1,0,0,0,0.000000," ","integrate(x^3*(a+b*arccos(c*x))/(-c^2*d*x^2+d),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{x^{2}}{c^{2} d} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4} d}\right)} + \frac{{\left(c^{4} d \int \frac{c^{2} x^{2} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} + e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} \log\left(c x + 1\right) + e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} \log\left(-c x + 1\right)}{c^{7} d x^{4} - c^{5} d x^{2} - {\left(c^{5} d x^{2} - c^{3} d\right)} {\left(c x + 1\right)} {\left(c x - 1\right)}}\,{d x} - {\left(c^{2} x^{2} + \log\left(c x + 1\right) + \log\left(-c x + 1\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{-c x + 1}, c x\right)\right)} b}{2 \, c^{4} d}"," ",0,"-1/2*a*(x^2/(c^2*d) + log(c^2*x^2 - 1)/(c^4*d)) + 1/2*(2*c^4*d*integrate(1/2*(c^2*x^2*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)) + e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))*log(c*x + 1) + e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))*log(-c*x + 1))/(c^7*d*x^4 - c^5*d*x^2 + (c^5*d*x^2 - c^3*d)*e^(log(c*x + 1) + log(-c*x + 1))), x) - (c^2*x^2 + log(c*x + 1) + log(-c*x + 1))*arctan2(sqrt(c*x + 1)*sqrt(-c*x + 1), c*x))*b/(c^4*d)","F",0
2,0,0,0,0.000000," ","integrate(x^2*(a+b*arccos(c*x))/(-c^2*d*x^2+d),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{2 \, x}{c^{2} d} - \frac{\log\left(c x + 1\right)}{c^{3} d} + \frac{\log\left(c x - 1\right)}{c^{3} d}\right)} - \frac{-{\left(c^{3} d {\left(\frac{2 \, \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{3} d} + \int -\frac{\sqrt{c x + 1} \sqrt{-c x + 1} {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}}{c^{4} d x^{2} - c^{2} d}\,{d x}\right)} - {\left(2 \, c x - \log\left(c x + 1\right) + \log\left(-c x + 1\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{-c x + 1}, c x\right)\right)} b}{2 \, c^{3} d}"," ",0,"-1/2*a*(2*x/(c^2*d) - log(c*x + 1)/(c^3*d) + log(c*x - 1)/(c^3*d)) - 1/2*(2*c^3*d*integrate(-1/2*(2*c*x - log(c*x + 1) + log(-c*x + 1))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^4*d*x^2 - c^2*d), x) + (2*c*x - log(c*x + 1) + log(-c*x + 1))*arctan2(sqrt(c*x + 1)*sqrt(-c*x + 1), c*x))*b/(c^3*d)","F",0
3,0,0,0,0.000000," ","integrate(x*(a+b*arccos(c*x))/(-c^2*d*x^2+d),x, algorithm=""maxima"")","\frac{{\left(c^{2} d \int \frac{e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} \log\left(c x + 1\right) + e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} \log\left(-c x + 1\right)}{c^{5} d x^{4} - c^{3} d x^{2} - {\left(c^{3} d x^{2} - c d\right)} {\left(c x + 1\right)} {\left(c x - 1\right)}}\,{d x} - {\left(\log\left(c x + 1\right) + \log\left(-c x + 1\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{-c x + 1}, c x\right)\right)} b}{2 \, c^{2} d} - \frac{a \log\left(c^{2} d x^{2} - d\right)}{2 \, c^{2} d}"," ",0,"1/2*(2*c^2*d*integrate(1/2*(e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))*log(c*x + 1) + e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))*log(-c*x + 1))/(c^5*d*x^4 - c^3*d*x^2 + (c^3*d*x^2 - c*d)*e^(log(c*x + 1) + log(-c*x + 1))), x) - (log(c*x + 1) + log(-c*x + 1))*arctan2(sqrt(c*x + 1)*sqrt(-c*x + 1), c*x))*b/(c^2*d) - 1/2*a*log(c^2*d*x^2 - d)/(c^2*d)","F",0
