1,1,13,16,0.020806,"\text{Not used}","int(x + x^2 + 1,x)","\frac{x\,\left(2\,x^2+3\,x+6\right)}{6}","Not used",1,"(x*(3*x + 2*x^2 + 6))/6","B"
2,1,15,22,0.038530,"\text{Not used}","int(x^2*(x + 2*x^2)^2,x)","\frac{x^5\,\left(60\,x^2+70\,x+21\right)}{105}","Not used",1,"(x^5*(70*x + 60*x^2 + 21))/105","B"
3,1,15,22,0.029188,"\text{Not used}","int(x*(2*x + x^2 + 1),x)","\frac{x^2\,\left(3\,x^2+8\,x+6\right)}{12}","Not used",1,"(x^2*(8*x + 3*x^2 + 6))/12","B"
4,1,2,2,0.008702,"\text{Not used}","int(1/x,x)","\ln\left(x\right)","Not used",1,"log(x)","B"
5,1,22,36,0.118171,"\text{Not used}","int((x + 1)^3/(x - 1)^4,x)","\ln\left(x-1\right)-\frac{6\,x^2-6\,x+\frac{8}{3}}{{\left(x-1\right)}^3}","Not used",1,"log(x - 1) - (6*x^2 - 6*x + 8/3)/(x - 1)^3","B"
6,1,26,32,0.034335,"\text{Not used}","int(1/(x*(x - 1)*(x + 1)^2),x)","\frac{\ln\left(x-1\right)}{4}+\frac{3\,\ln\left(x+1\right)}{4}-\ln\left(x\right)-\frac{1}{2\,\left(x+1\right)}","Not used",1,"log(x - 1)/4 + (3*log(x + 1))/4 - log(x) - 1/(2*(x + 1))","B"
7,1,40,40,0.250080,"\text{Not used}","int((b + a*x)/((p - x)*(q - x)),x)","\frac{\ln\left(x-p\right)\,\left(b+a\,p\right)}{p-q}-\frac{\ln\left(x-q\right)\,\left(b+a\,q\right)}{p-q}","Not used",1,"(log(x - p)*(b + a*p))/(p - q) - (log(x - q)*(b + a*q))/(p - q)","B"
8,1,46,34,0.198061,"\text{Not used}","int(1/(c + b*x + a*x^2),x)","\frac{2\,\mathrm{atan}\left(\frac{b}{\sqrt{4\,a\,c-b^2}}+\frac{2\,a\,x}{\sqrt{4\,a\,c-b^2}}\right)}{\sqrt{4\,a\,c-b^2}}","Not used",1,"(2*atan(b/(4*a*c - b^2)^(1/2) + (2*a*x)/(4*a*c - b^2)^(1/2)))/(4*a*c - b^2)^(1/2)","B"
9,1,14,16,0.037972,"\text{Not used}","int((b + a*x)/(x^2 + 1),x)","\frac{a\,\ln\left(x^2+1\right)}{2}+b\,\mathrm{atan}\left(x\right)","Not used",1,"(a*log(x^2 + 1))/2 + b*atan(x)","B"
10,1,14,19,0.031131,"\text{Not used}","int(1/(x^2 - 2*x + 3),x)","\frac{\sqrt{2}\,\mathrm{atan}\left(\frac{\sqrt{2}\,\left(x-1\right)}{2}\right)}{2}","Not used",1,"(2^(1/2)*atan((2^(1/2)*(x - 1))/2))/2","B"
11,1,49,49,0.125691,"\text{Not used}","int(1/((x^2 + 1)^2*(x - 1)^2),x)","-\frac{\ln\left(x-1\right)}{2}-\frac{\frac{x^2}{4}+\frac{x}{4}}{x^3-x^2+x-1}+\ln\left(x-\mathrm{i}\right)\,\left(\frac{1}{4}-\frac{1}{8}{}\mathrm{i}\right)+\ln\left(x+1{}\mathrm{i}\right)\,\left(\frac{1}{4}+\frac{1}{8}{}\mathrm{i}\right)","Not used",1,"log(x - 1i)*(1/4 - 1i/8) - log(x - 1)/2 + log(x + 1i)*(1/4 + 1i/8) - (x/4 + x^2/4)/(x - x^2 + x^3 - 1)","B"
12,1,87,68,0.568062,"\text{Not used}","int(-x/((a - x)*(b - x)*(c - x)),x)","\ln\left(x-a\right)\,\left(\frac{b}{\left(a-b\right)\,\left(b-c\right)}-\frac{c}{\left(a-c\right)\,\left(b-c\right)}\right)-\frac{b\,\ln\left(x-b\right)}{\left(a-b\right)\,\left(b-c\right)}+\frac{c\,\ln\left(x-c\right)}{\left(a-c\right)\,\left(b-c\right)}","Not used",1,"log(x - a)*(b/((a - b)*(b - c)) - c/((a - c)*(b - c))) - (b*log(x - b))/((a - b)*(b - c)) + (c*log(x - c))/((a - c)*(b - c))","B"
13,1,256,47,0.304298,"\text{Not used}","int(x/((a^2 + x^2)*(b^2 + x^2)),x)","\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x^2\,\left(8\,a^2+8\,b^2\right)+16\,a^2\,b^2}{2\,\left(a^2-b^2\right)}-4\,x^2\right)\,1{}\mathrm{i}}{2\,\left(a^2-b^2\right)}-\frac{\left(\frac{x^2\,\left(8\,a^2+8\,b^2\right)+16\,a^2\,b^2}{2\,\left(a^2-b^2\right)}+4\,x^2\right)\,1{}\mathrm{i}}{2\,\left(a^2-b^2\right)}}{\frac{\frac{x^2\,\left(8\,a^2+8\,b^2\right)+16\,a^2\,b^2}{2\,\left(a^2-b^2\right)}-4\,x^2}{2\,\left(a^2-b^2\right)}+\frac{\frac{x^2\,\left(8\,a^2+8\,b^2\right)+16\,a^2\,b^2}{2\,\left(a^2-b^2\right)}+4\,x^2}{2\,\left(a^2-b^2\right)}}\right)\,1{}\mathrm{i}}{a^2-b^2}","Not used",1,"(atan(((((x^2*(8*a^2 + 8*b^2) + 16*a^2*b^2)/(2*(a^2 - b^2)) - 4*x^2)*1i)/(2*(a^2 - b^2)) - (((x^2*(8*a^2 + 8*b^2) + 16*a^2*b^2)/(2*(a^2 - b^2)) + 4*x^2)*1i)/(2*(a^2 - b^2)))/(((x^2*(8*a^2 + 8*b^2) + 16*a^2*b^2)/(2*(a^2 - b^2)) - 4*x^2)/(2*(a^2 - b^2)) + ((x^2*(8*a^2 + 8*b^2) + 16*a^2*b^2)/(2*(a^2 - b^2)) + 4*x^2)/(2*(a^2 - b^2))))*1i)/(a^2 - b^2)","B"
14,1,191,40,0.175072,"\text{Not used}","int(x^2/((a^2 + x^2)*(b^2 + x^2)),x)","-\frac{a\,\mathrm{atan}\left(\frac{x\,\left(2\,a^4+2\,b^4\right)-\frac{a^2\,x\,\left(8\,a^6-8\,a^4\,b^2-8\,a^2\,b^4+8\,b^6\right)}{{\left(2\,a^2-2\,b^2\right)}^2}}{a\,b^2\,\left(2\,a^2-2\,b^2\right)}\right)}{a^2-b^2}-\frac{b\,\mathrm{atan}\left(\frac{x\,\left(2\,a^4+2\,b^4\right)-\frac{b^2\,x\,\left(8\,a^6-8\,a^4\,b^2-8\,a^2\,b^4+8\,b^6\right)}{{\left(2\,a^2-2\,b^2\right)}^2}}{a^2\,b\,\left(2\,a^2-2\,b^2\right)}\right)}{a^2-b^2}","Not used",1,"- (a*atan((x*(2*a^4 + 2*b^4) - (a^2*x*(8*a^6 + 8*b^6 - 8*a^2*b^4 - 8*a^4*b^2))/(2*a^2 - 2*b^2)^2)/(a*b^2*(2*a^2 - 2*b^2))))/(a^2 - b^2) - (b*atan((x*(2*a^4 + 2*b^4) - (b^2*x*(8*a^6 + 8*b^6 - 8*a^2*b^4 - 8*a^4*b^2))/(2*a^2 - 2*b^2)^2)/(a^2*b*(2*a^2 - 2*b^2))))/(a^2 - b^2)","B"
15,1,25,27,0.046119,"\text{Not used}","int(x/((x^2 + 1)*(x - 1)),x)","\frac{\ln\left(x-1\right)}{2}+\ln\left(x-\mathrm{i}\right)\,\left(-\frac{1}{4}-\frac{1}{4}{}\mathrm{i}\right)+\ln\left(x+1{}\mathrm{i}\right)\,\left(-\frac{1}{4}+\frac{1}{4}{}\mathrm{i}\right)","Not used",1,"log(x - 1)/2 - log(x - 1i)*(1/4 + 1i/4) - log(x + 1i)*(1/4 - 1i/4)","B"
16,1,46,41,0.205921,"\text{Not used}","int(x/(x^3 + 1),x)","-\frac{\ln\left(x+1\right)}{3}-\ln\left(x-\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)+\ln\left(x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)","Not used",1,"log(x + (3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/6 + 1/6) - log(x - (3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/6 - 1/6) - log(x + 1)/3","B"
17,1,33,43,0.043395,"\text{Not used}","int(x^3/((x^3 + 1)*(x - 1)^2),x)","\frac{3\,\ln\left(x-1\right)}{4}-\frac{\ln\left(x+1\right)}{12}-\frac{\ln\left(x^2-x+1\right)}{3}-\frac{1}{2\,\left(x-1\right)}","Not used",1,"(3*log(x - 1))/4 - log(x + 1)/12 - log(x^2 - x + 1)/3 - 1/(2*(x - 1))","B"
18,1,33,85,0.002023,"\text{Not used}","int(1/(x^4 + 1),x)","\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,x\,\left(\frac{1}{2}-\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(\frac{1}{4}+\frac{1}{4}{}\mathrm{i}\right)+\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,x\,\left(\frac{1}{2}+\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(\frac{1}{4}-\frac{1}{4}{}\mathrm{i}\right)","Not used",1,"2^(1/2)*atan(2^(1/2)*x*(1/2 - 1i/2))*(1/4 + 1i/4) + 2^(1/2)*atan(2^(1/2)*x*(1/2 + 1i/2))*(1/4 - 1i/4)","B"
19,1,33,85,0.205405,"\text{Not used}","int(x^2/(x^4 + 1),x)","\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,x\,\left(\frac{1}{2}-\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(\frac{1}{4}-\frac{1}{4}{}\mathrm{i}\right)+\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,x\,\left(\frac{1}{2}+\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(\frac{1}{4}+\frac{1}{4}{}\mathrm{i}\right)","Not used",1,"2^(1/2)*atan(2^(1/2)*x*(1/2 - 1i/2))*(1/4 - 1i/4) + 2^(1/2)*atan(2^(1/2)*x*(1/2 + 1i/2))*(1/4 + 1i/4)","B"
20,1,47,67,0.179403,"\text{Not used}","int(1/(x^2 + x^4 + 1),x)","\mathrm{atanh}\left(\frac{2\,x}{-1+\sqrt{3}\,1{}\mathrm{i}}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)+\mathrm{atanh}\left(\frac{2\,x}{1+\sqrt{3}\,1{}\mathrm{i}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)","Not used",1,"atanh((2*x)/(3^(1/2)*1i - 1))*((3^(1/2)*1i)/6 - 1/2) + atanh((2*x)/(3^(1/2)*1i + 1))*((3^(1/2)*1i)/6 + 1/2)","B"
21,1,18,18,0.220082,"\text{Not used}","int((a + b*x)^p,x)","\frac{{\left(a+b\,x\right)}^{p+1}}{b\,\left(p+1\right)}","Not used",1,"(a + b*x)^(p + 1)/(b*(p + 1))","B"
22,1,94,39,0.391841,"\text{Not used}","int(x*(a + b*x)^p,x)","\left\{\begin{array}{cl} -\frac{a\,\ln\left(a+b\,x\right)-b\,x}{b^2} & \text{\ if\ \ }p=-1\\ \frac{\ln\left(a+b\,x\right)+\frac{a}{a+b\,x}}{b^2} & \text{\ if\ \ }p=-2\\ \frac{2\,\left(\frac{{\left(a+b\,x\right)}^{p+2}}{2\,p+4}-\frac{a\,{\left(a+b\,x\right)}^{p+1}}{2\,p+2}\right)}{b^2} & \text{\ if\ \ }p\neq -1\wedge p\neq -2 \end{array}\right.","Not used",1,"piecewise(p == -1, -(a*log(a + b*x) - b*x)/b^2, p == -2, (log(a + b*x) + a/(a + b*x))/b^2, p ~= -1 & p ~= -2, (2*((a + b*x)^(p + 2)/(2*p + 4) - (a*(a + b*x)^(p + 1))/(2*p + 2)))/b^2)","B"
23,1,192,60,0.601354,"\text{Not used}","int(x^2*(a + b*x)^p,x)","\left\{\begin{array}{cl} \frac{2\,a^2\,\ln\left(a+b\,x\right)+b^2\,x^2-2\,a\,b\,x}{2\,b^3} & \text{\ if\ \ }p=-1\\ \frac{x}{b^2}-\frac{a^2}{b^3\,\left(a+b\,x\right)}-\frac{2\,a\,\ln\left(a+b\,x\right)}{b^3} & \text{\ if\ \ }p=-2\\ \frac{\ln\left(a+b\,x\right)+\frac{2\,a}{a+b\,x}-\frac{a^2}{2\,{\left(a+b\,x\right)}^2}}{b^3} & \text{\ if\ \ }p=-3\\ \frac{2\,{\left(a+b\,x\right)}^{p+1}\,\left(8\,a^2-8\,a\,b\,p\,x-8\,a\,b\,x+4\,b^2\,p^2\,x^2+12\,b^2\,p\,x^2+8\,b^2\,x^2\right)}{b^3\,\left(8\,p^3+48\,p^2+88\,p+48\right)} & \text{\ if\ \ }p\neq -1\wedge p\neq -2\wedge p\neq -3 \end{array}\right.","Not used",1,"piecewise(p == -1, (2*a^2*log(a + b*x) + b^2*x^2 - 2*a*b*x)/(2*b^3), p == -2, x/b^2 - a^2/(b^3*(a + b*x)) - (2*a*log(a + b*x))/b^3, p == -3, (log(a + b*x) + (2*a)/(a + b*x) - a^2/(2*(a + b*x)^2))/b^3, p ~= -1 & p ~= -2 & p ~= -3, (2*(a + b*x)^(p + 1)*(8*a^2 + 8*b^2*x^2 + 12*b^2*p*x^2 - 8*a*b*x + 4*b^2*p^2*x^2 - 8*a*b*p*x))/(b^3*(88*p + 48*p^2 + 8*p^3 + 48)))","B"
24,1,10,10,0.026093,"\text{Not used}","int(1/(a + b*x),x)","\frac{\ln\left(a+b\,x\right)}{b}","Not used",1,"log(a + b*x)/b","B"
25,1,12,12,0.117920,"\text{Not used}","int(1/(a + b*x)^2,x)","-\frac{1}{b\,\left(a+b\,x\right)}","Not used",1,"-1/(b*(a + b*x))","B"
26,1,18,18,0.034773,"\text{Not used}","int(x/(a + b*x),x)","-\frac{a\,\ln\left(a+b\,x\right)-b\,x}{b^2}","Not used",1,"-(a*log(a + b*x) - b*x)/b^2","B"
27,1,29,31,0.127454,"\text{Not used}","int(x^2/(a + b*x),x)","\frac{2\,a^2\,\ln\left(a+b\,x\right)+b^2\,x^2-2\,a\,b\,x}{2\,b^3}","Not used",1,"(2*a^2*log(a + b*x) + b^2*x^2 - 2*a*b*x)/(2*b^3)","B"
28,1,15,18,0.134096,"\text{Not used}","int(1/(x*(a + b*x)),x)","-\frac{2\,\mathrm{atanh}\left(\frac{2\,b\,x}{a}+1\right)}{a}","Not used",1,"-(2*atanh((2*b*x)/a + 1))/a","B"
29,1,25,28,0.053884,"\text{Not used}","int(1/(x^2*(a + b*x)),x)","\frac{2\,b\,\mathrm{atanh}\left(\frac{2\,b\,x}{a}+1\right)}{a^2}-\frac{1}{a\,x}","Not used",1,"(2*b*atanh((2*b*x)/a + 1))/a^2 - 1/(a*x)","B"
30,1,45,42,0.187605,"\text{Not used}","int(1/(x^2*(a + b*x)^2),x)","\frac{2\,b\,\ln\left(\frac{a+b\,x}{x}\right)}{a^3}-\frac{1}{a\,x\,\left(a+b\,x\right)}-\frac{2\,b}{a^2\,\left(a+b\,x\right)}","Not used",1,"(2*b*log((a + b*x)/x))/a^3 - 1/(a*x*(a + b*x)) - (2*b)/(a^2*(a + b*x))","B"
31,1,10,10,0.037258,"\text{Not used}","int(1/(c^2 + x^2),x)","\frac{\mathrm{atan}\left(\frac{x}{c}\right)}{c}","Not used",1,"atan(x/c)/c","B"
32,1,10,10,0.159082,"\text{Not used}","int(1/(c^2 - x^2),x)","\frac{\mathrm{atanh}\left(\frac{x}{c}\right)}{c}","Not used",1,"atanh(x/c)/c","B"
33,1,72,78,0.276825,"\text{Not used}","int(1/(2*x^3 - 1),x)","\frac{2^{2/3}\,\ln\left(x-\frac{2^{2/3}}{2}\right)}{6}+\frac{2^{2/3}\,\ln\left(x-\frac{2^{2/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{4}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}-\frac{2^{2/3}\,\ln\left(x+\frac{2^{2/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{4}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}","Not used",1,"(2^(2/3)*log(x - 2^(2/3)/2))/6 + (2^(2/3)*log(x - (2^(2/3)*(3^(1/2)*1i - 1))/4)*(3^(1/2)*1i - 1))/12 - (2^(2/3)*log(x + (2^(2/3)*(3^(1/2)*1i + 1))/4)*(3^(1/2)*1i + 1))/12","B"
