^2*d*f*g*p^2 - e*h*sqrt(-(81*b^4*d*e^2*f^4 - 18*b^4*d^2*e*f^2*g^2 + b^4*d^3*g^4)*p^4/(e^3*h^2)))/(e*h))) + (36*b*f*p - 9*a*f + (4*b*g*p - 3*a*g)*x - 3*(b*g*p*x + 3*b*f*p)*log(e*x^2 + d) - 3*(b*g*x + 3*b*f)*log(c))*sqrt(h*x))/h","B",0
607,1,1162,0,1.086746," ","integrate((g*x+f)*(a+b*log(c*(e*x^2+d)^p))/(h*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(h^{2} x \sqrt{-\frac{2 \, b^{2} f g p^{2} + h^{3} \sqrt{-\frac{{\left(b^{4} e^{2} f^{4} - 2 \, b^{4} d e f^{2} g^{2} + b^{4} d^{2} g^{4}\right)} p^{4}}{d e h^{6}}}}{h^{3}}} \log\left(-32 \, {\left(b^{3} e^{2} f^{4} - b^{3} d^{2} g^{4}\right)} \sqrt{h x} p^{3} + 32 \, {\left(d e f h^{5} \sqrt{-\frac{{\left(b^{4} e^{2} f^{4} - 2 \, b^{4} d e f^{2} g^{2} + b^{4} d^{2} g^{4}\right)} p^{4}}{d e h^{6}}} - {\left(b^{2} d e f^{2} g - b^{2} d^{2} g^{3}\right)} h^{2} p^{2}\right)} \sqrt{-\frac{2 \, b^{2} f g p^{2} + h^{3} \sqrt{-\frac{{\left(b^{4} e^{2} f^{4} - 2 \, b^{4} d e f^{2} g^{2} + b^{4} d^{2} g^{4}\right)} p^{4}}{d e h^{6}}}}{h^{3}}}\right) - h^{2} x \sqrt{-\frac{2 \, b^{2} f g p^{2} + h^{3} \sqrt{-\frac{{\left(b^{4} e^{2} f^{4} - 2 \, b^{4} d e f^{2} g^{2} + b^{4} d^{2} g^{4}\right)} p^{4}}{d e h^{6}}}}{h^{3}}} \log\left(-32 \, {\left(b^{3} e^{2} f^{4} - b^{3} d^{2} g^{4}\right)} \sqrt{h x} p^{3} - 32 \, {\left(d e f h^{5} \sqrt{-\frac{{\left(b^{4} e^{2} f^{4} - 2 \, b^{4} d e f^{2} g^{2} + b^{4} d^{2} g^{4}\right)} p^{4}}{d e h^{6}}} - {\left(b^{2} d e f^{2} g - b^{2} d^{2} g^{3}\right)} h^{2} p^{2}\right)} \sqrt{-\frac{2 \, b^{2} f g p^{2} + h^{3} \sqrt{-\frac{{\left(b^{4} e^{2} f^{4} - 2 \, b^{4} d e f^{2} g^{2} + b^{4} d^{2} g^{4}\right)} p^{4}}{d e h^{6}}}}{h^{3}}}\right) - h^{2} x \sqrt{-\frac{2 \, b^{2} f g p^{2} - h^{3} \sqrt{-\frac{{\left(b^{4} e^{2} f^{4} - 2 \, b^{4} d e f^{2} g^{2} + b^{4} d^{2} g^{4}\right)} p^{4}}{d e h^{6}}}}{h^{3}}} \log\left(-32 \, {\left(b^{3} e^{2} f^{4} - b^{3} d^{2} g^{4}\right)} \sqrt{h x} p^{3} + 32 \, {\left(d e f h^{5} \sqrt{-\frac{{\left(b^{4} e^{2} f^{4} - 2 \, b^{4} d e f^{2} g^{2} + b^{4} d^{2} g^{4}\right)} p^{4}}{d e h^{6}}} + {\left(b^{2} d e f^{2} g - b^{2} d^{2} g^{3}\right)} h^{2} p^{2}\right)} \sqrt{-\frac{2 \, b^{2} f g p^{2} - h^{3} \sqrt{-\frac{{\left(b^{4} e^{2} f^{4} - 2 \, b^{4} d e f^{2} g^{2} + b^{4} d^{2} g^{4}\right)} p^{4}}{d e h^{6}}}}{h^{3}}}\right) + h^{2} x \sqrt{-\frac{2 \, b^{2} f g p^{2} - h^{3} \sqrt{-\frac{{\left(b^{4} e^{2} f^{4} - 2 \, b^{4} d e f^{2} g^{2} + b^{4} d^{2} g^{4}\right)} p^{4}}{d e h^{6}}}}{h^{3}}} \log\left(-32 \, {\left(b^{3} e^{2} f^{4} - b^{3} d^{2} g^{4}\right)} \sqrt{h x} p^{3} - 32 \, {\left(d e f h^{5} \sqrt{-\frac{{\left(b^{4} e^{2} f^{4} - 2 \, b^{4} d e f^{2} g^{2} + b^{4} d^{2} g^{4}\right)} p^{4}}{d e h^{6}}} + {\left(b^{2} d e f^{2} g - b^{2} d^{2} g^{3}\right)} h^{2} p^{2}\right)} \sqrt{-\frac{2 \, b^{2} f g p^{2} - h^{3} \sqrt{-\frac{{\left(b^{4} e^{2} f^{4} - 2 \, b^{4} d e f^{2} g^{2} + b^{4} d^{2} g^{4}\right)} p^{4}}{d e h^{6}}}}{h^{3}}}\right) - {\left(a f + {\left(4 \, b g p - a g\right)} x - {\left(b g p x - b f p\right)} \log\left(e x^{2} + d\right) - {\left(b g x - b f\right)} \log\left(c\right)\right)} \sqrt{h x}\right)}}{h^{2} x}"," ",0,"2*(h^2*x*sqrt(-(2*b^2*f*g*p^2 + h^3*sqrt(-(b^4*e^2*f^4 - 2*b^4*d*e*f^2*g^2 + b^4*d^2*g^4)*p^4/(d*e*h^6)))/h^3)*log(-32*(b^3*e^2*f^4 - b^3*d^2*g^4)*sqrt(h*x)*p^3 + 32*(d*e*f*h^5*sqrt(-(b^4*e^2*f^4 - 2*b^4*d*e*f^2*g^2 + b^4*d^2*g^4)*p^4/(d*e*h^6)) - (b^2*d*e*f^2*g - b^2*d^2*g^3)*h^2*p^2)*sqrt(-(2*b^2*f*g*p^2 + h^3*sqrt(-(b^4*e^2*f^4 - 2*b^4*d*e*f^2*g^2 + b^4*d^2*g^4)*p^4/(d*e*h^6)))/h^3)) - h^2*x*sqrt(-(2*b^2*f*g*p^2 + h^3*sqrt(-(b^4*e^2*f^4 - 2*b^4*d*e*f^2*g^2 + b^4*d^2*g^4)*p^4/(d*e*h^6)))/h^3)*log(-32*(b^3*e^2*f^4 - b^3*d^2*g^4)*sqrt(h*x)*p^3 - 32*(d*e*f*h^5*sqrt(-(b^4*e^2*f^4 - 2*b^4*d*e*f^2*g^2 + b^4*d^2*g^4)*p^4/(d*e*h^6)) - (b^2*d*e*f^2*g - b^2*d^2*g^3)*h^2*p^2)*sqrt(-(2*b^2*f*g*p^2 + h^3*sqrt(-(b^4*e^2*f^4 - 2*b^4*d*e*f^2*g^2 + b^4*d^2*g^4)*p^4/(d*e*h^6)))/h^3)) - h^2*x*sqrt(-(2*b^2*f*g*p^2 - h^3*sqrt(-(b^4*e^2*f^4 - 2*b^4*d*e*f^2*g^2 + b^4*d^2*g^4)*p^4/(d*e*h^6)))/h^3)*log(-32*(b^3*e^2*f^4 - b^3*d^2*g^4)*sqrt(h*x)*p^3 + 32*(d*e*f*h^5*sqrt(-(b^4*e^2*f^4 - 2*b^4*d*e*f^2*g^2 + b^4*d^2*g^4)*p^4/(d*e*h^6)) + (b^2*d*e*f^2*g - b^2*d^2*g^3)*h^2*p^2)*sqrt(-(2*b^2*f*g*p^2 - h^3*sqrt(-(b^4*e^2*f^4 - 2*b^4*d*e*f^2*g^2 + b^4*d^2*g^4)*p^4/(d*e*h^6)))/h^3)) + h^2*x*sqrt(-(2*b^2*f*g*p^2 - h^3*sqrt(-(b^4*e^2*f^4 - 2*b^4*d*e*f^2*g^2 + b^4*d^2*g^4)*p^4/(d*e*h^6)))/h^3)*log(-32*(b^3*e^2*f^4 - b^3*d^2*g^4)*sqrt(h*x)*p^3 - 32*(d*e*f*h^5*sqrt(-(b^4*e^2*f^4 - 2*b^4*d*e*f^2*g^2 + b^4*d^2*g^4)*p^4/(d*e*h^6)) + (b^2*d*e*f^2*g - b^2*d^2*g^3)*h^2*p^2)*sqrt(-(2*b^2*f*g*p^2 - h^3*sqrt(-(b^4*e^2*f^4 - 2*b^4*d*e*f^2*g^2 + b^4*d^2*g^4)*p^4/(d*e*h^6)))/h^3)) - (a*f + (4*b*g*p - a*g)*x - (b*g*p*x - b*f*p)*log(e*x^2 + d) - (b*g*x - b*f)*log(c))*sqrt(h*x))/(h^2*x)","B",0
608,1,1236,0,1.074080," ","integrate((g*x+f)*(a+b*log(c*(e*x^2+d)^p))/(h*x)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(h^{3} x^{2} \sqrt{-\frac{6 \, b^{2} e f g p^{2} + d h^{5} \sqrt{-\frac{{\left(b^{4} e^{3} f^{4} - 18 \, b^{4} d e^{2} f^{2} g^{2} + 81 \, b^{4} d^{2} e g^{4}\right)} p^{4}}{d^{3} h^{10}}}}{d h^{5}}} \log\left(-32 \, {\left(b^{3} e^{3} f^{4} - 81 \, b^{3} d^{2} e g^{4}\right)} \sqrt{h x} p^{3} + 32 \, {\left(3 \, d^{3} g h^{8} \sqrt{-\frac{{\left(b^{4} e^{3} f^{4} - 18 \, b^{4} d e^{2} f^{2} g^{2} + 81 \, b^{4} d^{2} e g^{4}\right)} p^{4}}{d^{3} h^{10}}} + {\left(b^{2} d e^{2} f^{3} - 9 \, b^{2} d^{2} e f g^{2}\right)} h^{3} p^{2}\right)} \sqrt{-\frac{6 \, b^{2} e f g p^{2} + d h^{5} \sqrt{-\frac{{\left(b^{4} e^{3} f^{4} - 18 \, b^{4} d e^{2} f^{2} g^{2} + 81 \, b^{4} d^{2} e g^{4}\right)} p^{4}}{d^{3} h^{10}}}}{d h^{5}}}\right) - h^{3} x^{2} \sqrt{-\frac{6 \, b^{2} e f g p^{2} + d h^{5} \sqrt{-\frac{{\left(b^{4} e^{3} f^{4} - 18 \, b^{4} d e^{2} f^{2} g^{2} + 81 \, b^{4} d^{2} e g^{4}\right)} p^{4}}{d^{3} h^{10}}}}{d h^{5}}} \log\left(-32 \, {\left(b^{3} e^{3} f^{4} - 81 \, b^{3} d^{2} e g^{4}\right)} \sqrt{h x} p^{3} - 32 \, {\left(3 \, d^{3} g h^{8} \sqrt{-\frac{{\left(b^{4} e^{3} f^{4} - 18 \, b^{4} d e^{2} f^{2} g^{2} + 81 \, b^{4} d^{2} e g^{4}\right)} p^{4}}{d^{3} h^{10}}} + {\left(b^{2} d e^{2} f^{3} - 9 \, b^{2} d^{2} e f g^{2}\right)} h^{3} p^{2}\right)} \sqrt{-\frac{6 \, b^{2} e f g p^{2} + d h^{5} \sqrt{-\frac{{\left(b^{4} e^{3} f^{4} - 18 \, b^{4} d e^{2} f^{2} g^{2} + 81 \, b^{4} d^{2} e g^{4}\right)} p^{4}}{d^{3} h^{10}}}}{d h^{5}}}\right) - h^{3} x^{2} \sqrt{-\frac{6 \, b^{2} e f g p^{2} - d h^{5} \sqrt{-\frac{{\left(b^{4} e^{3} f^{4} - 18 \, b^{4} d e^{2} f^{2} g^{2} + 81 \, b^{4} d^{2} e g^{4}\right)} p^{4}}{d^{3} h^{10}}}}{d h^{5}}} \log\left(-32 \, {\left(b^{3} e^{3} f^{4} - 81 \, b^{3} d^{2} e g^{4}\right)} \sqrt{h x} p^{3} + 32 \, {\left(3 \, d^{3} g h^{8} \sqrt{-\frac{{\left(b^{4} e^{3} f^{4} - 18 \, b^{4} d e^{2} f^{2} g^{2} + 81 \, b^{4} d^{2} e g^{4}\right)} p^{4}}{d^{3} h^{10}}} - {\left(b^{2} d e^{2} f^{3} - 9 \, b^{2} d^{2} e f g^{2}\right)} h^{3} p^{2}\right)} \sqrt{-\frac{6 \, b^{2} e f g p^{2} - d h^{5} \sqrt{-\frac{{\left(b^{4} e^{3} f^{4} - 18 \, b^{4} d e^{2} f^{2} g^{2} + 81 \, b^{4} d^{2} e g^{4}\right)} p^{4}}{d^{3} h^{10}}}}{d h^{5}}}\right) + h^{3} x^{2} \sqrt{-\frac{6 \, b^{2} e f g p^{2} - d h^{5} \sqrt{-\frac{{\left(b^{4} e^{3} f^{4} - 18 \, b^{4} d e^{2} f^{2} g^{2} + 81 \, b^{4} d^{2} e g^{4}\right)} p^{4}}{d^{3} h^{10}}}}{d h^{5}}} \log\left(-32 \, {\left(b^{3} e^{3} f^{4} - 81 \, b^{3} d^{2} e g^{4}\right)} \sqrt{h x} p^{3} - 32 \, {\left(3 \, d^{3} g h^{8} \sqrt{-\frac{{\left(b^{4} e^{3} f^{4} - 18 \, b^{4} d e^{2} f^{2} g^{2} + 81 \, b^{4} d^{2} e g^{4}\right)} p^{4}}{d^{3} h^{10}}} - {\left(b^{2} d e^{2} f^{3} - 9 \, b^{2} d^{2} e f g^{2}\right)} h^{3} p^{2}\right)} \sqrt{-\frac{6 \, b^{2} e f g p^{2} - d h^{5} \sqrt{-\frac{{\left(b^{4} e^{3} f^{4} - 18 \, b^{4} d e^{2} f^{2} g^{2} + 81 \, b^{4} d^{2} e g^{4}\right)} p^{4}}{d^{3} h^{10}}}}{d h^{5}}}\right) + {\left(3 \, a g x + a f + {\left(3 \, b g p x + b f p\right)} \log\left(e x^{2} + d\right) + {\left(3 \, b g x + b f\right)} \log\left(c\right)\right)} \sqrt{h x}\right)}}{3 \, h^{3} x^{2}}"," ",0,"-2/3*(h^3*x^2*sqrt(-(6*b^2*e*f*g*p^2 + d*h^5*sqrt(-(b^4*e^3*f^4 - 18*b^4*d*e^2*f^2*g^2 + 81*b^4*d^2*e*g^4)*p^4/(d^3*h^10)))/(d*h^5))*log(-32*(b^3*e^3*f^4 - 81*b^3*d^2*e*g^4)*sqrt(h*x)*p^3 + 32*(3*d^3*g*h^8*sqrt(-(b^4*e^3*f^4 - 18*b^4*d*e^2*f^2*g^2 + 81*b^4*d^2*e*g^4)*p^4/(d^3*h^10)) + (b^2*d*e^2*f^3 - 9*b^2*d^2*e*f*g^2)*h^3*p^2)*sqrt(-(6*b^2*e*f*g*p^2 + d*h^5*sqrt(-(b^4*e^3*f^4 - 18*b^4*d*e^2*f^2*g^2 + 81*b^4*d^2*e*g^4)*p^4/(d^3*h^10)))/(d*h^5))) - h^3*x^2*sqrt(-(6*b^2*e*f*g*p^2 + d*h^5*sqrt(-(b^4*e^3*f^4 - 18*b^4*d*e^2*f^2*g^2 + 81*b^4*d^2*e*g^4)*p^4/(d^3*h^10)))/(d*h^5))*log(-32*(b^3*e^3*f^4 - 81*b^3*d^2*e*g^4)*sqrt(h*x)*p^3 - 32*(3*d^3*g*h^8*sqrt(-(b^4*e^3*f^4 - 18*b^4*d*e^2*f^2*g^2 + 81*b^4*d^2*e*g^4)*p^4/(d^3*h^10)) + (b^2*d*e^2*f^3 - 9*b^2*d^2*e*f*g^2)*h^3*p^2)*sqrt(-(6*b^2*e*f*g*p^2 + d*h^5*sqrt(-(b^4*e^3*f^4 - 18*b^4*d*e^2*f^2*g^2 + 81*b^4*d^2*e*g^4)*p^4/(d^3*h^10)))/(d*h^5))) - h^3*x^2*sqrt(-(6*b^2*e*f*g*p^2 - d*h^5*sqrt(-(b^4*e^3*f^4 - 18*b^4*d*e^2*f^2*g^2 + 81*b^4*d^2*e*g^4)*p^4/(d^3*h^10)))/(d*h^5))*log(-32*(b^3*e^3*f^4 - 81*b^3*d^2*e*g^4)*sqrt(h*x)*p^3 + 32*(3*d^3*g*h^8*sqrt(-(b^4*e^3*f^4 - 18*b^4*d*e^2*f^2*g^2 + 81*b^4*d^2*e*g^4)*p^4/(d^3*h^10)) - (b^2*d*e^2*f^3 - 9*b^2*d^2*e*f*g^2)*h^3*p^2)*sqrt(-(6*b^2*e*f*g*p^2 - d*h^5*sqrt(-(b^4*e^3*f^4 - 18*b^4*d*e^2*f^2*g^2 + 81*b^4*d^2*e*g^4)*p^4/(d^3*h^10)))/(d*h^5))) + h^3*x^2*sqrt(-(6*b^2*e*f*g*p^2 - d*h^5*sqrt(-(b^4*e^3*f^4 - 18*b^4*d*e^2*f^2*g^2 + 81*b^4*d^2*e*g^4)*p^4/(d^3*h^10)))/(d*h^5))*log(-32*(b^3*e^3*f^4 - 81*b^3*d^2*e*g^4)*sqrt(h*x)*p^3 - 32*(3*d^3*g*h^8*sqrt(-(b^4*e^3*f^4 - 18*b^4*d*e^2*f^2*g^2 + 81*b^4*d^2*e*g^4)*p^4/(d^3*h^10)) - (b^2*d*e^2*f^3 - 9*b^2*d^2*e*f*g^2)*h^3*p^2)*sqrt(-(6*b^2*e*f*g*p^2 - d*h^5*sqrt(-(b^4*e^3*f^4 - 18*b^4*d*e^2*f^2*g^2 + 81*b^4*d^2*e*g^4)*p^4/(d^3*h^10)))/(d*h^5))) + (3*a*g*x + a*f + (3*b*g*p*x + b*f*p)*log(e*x^2 + d) + (3*b*g*x + b*f)*log(c))*sqrt(h*x))/(h^3*x^2)","B",0
609,1,1348,0,1.032409," ","integrate((g*x+f)*(a+b*log(c*(e*x^2+d)^p))/(h*x)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(d h^{4} x^{3} \sqrt{\frac{d^{2} h^{7} \sqrt{-\frac{{\left(81 \, b^{4} e^{5} f^{4} - 450 \, b^{4} d e^{4} f^{2} g^{2} + 625 \, b^{4} d^{2} e^{3} g^{4}\right)} p^{4}}{d^{5} h^{14}}} + 30 \, b^{2} e^{2} f g p^{2}}{d^{2} h^{7}}} \log\left(-32 \, {\left(81 \, b^{3} e^{4} f^{4} - 625 \, b^{3} d^{2} e^{2} g^{4}\right)} \sqrt{h x} p^{3} + 32 \, {\left(3 \, d^{4} f h^{11} \sqrt{-\frac{{\left(81 \, b^{4} e^{5} f^{4} - 450 \, b^{4} d e^{4} f^{2} g^{2} + 625 \, b^{4} d^{2} e^{3} g^{4}\right)} p^{4}}{d^{5} h^{14}}} - 5 \, {\left(9 \, b^{2} d^{2} e^{2} f^{2} g - 25 \, b^{2} d^{3} e g^{3}\right)} h^{4} p^{2}\right)} \sqrt{\frac{d^{2} h^{7} \sqrt{-\frac{{\left(81 \, b^{4} e^{5} f^{4} - 450 \, b^{4} d e^{4} f^{2} g^{2} + 625 \, b^{4} d^{2} e^{3} g^{4}\right)} p^{4}}{d^{5} h^{14}}} + 30 \, b^{2} e^{2} f g p^{2}}{d^{2} h^{7}}}\right) - d h^{4} x^{3} \sqrt{\frac{d^{2} h^{7} \sqrt{-\frac{{\left(81 \, b^{4} e^{5} f^{4} - 450 \, b^{4} d e^{4} f^{2} g^{2} + 625 \, b^{4} d^{2} e^{3} g^{4}\right)} p^{4}}{d^{5} h^{14}}} + 30 \, b^{2} e^{2} f g p^{2}}{d^{2} h^{7}}} \log\left(-32 \, {\left(81 \, b^{3} e^{4} f^{4} - 625 \, b^{3} d^{2} e^{2} g^{4}\right)} \sqrt{h x} p^{3} - 32 \, {\left(3 \, d^{4} f h^{11} \sqrt{-\frac{{\left(81 \, b^{4} e^{5} f^{4} - 450 \, b^{4} d e^{4} f^{2} g^{2} + 625 \, b^{4} d^{2} e^{3} g^{4}\right)} p^{4}}{d^{5} h^{14}}} - 5 \, {\left(9 \, b^{2} d^{2} e^{2} f^{2} g - 25 \, b^{2} d^{3} e g^{3}\right)} h^{4} p^{2}\right)} \sqrt{\frac{d^{2} h^{7} \sqrt{-\frac{{\left(81 \, b^{4} e^{5} f^{4} - 450 \, b^{4} d e^{4} f^{2} g^{2} + 625 \, b^{4} d^{2} e^{3} g^{4}\right)} p^{4}}{d^{5} h^{14}}} + 30 \, b^{2} e^{2} f g p^{2}}{d^{2} h^{7}}}\right) - d h^{4} x^{3} \sqrt{-\frac{d^{2} h^{7} \sqrt{-\frac{{\left(81 \, b^{4} e^{5} f^{4} - 450 \, b^{4} d e^{4} f^{2} g^{2} + 625 \, b^{4} d^{2} e^{3} g^{4}\right)} p^{4}}{d^{5} h^{14}}} - 30 \, b^{2} e^{2} f g p^{2}}{d^{2} h^{7}}} \log\left(-32 \, {\left(81 \, b^{3} e^{4} f^{4} - 625 \, b^{3} d^{2} e^{2} g^{4}\right)} \sqrt{h x} p^{3} + 32 \, {\left(3 \, d^{4} f h^{11} \sqrt{-\frac{{\left(81 \, b^{4} e^{5} f^{4} - 450 \, b^{4} d e^{4} f^{2} g^{2} + 625 \, b^{4} d^{2} e^{3} g^{4}\right)} p^{4}}{d^{5} h^{14}}} + 5 \, {\left(9 \, b^{2} d^{2} e^{2} f^{2} g - 25 \, b^{2} d^{3} e g^{3}\right)} h^{4} p^{2}\right)} \sqrt{-\frac{d^{2} h^{7} \sqrt{-\frac{{\left(81 \, b^{4} e^{5} f^{4} - 450 \, b^{4} d e^{4} f^{2} g^{2} + 625 \, b^{4} d^{2} e^{3} g^{4}\right)} p^{4}}{d^{5} h^{14}}} - 30 \, b^{2} e^{2} f g p^{2}}{d^{2} h^{7}}}\right) + d h^{4} x^{3} \sqrt{-\frac{d^{2} h^{7} \sqrt{-\frac{{\left(81 \, b^{4} e^{5} f^{4} - 450 \, b^{4} d e^{4} f^{2} g^{2} + 625 \, b^{4} d^{2} e^{3} g^{4}\right)} p^{4}}{d^{5} h^{14}}} - 30 \, b^{2} e^{2} f g p^{2}}{d^{2} h^{7}}} \log\left(-32 \, {\left(81 \, b^{3} e^{4} f^{4} - 625 \, b^{3} d^{2} e^{2} g^{4}\right)} \sqrt{h x} p^{3} - 32 \, {\left(3 \, d^{4} f h^{11} \sqrt{-\frac{{\left(81 \, b^{4} e^{5} f^{4} - 450 \, b^{4} d e^{4} f^{2} g^{2} + 625 \, b^{4} d^{2} e^{3} g^{4}\right)} p^{4}}{d^{5} h^{14}}} + 5 \, {\left(9 \, b^{2} d^{2} e^{2} f^{2} g - 25 \, b^{2} d^{3} e g^{3}\right)} h^{4} p^{2}\right)} \sqrt{-\frac{d^{2} h^{7} \sqrt{-\frac{{\left(81 \, b^{4} e^{5} f^{4} - 450 \, b^{4} d e^{4} f^{2} g^{2} + 625 \, b^{4} d^{2} e^{3} g^{4}\right)} p^{4}}{d^{5} h^{14}}} - 30 \, b^{2} e^{2} f g p^{2}}{d^{2} h^{7}}}\right) - {\left(12 \, b e f p x^{2} + 5 \, a d g x + 3 \, a d f + {\left(5 \, b d g p x + 3 \, b d f p\right)} \log\left(e x^{2} + d\right) + {\left(5 \, b d g x + 3 \, b d f\right)} \log\left(c\right)\right)} \sqrt{h x}\right)}}{15 \, d h^{4} x^{3}}"," ",0,"2/15*(d*h^4*x^3*sqrt((d^2*h^7*sqrt(-(81*b^4*e^5*f^4 - 450*b^4*d*e^4*f^2*g^2 + 625*b^4*d^2*e^3*g^4)*p^4/(d^5*h^14)) + 30*b^2*e^2*f*g*p^2)/(d^2*h^7))*log(-32*(81*b^3*e^4*f^4 - 625*b^3*d^2*e^2*g^4)*sqrt(h*x)*p^3 + 32*(3*d^4*f*h^11*sqrt(-(81*b^4*e^5*f^4 - 450*b^4*d*e^4*f^2*g^2 + 625*b^4*d^2*e^3*g^4)*p^4/(d^5*h^14)) - 5*(9*b^2*d^2*e^2*f^2*g - 25*b^2*d^3*e*g^3)*h^4*p^2)*sqrt((d^2*h^7*sqrt(-(81*b^4*e^5*f^4 - 450*b^4*d*e^4*f^2*g^2 + 625*b^4*d^2*e^3*g^4)*p^4/(d^5*h^14)) + 30*b^2*e^2*f*g*p^2)/(d^2*h^7))) - d*h^4*x^3*sqrt((d^2*h^7*sqrt(-(81*b^4*e^5*f^4 - 450*b^4*d*e^4*f^2*g^2 + 625*b^4*d^2*e^3*g^4)*p^4/(d^5*h^14)) + 30*b^2*e^2*f*g*p^2)/(d^2*h^7))*log(-32*(81*b^3*e^4*f^4 - 625*b^3*d^2*e^2*g^4)*sqrt(h*x)*p^3 - 32*(3*d^4*f*h^11*sqrt(-(81*b^4*e^5*f^4 - 450*b^4*d*e^4*f^2*g^2 + 625*b^4*d^2*e^3*g^4)*p^4/(d^5*h^14)) - 5*(9*b^2*d^2*e^2*f^2*g - 25*b^2*d^3*e*g^3)*h^4*p^2)*sqrt((d^2*h^7*sqrt(-(81*b^4*e^5*f^4 - 450*b^4*d*e^4*f^2*g^2 + 625*b^4*d^2*e^3*g^4)*p^4/(d^5*h^14)) + 30*b^2*e^2*f*g*p^2)/(d^2*h^7))) - d*h^4*x^3*sqrt(-(d^2*h^7*sqrt(-(81*b^4*e^5*f^4 - 450*b^4*d*e^4*f^2*g^2 + 625*b^4*d^2*e^3*g^4)*p^4/(d^5*h^14)) - 30*b^2*e^2*f*g*p^2)/(d^2*h^7))*log(-32*(81*b^3*e^4*f^4 - 625*b^3*d^2*e^2*g^4)*sqrt(h*x)*p^3 + 32*(3*d^4*f*h^11*sqrt(-(81*b^4*e^5*f^4 - 450*b^4*d*e^4*f^2*g^2 + 625*b^4*d^2*e^3*g^4)*p^4/(d^5*h^14)) + 5*(9*b^2*d^2*e^2*f^2*g - 25*b^2*d^3*e*g^3)*h^4*p^2)*sqrt(-(d^2*h^7*sqrt(-(81*b^4*e^5*f^4 - 450*b^4*d*e^4*f^2*g^2 + 625*b^4*d^2*e^3*g^4)*p^4/(d^5*h^14)) - 30*b^2*e^2*f*g*p^2)/(d^2*h^7))) + d*h^4*x^3*sqrt(-(d^2*h^7*sqrt(-(81*b^4*e^5*f^4 - 450*b^4*d*e^4*f^2*g^2 + 625*b^4*d^2*e^3*g^4)*p^4/(d^5*h^14)) - 30*b^2*e^2*f*g*p^2)/(d^2*h^7))*log(-32*(81*b^3*e^4*f^4 - 625*b^3*d^2*e^2*g^4)*sqrt(h*x)*p^3 - 32*(3*d^4*f*h^11*sqrt(-(81*b^4*e^5*f^4 - 450*b^4*d*e^4*f^2*g^2 + 625*b^4*d^2*e^3*g^4)*p^4/(d^5*h^14)) + 5*(9*b^2*d^2*e^2*f^2*g - 25*b^2*d^3*e*g^3)*h^4*p^2)*sqrt(-(d^2*h^7*sqrt(-(81*b^4*e^5*f^4 - 450*b^4*d*e^4*f^2*g^2 + 625*b^4*d^2*e^3*g^4)*p^4/(d^5*h^14)) - 30*b^2*e^2*f*g*p^2)/(d^2*h^7))) - (12*b*e*f*p*x^2 + 5*a*d*g*x + 3*a*d*f + (5*b*d*g*p*x + 3*b*d*f*p)*log(e*x^2 + d) + (5*b*d*g*x + 3*b*d*f)*log(c))*sqrt(h*x))/(d*h^4*x^3)","B",0
610,1,1369,0,1.126582," ","integrate((g*x+f)*(a+b*log(c*(e*x^2+d)^p))/(h*x)^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, d h^{5} x^{4} \sqrt{-\frac{d^{3} h^{9} \sqrt{-\frac{{\left(625 \, b^{4} e^{7} f^{4} - 2450 \, b^{4} d e^{6} f^{2} g^{2} + 2401 \, b^{4} d^{2} e^{5} g^{4}\right)} p^{4}}{d^{7} h^{18}}} + 70 \, b^{2} e^{3} f g p^{2}}{d^{3} h^{9}}} \log\left(-32 \, {\left(625 \, b^{3} e^{6} f^{4} - 2401 \, b^{3} d^{2} e^{4} g^{4}\right)} \sqrt{h x} p^{3} + 32 \, {\left(7 \, d^{6} g h^{14} \sqrt{-\frac{{\left(625 \, b^{4} e^{7} f^{4} - 2450 \, b^{4} d e^{6} f^{2} g^{2} + 2401 \, b^{4} d^{2} e^{5} g^{4}\right)} p^{4}}{d^{7} h^{18}}} + 5 \, {\left(25 \, b^{2} d^{2} e^{4} f^{3} - 49 \, b^{2} d^{3} e^{3} f g^{2}\right)} h^{5} p^{2}\right)} \sqrt{-\frac{d^{3} h^{9} \sqrt{-\frac{{\left(625 \, b^{4} e^{7} f^{4} - 2450 \, b^{4} d e^{6} f^{2} g^{2} + 2401 \, b^{4} d^{2} e^{5} g^{4}\right)} p^{4}}{d^{7} h^{18}}} + 70 \, b^{2} e^{3} f g p^{2}}{d^{3} h^{9}}}\right) - 3 \, d h^{5} x^{4} \sqrt{-\frac{d^{3} h^{9} \sqrt{-\frac{{\left(625 \, b^{4} e^{7} f^{4} - 2450 \, b^{4} d e^{6} f^{2} g^{2} + 2401 \, b^{4} d^{2} e^{5} g^{4}\right)} p^{4}}{d^{7} h^{18}}} + 70 \, b^{2} e^{3} f g p^{2}}{d^{3} h^{9}}} \log\left(-32 \, {\left(625 \, b^{3} e^{6} f^{4} - 2401 \, b^{3} d^{2} e^{4} g^{4}\right)} \sqrt{h x} p^{3} - 32 \, {\left(7 \, d^{6} g h^{14} \sqrt{-\frac{{\left(625 \, b^{4} e^{7} f^{4} - 2450 \, b^{4} d e^{6} f^{2} g^{2} + 2401 \, b^{4} d^{2} e^{5} g^{4}\right)} p^{4}}{d^{7} h^{18}}} + 5 \, {\left(25 \, b^{2} d^{2} e^{4} f^{3} - 49 \, b^{2} d^{3} e^{3} f g^{2}\right)} h^{5} p^{2}\right)} \sqrt{-\frac{d^{3} h^{9} \sqrt{-\frac{{\left(625 \, b^{4} e^{7} f^{4} - 2450 \, b^{4} d e^{6} f^{2} g^{2} + 2401 \, b^{4} d^{2} e^{5} g^{4}\right)} p^{4}}{d^{7} h^{18}}} + 70 \, b^{2} e^{3} f g p^{2}}{d^{3} h^{9}}}\right) - 3 \, d h^{5} x^{4} \sqrt{\frac{d^{3} h^{9} \sqrt{-\frac{{\left(625 \, b^{4} e^{7} f^{4} - 2450 \, b^{4} d e^{6} f^{2} g^{2} + 2401 \, b^{4} d^{2} e^{5} g^{4}\right)} p^{4}}{d^{7} h^{18}}} - 70 \, b^{2} e^{3} f g p^{2}}{d^{3} h^{9}}} \log\left(-32 \, {\left(625 \, b^{3} e^{6} f^{4} - 2401 \, b^{3} d^{2} e^{4} g^{4}\right)} \sqrt{h x} p^{3} + 32 \, {\left(7 \, d^{6} g h^{14} \sqrt{-\frac{{\left(625 \, b^{4} e^{7} f^{4} - 2450 \, b^{4} d e^{6} f^{2} g^{2} + 2401 \, b^{4} d^{2} e^{5} g^{4}\right)} p^{4}}{d^{7} h^{18}}} - 5 \, {\left(25 \, b^{2} d^{2} e^{4} f^{3} - 49 \, b^{2} d^{3} e^{3} f g^{2}\right)} h^{5} p^{2}\right)} \sqrt{\frac{d^{3} h^{9} \sqrt{-\frac{{\left(625 \, b^{4} e^{7} f^{4} - 2450 \, b^{4} d e^{6} f^{2} g^{2} + 2401 \, b^{4} d^{2} e^{5} g^{4}\right)} p^{4}}{d^{7} h^{18}}} - 70 \, b^{2} e^{3} f g p^{2}}{d^{3} h^{9}}}\right) + 3 \, d h^{5} x^{4} \sqrt{\frac{d^{3} h^{9} \sqrt{-\frac{{\left(625 \, b^{4} e^{7} f^{4} - 2450 \, b^{4} d e^{6} f^{2} g^{2} + 2401 \, b^{4} d^{2} e^{5} g^{4}\right)} p^{4}}{d^{7} h^{18}}} - 70 \, b^{2} e^{3} f g p^{2}}{d^{3} h^{9}}} \log\left(-32 \, {\left(625 \, b^{3} e^{6} f^{4} - 2401 \, b^{3} d^{2} e^{4} g^{4}\right)} \sqrt{h x} p^{3} - 32 \, {\left(7 \, d^{6} g h^{14} \sqrt{-\frac{{\left(625 \, b^{4} e^{7} f^{4} - 2450 \, b^{4} d e^{6} f^{2} g^{2} + 2401 \, b^{4} d^{2} e^{5} g^{4}\right)} p^{4}}{d^{7} h^{18}}} - 5 \, {\left(25 \, b^{2} d^{2} e^{4} f^{3} - 49 \, b^{2} d^{3} e^{3} f g^{2}\right)} h^{5} p^{2}\right)} \sqrt{\frac{d^{3} h^{9} \sqrt{-\frac{{\left(625 \, b^{4} e^{7} f^{4} - 2450 \, b^{4} d e^{6} f^{2} g^{2} + 2401 \, b^{4} d^{2} e^{5} g^{4}\right)} p^{4}}{d^{7} h^{18}}} - 70 \, b^{2} e^{3} f g p^{2}}{d^{3} h^{9}}}\right) - {\left(84 \, b e g p x^{3} + 20 \, b e f p x^{2} + 21 \, a d g x + 15 \, a d f + 3 \, {\left(7 \, b d g p x + 5 \, b d f p\right)} \log\left(e x^{2} + d\right) + 3 \, {\left(7 \, b d g x + 5 \, b d f\right)} \log\left(c\right)\right)} \sqrt{h x}\right)}}{105 \, d h^{5} x^{4}}"," ",0,"2/105*(3*d*h^5*x^4*sqrt(-(d^3*h^9*sqrt(-(625*b^4*e^7*f^4 - 2450*b^4*d*e^6*f^2*g^2 + 2401*b^4*d^2*e^5*g^4)*p^4/(d^7*h^18)) + 70*b^2*e^3*f*g*p^2)/(d^3*h^9))*log(-32*(625*b^3*e^6*f^4 - 2401*b^3*d^2*e^4*g^4)*sqrt(h*x)*p^3 + 32*(7*d^6*g*h^14*sqrt(-(625*b^4*e^7*f^4 - 2450*b^4*d*e^6*f^2*g^2 + 2401*b^4*d^2*e^5*g^4)*p^4/(d^7*h^18)) + 5*(25*b^2*d^2*e^4*f^3 - 49*b^2*d^3*e^3*f*g^2)*h^5*p^2)*sqrt(-(d^3*h^9*sqrt(-(625*b^4*e^7*f^4 - 2450*b^4*d*e^6*f^2*g^2 + 2401*b^4*d^2*e^5*g^4)*p^4/(d^7*h^18)) + 70*b^2*e^3*f*g*p^2)/(d^3*h^9))) - 3*d*h^5*x^4*sqrt(-(d^3*h^9*sqrt(-(625*b^4*e^7*f^4 - 2450*b^4*d*e^6*f^2*g^2 + 2401*b^4*d^2*e^5*g^4)*p^4/(d^7*h^18)) + 70*b^2*e^3*f*g*p^2)/(d^3*h^9))*log(-32*(625*b^3*e^6*f^4 - 2401*b^3*d^2*e^4*g^4)*sqrt(h*x)*p^3 - 32*(7*d^6*g*h^14*sqrt(-(625*b^4*e^7*f^4 - 2450*b^4*d*e^6*f^2*g^2 + 2401*b^4*d^2*e^5*g^4)*p^4/(d^7*h^18)) + 5*(25*b^2*d^2*e^4*f^3 - 49*b^2*d^3*e^3*f*g^2)*h^5*p^2)*sqrt(-(d^3*h^9*sqrt(-(625*b^4*e^7*f^4 - 2450*b^4*d*e^6*f^2*g^2 + 2401*b^4*d^2*e^5*g^4)*p^4/(d^7*h^18)) + 70*b^2*e^3*f*g*p^2)/(d^3*h^9))) - 3*d*h^5*x^4*sqrt((d^3*h^9*sqrt(-(625*b^4*e^7*f^4 - 2450*b^4*d*e^6*f^2*g^2 + 2401*b^4*d^2*e^5*g^4)*p^4/(d^7*h^18)) - 70*b^2*e^3*f*g*p^2)/(d^3*h^9))*log(-32*(625*b^3*e^6*f^4 - 2401*b^3*d^2*e^4*g^4)*sqrt(h*x)*p^3 + 32*(7*d^6*g*h^14*sqrt(-(625*b^4*e^7*f^4 - 2450*b^4*d*e^6*f^2*g^2 + 2401*b^4*d^2*e^5*g^4)*p^4/(d^7*h^18)) - 5*(25*b^2*d^2*e^4*f^3 - 49*b^2*d^3*e^3*f*g^2)*h^5*p^2)*sqrt((d^3*h^9*sqrt(-(625*b^4*e^7*f^4 - 2450*b^4*d*e^6*f^2*g^2 + 2401*b^4*d^2*e^5*g^4)*p^4/(d^7*h^18)) - 70*b^2*e^3*f*g*p^2)/(d^3*h^9))) + 3*d*h^5*x^4*sqrt((d^3*h^9*sqrt(-(625*b^4*e^7*f^4 - 2450*b^4*d*e^6*f^2*g^2 + 2401*b^4*d^2*e^5*g^4)*p^4/(d^7*h^18)) - 70*b^2*e^3*f*g*p^2)/(d^3*h^9))*log(-32*(625*b^3*e^6*f^4 - 2401*b^3*d^2*e^4*g^4)*sqrt(h*x)*p^3 - 32*(7*d^6*g*h^14*sqrt(-(625*b^4*e^7*f^4 - 2450*b^4*d*e^6*f^2*g^2 + 2401*b^4*d^2*e^5*g^4)*p^4/(d^7*h^18)) - 5*(25*b^2*d^2*e^4*f^3 - 49*b^2*d^3*e^3*f*g^2)*h^5*p^2)*sqrt((d^3*h^9*sqrt(-(625*b^4*e^7*f^4 - 2450*b^4*d*e^6*f^2*g^2 + 2401*b^4*d^2*e^5*g^4)*p^4/(d^7*h^18)) - 70*b^2*e^3*f*g*p^2)/(d^3*h^9))) - (84*b*e*g*p*x^3 + 20*b*e*f*p*x^2 + 21*a*d*g*x + 15*a*d*f + 3*(7*b*d*g*p*x + 5*b*d*f*p)*log(e*x^2 + d) + 3*(7*b*d*g*x + 5*b*d*f)*log(c))*sqrt(h*x))/(d*h^5*x^4)","B",0
611,1,2178,0,0.999590," ","integrate((g*x+f)^2*(a+b*log(c*(e*x^2+d)^p))/(h*x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, e h \sqrt{-\frac{e^{2} h \sqrt{-\frac{{\left(50625 \, b^{4} d e^{4} f^{8} - 85500 \, b^{4} d^{2} e^{3} f^{6} g^{2} + 40150 \, b^{4} d^{3} e^{2} f^{4} g^{4} - 3420 \, b^{4} d^{4} e f^{2} g^{6} + 81 \, b^{4} d^{5} g^{8}\right)} p^{4}}{e^{5} h^{2}}} + 60 \, {\left(5 \, b^{2} d e f^{3} g - b^{2} d^{2} f g^{3}\right)} p^{2}}{e^{2} h}} \log\left(16 \, {\left(50625 \, b^{3} e^{4} f^{8} - 40500 \, b^{3} d e^{3} f^{6} g^{2} + 2150 \, b^{3} d^{2} e^{2} f^{4} g^{4} - 1620 \, b^{3} d^{3} e f^{2} g^{6} + 81 \, b^{3} d^{4} g^{8}\right)} \sqrt{h x} p^{3} + 16 \, {\left(10 \, e^{4} f g h^{2} \sqrt{-\frac{{\left(50625 \, b^{4} d e^{4} f^{8} - 85500 \, b^{4} d^{2} e^{3} f^{6} g^{2} + 40150 \, b^{4} d^{3} e^{2} f^{4} g^{4} - 3420 \, b^{4} d^{4} e f^{2} g^{6} + 81 \, b^{4} d^{5} g^{8}\right)} p^{4}}{e^{5} h^{2}}} + 3 \, {\left(1125 \, b^{2} e^{4} f^{6} - 1175 \, b^{2} d e^{3} f^{4} g^{2} + 235 \, b^{2} d^{2} e^{2} f^{2} g^{4} - 9 \, b^{2} d^{3} e g^{6}\right)} h p^{2}\right)} \sqrt{-\frac{e^{2} h \sqrt{-\frac{{\left(50625 \, b^{4} d e^{4} f^{8} - 85500 \, b^{4} d^{2} e^{3} f^{6} g^{2} + 40150 \, b^{4} d^{3} e^{2} f^{4} g^{4} - 3420 \, b^{4} d^{4} e f^{2} g^{6} + 81 \, b^{4} d^{5} g^{8}\right)} p^{4}}{e^{5} h^{2}}} + 60 \, {\left(5 \, b^{2} d e f^{3} g - b^{2} d^{2} f g^{3}\right)} p^{2}}{e^{2} h}}\right) - 15 \, e h \sqrt{-\frac{e^{2} h \sqrt{-\frac{{\left(50625 \, b^{4} d e^{4} f^{8} - 85500 \, b^{4} d^{2} e^{3} f^{6} g^{2} + 40150 \, b^{4} d^{3} e^{2} f^{4} g^{4} - 3420 \, b^{4} d^{4} e f^{2} g^{6} + 81 \, b^{4} d^{5} g^{8}\right)} p^{4}}{e^{5} h^{2}}} + 60 \, {\left(5 \, b^{2} d e f^{3} g - b^{2} d^{2} f g^{3}\right)} p^{2}}{e^{2} h}} \log\left(16 \, {\left(50625 \, b^{3} e^{4} f^{8} - 40500 \, b^{3} d e^{3} f^{6} g^{2} + 2150 \, b^{3} d^{2} e^{2} f^{4} g^{4} - 1620 \, b^{3} d^{3} e f^{2} g^{6} + 81 \, b^{3} d^{4} g^{8}\right)} \sqrt{h x} p^{3} - 16 \, {\left(10 \, e^{4} f g h^{2} \sqrt{-\frac{{\left(50625 \, b^{4} d e^{4} f^{8} - 85500 \, b^{4} d^{2} e^{3} f^{6} g^{2} + 40150 \, b^{4} d^{3} e^{2} f^{4} g^{4} - 3420 \, b^{4} d^{4} e f^{2} g^{6} + 81 \, b^{4} d^{5} g^{8}\right)} p^{4}}{e^{5} h^{2}}} + 3 \, {\left(1125 \, b^{2} e^{4} f^{6} - 1175 \, b^{2} d e^{3} f^{4} g^{2} + 235 \, b^{2} d^{2} e^{2} f^{2} g^{4} - 9 \, b^{2} d^{3} e g^{6}\right)} h p^{2}\right)} \sqrt{-\frac{e^{2} h \sqrt{-\frac{{\left(50625 \, b^{4} d e^{4} f^{8} - 85500 \, b^{4} d^{2} e^{3} f^{6} g^{2} + 40150 \, b^{4} d^{3} e^{2} f^{4} g^{4} - 3420 \, b^{4} d^{4} e f^{2} g^{6} + 81 \, b^{4} d^{5} g^{8}\right)} p^{4}}{e^{5} h^{2}}} + 60 \, {\left(5 \, b^{2} d e f^{3} g - b^{2} d^{2} f g^{3}\right)} p^{2}}{e^{2} h}}\right) - 15 \, e h \sqrt{\frac{e^{2} h \sqrt{-\frac{{\left(50625 \, b^{4} d e^{4} f^{8} - 85500 \, b^{4} d^{2} e^{3} f^{6} g^{2} + 40150 \, b^{4} d^{3} e^{2} f^{4} g^{4} - 3420 \, b^{4} d^{4} e f^{2} g^{6} + 81 \, b^{4} d^{5} g^{8}\right)} p^{4}}{e^{5} h^{2}}} - 60 \, {\left(5 \, b^{2} d e f^{3} g - b^{2} d^{2} f g^{3}\right)} p^{2}}{e^{2} h}} \log\left(16 \, {\left(50625 \, b^{3} e^{4} f^{8} - 40500 \, b^{3} d e^{3} f^{6} g^{2} + 2150 \, b^{3} d^{2} e^{2} f^{4} g^{4} - 1620 \, b^{3} d^{3} e f^{2} g^{6} + 81 \, b^{3} d^{4} g^{8}\right)} \sqrt{h x} p^{3} + 16 \, {\left(10 \, e^{4} f g h^{2} \sqrt{-\frac{{\left(50625 \, b^{4} d e^{4} f^{8} - 85500 \, b^{4} d^{2} e^{3} f^{6} g^{2} + 40150 \, b^{4} d^{3} e^{2} f^{4} g^{4} - 3420 \, b^{4} d^{4} e f^{2} g^{6} + 81 \, b^{4} d^{5} g^{8}\right)} p^{4}}{e^{5} h^{2}}} - 3 \, {\left(1125 \, b^{2} e^{4} f^{6} - 1175 \, b^{2} d e^{3} f^{4} g^{2} + 235 \, b^{2} d^{2} e^{2} f^{2} g^{4} - 9 \, b^{2} d^{3} e g^{6}\right)} h p^{2}\right)} \sqrt{\frac{e^{2} h \sqrt{-\frac{{\left(50625 \, b^{4} d e^{4} f^{8} - 85500 \, b^{4} d^{2} e^{3} f^{6} g^{2} + 40150 \, b^{4} d^{3} e^{2} f^{4} g^{4} - 3420 \, b^{4} d^{4} e f^{2} g^{6} + 81 \, b^{4} d^{5} g^{8}\right)} p^{4}}{e^{5} h^{2}}} - 60 \, {\left(5 \, b^{2} d e f^{3} g - b^{2} d^{2} f g^{3}\right)} p^{2}}{e^{2} h}}\right) + 15 \, e h \sqrt{\frac{e^{2} h \sqrt{-\frac{{\left(50625 \, b^{4} d e^{4} f^{8} - 85500 \, b^{4} d^{2} e^{3} f^{6} g^{2} + 40150 \, b^{4} d^{3} e^{2} f^{4} g^{4} - 3420 \, b^{4} d^{4} e f^{2} g^{6} + 81 \, b^{4} d^{5} g^{8}\right)} p^{4}}{e^{5} h^{2}}} - 60 \, {\left(5 \, b^{2} d e f^{3} g - b^{2} d^{2} f g^{3}\right)} p^{2}}{e^{2} h}} \log\left(16 \, {\left(50625 \, b^{3} e^{4} f^{8} - 40500 \, b^{3} d e^{3} f^{6} g^{2} + 2150 \, b^{3} d^{2} e^{2} f^{4} g^{4} - 1620 \, b^{3} d^{3} e f^{2} g^{6} + 81 \, b^{3} d^{4} g^{8}\right)} \sqrt{h x} p^{3} - 16 \, {\left(10 \, e^{4} f g h^{2} \sqrt{-\frac{{\left(50625 \, b^{4} d e^{4} f^{8} - 85500 \, b^{4} d^{2} e^{3} f^{6} g^{2} + 40150 \, b^{4} d^{3} e^{2} f^{4} g^{4} - 3420 \, b^{4} d^{4} e f^{2} g^{6} + 81 \, b^{4} d^{5} g^{8}\right)} p^{4}}{e^{5} h^{2}}} - 3 \, {\left(1125 \, b^{2} e^{4} f^{6} - 1175 \, b^{2} d e^{3} f^{4} g^{2} + 235 \, b^{2} d^{2} e^{2} f^{2} g^{4} - 9 \, b^{2} d^{3} e g^{6}\right)} h p^{2}\right)} \sqrt{\frac{e^{2} h \sqrt{-\frac{{\left(50625 \, b^{4} d e^{4} f^{8} - 85500 \, b^{4} d^{2} e^{3} f^{6} g^{2} + 40150 \, b^{4} d^{3} e^{2} f^{4} g^{4} - 3420 \, b^{4} d^{4} e f^{2} g^{6} + 81 \, b^{4} d^{5} g^{8}\right)} p^{4}}{e^{5} h^{2}}} - 60 \, {\left(5 \, b^{2} d e f^{3} g - b^{2} d^{2} f g^{3}\right)} p^{2}}{e^{2} h}}\right) + {\left(225 \, a e f^{2} - 9 \, {\left(4 \, b e g^{2} p - 5 \, a e g^{2}\right)} x^{2} - 180 \, {\left(5 \, b e f^{2} - b d g^{2}\right)} p - 50 \, {\left(4 \, b e f g p - 3 \, a e f g\right)} x + 15 \, {\left(3 \, b e g^{2} p x^{2} + 10 \, b e f g p x + 15 \, b e f^{2} p\right)} \log\left(e x^{2} + d\right) + 15 \, {\left(3 \, b e g^{2} x^{2} + 10 \, b e f g x + 15 \, b e f^{2}\right)} \log\left(c\right)\right)} \sqrt{h x}\right)}}{225 \, e h}"," ",0,"2/225*(15*e*h*sqrt(-(e^2*h*sqrt(-(50625*b^4*d*e^4*f^8 - 85500*b^4*d^2*e^3*f^6*g^2 + 40150*b^4*d^3*e^2*f^4*g^4 - 3420*b^4*d^4*e*f^2*g^6 + 81*b^4*d^5*g^8)*p^4/(e^5*h^2)) + 60*(5*b^2*d*e*f^3*g - b^2*d^2*f*g^3)*p^2)/(e^2*h))*log(16*(50625*b^3*e^4*f^8 - 40500*b^3*d*e^3*f^6*g^2 + 2150*b^3*d^2*e^2*f^4*g^4 - 1620*b^3*d^3*e*f^2*g^6 + 81*b^3*d^4*g^8)*sqrt(h*x)*p^3 + 16*(10*e^4*f*g*h^2*sqrt(-(50625*b^4*d*e^4*f^8 - 85500*b^4*d^2*e^3*f^6*g^2 + 40150*b^4*d^3*e^2*f^4*g^4 - 3420*b^4*d^4*e*f^2*g^6 + 81*b^4*d^5*g^8)*p^4/(e^5*h^2)) + 3*(1125*b^2*e^4*f^6 - 1175*b^2*d*e^3*f^4*g^2 + 235*b^2*d^2*e^2*f^2*g^4 - 9*b^2*d^3*e*g^6)*h*p^2)*sqrt(-(e^2*h*sqrt(-(50625*b^4*d*e^4*f^8 - 85500*b^4*d^2*e^3*f^6*g^2 + 40150*b^4*d^3*e^2*f^4*g^4 - 3420*b^4*d^4*e*f^2*g^6 + 81*b^4*d^5*g^8)*p^4/(e^5*h^2)) + 60*(5*b^2*d*e*f^3*g - b^2*d^2*f*g^3)*p^2)/(e^2*h))) - 15*e*h*sqrt(-(e^2*h*sqrt(-(50625*b^4*d*e^4*f^8 - 85500*b^4*d^2*e^3*f^6*g^2 + 40150*b^4*d^3*e^2*f^4*g^4 - 3420*b^4*d^4*e*f^2*g^6 + 81*b^4*d^5*g^8)*p^4/(e^5*h^2)) + 60*(5*b^2*d*e*f^3*g - b^2*d^2*f*g^3)*p^2)/(e^2*h))*log(16*(50625*b^3*e^4*f^8 - 40500*b^3*d*e^3*f^6*g^2 + 2150*b^3*d^2*e^2*f^4*g^4 - 1620*b^3*d^3*e*f^2*g^6 + 81*b^3*d^4*g^8)*sqrt(h*x)*p^3 - 16*(10*e^4*f*g*h^2*sqrt(-(50625*b^4*d*e^4*f^8 - 85500*b^4*d^2*e^3*f^6*g^2 + 40150*b^4*d^3*e^2*f^4*g^4 - 3420*b^4*d^4*e*f^2*g^6 + 81*b^4*d^5*g^8)*p^4/(e^5*h^2)) + 3*(1125*b^2*e^4*f^6 - 1175*b^2*d*e^3*f^4*g^2 + 235*b^2*d^2*e^2*f^2*g^4 - 9*b^2*d^3*e*g^6)*h*p^2)*sqrt(-(e^2*h*sqrt(-(50625*b^4*d*e^4*f^8 - 85500*b^4*d^2*e^3*f^6*g^2 + 40150*b^4*d^3*e^2*f^4*g^4 - 3420*b^4*d^4*e*f^2*g^6 + 81*b^4*d^5*g^8)*p^4/(e^5*h^2)) + 60*(5*b^2*d*e*f^3*g - b^2*d^2*f*g^3)*p^2)/(e^2*h))) - 15*e*h*sqrt((e^2*h*sqrt(-(50625*b^4*d*e^4*f^8 - 85500*b^4*d^2*e^3*f^6*g^2 + 40150*b^4*d^3*e^2*f^4*g^4 - 3420*b^4*d^4*e*f^2*g^6 + 81*b^4*d^5*g^8)*p^4/(e^5*h^2)) - 60*(5*b^2*d*e*f^3*g - b^2*d^2*f*g^3)*p^2)/(e^2*h))*log(16*(50625*b^3*e^4*f^8 - 40500*b^3*d*e^3*f^6*g^2 + 2150*b^3*d^2*e^2*f^4*g^4 - 1620*b^3*d^3*e*f^2*g^6 + 81*b^3*d^4*g^8)*sqrt(h*x)*p^3 + 16*(10*e^4*f*g*h^2*sqrt(-(50625*b^4*d*e^4*f^8 - 85500*b^4*d^2*e^3*f^6*g^2 + 40150*b^4*d^3*e^2*f^4*g^4 - 3420*b^4*d^4*e*f^2*g^6 + 81*b^4*d^5*g^8)*p^4/(e^5*h^2)) - 3*(1125*b^2*e^4*f^6 - 1175*b^2*d*e^3*f^4*g^2 + 235*b^2*d^2*e^2*f^2*g^4 - 9*b^2*d^3*e*g^6)*h*p^2)*sqrt((e^2*h*sqrt(-(50625*b^4*d*e^4*f^8 - 85500*b^4*d^2*e^3*f^6*g^2 + 40150*b^4*d^3*e^2*f^4*g^4 - 3420*b^4*d^4*e*f^2*g^6 + 81*b^4*d^5*g^8)*p^4/(e^5*h^2)) - 60*(5*b^2*d*e*f^3*g - b^2*d^2*f*g^3)*p^2)/(e^2*h))) + 15*e*h*sqrt((e^2*h*sqrt(-(50625*b^4*d*e^4*f^8 - 85500*b^4*d^2*e^3*f^6*g^2 + 40150*b^4*d^3*e^2*f^4*g^4 - 3420*b^4*d^4*e*f^2*g^6 + 81*b^4*d^5*g^8)*p^4/(e^5*h^2)) - 60*(5*b^2*d*e*f^3*g - b^2*d^2*f*g^3)*p^2)/(e^2*h))*log(16*(50625*b^3*e^4*f^8 - 40500*b^3*d*e^3*f^6*g^2 + 2150*b^3*d^2*e^2*f^4*g^4 - 1620*b^3*d^3*e*f^2*g^6 + 81*b^3*d^4*g^8)*sqrt(h*x)*p^3 - 16*(10*e^4*f*g*h^2*sqrt(-(50625*b^4*d*e^4*f^8 - 85500*b^4*d^2*e^3*f^6*g^2 + 40150*b^4*d^3*e^2*f^4*g^4 - 3420*b^4*d^4*e*f^2*g^6 + 81*b^4*d^5*g^8)*p^4/(e^5*h^2)) - 3*(1125*b^2*e^4*f^6 - 1175*b^2*d*e^3*f^4*g^2 + 235*b^2*d^2*e^2*f^2*g^4 - 9*b^2*d^3*e*g^6)*h*p^2)*sqrt((e^2*h*sqrt(-(50625*b^4*d*e^4*f^8 - 85500*b^4*d^2*e^3*f^6*g^2 + 40150*b^4*d^3*e^2*f^4*g^4 - 3420*b^4*d^4*e*f^2*g^6 + 81*b^4*d^5*g^8)*p^4/(e^5*h^2)) - 60*(5*b^2*d*e*f^3*g - b^2*d^2*f*g^3)*p^2)/(e^2*h))) + (225*a*e*f^2 - 9*(4*b*e*g^2*p - 5*a*e*g^2)*x^2 - 180*(5*b*e*f^2 - b*d*g^2)*p - 50*(4*b*e*f*g*p - 3*a*e*f*g)*x + 15*(3*b*e*g^2*p*x^2 + 10*b*e*f*g*p*x + 15*b*e*f^2*p)*log(e*x^2 + d) + 15*(3*b*e*g^2*x^2 + 10*b*e*f*g*x + 15*b*e*f^2)*log(c))*sqrt(h*x))/(e*h)","B",0
612,1,2118,0,1.068256," ","integrate((g*x+f)^2*(a+b*log(c*(e*x^2+d)^p))/(h*x)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, h^{2} x \sqrt{-\frac{e h^{3} \sqrt{-\frac{{\left(81 \, b^{4} e^{4} f^{8} - 540 \, b^{4} d e^{3} f^{6} g^{2} + 918 \, b^{4} d^{2} e^{2} f^{4} g^{4} - 60 \, b^{4} d^{3} e f^{2} g^{6} + b^{4} d^{4} g^{8}\right)} p^{4}}{d e^{3} h^{6}}} + 12 \, {\left(3 \, b^{2} e f^{3} g + b^{2} d f g^{3}\right)} p^{2}}{e h^{3}}} \log\left(32 \, {\left(81 \, b^{3} e^{4} f^{8} + 108 \, b^{3} d e^{3} f^{6} g^{2} - 1242 \, b^{3} d^{2} e^{2} f^{4} g^{4} + 12 \, b^{3} d^{3} e f^{2} g^{6} + b^{3} d^{4} g^{8}\right)} \sqrt{h x} p^{3} + 32 \, {\left({\left(3 \, d e^{3} f^{2} + d^{2} e^{2} g^{2}\right)} h^{5} \sqrt{-\frac{{\left(81 \, b^{4} e^{4} f^{8} - 540 \, b^{4} d e^{3} f^{6} g^{2} + 918 \, b^{4} d^{2} e^{2} f^{4} g^{4} - 60 \, b^{4} d^{3} e f^{2} g^{6} + b^{4} d^{4} g^{8}\right)} p^{4}}{d e^{3} h^{6}}} - 6 \, {\left(9 \, b^{2} d e^{3} f^{5} g - 30 \, b^{2} d^{2} e^{2} f^{3} g^{3} + b^{2} d^{3} e f g^{5}\right)} h^{2} p^{2}\right)} \sqrt{-\frac{e h^{3} \sqrt{-\frac{{\left(81 \, b^{4} e^{4} f^{8} - 540 \, b^{4} d e^{3} f^{6} g^{2} + 918 \, b^{4} d^{2} e^{2} f^{4} g^{4} - 60 \, b^{4} d^{3} e f^{2} g^{6} + b^{4} d^{4} g^{8}\right)} p^{4}}{d e^{3} h^{6}}} + 12 \, {\left(3 \, b^{2} e f^{3} g + b^{2} d f g^{3}\right)} p^{2}}{e h^{3}}}\right) - 3 \, h^{2} x \sqrt{-\frac{e h^{3} \sqrt{-\frac{{\left(81 \, b^{4} e^{4} f^{8} - 540 \, b^{4} d e^{3} f^{6} g^{2} + 918 \, b^{4} d^{2} e^{2} f^{4} g^{4} - 60 \, b^{4} d^{3} e f^{2} g^{6} + b^{4} d^{4} g^{8}\right)} p^{4}}{d e^{3} h^{6}}} + 12 \, {\left(3 \, b^{2} e f^{3} g + b^{2} d f g^{3}\right)} p^{2}}{e h^{3}}} \log\left(32 \, {\left(81 \, b^{3} e^{4} f^{8} + 108 \, b^{3} d e^{3} f^{6} g^{2} - 1242 \, b^{3} d^{2} e^{2} f^{4} g^{4} + 12 \, b^{3} d^{3} e f^{2} g^{6} + b^{3} d^{4} g^{8}\right)} \sqrt{h x} p^{3} - 32 \, {\left({\left(3 \, d e^{3} f^{2} + d^{2} e^{2} g^{2}\right)} h^{5} \sqrt{-\frac{{\left(81 \, b^{4} e^{4} f^{8} - 540 \, b^{4} d e^{3} f^{6} g^{2} + 918 \, b^{4} d^{2} e^{2} f^{4} g^{4} - 60 \, b^{4} d^{3} e f^{2} g^{6} + b^{4} d^{4} g^{8}\right)} p^{4}}{d e^{3} h^{6}}} - 6 \, {\left(9 \, b^{2} d e^{3} f^{5} g - 30 \, b^{2} d^{2} e^{2} f^{3} g^{3} + b^{2} d^{3} e f g^{5}\right)} h^{2} p^{2}\right)} \sqrt{-\frac{e h^{3} \sqrt{-\frac{{\left(81 \, b^{4} e^{4} f^{8} - 540 \, b^{4} d e^{3} f^{6} g^{2} + 918 \, b^{4} d^{2} e^{2} f^{4} g^{4} - 60 \, b^{4} d^{3} e f^{2} g^{6} + b^{4} d^{4} g^{8}\right)} p^{4}}{d e^{3} h^{6}}} + 12 \, {\left(3 \, b^{2} e f^{3} g + b^{2} d f g^{3}\right)} p^{2}}{e h^{3}}}\right) - 3 \, h^{2} x \sqrt{\frac{e h^{3} \sqrt{-\frac{{\left(81 \, b^{4} e^{4} f^{8} - 540 \, b^{4} d e^{3} f^{6} g^{2} + 918 \, b^{4} d^{2} e^{2} f^{4} g^{4} - 60 \, b^{4} d^{3} e f^{2} g^{6} + b^{4} d^{4} g^{8}\right)} p^{4}}{d e^{3} h^{6}}} - 12 \, {\left(3 \, b^{2} e f^{3} g + b^{2} d f g^{3}\right)} p^{2}}{e h^{3}}} \log\left(32 \, {\left(81 \, b^{3} e^{4} f^{8} + 108 \, b^{3} d e^{3} f^{6} g^{2} - 1242 \, b^{3} d^{2} e^{2} f^{4} g^{4} + 12 \, b^{3} d^{3} e f^{2} g^{6} + b^{3} d^{4} g^{8}\right)} \sqrt{h x} p^{3} + 32 \, {\left({\left(3 \, d e^{3} f^{2} + d^{2} e^{2} g^{2}\right)} h^{5} \sqrt{-\frac{{\left(81 \, b^{4} e^{4} f^{8} - 540 \, b^{4} d e^{3} f^{6} g^{2} + 918 \, b^{4} d^{2} e^{2} f^{4} g^{4} - 60 \, b^{4} d^{3} e f^{2} g^{6} + b^{4} d^{4} g^{8}\right)} p^{4}}{d e^{3} h^{6}}} + 6 \, {\left(9 \, b^{2} d e^{3} f^{5} g - 30 \, b^{2} d^{2} e^{2} f^{3} g^{3} + b^{2} d^{3} e f g^{5}\right)} h^{2} p^{2}\right)} \sqrt{\frac{e h^{3} \sqrt{-\frac{{\left(81 \, b^{4} e^{4} f^{8} - 540 \, b^{4} d e^{3} f^{6} g^{2} + 918 \, b^{4} d^{2} e^{2} f^{4} g^{4} - 60 \, b^{4} d^{3} e f^{2} g^{6} + b^{4} d^{4} g^{8}\right)} p^{4}}{d e^{3} h^{6}}} - 12 \, {\left(3 \, b^{2} e f^{3} g + b^{2} d f g^{3}\right)} p^{2}}{e h^{3}}}\right) + 3 \, h^{2} x \sqrt{\frac{e h^{3} \sqrt{-\frac{{\left(81 \, b^{4} e^{4} f^{8} - 540 \, b^{4} d e^{3} f^{6} g^{2} + 918 \, b^{4} d^{2} e^{2} f^{4} g^{4} - 60 \, b^{4} d^{3} e f^{2} g^{6} + b^{4} d^{4} g^{8}\right)} p^{4}}{d e^{3} h^{6}}} - 12 \, {\left(3 \, b^{2} e f^{3} g + b^{2} d f g^{3}\right)} p^{2}}{e h^{3}}} \log\left(32 \, {\left(81 \, b^{3} e^{4} f^{8} + 108 \, b^{3} d e^{3} f^{6} g^{2} - 1242 \, b^{3} d^{2} e^{2} f^{4} g^{4} + 12 \, b^{3} d^{3} e f^{2} g^{6} + b^{3} d^{4} g^{8}\right)} \sqrt{h x} p^{3} - 32 \, {\left({\left(3 \, d e^{3} f^{2} + d^{2} e^{2} g^{2}\right)} h^{5} \sqrt{-\frac{{\left(81 \, b^{4} e^{4} f^{8} - 540 \, b^{4} d e^{3} f^{6} g^{2} + 918 \, b^{4} d^{2} e^{2} f^{4} g^{4} - 60 \, b^{4} d^{3} e f^{2} g^{6} + b^{4} d^{4} g^{8}\right)} p^{4}}{d e^{3} h^{6}}} + 6 \, {\left(9 \, b^{2} d e^{3} f^{5} g - 30 \, b^{2} d^{2} e^{2} f^{3} g^{3} + b^{2} d^{3} e f g^{5}\right)} h^{2} p^{2}\right)} \sqrt{\frac{e h^{3} \sqrt{-\frac{{\left(81 \, b^{4} e^{4} f^{8} - 540 \, b^{4} d e^{3} f^{6} g^{2} + 918 \, b^{4} d^{2} e^{2} f^{4} g^{4} - 