4,0,0,0,0.000000," ","integrate((a+b*arccos(c*x))/(-c^2*d*x^2+d),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{\log\left(c x + 1\right)}{c d} - \frac{\log\left(c x - 1\right)}{c d}\right)} - \frac{{\left(c d \int \frac{\sqrt{c x + 1} \sqrt{-c x + 1} {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}}{c^{2} d x^{2} - d}\,{d x} - {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{-c x + 1}, c x\right)\right)} b}{2 \, c d}"," ",0,"1/2*a*(log(c*x + 1)/(c*d) - log(c*x - 1)/(c*d)) - 1/2*(2*c*d*integrate(1/2*sqrt(c*x + 1)*sqrt(-c*x + 1)*(log(c*x + 1) - log(-c*x + 1))/(c^2*d*x^2 - d), x) - (log(c*x + 1) - log(-c*x + 1))*arctan2(sqrt(c*x + 1)*sqrt(-c*x + 1), c*x))*b/(c*d)","F",0
5,0,0,0,0.000000," ","integrate((a+b*arccos(c*x))/x/(-c^2*d*x^2+d),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{\log\left(c x + 1\right)}{d} + \frac{\log\left(c x - 1\right)}{d} - \frac{2 \, \log\left(x\right)}{d}\right)} - b \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{-c x + 1}, c x\right)}{c^{2} d x^{3} - d x}\,{d x}"," ",0,"-1/2*a*(log(c*x + 1)/d + log(c*x - 1)/d - 2*log(x)/d) - b*integrate(arctan2(sqrt(c*x + 1)*sqrt(-c*x + 1), c*x)/(c^2*d*x^3 - d*x), x)","F",0
6,0,0,0,0.000000," ","integrate((a+b*arccos(c*x))/x^2/(-c^2*d*x^2+d),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{c \log\left(c x + 1\right)}{d} - \frac{c \log\left(c x - 1\right)}{d} - \frac{2}{d x}\right)} - \frac{{\left(d x \int \frac{{\left(c^{2} x \log\left(c x + 1\right) - c^{2} x \log\left(-c x + 1\right) - 2 \, c\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{2} d x^{3} - d x}\,{d x} - {\left(c x \log\left(c x + 1\right) - c x \log\left(-c x + 1\right) - 2\right)} \arctan\left(\sqrt{c x + 1} \sqrt{-c x + 1}, c x\right)\right)} b}{2 \, d x}"," ",0,"1/2*a*(c*log(c*x + 1)/d - c*log(c*x - 1)/d - 2/(d*x)) - 1/2*(2*d*x*integrate(1/2*(c^2*x*log(c*x + 1) - c^2*x*log(-c*x + 1) - 2*c)*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^2*d*x^3 - d*x), x) - (c*x*log(c*x + 1) - c*x*log(-c*x + 1) - 2)*arctan2(sqrt(c*x + 1)*sqrt(-c*x + 1), c*x))*b/(d*x)","F",0
7,0,0,0,0.000000," ","integrate((a+b*arccos(c*x))/x^3/(-c^2*d*x^2+d),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{c^{2} \log\left(c x + 1\right)}{d} + \frac{c^{2} \log\left(c x - 1\right)}{d} - \frac{2 \, c^{2} \log\left(x\right)}{d} + \frac{1}{d x^{2}}\right)} a - b \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{-c x + 1}, c x\right)}{c^{2} d x^{5} - d x^{3}}\,{d x}"," ",0,"-1/2*(c^2*log(c*x + 1)/d + c^2*log(c*x - 1)/d - 2*c^2*log(x)/d + 1/(d*x^2))*a - b*integrate(arctan2(sqrt(c*x + 1)*sqrt(-c*x + 1), c*x)/(c^2*d*x^5 - d*x^3), x)","F",0