34,1,72,74,0.356073,"\text{Not used}","int(1/(x^3 - 2),x)","\frac{2^{1/3}\,\ln\left(x-2^{1/3}\right)}{6}+\frac{2^{1/3}\,\ln\left(x-\frac{2^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}-\frac{2^{1/3}\,\ln\left(x+\frac{2^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}","Not used",1,"(2^(1/3)*log(x - 2^(1/3)))/6 + (2^(1/3)*log(x - (2^(1/3)*(3^(1/2)*1i - 1))/2)*(3^(1/2)*1i - 1))/12 - (2^(1/3)*log(x + (2^(1/3)*(3^(1/2)*1i + 1))/2)*(3^(1/2)*1i + 1))/12","B"
35,1,101,115,0.314631,"\text{Not used}","int(-1/(b - a*x^3),x)","\frac{\ln\left(a^{1/3}\,x-b^{1/3}\right)}{3\,a^{1/3}\,b^{2/3}}+\frac{\ln\left(3\,a^2\,x-\frac{3\,a^{5/3}\,b^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{6\,a^{1/3}\,b^{2/3}}-\frac{\ln\left(3\,a^2\,x+\frac{3\,a^{5/3}\,b^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{6\,a^{1/3}\,b^{2/3}}","Not used",1,"log(a^(1/3)*x - b^(1/3))/(3*a^(1/3)*b^(2/3)) + (log(3*a^2*x - (3*a^(5/3)*b^(1/3)*(3^(1/2)*1i - 1))/2)*(3^(1/2)*1i - 1))/(6*a^(1/3)*b^(2/3)) - (log(3*a^2*x + (3*a^(5/3)*b^(1/3)*(3^(1/2)*1i + 1))/2)*(3^(1/2)*1i + 1))/(6*a^(1/3)*b^(2/3))","B"
36,1,20,35,0.158169,"\text{Not used}","int(1/(x^4 - 2),x)","-\frac{2^{1/4}\,\left(\mathrm{atan}\left(\frac{2^{3/4}\,x}{2}\right)+\mathrm{atanh}\left(\frac{2^{3/4}\,x}{2}\right)\right)}{4}","Not used",1,"-(2^(1/4)*(atan((2^(3/4)*x)/2) + atanh((2^(3/4)*x)/2)))/4","B"
37,1,18,35,0.175208,"\text{Not used}","int(1/(5*x^4 - 1),x)","-\frac{5^{3/4}\,\left(\mathrm{atan}\left(5^{1/4}\,x\right)+\mathrm{atanh}\left(5^{1/4}\,x\right)\right)}{10}","Not used",1,"-(5^(3/4)*(atan(5^(1/4)*x) + atanh(5^(1/4)*x)))/10","B"
38,1,45,171,0.110858,"\text{Not used}","int(1/(3*x^4 + 7),x)","\sqrt{2}\,{189}^{1/4}\,\mathrm{atan}\left(\sqrt{2}\,{189}^{3/4}\,x\,\left(\frac{1}{126}-\frac{1}{126}{}\mathrm{i}\right)\right)\,\left(\frac{1}{84}+\frac{1}{84}{}\mathrm{i}\right)+\sqrt{2}\,{189}^{1/4}\,\mathrm{atan}\left(\sqrt{2}\,{189}^{3/4}\,x\,\left(\frac{1}{126}+\frac{1}{126}{}\mathrm{i}\right)\right)\,\left(\frac{1}{84}-\frac{1}{84}{}\mathrm{i}\right)","Not used",1,"2^(1/2)*189^(1/4)*atan(2^(1/2)*189^(3/4)*x*(1/126 - 1i/126))*(1/84 + 1i/84) + 2^(1/2)*189^(1/4)*atan(2^(1/2)*189^(3/4)*x*(1/126 + 1i/126))*(1/84 - 1i/84)","B"
39,1,93,73,0.224228,"\text{Not used}","int(1/(3*x^2 + x^4 - 1),x)","-\frac{\sqrt{26}\,\mathrm{atanh}\left(\frac{\sqrt{26}\,x}{2\,\sqrt{\sqrt{13}+3}}+\frac{3\,\sqrt{13}\,\sqrt{26}\,x}{26\,\sqrt{\sqrt{13}+3}}\right)\,\sqrt{\sqrt{13}+3}}{26}-\frac{\sqrt{26}\,\mathrm{atanh}\left(\frac{\sqrt{26}\,x}{2\,\sqrt{3-\sqrt{13}}}-\frac{3\,\sqrt{13}\,\sqrt{26}\,x}{26\,\sqrt{3-\sqrt{13}}}\right)\,\sqrt{3-\sqrt{13}}}{26}","Not used",1,"- (26^(1/2)*atanh((26^(1/2)*x)/(2*(13^(1/2) + 3)^(1/2)) + (3*13^(1/2)*26^(1/2)*x)/(26*(13^(1/2) + 3)^(1/2)))*(13^(1/2) + 3)^(1/2))/26 - (26^(1/2)*atanh((26^(1/2)*x)/(2*(3 - 13^(1/2))^(1/2)) - (3*13^(1/2)*26^(1/2)*x)/(26*(3 - 13^(1/2))^(1/2)))*(3 - 13^(1/2))^(1/2))/26","B"
40,1,93,73,0.134618,"\text{Not used}","int(-1/(3*x^2 - x^4 + 1),x)","-\frac{\sqrt{26}\,\mathrm{atanh}\left(\frac{\sqrt{26}\,x}{2\,\sqrt{\sqrt{13}-3}}-\frac{3\,\sqrt{13}\,\sqrt{26}\,x}{26\,\sqrt{\sqrt{13}-3}}\right)\,\sqrt{\sqrt{13}-3}}{26}-\frac{\sqrt{26}\,\mathrm{atanh}\left(\frac{\sqrt{26}\,x}{2\,\sqrt{-\sqrt{13}-3}}+\frac{3\,\sqrt{13}\,\sqrt{26}\,x}{26\,\sqrt{-\sqrt{13}-3}}\right)\,\sqrt{-\sqrt{13}-3}}{26}","Not used",1,"- (26^(1/2)*atanh((26^(1/2)*x)/(2*(13^(1/2) - 3)^(1/2)) - (3*13^(1/2)*26^(1/2)*x)/(26*(13^(1/2) - 3)^(1/2)))*(13^(1/2) - 3)^(1/2))/26 - (26^(1/2)*atanh((26^(1/2)*x)/(2*(- 13^(1/2) - 3)^(1/2)) + (3*13^(1/2)*26^(1/2)*x)/(26*(- 13^(1/2) - 3)^(1/2)))*(- 13^(1/2) - 3)^(1/2))/26","B"
41,1,67,72,0.097637,"\text{Not used}","int(1/(x^4 - 3*x^2 + 1),x)","\mathrm{atanh}\left(\frac{4\,x}{\sqrt{5}-3}-\frac{2\,\sqrt{5}\,x}{\sqrt{5}-3}\right)\,\left(\frac{\sqrt{5}}{10}-\frac{1}{2}\right)+\mathrm{atanh}\left(\frac{4\,x}{\sqrt{5}+3}+\frac{2\,\sqrt{5}\,x}{\sqrt{5}+3}\right)\,\left(\frac{\sqrt{5}}{10}+\frac{1}{2}\right)","Not used",1,"atanh((4*x)/(5^(1/2) - 3) - (2*5^(1/2)*x)/(5^(1/2) - 3))*(5^(1/2)/10 - 1/2) + atanh((4*x)/(5^(1/2) + 3) + (2*5^(1/2)*x)/(5^(1/2) + 3))*(5^(1/2)/10 + 1/2)","B"
42,1,98,67,0.230630,"\text{Not used}","int(1/(x^4 - 4*x^2 + 1),x)","\mathrm{atanh}\left(\frac{5\,\sqrt{2}\,x}{\sqrt{2}\,\sqrt{6}+4}+\frac{3\,\sqrt{6}\,x}{\sqrt{2}\,\sqrt{6}+4}\right)\,\left(\frac{\sqrt{2}}{4}+\frac{\sqrt{6}}{12}\right)-\mathrm{atanh}\left(\frac{5\,\sqrt{2}\,x}{\sqrt{2}\,\sqrt{6}-4}-\frac{3\,\sqrt{6}\,x}{\sqrt{2}\,\sqrt{6}-4}\right)\,\left(\frac{\sqrt{2}}{4}-\frac{\sqrt{6}}{12}\right)","Not used",1,"atanh((5*2^(1/2)*x)/(2^(1/2)*6^(1/2) + 4) + (3*6^(1/2)*x)/(2^(1/2)*6^(1/2) + 4))*(2^(1/2)/4 + 6^(1/2)/12) - atanh((5*2^(1/2)*x)/(2^(1/2)*6^(1/2) - 4) - (3*6^(1/2)*x)/(2^(1/2)*6^(1/2) - 4))*(2^(1/2)/4 - 6^(1/2)/12)","B"
43,1,117,67,0.196598,"\text{Not used}","int(1/(4*x^2 + x^4 + 1),x)","2\,\mathrm{atanh}\left(\frac{24\,x\,\sqrt{\frac{\sqrt{3}}{48}-\frac{1}{24}}}{2\,\sqrt{3}-4}-\frac{16\,\sqrt{3}\,x\,\sqrt{\frac{\sqrt{3}}{48}-\frac{1}{24}}}{2\,\sqrt{3}-4}\right)\,\sqrt{\frac{\sqrt{3}}{48}-\frac{1}{24}}-2\,\mathrm{atanh}\left(\frac{24\,x\,\sqrt{-\frac{\sqrt{3}}{48}-\frac{1}{24}}}{2\,\sqrt{3}+4}+\frac{16\,\sqrt{3}\,x\,\sqrt{-\frac{\sqrt{3}}{48}-\frac{1}{24}}}{2\,\sqrt{3}+4}\right)\,\sqrt{-\frac{\sqrt{3}}{48}-\frac{1}{24}}","Not used",1,"2*atanh((24*x*(3^(1/2)/48 - 1/24)^(1/2))/(2*3^(1/2) - 4) - (16*3^(1/2)*x*(3^(1/2)/48 - 1/24)^(1/2))/(2*3^(1/2) - 4))*(3^(1/2)/48 - 1/24)^(1/2) - 2*atanh((24*x*(- 3^(1/2)/48 - 1/24)^(1/2))/(2*3^(1/2) + 4) + (16*3^(1/2)*x*(- 3^(1/2)/48 - 1/24)^(1/2))/(2*3^(1/2) + 4))*(- 3^(1/2)/48 - 1/24)^(1/2)","B"
44,1,61,196,0.224719,"\text{Not used}","int(1/(x^2 + x^4 + 2),x)","\frac{\mathrm{atan}\left(\frac{\sqrt{7}\,x\,\sqrt{7-\sqrt{7}\,7{}\mathrm{i}}}{14}\right)\,\sqrt{7-\sqrt{7}\,7{}\mathrm{i}}\,1{}\mathrm{i}}{14}-\frac{\sqrt{7}\,\mathrm{atan}\left(\frac{x\,\sqrt{1+\sqrt{7}\,1{}\mathrm{i}}}{2}\right)\,\sqrt{1+\sqrt{7}\,1{}\mathrm{i}}\,1{}\mathrm{i}}{14}","Not used",1,"(atan((7^(1/2)*x*(7 - 7^(1/2)*7i)^(1/2))/14)*(7 - 7^(1/2)*7i)^(1/2)*1i)/14 - (7^(1/2)*atan((x*(7^(1/2)*1i + 1)^(1/2))/2)*(7^(1/2)*1i + 1)^(1/2)*1i)/14","B"
45,1,132,196,0.110072,"\text{Not used}","int(1/(x^4 - x^2 + 2),x)","\frac{\mathrm{atan}\left(\frac{x\,\sqrt{-7-\sqrt{7}\,7{}\mathrm{i}}\,1{}\mathrm{i}}{4\,\left(\frac{1}{2}+\frac{\sqrt{7}\,1{}\mathrm{i}}{2}\right)}+\frac{\sqrt{7}\,x\,\sqrt{-7-\sqrt{7}\,7{}\mathrm{i}}}{28\,\left(\frac{1}{2}+\frac{\sqrt{7}\,1{}\mathrm{i}}{2}\right)}\right)\,\sqrt{-7-\sqrt{7}\,7{}\mathrm{i}}\,1{}\mathrm{i}}{14}+\frac{\sqrt{7}\,\mathrm{atan}\left(\frac{x\,\sqrt{-1+\sqrt{7}\,1{}\mathrm{i}}}{4\,\left(-\frac{1}{2}+\frac{\sqrt{7}\,1{}\mathrm{i}}{2}\right)}-\frac{\sqrt{7}\,x\,\sqrt{-1+\sqrt{7}\,1{}\mathrm{i}}\,1{}\mathrm{i}}{4\,\left(-\frac{1}{2}+\frac{\sqrt{7}\,1{}\mathrm{i}}{2}\right)}\right)\,\sqrt{-1+\sqrt{7}\,1{}\mathrm{i}}\,1{}\mathrm{i}}{14}","Not used",1,"(atan((x*(- 7^(1/2)*7i - 7)^(1/2)*1i)/(4*((7^(1/2)*1i)/2 + 1/2)) + (7^(1/2)*x*(- 7^(1/2)*7i - 7)^(1/2))/(28*((7^(1/2)*1i)/2 + 1/2)))*(- 7^(1/2)*7i - 7)^(1/2)*1i)/14 + (7^(1/2)*atan((x*(7^(1/2)*1i - 1)^(1/2))/(4*((7^(1/2)*1i)/2 - 1/2)) - (7^(1/2)*x*(7^(1/2)*1i - 1)^(1/2)*1i)/(4*((7^(1/2)*1i)/2 - 1/2)))*(7^(1/2)*1i - 1)^(1/2)*1i)/14","B"
46,1,88,73,0.090940,"\text{Not used}","int(1/(x^6 - 1),x)","-\frac{\mathrm{atanh}\left(x\right)}{3}-\mathrm{atan}\left(\frac{x\,1{}\mathrm{i}}{1+\sqrt{3}\,1{}\mathrm{i}}+\frac{\sqrt{3}\,x}{1+\sqrt{3}\,1{}\mathrm{i}}\right)\,\left(\frac{\sqrt{3}}{6}+\frac{1}{6}{}\mathrm{i}\right)-\mathrm{atan}\left(\frac{x\,1{}\mathrm{i}}{-1+\sqrt{3}\,1{}\mathrm{i}}-\frac{\sqrt{3}\,x}{-1+\sqrt{3}\,1{}\mathrm{i}}\right)\,\left(\frac{\sqrt{3}}{6}-\frac{1}{6}{}\mathrm{i}\right)","Not used",1,"- atanh(x)/3 - atan((x*1i)/(3^(1/2)*1i + 1) + (3^(1/2)*x)/(3^(1/2)*1i + 1))*(3^(1/2)/6 + 1i/6) - atan((x*1i)/(3^(1/2)*1i - 1) - (3^(1/2)*x)/(3^(1/2)*1i - 1))*(3^(1/2)/6 - 1i/6)","B"
47,1,140,138,0.210070,"\text{Not used}","int(1/(x^6 - 2),x)","-\frac{2^{1/6}\,\mathrm{atanh}\left(\frac{2^{5/6}\,x}{2}\right)}{6}+\frac{2^{1/6}\,\mathrm{atan}\left(\frac{2^{1/6}\,x\,1{}\mathrm{i}}{2\,\left(-\frac{2^{1/3}}{2}+\frac{2^{1/3}\,\sqrt{3}\,1{}\mathrm{i}}{2}\right)}-\frac{2^{1/6}\,\sqrt{3}\,x}{2\,\left(-\frac{2^{1/3}}{2}+\frac{2^{1/3}\,\sqrt{3}\,1{}\mathrm{i}}{2}\right)}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{12}+\frac{2^{1/6}\,\mathrm{atan}\left(\frac{2^{1/6}\,x\,1{}\mathrm{i}}{2\,\left(\frac{2^{1/3}}{2}+\frac{2^{1/3}\,\sqrt{3}\,1{}\mathrm{i}}{2}\right)}+\frac{2^{1/6}\,\sqrt{3}\,x}{2\,\left(\frac{2^{1/3}}{2}+\frac{2^{1/3}\,\sqrt{3}\,1{}\mathrm{i}}{2}\right)}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{12}","Not used",1,"(2^(1/6)*atan((2^(1/6)*x*1i)/(2*((2^(1/3)*3^(1/2)*1i)/2 - 2^(1/3)/2)) - (2^(1/6)*3^(1/2)*x)/(2*((2^(1/3)*3^(1/2)*1i)/2 - 2^(1/3)/2)))*(3^(1/2)*1i + 1)*1i)/12 - (2^(1/6)*atanh((2^(5/6)*x)/2))/6 + (2^(1/6)*atan((2^(1/6)*x*1i)/(2*((2^(1/3)*3^(1/2)*1i)/2 + 2^(1/3)/2)) + (2^(1/6)*3^(1/2)*x)/(2*((2^(1/3)*3^(1/2)*1i)/2 + 2^(1/3)/2)))*(3^(1/2)*1i - 1)*1i)/12","B"
48,1,135,138,0.128966,"\text{Not used}","int(1/(x^6 + 2),x)","\frac{2^{1/6}\,\mathrm{atan}\left(\frac{2^{5/6}\,x}{2}\right)}{6}+\frac{2^{1/6}\,\mathrm{atan}\left(\frac{2^{1/6}\,x}{2\,\left(-\frac{2^{1/3}}{2}+\frac{2^{1/3}\,\sqrt{3}\,1{}\mathrm{i}}{2}\right)}+\frac{2^{1/6}\,\sqrt{3}\,x\,1{}\mathrm{i}}{2\,\left(-\frac{2^{1/3}}{2}+\frac{2^{1/3}\,\sqrt{3}\,1{}\mathrm{i}}{2}\right)}\right)\,\left(\sqrt{3}-\mathrm{i}\right)\,1{}\mathrm{i}}{12}+\frac{2^{1/6}\,\mathrm{atan}\left(\frac{2^{1/6}\,x}{2\,\left(\frac{2^{1/3}}{2}+\frac{2^{1/3}\,\sqrt{3}\,1{}\mathrm{i}}{2}\right)}-\frac{2^{1/6}\,\sqrt{3}\,x\,1{}\mathrm{i}}{2\,\left(\frac{2^{1/3}}{2}+\frac{2^{1/3}\,\sqrt{3}\,1{}\mathrm{i}}{2}\right)}\right)\,\left(\sqrt{3}+1{}\mathrm{i}\right)\,1{}\mathrm{i}}{12}","Not used",1,"(2^(1/6)*atan((2^(5/6)*x)/2))/6 + (2^(1/6)*atan((2^(1/6)*x)/(2*((2^(1/3)*3^(1/2)*1i)/2 - 2^(1/3)/2)) + (2^(1/6)*3^(1/2)*x*1i)/(2*((2^(1/3)*3^(1/2)*1i)/2 - 2^(1/3)/2)))*(3^(1/2) - 1i)*1i)/12 + (2^(1/6)*atan((2^(1/6)*x)/(2*((2^(1/3)*3^(1/2)*1i)/2 + 2^(1/3)/2)) - (2^(1/6)*3^(1/2)*x*1i)/(2*((2^(1/3)*3^(1/2)*1i)/2 + 2^(1/3)/2)))*(3^(1/2) + 1i)*1i)/12","B"