60 \, b^{4} d^{3} e f^{2} g^{6} + b^{4} d^{4} g^{8}\right)} p^{4}}{d e^{3} h^{6}}} - 12 \, {\left(3 \, b^{2} e f^{3} g + b^{2} d f g^{3}\right)} p^{2}}{e h^{3}}}\right) + {\left(9 \, a f^{2} + {\left(4 \, b g^{2} p - 3 \, a g^{2}\right)} x^{2} + 18 \, {\left(4 \, b f g p - a f g\right)} x - 3 \, {\left(b g^{2} p x^{2} + 6 \, b f g p x - 3 \, b f^{2} p\right)} \log\left(e x^{2} + d\right) - 3 \, {\left(b g^{2} x^{2} + 6 \, b f g x - 3 \, b f^{2}\right)} \log\left(c\right)\right)} \sqrt{h x}\right)}}{9 \, h^{2} x}"," ",0,"-2/9*(3*h^2*x*sqrt(-(e*h^3*sqrt(-(81*b^4*e^4*f^8 - 540*b^4*d*e^3*f^6*g^2 + 918*b^4*d^2*e^2*f^4*g^4 - 60*b^4*d^3*e*f^2*g^6 + b^4*d^4*g^8)*p^4/(d*e^3*h^6)) + 12*(3*b^2*e*f^3*g + b^2*d*f*g^3)*p^2)/(e*h^3))*log(32*(81*b^3*e^4*f^8 + 108*b^3*d*e^3*f^6*g^2 - 1242*b^3*d^2*e^2*f^4*g^4 + 12*b^3*d^3*e*f^2*g^6 + b^3*d^4*g^8)*sqrt(h*x)*p^3 + 32*((3*d*e^3*f^2 + d^2*e^2*g^2)*h^5*sqrt(-(81*b^4*e^4*f^8 - 540*b^4*d*e^3*f^6*g^2 + 918*b^4*d^2*e^2*f^4*g^4 - 60*b^4*d^3*e*f^2*g^6 + b^4*d^4*g^8)*p^4/(d*e^3*h^6)) - 6*(9*b^2*d*e^3*f^5*g - 30*b^2*d^2*e^2*f^3*g^3 + b^2*d^3*e*f*g^5)*h^2*p^2)*sqrt(-(e*h^3*sqrt(-(81*b^4*e^4*f^8 - 540*b^4*d*e^3*f^6*g^2 + 918*b^4*d^2*e^2*f^4*g^4 - 60*b^4*d^3*e*f^2*g^6 + b^4*d^4*g^8)*p^4/(d*e^3*h^6)) + 12*(3*b^2*e*f^3*g + b^2*d*f*g^3)*p^2)/(e*h^3))) - 3*h^2*x*sqrt(-(e*h^3*sqrt(-(81*b^4*e^4*f^8 - 540*b^4*d*e^3*f^6*g^2 + 918*b^4*d^2*e^2*f^4*g^4 - 60*b^4*d^3*e*f^2*g^6 + b^4*d^4*g^8)*p^4/(d*e^3*h^6)) + 12*(3*b^2*e*f^3*g + b^2*d*f*g^3)*p^2)/(e*h^3))*log(32*(81*b^3*e^4*f^8 + 108*b^3*d*e^3*f^6*g^2 - 1242*b^3*d^2*e^2*f^4*g^4 + 12*b^3*d^3*e*f^2*g^6 + b^3*d^4*g^8)*sqrt(h*x)*p^3 - 32*((3*d*e^3*f^2 + d^2*e^2*g^2)*h^5*sqrt(-(81*b^4*e^4*f^8 - 540*b^4*d*e^3*f^6*g^2 + 918*b^4*d^2*e^2*f^4*g^4 - 60*b^4*d^3*e*f^2*g^6 + b^4*d^4*g^8)*p^4/(d*e^3*h^6)) - 6*(9*b^2*d*e^3*f^5*g - 30*b^2*d^2*e^2*f^3*g^3 + b^2*d^3*e*f*g^5)*h^2*p^2)*sqrt(-(e*h^3*sqrt(-(81*b^4*e^4*f^8 - 540*b^4*d*e^3*f^6*g^2 + 918*b^4*d^2*e^2*f^4*g^4 - 60*b^4*d^3*e*f^2*g^6 + b^4*d^4*g^8)*p^4/(d*e^3*h^6)) + 12*(3*b^2*e*f^3*g + b^2*d*f*g^3)*p^2)/(e*h^3))) - 3*h^2*x*sqrt((e*h^3*sqrt(-(81*b^4*e^4*f^8 - 540*b^4*d*e^3*f^6*g^2 + 918*b^4*d^2*e^2*f^4*g^4 - 60*b^4*d^3*e*f^2*g^6 + b^4*d^4*g^8)*p^4/(d*e^3*h^6)) - 12*(3*b^2*e*f^3*g + b^2*d*f*g^3)*p^2)/(e*h^3))*log(32*(81*b^3*e^4*f^8 + 108*b^3*d*e^3*f^6*g^2 - 1242*b^3*d^2*e^2*f^4*g^4 + 12*b^3*d^3*e*f^2*g^6 + b^3*d^4*g^8)*sqrt(h*x)*p^3 + 32*((3*d*e^3*f^2 + d^2*e^2*g^2)*h^5*sqrt(-(81*b^4*e^4*f^8 - 540*b^4*d*e^3*f^6*g^2 + 918*b^4*d^2*e^2*f^4*g^4 - 60*b^4*d^3*e*f^2*g^6 + b^4*d^4*g^8)*p^4/(d*e^3*h^6)) + 6*(9*b^2*d*e^3*f^5*g - 30*b^2*d^2*e^2*f^3*g^3 + b^2*d^3*e*f*g^5)*h^2*p^2)*sqrt((e*h^3*sqrt(-(81*b^4*e^4*f^8 - 540*b^4*d*e^3*f^6*g^2 + 918*b^4*d^2*e^2*f^4*g^4 - 60*b^4*d^3*e*f^2*g^6 + b^4*d^4*g^8)*p^4/(d*e^3*h^6)) - 12*(3*b^2*e*f^3*g + b^2*d*f*g^3)*p^2)/(e*h^3))) + 3*h^2*x*sqrt((e*h^3*sqrt(-(81*b^4*e^4*f^8 - 540*b^4*d*e^3*f^6*g^2 + 918*b^4*d^2*e^2*f^4*g^4 - 60*b^4*d^3*e*f^2*g^6 + b^4*d^4*g^8)*p^4/(d*e^3*h^6)) - 12*(3*b^2*e*f^3*g + b^2*d*f*g^3)*p^2)/(e*h^3))*log(32*(81*b^3*e^4*f^8 + 108*b^3*d*e^3*f^6*g^2 - 1242*b^3*d^2*e^2*f^4*g^4 + 12*b^3*d^3*e*f^2*g^6 + b^3*d^4*g^8)*sqrt(h*x)*p^3 - 32*((3*d*e^3*f^2 + d^2*e^2*g^2)*h^5*sqrt(-(81*b^4*e^4*f^8 - 540*b^4*d*e^3*f^6*g^2 + 918*b^4*d^2*e^2*f^4*g^4 - 60*b^4*d^3*e*f^2*g^6 + b^4*d^4*g^8)*p^4/(d*e^3*h^6)) + 6*(9*b^2*d*e^3*f^5*g - 30*b^2*d^2*e^2*f^3*g^3 + b^2*d^3*e*f*g^5)*h^2*p^2)*sqrt((e*h^3*sqrt(-(81*b^4*e^4*f^8 - 540*b^4*d*e^3*f^6*g^2 + 918*b^4*d^2*e^2*f^4*g^4 - 60*b^4*d^3*e*f^2*g^6 + b^4*d^4*g^8)*p^4/(d*e^3*h^6)) - 12*(3*b^2*e*f^3*g + b^2*d*f*g^3)*p^2)/(e*h^3))) + (9*a*f^2 + (4*b*g^2*p - 3*a*g^2)*x^2 + 18*(4*b*f*g*p - a*f*g)*x - 3*(b*g^2*p*x^2 + 6*b*f*g*p*x - 3*b*f^2*p)*log(e*x^2 + d) - 3*(b*g^2*x^2 + 6*b*f*g*x - 3*b*f^2)*log(c))*sqrt(h*x))/(h^2*x)","B",0
613,1,2112,0,1.151289," ","integrate((g*x+f)^2*(a+b*log(c*(e*x^2+d)^p))/(h*x)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(h^{3} x^{2} \sqrt{-\frac{d h^{5} \sqrt{-\frac{{\left(b^{4} e^{4} f^{8} - 60 \, b^{4} d e^{3} f^{6} g^{2} + 918 \, b^{4} d^{2} e^{2} f^{4} g^{4} - 540 \, b^{4} d^{3} e f^{2} g^{6} + 81 \, b^{4} d^{4} g^{8}\right)} p^{4}}{d^{3} e h^{10}}} + 12 \, {\left(b^{2} e f^{3} g + 3 \, b^{2} d f g^{3}\right)} p^{2}}{d h^{5}}} \log\left(16 \, {\left(b^{3} e^{4} f^{8} + 12 \, b^{3} d e^{3} f^{6} g^{2} - 1242 \, b^{3} d^{2} e^{2} f^{4} g^{4} + 108 \, b^{3} d^{3} e f^{2} g^{6} + 81 \, b^{3} d^{4} g^{8}\right)} \sqrt{h x} p^{3} + 16 \, {\left(6 \, d^{3} e f g h^{8} \sqrt{-\frac{{\left(b^{4} e^{4} f^{8} - 60 \, b^{4} d e^{3} f^{6} g^{2} + 918 \, b^{4} d^{2} e^{2} f^{4} g^{4} - 540 \, b^{4} d^{3} e f^{2} g^{6} + 81 \, b^{4} d^{4} g^{8}\right)} p^{4}}{d^{3} e h^{10}}} + {\left(b^{2} d e^{3} f^{6} - 27 \, b^{2} d^{2} e^{2} f^{4} g^{2} - 81 \, b^{2} d^{3} e f^{2} g^{4} + 27 \, b^{2} d^{4} g^{6}\right)} h^{3} p^{2}\right)} \sqrt{-\frac{d h^{5} \sqrt{-\frac{{\left(b^{4} e^{4} f^{8} - 60 \, b^{4} d e^{3} f^{6} g^{2} + 918 \, b^{4} d^{2} e^{2} f^{4} g^{4} - 540 \, b^{4} d^{3} e f^{2} g^{6} + 81 \, b^{4} d^{4} g^{8}\right)} p^{4}}{d^{3} e h^{10}}} + 12 \, {\left(b^{2} e f^{3} g + 3 \, b^{2} d f g^{3}\right)} p^{2}}{d h^{5}}}\right) - h^{3} x^{2} \sqrt{-\frac{d h^{5} \sqrt{-\frac{{\left(b^{4} e^{4} f^{8} - 60 \, b^{4} d e^{3} f^{6} g^{2} + 918 \, b^{4} d^{2} e^{2} f^{4} g^{4} - 540 \, b^{4} d^{3} e f^{2} g^{6} + 81 \, b^{4} d^{4} g^{8}\right)} p^{4}}{d^{3} e h^{10}}} + 12 \, {\left(b^{2} e f^{3} g + 3 \, b^{2} d f g^{3}\right)} p^{2}}{d h^{5}}} \log\left(16 \, {\left(b^{3} e^{4} f^{8} + 12 \, b^{3} d e^{3} f^{6} g^{2} - 1242 \, b^{3} d^{2} e^{2} f^{4} g^{4} + 108 \, b^{3} d^{3} e f^{2} g^{6} + 81 \, b^{3} d^{4} g^{8}\right)} \sqrt{h x} p^{3} - 16 \, {\left(6 \, d^{3} e f g h^{8} \sqrt{-\frac{{\left(b^{4} e^{4} f^{8} - 60 \, b^{4} d e^{3} f^{6} g^{2} + 918 \, b^{4} d^{2} e^{2} f^{4} g^{4} - 540 \, b^{4} d^{3} e f^{2} g^{6} + 81 \, b^{4} d^{4} g^{8}\right)} p^{4}}{d^{3} e h^{10}}} + {\left(b^{2} d e^{3} f^{6} - 27 \, b^{2} d^{2} e^{2} f^{4} g^{2} - 81 \, b^{2} d^{3} e f^{2} g^{4} + 27 \, b^{2} d^{4} g^{6}\right)} h^{3} p^{2}\right)} \sqrt{-\frac{d h^{5} \sqrt{-\frac{{\left(b^{4} e^{4} f^{8} - 60 \, b^{4} d e^{3} f^{6} g^{2} + 918 \, b^{4} d^{2} e^{2} f^{4} g^{4} - 540 \, b^{4} d^{3} e f^{2} g^{6} + 81 \, b^{4} d^{4} g^{8}\right)} p^{4}}{d^{3} e h^{10}}} + 12 \, {\left(b^{2} e f^{3} g + 3 \, b^{2} d f g^{3}\right)} p^{2}}{d h^{5}}}\right) - h^{3} x^{2} \sqrt{\frac{d h^{5} \sqrt{-\frac{{\left(b^{4} e^{4} f^{8} - 60 \, b^{4} d e^{3} f^{6} g^{2} + 918 \, b^{4} d^{2} e^{2} f^{4} g^{4} - 540 \, b^{4} d^{3} e f^{2} g^{6} + 81 \, b^{4} d^{4} g^{8}\right)} p^{4}}{d^{3} e h^{10}}} - 12 \, {\left(b^{2} e f^{3} g + 3 \, b^{2} d f g^{3}\right)} p^{2}}{d h^{5}}} \log\left(16 \, {\left(b^{3} e^{4} f^{8} + 12 \, b^{3} d e^{3} f^{6} g^{2} - 1242 \, b^{3} d^{2} e^{2} f^{4} g^{4} + 108 \, b^{3} d^{3} e f^{2} g^{6} + 81 \, b^{3} d^{4} g^{8}\right)} \sqrt{h x} p^{3} + 16 \, {\left(6 \, d^{3} e f g h^{8} \sqrt{-\frac{{\left(b^{4} e^{4} f^{8} - 60 \, b^{4} d e^{3} f^{6} g^{2} + 918 \, b^{4} d^{2} e^{2} f^{4} g^{4} - 540 \, b^{4} d^{3} e f^{2} g^{6} + 81 \, b^{4} d^{4} g^{8}\right)} p^{4}}{d^{3} e h^{10}}} - {\left(b^{2} d e^{3} f^{6} - 27 \, b^{2} d^{2} e^{2} f^{4} g^{2} - 81 \, b^{2} d^{3} e f^{2} g^{4} + 27 \, b^{2} d^{4} g^{6}\right)} h^{3} p^{2}\right)} \sqrt{\frac{d h^{5} \sqrt{-\frac{{\left(b^{4} e^{4} f^{8} - 60 \, b^{4} d e^{3} f^{6} g^{2} + 918 \, b^{4} d^{2} e^{2} f^{4} g^{4} - 540 \, b^{4} d^{3} e f^{2} g^{6} + 81 \, b^{4} d^{4} g^{8}\right)} p^{4}}{d^{3} e h^{10}}} - 12 \, {\left(b^{2} e f^{3} g + 3 \, b^{2} d f g^{3}\right)} p^{2}}{d h^{5}}}\right) + h^{3} x^{2} \sqrt{\frac{d h^{5} \sqrt{-\frac{{\left(b^{4} e^{4} f^{8} - 60 \, b^{4} d e^{3} f^{6} g^{2} + 918 \, b^{4} d^{2} e^{2} f^{4} g^{4} - 540 \, b^{4} d^{3} e f^{2} g^{6} + 81 \, b^{4} d^{4} g^{8}\right)} p^{4}}{d^{3} e h^{10}}} - 12 \, {\left(b^{2} e f^{3} g + 3 \, b^{2} d f g^{3}\right)} p^{2}}{d h^{5}}} \log\left(16 \, {\left(b^{3} e^{4} f^{8} + 12 \, b^{3} d e^{3} f^{6} g^{2} - 1242 \, b^{3} d^{2} e^{2} f^{4} g^{4} + 108 \, b^{3} d^{3} e f^{2} g^{6} + 81 \, b^{3} d^{4} g^{8}\right)} \sqrt{h x} p^{3} - 16 \, {\left(6 \, d^{3} e f g h^{8} \sqrt{-\frac{{\left(b^{4} e^{4} f^{8} - 60 \, b^{4} d e^{3} f^{6} g^{2} + 918 \, b^{4} d^{2} e^{2} f^{4} g^{4} - 540 \, b^{4} d^{3} e f^{2} g^{6} + 81 \, b^{4} d^{4} g^{8}\right)} p^{4}}{d^{3} e h^{10}}} - {\left(b^{2} d e^{3} f^{6} - 27 \, b^{2} d^{2} e^{2} f^{4} g^{2} - 81 \, b^{2} d^{3} e f^{2} g^{4} + 27 \, b^{2} d^{4} g^{6}\right)} h^{3} p^{2}\right)} \sqrt{\frac{d h^{5} \sqrt{-\frac{{\left(b^{4} e^{4} f^{8} - 60 \, b^{4} d e^{3} f^{6} g^{2} + 918 \, b^{4} d^{2} e^{2} f^{4} g^{4} - 540 \, b^{4} d^{3} e f^{2} g^{6} + 81 \, b^{4} d^{4} g^{8}\right)} p^{4}}{d^{3} e h^{10}}} - 12 \, {\left(b^{2} e f^{3} g + 3 \, b^{2} d f g^{3}\right)} p^{2}}{d h^{5}}}\right) - {\left(6 \, a f g x + a f^{2} + 3 \, {\left(4 \, b g^{2} p - a g^{2}\right)} x^{2} - {\left(3 \, b g^{2} p x^{2} - 6 \, b f g p x - b f^{2} p\right)} \log\left(e x^{2} + d\right) - {\left(3 \, b g^{2} x^{2} - 6 \, b f g x - b f^{2}\right)} \log\left(c\right)\right)} \sqrt{h x}\right)}}{3 \, h^{3} x^{2}}"," ",0,"2/3*(h^3*x^2*sqrt(-(d*h^5*sqrt(-(b^4*e^4*f^8 - 60*b^4*d*e^3*f^6*g^2 + 918*b^4*d^2*e^2*f^4*g^4 - 540*b^4*d^3*e*f^2*g^6 + 81*b^4*d^4*g^8)*p^4/(d^3*e*h^10)) + 12*(b^2*e*f^3*g + 3*b^2*d*f*g^3)*p^2)/(d*h^5))*log(16*(b^3*e^4*f^8 + 12*b^3*d*e^3*f^6*g^2 - 1242*b^3*d^2*e^2*f^4*g^4 + 108*b^3*d^3*e*f^2*g^6 + 81*b^3*d^4*g^8)*sqrt(h*x)*p^3 + 16*(6*d^3*e*f*g*h^8*sqrt(-(b^4*e^4*f^8 - 60*b^4*d*e^3*f^6*g^2 + 918*b^4*d^2*e^2*f^4*g^4 - 540*b^4*d^3*e*f^2*g^6 + 81*b^4*d^4*g^8)*p^4/(d^3*e*h^10)) + (b^2*d*e^3*f^6 - 27*b^2*d^2*e^2*f^4*g^2 - 81*b^2*d^3*e*f^2*g^4 + 27*b^2*d^4*g^6)*h^3*p^2)*sqrt(-(d*h^5*sqrt(-(b^4*e^4*f^8 - 60*b^4*d*e^3*f^6*g^2 + 918*b^4*d^2*e^2*f^4*g^4 - 540*b^4*d^3*e*f^2*g^6 + 81*b^4*d^4*g^8)*p^4/(d^3*e*h^10)) + 12*(b^2*e*f^3*g + 3*b^2*d*f*g^3)*p^2)/(d*h^5))) - h^3*x^2*sqrt(-(d*h^5*sqrt(-(b^4*e^4*f^8 - 60*b^4*d*e^3*f^6*g^2 + 918*b^4*d^2*e^2*f^4*g^4 - 540*b^4*d^3*e*f^2*g^6 + 81*b^4*d^4*g^8)*p^4/(d^3*e*h^10)) + 12*(b^2*e*f^3*g + 3*b^2*d*f*g^3)*p^2)/(d*h^5))*log(16*(b^3*e^4*f^8 + 12*b^3*d*e^3*f^6*g^2 - 1242*b^3*d^2*e^2*f^4*g^4 + 108*b^3*d^3*e*f^2*g^6 + 81*b^3*d^4*g^8)*sqrt(h*x)*p^3 - 16*(6*d^3*e*f*g*h^8*sqrt(-(b^4*e^4*f^8 - 60*b^4*d*e^3*f^6*g^2 + 918*b^4*d^2*e^2*f^4*g^4 - 540*b^4*d^3*e*f^2*g^6 + 81*b^4*d^4*g^8)*p^4/(d^3*e*h^10)) + (b^2*d*e^3*f^6 - 27*b^2*d^2*e^2*f^4*g^2 - 81*b^2*d^3*e*f^2*g^4 + 27*b^2*d^4*g^6)*h^3*p^2)*sqrt(-(d*h^5*sqrt(-(b^4*e^4*f^8 - 60*b^4*d*e^3*f^6*g^2 + 918*b^4*d^2*e^2*f^4*g^4 - 540*b^4*d^3*e*f^2*g^6 + 81*b^4*d^4*g^8)*p^4/(d^3*e*h^10)) + 12*(b^2*e*f^3*g + 3*b^2*d*f*g^3)*p^2)/(d*h^5))) - h^3*x^2*sqrt((d*h^5*sqrt(-(b^4*e^4*f^8 - 60*b^4*d*e^3*f^6*g^2 + 918*b^4*d^2*e^2*f^4*g^4 - 540*b^4*d^3*e*f^2*g^6 + 81*b^4*d^4*g^8)*p^4/(d^3*e*h^10)) - 12*(b^2*e*f^3*g + 3*b^2*d*f*g^3)*p^2)/(d*h^5))*log(16*(b^3*e^4*f^8 + 12*b^3*d*e^3*f^6*g^2 - 1242*b^3*d^2*e^2*f^4*g^4 + 108*b^3*d^3*e*f^2*g^6 + 81*b^3*d^4*g^8)*sqrt(h*x)*p^3 + 16*(6*d^3*e*f*g*h^8*sqrt(-(b^4*e^4*f^8 - 60*b^4*d*e^3*f^6*g^2 + 918*b^4*d^2*e^2*f^4*g^4 - 540*b^4*d^3*e*f^2*g^6 + 81*b^4*d^4*g^8)*p^4/(d^3*e*h^10)) - (b^2*d*e^3*f^6 - 27*b^2*d^2*e^2*f^4*g^2 - 81*b^2*d^3*e*f^2*g^4 + 27*b^2*d^4*g^6)*h^3*p^2)*sqrt((d*h^5*sqrt(-(b^4*e^4*f^8 - 60*b^4*d*e^3*f^6*g^2 + 918*b^4*d^2*e^2*f^4*g^4 - 540*b^4*d^3*e*f^2*g^6 + 81*b^4*d^4*g^8)*p^4/(d^3*e*h^10)) - 12*(b^2*e*f^3*g + 3*b^2*d*f*g^3)*p^2)/(d*h^5))) + h^3*x^2*sqrt((d*h^5*sqrt(-(b^4*e^4*f^8 - 60*b^4*d*e^3*f^6*g^2 + 918*b^4*d^2*e^2*f^4*g^4 - 540*b^4*d^3*e*f^2*g^6 + 81*b^4*d^4*g^8)*p^4/(d^3*e*h^10)) - 12*(b^2*e*f^3*g + 3*b^2*d*f*g^3)*p^2)/(d*h^5))*log(16*(b^3*e^4*f^8 + 12*b^3*d*e^3*f^6*g^2 - 1242*b^3*d^2*e^2*f^4*g^4 + 108*b^3*d^3*e*f^2*g^6 + 81*b^3*d^4*g^8)*sqrt(h*x)*p^3 - 16*(6*d^3*e*f*g*h^8*sqrt(-(b^4*e^4*f^8 - 60*b^4*d*e^3*f^6*g^2 + 918*b^4*d^2*e^2*f^4*g^4 - 540*b^4*d^3*e*f^2*g^6 + 81*b^4*d^4*g^8)*p^4/(d^3*e*h^10)) - (b^2*d*e^3*f^6 - 27*b^2*d^2*e^2*f^4*g^2 - 81*b^2*d^3*e*f^2*g^4 + 27*b^2*d^4*g^6)*h^3*p^2)*sqrt((d*h^5*sqrt(-(b^4*e^4*f^8 - 60*b^4*d*e^3*f^6*g^2 + 918*b^4*d^2*e^2*f^4*g^4 - 540*b^4*d^3*e*f^2*g^6 + 81*b^4*d^4*g^8)*p^4/(d^3*e*h^10)) - 12*(b^2*e*f^3*g + 3*b^2*d*f*g^3)*p^2)/(d*h^5))) - (6*a*f*g*x + a*f^2 + 3*(4*b*g^2*p - a*g^2)*x^2 - (3*b*g^2*p*x^2 - 6*b*f*g*p*x - b*f^2*p)*log(e*x^2 + d) - (3*b*g^2*x^2 - 6*b*f*g*x - b*f^2)*log(c))*sqrt(h*x))/(h^3*x^2)","B",0