8,0,0,0,0.000000," ","integrate(x^4*(a+b*arccos(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, a {\left(\frac{2 \, x}{c^{6} d^{2} x^{2} - c^{4} d^{2}} - \frac{4 \, x}{c^{4} d^{2}} + \frac{3 \, \log\left(c x + 1\right)}{c^{5} d^{2}} - \frac{3 \, \log\left(c x - 1\right)}{c^{5} d^{2}}\right)} + \frac{{\left({\left(4 \, c^{3} x^{3} - 6 \, c x - 3 \, {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) + 3 \, {\left(c^{2} x^{2} - 1\right)} \log\left(-c x + 1\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{-c x + 1}, c x\right) - {\left(c^{7} d^{2} x^{2} - c^{5} d^{2}\right)} \int \frac{{\left(4 \, c^{3} x^{3} - 6 \, c x - 3 \, {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) + 3 \, {\left(c^{2} x^{2} - 1\right)} \log\left(-c x + 1\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{8} d^{2} x^{4} - 2 \, c^{6} d^{2} x^{2} + c^{4} d^{2}}\,{d x}\right)} b}{4 \, {\left(c^{7} d^{2} x^{2} - c^{5} d^{2}\right)}}"," ",0,"-1/4*a*(2*x/(c^6*d^2*x^2 - c^4*d^2) - 4*x/(c^4*d^2) + 3*log(c*x + 1)/(c^5*d^2) - 3*log(c*x - 1)/(c^5*d^2)) + 1/4*((4*c^3*x^3 - 6*c*x - 3*(c^2*x^2 - 1)*log(c*x + 1) + 3*(c^2*x^2 - 1)*log(-c*x + 1))*arctan2(sqrt(c*x + 1)*sqrt(-c*x + 1), c*x) + 4*(c^7*d^2*x^2 - c^5*d^2)*integrate(-1/4*(4*c^3*x^3 - 6*c*x - 3*(c^2*x^2 - 1)*log(c*x + 1) + 3*(c^2*x^2 - 1)*log(-c*x + 1))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^8*d^2*x^4 - 2*c^6*d^2*x^2 + c^4*d^2), x))*b/(c^7*d^2*x^2 - c^5*d^2)","F",0
9,0,0,0,0.000000," ","integrate(x^3*(a+b*arccos(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{1}{c^{6} d^{2} x^{2} - c^{4} d^{2}} - \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4} d^{2}}\right)} + \frac{{\left({\left({\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) + {\left(c^{2} x^{2} - 1\right)} \log\left(-c x + 1\right) - 1\right)} \arctan\left(\sqrt{c x + 1} \sqrt{-c x + 1}, c x\right) - {\left(c^{6} d^{2} x^{2} - c^{4} d^{2}\right)} \int \frac{{\left(c^{2} x^{2} - 1\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} \log\left(c x + 1\right) + {\left(c^{2} x^{2} - 1\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} \log\left(-c x + 1\right) - e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)}}{c^{9} d^{2} x^{6} - 2 \, c^{7} d^{2} x^{4} + c^{5} d^{2} x^{2} - {\left(c^{7} d^{2} x^{4} - 2 \, c^{5} d^{2} x^{2} + c^{3} d^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)}}\,{d x}\right)} b}{2 \, {\left(c^{6} d^{2} x^{2} - c^{4} d^{2}\right)}}"," ",0,"-1/2*a*(1/(c^6*d^2*x^2 - c^4*d^2) - log(c^2*x^2 - 1)/(c^4*d^2)) + 1/2*(((c^2*x^2 - 1)*log(c*x + 1) + (c^2*x^2 - 1)*log(-c*x + 1) - 1)*arctan2(sqrt(c*x + 1)*sqrt(-c*x + 1), c*x) - 2*(c^6*d^2*x^2 - c^4*d^2)*integrate(1/2*((c^2*x^2 - 1)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))*log(c*x + 1) + (c^2*x^2 - 1)*e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))*log(-c*x + 1) - e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1)))/(c^9*d^2*x^6 - 2*c^7*d^2*x^4 + c^5*d^2*x^2 + (c^7*d^2*x^4 - 2*c^5*d^2*x^2 + c^3*d^2)*e^(log(c*x + 1) + log(-c*x + 1))), x))*b/(c^6*d^2*x^2 - c^4*d^2)","F",0
10,0,0,0,0.000000," ","integrate(x^2*(a+b*arccos(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, a {\left(\frac{2 \, x}{c^{4} d^{2} x^{2} - c^{2} d^{2}} + \frac{\log\left(c x + 1\right)}{c^{3} d^{2}} - \frac{\log\left(c x - 1\right)}{c^{3} d^{2}}\right)} - \frac{{\left({\left(2 \, c x + {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) - {\left(c^{2} x^{2} - 1\right)} \log\left(-c x + 1\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{-c x + 1}, c x\right) - {\left(c^{5} d^{2} x^{2} - c^{3} d^{2}\right)} \int \frac{{\left(2 \, c x + {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) - {\left(c^{2} x^{2} - 1\right)} \log\left(-c x + 1\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{6} d^{2} x^{4} - 2 \, c^{4} d^{2} x^{2} + c^{2} d^{2}}\,{d x}\right)} b}{4 \, {\left(c^{5} d^{2} x^{2} - c^{3} d^{2}\right)}}"," ",0,"-1/4*a*(2*x/(c^4*d^2*x^2 - c^2*d^2) + log(c*x + 1)/(c^3*d^2) - log(c*x - 1)/(c^3*d^2)) - 1/4*((2*c*x + (c^2*x^2 - 1)*log(c*x + 1) - (c^2*x^2 - 1)*log(-c*x + 1))*arctan2(sqrt(c*x + 1)*sqrt(-c*x + 1), c*x) - 4*(c^5*d^2*x^2 - c^3*d^2)*integrate(1/4*(2*c*x + (c^2*x^2 - 1)*log(c*x + 1) - (c^2*x^2 - 1)*log(-c*x + 1))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^6*d^2*x^4 - 2*c^4*d^2*x^2 + c^2*d^2), x))*b/(c^5*d^2*x^2 - c^3*d^2)","F",0
11,1,136,0,0.514178," ","integrate(x*(a+b*arccos(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left({\left(\frac{\sqrt{-c^{2} x^{2} + 1} c^{2} d^{2}}{c^{7} d^{4} x + c^{6} d^{4}} + \frac{\sqrt{-c^{2} x^{2} + 1} c^{2} d^{2}}{c^{7} d^{4} x - c^{6} d^{4}}\right)} c^{2} + \frac{2 \, \arccos\left(c x\right)}{c^{4} d^{2} x^{2} - c^{2} d^{2}}\right)} b - \frac{a}{2 \, {\left(c^{4} d^{2} x^{2} - c^{2} d^{2}\right)}}"," ",0,"-1/4*((sqrt(-c^2*x^2 + 1)*c^2*d^2/(c^7*d^4*x + c^6*d^4) + sqrt(-c^2*x^2 + 1)*c^2*d^2/(c^7*d^4*x - c^6*d^4))*c^2 + 2*arccos(c*x)/(c^4*d^2*x^2 - c^2*d^2))*b - 1/2*a/(c^4*d^2*x^2 - c^2*d^2)","B",0
12,0,0,0,0.000000," ","integrate((a+b*arccos(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, a {\left(\frac{2 \, x}{c^{2} d^{2} x^{2} - d^{2}} - \frac{\log\left(c x + 1\right)}{c d^{2}} + \frac{\log\left(c x - 1\right)}{c d^{2}}\right)} - \frac{{\left({\left(2 \, c x - {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) + {\left(c^{2} x^{2} - 1\right)} \log\left(-c x + 1\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{-c x + 1}, c x\right) - {\left(c^{3} d^{2} x^{2} - c d^{2}\right)} \int \frac{{\left(2 \, c x - {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) + {\left(c^{2} x^{2} - 1\right)} \log\left(-c x + 1\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}}\,{d x}\right)} b}{4 \, {\left(c^{3} d^{2} x^{2} - c d^{2}\right)}}"," ",0,"-1/4*a*(2*x/(c^2*d^2*x^2 - d^2) - log(c*x + 1)/(c*d^2) + log(c*x - 1)/(c*d^2)) - 1/4*((2*c*x - (c^2*x^2 - 1)*log(c*x + 1) + (c^2*x^2 - 1)*log(-c*x + 1))*arctan2(sqrt(c*x + 1)*sqrt(-c*x + 1), c*x) + 4*(c^3*d^2*x^2 - c*d^2)*integrate(-1/4*(2*c*x - (c^2*x^2 - 1)*log(c*x + 1) + (c^2*x^2 - 1)*log(-c*x + 1))*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x))*b/(c^3*d^2*x^2 - c*d^2)","F",0
13,0,0,0,0.000000," ","integrate((a+b*arccos(c*x))/x/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{1}{c^{2} d^{2} x^{2} - d^{2}} + \frac{\log\left(c x + 1\right)}{d^{2}} + \frac{\log\left(c x - 1\right)}{d^{2}} - \frac{2 \, \log\left(x\right)}{d^{2}}\right)} + b \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{-c x + 1}, c x\right)}{c^{4} d^{2} x^{5} - 2 \, c^{2} d^{2} x^{3} + d^{2} x}\,{d x}"," ",0,"-1/2*a*(1/(c^2*d^2*x^2 - d^2) + log(c*x + 1)/d^2 + log(c*x - 1)/d^2 - 2*log(x)/d^2) + b*integrate(arctan2(sqrt(c*x + 1)*sqrt(-c*x + 1), c*x)/(c^4*d^2*x^5 - 2*c^2*d^2*x^3 + d^2*x), x)","F",0