49,1,288,339,0.303771,"\text{Not used}","int(1/(x^8 + 1),x)","\mathrm{atan}\left(\frac{x\,\sqrt{-\sqrt{2}-2}\,1{}\mathrm{i}}{\sqrt{2-\sqrt{2}}\,\sqrt{-\sqrt{2}-2}+\sqrt{2}}-\frac{x\,\sqrt{2-\sqrt{2}}\,1{}\mathrm{i}}{\sqrt{2-\sqrt{2}}\,\sqrt{-\sqrt{2}-2}+\sqrt{2}}\right)\,\left(\frac{\sqrt{-\sqrt{2}-2}\,1{}\mathrm{i}}{8}-\frac{\sqrt{2-\sqrt{2}}\,1{}\mathrm{i}}{8}\right)-\mathrm{atan}\left(\frac{x\,\sqrt{\sqrt{2}-2}\,1{}\mathrm{i}}{\sqrt{2}+\sqrt{\sqrt{2}-2}\,\sqrt{\sqrt{2}+2}}+\frac{x\,\sqrt{\sqrt{2}+2}\,1{}\mathrm{i}}{\sqrt{2}+\sqrt{\sqrt{2}-2}\,\sqrt{\sqrt{2}+2}}\right)\,\left(\frac{\sqrt{\sqrt{2}-2}\,1{}\mathrm{i}}{8}+\frac{\sqrt{\sqrt{2}+2}\,1{}\mathrm{i}}{8}\right)+\mathrm{atan}\left(-\frac{\sqrt{2}\,x\,\sqrt{\sqrt{2}+2}}{2}+x\,\sqrt{\sqrt{2}+2}\,\left(\frac{1}{2}+\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(\frac{\sqrt{2}\,1{}\mathrm{i}}{16}-\frac{1}{16}-\frac{1}{16}{}\mathrm{i}\right)\,\sqrt{\sqrt{2}+2}\,2{}\mathrm{i}-\mathrm{atan}\left(x\,\sqrt{\sqrt{2}+2}\,\left(\frac{1}{2}-\frac{1}{2}{}\mathrm{i}\right)+\frac{\sqrt{2}\,x\,\sqrt{\sqrt{2}+2}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\sqrt{2}}{16}-\frac{1}{16}+\frac{1}{16}{}\mathrm{i}\right)\,\sqrt{\sqrt{2}+2}\,2{}\mathrm{i}","Not used",1,"atan((x*(- 2^(1/2) - 2)^(1/2)*1i)/((2 - 2^(1/2))^(1/2)*(- 2^(1/2) - 2)^(1/2) + 2^(1/2)) - (x*(2 - 2^(1/2))^(1/2)*1i)/((2 - 2^(1/2))^(1/2)*(- 2^(1/2) - 2)^(1/2) + 2^(1/2)))*(((- 2^(1/2) - 2)^(1/2)*1i)/8 - ((2 - 2^(1/2))^(1/2)*1i)/8) - atan((x*(2^(1/2) - 2)^(1/2)*1i)/(2^(1/2) + (2^(1/2) - 2)^(1/2)*(2^(1/2) + 2)^(1/2)) + (x*(2^(1/2) + 2)^(1/2)*1i)/(2^(1/2) + (2^(1/2) - 2)^(1/2)*(2^(1/2) + 2)^(1/2)))*(((2^(1/2) - 2)^(1/2)*1i)/8 + ((2^(1/2) + 2)^(1/2)*1i)/8) + atan(x*(2^(1/2) + 2)^(1/2)*(1/2 + 1i/2) - (2^(1/2)*x*(2^(1/2) + 2)^(1/2))/2)*((2^(1/2)*1i)/16 - (1/16 + 1i/16))*(2^(1/2) + 2)^(1/2)*2i - atan(x*(2^(1/2) + 2)^(1/2)*(1/2 - 1i/2) + (2^(1/2)*x*(2^(1/2) + 2)^(1/2)*1i)/2)*(2^(1/2)/16 - (1/16 - 1i/16))*(2^(1/2) + 2)^(1/2)*2i","B"
50,1,45,97,0.164698,"\text{Not used}","int(1/(x^8 - 1),x)","\frac{\mathrm{atan}\left(x\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{4}-\frac{\mathrm{atan}\left(x\right)}{4}+\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,x\,\left(\frac{1}{2}-\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{1}{8}-\frac{1}{8}{}\mathrm{i}\right)+\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,x\,\left(\frac{1}{2}+\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{1}{8}+\frac{1}{8}{}\mathrm{i}\right)","Not used",1,"(atan(x*1i)*1i)/4 - atan(x)/4 - 2^(1/2)*atan(2^(1/2)*x*(1/2 - 1i/2))*(1/8 + 1i/8) - 2^(1/2)*atan(2^(1/2)*x*(1/2 + 1i/2))*(1/8 - 1i/8)","B"
51,1,53,275,0.099615,"\text{Not used}","int(1/(x^8 - x^4 + 1),x)","\sqrt{6}\,\mathrm{atan}\left(\frac{\sqrt{6}\,x\,\left(\frac{1}{3}+\frac{1}{3}{}\mathrm{i}\right)}{\frac{2\,x^2}{3}-\frac{2}{3}{}\mathrm{i}}\right)\,\left(-\frac{1}{12}-\frac{1}{12}{}\mathrm{i}\right)+\sqrt{6}\,\mathrm{atan}\left(\frac{\sqrt{6}\,x\,\left(\frac{1}{3}-\frac{1}{3}{}\mathrm{i}\right)}{\frac{2\,x^2}{3}+\frac{2}{3}{}\mathrm{i}}\right)\,\left(-\frac{1}{12}+\frac{1}{12}{}\mathrm{i}\right)","Not used",1,"- 6^(1/2)*atan((6^(1/2)*x*(1/3 + 1i/3))/((2*x^2)/3 - 2i/3))*(1/12 + 1i/12) - 6^(1/2)*atan((6^(1/2)*x*(1/3 - 1i/3))/((2*x^2)/3 + 2i/3))*(1/12 - 1i/12)","B"
52,1,52,49,0.219157,"\text{Not used}","int(x^7/(x^12 + 1),x)","-\frac{\ln\left(x^4+1\right)}{12}-\ln\left(x^4-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}-\frac{1}{2}\right)\,\left(-\frac{1}{24}+\frac{\sqrt{3}\,1{}\mathrm{i}}{24}\right)+\ln\left(x^4+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}-\frac{1}{2}\right)\,\left(\frac{1}{24}+\frac{\sqrt{3}\,1{}\mathrm{i}}{24}\right)","Not used",1,"log((3^(1/2)*1i)/2 + x^4 - 1/2)*((3^(1/2)*1i)/24 + 1/24) - log(x^4 - (3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/24 - 1/24) - log(x^4 + 1)/12","B"
53,1,6,8,0.023370,"\text{Not used}","int(log(x),x)","x\,\left(\ln\left(x\right)-1\right)","Not used",1,"x*(log(x) - 1)","B"
54,1,9,17,0.033528,"\text{Not used}","int(x*log(x),x)","\frac{x^2\,\left(\ln\left(x\right)-\frac{1}{2}\right)}{2}","Not used",1,"(x^2*(log(x) - 1/2))/2","B"
55,1,9,17,0.032166,"\text{Not used}","int(x^2*log(x),x)","\frac{x^3\,\left(\ln\left(x\right)-\frac{1}{3}\right)}{3}","Not used",1,"(x^3*(log(x) - 1/3))/3","B"
56,1,32,26,0.238989,"\text{Not used}","int(x^p*log(x),x)","\left\{\begin{array}{cl} \frac{{\ln\left(x\right)}^2}{2} & \text{\ if\ \ }p=-1\\ \frac{x^{p+1}\,\left(\ln\left(x\right)\,\left(p+1\right)-1\right)}{{\left(p+1\right)}^2} & \text{\ if\ \ }p\neq -1 \end{array}\right.","Not used",1,"piecewise(p == -1, log(x)^2/2, p ~= -1, (x^(p + 1)*(log(x)*(p + 1) - 1))/(p + 1)^2)","B"
57,1,12,15,0.030069,"\text{Not used}","int(log(x)^2,x)","x\,\left({\ln\left(x\right)}^2-2\,\ln\left(x\right)+2\right)","Not used",1,"x*(log(x)^2 - 2*log(x) + 2)","B"
58,1,71,127,0.176713,"\text{Not used}","int(x^9*log(x)^11,x)","\frac{6237\,x^{10}\,\left(\frac{15625000\,{\ln\left(x\right)}^{11}}{6237}-\frac{1562500\,{\ln\left(x\right)}^{10}}{567}+\frac{1562500\,{\ln\left(x\right)}^9}{567}-\frac{156250\,{\ln\left(x\right)}^8}{63}+\frac{125000\,{\ln\left(x\right)}^7}{63}-\frac{12500\,{\ln\left(x\right)}^6}{9}+\frac{2500\,{\ln\left(x\right)}^5}{3}-\frac{1250\,{\ln\left(x\right)}^4}{3}+\frac{500\,{\ln\left(x\right)}^3}{3}-50\,{\ln\left(x\right)}^2+10\,\ln\left(x\right)-1\right)}{156250000}","Not used",1,"(6237*x^10*(10*log(x) - 50*log(x)^2 + (500*log(x)^3)/3 - (1250*log(x)^4)/3 + (2500*log(x)^5)/3 - (12500*log(x)^6)/9 + (125000*log(x)^7)/63 - (156250*log(x)^8)/63 + (1562500*log(x)^9)/567 - (1562500*log(x)^10)/567 + (15625000*log(x)^11)/6237 - 1))/156250000","B"
59,1,6,8,0.059621,"\text{Not used}","int(log(x)^2/x,x)","\frac{{\ln\left(x\right)}^3}{3}","Not used",1,"log(x)^3/3","B"
60,1,2,2,0.003738,"\text{Not used}","int(1/log(x),x)","\mathrm{logint}\left(x\right)","Not used",1,"logint(x)","B"
61,1,4,4,0.015583,"\text{Not used}","int(1/log(x + 1),x)","\mathrm{logint}\left(x+1\right)","Not used",1,"logint(x + 1)","B"
62,1,3,3,0.120419,"\text{Not used}","int(1/(x*log(x)),x)","\ln\left(\ln\left(x\right)\right)","Not used",1,"log(log(x))","B"
63,1,17,17,0.029522,"\text{Not used}","int(1/(x^2*log(x)^2),x)","-\mathrm{ei}\left(-\ln\left(x\right)\right)-\frac{1}{x\,\ln\left(x\right)}","Not used",1,"- ei(-log(x)) - 1/(x*log(x))","B"
64,1,22,12,0.146073,"\text{Not used}","int(log(x)^p/x,x)","\left\{\begin{array}{cl} \ln\left(\ln\left(x\right)\right) & \text{\ if\ \ }p=-1\\ \frac{{\ln\left(x\right)}^{p+1}}{p+1} & \text{\ if\ \ }p\neq -1 \end{array}\right.","Not used",1,"piecewise(p == -1, log(log(x)), p ~= -1, log(x)^(p + 1)/(p + 1))","B"
65,1,21,28,0.141088,"\text{Not used}","int(log(x)*(b + a*x),x)","-\frac{x\,\left(4\,b+a\,x-4\,b\,\ln\left(x\right)-2\,a\,x\,\ln\left(x\right)\right)}{4}","Not used",1,"-(x*(4*b + a*x - 4*b*log(x) - 2*a*x*log(x)))/4","B"
66,1,47,54,0.170391,"\text{Not used}","int(log(x)*(b + a*x)^2,x)","b^2\,x\,\ln\left(x\right)-\frac{a^2\,x^3}{9}-b^2\,x+\frac{a^2\,x^3\,\ln\left(x\right)}{3}-\frac{a\,b\,x^2}{2}+a\,b\,x^2\,\ln\left(x\right)","Not used",1,"b^2*x*log(x) - (a^2*x^3)/9 - b^2*x + (a^2*x^3*log(x))/3 - (a*b*x^2)/2 + a*b*x^2*log(x)","B"
67,1,35,29,0.232371,"\text{Not used}","int(log(x)/(b + a*x)^2,x)","\frac{x^2\,\ln\left(x\right)}{b\,\left(a\,x^2+b\,x\right)}-\frac{\ln\left(b+a\,x\right)}{a\,b}","Not used",1,"(x^2*log(x))/(b*(b*x + a*x^2)) - log(b + a*x)/(a*b)","B"
68,1,66,46,0.189114,"\text{Not used}","int(x*log(b + a*x),x)","\left\{\begin{array}{cl} \frac{x^2\,\left(\ln\left(a\,x\right)-\frac{1}{2}\right)}{2} & \text{\ if\ \ }b=0\\ \frac{\ln\left(b+a\,x\right)\,\left(x^2-\frac{b^2}{a^2}\right)}{2}-\frac{b^2\,\left(\frac{a^2\,x^2}{2\,b^2}-\frac{a\,x}{b}\right)}{2\,a^2} & \text{\ if\ \ }b\neq 0 \end{array}\right.","Not used",1,"piecewise(b == 0, (x^2*(log(a*x) - 1/2))/2, b ~= 0, (log(b + a*x)*(x^2 - b^2/a^2))/2 - (b^2*((a^2*x^2)/(2*b^2) - (a*x)/b))/(2*a^2))","B"
69,1,75,59,0.182120,"\text{Not used}","int(x^2*log(b + a*x),x)","\left\{\begin{array}{cl} \frac{x^3\,\left(\ln\left(a\,x\right)-\frac{1}{3}\right)}{3} & \text{\ if\ \ }b=0\\ \frac{\ln\left(b+a\,x\right)\,\left(x^3+\frac{b^3}{a^3}\right)}{3}-\frac{b^3\,\left(\frac{a^3\,x^3}{3\,b^3}-\frac{a^2\,x^2}{2\,b^2}+\frac{a\,x}{b}\right)}{3\,a^3} & \text{\ if\ \ }b\neq 0 \end{array}\right.","Not used",1,"piecewise(b == 0, (x^3*(log(a*x) - 1/3))/3, b ~= 0, (log(b + a*x)*(x^3 + b^3/a^3))/3 - (b^3*(- (a^2*x^2)/(2*b^2) + (a^3*x^3)/(3*b^3) + (a*x)/b))/(3*a^3))","B"
70,1,23,23,0.065679,"\text{Not used}","int(log(a^2 + x^2),x)","x\,\ln\left(a^2+x^2\right)-2\,x+2\,a\,\mathrm{atan}\left(\frac{x}{a}\right)","Not used",1,"x*log(a^2 + x^2) - 2*x + 2*a*atan(x/a)","B"
71,1,51,27,0.040784,"\text{Not used}","int(x*log(a^2 + x^2),x)","\frac{a^2\,\ln\left(x-\sqrt{-a^2}\right)}{2}+\frac{x^2\,\ln\left(a^2+x^2\right)}{2}-\frac{x^2}{2}+\frac{a^2\,\ln\left(x+\sqrt{-a^2}\right)}{2}","Not used",1,"(a^2*log(x - (-a^2)^(1/2)))/2 + (x^2*log(a^2 + x^2))/2 - x^2/2 + (a^2*log(x + (-a^2)^(1/2)))/2","B"
72,1,65,44,0.036037,"\text{Not used}","int(x^2*log(a^2 + x^2),x)","\frac{2\,a^2\,x}{3}-\frac{\ln\left(x-\sqrt{-a^2}\right)\,{\left(-a^2\right)}^{3/2}}{3}+\frac{x^3\,\ln\left(a^2+x^2\right)}{3}+\frac{\ln\left(x+\sqrt{-a^2}\right)\,{\left(-a^2\right)}^{3/2}}{3}-\frac{2\,x^3}{9}","Not used",1,"(2*a^2*x)/3 - (log(x - (-a^2)^(1/2))*(-a^2)^(3/2))/3 + (x^3*log(a^2 + x^2))/3 + (log(x + (-a^2)^(1/2))*(-a^2)^(3/2))/3 - (2*x^3)/9","B"
73,1,73,54,0.128336,"\text{Not used}","int(x^4*log(a^2 + x^2),x)","\frac{x^5\,\ln\left(a^2+x^2\right)}{5}-\frac{2\,a^4\,x}{5}-\frac{\ln\left(x-\sqrt{-a^2}\right)\,{\left(-a^2\right)}^{5/2}}{5}+\frac{\ln\left(x+\sqrt{-a^2}\right)\,{\left(-a^2\right)}^{5/2}}{5}-\frac{2\,x^5}{25}+\frac{2\,a^2\,x^3}{15}","Not used",1,"(x^5*log(a^2 + x^2))/5 - (2*a^4*x)/5 - (log(x - (-a^2)^(1/2))*(-a^2)^(5/2))/5 + (log(x + (-a^2)^(1/2))*(-a^2)^(5/2))/5 - (2*x^5)/25 + (2*a^2*x^3)/15","B"
74,1,25,25,0.074012,"\text{Not used}","int(log(x^2 - a^2),x)","x\,\ln\left(x^2-a^2\right)-2\,x+2\,a\,\mathrm{atanh}\left(\frac{x}{a}\right)","Not used",1,"x*log(x^2 - a^2) - 2*x + 2*a*atanh(x/a)","B"
75,0,-1,8,0.000000,"\text{Not used}","int(log(log(log(log(x)))),x)","\int \ln\left(\ln\left(\ln\left(\ln\left(x\right)\right)\right)\right) \,d x","Not used",0,"int(log(log(log(log(x)))), x)","F"
76,1,4,4,0.020892,"\text{Not used}","int(sin(x),x)","-\cos\left(x\right)","Not used",1,"-cos(x)","B"
77,1,2,2,0.027125,"\text{Not used}","int(cos(x),x)","\sin\left(x\right)","Not used",1,"sin(x)","B"
78,1,5,5,0.029212,"\text{Not used}","int(tan(x),x)","-\ln\left(\cos\left(x\right)\right)","Not used",1,"-log(cos(x))","B"
79,1,13,3,0.196825,"\text{Not used}","int(1/tan(x),x)","\ln\left(\mathrm{tan}\left(x\right)\right)-\frac{\ln\left({\mathrm{tan}\left(x\right)}^2+1\right)}{2}","Not used",1,"log(tan(x)) - log(tan(x)^2 + 1)/2","B"
80,1,27,21,0.246156,"\text{Not used}","int(1/(tan(x) + 1)^2,x)","\frac{\ln\left(\mathrm{tan}\left(x\right)+1\right)}{2}-\frac{\ln\left({\mathrm{tan}\left(x\right)}^2+1\right)}{4}-\frac{1}{2\,\left(\mathrm{tan}\left(x\right)+1\right)}","Not used",1,"log(tan(x) + 1)/2 - log(tan(x)^2 + 1)/4 - 1/(2*(tan(x) + 1))","B"
81,1,11,3,0.129440,"\text{Not used}","int(1/cos(x),x)","\ln\left(\frac{1}{\cos\left(x\right)}\right)+\ln\left(\sin\left(x\right)+1\right)","Not used",1,"log(1/cos(x)) + log(sin(x) + 1)","B"
82,1,5,5,0.044832,"\text{Not used}","int(1/sin(x),x)","\ln\left(\mathrm{tan}\left(\frac{x}{2}\right)\right)","Not used",1,"log(tan(x/2))","B"
83,1,10,14,0.031634,"\text{Not used}","int(sin(x)^2,x)","\frac{x}{2}-\frac{\sin\left(2\,x\right)}{4}","Not used",1,"x/2 - sin(2*x)/4","B"