614,1,2205,0,1.279335," ","integrate((g*x+f)^2*(a+b*log(c*(e*x^2+d)^p))/(h*x)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(d h^{4} x^{3} \sqrt{\frac{d^{2} h^{7} \sqrt{-\frac{{\left(81 \, b^{4} e^{5} f^{8} - 3420 \, b^{4} d e^{4} f^{6} g^{2} + 40150 \, b^{4} d^{2} e^{3} f^{4} g^{4} - 85500 \, b^{4} d^{3} e^{2} f^{2} g^{6} + 50625 \, b^{4} d^{4} e g^{8}\right)} p^{4}}{d^{5} h^{14}}} + 60 \, {\left(b^{2} e^{2} f^{3} g - 5 \, b^{2} d e f g^{3}\right)} p^{2}}{d^{2} h^{7}}} \log\left(32 \, {\left(81 \, b^{3} e^{5} f^{8} - 1620 \, b^{3} d e^{4} f^{6} g^{2} + 2150 \, b^{3} d^{2} e^{3} f^{4} g^{4} - 40500 \, b^{3} d^{3} e^{2} f^{2} g^{6} + 50625 \, b^{3} d^{4} e g^{8}\right)} \sqrt{h x} p^{3} + 32 \, {\left(3 \, {\left(d^{4} e f^{2} - 5 \, d^{5} g^{2}\right)} h^{11} \sqrt{-\frac{{\left(81 \, b^{4} e^{5} f^{8} - 3420 \, b^{4} d e^{4} f^{6} g^{2} + 40150 \, b^{4} d^{2} e^{3} f^{4} g^{4} - 85500 \, b^{4} d^{3} e^{2} f^{2} g^{6} + 50625 \, b^{4} d^{4} e g^{8}\right)} p^{4}}{d^{5} h^{14}}} - 10 \, {\left(9 \, b^{2} d^{2} e^{3} f^{5} g - 190 \, b^{2} d^{3} e^{2} f^{3} g^{3} + 225 \, b^{2} d^{4} e f g^{5}\right)} h^{4} p^{2}\right)} \sqrt{\frac{d^{2} h^{7} \sqrt{-\frac{{\left(81 \, b^{4} e^{5} f^{8} - 3420 \, b^{4} d e^{4} f^{6} g^{2} + 40150 \, b^{4} d^{2} e^{3} f^{4} g^{4} - 85500 \, b^{4} d^{3} e^{2} f^{2} g^{6} + 50625 \, b^{4} d^{4} e g^{8}\right)} p^{4}}{d^{5} h^{14}}} + 60 \, {\left(b^{2} e^{2} f^{3} g - 5 \, b^{2} d e f g^{3}\right)} p^{2}}{d^{2} h^{7}}}\right) - d h^{4} x^{3} \sqrt{\frac{d^{2} h^{7} \sqrt{-\frac{{\left(81 \, b^{4} e^{5} f^{8} - 3420 \, b^{4} d e^{4} f^{6} g^{2} + 40150 \, b^{4} d^{2} e^{3} f^{4} g^{4} - 85500 \, b^{4} d^{3} e^{2} f^{2} g^{6} + 50625 \, b^{4} d^{4} e g^{8}\right)} p^{4}}{d^{5} h^{14}}} + 60 \, {\left(b^{2} e^{2} f^{3} g - 5 \, b^{2} d e f g^{3}\right)} p^{2}}{d^{2} h^{7}}} \log\left(32 \, {\left(81 \, b^{3} e^{5} f^{8} - 1620 \, b^{3} d e^{4} f^{6} g^{2} + 2150 \, b^{3} d^{2} e^{3} f^{4} g^{4} - 40500 \, b^{3} d^{3} e^{2} f^{2} g^{6} + 50625 \, b^{3} d^{4} e g^{8}\right)} \sqrt{h x} p^{3} - 32 \, {\left(3 \, {\left(d^{4} e f^{2} - 5 \, d^{5} g^{2}\right)} h^{11} \sqrt{-\frac{{\left(81 \, b^{4} e^{5} f^{8} - 3420 \, b^{4} d e^{4} f^{6} g^{2} + 40150 \, b^{4} d^{2} e^{3} f^{4} g^{4} - 85500 \, b^{4} d^{3} e^{2} f^{2} g^{6} + 50625 \, b^{4} d^{4} e g^{8}\right)} p^{4}}{d^{5} h^{14}}} - 10 \, {\left(9 \, b^{2} d^{2} e^{3} f^{5} g - 190 \, b^{2} d^{3} e^{2} f^{3} g^{3} + 225 \, b^{2} d^{4} e f g^{5}\right)} h^{4} p^{2}\right)} \sqrt{\frac{d^{2} h^{7} \sqrt{-\frac{{\left(81 \, b^{4} e^{5} f^{8} - 3420 \, b^{4} d e^{4} f^{6} g^{2} + 40150 \, b^{4} d^{2} e^{3} f^{4} g^{4} - 85500 \, b^{4} d^{3} e^{2} f^{2} g^{6} + 50625 \, b^{4} d^{4} e g^{8}\right)} p^{4}}{d^{5} h^{14}}} + 60 \, {\left(b^{2} e^{2} f^{3} g - 5 \, b^{2} d e f g^{3}\right)} p^{2}}{d^{2} h^{7}}}\right) - d h^{4} x^{3} \sqrt{-\frac{d^{2} h^{7} \sqrt{-\frac{{\left(81 \, b^{4} e^{5} f^{8} - 3420 \, b^{4} d e^{4} f^{6} g^{2} + 40150 \, b^{4} d^{2} e^{3} f^{4} g^{4} - 85500 \, b^{4} d^{3} e^{2} f^{2} g^{6} + 50625 \, b^{4} d^{4} e g^{8}\right)} p^{4}}{d^{5} h^{14}}} - 60 \, {\left(b^{2} e^{2} f^{3} g - 5 \, b^{2} d e f g^{3}\right)} p^{2}}{d^{2} h^{7}}} \log\left(32 \, {\left(81 \, b^{3} e^{5} f^{8} - 1620 \, b^{3} d e^{4} f^{6} g^{2} + 2150 \, b^{3} d^{2} e^{3} f^{4} g^{4} - 40500 \, b^{3} d^{3} e^{2} f^{2} g^{6} + 50625 \, b^{3} d^{4} e g^{8}\right)} \sqrt{h x} p^{3} + 32 \, {\left(3 \, {\left(d^{4} e f^{2} - 5 \, d^{5} g^{2}\right)} h^{11} \sqrt{-\frac{{\left(81 \, b^{4} e^{5} f^{8} - 3420 \, b^{4} d e^{4} f^{6} g^{2} + 40150 \, b^{4} d^{2} e^{3} f^{4} g^{4} - 85500 \, b^{4} d^{3} e^{2} f^{2} g^{6} + 50625 \, b^{4} d^{4} e g^{8}\right)} p^{4}}{d^{5} h^{14}}} + 10 \, {\left(9 \, b^{2} d^{2} e^{3} f^{5} g - 190 \, b^{2} d^{3} e^{2} f^{3} g^{3} + 225 \, b^{2} d^{4} e f g^{5}\right)} h^{4} p^{2}\right)} \sqrt{-\frac{d^{2} h^{7} \sqrt{-\frac{{\left(81 \, b^{4} e^{5} f^{8} - 3420 \, b^{4} d e^{4} f^{6} g^{2} + 40150 \, b^{4} d^{2} e^{3} f^{4} g^{4} - 85500 \, b^{4} d^{3} e^{2} f^{2} g^{6} + 50625 \, b^{4} d^{4} e g^{8}\right)} p^{4}}{d^{5} h^{14}}} - 60 \, {\left(b^{2} e^{2} f^{3} g - 5 \, b^{2} d e f g^{3}\right)} p^{2}}{d^{2} h^{7}}}\right) + d h^{4} x^{3} \sqrt{-\frac{d^{2} h^{7} \sqrt{-\frac{{\left(81 \, b^{4} e^{5} f^{8} - 3420 \, b^{4} d e^{4} f^{6} g^{2} + 40150 \, b^{4} d^{2} e^{3} f^{4} g^{4} - 85500 \, b^{4} d^{3} e^{2} f^{2} g^{6} + 50625 \, b^{4} d^{4} e g^{8}\right)} p^{4}}{d^{5} h^{14}}} - 60 \, {\left(b^{2} e^{2} f^{3} g - 5 \, b^{2} d e f g^{3}\right)} p^{2}}{d^{2} h^{7}}} \log\left(32 \, {\left(81 \, b^{3} e^{5} f^{8} - 1620 \, b^{3} d e^{4} f^{6} g^{2} + 2150 \, b^{3} d^{2} e^{3} f^{4} g^{4} - 40500 \, b^{3} d^{3} e^{2} f^{2} g^{6} + 50625 \, b^{3} d^{4} e g^{8}\right)} \sqrt{h x} p^{3} - 32 \, {\left(3 \, {\left(d^{4} e f^{2} - 5 \, d^{5} g^{2}\right)} h^{11} \sqrt{-\frac{{\left(81 \, b^{4} e^{5} f^{8} - 3420 \, b^{4} d e^{4} f^{6} g^{2} + 40150 \, b^{4} d^{2} e^{3} f^{4} g^{4} - 85500 \, b^{4} d^{3} e^{2} f^{2} g^{6} + 50625 \, b^{4} d^{4} e g^{8}\right)} p^{4}}{d^{5} h^{14}}} + 10 \, {\left(9 \, b^{2} d^{2} e^{3} f^{5} g - 190 \, b^{2} d^{3} e^{2} f^{3} g^{3} + 225 \, b^{2} d^{4} e f g^{5}\right)} h^{4} p^{2}\right)} \sqrt{-\frac{d^{2} h^{7} \sqrt{-\frac{{\left(81 \, b^{4} e^{5} f^{8} - 3420 \, b^{4} d e^{4} f^{6} g^{2} + 40150 \, b^{4} d^{2} e^{3} f^{4} g^{4} - 85500 \, b^{4} d^{3} e^{2} f^{2} g^{6} + 50625 \, b^{4} d^{4} e g^{8}\right)} p^{4}}{d^{5} h^{14}}} - 60 \, {\left(b^{2} e^{2} f^{3} g - 5 \, b^{2} d e f g^{3}\right)} p^{2}}{d^{2} h^{7}}}\right) + {\left(10 \, a d f g x + 3 \, a d f^{2} + 3 \, {\left(4 \, b e f^{2} p + 5 \, a d g^{2}\right)} x^{2} + {\left(15 \, b d g^{2} p x^{2} + 10 \, b d f g p x + 3 \, b d f^{2} p\right)} \log\left(e x^{2} + d\right) + {\left(15 \, b d g^{2} x^{2} + 10 \, b d f g x + 3 \, b d f^{2}\right)} \log\left(c\right)\right)} \sqrt{h x}\right)}}{15 \, d h^{4} x^{3}}"," ",0,"-2/15*(d*h^4*x^3*sqrt((d^2*h^7*sqrt(-(81*b^4*e^5*f^8 - 3420*b^4*d*e^4*f^6*g^2 + 40150*b^4*d^2*e^3*f^4*g^4 - 85500*b^4*d^3*e^2*f^2*g^6 + 50625*b^4*d^4*e*g^8)*p^4/(d^5*h^14)) + 60*(b^2*e^2*f^3*g - 5*b^2*d*e*f*g^3)*p^2)/(d^2*h^7))*log(32*(81*b^3*e^5*f^8 - 1620*b^3*d*e^4*f^6*g^2 + 2150*b^3*d^2*e^3*f^4*g^4 - 40500*b^3*d^3*e^2*f^2*g^6 + 50625*b^3*d^4*e*g^8)*sqrt(h*x)*p^3 + 32*(3*(d^4*e*f^2 - 5*d^5*g^2)*h^11*sqrt(-(81*b^4*e^5*f^8 - 3420*b^4*d*e^4*f^6*g^2 + 40150*b^4*d^2*e^3*f^4*g^4 - 85500*b^4*d^3*e^2*f^2*g^6 + 50625*b^4*d^4*e*g^8)*p^4/(d^5*h^14)) - 10*(9*b^2*d^2*e^3*f^5*g - 190*b^2*d^3*e^2*f^3*g^3 + 225*b^2*d^4*e*f*g^5)*h^4*p^2)*sqrt((d^2*h^7*sqrt(-(81*b^4*e^5*f^8 - 3420*b^4*d*e^4*f^6*g^2 + 40150*b^4*d^2*e^3*f^4*g^4 - 85500*b^4*d^3*e^2*f^2*g^6 + 50625*b^4*d^4*e*g^8)*p^4/(d^5*h^14)) + 60*(b^2*e^2*f^3*g - 5*b^2*d*e*f*g^3)*p^2)/(d^2*h^7))) - d*h^4*x^3*sqrt((d^2*h^7*sqrt(-(81*b^4*e^5*f^8 - 3420*b^4*d*e^4*f^6*g^2 + 40150*b^4*d^2*e^3*f^4*g^4 - 85500*b^4*d^3*e^2*f^2*g^6 + 50625*b^4*d^4*e*g^8)*p^4/(d^5*h^14)) + 60*(b^2*e^2*f^3*g - 5*b^2*d*e*f*g^3)*p^2)/(d^2*h^7))*log(32*(81*b^3*e^5*f^8 - 1620*b^3*d*e^4*f^6*g^2 + 2150*b^3*d^2*e^3*f^4*g^4 - 40500*b^3*d^3*e^2*f^2*g^6 + 50625*b^3*d^4*e*g^8)*sqrt(h*x)*p^3 - 32*(3*(d^4*e*f^2 - 5*d^5*g^2)*h^11*sqrt(-(81*b^4*e^5*f^8 - 3420*b^4*d*e^4*f^6*g^2 + 40150*b^4*d^2*e^3*f^4*g^4 - 85500*b^4*d^3*e^2*f^2*g^6 + 50625*b^4*d^4*e*g^8)*p^4/(d^5*h^14)) - 10*(9*b^2*d^2*e^3*f^5*g - 190*b^2*d^3*e^2*f^3*g^3 + 225*b^2*d^4*e*f*g^5)*h^4*p^2)*sqrt((d^2*h^7*sqrt(-(81*b^4*e^5*f^8 - 3420*b^4*d*e^4*f^6*g^2 + 40150*b^4*d^2*e^3*f^4*g^4 - 85500*b^4*d^3*e^2*f^2*g^6 + 50625*b^4*d^4*e*g^8)*p^4/(d^5*h^14)) + 60*(b^2*e^2*f^3*g - 5*b^2*d*e*f*g^3)*p^2)/(d^2*h^7))) - d*h^4*x^3*sqrt(-(d^2*h^7*sqrt(-(81*b^4*e^5*f^8 - 3420*b^4*d*e^4*f^6*g^2 + 40150*b^4*d^2*e^3*f^4*g^4 - 85500*b^4*d^3*e^2*f^2*g^6 + 50625*b^4*d^4*e*g^8)*p^4/(d^5*h^14)) - 60*(b^2*e^2*f^3*g - 5*b^2*d*e*f*g^3)*p^2)/(d^2*h^7))*log(32*(81*b^3*e^5*f^8 - 1620*b^3*d*e^4*f^6*g^2 + 2150*b^3*d^2*e^3*f^4*g^4 - 40500*b^3*d^3*e^2*f^2*g^6 + 50625*b^3*d^4*e*g^8)*sqrt(h*x)*p^3 + 32*(3*(d^4*e*f^2 - 5*d^5*g^2)*h^11*sqrt(-(81*b^4*e^5*f^8 - 3420*b^4*d*e^4*f^6*g^2 + 40150*b^4*d^2*e^3*f^4*g^4 - 85500*b^4*d^3*e^2*f^2*g^6 + 50625*b^4*d^4*e*g^8)*p^4/(d^5*h^14)) + 10*(9*b^2*d^2*e^3*f^5*g - 190*b^2*d^3*e^2*f^3*g^3 + 225*b^2*d^4*e*f*g^5)*h^4*p^2)*sqrt(-(d^2*h^7*sqrt(-(81*b^4*e^5*f^8 - 3420*b^4*d*e^4*f^6*g^2 + 40150*b^4*d^2*e^3*f^4*g^4 - 85500*b^4*d^3*e^2*f^2*g^6 + 50625*b^4*d^4*e*g^8)*p^4/(d^5*h^14)) - 60*(b^2*e^2*f^3*g - 5*b^2*d*e*f*g^3)*p^2)/(d^2*h^7))) + d*h^4*x^3*sqrt(-(d^2*h^7*sqrt(-(81*b^4*e^5*f^8 - 3420*b^4*d*e^4*f^6*g^2 + 40150*b^4*d^2*e^3*f^4*g^4 - 85500*b^4*d^3*e^2*f^2*g^6 + 50625*b^4*d^4*e*g^8)*p^4/(d^5*h^14)) - 60*(b^2*e^2*f^3*g - 5*b^2*d*e*f*g^3)*p^2)/(d^2*h^7))*log(32*(81*b^3*e^5*f^8 - 1620*b^3*d*e^4*f^6*g^2 + 2150*b^3*d^2*e^3*f^4*g^4 - 40500*b^3*d^3*e^2*f^2*g^6 + 50625*b^3*d^4*e*g^8)*sqrt(h*x)*p^3 - 32*(3*(d^4*e*f^2 - 5*d^5*g^2)*h^11*sqrt(-(81*b^4*e^5*f^8 - 3420*b^4*d*e^4*f^6*g^2 + 40150*b^4*d^2*e^3*f^4*g^4 - 85500*b^4*d^3*e^2*f^2*g^6 + 50625*b^4*d^4*e*g^8)*p^4/(d^5*h^14)) + 10*(9*b^2*d^2*e^3*f^5*g - 190*b^2*d^3*e^2*f^3*g^3 + 225*b^2*d^4*e*f*g^5)*h^4*p^2)*sqrt(-(d^2*h^7*sqrt(-(81*b^4*e^5*f^8 - 3420*b^4*d*e^4*f^6*g^2 + 40150*b^4*d^2*e^3*f^4*g^4 - 85500*b^4*d^3*e^2*f^2*g^6 + 50625*b^4*d^4*e*g^8)*p^4/(d^5*h^14)) - 60*(b^2*e^2*f^3*g - 5*b^2*d*e*f*g^3)*p^2)/(d^2*h^7))) + (10*a*d*f*g*x + 3*a*d*f^2 + 3*(4*b*e*f^2*p + 5*a*d*g^2)*x^2 + (15*b*d*g^2*p*x^2 + 10*b*d*f*g*p*x + 3*b*d*f^2*p)*log(e*x^2 + d) + (15*b*d*g^2*x^2 + 10*b*d*f*g*x + 3*b*d*f^2)*log(c))*sqrt(h*x))/(d*h^4*x^3)","B",0
615,1,2283,0,1.431961," ","integrate((g*x+f)^2*(a+b*log(c*(e*x^2+d)^p))/(h*x)^(9/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(d h^{5} x^{4} \sqrt{-\frac{d^{3} h^{9} \sqrt{-\frac{{\left(50625 \, b^{4} e^{7} f^{8} - 1266300 \, b^{4} d e^{6} f^{6} g^{2} + 8469846 \, b^{4} d^{2} e^{5} f^{4} g^{4} - 6894300 \, b^{4} d^{3} e^{4} f^{2} g^{6} + 1500625 \, b^{4} d^{4} e^{3} g^{8}\right)} p^{4}}{d^{7} h^{18}}} + 420 \, {\left(3 \, b^{2} e^{3} f^{3} g - 7 \, b^{2} d e^{2} f g^{3}\right)} p^{2}}{d^{3} h^{9}}} \log\left(16 \, {\left(50625 \, b^{3} e^{6} f^{8} - 472500 \, b^{3} d e^{5} f^{6} g^{2} - 1457946 \, b^{3} d^{2} e^{4} f^{4} g^{4} - 2572500 \, b^{3} d^{3} e^{3} f^{2} g^{6} + 1500625 \, b^{3} d^{4} e^{2} g^{8}\right)} \sqrt{h x} p^{3} + 16 \, {\left(42 \, d^{6} f g h^{14} \sqrt{-\frac{{\left(50625 \, b^{4} e^{7} f^{8} - 1266300 \, b^{4} d e^{6} f^{6} g^{2} + 8469846 \, b^{4} d^{2} e^{5} f^{4} g^{4} - 6894300 \, b^{4} d^{3} e^{4} f^{2} g^{6} + 1500625 \, b^{4} d^{4} e^{3} g^{8}\right)} p^{4}}{d^{7} h^{18}}} + 5 \, {\left(675 \, b^{2} d^{2} e^{4} f^{6} - 10017 \, b^{2} d^{3} e^{3} f^{4} g^{2} + 23373 \, b^{2} d^{4} e^{2} f^{2} g^{4} - 8575 \, b^{2} d^{5} e g^{6}\right)} h^{5} p^{2}\right)} \sqrt{-\frac{d^{3} h^{9} \sqrt{-\frac{{\left(50625 \, b^{4} e^{7} f^{8} - 1266300 \, b^{4} d e^{6} f^{6} g^{2} + 8469846 \, b^{4} d^{2} e^{5} f^{4} g^{4} - 6894300 \, b^{4} d^{3} e^{4} f^{2} g^{6} + 1500625 \, b^{4} d^{4} e^{3} g^{8}\right)} p^{4}}{d^{7} h^{18}}} + 420 \, {\left(3 \, b^{2} e^{3} f^{3} g - 7 \, b^{2} d e^{2} f g^{3}\right)} p^{2}}{d^{3} h^{9}}}\right) - d h^{5} x^{4} \sqrt{-\frac{d^{3} h^{9} \sqrt{-\frac{{\left(50625 \, b^{4} e^{7} f^{8} - 1266300 \, b^{4} d e^{6} f^{6} g^{2} + 8469846 \, b^{4} d^{2} e^{5} f^{4} g^{4} - 6894300 \, b^{4} d^{3} e^{4} f^{2} g^{6} + 1500625 \, b^{4} d^{4} e^{3} g^{8}\right)} p^{4}}{d^{7} h^{18}}} + 420 \, {\left(3 \, b^{2} e^{3} f^{3} g - 7 \, b^{2} d e^{2} f g^{3}\right)} p^{2}}{d^{3} h^{9}}} \log\left(16 \, {\left(50625 \, b^{3} e^{6} f^{8} - 472500 \, b^{3} d e^{5} f^{6} g^{2} - 1457946 \, b^{3} d^{2} e^{4} f^{4} g^{4} - 2572500 \, b^{3} d^{3} e^{3} f^{2} g^{6} + 1500625 \, b^{3} d^{4} e^{2} g^{8}\right)} \sqrt{h x} p^{3} - 16 \, {\left(42 \, d^{6} f g h^{14} \sqrt{-\frac{{\left(50625 \, b^{4} e^{7} f^{8} - 1266300 \, b^{4} d e^{6} f^{6} g^{2} + 8469846 \, b^{4} d^{2} e^{5} f^{4} g^{4} - 6894300 \, b^{4} d^{3} e^{4} f^{2} g^{6} + 1500625 \, b^{4} d^{4} e^{3} g^{8}\right)} p^{4}}{d^{7} h^{18}}} + 5 \, {\left(675 \, b^{2} d^{2} e^{4} f^{6} - 10017 \, b^{2} d^{3} e^{3} f^{4} g^{2} + 23373 \, b^{2} d^{4} e^{2} f^{2} g^{4} - 8575 \, b^{2} d^{5} e g^{6}\right)} h^{5} p^{2}\right)} \sqrt{-\frac{d^{3} h^{9} \sqrt{-\frac{{\left(50625 \, b^{4} e^{7} f^{8} - 1266300 \, b^{4} d e^{6} f^{6} g^{2} + 8469846 \, b^{4} d^{2} e^{5} f^{4} g^{4} - 6894300 \, b^{4} d^{3} e^{4} f^{2} g^{6} + 1500625 \, b^{4} d^{4} e^{3} g^{8}\right)} p^{4}}{d^{7} h^{18}}} + 420 \, {\left(3 \, b^{2} e^{3} f^{3} g - 7 \, b^{2} d e^{2} f g^{3}\right)} p^{2}}{d^{3} h^{9}}}\right) - d h^{5} x^{4} \sqrt{\frac{d^{3} h^{9} \sqrt{-\frac{{\left(50625 \, b^{4} e^{7} f^{8} - 1266300 \, b^{4} d e^{6} f^{6} g^{2} + 8469846 \, b^{4} d^{2} e^{5} f^{4} g^{4} - 6894300 \, b^{4} d^{3} e^{4} f^{2} g^{6} + 1500625 \, b^{4} d^{4} e^{3} g^{8}\right)} p^{4}}{d^{7} h^{18}}} - 420 \, {\left(3 \, b^{2} e^{3} f^{3} g - 7 \, b^{2} d e^{2} f g^{3}\right)} p^{2}}{d^{3} h^{9}}} \log\left(16 \, {\left(50625 \, b^{3} e^{6} f^{8} - 472500 \, b^{3} d e^{5} f^{6} g^{2} - 1457946 \, b^{3} d^{2} e^{4} f^{4} g^{4} - 2572500 \, b^{3} d^{3} e^{3} f^{2} g^{6} + 1500625 \, b^{3} d^{4} e^{2} g^{8}\right)} \sqrt{h x} p^{3} + 16 \, {\left(42 \, d^{6} f g h^{14} \sqrt{-\frac{{\left(50625 \, b^{4} e^{7} f^{8} - 1266300 \, b^{4} d e^{6} f^{6} g^{2} + 8469846 \, b^{4} d^{2} e^{5} f^{4} g^{4} - 6894300 \, b^{4} d^{3} e^{4} f^{2} g^{6} + 1500625 \, b^{4} d^{4} e^{3} g^{8}\right)} p^{4}}{d^{7} h^{18}}} - 5 \, {\left(675 \, b^{2} d^{2} e^{4} f^{6} - 10017 \, b^{2} d^{3} e^{3} f^{4} g^{2} + 23373 \, b^{2} d^{4} e^{2} f^{2} g^{4} - 8575 \, b^{2} d^{5} e g^{6}\right)} h^{5} p^{2}\right)} \sqrt{\frac{d^{3} h^{9} \sqrt{-\frac{{\left(50625 \, b^{4} e^{7} f^{8} - 1266300 \, b^{4} d e^{6} f^{6} g^{2} + 8469846 \, b^{4} d^{2} e^{5} f^{4} g^{4} - 6894300 \, b^{4} d^{3} e^{4} f^{2} g^{6} + 1500625 \, b^{4} d^{4} e^{3} g^{8}\right)} p^{4}}{d^{7} h^{18}}} - 420 \, {\left(3 \, b^{2} e^{3} f^{3} g - 7 \, b^{2} d e^{2} f g^{3}\right)} p^{2}}{d^{3} h^{9}}}\right) + d h^{5} x^{4} \sqrt{\frac{d^{3} h^{9} \sqrt{-\frac{{\left(50625 \, b^{4} e^{7} f^{8} - 1266300 \, b^{4} d e^{6} f^{6} g^{2} + 8469846 \, b^{4} d^{2} e^{5} f^{4} g^{4} - 6894300 \, b^{4} d^{3} e^{4} f^{2} g^{6} + 1500625 \, b^{4} d^{4} e^{3} g^{8}\right)} p^{4}}{d^{7} h^{18}}} - 420 \, {\left(3 \, b^{2} e^{3} f^{3} g - 7 \, b^{2} d e^{2} f g^{3}\right)} p^{2}}{d^{3} h^{9}}} \log\left(16 \, {\left(50625 \, b^{3} e^{6} f^{8} - 472500 \, b^{3} d e^{5} f^{6} g^{2} - 1457946 \, b^{3} d^{2} e^{4} f^{4} g^{4} - 2572500 \, b^{3} d^{3} e^{3} f^{2} g^{6} + 1500625 \, b^{3} d^{4} e^{2} g^{8}\right)} \sqrt{h x} p^{3} - 16 \, {\left(42 \, d^{6} f g h^{14} \sqrt{-\frac{{\left(50625 \, b^{4} e^{7} f^{8} - 1266300 \, b^{4} d e^{6} f^{6} g^{2} + 8469846 \, b^{4} d^{2} e^{5} f^{4} g^{4} - 6894300 \, b^{4} d^{3} e^{4} f^{2} g^{6} + 1500625 \, b^{4} d^{4} e^{3} g^{8}\right)} p^{4}}{d^{7} h^{18}}} - 5 \, {\left(675 \, b^{2} d^{2} e^{4} f^{6} - 10017 \, b^{2} d^{3} e^{3} f^{4} g^{2} + 23373 \, b^{2} d^{4} e^{2} f^{2} g^{4} - 8575 \, b^{2} d^{5} e g^{6}\right)} h^{5} p^{2}\right)} \sqrt{\frac{d^{3} h^{9} \sqrt{-\frac{{\left(50625 \, b^{4} e^{7} f^{8} - 1266300 \, b^{4} d e^{6} f^{6} g^{2} + 8469846 \, b^{4} d^{2} e^{5} f^{4} g^{4} - 6894300 \, b^{4} d^{3} e^{4} f^{2} g^{6} + 1500625 \, b^{4} d^{4} e^{3} g^{8}\right)} p^{4}}{d^{7} h^{18}}} - 420 \, {\left(3 \, b^{2} e^{3} f^{3} g - 7 \, b^{2} d e^{2} f g^{3}\right)} p^{2}}{d^{3} h^{9}}}\right) + {\left(168 \, b e f g p x^{3} + 42 \, a d f g x + 15 \, a d f^{2} + 5 \, {\left(4 \, b e f^{2} p + 7 \, a d g^{2}\right)} x^{2} + {\left(35 \, b d g^{2} p x^{2} + 42 \, b d f g p x + 15 \, b d f^{2} p\right)} \log\left(e x^{2} + d\right) + {\left(35 \, b d g^{2} x^{2} + 42 \, b d f g x + 15 \, b d f^{2}\right)} \log\left(c\right)\right)} \sqrt{h x}\right)}}{105 \, d h^{5} x^{4}}"," ",0,"-2/105*(d*h^5*x^4*sqrt(-(d^3*h^9*sqrt(-(50625*b^4*e^7*f^8 - 1266300*b^4*d*e^6*f^6*g^2 + 8469846*b^4*d^2*e^5*f^4*g^4 - 6894300*b^4*d^3*e^4*f^2*g^6 + 1500625*b^4*d^4*e^3*g^8)*p^4/(d^7*h^18)) + 420*(3*b^2*e^3*f^3*g - 7*b^2*d*e^2*f*g^3)*p^2)/(d^3*h^9))*log(16*(50625*b^3*e^6*f^8 - 472500*b^3*d*e^5*f^6*g^2 - 1457946*b^3*d^2*e^4*f^4*g^4 - 2572500*b^3*d^3*e^3*f^2*g^6 + 1500625*b^3*d^4*e^2*g^8)*sqrt(h*x)*p^3 + 16*(42*d^6*f*g*h^14*sqrt(-(50625*b^4*e^7*f^8 - 1266300*b^4*d*e^6*f^6*g^2 + 8469846*b^4*d^2*e^5*f^4*g^4 - 6894300*b^4*d^3*e^4*f^2*g^6 + 1500625*b^4*d^4*e^3*g^8)*p^4/(d^7*h^18)) + 5*(675*b^2*d^2*e^4*f^6 - 10017*b^2*d^3*e^3*f^4*g^2 + 23373*b^2*d^4*e^2*f^2*g^4 - 8575*b^2*d^5*e*g^6)*h^5*p^2)*sqrt(-(d^3*h^9*sqrt(-(50625*b^4*e^7*f^8 - 1266300*b^4*d*e^6*f^6*g^2 + 8469846*b^4*d^2*e^5*f^4*g^4 - 6894300*b^4*d^3*e^4*f^2*g^6 + 1500625*b^4*d^4*e^3*g^8)*p^4/(d^7*h^18)) + 420*(3*b^2*e^3*f^3*g - 7*b^2*d*e^2*f*g^3)*p^2)/(d^3*h^9))) - d*h^5*x^4*sqrt(-(d^3*h^9*sqrt(-(50625*b^4*e^7*f^8 - 1266300*b^4*d*e^6*f^6*g^2 + 8469846*b^4*d^2*e^5*f^4*g^4 - 6894300*b^4*d^3*e^4*f^2*g^6 + 1500625*b^4*d^4*e^3*g^8)*p^4/(d^7*h^18)) + 420*(3*b^2*e^3*f^3*g - 7*b^2*d*e^2*f*g^3)*p^2)/(d^3*h^9))*log(16*(50625*b^3*e^6*f^8 - 472500*b^3*d*e^5*f^6*g^2 - 1457946*b^3*d^2*e^4*f^4*g^4 - 2572500*b^3*d^3*e^3*f^2*g^6 + 1500625*b^3*d^4*e^2*g^8)*sqrt(h*x)*p^3 - 16*(42*d^6*f*g*h^14*sqrt(-(50625*b^4*e^7*f^8 - 1266300*b^4*d*e^6*f^6*g^2 + 8469846*b^4*d^2*e^5*f^4*g^4 - 6894300*b^4*d^3*e^4*f^2*g^6 + 1500625*b^4*d^4*e^3*g^8)*p^4/(d^7*h^18)) + 5*(675*b^2*d^2*e^4*f^6 - 10017*b^2*d^3*e^3*f^4*g^2 + 23373*b^2*d^4*e^2*f^2*g^4 - 8575*b^2*d^5*e*g^6)*h^5*p^2)*sqrt(-(d^3*h^9*sqrt(-(50625*b^4*e^7*f^8 - 1266300*b^4*d*e^6*f^6*g^2 + 8469846*b^4*d^2*e^5*f^4*g^4 - 6894300*b^4*d^3*e^4*f^2*g^6 + 1500625*b^4*d^4*e^3*g^8)*p^4/(d^7*h^18)) + 420*(3*b^2*e^3*f^3*g - 7*b^2*d*e^2*f*g^3)*p^2)/(d^3*h^9))) - d*h^5*x^4*sqrt((d^3*h^9*sqrt(-(50625*b^4*e^7*f^8 - 1266300*b^4*d*e^6*f^6*g^2 + 8469846*b^4*d^2*e^5*f^4*g^4 - 6894300*b^4*d^3*e^4*f^2*g^6 + 1500625*b^4*d^4*e^3*g^8)*p^4/(d^7*h^18)) - 420*(3*b^2*e^3*f^3*g - 7*b^2*d*e^2*f*g^3)*p^2)/(d^3*h^9))*log(16*(50625*b^3*e^6*f^8 - 472500*b^3*d*e^5*f^6*g^2 - 1457946*b^3*d^2*e^4*f^4*g^4 - 2572500*b^3*d^3*e^3*f^2*g^6 + 1500625*b^3*d^4*e^2*g^8)*sqrt(h*x)*p^3 + 16*(42*d^6*f*g*h^14*sqrt(-(50625*b^4*e^7*f^8 - 1266300*b^4*d*e^6*f^6*g^2 + 8469846*b^4*d^2*e^5*f^4*g^4 - 6894300*b^4*d^3*e^4*f^2*g^6 + 1500625*b^4*d^4*e^3*g^8)*p^4/(d^7*h^18)) - 5*(675*b^2*d^2*e^4*f^6 - 10017*b^2*d^3*e^3*f^4*g^2 + 23373*b^2*d^4*e^2*f^2*g^4 - 8575*b^2*d^5*e*g^6)*h^5*p^2)*sqrt((d^3*h^9*sqrt(-(50625*b^4*e^7*f^8 - 1266300*b^4*d*e^6*f^6*g^2 + 8469846*b^4*d^2*e^5*f^4*g^4 - 6894300*b^4*d^3*e^4*f^2*g^6 + 1500625*b^4*d^4*e^3*g^8)*p^4/(d^7*h^18)) - 420*(3*b^2*e^3*f^3*g - 7*b^2*d*e^2*f*g^3)*p^2)/(d^3*h^9))) + d*h^5*x^4*sqrt((d^3*h^9*sqrt(-(50625*b^4*e^7*f^8 - 1266300*b^4*d*e^6*f^6*g^2 + 8469846*b^4*d^2*e^5*f^4*g^4 - 6894300*b^4*d^3*e^4*f^2*g^6 + 1500625*b^4*d^4*e^3*g^8)*p^4/(d^7*h^18)) - 420*(3*b^2*e^3*f^3*g - 7*b^2*d*e^2*f*g^3)*p^2)/(d^3*h^9))*log(16*(50625*b^3*e^6*f^8 - 472500*b^3*d*e^5*f^6*g^2 - 1457946*b^3*d^2*e^4*f^4*g^4 - 2572500*b^3*d^3*e^3*f^2*g^6 + 1500625*b^3*d^4*e^2*g^8)*sqrt(h*x)*p^3 - 16*(42*d^6*f*g*h^14*sqrt(-(50625*b^4*e^7*f^8 - 1266300*b^4*d*e^6*f^6*g^2 + 8469846*b^4*d^2*e^5*f^4*g^4 - 6894300*b^4*d^3*e^4*f^2*g^6 + 1500625*b^4*d^4*e^3*g^8)*p^4/(d^7*h^18)) - 5*(675*b^2*d^2*e^4*f^6 - 10017*b^2*d^3*e^3*f^4*g^2 + 23373*b^2*d^4*e^2*f^2*g^4 - 8575*b^2*d^5*e*g^6)*h^5*p^2)*sqrt((d^3*h^9*sqrt(-(50625*b^4*e^7*f^8 - 1266300*b^4*d*e^6*f^6*g^2 + 8469846*b^4*d^2*e^5*f^4*g^4 - 6894300*b^4*d^3*e^4*f^2*g^6 + 1500625*b^4*d^4*e^3*g^8)*p^4/(d^7*h^18)) - 420*(3*b^2*e^3*f^3*g - 7*b^2*d*e^2*f*g^3)*p^2)/(d^3*h^9))) + (168*b*e*f*g*p*x^3 + 42*a*d*f*g*x + 15*a*d*f^2 + 5*(4*b*e*f^2*p + 7*a*d*g^2)*x^2 + (35*b*d*g^2*p*x^2 + 42*b*d*f*g*p*x + 15*b*d*f^2*p)*log(e*x^2 + d) + (35*b*d*g^2*x^2 + 42*b*d*f*g*x + 15*b*d*f^2)*log(c))*sqrt(h*x))/(d*h^5*x^4)","B",0
616,0,0,0,1.290070," ","integrate((h*x)^(1/2)*(a+b*log(c*(e*x^2+d)^p))/(g*x+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{h x} b \log\left({\left(e x^{2} + d\right)}^{p} c\right) + \sqrt{h x} a}{g x + f}, x\right)"," ",0,"integral((sqrt(h*x)*b*log((e*x^2 + d)^p*c) + sqrt(h*x)*a)/(g*x + f), x)","F",0
617,0,0,0,0.962635," ","integrate((a+b*log(c*(e*x^2+d)^p))/(h*x)^(1/2)/(g*x+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{h x} b \log\left({\left(e x^{2} + d\right)}^{p} c\right) + \sqrt{h x} a}{g h x^{2} + f h x}, x\right)"," ",0,"integral((sqrt(h*x)*b*log((e*x^2 + d)^p*c) + sqrt(h*x)*a)/(g*h*x^2 + f*h*x), x)","F",0
618,0,0,0,1.086158," ","integrate((a+b*log(c*(e*x^2+d)^p))/(h*x)^(3/2)/(g*x+f),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{h x} b \log\left({\left(e x^{2} + d\right)}^{p} c\right) + \sqrt{h x} a}{g h^{2} x^{3} + f h^{2} x^{2}}, x\right)"," ",0,"integral((sqrt(h*x)*b*log((e*x^2 + d)^p*c) + sqrt(h*x)*a)/(g*h^2*x^3 + f*h^2*x^2), x)","F",0
619,1,35,0,1.234273," ","integrate(log(f*x^p)*log(1+e*x^m)/x,x, algorithm=""fricas"")","-\frac{{\left(m p \log\left(x\right) + m \log\left(f\right)\right)} {\rm Li}_2\left(-e x^{m}\right) - p {\rm polylog}\left(3, -e x^{m}\right)}{m^{2}}"," ",0,"-((m*p*log(x) + m*log(f))*dilog(-e*x^m) - p*polylog(3, -e*x^m))/m^2","C",0
620,1,105,0,0.741510," ","integrate(x^(-1+m)*log(f*x^p)^2/(d+e*x^m),x, algorithm=""fricas"")","\frac{m^{2} \log\left(e x^{m} + d\right) \log\left(f\right)^{2} - 2 \, p^{2} {\rm polylog}\left(3, -\frac{e x^{m}}{d}\right) + 2 \, {\left(m p^{2} \log\left(x\right) + m p \log\left(f\right)\right)} {\rm Li}_2\left(-\frac{e x^{m} + d}{d} + 1\right) + {\left(m^{2} p^{2} \log\left(x\right)^{2} + 2 \, m^{2} p \log\left(f\right) \log\left(x\right)\right)} \log\left(\frac{e x^{m} + d}{d}\right)}{e m^{3}}"," ",0,"(m^2*log(e*x^m + d)*log(f)^2 - 2*p^2*polylog(3, -e*x^m/d) + 2*(m*p^2*log(x) + m*p*log(f))*dilog(-(e*x^m + d)/d + 1) + (m^2*p^2*log(x)^2 + 2*m^2*p*log(f)*log(x))*log((e*x^m + d)/d))/(e*m^3)","C",0
621,1,417,0,1.102756," ","integrate(log(f*x^p)^3*(a+b*log(c*(d+e*x^m)^n))/x,x, algorithm=""fricas"")","\frac{24 \, b n p^{3} {\rm polylog}\left(5, -\frac{e x^{m}}{d}\right) + 4 \, {\left(b m^{4} \log\left(c\right) + a m^{4}\right)} \log\left(f\right)^{3} \log\left(x\right) + 6 \, {\left(b m^{4} p \log\left(c\right) + a m^{4} p\right)} \log\left(f\right)^{2} \log\left(x\right)^{2} + 4 \, {\left(b m^{4} p^{2} \log\left(c\right) + a m^{4} p^{2}\right)} \log\left(f\right) \log\left(x\right)^{3} + {\left(b m^{4} p^{3} \log\left(c\right) + a m^{4} p^{3}\right)} \log\left(x\right)^{4} - 4 \, {\left(b m^{3} n p^{3} \log\left(x\right)^{3} + 3 \, b m^{3} n p^{2} \log\left(f\right) \log\left(x\right)^{2} + 3 \, b m^{3} n p \log\left(f\right)^{2} \log\left(x\right) + b m^{3} n \log\left(f\right)^{3}\right)} {\rm Li}_2\left(-\frac{e x^{m} + d}{d} + 1\right) + {\left(b m^{4} n p^{3} \log\left(x\right)^{4} + 4 \, b m^{4} n p^{2} \log\left(f\right) \log\left(x\right)^{3} + 6 \, b m^{4} n p \log\left(f\right)^{2} \log\left(x\right)^{2} + 4 \, b m^{4} n \log\left(f\right)^{3} \log\left(x\right)\right)} \log\left(e x^{m} + d\right) - {\left(b m^{4} n p^{3} \log\left(x\right)^{4} + 4 \, b m^{4} n p^{2} \log\left(f\right) \log\left(x\right)^{3} + 6 \, b m^{4} n p \log\left(f\right)^{2} \log\left(x\right)^{2} + 4 \, b m^{4} n \log\left(f\right)^{3} \log\left(x\right)\right)} \log\left(\frac{e x^{m} + d}{d}\right) - 24 \, {\left(b m n p^{3} \log\left(x\right) + b m n p^{2} \log\left(f\right)\right)} {\rm polylog}\left(4, -\frac{e x^{m}}{d}\right) + 12 \, {\left(b m^{2} n p^{3} \log\left(x\right)^{2} + 2 \, b m^{2} n p^{2} \log\left(f\right) \log\left(x\right) + b m^{2} n p \log\left(f\right)^{2}\right)} {\rm polylog}\left(3, -\frac{e x^{m}}{d}\right)}{4 \, m^{4}}"," ",0,"1/4*(24*b*n*p^3*polylog(5, -e*x^m/d) + 4*(b*m^4*log(c) + a*m^4)*log(f)^3*log(x) + 6*(b*m^4*p*log(c) + a*m^4*p)*log(f)^2*log(x)^2 + 4*(b*m^4*p^2*log(c) + a*m^4*p^2)*log(f)*log(x)^3 + (b*m^4*p^3*log(c) + a*m^4*p^3)*log(x)^4 - 4*(b*m^3*n*p^3*log(x)^3 + 3*b*m^3*n*p^2*log(f)*log(x)^2 + 3*b*m^3*n*p*log(f)^2*log(x) + b*m^3*n*log(f)^3)*dilog(-(e*x^m + d)/d + 1) + (b*m^4*n*p^3*log(x)^4 + 4*b*m^4*n*p^2*log(f)*log(x)^3 + 6*b*m^4*n*p*log(f)^2*log(x)^2 + 4*b*m^4*n*log(f)^3*log(x))*log(e*x^m + d) - (b*m^4*n*p^3*log(x)^4 + 4*b*m^4*n*p^2*log(f)*log(x)^3 + 6*b*m^4*n*p*log(f)^2*log(x)^2 + 4*b*m^4*n*log(f)^3*log(x))*log((e*x^m + d)/d) - 24*(b*m*n*p^3*log(x) + b*m*n*p^2*log(f))*polylog(4, -e*x^m/d) + 12*(b*m^2*n*p^3*log(x)^2 + 2*b*m^2*n*p^2*log(f)*log(x) + b*m^2*n*p*log(f)^2)*polylog(3, -e*x^m/d))/m^4","C",0