14,0,0,0,0.000000," ","integrate((a+b*arccos(c*x))/x^2/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, a {\left(\frac{2 \, {\left(3 \, c^{2} x^{2} - 2\right)}}{c^{2} d^{2} x^{3} - d^{2} x} - \frac{3 \, c \log\left(c x + 1\right)}{d^{2}} + \frac{3 \, c \log\left(c x - 1\right)}{d^{2}}\right)} - \frac{{\left({\left(6 \, c^{2} x^{2} - 3 \, {\left(c^{3} x^{3} - c x\right)} \log\left(c x + 1\right) + 3 \, {\left(c^{3} x^{3} - c x\right)} \log\left(-c x + 1\right) - 4\right)} \arctan\left(\sqrt{c x + 1} \sqrt{-c x + 1}, c x\right) - {\left(c^{2} d^{2} x^{3} - d^{2} x\right)} \int \frac{{\left(6 \, c^{3} x^{2} - 3 \, {\left(c^{4} x^{3} - c^{2} x\right)} \log\left(c x + 1\right) + 3 \, {\left(c^{4} x^{3} - c^{2} x\right)} \log\left(-c x + 1\right) - 4 \, c\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}{c^{4} d^{2} x^{5} - 2 \, c^{2} d^{2} x^{3} + d^{2} x}\,{d x}\right)} b}{4 \, {\left(c^{2} d^{2} x^{3} - d^{2} x\right)}}"," ",0,"-1/4*a*(2*(3*c^2*x^2 - 2)/(c^2*d^2*x^3 - d^2*x) - 3*c*log(c*x + 1)/d^2 + 3*c*log(c*x - 1)/d^2) - 1/4*((6*c^2*x^2 - 3*(c^3*x^3 - c*x)*log(c*x + 1) + 3*(c^3*x^3 - c*x)*log(-c*x + 1) - 4)*arctan2(sqrt(c*x + 1)*sqrt(-c*x + 1), c*x) + 4*(c^2*d^2*x^3 - d^2*x)*integrate(-1/4*(6*c^3*x^2 - 3*(c^4*x^3 - c^2*x)*log(c*x + 1) + 3*(c^4*x^3 - c^2*x)*log(-c*x + 1) - 4*c)*sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^4*d^2*x^5 - 2*c^2*d^2*x^3 + d^2*x), x))*b/(c^2*d^2*x^3 - d^2*x)","F",0
15,0,0,0,0.000000," ","integrate((a+b*arccos(c*x))/x^3/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{2 \, c^{2} \log\left(c x + 1\right)}{d^{2}} + \frac{2 \, c^{2} \log\left(c x - 1\right)}{d^{2}} - \frac{4 \, c^{2} \log\left(x\right)}{d^{2}} + \frac{2 \, c^{2} x^{2} - 1}{c^{2} d^{2} x^{4} - d^{2} x^{2}}\right)} + b \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{-c x + 1}, c x\right)}{c^{4} d^{2} x^{7} - 2 \, c^{2} d^{2} x^{5} + d^{2} x^{3}}\,{d x}"," ",0,"-1/2*a*(2*c^2*log(c*x + 1)/d^2 + 2*c^2*log(c*x - 1)/d^2 - 4*c^2*log(x)/d^2 + (2*c^2*x^2 - 1)/(c^2*d^2*x^4 - d^2*x^2)) + b*integrate(arctan2(sqrt(c*x + 1)*sqrt(-c*x + 1), c*x)/(c^4*d^2*x^7 - 2*c^2*d^2*x^5 + d^2*x^3), x)","F",0
16,1,165,0,0.419114," ","integrate(x^3*(e*x^2+d)*(a+b*arccos(c*x)),x, algorithm=""maxima"")","\frac{1}{6} \, a e x^{6} + \frac{1}{4} \, a d x^{4} + \frac{1}{32} \, {\left(8 \, x^{4} \arccos\left(c x\right) - {\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{4}} - \frac{3 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b d + \frac{1}{288} \, {\left(48 \, x^{6} \arccos\left(c x\right) - {\left(\frac{8 \, \sqrt{-c^{2} x^{2} + 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{6}} - \frac{15 \, \arcsin\left(c x\right)}{c^{7}}\right)} c\right)} b e"," ",0,"1/6*a*e*x^6 + 1/4*a*d*x^4 + 1/32*(8*x^4*arccos(c*x) - (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*d + 1/288*(48*x^6*arccos(c*x) - (8*sqrt(-c^2*x^2 + 1)*x^5/c^2 + 10*sqrt(-c^2*x^2 + 1)*x^3/c^4 + 15*sqrt(-c^2*x^2 + 1)*x/c^6 - 15*arcsin(c*x)/c^7)*c)*b*e","A",0