84,1,16,20,0.157706,"\text{Not used}","int(x^3*sin(x^2),x)","\frac{\sin\left(x^2\right)}{2}-\frac{x^2\,\cos\left(x^2\right)}{2}","Not used",1,"sin(x^2)/2 - (x^2*cos(x^2))/2","B"
85,1,10,13,0.034433,"\text{Not used}","int(sin(x)^3,x)","\frac{\cos\left(x\right)\,\left({\cos\left(x\right)}^2-3\right)}{3}","Not used",1,"(cos(x)*(cos(x)^2 - 3))/3","B"
86,1,35,44,0.315041,"\text{Not used}","int(sin(x)^p,x)","-\frac{\cos\left(x\right)\,{\sin\left(x\right)}^{p+1}\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{1}{2}-\frac{p}{2};\ \frac{3}{2};\ {\cos\left(x\right)}^2\right)}{{\left({\sin\left(x\right)}^2\right)}^{\frac{p}{2}+\frac{1}{2}}}","Not used",1,"-(cos(x)*sin(x)^(p + 1)*hypergeom([1/2, 1/2 - p/2], 3/2, cos(x)^2))/(sin(x)^2)^(p/2 + 1/2)","B"
87,1,15,19,0.044532,"\text{Not used}","int(cos(x)*(sin(x)^2 + 1)^2,x)","\frac{{\sin\left(x\right)}^5}{5}+\frac{2\,{\sin\left(x\right)}^3}{3}+\sin\left(x\right)","Not used",1,"sin(x) + (2*sin(x)^3)/3 + sin(x)^5/5","B"
88,1,10,14,0.026484,"\text{Not used}","int(cos(x)^2,x)","\frac{x}{2}+\frac{\sin\left(2\,x\right)}{4}","Not used",1,"x/2 + sin(2*x)/4","B"
89,1,9,11,0.030765,"\text{Not used}","int(cos(x)^3,x)","\sin\left(x\right)-\frac{{\sin\left(x\right)}^3}{3}","Not used",1,"sin(x) - sin(x)^3/3","B"
90,1,2,2,0.022908,"\text{Not used}","int(1/cos(x)^2,x)","\mathrm{tan}\left(x\right)","Not used",1,"tan(x)","B"
91,1,6,15,0.028132,"\text{Not used}","int(sin(2*x)*sin(x),x)","\frac{2\,{\sin\left(x\right)}^3}{3}","Not used",1,"(2*sin(x)^3)/3","B"
92,1,8,8,0.020791,"\text{Not used}","int(x*sin(x),x)","\sin\left(x\right)-x\,\cos\left(x\right)","Not used",1,"sin(x) - x*cos(x)","B"
93,1,15,17,0.027804,"\text{Not used}","int(x^2*sin(x),x)","2\,x\,\sin\left(x\right)-\cos\left(x\right)\,\left(x^2-2\right)","Not used",1,"2*x*sin(x) - cos(x)*(x^2 - 2)","B"
94,1,19,25,0.055137,"\text{Not used}","int(x*sin(x)^2,x)","\frac{{\sin\left(x\right)}^2}{4}-\frac{x\,\sin\left(2\,x\right)}{4}+\frac{x^2}{4}","Not used",1,"sin(x)^2/4 - (x*sin(2*x))/4 + x^2/4","B"
95,1,28,41,0.155172,"\text{Not used}","int(x^2*sin(x)^2,x)","\frac{\sin\left(2\,x\right)}{8}-\frac{x\,\cos\left(2\,x\right)}{4}-\frac{x^2\,\sin\left(2\,x\right)}{4}+\frac{x^3}{6}","Not used",1,"sin(2*x)/8 - (x*cos(2*x))/4 - (x^2*sin(2*x))/4 + x^3/6","B"
96,1,25,33,0.065821,"\text{Not used}","int(x*sin(x)^3,x)","\frac{x\,{\cos\left(x\right)}^3}{3}-\frac{\sin\left(x\right)\,{\cos\left(x\right)}^2}{9}-x\,\cos\left(x\right)+\frac{7\,\sin\left(x\right)}{9}","Not used",1,"(7*sin(x))/9 + (x*cos(x)^3)/3 - (cos(x)^2*sin(x))/9 - x*cos(x)","B"
97,1,7,7,0.018993,"\text{Not used}","int(x*cos(x),x)","\cos\left(x\right)+x\,\sin\left(x\right)","Not used",1,"cos(x) + x*sin(x)","B"
98,1,14,16,0.025749,"\text{Not used}","int(x^2*cos(x),x)","\sin\left(x\right)\,\left(x^2-2\right)+2\,x\,\cos\left(x\right)","Not used",1,"sin(x)*(x^2 - 2) + 2*x*cos(x)","B"
99,1,19,25,0.150862,"\text{Not used}","int(x*cos(x)^2,x)","\frac{x\,\sin\left(2\,x\right)}{4}-\frac{{\sin\left(x\right)}^2}{4}+\frac{x^2}{4}","Not used",1,"(x*sin(2*x))/4 - sin(x)^2/4 + x^2/4","B"
100,1,28,41,0.064524,"\text{Not used}","int(x^2*cos(x)^2,x)","\frac{x\,\cos\left(2\,x\right)}{4}-\frac{\sin\left(2\,x\right)}{8}+\frac{x^2\,\sin\left(2\,x\right)}{4}+\frac{x^3}{6}","Not used",1,"(x*cos(2*x))/4 - sin(2*x)/8 + (x^2*sin(2*x))/4 + x^3/6","B"
101,1,25,33,0.168980,"\text{Not used}","int(x*cos(x)^3,x)","\frac{{\cos\left(x\right)}^3}{9}+\frac{x\,\sin\left(x\right)\,{\cos\left(x\right)}^2}{3}+\frac{2\,\cos\left(x\right)}{3}+\frac{2\,x\,\sin\left(x\right)}{3}","Not used",1,"(2*cos(x))/3 + cos(x)^3/9 + (2*x*sin(x))/3 + (x*cos(x)^2*sin(x))/3","B"
102,0,-1,2,0.000000,"\text{Not used}","int(sin(x)/x,x)","\mathrm{sinint}\left(x\right)","Not used",1,"sinint(x)","F"
103,0,-1,2,0.000000,"\text{Not used}","int(cos(x)/x,x)","\mathrm{cosint}\left(x\right)","Not used",1,"cosint(x)","F"
104,0,-1,10,0.000000,"\text{Not used}","int(sin(x)/x^2,x)","\mathrm{cosint}\left(x\right)-\frac{\sin\left(x\right)}{x}","Not used",1,"cosint(x) - sin(x)/x","F"
105,0,-1,15,0.000000,"\text{Not used}","int(sin(x)^2/x,x)","\frac{\ln\left(x\right)}{2}-\frac{\mathrm{cosint}\left(2\,x\right)}{2}","Not used",1,"log(x)/2 - cosint(2*x)/2","F"
106,1,16,12,0.020910,"\text{Not used}","int(tan(x)^3,x)","\ln\left(\cos\left(x\right)\right)-\frac{{\cos\left(x\right)}^2-1}{2\,{\cos\left(x\right)}^2}","Not used",1,"log(cos(x)) - (cos(x)^2 - 1)/(2*cos(x)^2)","B"
107,1,11,11,0.021463,"\text{Not used}","int(sin(a + b*x),x)","-\frac{\cos\left(a+b\,x\right)}{b}","Not used",1,"-cos(a + b*x)/b","B"
108,1,10,10,0.021904,"\text{Not used}","int(cos(a + b*x),x)","\frac{\sin\left(a+b\,x\right)}{b}","Not used",1,"sin(a + b*x)/b","B"
109,1,16,12,0.233701,"\text{Not used}","int(tan(a + b*x),x)","\frac{\ln\left({\mathrm{tan}\left(a+b\,x\right)}^2+1\right)}{2\,b}","Not used",1,"log(tan(a + b*x)^2 + 1)/(2*b)","B"
110,1,28,11,0.189743,"\text{Not used}","int(1/tan(a + b*x),x)","\frac{\ln\left(\mathrm{tan}\left(a+b\,x\right)\right)}{b}-\frac{\ln\left({\mathrm{tan}\left(a+b\,x\right)}^2+1\right)}{2\,b}","Not used",1,"log(tan(a + b*x))/b - log(tan(a + b*x)^2 + 1)/(2*b)","B"
111,1,12,12,0.116911,"\text{Not used}","int(1/sin(a + b*x),x)","-\frac{\mathrm{atanh}\left(\cos\left(a+b\,x\right)\right)}{b}","Not used",1,"-atanh(cos(a + b*x))/b","B"
112,1,11,11,0.023606,"\text{Not used}","int(1/cos(a + b*x),x)","\frac{\mathrm{atanh}\left(\sin\left(a+b\,x\right)\right)}{b}","Not used",1,"atanh(sin(a + b*x))/b","B"
113,1,18,25,0.208740,"\text{Not used}","int(sin(a + b*x)^2,x)","\frac{x}{2}-\frac{\sin\left(2\,a+2\,b\,x\right)}{4\,b}","Not used",1,"x/2 - sin(2*a + 2*b*x)/(4*b)","B"
114,1,24,27,0.147045,"\text{Not used}","int(sin(a + b*x)^3,x)","-\frac{3\,\cos\left(a+b\,x\right)-{\cos\left(a+b\,x\right)}^3}{3\,b}","Not used",1,"-(3*cos(a + b*x) - cos(a + b*x)^3)/(3*b)","B"
115,1,18,25,0.176962,"\text{Not used}","int(cos(a + b*x)^2,x)","\frac{x}{2}+\frac{\sin\left(2\,a+2\,b\,x\right)}{4\,b}","Not used",1,"x/2 + sin(2*a + 2*b*x)/(4*b)","B"
116,1,24,26,0.025445,"\text{Not used}","int(cos(a + b*x)^3,x)","\frac{3\,\sin\left(a+b\,x\right)-{\sin\left(a+b\,x\right)}^3}{3\,b}","Not used",1,"(3*sin(a + b*x) - sin(a + b*x)^3)/(3*b)","B"
117,1,10,10,0.144548,"\text{Not used}","int(1/cos(a + b*x)^2,x)","\frac{\mathrm{tan}\left(a+b\,x\right)}{b}","Not used",1,"tan(a + b*x)/b","B"
118,1,4,9,0.171145,"\text{Not used}","int(1/(cos(x) + 1),x)","\mathrm{tan}\left(\frac{x}{2}\right)","Not used",1,"tan(x/2)","B"
119,1,6,12,0.165543,"\text{Not used}","int(-1/(cos(x) - 1),x)","-\mathrm{cot}\left(\frac{x}{2}\right)","Not used",1,"-cot(x/2)","B"
120,1,10,10,0.024385,"\text{Not used}","int(1/(sin(x) + 1),x)","-\frac{2}{\mathrm{tan}\left(\frac{x}{2}\right)+1}","Not used",1,"-2/(tan(x/2) + 1)","B"
121,1,10,11,0.034236,"\text{Not used}","int(-1/(sin(x) - 1),x)","-\frac{2}{\mathrm{tan}\left(\frac{x}{2}\right)-1}","Not used",1,"-2/(tan(x/2) - 1)","B"
122,1,45,40,0.383418,"\text{Not used}","int(1/(a + b*sin(x)),x)","\frac{2\,\mathrm{atan}\left(\frac{b}{\sqrt{a^2-b^2}}+\frac{a\,\mathrm{tan}\left(\frac{x}{2}\right)}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}","Not used",1,"(2*atan(b/(a^2 - b^2)^(1/2) + (a*tan(x/2))/(a^2 - b^2)^(1/2)))/(a^2 - b^2)^(1/2)","B"
123,1,58,47,0.259545,"\text{Not used}","int(1/(a + cos(x) + b*sin(x)),x)","\left\{\begin{array}{cl} \frac{\ln\left(b\,\mathrm{tan}\left(\frac{x}{2}\right)+1\right)}{b} & \text{\ if\ \ }a=1\\ \frac{2\,\mathrm{atan}\left(\frac{b+\mathrm{tan}\left(\frac{x}{2}\right)\,\left(a-1\right)}{\sqrt{a^2-b^2-1}}\right)}{\sqrt{a^2-b^2-1}} & \text{\ if\ \ }a\neq 1 \end{array}\right.","Not used",1,"piecewise(a == 1, log(b*tan(x/2) + 1)/b, a ~= 1, (2*atan((b + tan(x/2)*(a - 1))/(a^2 - b^2 - 1)^(1/2)))/(a^2 - b^2 - 1)^(1/2))","B"
124,1,52,73,0.137412,"\text{Not used}","int(x^2*sin(a + b*x)^2,x)","\frac{x^3}{6}+\frac{\sin\left(2\,a+2\,b\,x\right)}{8\,b^3}-\frac{x\,\cos\left(2\,a+2\,b\,x\right)}{4\,b^2}-\frac{x^2\,\sin\left(2\,a+2\,b\,x\right)}{4\,b}","Not used",1,"x^3/6 + sin(2*a + 2*b*x)/(8*b^3) - (x*cos(2*a + 2*b*x))/(4*b^2) - (x^2*sin(2*a + 2*b*x))/(4*b)","B"
125,1,9,15,0.025277,"\text{Not used}","int(cos(2*x)*cos(x),x)","\sin\left(x\right)-\frac{2\,{\sin\left(x\right)}^3}{3}","Not used",1,"sin(x) - (2*sin(x)^3)/3","B"
126,1,52,73,0.102509,"\text{Not used}","int(x^2*cos(a + b*x)^2,x)","\frac{x^3}{6}-\frac{\sin\left(2\,a+2\,b\,x\right)}{8\,b^3}+\frac{x\,\cos\left(2\,a+2\,b\,x\right)}{4\,b^2}+\frac{x^2\,\sin\left(2\,a+2\,b\,x\right)}{4\,b}","Not used",1,"x^3/6 - sin(2*a + 2*b*x)/(8*b^3) + (x*cos(2*a + 2*b*x))/(4*b^2) + (x^2*sin(2*a + 2*b*x))/(4*b)","B"
127,1,21,14,0.167560,"\text{Not used}","int(1/tan(x)^3,x)","\frac{\ln\left({\mathrm{tan}\left(x\right)}^2+1\right)}{2}-\ln\left(\mathrm{tan}\left(x\right)\right)-\frac{1}{2\,{\mathrm{tan}\left(x\right)}^2}","Not used",1,"log(tan(x)^2 + 1)/2 - log(tan(x)) - 1/(2*tan(x)^2)","B"
128,0,-1,104,0.000000,"\text{Not used}","int(x^3*tan(x)^4,x)","\int x^3\,{\mathrm{tan}\left(x\right)}^4 \,d x","Not used",1,"int(x^3*tan(x)^4, x)","F"
129,0,-1,153,0.000000,"\text{Not used}","int(x^3*tan(x)^6,x)","\int x^3\,{\mathrm{tan}\left(x\right)}^6 \,d x","Not used",1,"int(x^3*tan(x)^6, x)","F"
130,1,13,15,0.022277,"\text{Not used}","int(x*tan(x)^2,x)","\ln\left(\cos\left(x\right)\right)+x\,\mathrm{tan}\left(x\right)-\frac{x^2}{2}","Not used",1,"log(cos(x)) + x*tan(x) - x^2/2","B"
131,1,13,15,0.043748,"\text{Not used}","int(cos(3*x)*sin(2*x),x)","2\,{\cos\left(x\right)}^3-\frac{8\,{\cos\left(x\right)}^5}{5}","Not used",1,"2*cos(x)^3 - (8*cos(x)^5)/5","B"
132,1,18,24,0.044203,"\text{Not used}","int(cos(x)^2*sin(x)^2,x)","\frac{\cos\left(x\right)\,{\sin\left(x\right)}^3}{4}-\frac{\cos\left(x\right)\,\sin\left(x\right)}{8}+\frac{x}{8}","Not used",1,"x/8 - (cos(x)*sin(x))/8 + (cos(x)*sin(x)^3)/4","B"
133,1,6,7,0.063618,"\text{Not used}","int(1/(cos(x)^2*sin(x)^2),x)","-2\,\mathrm{cot}\left(2\,x\right)","Not used",1,"-2*cot(2*x)","B"
134,1,22,32,0.023605,"\text{Not used}","int(d^x*sin(x),x)","-\frac{d^x\,\left(\cos\left(x\right)-\ln\left(d\right)\,\sin\left(x\right)\right)}{{\ln\left(d\right)}^2+1}","Not used",1,"-(d^x*(cos(x) - log(d)*sin(x)))/(log(d)^2 + 1)","B"
135,1,20,31,0.017426,"\text{Not used}","int(d^x*cos(x),x)","\frac{d^x\,\left(\sin\left(x\right)+\ln\left(d\right)\,\cos\left(x\right)\right)}{{\ln\left(d\right)}^2+1}","Not used",1,"(d^x*(sin(x) + log(d)*cos(x)))/(log(d)^2 + 1)","B"
136,1,57,84,0.284708,"\text{Not used}","int(d^x*x*sin(x),x)","\frac{d^x\,\left(\sin\left(x\right)+2\,\ln\left(d\right)\,\cos\left(x\right)-{\ln\left(d\right)}^2\,\sin\left(x\right)-x\,\cos\left(x\right)+x\,\ln\left(d\right)\,\sin\left(x\right)-x\,{\ln\left(d\right)}^2\,\cos\left(x\right)+x\,{\ln\left(d\right)}^3\,\sin\left(x\right)\right)}{{\left({\ln\left(d\right)}^2+1\right)}^2}","Not used",1,"(d^x*(sin(x) + 2*log(d)*cos(x) - log(d)^2*sin(x) - x*cos(x) + x*log(d)*sin(x) - x*log(d)^2*cos(x) + x*log(d)^3*sin(x)))/(log(d)^2 + 1)^2","B"