622,1,281,0,1.383470," ","integrate(log(f*x^p)^2*(a+b*log(c*(d+e*x^m)^n))/x,x, algorithm=""fricas"")","-\frac{6 \, b n p^{2} {\rm polylog}\left(4, -\frac{e x^{m}}{d}\right) - 3 \, {\left(b m^{3} \log\left(c\right) + a m^{3}\right)} \log\left(f\right)^{2} \log\left(x\right) - 3 \, {\left(b m^{3} p \log\left(c\right) + a m^{3} p\right)} \log\left(f\right) \log\left(x\right)^{2} - {\left(b m^{3} p^{2} \log\left(c\right) + a m^{3} p^{2}\right)} \log\left(x\right)^{3} + 3 \, {\left(b m^{2} n p^{2} \log\left(x\right)^{2} + 2 \, b m^{2} n p \log\left(f\right) \log\left(x\right) + b m^{2} n \log\left(f\right)^{2}\right)} {\rm Li}_2\left(-\frac{e x^{m} + d}{d} + 1\right) - {\left(b m^{3} n p^{2} \log\left(x\right)^{3} + 3 \, b m^{3} n p \log\left(f\right) \log\left(x\right)^{2} + 3 \, b m^{3} n \log\left(f\right)^{2} \log\left(x\right)\right)} \log\left(e x^{m} + d\right) + {\left(b m^{3} n p^{2} \log\left(x\right)^{3} + 3 \, b m^{3} n p \log\left(f\right) \log\left(x\right)^{2} + 3 \, b m^{3} n \log\left(f\right)^{2} \log\left(x\right)\right)} \log\left(\frac{e x^{m} + d}{d}\right) - 6 \, {\left(b m n p^{2} \log\left(x\right) + b m n p \log\left(f\right)\right)} {\rm polylog}\left(3, -\frac{e x^{m}}{d}\right)}{3 \, m^{3}}"," ",0,"-1/3*(6*b*n*p^2*polylog(4, -e*x^m/d) - 3*(b*m^3*log(c) + a*m^3)*log(f)^2*log(x) - 3*(b*m^3*p*log(c) + a*m^3*p)*log(f)*log(x)^2 - (b*m^3*p^2*log(c) + a*m^3*p^2)*log(x)^3 + 3*(b*m^2*n*p^2*log(x)^2 + 2*b*m^2*n*p*log(f)*log(x) + b*m^2*n*log(f)^2)*dilog(-(e*x^m + d)/d + 1) - (b*m^3*n*p^2*log(x)^3 + 3*b*m^3*n*p*log(f)*log(x)^2 + 3*b*m^3*n*log(f)^2*log(x))*log(e*x^m + d) + (b*m^3*n*p^2*log(x)^3 + 3*b*m^3*n*p*log(f)*log(x)^2 + 3*b*m^3*n*log(f)^2*log(x))*log((e*x^m + d)/d) - 6*(b*m*n*p^2*log(x) + b*m*n*p*log(f))*polylog(3, -e*x^m/d))/m^3","C",0
623,1,161,0,1.239362," ","integrate(log(f*x^p)*(a+b*log(c*(d+e*x^m)^n))/x,x, algorithm=""fricas"")","\frac{2 \, b n p {\rm polylog}\left(3, -\frac{e x^{m}}{d}\right) + 2 \, {\left(b m^{2} \log\left(c\right) + a m^{2}\right)} \log\left(f\right) \log\left(x\right) + {\left(b m^{2} p \log\left(c\right) + a m^{2} p\right)} \log\left(x\right)^{2} - 2 \, {\left(b m n p \log\left(x\right) + b m n \log\left(f\right)\right)} {\rm Li}_2\left(-\frac{e x^{m} + d}{d} + 1\right) + {\left(b m^{2} n p \log\left(x\right)^{2} + 2 \, b m^{2} n \log\left(f\right) \log\left(x\right)\right)} \log\left(e x^{m} + d\right) - {\left(b m^{2} n p \log\left(x\right)^{2} + 2 \, b m^{2} n \log\left(f\right) \log\left(x\right)\right)} \log\left(\frac{e x^{m} + d}{d}\right)}{2 \, m^{2}}"," ",0,"1/2*(2*b*n*p*polylog(3, -e*x^m/d) + 2*(b*m^2*log(c) + a*m^2)*log(f)*log(x) + (b*m^2*p*log(c) + a*m^2*p)*log(x)^2 - 2*(b*m*n*p*log(x) + b*m*n*log(f))*dilog(-(e*x^m + d)/d + 1) + (b*m^2*n*p*log(x)^2 + 2*b*m^2*n*log(f)*log(x))*log(e*x^m + d) - (b*m^2*n*p*log(x)^2 + 2*b*m^2*n*log(f)*log(x))*log((e*x^m + d)/d))/m^2","C",0
624,1,69,0,0.936066," ","integrate((a+b*log(c*(d+e*x^m)^n))/x,x, algorithm=""fricas"")","\frac{b m n \log\left(e x^{m} + d\right) \log\left(x\right) - b m n \log\left(x\right) \log\left(\frac{e x^{m} + d}{d}\right) - b n {\rm Li}_2\left(-\frac{e x^{m} + d}{d} + 1\right) + {\left(b m \log\left(c\right) + a m\right)} \log\left(x\right)}{m}"," ",0,"(b*m*n*log(e*x^m + d)*log(x) - b*m*n*log(x)*log((e*x^m + d)/d) - b*n*dilog(-(e*x^m + d)/d + 1) + (b*m*log(c) + a*m)*log(x))/m","A",0
625,0,0,0,1.151356," ","integrate((a+b*log(c*(d+e*x^m)^n))/x/log(f*x^p),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \log\left({\left(e x^{m} + d\right)}^{n} c\right) + a}{x \log\left(f x^{p}\right)}, x\right)"," ",0,"integral((b*log((e*x^m + d)^n*c) + a)/(x*log(f*x^p)), x)","F",0
626,0,0,0,0.994905," ","integrate((a+b*log(c*(d+e*x^m)^n))/x/log(f*x^p)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \log\left({\left(e x^{m} + d\right)}^{n} c\right) + a}{x \log\left(f x^{p}\right)^{2}}, x\right)"," ",0,"integral((b*log((e*x^m + d)^n*c) + a)/(x*log(f*x^p)^2), x)","F",0
627,0,0,0,1.366972," ","integrate((a+b*log(c*(d+e*x^m)^n))/x/log(f*x^p)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \log\left({\left(e x^{m} + d\right)}^{n} c\right) + a}{x \log\left(f x^{p}\right)^{3}}, x\right)"," ",0,"integral((b*log((e*x^m + d)^n*c) + a)/(x*log(f*x^p)^3), x)","F",0
628,0,0,0,1.321168," ","integrate(log(c*(d+e*(g*x+f)^p)^q),x, algorithm=""fricas"")","{\rm integral}\left(\log\left({\left({\left(g x + f\right)}^{p} e + d\right)}^{q} c\right), x\right)"," ",0,"integral(log(((g*x + f)^p*e + d)^q*c), x)","F",0
629,1,1357,0,4.016265," ","integrate(log(c*(d+e*(g*x+f)^3)^q),x, algorithm=""fricas"")","\frac{4 \, g q x \log\left(e g^{3} x^{3} + 3 \, e f g^{2} x^{2} + 3 \, e f^{2} g x + e f^{3} + d\right) - 12 \, g q x - 4 \, \sqrt{3} g \sqrt{\frac{{\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{d q^{3}}{2 \, e g^{3}} + \frac{e f^{3} q^{3} + d q^{3}}{2 \, e g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)}^{2} g^{2} + 4 \, {\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{d q^{3}}{2 \, e g^{3}} + \frac{e f^{3} q^{3} + d q^{3}}{2 \, e g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)} f g q + 4 \, f^{2} q^{2}}{g^{2}}} \arctan\left(-\frac{2 \, \sqrt{3} \sqrt{4 \, g^{2} q^{2} x^{2} + 12 \, f g q^{2} x + {\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{d q^{3}}{2 \, e g^{3}} + \frac{e f^{3} q^{3} + d q^{3}}{2 \, e g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)}^{2} g^{2} + 12 \, f^{2} q^{2} + 2 \, {\left(g^{2} q x + 3 \, f g q\right)} {\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{d q^{3}}{2 \, e g^{3}} + \frac{e f^{3} q^{3} + d q^{3}}{2 \, e g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)}} {\left({\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{d q^{3}}{2 \, e g^{3}} + \frac{e f^{3} q^{3} + d q^{3}}{2 \, e g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)} e g^{2} + 2 \, e f g q\right)} \sqrt{\frac{{\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{d q^{3}}{2 \, e g^{3}} + \frac{e f^{3} q^{3} + d q^{3}}{2 \, e g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)}^{2} g^{2} + 4 \, {\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{d q^{3}}{2 \, e g^{3}} + \frac{e f^{3} q^{3} + d q^{3}}{2 \, e g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)} f g q + 4 \, f^{2} q^{2}}{g^{2}}} - \sqrt{3} {\left(8 \, e f g^{2} q^{2} x + {\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{d q^{3}}{2 \, e g^{3}} + \frac{e f^{3} q^{3} + d q^{3}}{2 \, e g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)}^{2} e g^{3} + 12 \, e f^{2} g q^{2} + 4 \, {\left(e g^{3} q x + 2 \, e f g^{2} q\right)} {\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{d q^{3}}{2 \, e g^{3}} + \frac{e f^{3} q^{3} + d q^{3}}{2 \, e g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)}\right)} \sqrt{\frac{{\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{d q^{3}}{2 \, e g^{3}} + \frac{e f^{3} q^{3} + d q^{3}}{2 \, e g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)}^{2} g^{2} + 4 \, {\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{d q^{3}}{2 \, e g^{3}} + \frac{e f^{3} q^{3} + d q^{3}}{2 \, e g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)} f g q + 4 \, f^{2} q^{2}}{g^{2}}}}{24 \, d q^{3}}\right) - 2 \, {\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{d q^{3}}{2 \, e g^{3}} + \frac{e f^{3} q^{3} + d q^{3}}{2 \, e g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)} g \log\left(q x - \frac{1}{2} \, {\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{d q^{3}}{2 \, e g^{3}} + \frac{e f^{3} q^{3} + d q^{3}}{2 \, e g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{f q}{g}\right) + 4 \, g x \log\left(c\right) + {\left({\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{d q^{3}}{2 \, e g^{3}} + \frac{e f^{3} q^{3} + d q^{3}}{2 \, e g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)} g + 6 \, f q\right)} \log\left(4 \, g^{2} q^{2} x^{2} + 12 \, f g q^{2} x + {\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{d q^{3}}{2 \, e g^{3}} + \frac{e f^{3} q^{3} + d q^{3}}{2 \, e g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)}^{2} g^{2} + 12 \, f^{2} q^{2} + 2 \, {\left(g^{2} q x + 3 \, f g q\right)} {\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{d q^{3}}{2 \, e g^{3}} + \frac{e f^{3} q^{3} + d q^{3}}{2 \, e g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)}\right)}{4 \, g}"," ",0,"1/4*(4*g*q*x*log(e*g^3*x^3 + 3*e*f*g^2*x^2 + 3*e*f^2*g*x + e*f^3 + d) - 12*g*q*x - 4*sqrt(3)*g*sqrt((((-1/2*f^3*q^3/g^3 + 1/2*d*q^3/(e*g^3) + 1/2*(e*f^3*q^3 + d*q^3)/(e*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g)^2*g^2 + 4*((-1/2*f^3*q^3/g^3 + 1/2*d*q^3/(e*g^3) + 1/2*(e*f^3*q^3 + d*q^3)/(e*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g)*f*g*q + 4*f^2*q^2)/g^2)*arctan(-1/24*(2*sqrt(3)*sqrt(4*g^2*q^2*x^2 + 12*f*g*q^2*x + ((-1/2*f^3*q^3/g^3 + 1/2*d*q^3/(e*g^3) + 1/2*(e*f^3*q^3 + d*q^3)/(e*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g)^2*g^2 + 12*f^2*q^2 + 2*(g^2*q*x + 3*f*g*q)*((-1/2*f^3*q^3/g^3 + 1/2*d*q^3/(e*g^3) + 1/2*(e*f^3*q^3 + d*q^3)/(e*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g))*(((-1/2*f^3*q^3/g^3 + 1/2*d*q^3/(e*g^3) + 1/2*(e*f^3*q^3 + d*q^3)/(e*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g)*e*g^2 + 2*e*f*g*q)*sqrt((((-1/2*f^3*q^3/g^3 + 1/2*d*q^3/(e*g^3) + 1/2*(e*f^3*q^3 + d*q^3)/(e*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g)^2*g^2 + 4*((-1/2*f^3*q^3/g^3 + 1/2*d*q^3/(e*g^3) + 1/2*(e*f^3*q^3 + d*q^3)/(e*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g)*f*g*q + 4*f^2*q^2)/g^2) - sqrt(3)*(8*e*f*g^2*q^2*x + ((-1/2*f^3*q^3/g^3 + 1/2*d*q^3/(e*g^3) + 1/2*(e*f^3*q^3 + d*q^3)/(e*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g)^2*e*g^3 + 12*e*f^2*g*q^2 + 4*(e*g^3*q*x + 2*e*f*g^2*q)*((-1/2*f^3*q^3/g^3 + 1/2*d*q^3/(e*g^3) + 1/2*(e*f^3*q^3 + d*q^3)/(e*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g))*sqrt((((-1/2*f^3*q^3/g^3 + 1/2*d*q^3/(e*g^3) + 1/2*(e*f^3*q^3 + d*q^3)/(e*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g)^2*g^2 + 4*((-1/2*f^3*q^3/g^3 + 1/2*d*q^3/(e*g^3) + 1/2*(e*f^3*q^3 + d*q^3)/(e*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g)*f*g*q + 4*f^2*q^2)/g^2))/(d*q^3)) - 2*((-1/2*f^3*q^3/g^3 + 1/2*d*q^3/(e*g^3) + 1/2*(e*f^3*q^3 + d*q^3)/(e*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g)*g*log(q*x - 1/2*(-1/2*f^3*q^3/g^3 + 1/2*d*q^3/(e*g^3) + 1/2*(e*f^3*q^3 + d*q^3)/(e*g^3))^(1/3)*(I*sqrt(3) + 1) + f*q/g) + 4*g*x*log(c) + (((-1/2*f^3*q^3/g^3 + 1/2*d*q^3/(e*g^3) + 1/2*(e*f^3*q^3 + d*q^3)/(e*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g)*g + 6*f*q)*log(4*g^2*q^2*x^2 + 12*f*g*q^2*x + ((-1/2*f^3*q^3/g^3 + 1/2*d*q^3/(e*g^3) + 1/2*(e*f^3*q^3 + d*q^3)/(e*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g)^2*g^2 + 12*f^2*q^2 + 2*(g^2*q*x + 3*f*g*q)*((-1/2*f^3*q^3/g^3 + 1/2*d*q^3/(e*g^3) + 1/2*(e*f^3*q^3 + d*q^3)/(e*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g)))/g","C",0
630,1,206,0,1.335855," ","integrate(log(c*(d+e*(g*x+f)^2)^q),x, algorithm=""fricas"")","\left[-\frac{2 \, g q x - g x \log\left(c\right) - q \sqrt{-\frac{d}{e}} \log\left(\frac{e g^{2} x^{2} + 2 \, e f g x + e f^{2} + 2 \, {\left(e g x + e f\right)} \sqrt{-\frac{d}{e}} - d}{e g^{2} x^{2} + 2 \, e f g x + e f^{2} + d}\right) - {\left(g q x + f q\right)} \log\left(e g^{2} x^{2} + 2 \, e f g x + e f^{2} + d\right)}{g}, -\frac{2 \, g q x - g x \log\left(c\right) - 2 \, q \sqrt{\frac{d}{e}} \arctan\left(\frac{{\left(e g x + e f\right)} \sqrt{\frac{d}{e}}}{d}\right) - {\left(g q x + f q\right)} \log\left(e g^{2} x^{2} + 2 \, e f g x + e f^{2} + d\right)}{g}\right]"," ",0,"[-(2*g*q*x - g*x*log(c) - q*sqrt(-d/e)*log((e*g^2*x^2 + 2*e*f*g*x + e*f^2 + 2*(e*g*x + e*f)*sqrt(-d/e) - d)/(e*g^2*x^2 + 2*e*f*g*x + e*f^2 + d)) - (g*q*x + f*q)*log(e*g^2*x^2 + 2*e*f*g*x + e*f^2 + d))/g, -(2*g*q*x - g*x*log(c) - 2*q*sqrt(d/e)*arctan((e*g*x + e*f)*sqrt(d/e)/d) - (g*q*x + f*q)*log(e*g^2*x^2 + 2*e*f*g*x + e*f^2 + d))/g]","A",0