17,1,144,0,0.419676," ","integrate(x^2*(e*x^2+d)*(a+b*arccos(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a e x^{5} + \frac{1}{3} \, a d x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \arccos\left(c x\right) - c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b d + \frac{1}{75} \, {\left(15 \, x^{5} \arccos\left(c x\right) - {\left(\frac{3 \, \sqrt{-c^{2} x^{2} + 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{-c^{2} x^{2} + 1}}{c^{6}}\right)} c\right)} b e"," ",0,"1/5*a*e*x^5 + 1/3*a*d*x^3 + 1/9*(3*x^3*arccos(c*x) - c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*d + 1/75*(15*x^5*arccos(c*x) - (3*sqrt(-c^2*x^2 + 1)*x^4/c^2 + 4*sqrt(-c^2*x^2 + 1)*x^2/c^4 + 8*sqrt(-c^2*x^2 + 1)/c^6)*c)*b*e","A",0
18,1,124,0,0.419664," ","integrate(x*(e*x^2+d)*(a+b*arccos(c*x)),x, algorithm=""maxima"")","\frac{1}{4} \, a e x^{4} + \frac{1}{2} \, a d x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \arccos\left(c x\right) - c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x}{c^{2}} - \frac{\arcsin\left(c x\right)}{c^{3}}\right)}\right)} b d + \frac{1}{32} \, {\left(8 \, x^{4} \arccos\left(c x\right) - {\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{-c^{2} x^{2} + 1} x}{c^{4}} - \frac{3 \, \arcsin\left(c x\right)}{c^{5}}\right)} c\right)} b e"," ",0,"1/4*a*e*x^4 + 1/2*a*d*x^2 + 1/4*(2*x^2*arccos(c*x) - c*(sqrt(-c^2*x^2 + 1)*x/c^2 - arcsin(c*x)/c^3))*b*d + 1/32*(8*x^4*arccos(c*x) - (2*sqrt(-c^2*x^2 + 1)*x^3/c^2 + 3*sqrt(-c^2*x^2 + 1)*x/c^4 - 3*arcsin(c*x)/c^5)*c)*b*e","A",0
19,1,94,0,0.416409," ","integrate((e*x^2+d)*(a+b*arccos(c*x)),x, algorithm=""maxima"")","\frac{1}{3} \, a e x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \arccos\left(c x\right) - c {\left(\frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{c^{4}}\right)}\right)} b e + a d x + \frac{{\left(c x \arccos\left(c x\right) - \sqrt{-c^{2} x^{2} + 1}\right)} b d}{c}"," ",0,"1/3*a*e*x^3 + 1/9*(3*x^3*arccos(c*x) - c*(sqrt(-c^2*x^2 + 1)*x^2/c^2 + 2*sqrt(-c^2*x^2 + 1)/c^4))*b*e + a*d*x + (c*x*arccos(c*x) - sqrt(-c^2*x^2 + 1))*b*d/c","A",0
20,0,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arccos(c*x))/x,x, algorithm=""maxima"")","\frac{1}{2} \, a e x^{2} + a d \log\left(x\right) + \int \frac{{\left(b e x^{2} + b d\right)} \arctan\left(\sqrt{c x + 1} \sqrt{-c x + 1}, c x\right)}{x}\,{d x}"," ",0,"1/2*a*e*x^2 + a*d*log(x) + integrate((b*e*x^2 + b*d)*arctan2(sqrt(c*x + 1)*sqrt(-c*x + 1), c*x)/x, x)","F",0
21,1,81,0,0.416111," ","integrate((e*x^2+d)*(a+b*arccos(c*x))/x^2,x, algorithm=""maxima"")","{\left(c \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{\arccos\left(c x\right)}{x}\right)} b d + a e x + \frac{{\left(c x \arccos\left(c x\right) - \sqrt{-c^{2} x^{2} + 1}\right)} b e}{c} - \frac{a d}{x}"," ",0,"(c*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) - arccos(c*x)/x)*b*d + a*e*x + (c*x*arccos(c*x) - sqrt(-c^2*x^2 + 1))*b*e/c - a*d/x","A",0
22,0,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arccos(c*x))/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, b d {\left(\frac{\sqrt{-c^{2} x^{2} + 1} c}{x} - \frac{\arccos\left(c x\right)}{x^{2}}\right)} + b e \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{-c x + 1}, c x\right)}{x}\,{d x} + a e \log\left(x\right) - \frac{a d}{2 \, x^{2}}"," ",0,"1/2*b*d*(sqrt(-c^2*x^2 + 1)*c/x - arccos(c*x)/x^2) + b*e*integrate(arctan2(sqrt(c*x + 1)*sqrt(-c*x + 1), c*x)/x, x) + a*e*log(x) - 1/2*a*d/x^2","F",0