137,1,55,83,0.213358,"\text{Not used}","int(d^x*x*cos(x),x)","\frac{d^x\,\left(\cos\left(x\right)-2\,\ln\left(d\right)\,\sin\left(x\right)-{\ln\left(d\right)}^2\,\cos\left(x\right)+x\,\sin\left(x\right)+x\,\ln\left(d\right)\,\cos\left(x\right)+x\,{\ln\left(d\right)}^3\,\cos\left(x\right)+x\,{\ln\left(d\right)}^2\,\sin\left(x\right)\right)}{{\left({\ln\left(d\right)}^2+1\right)}^2}","Not used",1,"(d^x*(cos(x) - 2*log(d)*sin(x) - log(d)^2*cos(x) + x*sin(x) + x*log(d)*cos(x) + x*log(d)^3*cos(x) + x*log(d)^2*sin(x)))/(log(d)^2 + 1)^2","B"
138,1,133,162,0.392273,"\text{Not used}","int(d^x*x^2*sin(x),x)","\frac{d^x\,\left(2\,\cos\left(x\right)-x^2\,\cos\left(x\right)+2\,x\,\sin\left(x\right)\right)+d^x\,{\ln\left(d\right)}^3\,\left(2\,\sin\left(x\right)+2\,x^2\,\sin\left(x\right)+4\,x\,\cos\left(x\right)\right)-d^x\,{\ln\left(d\right)}^2\,\left(6\,\cos\left(x\right)+2\,x^2\,\cos\left(x\right)\right)+d^x\,\ln\left(d\right)\,\left(x^2\,\sin\left(x\right)-6\,\sin\left(x\right)+4\,x\,\cos\left(x\right)\right)-d^x\,{\ln\left(d\right)}^4\,\left(x^2\,\cos\left(x\right)+2\,x\,\sin\left(x\right)\right)+d^x\,x^2\,{\ln\left(d\right)}^5\,\sin\left(x\right)}{{\left({\ln\left(d\right)}^2+1\right)}^3}","Not used",1,"(d^x*(2*cos(x) - x^2*cos(x) + 2*x*sin(x)) + d^x*log(d)^3*(2*sin(x) + 2*x^2*sin(x) + 4*x*cos(x)) - d^x*log(d)^2*(6*cos(x) + 2*x^2*cos(x)) + d^x*log(d)*(x^2*sin(x) - 6*sin(x) + 4*x*cos(x)) - d^x*log(d)^4*(x^2*cos(x) + 2*x*sin(x)) + d^x*x^2*log(d)^5*sin(x))/(log(d)^2 + 1)^3","B"
139,1,132,161,0.348365,"\text{Not used}","int(d^x*x^2*cos(x),x)","\frac{d^x\,\left(x^2\,\sin\left(x\right)-2\,\sin\left(x\right)+2\,x\,\cos\left(x\right)\right)+d^x\,{\ln\left(d\right)}^3\,\left(2\,\cos\left(x\right)+2\,x^2\,\cos\left(x\right)-4\,x\,\sin\left(x\right)\right)+d^x\,{\ln\left(d\right)}^2\,\left(6\,\sin\left(x\right)+2\,x^2\,\sin\left(x\right)\right)-d^x\,\ln\left(d\right)\,\left(6\,\cos\left(x\right)-x^2\,\cos\left(x\right)+4\,x\,\sin\left(x\right)\right)+d^x\,{\ln\left(d\right)}^4\,\left(x^2\,\sin\left(x\right)-2\,x\,\cos\left(x\right)\right)+d^x\,x^2\,{\ln\left(d\right)}^5\,\cos\left(x\right)}{{\left({\ln\left(d\right)}^2+1\right)}^3}","Not used",1,"(d^x*(x^2*sin(x) - 2*sin(x) + 2*x*cos(x)) + d^x*log(d)^3*(2*cos(x) + 2*x^2*cos(x) - 4*x*sin(x)) + d^x*log(d)^2*(6*sin(x) + 2*x^2*sin(x)) - d^x*log(d)*(6*cos(x) - x^2*cos(x) + 4*x*sin(x)) + d^x*log(d)^4*(x^2*sin(x) - 2*x*cos(x)) + d^x*x^2*log(d)^5*cos(x))/(log(d)^2 + 1)^3","B"
140,1,231,261,0.626755,"\text{Not used}","int(d^x*x^3*sin(x),x)","-\frac{d^x\,\left(6\,\sin\left(x\right)+x^3\,\cos\left(x\right)-3\,x^2\,\sin\left(x\right)-6\,x\,\cos\left(x\right)\right)-d^x\,{\ln\left(d\right)}^5\,\left(6\,x^2\,\cos\left(x\right)+3\,x^3\,\sin\left(x\right)+6\,x\,\sin\left(x\right)\right)+d^x\,{\ln\left(d\right)}^4\,\left(6\,\sin\left(x\right)+3\,x^3\,\cos\left(x\right)+3\,x^2\,\sin\left(x\right)+18\,x\,\cos\left(x\right)\right)-d^x\,{\ln\left(d\right)}^3\,\left(24\,\cos\left(x\right)+12\,x^2\,\cos\left(x\right)+3\,x^3\,\sin\left(x\right)-12\,x\,\sin\left(x\right)\right)-d^x\,{\ln\left(d\right)}^2\,\left(36\,\sin\left(x\right)-3\,x^3\,\cos\left(x\right)+3\,x^2\,\sin\left(x\right)-12\,x\,\cos\left(x\right)\right)+d^x\,{\ln\left(d\right)}^6\,\left(x^3\,\cos\left(x\right)+3\,x^2\,\sin\left(x\right)\right)+d^x\,\ln\left(d\right)\,\left(24\,\cos\left(x\right)-6\,x^2\,\cos\left(x\right)-x^3\,\sin\left(x\right)+18\,x\,\sin\left(x\right)\right)-d^x\,x^3\,{\ln\left(d\right)}^7\,\sin\left(x\right)}{{\left({\ln\left(d\right)}^2+1\right)}^4}","Not used",1,"-(d^x*(6*sin(x) + x^3*cos(x) - 3*x^2*sin(x) - 6*x*cos(x)) - d^x*log(d)^5*(6*x^2*cos(x) + 3*x^3*sin(x) + 6*x*sin(x)) + d^x*log(d)^4*(6*sin(x) + 3*x^3*cos(x) + 3*x^2*sin(x) + 18*x*cos(x)) - d^x*log(d)^3*(24*cos(x) + 12*x^2*cos(x) + 3*x^3*sin(x) - 12*x*sin(x)) - d^x*log(d)^2*(36*sin(x) - 3*x^3*cos(x) + 3*x^2*sin(x) - 12*x*cos(x)) + d^x*log(d)^6*(x^3*cos(x) + 3*x^2*sin(x)) + d^x*log(d)*(24*cos(x) - 6*x^2*cos(x) - x^3*sin(x) + 18*x*sin(x)) - d^x*x^3*log(d)^7*sin(x))/(log(d)^2 + 1)^4","B"
141,1,232,260,0.640023,"\text{Not used}","int(d^x*x^3*cos(x),x)","-\frac{d^x\,\left(6\,\cos\left(x\right)-3\,x^2\,\cos\left(x\right)-x^3\,\sin\left(x\right)+6\,x\,\sin\left(x\right)\right)-d^x\,{\ln\left(d\right)}^5\,\left(3\,x^3\,\cos\left(x\right)-6\,x^2\,\sin\left(x\right)+6\,x\,\cos\left(x\right)\right)+d^x\,{\ln\left(d\right)}^4\,\left(6\,\cos\left(x\right)+3\,x^2\,\cos\left(x\right)-3\,x^3\,\sin\left(x\right)-18\,x\,\sin\left(x\right)\right)+d^x\,{\ln\left(d\right)}^3\,\left(24\,\sin\left(x\right)-3\,x^3\,\cos\left(x\right)+12\,x^2\,\sin\left(x\right)+12\,x\,\cos\left(x\right)\right)-d^x\,{\ln\left(d\right)}^2\,\left(36\,\cos\left(x\right)+3\,x^2\,\cos\left(x\right)+3\,x^3\,\sin\left(x\right)+12\,x\,\sin\left(x\right)\right)+d^x\,{\ln\left(d\right)}^6\,\left(3\,x^2\,\cos\left(x\right)-x^3\,\sin\left(x\right)\right)-d^x\,\ln\left(d\right)\,\left(24\,\sin\left(x\right)+x^3\,\cos\left(x\right)-6\,x^2\,\sin\left(x\right)-18\,x\,\cos\left(x\right)\right)-d^x\,x^3\,{\ln\left(d\right)}^7\,\cos\left(x\right)}{{\left({\ln\left(d\right)}^2+1\right)}^4}","Not used",1,"-(d^x*(6*cos(x) - 3*x^2*cos(x) - x^3*sin(x) + 6*x*sin(x)) - d^x*log(d)^5*(3*x^3*cos(x) - 6*x^2*sin(x) + 6*x*cos(x)) + d^x*log(d)^4*(6*cos(x) + 3*x^2*cos(x) - 3*x^3*sin(x) - 18*x*sin(x)) + d^x*log(d)^3*(24*sin(x) - 3*x^3*cos(x) + 12*x^2*sin(x) + 12*x*cos(x)) - d^x*log(d)^2*(36*cos(x) + 3*x^2*cos(x) + 3*x^3*sin(x) + 12*x*sin(x)) + d^x*log(d)^6*(3*x^2*cos(x) - x^3*sin(x)) - d^x*log(d)*(24*sin(x) + x^3*cos(x) - 6*x^2*sin(x) - 18*x*cos(x)) - d^x*x^3*log(d)^7*cos(x))/(log(d)^2 + 1)^4","B"
142,1,14,25,0.166394,"\text{Not used}","int(sin(2*x)*sin(3*x)*sin(x),x)","-\frac{{\sin\left(x\right)}^4\,\left(8\,{\sin\left(x\right)}^2-9\right)}{6}","Not used",1,"-(sin(x)^4*(8*sin(x)^2 - 9))/6","B"
143,1,22,30,0.275730,"\text{Not used}","int(cos(2*x)*cos(3*x)*cos(x),x)","\frac{x}{4}+\frac{\sin\left(2\,x\right)}{8}+\frac{\sin\left(4\,x\right)}{16}+\frac{\sin\left(6\,x\right)}{24}","Not used",1,"x/4 + sin(2*x)/8 + sin(4*x)/16 + sin(6*x)/24","B"
144,1,67,85,0.230124,"\text{Not used}","int(x^2*sin(k*x)^3,x)","\frac{\frac{14\,\cos\left(k\,x\right)}{9}-\frac{2\,{\cos\left(k\,x\right)}^3}{27}+k\,\left(\frac{14\,x\,\sin\left(k\,x\right)}{9}-\frac{2\,x\,{\cos\left(k\,x\right)}^2\,\sin\left(k\,x\right)}{9}\right)+k^2\,\left(\frac{x^2\,{\cos\left(k\,x\right)}^3}{3}-x^2\,\cos\left(k\,x\right)\right)}{k^3}","Not used",1,"((14*cos(k*x))/9 - (2*cos(k*x)^3)/27 + k*((14*x*sin(k*x))/9 - (2*x*cos(k*x)^2*sin(k*x))/9) + k^2*((x^2*cos(k*x)^3)/3 - x^2*cos(k*x)))/k^3","B"
145,0,-1,14,0.000000,"\text{Not used}","int((x*cos(k/sin(x))*cos(x))/sin(x)^2,x)","\int \frac{x\,\cos\left(\frac{k}{\sin\left(x\right)}\right)\,\cos\left(x\right)}{{\sin\left(x\right)}^2} \,d x","Not used",0,"int((x*cos(k/sin(x))*cos(x))/sin(x)^2, x)","F"
146,1,10,12,0.175398,"\text{Not used}","int(cos(x)/(tan(x/2)*sin(x)),x)","-x-\mathrm{cot}\left(\frac{x}{2}\right)","Not used",1,"- x - cot(x/2)","B"
147,1,133,77,0.485061,"\text{Not used}","int(sin(a*x)/(b + c*sin(a*x))^2,x)","-\frac{\frac{2\,b}{b^2-c^2}+\frac{2\,c\,\mathrm{tan}\left(\frac{a\,x}{2}\right)}{b^2-c^2}}{a\,\left(b\,{\mathrm{tan}\left(\frac{a\,x}{2}\right)}^2+2\,c\,\mathrm{tan}\left(\frac{a\,x}{2}\right)+b\right)}-\frac{2\,c\,\mathrm{atan}\left(\frac{\left(\frac{2\,c^2}{{\left(b+c\right)}^{3/2}\,{\left(b-c\right)}^{3/2}}+\frac{2\,b\,c\,\mathrm{tan}\left(\frac{a\,x}{2}\right)}{{\left(b+c\right)}^{3/2}\,{\left(b-c\right)}^{3/2}}\right)\,\left(b^2-c^2\right)}{2\,c}\right)}{a\,{\left(b+c\right)}^{3/2}\,{\left(b-c\right)}^{3/2}}","Not used",1,"- ((2*b)/(b^2 - c^2) + (2*c*tan((a*x)/2))/(b^2 - c^2))/(a*(b + 2*c*tan((a*x)/2) + b*tan((a*x)/2)^2)) - (2*c*atan((((2*c^2)/((b + c)^(3/2)*(b - c)^(3/2)) + (2*b*c*tan((a*x)/2))/((b + c)^(3/2)*(b - c)^(3/2)))*(b^2 - c^2))/(2*c)))/(a*(b + c)^(3/2)*(b - c)^(3/2))","B"
148,1,13,17,0.133086,"\text{Not used}","int(sin(log(x)),x)","-\frac{\sqrt{2}\,x\,\cos\left(\frac{\pi }{4}+\ln\left(x\right)\right)}{2}","Not used",1,"-(2^(1/2)*x*cos(pi/4 + log(x)))/2","B"
149,1,13,17,0.148204,"\text{Not used}","int(cos(log(x)),x)","\frac{\sqrt{2}\,x\,\sin\left(\frac{\pi }{4}+\ln\left(x\right)\right)}{2}","Not used",1,"(2^(1/2)*x*sin(pi/4 + log(x)))/2","B"
150,1,2,3,0.007234,"\text{Not used}","int(exp(x),x)","{\mathrm{e}}^x","Not used",1,"exp(x)","B"
151,1,8,8,0.155256,"\text{Not used}","int(a^x,x)","\frac{a^x}{\ln\left(a\right)}","Not used",1,"a^x/log(a)","B"
152,1,8,9,0.027291,"\text{Not used}","int(exp(a*x),x)","\frac{{\mathrm{e}}^{a\,x}}{a}","Not used",1,"exp(a*x)/a","B"
153,1,4,4,0.013779,"\text{Not used}","int(exp(a*x)/x,x)","\mathrm{ei}\left(a\,x\right)","Not used",1,"ei(a*x)","B"
154,1,22,24,0.093116,"\text{Not used}","int(1/(a + b*exp(m*x)),x)","-\frac{\ln\left(a+b\,{\mathrm{e}}^{m\,x}\right)-m\,x}{a\,m}","Not used",1,"-(log(a + b*exp(m*x)) - m*x)/(a*m)","B"
155,1,10,12,0.044823,"\text{Not used}","int(exp(2*x)/(exp(x) + 1),x)","{\mathrm{e}}^x-\ln\left({\mathrm{e}}^x+1\right)","Not used",1,"exp(x) - log(exp(x) + 1)","B"
156,1,14,13,0.052135,"\text{Not used}","int(exp(2*x + a*x),x)","\frac{{\mathrm{e}}^{2\,x+a\,x}}{a+2}","Not used",1,"exp(2*x + a*x)/(a + 2)","B"
157,1,21,31,0.227774,"\text{Not used}","int(1/(a*exp(m*x) + b*exp(-m*x)),x)","\frac{\mathrm{atan}\left(\frac{a\,{\mathrm{e}}^{m\,x}}{\sqrt{a\,b}}\right)}{m\,\sqrt{a\,b}}","Not used",1,"atan((a*exp(m*x))/(a*b)^(1/2))/(m*(a*b)^(1/2))","B"
158,1,13,21,0.026750,"\text{Not used}","int(x*exp(a*x),x)","\frac{{\mathrm{e}}^{a\,x}\,\left(a\,x-1\right)}{a^2}","Not used",1,"(exp(a*x)*(a*x - 1))/a^2","B"
159,1,101,163,0.362407,"\text{Not used}","int(x^20*exp(x),x)","{\mathrm{e}}^x\,\left(x^{20}-20\,x^{19}+380\,x^{18}-6840\,x^{17}+116280\,x^{16}-1860480\,x^{15}+27907200\,x^{14}-390700800\,x^{13}+5079110400\,x^{12}-60949324800\,x^{11}+670442572800\,x^{10}-6704425728000\,x^9+60339831552000\,x^8-482718652416000\,x^7+3379030566912000\,x^6-20274183401472000\,x^5+101370917007360000\,x^4-405483668029440000\,x^3+1216451004088320000\,x^2-2432902008176640000\,x+2432902008176640000\right)","Not used",1,"exp(x)*(1216451004088320000*x^2 - 2432902008176640000*x - 405483668029440000*x^3 + 101370917007360000*x^4 - 20274183401472000*x^5 + 3379030566912000*x^6 - 482718652416000*x^7 + 60339831552000*x^8 - 6704425728000*x^9 + 670442572800*x^10 - 60949324800*x^11 + 5079110400*x^12 - 390700800*x^13 + 27907200*x^14 - 1860480*x^15 + 116280*x^16 - 6840*x^17 + 380*x^18 - 20*x^19 + x^20 + 2432902008176640000)","B"
160,1,18,18,0.203787,"\text{Not used}","int(a^x/b^x,x)","\frac{a^x}{b^x\,\left(\ln\left(a\right)-\ln\left(b\right)\right)}","Not used",1,"a^x/(b^x*(log(a) - log(b)))","B"
161,1,14,14,0.166726,"\text{Not used}","int(a^x*b^x,x)","\frac{a^x\,b^x}{\ln\left(a\right)+\ln\left(b\right)}","Not used",1,"(a^x*b^x)/(log(a) + log(b))","B"
162,1,19,17,0.130529,"\text{Not used}","int(a^x/x^2,x)","-\ln\left(a\right)\,\mathrm{expint}\left(-x\,\ln\left(a\right)\right)-\frac{a^x}{x}","Not used",1,"- log(a)*expint(-x*log(a)) - a^x/x","B"