631,1,46,0,1.265929," ","integrate(log(c*(d+e*(g*x+f))^q),x, algorithm=""fricas"")","-\frac{e g q x - e g x \log\left(c\right) - {\left(e g q x + {\left(e f + d\right)} q\right)} \log\left(e g x + e f + d\right)}{e g}"," ",0,"-(e*g*q*x - e*g*x*log(c) - (e*g*q*x + (e*f + d)*q)*log(e*g*x + e*f + d))/(e*g)","A",0
632,1,65,0,1.124478," ","integrate(log(c*(d+e/(g*x+f))^q),x, algorithm=""fricas"")","\frac{d g q x \log\left(\frac{d g x + d f + e}{g x + f}\right) - d f q \log\left(g x + f\right) + d g x \log\left(c\right) + {\left(d f + e\right)} q \log\left(d g x + d f + e\right)}{d g}"," ",0,"(d*g*q*x*log((d*g*x + d*f + e)/(g*x + f)) - d*f*q*log(g*x + f) + d*g*x*log(c) + (d*f + e)*q*log(d*g*x + d*f + e))/(d*g)","A",0
633,1,287,0,0.935208," ","integrate(log(c*(d+e/(g*x+f)^2)^q),x, algorithm=""fricas"")","\left[\frac{g q x \log\left(\frac{d g^{2} x^{2} + 2 \, d f g x + d f^{2} + e}{g^{2} x^{2} + 2 \, f g x + f^{2}}\right) + f q \log\left(d g^{2} x^{2} + 2 \, d f g x + d f^{2} + e\right) - 2 \, f q \log\left(g x + f\right) + g x \log\left(c\right) + q \sqrt{-\frac{e}{d}} \log\left(\frac{d g^{2} x^{2} + 2 \, d f g x + d f^{2} + 2 \, {\left(d g x + d f\right)} \sqrt{-\frac{e}{d}} - e}{d g^{2} x^{2} + 2 \, d f g x + d f^{2} + e}\right)}{g}, \frac{g q x \log\left(\frac{d g^{2} x^{2} + 2 \, d f g x + d f^{2} + e}{g^{2} x^{2} + 2 \, f g x + f^{2}}\right) + f q \log\left(d g^{2} x^{2} + 2 \, d f g x + d f^{2} + e\right) - 2 \, f q \log\left(g x + f\right) + g x \log\left(c\right) + 2 \, q \sqrt{\frac{e}{d}} \arctan\left(\frac{{\left(d g x + d f\right)} \sqrt{\frac{e}{d}}}{e}\right)}{g}\right]"," ",0,"[(g*q*x*log((d*g^2*x^2 + 2*d*f*g*x + d*f^2 + e)/(g^2*x^2 + 2*f*g*x + f^2)) + f*q*log(d*g^2*x^2 + 2*d*f*g*x + d*f^2 + e) - 2*f*q*log(g*x + f) + g*x*log(c) + q*sqrt(-e/d)*log((d*g^2*x^2 + 2*d*f*g*x + d*f^2 + 2*(d*g*x + d*f)*sqrt(-e/d) - e)/(d*g^2*x^2 + 2*d*f*g*x + d*f^2 + e)))/g, (g*q*x*log((d*g^2*x^2 + 2*d*f*g*x + d*f^2 + e)/(g^2*x^2 + 2*f*g*x + f^2)) + f*q*log(d*g^2*x^2 + 2*d*f*g*x + d*f^2 + e) - 2*f*q*log(g*x + f) + g*x*log(c) + 2*q*sqrt(e/d)*arctan((d*g*x + d*f)*sqrt(e/d)/e))/g]","B",0
634,1,1392,0,4.975262," ","integrate(log(c*(d+e/(g*x+f)^3)^q),x, algorithm=""fricas"")","\frac{4 \, g q x \log\left(\frac{d g^{3} x^{3} + 3 \, d f g^{2} x^{2} + 3 \, d f^{2} g x + d f^{3} + e}{g^{3} x^{3} + 3 \, f g^{2} x^{2} + 3 \, f^{2} g x + f^{3}}\right) - 4 \, \sqrt{3} g \sqrt{\frac{{\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{e q^{3}}{2 \, d g^{3}} + \frac{d f^{3} q^{3} + e q^{3}}{2 \, d g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)}^{2} g^{2} + 4 \, {\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{e q^{3}}{2 \, d g^{3}} + \frac{d f^{3} q^{3} + e q^{3}}{2 \, d g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)} f g q + 4 \, f^{2} q^{2}}{g^{2}}} \arctan\left(-\frac{2 \, \sqrt{3} \sqrt{4 \, g^{2} q^{2} x^{2} + 12 \, f g q^{2} x + {\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{e q^{3}}{2 \, d g^{3}} + \frac{d f^{3} q^{3} + e q^{3}}{2 \, d g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)}^{2} g^{2} + 12 \, f^{2} q^{2} + 2 \, {\left(g^{2} q x + 3 \, f g q\right)} {\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{e q^{3}}{2 \, d g^{3}} + \frac{d f^{3} q^{3} + e q^{3}}{2 \, d g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)}} {\left({\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{e q^{3}}{2 \, d g^{3}} + \frac{d f^{3} q^{3} + e q^{3}}{2 \, d g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)} d g^{2} + 2 \, d f g q\right)} \sqrt{\frac{{\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{e q^{3}}{2 \, d g^{3}} + \frac{d f^{3} q^{3} + e q^{3}}{2 \, d g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)}^{2} g^{2} + 4 \, {\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{e q^{3}}{2 \, d g^{3}} + \frac{d f^{3} q^{3} + e q^{3}}{2 \, d g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)} f g q + 4 \, f^{2} q^{2}}{g^{2}}} - \sqrt{3} {\left(8 \, d f g^{2} q^{2} x + {\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{e q^{3}}{2 \, d g^{3}} + \frac{d f^{3} q^{3} + e q^{3}}{2 \, d g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)}^{2} d g^{3} + 12 \, d f^{2} g q^{2} + 4 \, {\left(d g^{3} q x + 2 \, d f g^{2} q\right)} {\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{e q^{3}}{2 \, d g^{3}} + \frac{d f^{3} q^{3} + e q^{3}}{2 \, d g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)}\right)} \sqrt{\frac{{\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{e q^{3}}{2 \, d g^{3}} + \frac{d f^{3} q^{3} + e q^{3}}{2 \, d g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)}^{2} g^{2} + 4 \, {\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{e q^{3}}{2 \, d g^{3}} + \frac{d f^{3} q^{3} + e q^{3}}{2 \, d g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)} f g q + 4 \, f^{2} q^{2}}{g^{2}}}}{24 \, e q^{3}}\right) - 12 \, f q \log\left(g x + f\right) - 2 \, {\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{e q^{3}}{2 \, d g^{3}} + \frac{d f^{3} q^{3} + e q^{3}}{2 \, d g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)} g \log\left(q x - \frac{1}{2} \, {\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{e q^{3}}{2 \, d g^{3}} + \frac{d f^{3} q^{3} + e q^{3}}{2 \, d g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{f q}{g}\right) + 4 \, g x \log\left(c\right) + {\left({\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{e q^{3}}{2 \, d g^{3}} + \frac{d f^{3} q^{3} + e q^{3}}{2 \, d g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)} g + 6 \, f q\right)} \log\left(4 \, g^{2} q^{2} x^{2} + 12 \, f g q^{2} x + {\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{e q^{3}}{2 \, d g^{3}} + \frac{d f^{3} q^{3} + e q^{3}}{2 \, d g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)}^{2} g^{2} + 12 \, f^{2} q^{2} + 2 \, {\left(g^{2} q x + 3 \, f g q\right)} {\left({\left(-\frac{f^{3} q^{3}}{2 \, g^{3}} + \frac{e q^{3}}{2 \, d g^{3}} + \frac{d f^{3} q^{3} + e q^{3}}{2 \, d g^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - \frac{2 \, f q}{g}\right)}\right)}{4 \, g}"," ",0,"1/4*(4*g*q*x*log((d*g^3*x^3 + 3*d*f*g^2*x^2 + 3*d*f^2*g*x + d*f^3 + e)/(g^3*x^3 + 3*f*g^2*x^2 + 3*f^2*g*x + f^3)) - 4*sqrt(3)*g*sqrt((((-1/2*f^3*q^3/g^3 + 1/2*e*q^3/(d*g^3) + 1/2*(d*f^3*q^3 + e*q^3)/(d*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g)^2*g^2 + 4*((-1/2*f^3*q^3/g^3 + 1/2*e*q^3/(d*g^3) + 1/2*(d*f^3*q^3 + e*q^3)/(d*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g)*f*g*q + 4*f^2*q^2)/g^2)*arctan(-1/24*(2*sqrt(3)*sqrt(4*g^2*q^2*x^2 + 12*f*g*q^2*x + ((-1/2*f^3*q^3/g^3 + 1/2*e*q^3/(d*g^3) + 1/2*(d*f^3*q^3 + e*q^3)/(d*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g)^2*g^2 + 12*f^2*q^2 + 2*(g^2*q*x + 3*f*g*q)*((-1/2*f^3*q^3/g^3 + 1/2*e*q^3/(d*g^3) + 1/2*(d*f^3*q^3 + e*q^3)/(d*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g))*(((-1/2*f^3*q^3/g^3 + 1/2*e*q^3/(d*g^3) + 1/2*(d*f^3*q^3 + e*q^3)/(d*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g)*d*g^2 + 2*d*f*g*q)*sqrt((((-1/2*f^3*q^3/g^3 + 1/2*e*q^3/(d*g^3) + 1/2*(d*f^3*q^3 + e*q^3)/(d*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g)^2*g^2 + 4*((-1/2*f^3*q^3/g^3 + 1/2*e*q^3/(d*g^3) + 1/2*(d*f^3*q^3 + e*q^3)/(d*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g)*f*g*q + 4*f^2*q^2)/g^2) - sqrt(3)*(8*d*f*g^2*q^2*x + ((-1/2*f^3*q^3/g^3 + 1/2*e*q^3/(d*g^3) + 1/2*(d*f^3*q^3 + e*q^3)/(d*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g)^2*d*g^3 + 12*d*f^2*g*q^2 + 4*(d*g^3*q*x + 2*d*f*g^2*q)*((-1/2*f^3*q^3/g^3 + 1/2*e*q^3/(d*g^3) + 1/2*(d*f^3*q^3 + e*q^3)/(d*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g))*sqrt((((-1/2*f^3*q^3/g^3 + 1/2*e*q^3/(d*g^3) + 1/2*(d*f^3*q^3 + e*q^3)/(d*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g)^2*g^2 + 4*((-1/2*f^3*q^3/g^3 + 1/2*e*q^3/(d*g^3) + 1/2*(d*f^3*q^3 + e*q^3)/(d*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g)*f*g*q + 4*f^2*q^2)/g^2))/(e*q^3)) - 12*f*q*log(g*x + f) - 2*((-1/2*f^3*q^3/g^3 + 1/2*e*q^3/(d*g^3) + 1/2*(d*f^3*q^3 + e*q^3)/(d*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g)*g*log(q*x - 1/2*(-1/2*f^3*q^3/g^3 + 1/2*e*q^3/(d*g^3) + 1/2*(d*f^3*q^3 + e*q^3)/(d*g^3))^(1/3)*(I*sqrt(3) + 1) + f*q/g) + 4*g*x*log(c) + (((-1/2*f^3*q^3/g^3 + 1/2*e*q^3/(d*g^3) + 1/2*(d*f^3*q^3 + e*q^3)/(d*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g)*g + 6*f*q)*log(4*g^2*q^2*x^2 + 12*f*g*q^2*x + ((-1/2*f^3*q^3/g^3 + 1/2*e*q^3/(d*g^3) + 1/2*(d*f^3*q^3 + e*q^3)/(d*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g)^2*g^2 + 12*f^2*q^2 + 2*(g^2*q*x + 3*f*g*q)*((-1/2*f^3*q^3/g^3 + 1/2*e*q^3/(d*g^3) + 1/2*(d*f^3*q^3 + e*q^3)/(d*g^3))^(1/3)*(I*sqrt(3) + 1) - 2*f*q/g)))/g","C",0
635,0,0,0,1.251247," ","integrate((a+b*log(c*(d+e/(g*x+f))^p))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \log\left(c \left(\frac{d g x + d f + e}{g x + f}\right)^{p}\right) + a\right)}^{n}, x\right)"," ",0,"integral((b*log(c*((d*g*x + d*f + e)/(g*x + f))^p) + a)^n, x)","F",0
636,0,0,0,1.197506," ","integrate((a+b*log(c*(d+e/(g*x+f))^p))^4,x, algorithm=""fricas"")","{\rm integral}\left(b^{4} \log\left(c \left(\frac{d g x + d f + e}{g x + f}\right)^{p}\right)^{4} + 4 \, a b^{3} \log\left(c \left(\frac{d g x + d f + e}{g x + f}\right)^{p}\right)^{3} + 6 \, a^{2} b^{2} \log\left(c \left(\frac{d g x + d f + e}{g x + f}\right)^{p}\right)^{2} + 4 \, a^{3} b \log\left(c \left(\frac{d g x + d f + e}{g x + f}\right)^{p}\right) + a^{4}, x\right)"," ",0,"integral(b^4*log(c*((d*g*x + d*f + e)/(g*x + f))^p)^4 + 4*a*b^3*log(c*((d*g*x + d*f + e)/(g*x + f))^p)^3 + 6*a^2*b^2*log(c*((d*g*x + d*f + e)/(g*x + f))^p)^2 + 4*a^3*b*log(c*((d*g*x + d*f + e)/(g*x + f))^p) + a^4, x)","F",0
637,0,0,0,1.601218," ","integrate((a+b*log(c*(d+e/(g*x+f))^p))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} \log\left(c \left(\frac{d g x + d f + e}{g x + f}\right)^{p}\right)^{3} + 3 \, a b^{2} \log\left(c \left(\frac{d g x + d f + e}{g x + f}\right)^{p}\right)^{2} + 3 \, a^{2} b \log\left(c \left(\frac{d g x + d f + e}{g x + f}\right)^{p}\right) + a^{3}, x\right)"," ",0,"integral(b^3*log(c*((d*g*x + d*f + e)/(g*x + f))^p)^3 + 3*a*b^2*log(c*((d*g*x + d*f + e)/(g*x + f))^p)^2 + 3*a^2*b*log(c*((d*g*x + d*f + e)/(g*x + f))^p) + a^3, x)","F",0
638,0,0,0,0.709472," ","integrate((a+b*log(c*(d+e/(g*x+f))^p))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} \log\left(c \left(\frac{d g x + d f + e}{g x + f}\right)^{p}\right)^{2} + 2 \, a b \log\left(c \left(\frac{d g x + d f + e}{g x + f}\right)^{p}\right) + a^{2}, x\right)"," ",0,"integral(b^2*log(c*((d*g*x + d*f + e)/(g*x + f))^p)^2 + 2*a*b*log(c*((d*g*x + d*f + e)/(g*x + f))^p) + a^2, x)","F",0
639,1,76,0,0.904590," ","integrate(a+b*log(c*(d+e/(g*x+f))^p),x, algorithm=""fricas"")","\frac{b d g p x \log\left(\frac{d g x + d f + e}{g x + f}\right) - b d f p \log\left(g x + f\right) + b d g x \log\left(c\right) + a d g x + {\left(b d f + b e\right)} p \log\left(d g x + d f + e\right)}{d g}"," ",0,"(b*d*g*p*x*log((d*g*x + d*f + e)/(g*x + f)) - b*d*f*p*log(g*x + f) + b*d*g*x*log(c) + a*d*g*x + (b*d*f + b*e)*p*log(d*g*x + d*f + e))/(d*g)","A",0
640,0,0,0,1.051546," ","integrate(1/(a+b*log(c*(d+e/(g*x+f))^p)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b \log\left(c \left(\frac{d g x + d f + e}{g x + f}\right)^{p}\right) + a}, x\right)"," ",0,"integral(1/(b*log(c*((d*g*x + d*f + e)/(g*x + f))^p) + a), x)","F",0
641,0,0,0,1.286648," ","integrate(1/(a+b*log(c*(d+e/(g*x+f))^p))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} \log\left(c \left(\frac{d g x + d f + e}{g x + f}\right)^{p}\right)^{2} + 2 \, a b \log\left(c \left(\frac{d g x + d f + e}{g x + f}\right)^{p}\right) + a^{2}}, x\right)"," ",0,"integral(1/(b^2*log(c*((d*g*x + d*f + e)/(g*x + f))^p)^2 + 2*a*b*log(c*((d*g*x + d*f + e)/(g*x + f))^p) + a^2), x)","F",0