23,1,119,0,0.414907," ","integrate((e*x^2+d)*(a+b*arccos(c*x))/x^4,x, algorithm=""maxima"")","\frac{1}{6} \, {\left({\left(c^{2} \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) + \frac{\sqrt{-c^{2} x^{2} + 1}}{x^{2}}\right)} c - \frac{2 \, \arccos\left(c x\right)}{x^{3}}\right)} b d + {\left(c \log\left(\frac{2 \, \sqrt{-c^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{\arccos\left(c x\right)}{x}\right)} b e - \frac{a e}{x} - \frac{a d}{3 \, x^{3}}"," ",0,"1/6*((c^2*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) + sqrt(-c^2*x^2 + 1)/x^2)*c - 2*arccos(c*x)/x^3)*b*d + (c*log(2*sqrt(-c^2*x^2 + 1)/abs(x) + 2/abs(x)) - arccos(c*x)/x)*b*e - a*e/x - 1/3*a*d/x^3","A",0
24,1,160,0,0.414754," ","integrate((d*x^2+c)^2*arccos(a*x),x, algorithm=""maxima"")","-\frac{1}{225} \, {\left(\frac{9 \, \sqrt{-a^{2} x^{2} + 1} d^{2} x^{4}}{a^{2}} + \frac{50 \, \sqrt{-a^{2} x^{2} + 1} c d x^{2}}{a^{2}} + \frac{225 \, \sqrt{-a^{2} x^{2} + 1} c^{2}}{a^{2}} + \frac{12 \, \sqrt{-a^{2} x^{2} + 1} d^{2} x^{2}}{a^{4}} + \frac{100 \, \sqrt{-a^{2} x^{2} + 1} c d}{a^{4}} + \frac{24 \, \sqrt{-a^{2} x^{2} + 1} d^{2}}{a^{6}}\right)} a + \frac{1}{15} \, {\left(3 \, d^{2} x^{5} + 10 \, c d x^{3} + 15 \, c^{2} x\right)} \arccos\left(a x\right)"," ",0,"-1/225*(9*sqrt(-a^2*x^2 + 1)*d^2*x^4/a^2 + 50*sqrt(-a^2*x^2 + 1)*c*d*x^2/a^2 + 225*sqrt(-a^2*x^2 + 1)*c^2/a^2 + 12*sqrt(-a^2*x^2 + 1)*d^2*x^2/a^4 + 100*sqrt(-a^2*x^2 + 1)*c*d/a^4 + 24*sqrt(-a^2*x^2 + 1)*d^2/a^6)*a + 1/15*(3*d^2*x^5 + 10*c*d*x^3 + 15*c^2*x)*arccos(a*x)","A",0
25,1,267,0,0.422269," ","integrate((d*x^2+c)^3*arccos(a*x),x, algorithm=""maxima"")","-\frac{1}{3675} \, {\left(\frac{75 \, \sqrt{-a^{2} x^{2} + 1} d^{3} x^{6}}{a^{2}} + \frac{441 \, \sqrt{-a^{2} x^{2} + 1} c d^{2} x^{4}}{a^{2}} + \frac{1225 \, \sqrt{-a^{2} x^{2} + 1} c^{2} d x^{2}}{a^{2}} + \frac{90 \, \sqrt{-a^{2} x^{2} + 1} d^{3} x^{4}}{a^{4}} + \frac{3675 \, \sqrt{-a^{2} x^{2} + 1} c^{3}}{a^{2}} + \frac{588 \, \sqrt{-a^{2} x^{2} + 1} c d^{2} x^{2}}{a^{4}} + \frac{2450 \, \sqrt{-a^{2} x^{2} + 1} c^{2} d}{a^{4}} + \frac{120 \, \sqrt{-a^{2} x^{2} + 1} d^{3} x^{2}}{a^{6}} + \frac{1176 \, \sqrt{-a^{2} x^{2} + 1} c d^{2}}{a^{6}} + \frac{240 \, \sqrt{-a^{2} x^{2} + 1} d^{3}}{a^{8}}\right)} a + \frac{1}{35} \, {\left(5 \, d^{3} x^{7} + 21 \, c d^{2} x^{5} + 35 \, c^{2} d x^{3} + 35 \, c^{3} x\right)} \arccos\left(a x\right)"," ",0,"-1/3675*(75*sqrt(-a^2*x^2 + 1)*d^3*x^6/a^2 + 441*sqrt(-a^2*x^2 + 1)*c*d^2*x^4/a^2 + 1225*sqrt(-a^2*x^2 + 1)*c^2*d*x^2/a^2 + 90*sqrt(-a^2*x^2 + 1)*d^3*x^4/a^4 + 3675*sqrt(-a^2*x^2 + 1)*c^3/a^2 + 588*sqrt(-a^2*x^2 + 1)*c*d^2*x^2/a^4 + 2450*sqrt(-a^2*x^2 + 1)*c^2*d/a^4 + 120*sqrt(-a^2*x^2 + 1)*d^3*x^2/a^6 + 1176*sqrt(-a^2*x^2 + 1)*c*d^2/a^6 + 240*sqrt(-a^2*x^2 + 1)*d^3/a^8)*a + 1/35*(5*d^3*x^7 + 21*c*d^2*x^5 + 35*c^2*d*x^3 + 35*c^3*x)*arccos(a*x)","A",0