163,0,-1,64,0.000000,"\text{Not used}","int((a^x*x)/(b*x + 1)^2,x)","\int \frac{a^x\,x}{{\left(b\,x+1\right)}^2} \,d x","Not used",1,"int((a^x*x)/(b*x + 1)^2, x)","F"
164,1,15,16,0.195814,"\text{Not used}","int((x*exp(a*x))/(a*x + 1)^2,x)","\frac{{\mathrm{e}}^{a\,x}}{a^2\,\left(a\,x+1\right)}","Not used",1,"exp(a*x)/(a^2*(a*x + 1))","B"
165,1,11,13,0.026451,"\text{Not used}","int(k^(x^2)*x,x)","\frac{k^{x^2}}{2\,\ln\left(k\right)}","Not used",1,"k^(x^2)/(2*log(k))","B"
166,1,7,11,0.016557,"\text{Not used}","int(exp(x^2),x)","\frac{\sqrt{\pi }\,\mathrm{erfi}\left(x\right)}{2}","Not used",1,"(pi^(1/2)*erfi(x))/2","B"
167,1,6,9,0.018255,"\text{Not used}","int(x*exp(x^2),x)","\frac{{\mathrm{e}}^{x^2}}{2}","Not used",1,"exp(x^2)/2","B"
168,1,17,27,0.157958,"\text{Not used}","int((exp(1/x)*(x + 1))/x^4,x)","-\frac{{\mathrm{e}}^{1/x}\,\left(x^2-x+1\right)}{x^2}","Not used",1,"-(exp(1/x)*(x^2 - x + 1))/x^2","B"
169,0,-1,25,0.000000,"\text{Not used}","int((exp(2*x^2 - x*exp(x^2) + 1)*(x + 2*x^3))/(x*exp(x^2) - 1)^2,x)","\int \frac{{\mathrm{e}}^{2\,x^2-x\,{\mathrm{e}}^{x^2}+1}\,\left(2\,x^3+x\right)}{{\left(x\,{\mathrm{e}}^{x^2}-1\right)}^2} \,d x","Not used",1,"int((exp(2*x^2 - x*exp(x^2) + 1)*(x + 2*x^3))/(x*exp(x^2) - 1)^2, x)","F"
170,0,-1,12,0.000000,"\text{Not used}","int(exp(exp(exp(exp(x)))),x)","\int {\mathrm{e}}^{{\mathrm{e}}^{{\mathrm{e}}^{{\mathrm{e}}^x}}} \,d x","Not used",0,"int(exp(exp(exp(exp(x)))), x)","F"
171,1,10,11,0.026305,"\text{Not used}","int(exp(x)*log(x),x)","{\mathrm{e}}^x\,\ln\left(x\right)-\mathrm{ei}\left(x\right)","Not used",1,"exp(x)*log(x) - ei(x)","B"
172,1,28,22,0.219265,"\text{Not used}","int(x*exp(x)*log(x),x)","\mathrm{ei}\left(x\right)-\frac{x\,{\mathrm{e}}^x+x\,{\mathrm{e}}^x\,\ln\left(x\right)-x^2\,{\mathrm{e}}^x\,\ln\left(x\right)}{x}","Not used",1,"ei(x) - (x*exp(x) + x*exp(x)*log(x) - x^2*exp(x)*log(x))/x","B"
173,1,11,23,0.041604,"\text{Not used}","int(log(exp(x))*exp(2*x),x)","\frac{{\mathrm{e}}^{2\,x}\,\left(2\,x-1\right)}{4}","Not used",1,"(exp(2*x)*(2*x - 1))/4","B"
174,1,12,16,0.030010,"\text{Not used}","int(2*x + 2^(1/2)*x^2,x)","\frac{x^2\,\left(\sqrt{2}\,x+3\right)}{3}","Not used",1,"(x^2*(2^(1/2)*x + 3))/3","B"
175,1,49,57,0.094235,"\text{Not used}","int(log(x)/(b + a*x)^(1/2),x)","\frac{2\,\sqrt{b}\,\ln\left(\frac{2\,b+a\,x+2\,\sqrt{b}\,\sqrt{b+a\,x}}{x}\right)}{a}+\frac{2\,\left(\ln\left(x\right)-2\right)\,\sqrt{b+a\,x}}{a}","Not used",1,"(2*b^(1/2)*log((2*b + a*x + 2*b^(1/2)*(b + a*x)^(1/2))/x))/a + (2*(log(x) - 2)*(b + a*x)^(1/2))/a","B"
176,1,88,116,0.169328,"\text{Not used}","int((a + b*x)^(1/2)*(c + d*x)^(1/2),x)","\left(\frac{x}{2}+\frac{a\,d+b\,c}{4\,b\,d}\right)\,\sqrt{a+b\,x}\,\sqrt{c+d\,x}-\frac{\ln\left(a\,d+b\,c+2\,b\,d\,x+2\,\sqrt{b}\,\sqrt{d}\,\sqrt{a+b\,x}\,\sqrt{c+d\,x}\right)\,{\left(a\,d-b\,c\right)}^2}{8\,b^{3/2}\,d^{3/2}}","Not used",1,"(x/2 + (a*d + b*c)/(4*b*d))*(a + b*x)^(1/2)*(c + d*x)^(1/2) - (log(a*d + b*c + 2*b*d*x + 2*b^(1/2)*d^(1/2)*(a + b*x)^(1/2)*(c + d*x)^(1/2))*(a*d - b*c)^2)/(8*b^(3/2)*d^(3/2))","B"
177,1,12,16,0.025100,"\text{Not used}","int((a + b*x)^(1/2),x)","\frac{2\,{\left(a+b\,x\right)}^{3/2}}{3\,b}","Not used",1,"(2*(a + b*x)^(3/2))/(3*b)","B"
178,1,25,34,0.029611,"\text{Not used}","int(x*(a + b*x)^(1/2),x)","-\frac{10\,a\,{\left(a+b\,x\right)}^{3/2}-6\,{\left(a+b\,x\right)}^{5/2}}{15\,b^2}","Not used",1,"-(10*a*(a + b*x)^(3/2) - 6*(a + b*x)^(5/2))/(15*b^2)","B"
179,1,37,53,0.148210,"\text{Not used}","int(x^2*(a + b*x)^(1/2),x)","\frac{30\,{\left(a+b\,x\right)}^{7/2}-84\,a\,{\left(a+b\,x\right)}^{5/2}+70\,a^2\,{\left(a+b\,x\right)}^{3/2}}{105\,b^3}","Not used",1,"(30*(a + b*x)^(7/2) - 84*a*(a + b*x)^(5/2) + 70*a^2*(a + b*x)^(3/2))/(105*b^3)","B"
180,1,27,35,0.145970,"\text{Not used}","int((a + b*x)^(1/2)/x,x)","2\,\sqrt{a+b\,x}-2\,\sqrt{a}\,\mathrm{atanh}\left(\frac{\sqrt{a+b\,x}}{\sqrt{a}}\right)","Not used",1,"2*(a + b*x)^(1/2) - 2*a^(1/2)*atanh((a + b*x)^(1/2)/a^(1/2))","B"
181,1,31,39,0.053911,"\text{Not used}","int((a + b*x)^(1/2)/x^2,x)","-\frac{\sqrt{a+b\,x}}{x}-\frac{b\,\mathrm{atanh}\left(\frac{\sqrt{a+b\,x}}{\sqrt{a}}\right)}{\sqrt{a}}","Not used",1,"- (a + b*x)^(1/2)/x - (b*atanh((a + b*x)^(1/2)/a^(1/2)))/a^(1/2)","B"
182,1,12,14,0.018004,"\text{Not used}","int(1/(a + b*x)^(1/2),x)","\frac{2\,\sqrt{a+b\,x}}{b}","Not used",1,"(2*(a + b*x)^(1/2))/b","B"
183,1,25,32,0.028744,"\text{Not used}","int(x/(a + b*x)^(1/2),x)","-\frac{6\,a\,\sqrt{a+b\,x}-2\,{\left(a+b\,x\right)}^{3/2}}{3\,b^2}","Not used",1,"-(6*a*(a + b*x)^(1/2) - 2*(a + b*x)^(3/2))/(3*b^2)","B"
184,1,37,51,0.037562,"\text{Not used}","int(x^2/(a + b*x)^(1/2),x)","\frac{6\,{\left(a+b\,x\right)}^{5/2}-20\,a\,{\left(a+b\,x\right)}^{3/2}+30\,a^2\,\sqrt{a+b\,x}}{15\,b^3}","Not used",1,"(6*(a + b*x)^(5/2) - 20*a*(a + b*x)^(3/2) + 30*a^2*(a + b*x)^(1/2))/(15*b^3)","B"
185,1,17,23,0.143986,"\text{Not used}","int(1/(x*(a + b*x)^(1/2)),x)","-\frac{2\,\mathrm{atanh}\left(\frac{\sqrt{a+b\,x}}{\sqrt{a}}\right)}{\sqrt{a}}","Not used",1,"-(2*atanh((a + b*x)^(1/2)/a^(1/2)))/a^(1/2)","B"
186,1,33,41,0.159485,"\text{Not used}","int(1/(x^2*(a + b*x)^(1/2)),x)","\frac{b\,\mathrm{atanh}\left(\frac{\sqrt{a+b\,x}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{\sqrt{a+b\,x}}{a\,x}","Not used",1,"(b*atanh((a + b*x)^(1/2)/a^(1/2)))/a^(3/2) - (a + b*x)^(1/2)/(a*x)","B"
187,1,21,23,0.250972,"\text{Not used}","int((a + b*x)^(p/2),x)","\frac{2\,{\left(a+b\,x\right)}^{\frac{p}{2}+1}}{b\,\left(p+2\right)}","Not used",1,"(2*(a + b*x)^(p/2 + 1))/(b*(p + 2))","B"
188,1,94,48,0.448415,"\text{Not used}","int(x*(a + b*x)^(p/2),x)","\left\{\begin{array}{cl} -\frac{a\,\ln\left(a+b\,x\right)-b\,x}{b^2} & \text{\ if\ \ }p=-2\\ \frac{\ln\left(a+b\,x\right)+\frac{a}{a+b\,x}}{b^2} & \text{\ if\ \ }p=-4\\ \frac{2\,\left(\frac{{\left(a+b\,x\right)}^{\frac{p}{2}+2}}{p+4}-\frac{a\,{\left(a+b\,x\right)}^{\frac{p}{2}+1}}{p+2}\right)}{b^2} & \text{\ if\ \ }p\neq -2\wedge p\neq -4 \end{array}\right.","Not used",1,"piecewise(p == -2, -(a*log(a + b*x) - b*x)/b^2, p == -4, (log(a + b*x) + a/(a + b*x))/b^2, p ~= -2 & p ~= -4, (2*((a + b*x)^(p/2 + 2)/(p + 4) - (a*(a + b*x)^(p/2 + 1))/(p + 2)))/b^2)","B"
189,1,43,55,0.162191,"\text{Not used}","int(atan((2^(1/2)*(2*x - 2^(1/2)))/2),x)","\mathrm{atan}\left(\frac{\sqrt{2}\,\left(2\,x-\sqrt{2}\right)}{2}\right)\,\left(x-\frac{\sqrt{2}}{2}\right)-\frac{\sqrt{2}\,\ln\left({\left(2\,x-\sqrt{2}\right)}^2+2\right)}{4}","Not used",1,"atan((2^(1/2)*(2*x - 2^(1/2)))/2)*(x - 2^(1/2)/2) - (2^(1/2)*log((2*x - 2^(1/2))^2 + 2))/4","B"
190,1,10,12,0.197429,"\text{Not used}","int(1/(x^2 - 1)^(1/2),x)","\ln\left(x+\sqrt{x^2-1}\right)","Not used",1,"log(x + (x^2 - 1)^(1/2))","B"
191,1,30,43,0.217248,"\text{Not used}","int(x^(1/2)*(x + 1)^(1/2),x)","\sqrt{x}\,\left(\frac{x}{2}+\frac{1}{4}\right)\,\sqrt{x+1}-\frac{\ln\left(x+\sqrt{x}\,\sqrt{x+1}+\frac{1}{2}\right)}{8}","Not used",1,"x^(1/2)*(x/2 + 1/4)*(x + 1)^(1/2) - log(x + x^(1/2)*(x + 1)^(1/2) + 1/2)/8","B"
192,1,16,22,0.245326,"\text{Not used}","int(sin(x^(1/2)),x)","2\,\sin\left(\sqrt{x}\right)-2\,\sqrt{x}\,\cos\left(\sqrt{x}\right)","Not used",1,"2*sin(x^(1/2)) - 2*x^(1/2)*cos(x^(1/2))","B"
193,1,11,13,0.347867,"\text{Not used}","int(x/(1 - x^2)^(9/8),x)","\frac{4}{{\left(1-x^2\right)}^{1/8}}","Not used",1,"4/(1 - x^2)^(1/8)","B"
194,1,16,8,0.312415,"\text{Not used}","int(x/(1 - x^4)^(1/2),x)","\frac{\mathrm{atan}\left(\frac{x^2}{\sqrt{1-x^4}}\right)}{2}","Not used",1,"atan(x^2/(1 - x^4)^(1/2))/2","B"
195,1,10,14,0.186438,"\text{Not used}","int(1/(x*(x^4 + 1)^(1/2)),x)","-\frac{\mathrm{atanh}\left(\sqrt{x^4+1}\right)}{2}","Not used",1,"-atanh((x^4 + 1)^(1/2))/2","B"
196,1,18,18,0.359431,"\text{Not used}","int(x/(x^2 + x^4 + 1)^(1/2),x)","\frac{\ln\left(\sqrt{x^4+x^2+1}+x^2+\frac{1}{2}\right)}{2}","Not used",1,"log((x^2 + x^4 + 1)^(1/2) + x^2 + 1/2)/2","B"
197,1,32,30,0.538113,"\text{Not used}","int(1/(x*(x^2 - x^4 - 1)^(1/2)),x)","\frac{\ln\left(\frac{1}{x^2}\right)\,1{}\mathrm{i}}{2}+\frac{\ln\left(x^2-2+\sqrt{-x^4+x^2-1}\,2{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}","Not used",1,"(log(1/x^2)*1i)/2 + (log((x^2 - x^4 - 1)^(1/2)*2i + x^2 - 2)*1i)/2","B"
198,1,14,17,0.151373,"\text{Not used}","int((x + 1)/((x^2 + 1)^(1/2)*(x - 1)^2),x)","-\frac{\sqrt{x^2+1}}{x-1}","Not used",1,"-(x^2 + 1)^(1/2)/(x - 1)","B"
199,1,2,2,0.028429,"\text{Not used}","int(1/(x^2 + 1)^(1/2),x)","\mathrm{asinh}\left(x\right)","Not used",1,"asinh(x)","B"
200,1,14,20,0.344603,"\text{Not used}","int(((x^(1/2)*(x + 1)^(1/2))/2 + (x^(1/2)*(x + 2)^(1/2))/2 + ((x + 1)^(1/2)*(x + 2)^(1/2))/2)/(x^(1/2)*(x + 1)^(1/2)*(x + 2)^(1/2)),x)","\sqrt{x+1}+\sqrt{x+2}+\sqrt{x}","Not used",1,"(x + 1)^(1/2) + (x + 2)^(1/2) + x^(1/2)","B"
201,1,20,24,0.309577,"\text{Not used}","int(-((x^3 + 1)^(1/2) + (3*x^2*(x^5 - 2*x + 1)^(1/2))/2 - (5*x^4*(x^3 + 1)^(1/2))/2)/((x^3 + 1)^(1/2)*(x^5 - 2*x + 1)^(1/2)),x)","\sqrt{x^5-2\,x+1}-\sqrt{x^3+1}","Not used",1,"(x^5 - 2*x + 1)^(1/2) - (x^3 + 1)^(1/2)","B"
202,1,23,27,0.686731,"\text{Not used}","int(1/(x^2 - 1)^(1/2) + 10/(x^2 - 4)^(1/2),x)","\ln\left(x+\sqrt{x^2-1}\right)+10\,\ln\left(x+\sqrt{x^2-4}\right)","Not used",1,"log(x + (x^2 - 1)^(1/2)) + 10*log(x + (x^2 - 4)^(1/2))","B"
203,0,-1,82,0.000000,"\text{Not used}","int((x + (a^2 + x^2)^(1/2))^(1/2)/x,x)","\int \frac{\sqrt{x+\sqrt{a^2+x^2}}}{x} \,d x","Not used",1,"int((x + (a^2 + x^2)^(1/2))^(1/2)/x, x)","F"
204,1,169,12,0.061492,"\text{Not used}","int((3*x^2)/(2*((x^3 + 1)^(1/2) + x^3 + 1)),x)","\frac{3\,\ln\left(x\right)}{2}+\frac{3\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{\frac{x-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{\frac{1}{2}-x+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2};\mathrm{asin}\left(\sqrt{\frac{x+1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"(3*log(x))/2 + (3*((3^(1/2)*1i)/2 + 3/2)*((x + (3^(1/2)*1i)/2 - 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(((3^(1/2)*1i)/2 - x + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi((3^(1/2)*1i)/2 + 3/2, asin(((x + 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(x^3 - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) - ((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2))^(1/2)","B"
205,1,32,40,0.478738,"\text{Not used}","int(1/(2*h*r^2 - alpha^2)^(1/2),r)","\frac{\sqrt{2}\,\ln\left(\sqrt{2\,h\,r^2-\alpha ^2}+\sqrt{2}\,\sqrt{h}\,r\right)}{2\,\sqrt{h}}","Not used",1,"(2^(1/2)*log((2*h*r^2 - alpha^2)^(1/2) + 2^(1/2)*h^(1/2)*r))/(2*h^(1/2))","B"
206,1,40,46,0.664946,"\text{Not used}","int(1/(r*(2*h*r^2 - alpha^2 - epsilon^2)^(1/2)),r)","\frac{\mathrm{atan}\left(\frac{\sqrt{-\alpha ^2-\epsilon ^2+2\,h\,r^2}}{\sqrt{\alpha ^2+\epsilon ^2}}\right)}{\sqrt{\alpha ^2+\epsilon ^2}}","Not used",1,"atan((2*h*r^2 - alpha^2 - epsilon^2)^(1/2)/(alpha^2 + epsilon^2)^(1/2))/(alpha^2 + epsilon^2)^(1/2)","B"
207,1,51,37,0.104788,"\text{Not used}","int(1/(r*(2*h*r^2 - 2*k*r - alpha^2)^(1/2)),r)","-\frac{\ln\left(\frac{\sqrt{-\alpha ^2}\,\sqrt{-\alpha ^2+2\,h\,r^2-2\,k\,r}}{r}-\frac{\alpha ^2}{r}-k\right)}{\sqrt{-\alpha ^2}}","Not used",1,"-log(((-alpha^2)^(1/2)*(2*h*r^2 - 2*k*r - alpha^2)^(1/2))/r - alpha^2/r - k)/(-alpha^2)^(1/2)","B"
208,1,72,61,0.246381,"\text{Not used}","int(1/(r*(2*h*r^2 - 2*k*r - alpha^2 - epsilon^2)^(1/2)),r)","-\frac{\ln\left(\frac{\sqrt{-\alpha ^2-\epsilon ^2}\,\sqrt{-\alpha ^2-\epsilon ^2+2\,h\,r^2-2\,k\,r}}{r}-\frac{\alpha ^2+\epsilon ^2}{r}-k\right)}{\sqrt{-\alpha ^2-\epsilon ^2}}","Not used",1,"-log(((- alpha^2 - epsilon^2)^(1/2)*(2*h*r^2 - 2*k*r - alpha^2 - epsilon^2)^(1/2))/r - (alpha^2 + epsilon^2)/r - k)/(- alpha^2 - epsilon^2)^(1/2)","B"
209,1,19,23,0.289282,"\text{Not used}","int(r/(2*e*r^2 - alpha^2)^(1/2),r)","\frac{\sqrt{2\,e\,r^2-\alpha ^2}}{2\,e}","Not used",1,"(2*e*r^2 - alpha^2)^(1/2)/(2*e)","B"
210,1,24,28,0.271993,"\text{Not used}","int(r/(2*e*r^2 - alpha^2 - epsilon^2)^(1/2),r)","\frac{\sqrt{-\alpha ^2-\epsilon ^2+2\,e\,r^2}}{2\,e}","Not used",1,"(2*e*r^2 - alpha^2 - epsilon^2)^(1/2)/(2*e)","B"
211,1,50,56,0.978566,"\text{Not used}","int(r/(2*e*r^2 - 2*k*r^4 - alpha^2)^(1/2),r)","\frac{\sqrt{2}\,\ln\left(\sqrt{-\alpha ^2-2\,k\,r^4+2\,e\,r^2}+\frac{\sqrt{2}\,\left(e-2\,k\,r^2\right)}{2\,\sqrt{-k}}\right)}{4\,\sqrt{-k}}","Not used",1,"(2^(1/2)*log((2*e*r^2 - 2*k*r^4 - alpha^2)^(1/2) + (2^(1/2)*(e - 2*k*r^2))/(2*(-k)^(1/2))))/(4*(-k)^(1/2))","B"
212,1,67,81,0.237378,"\text{Not used}","int(r/(2*e*r^2 - 2*k*r - alpha^2)^(1/2),r)","\frac{\sqrt{-\alpha ^2+2\,e\,r^2-2\,k\,r}}{2\,e}+\frac{\sqrt{2}\,k\,\ln\left(\sqrt{-\alpha ^2+2\,e\,r^2-2\,k\,r}-\frac{\sqrt{2}\,\left(k-2\,e\,r\right)}{2\,\sqrt{e}}\right)}{4\,e^{3/2}}","Not used",1,"(2*e*r^2 - 2*k*r - alpha^2)^(1/2)/(2*e) + (2^(1/2)*k*log((2*e*r^2 - 2*k*r - alpha^2)^(1/2) - (2^(1/2)*(k - 2*e*r))/(2*e^(1/2))))/(4*e^(3/2))","B"
213,1,54,44,0.399559,"\text{Not used}","int(1/(r*(2*h*r^2 - 2*k*r^4 - alpha^2)^(1/2)),r)","-\frac{\ln\left(\frac{1}{r^2}\right)+\ln\left(h\,r^2-\alpha ^2+\sqrt{-\alpha ^2}\,\sqrt{-\alpha ^2-2\,k\,r^4+2\,h\,r^2}\right)}{2\,\sqrt{-\alpha ^2}}","Not used",1,"-(log(1/r^2) + log(h*r^2 - alpha^2 + (-alpha^2)^(1/2)*(2*h*r^2 - 2*k*r^4 - alpha^2)^(1/2)))/(2*(-alpha^2)^(1/2))","B"
214,1,72,68,0.442092,"\text{Not used}","int(1/(r*(2*h*r^2 - 2*k*r^4 - alpha^2 - epsilon^2)^(1/2)),r)","-\frac{\ln\left(h-\frac{\alpha ^2+\epsilon ^2}{r^2}+\frac{\sqrt{-\alpha ^2-\epsilon ^2}\,\sqrt{-\alpha ^2-\epsilon ^2-2\,k\,r^4+2\,h\,r^2}}{r^2}\right)}{2\,\sqrt{-\alpha ^2-\epsilon ^2}}","Not used",1,"-log(h - (alpha^2 + epsilon^2)/r^2 + ((- alpha^2 - epsilon^2)^(1/2)*(2*h*r^2 - 2*k*r^4 - alpha^2 - epsilon^2)^(1/2))/r^2)/(2*(- alpha^2 - epsilon^2)^(1/2))","B"
215,1,11,13,0.089098,"\text{Not used}","int(a*cos(3*x + 5)*sin(3*x + 5)^2,x)","\frac{a\,{\sin\left(3\,x+5\right)}^3}{9}","Not used",1,"(a*sin(3*x + 5)^3)/9","B"
216,1,11,19,0.164716,"\text{Not used}","int(log(x^2)/x^3,x)","-\frac{\ln\left(x^2\right)+1}{2\,x^2}","Not used",1,"-(log(x^2) + 1)/(2*x^2)","B"
217,1,12,12,0.083170,"\text{Not used}","int(x*sin(a + x),x)","\sin\left(a+x\right)-x\,\cos\left(a+x\right)","Not used",1,"sin(a + x) - x*cos(a + x)","B"
218,1,10,11,0.216314,"\text{Not used}","int(-(exp(-x)*(log(x)*(x - 1) + 1))/log(x)^2,x)","\frac{x\,{\mathrm{e}}^{-x}}{\ln\left(x\right)}","Not used",1,"(x*exp(-x))/log(x)","B"
219,1,22,27,0.153968,"\text{Not used}","int(x^3/(b + a*x^2),x)","-\frac{b\,\ln\left(a\,x^2+b\right)-a\,x^2}{2\,a^2}","Not used",1,"-(b*log(b + a*x^2) - a*x^2)/(2*a^2)","B"
220,1,15,33,0.299496,"\text{Not used}","int(x^(1/2)/(x + 1)^(7/2),x)","\frac{2\,x^{3/2}\,\left(2\,x+5\right)}{15\,{\left(x+1\right)}^{5/2}}","Not used",1,"(2*x^(3/2)*(2*x + 5))/(15*(x + 1)^(5/2))","B"
221,1,8,9,0.197183,"\text{Not used}","int(1/(x*(x + 1)),x)","-\ln\left(\frac{1}{x}+1\right)","Not used",1,"-log(1/x + 1)","B"
222,1,13,19,0.075083,"\text{Not used}","int(1/(x^(1/2)*(2*x - 1)),x)","-\sqrt{2}\,\mathrm{atanh}\left(\sqrt{2\,x}\right)","Not used",1,"-2^(1/2)*atanh((2*x)^(1/2))","B"
223,1,12,19,0.023904,"\text{Not used}","int(x^(1/2)*(x^2 + 1),x)","\frac{2\,x^{3/2}\,\left(3\,x^2+7\right)}{21}","Not used",1,"(2*x^(3/2)*(3*x^2 + 7))/21","B"
224,1,119,88,0.181455,"\text{Not used}","int((x - a)^(1/3)/x,x)","{\left(-a\right)}^{1/3}\,\ln\left(-9\,{\left(-a\right)}^{4/3}-9\,a\,{\left(x-a\right)}^{1/3}\right)+3\,{\left(x-a\right)}^{1/3}+\frac{{\left(-a\right)}^{1/3}\,\ln\left(\frac{9\,{\left(-a\right)}^{4/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}+9\,a\,{\left(x-a\right)}^{1/3}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}-\frac{{\left(-a\right)}^{1/3}\,\ln\left(\frac{9\,{\left(-a\right)}^{4/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}-9\,a\,{\left(x-a\right)}^{1/3}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}","Not used",1,"(-a)^(1/3)*log(- 9*(-a)^(4/3) - 9*a*(x - a)^(1/3)) + 3*(x - a)^(1/3) + ((-a)^(1/3)*log((9*(-a)^(4/3)*(3^(1/2)*1i - 1))/2 + 9*a*(x - a)^(1/3))*(3^(1/2)*1i - 1))/2 - ((-a)^(1/3)*log((9*(-a)^(4/3)*(3^(1/2)*1i + 1))/2 - 9*a*(x - a)^(1/3))*(3^(1/2)*1i + 1))/2","B"
225,1,9,9,0.021233,"\text{Not used}","int(x*sinh(x),x)","x\,\mathrm{cosh}\left(x\right)-\mathrm{sinh}\left(x\right)","Not used",1,"x*cosh(x) - sinh(x)","B"
226,1,9,9,0.025576,"\text{Not used}","int(x*cosh(x),x)","x\,\mathrm{sinh}\left(x\right)-\mathrm{cosh}\left(x\right)","Not used",1,"x*sinh(x) - cosh(x)","B"
227,1,7,9,0.186318,"\text{Not used}","int(sinh(2*x)/cosh(2*x),x)","\frac{\ln\left(\mathrm{cosh}\left(2\,x\right)\right)}{2}","Not used",1,"log(cosh(2*x))/2","B"
228,1,13,12,0.321420,"\text{Not used}","int((eps*sinh(x)*1i - 1)/(a*1i - x + eps*cosh(x)*1i),x)","\ln\left(x-a\,1{}\mathrm{i}-\mathrm{eps}\,\mathrm{cosh}\left(x\right)\,1{}\mathrm{i}\right)","Not used",1,"log(x - a*1i - eps*cosh(x)*1i)","B"
229,1,22,28,0.332055,"\text{Not used}","int(sin(2*x + 3)*cos(x)^2,x)","\frac{x\,\sin\left(3\right)}{4}-\frac{\cos\left(4\,x+3\right)}{16}-\frac{\cos\left(2\,x+3\right)}{4}","Not used",1,"(x*sin(3))/4 - cos(4*x + 3)/16 - cos(2*x + 3)/4","B"
230,1,14,21,0.019370,"\text{Not used}","int(x*atan(x),x)","\mathrm{atan}\left(x\right)\,\left(\frac{x^2}{2}+\frac{1}{2}\right)-\frac{x}{2}","Not used",1,"atan(x)*(x^2/2 + 1/2) - x/2","B"
231,1,15,21,0.047912,"\text{Not used}","int(x*acot(x),x)","\frac{x}{2}-\frac{\mathrm{atan}\left(x\right)}{2}+\frac{x^2\,\mathrm{acot}\left(x\right)}{2}","Not used",1,"x/2 - atan(x)/2 + (x^2*acot(x))/2","B"
232,1,41,23,0.143799,"\text{Not used}","int(x*log(a + x^2),x)","\frac{a\,\ln\left(x+\sqrt{-a}\right)}{2}+\frac{x^2\,\ln\left(x^2+a\right)}{2}+\frac{a\,\ln\left(x-\sqrt{-a}\right)}{2}-\frac{x^2}{2}","Not used",1,"(a*log(x + (-a)^(1/2)))/2 + (x^2*log(a + x^2))/2 + (a*log(x - (-a)^(1/2)))/2 - x^2/2","B"
233,1,14,18,0.026020,"\text{Not used}","int(sin(a + x)*cos(x),x)","\frac{x\,\sin\left(a\right)}{2}-\frac{\cos\left(a+2\,x\right)}{4}","Not used",1,"(x*sin(a))/2 - cos(a + 2*x)/4","B"
234,1,14,18,0.024348,"\text{Not used}","int(cos(a + x)*sin(x),x)","-\frac{\cos\left(a+2\,x\right)}{4}-\frac{x\,\sin\left(a\right)}{2}","Not used",1,"- cos(a + 2*x)/4 - (x*sin(a))/2","B"
235,1,16,12,0.138586,"\text{Not used}","int((sin(x) + 1)^(1/2),x)","\frac{2\,\left(\sin\left(x\right)-1\right)\,\sqrt{\sin\left(x\right)+1}}{\cos\left(x\right)}","Not used",1,"(2*(sin(x) - 1)*(sin(x) + 1)^(1/2))/cos(x)","B"
236,1,18,14,0.135678,"\text{Not used}","int((1 - sin(x))^(1/2),x)","\frac{2\,\sqrt{1-\sin\left(x\right)}\,\left(\sin\left(x\right)+1\right)}{\cos\left(x\right)}","Not used",1,"(2*(1 - sin(x))^(1/2)*(sin(x) + 1))/cos(x)","B"
237,1,10,12,0.145263,"\text{Not used}","int((cos(x) + 1)^(1/2),x)","\frac{2\,\sin\left(x\right)}{\sqrt{\cos\left(x\right)+1}}","Not used",1,"(2*sin(x))/(cos(x) + 1)^(1/2)","B"
238,1,12,14,0.033248,"\text{Not used}","int((1 - cos(x))^(1/2),x)","-\frac{2\,\sin\left(x\right)}{\sqrt{1-\cos\left(x\right)}}","Not used",1,"-(2*sin(x))/(1 - cos(x))^(1/2)","B"
239,1,21,21,0.192703,"\text{Not used}","int(-1/((x - 1)^(1/2) - x^(1/2)),x)","\frac{2\,x\,\sqrt{x-1}}{3}-\frac{2\,\sqrt{x-1}}{3}+\frac{2\,x^{3/2}}{3}","Not used",1,"(2*x*(x - 1)^(1/2))/3 - (2*(x - 1)^(1/2))/3 + (2*x^(3/2))/3","B"
240,1,18,24,0.105520,"\text{Not used}","int(-1/((x + 1)^(1/2) - 1),x)","-2\,\ln\left(\sqrt{x+1}-1\right)-2\,\sqrt{x+1}","Not used",1,"- 2*log((x + 1)^(1/2) - 1) - 2*(x + 1)^(1/2)","B"
241,1,8,12,0.036555,"\text{Not used}","int(x/(x^4 + 36)^(1/2),x)","\frac{\mathrm{asinh}\left(\frac{x^2}{6}\right)}{2}","Not used",1,"asinh(x^2/6)/2","B"
242,1,24,32,0.030340,"\text{Not used}","int(1/(x^(1/2) + x^(1/3)),x)","2\,\sqrt{x}-6\,\ln\left(x^{1/6}+1\right)-3\,x^{1/3}+6\,x^{1/6}","Not used",1,"2*x^(1/2) - 6*log(x^(1/6) + 1) - 3*x^(1/3) + 6*x^(1/6)","B"
243,1,26,33,0.060218,"\text{Not used}","int(log(3*x^2 + 2),x)","\frac{2\,\sqrt{6}\,\mathrm{atan}\left(\frac{\sqrt{6}\,x}{2}\right)}{3}-2\,x+x\,\ln\left(3\,x^2+2\right)","Not used",1,"(2*6^(1/2)*atan((6^(1/2)*x)/2))/3 - 2*x + x*log(3*x^2 + 2)","B"
244,1,3,3,0.024999,"\text{Not used}","int(cot(x),x)","\ln\left(\sin\left(x\right)\right)","Not used",1,"log(sin(x))","B"
245,1,10,12,0.028375,"\text{Not used}","int(cot(x)^4,x)","-\frac{{\mathrm{cot}\left(x\right)}^3}{3}+\mathrm{cot}\left(x\right)+x","Not used",1,"x + cot(x) - cot(x)^3/3","B"
246,1,3,3,0.011165,"\text{Not used}","int(tanh(x),x)","\ln\left(\mathrm{cosh}\left(x\right)\right)","Not used",1,"log(cosh(x))","B"
247,1,3,3,0.137221,"\text{Not used}","int(coth(x),x)","\ln\left(\mathrm{sinh}\left(x\right)\right)","Not used",1,"log(sinh(x))","B"
248,1,8,8,0.164972,"\text{Not used}","int(b^x,x)","\frac{b^x}{\ln\left(b\right)}","Not used",1,"b^x/log(b)","B"
249,0,-1,49,0.000000,"\text{Not used}","int((1/x^4 + x^4 + 2)^(1/2),x)","\int \sqrt{\frac{1}{x^4}+x^4+2} \,d x","Not used",1,"int((1/x^4 + x^4 + 2)^(1/2), x)","F"
250,1,10,16,0.144773,"\text{Not used}","int((2*x + 1)/(3*x + 2),x)","\frac{2\,x}{3}-\frac{\ln\left(x+\frac{2}{3}\right)}{9}","Not used",1,"(2*x)/3 - log(x + 2/3)/9","B"
251,1,32,40,0.041844,"\text{Not used}","int(x*log(x + (x^2 + 1)^(1/2)),x)","x\,\ln\left(x+\sqrt{x^2+1}\right)\,\left(\frac{x}{2}+\frac{1}{4\,x}\right)-\frac{x\,\sqrt{x^2+1}}{4}","Not used",1,"x*log(x + (x^2 + 1)^(1/2))*(x/2 + 1/(4*x)) - (x*(x^2 + 1)^(1/2))/4","B"
252,1,69,128,0.278409,"\text{Not used}","int(x*(exp(x)*sin(x) + 1)^2,x)","\frac{3\,x\,{\mathrm{e}}^{2\,x}}{8}-\frac{{\mathrm{e}}^{2\,x}}{8}+{\mathrm{e}}^x\,\cos\left(x\right)+\frac{x^2}{2}-\frac{x\,{\mathrm{e}}^{2\,x}\,{\cos\left(x\right)}^2}{4}+\frac{{\mathrm{e}}^{2\,x}\,\cos\left(x\right)\,\sin\left(x\right)}{8}-x\,{\mathrm{e}}^x\,\cos\left(x\right)+x\,{\mathrm{e}}^x\,\sin\left(x\right)-\frac{x\,{\mathrm{e}}^{2\,x}\,\cos\left(x\right)\,\sin\left(x\right)}{4}","Not used",1,"(3*x*exp(2*x))/8 - exp(2*x)/8 + exp(x)*cos(x) + x^2/2 - (x*exp(2*x)*cos(x)^2)/4 + (exp(2*x)*cos(x)*sin(x))/8 - x*exp(x)*cos(x) + x*exp(x)*sin(x) - (x*exp(2*x)*cos(x)*sin(x))/4","B"
253,1,17,30,0.170923,"\text{Not used}","int(x*exp(x)*cos(x),x)","\frac{{\mathrm{e}}^x\,\left(x\,\cos\left(x\right)-\sin\left(x\right)+x\,\sin\left(x\right)\right)}{2}","Not used",1,"(exp(x)*(x*cos(x) - sin(x) + x*sin(x)))/2","B"