26,1,400,0,0.421728," ","integrate((d*x^2+c)^4*arccos(a*x),x, algorithm=""maxima"")","-\frac{1}{99225} \, {\left(\frac{1225 \, \sqrt{-a^{2} x^{2} + 1} d^{4} x^{8}}{a^{2}} + \frac{8100 \, \sqrt{-a^{2} x^{2} + 1} c d^{3} x^{6}}{a^{2}} + \frac{23814 \, \sqrt{-a^{2} x^{2} + 1} c^{2} d^{2} x^{4}}{a^{2}} + \frac{1400 \, \sqrt{-a^{2} x^{2} + 1} d^{4} x^{6}}{a^{4}} + \frac{44100 \, \sqrt{-a^{2} x^{2} + 1} c^{3} d x^{2}}{a^{2}} + \frac{9720 \, \sqrt{-a^{2} x^{2} + 1} c d^{3} x^{4}}{a^{4}} + \frac{99225 \, \sqrt{-a^{2} x^{2} + 1} c^{4}}{a^{2}} + \frac{31752 \, \sqrt{-a^{2} x^{2} + 1} c^{2} d^{2} x^{2}}{a^{4}} + \frac{1680 \, \sqrt{-a^{2} x^{2} + 1} d^{4} x^{4}}{a^{6}} + \frac{88200 \, \sqrt{-a^{2} x^{2} + 1} c^{3} d}{a^{4}} + \frac{12960 \, \sqrt{-a^{2} x^{2} + 1} c d^{3} x^{2}}{a^{6}} + \frac{63504 \, \sqrt{-a^{2} x^{2} + 1} c^{2} d^{2}}{a^{6}} + \frac{2240 \, \sqrt{-a^{2} x^{2} + 1} d^{4} x^{2}}{a^{8}} + \frac{25920 \, \sqrt{-a^{2} x^{2} + 1} c d^{3}}{a^{8}} + \frac{4480 \, \sqrt{-a^{2} x^{2} + 1} d^{4}}{a^{10}}\right)} a + \frac{1}{315} \, {\left(35 \, d^{4} x^{9} + 180 \, c d^{3} x^{7} + 378 \, c^{2} d^{2} x^{5} + 420 \, c^{3} d x^{3} + 315 \, c^{4} x\right)} \arccos\left(a x\right)"," ",0,"-1/99225*(1225*sqrt(-a^2*x^2 + 1)*d^4*x^8/a^2 + 8100*sqrt(-a^2*x^2 + 1)*c*d^3*x^6/a^2 + 23814*sqrt(-a^2*x^2 + 1)*c^2*d^2*x^4/a^2 + 1400*sqrt(-a^2*x^2 + 1)*d^4*x^6/a^4 + 44100*sqrt(-a^2*x^2 + 1)*c^3*d*x^2/a^2 + 9720*sqrt(-a^2*x^2 + 1)*c*d^3*x^4/a^4 + 99225*sqrt(-a^2*x^2 + 1)*c^4/a^2 + 31752*sqrt(-a^2*x^2 + 1)*c^2*d^2*x^2/a^4 + 1680*sqrt(-a^2*x^2 + 1)*d^4*x^4/a^6 + 88200*sqrt(-a^2*x^2 + 1)*c^3*d/a^4 + 12960*sqrt(-a^2*x^2 + 1)*c*d^3*x^2/a^6 + 63504*sqrt(-a^2*x^2 + 1)*c^2*d^2/a^6 + 2240*sqrt(-a^2*x^2 + 1)*d^4*x^2/a^8 + 25920*sqrt(-a^2*x^2 + 1)*c*d^3/a^8 + 4480*sqrt(-a^2*x^2 + 1)*d^4/a^10)*a + 1/315*(35*d^4*x^9 + 180*c*d^3*x^7 + 378*c^2*d^2*x^5 + 420*c^3*d*x^3 + 315*c^4*x)*arccos(a*x)","A",0
27,0,0,0,0.000000," ","integrate(arccos(a*x)/(d*x^2+c),x, algorithm=""maxima"")","\int \frac{\arccos\left(a x\right)}{d x^{2} + c}\,{d x}"," ",0,"integrate(arccos(a*x)/(d*x^2 + c), x)","F",0
28,0,0,0,0.000000," ","integrate(arccos(a*x)/(d*x^2+c)^2,x, algorithm=""maxima"")","\int \frac{\arccos\left(a x\right)}{{\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(arccos(a*x)/(d*x^2 + c)^2, x)","F",0
29,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)*arccos(a*x),x, algorithm=""maxima"")","\int \sqrt{d x^{2} + c} \arccos\left(a x\right)\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)*arccos(a*x), x)","F",0
30,0,0,0,0.000000," ","integrate(arccos(a*x)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\arccos\left(a x\right)}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(arccos(a*x)/sqrt(d*x^2 + c), x)","F",0
31,-2,0,0,0.000000," ","integrate(arccos(a*x)/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(d-a^2*c>0)', see `assume?` for more details)Is d-a^2*c zero or nonzero?","F(-2)",0
32,-2,0,0,0.000000," ","integrate(arccos(a*x)/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(d-a^2*c>0)', see `assume?` for more details)Is d-a^2*c zero or nonzero?","F(-2)",0
33,-2,0,0,0.000000," ","integrate(arccos(a*x)/(d*x^2+c)^(7/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(d-a^2*c>0)', see `assume?` for more details)Is d-a^2*c zero or nonzero?","F(-2)",0