254,1,7,11,0.065547,"\text{Not used}","int(1/(x - 3)^4,x)","-\frac{1}{3\,{\left(x-3\right)}^3}","Not used",1,"-1/(3*(x - 3)^3)","B"
255,1,46,40,0.114516,"\text{Not used}","int(x/(x^3 - 1),x)","\frac{\ln\left(x-1\right)}{3}-\ln\left(x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)+\ln\left(x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)","Not used",1,"log(x - 1)/3 - log(x - (3^(1/2)*1i)/2 + 1/2)*((3^(1/2)*1i)/6 + 1/6) + log(x + (3^(1/2)*1i)/2 + 1/2)*((3^(1/2)*1i)/6 - 1/6)","B"
256,1,6,8,0.067078,"\text{Not used}","int(x/(x^4 - 1),x)","-\frac{\mathrm{atanh}\left(x^2\right)}{2}","Not used",1,"-atanh(x^2)/2","B"
257,0,-1,227,0.000000,"\text{Not used}","int((log(x)*(x^3 + 1))/(x^4 + 2),x)","\int \frac{\ln\left(x\right)\,\left(x^3+1\right)}{x^4+2} \,d x","Not used",1,"int((log(x)*(x^3 + 1))/(x^4 + 2), x)","F"
258,1,51,24,0.442625,"\text{Not used}","int(log(x + 1) + log(x + 2) + log(x),x)","\ln\left(x+1\right)-3\,x+2\,\ln\left(x+2\right)+x\,\ln\left(x+1\right)+x\,\ln\left(x\right)+\frac{\ln\left(x+2\right)\,\left(x^3+3\,x^2+2\,x\right)}{\left(x+1\right)\,\left(x+2\right)}","Not used",1,"log(x + 1) - 3*x + 2*log(x + 2) + x*log(x + 1) + x*log(x) + (log(x + 2)*(2*x + 3*x^2 + x^3))/((x + 1)*(x + 2))","B"
259,1,70,78,0.272162,"\text{Not used}","int(1/(x^3 + 5),x)","\frac{5^{1/3}\,\ln\left(x+5^{1/3}\right)}{15}+\frac{5^{1/3}\,\ln\left(x+\frac{5^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{30}-\frac{5^{1/3}\,\ln\left(x-\frac{5^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{30}","Not used",1,"(5^(1/3)*log(x + 5^(1/3)))/15 + (5^(1/3)*log(x + (5^(1/3)*(3^(1/2)*1i - 1))/2)*(3^(1/2)*1i - 1))/30 - (5^(1/3)*log(x - (5^(1/3)*(3^(1/2)*1i + 1))/2)*(3^(1/2)*1i + 1))/30","B"
260,1,2,2,0.002168,"\text{Not used}","int(1/(x^2 + 1)^(1/2),x)","\mathrm{asinh}\left(x\right)","Not used",1,"asinh(x)","B"
261,1,20,27,0.047789,"\text{Not used}","int((x^2 + 3)^(1/2),x)","\frac{3\,\mathrm{asinh}\left(\frac{\sqrt{3}\,x}{3}\right)}{2}+\frac{x\,\sqrt{x^2+3}}{2}","Not used",1,"(3*asinh((3^(1/2)*x)/3))/2 + (x*(x^2 + 3)^(1/2))/2","B"
262,1,10,10,0.031407,"\text{Not used}","int(x/(x + 1)^2,x)","\ln\left(x+1\right)+\frac{1}{x+1}","Not used",1,"log(x + 1) + 1/(x + 1)","B"
263,1,14,16,0.219918,"\text{Not used}","int(asin(x),x)","x\,\mathrm{asin}\left(x\right)+\sqrt{1-x^2}","Not used",1,"x*asin(x) + (1 - x^2)^(1/2)","B"
264,1,24,40,0.028927,"\text{Not used}","int(x^2*asin(x),x)","\frac{x^3\,\mathrm{asin}\left(x\right)}{3}+\frac{\sqrt{1-x^2}\,\left(x^2+2\right)}{9}","Not used",1,"(x^3*asin(x))/3 + ((1 - x^2)^(1/2)*(x^2 + 2))/9","B"
265,1,9,21,0.809688,"\text{Not used}","int(1/(cos(x)^2*(1/cos(x)^2 - 3*tan(x) + 1)),x)","-2\,\mathrm{atanh}\left(2\,\mathrm{tan}\left(x\right)-3\right)","Not used",1,"-2*atanh(2*tan(x) - 3)","B"
266,1,10,14,0.002088,"\text{Not used}","int(cos(x)^2,x)","\frac{x}{2}+\frac{\sin\left(2\,x\right)}{4}","Not used",1,"x/2 + sin(2*x)/4","B"
267,1,16,18,0.152101,"\text{Not used}","int(-(3*x - 5*x^2 + 2)/(x^2*(x - 2)),x)","3\,\ln\left(x-2\right)+2\,\ln\left(x\right)-\frac{1}{x}","Not used",1,"3*log(x - 2) + 2*log(x) - 1/x","B"
268,1,6,10,0.038173,"\text{Not used}","int(1/(4*x^2 + 9)^(1/2),x)","\frac{\mathrm{asinh}\left(\frac{2\,x}{3}\right)}{2}","Not used",1,"asinh((2*x)/3)/2","B"
269,1,4,6,0.029226,"\text{Not used}","int(1/(x^2 + 4)^(1/2),x)","\mathrm{asinh}\left(\frac{x}{2}\right)","Not used",1,"asinh(x/2)","B"
270,1,16,21,0.141746,"\text{Not used}","int(1/(9*x^2 - 12*x + 10),x)","\frac{\sqrt{6}\,\mathrm{atan}\left(\frac{\sqrt{6}\,\left(3\,x-2\right)}{6}\right)}{18}","Not used",1,"(6^(1/2)*atan((6^(1/2)*(3*x - 2))/6))/18","B"
271,1,45,53,0.060981,"\text{Not used}","int(1/(x^4 - 2*x^5 + 2*x^6 - 2*x^7 + x^8),x)","\frac{\ln\left(x^2+1\right)}{4}-\frac{5\,\ln\left(x-1\right)}{2}+2\,\ln\left(x\right)-\frac{-\frac{5\,x^3}{2}+x^2+\frac{2\,x}{3}+\frac{1}{3}}{x^3-x^4}","Not used",1,"log(x^2 + 1)/4 - (5*log(x - 1))/2 + 2*log(x) - ((2*x)/3 + x^2 - (5*x^3)/2 + 1/3)/(x^3 - x^4)","B"
272,1,46,49,0.209548,"\text{Not used}","int((d + c*x + a*x^3 + b*x^2)/(x*(x + 1)*(x - 3)),x)","\ln\left(x-3\right)\,\left(\frac{9\,a}{4}+\frac{3\,b}{4}+\frac{c}{4}+\frac{d}{12}\right)-\ln\left(x+1\right)\,\left(\frac{a}{4}-\frac{b}{4}+\frac{c}{4}-\frac{d}{4}\right)+a\,x-\frac{d\,\ln\left(x\right)}{3}","Not used",1,"log(x - 3)*((9*a)/4 + (3*b)/4 + c/4 + d/12) - log(x + 1)*(a/4 - b/4 + c/4 - d/4) + a*x - (d*log(x))/3","B"
273,0,-1,15,0.000000,"\text{Not used}","int(-1/(log(x^2 + 1) - 2)^5,x)","\int -\frac{1}{{\left(\ln\left(x^2+1\right)-2\right)}^5} \,d x","Not used",0,"int(-1/(log(x^2 + 1) - 2)^5, x)","F"
274,1,27,28,0.337852,"\text{Not used}","int((log(x) - 2)/(x + log(x)^2)^2 + ((2*log(x))/x + 1/x + 1)/(x + log(x)^2) + exp(x^2)/x + 2*x*exp(x^2)*log(x),x)","\ln\left({\ln\left(x\right)}^2+x\right)+{\mathrm{e}}^{x^2}\,\ln\left(x\right)-\frac{\ln\left(x\right)}{{\ln\left(x\right)}^2+x}","Not used",1,"log(x + log(x)^2) + exp(x^2)*log(x) - log(x)/(x + log(x)^2)","B"
275,1,140,199,1.111379,"\text{Not used}","int(x^4*exp(x/2 + x*z)*sin(Pi*z)^4,z)","\frac{x^3\,{\mathrm{e}}^{\frac{x}{2}+x\,z}\,\left(24\,\Pi ^4-\frac{x^4\,\cos\left(2\,\Pi \,z\right)}{2}+\frac{x^4\,\cos\left(4\,\Pi \,z\right)}{8}+\frac{3\,x^4}{8}+\frac{15\,\Pi ^2\,x^2}{2}-\Pi \,x^3\,\sin\left(2\,\Pi \,z\right)-16\,\Pi ^3\,x\,\sin\left(2\,\Pi \,z\right)+\frac{\Pi \,x^3\,\sin\left(4\,\Pi \,z\right)}{2}+2\,\Pi ^3\,x\,\sin\left(4\,\Pi \,z\right)-8\,\Pi ^2\,x^2\,\cos\left(2\,\Pi \,z\right)+\frac{\Pi ^2\,x^2\,\cos\left(4\,\Pi \,z\right)}{2}\right)}{64\,\Pi ^4+20\,\Pi ^2\,x^2+x^4}","Not used",1,"(x^3*exp(x/2 + x*z)*(24*Pi^4 - (x^4*cos(2*Pi*z))/2 + (x^4*cos(4*Pi*z))/8 + (3*x^4)/8 + (15*Pi^2*x^2)/2 - Pi*x^3*sin(2*Pi*z) - 16*Pi^3*x*sin(2*Pi*z) + (Pi*x^3*sin(4*Pi*z))/2 + 2*Pi^3*x*sin(4*Pi*z) - 8*Pi^2*x^2*cos(2*Pi*z) + (Pi^2*x^2*cos(4*Pi*z))/2))/(64*Pi^4 + x^4 + 20*Pi^2*x^2)","B"
276,1,15,18,0.154692,"\text{Not used}","int(erf(x),x)","\frac{{\mathrm{e}}^{-x^2}}{\sqrt{\pi }}+x\,\mathrm{erf}\left(x\right)","Not used",1,"exp(-x^2)/pi^(1/2) + x*erf(x)","B"
277,1,21,24,0.065502,"\text{Not used}","int(erf(a + x),x)","\mathrm{erf}\left(a+x\right)\,\left(a+x\right)+\frac{{\mathrm{e}}^{-{\left(a+x\right)}^2}}{\sqrt{\pi }}","Not used",1,"erf(a + x)*(a + x) + exp(-(a + x)^2)/pi^(1/2)","B"
278,0,-1,94,0.000000,"\text{Not used}","int(-(8*x + x^2 + 3*x^3 - 7*x^4 - 4*x^5 - 2*x^6 + 8)/((2*x^2 - 1)^2*(2*x^2 + 4*x^3 + x^4 + 1)^(1/2)),x)","\int -\frac{-2\,x^6-4\,x^5-7\,x^4+3\,x^3+x^2+8\,x+8}{{\left(2\,x^2-1\right)}^2\,\sqrt{x^4+4\,x^3+2\,x^2+1}} \,d x","Not used",1,"int(-(8*x + x^2 + 3*x^3 - 7*x^4 - 4*x^5 - 2*x^6 + 8)/((2*x^2 - 1)^2*(2*x^2 + 4*x^3 + x^4 + 1)^(1/2)), x)","F"
279,0,-1,142,0.000000,"\text{Not used}","int(((2*y + 1)*(1 - 5*y^2 - 5*y)^(1/2))/(y*(y + 1)*(y + 2)*(1 - y^2 - y)^(1/2)),y)","\int \frac{\left(2\,y+1\right)\,\sqrt{-5\,y^2-5\,y+1}}{y\,\left(y+1\right)\,\left(y+2\right)\,\sqrt{-y^2-y+1}} \,d y","Not used",1,"int(((2*y + 1)*(1 - 5*y^2 - 5*y)^(1/2))/(y*(y + 1)*(y + 2)*(1 - y^2 - y)^(1/2)), y)","F"
280,1,172,21,2.372606,"\text{Not used}","int(-(x*(4*(x^2 - 1)^(1/2) + (x^2 - 4)^(1/2) - x^2*(x^2 - 1)^(1/2) - x^2*(x^2 - 4)^(1/2)))/((x^4 - 5*x^2 + 4)*((x^2 - 1)^(1/2) + (x^2 - 4)^(1/2) + 1)),x)","\frac{\ln\left(x-\sqrt{5}\right)}{4}-\mathrm{atanh}\left(\frac{\sqrt{3}-\sqrt{x^2-1}}{\sqrt{x^2-4}}\right)+\frac{\mathrm{atanh}\left(\frac{\sqrt{x^2-1}}{2}\right)}{2}+\frac{\ln\left(x+\sqrt{5}\right)}{4}-\frac{7\,\mathrm{atanh}\left(\frac{4\,\left(\sqrt{3}-\sqrt{x^2-1}\right)}{\sqrt{x^2-4}\,\left(\frac{{\left(\sqrt{3}-\sqrt{x^2-1}\right)}^2}{x^2-4}+1\right)}\right)}{4}+\frac{5\,\mathrm{atanh}\left(\frac{12150\,\left(\sqrt{3}-\sqrt{x^2-1}\right)}{\sqrt{x^2-4}\,\left(\frac{6075\,{\left(\sqrt{3}-\sqrt{x^2-1}\right)}^2}{2\,\left(x^2-4\right)}+\frac{6075}{2}\right)}\right)}{4}-\frac{\mathrm{atanh}\left(\sqrt{x^2-4}\right)}{2}","Not used",1,"log(x - 5^(1/2))/4 - atanh((3^(1/2) - (x^2 - 1)^(1/2))/(x^2 - 4)^(1/2)) + atanh((x^2 - 1)^(1/2)/2)/2 + log(x + 5^(1/2))/4 - (7*atanh((4*(3^(1/2) - (x^2 - 1)^(1/2)))/((x^2 - 4)^(1/2)*((3^(1/2) - (x^2 - 1)^(1/2))^2/(x^2 - 4) + 1))))/4 + (5*atanh((12150*(3^(1/2) - (x^2 - 1)^(1/2)))/((x^2 - 4)^(1/2)*((6075*(3^(1/2) - (x^2 - 1)^(1/2))^2)/(2*(x^2 - 4)) + 6075/2))))/4 - atanh((x^2 - 4)^(1/2))/2","B"
281,0,-1,4030,0.000000,"\text{Not used}","int(x*(2*2^(1/2) - 1) - 2^(1/2)*(4*x + 2*x^2 + x^4 + 1)^(1/2),x)","\int x\,\left(2\,\sqrt{2}-1\right)-\sqrt{2}\,\sqrt{x^4+2\,x^2+4\,x+1} \,d x","Not used",1,"int(x*(2*2^(1/2) - 1) - 2^(1/2)*(4*x + 2*x^2 + x^4 + 1)^(1/2), x)","F"
282,1,265,330,0.767248,"\text{Not used}","int((exp(-x/y)*((Pi^2*(176*mc^3*x^3 - 24*mc^2*x^3 - 144*mc^5*x^2 + 12*mc*x^4 + 24*mc^6*x - 48*mc^7*x - 3*mc^8 + 4*mc^9 + 3*x^4))/384 - (Pi^2*mc^3*x^2*log(x/mc^2)*(8*x - 3*mc + 12*mc^2))/32))/x^2,x)","\mathrm{ei}\left(-\frac{x}{y}\right)\,\left(\frac{\frac{\Pi ^2\,{\mathrm{mc}}^8}{128}-\frac{\Pi ^2\,{\mathrm{mc}}^9}{96}}{y}+\frac{\Pi ^2\,{\mathrm{mc}}^6}{16}-\frac{\Pi ^2\,{\mathrm{mc}}^7}{8}+y\,\left(\frac{3\,\Pi ^2\,{\mathrm{mc}}^4}{32}-\frac{3\,\Pi ^2\,{\mathrm{mc}}^5}{8}\right)-\frac{\Pi ^2\,{\mathrm{mc}}^3\,y^2}{4}\right)-\frac{2\,\Pi ^2\,x^2\,y\,{\mathrm{e}}^{-\frac{x}{y}}\,\left(-72\,{\mathrm{mc}}^5+40\,{\mathrm{mc}}^3\,y-12\,{\mathrm{mc}}^2\,y+12\,\mathrm{mc}\,y^2+3\,y^2\right)+2\,\Pi ^2\,x^3\,y\,{\mathrm{e}}^{-\frac{x}{y}}\,\left(88\,{\mathrm{mc}}^3-12\,{\mathrm{mc}}^2+12\,y\,\mathrm{mc}+3\,y\right)+\Pi ^2\,{\mathrm{mc}}^8\,x\,{\mathrm{e}}^{-\frac{x}{y}}\,\left(4\,\mathrm{mc}-3\right)+3\,\Pi ^2\,x^4\,y\,{\mathrm{e}}^{-\frac{x}{y}}\,\left(4\,\mathrm{mc}+1\right)-96\,\Pi ^2\,{\mathrm{mc}}^3\,x^3\,y\,\ln\left(\frac{x}{{\mathrm{mc}}^2}\right)\,{\mathrm{e}}^{-\frac{x}{y}}-12\,\Pi ^2\,{\mathrm{mc}}^3\,x^2\,y\,\ln\left(\frac{x}{{\mathrm{mc}}^2}\right)\,{\mathrm{e}}^{-\frac{x}{y}}\,\left(12\,{\mathrm{mc}}^2-3\,\mathrm{mc}+8\,y\right)}{384\,x^2}","Not used",1,"ei(-x/y)*(((Pi^2*mc^8)/128 - (Pi^2*mc^9)/96)/y + (Pi^2*mc^6)/16 - (Pi^2*mc^7)/8 + y*((3*Pi^2*mc^4)/32 - (3*Pi^2*mc^5)/8) - (Pi^2*mc^3*y^2)/4) - (2*Pi^2*x^2*y*exp(-x/y)*(12*mc*y^2 - 12*mc^2*y + 40*mc^3*y - 72*mc^5 + 3*y^2) + 2*Pi^2*x^3*y*exp(-x/y)*(3*y + 12*mc*y - 12*mc^2 + 88*mc^3) + Pi^2*mc^8*x*exp(-x/y)*(4*mc - 3) + 3*Pi^2*x^4*y*exp(-x/y)*(4*mc + 1) - 96*Pi^2*mc^3*x^3*y*log(x/mc^2)*exp(-x/y) - 12*Pi^2*mc^3*x^2*y*log(x/mc^2)*exp(-x/y)*(8*y - 3*mc + 12*mc^2))/(384*x^2)","B"
283,1,4,4,0.020109,"\text{Not used}","int(sin(2*x)/cos(x),x)","-2\,\cos\left(x\right)","Not used",1,"-2*cos(x)","B"
284,1,103,71,0.280130,"\text{Not used}","int(-(3*x - 4*x^2 - 4*x^3 - 7*x^6 + 4*x^7 + 10*x^8 + 7*x^13 + 3)/(x^2 - 2*x + 4*x^3 + 2*x^4 + 2*x^7 + 2*x^8 - x^14 - 1),x)","\frac{\ln\left(\sqrt{2}\,x-x+\sqrt{2}\,x^2+x^7-1\right)}{2}+\frac{\ln\left(x^7-\sqrt{2}\,x-\sqrt{2}\,x^2-x-1\right)}{2}-\frac{\sqrt{2}\,\ln\left(\sqrt{2}\,x-x+\sqrt{2}\,x^2+x^7-1\right)}{2}+\frac{\sqrt{2}\,\ln\left(x^7-\sqrt{2}\,x-\sqrt{2}\,x^2-x-1\right)}{2}","Not used",1,"log(2^(1/2)*x - x + 2^(1/2)*x^2 + x^7 - 1)/2 + log(x^7 - 2^(1/2)*x - 2^(1/2)*x^2 - x - 1)/2 - (2^(1/2)*log(2^(1/2)*x - x + 2^(1/2)*x^2 + x^7 - 1))/2 + (2^(1/2)*log(x^7 - 2^(1/2)*x - 2^(1/2)*x^2 - x - 1))/2","B"