1,1,25,33,2.113555,"\text{Not used}","int(sin(x)^6/(a - a*cos(x)^2),x)","\frac{\sin\left(4\,x\right)}{32\,a}-\frac{\sin\left(2\,x\right)}{4\,a}+\frac{3\,x}{8\,a}","Not used",1,"sin(4*x)/(32*a) - sin(2*x)/(4*a) + (3*x)/(8*a)","B"
2,1,16,19,2.035226,"\text{Not used}","int(sin(x)^5/(a - a*cos(x)^2),x)","-\frac{3\,\cos\left(x\right)-{\cos\left(x\right)}^3}{3\,a}","Not used",1,"-(3*cos(x) - cos(x)^3)/(3*a)","B"
3,1,15,20,2.036606,"\text{Not used}","int(sin(x)^4/(a - a*cos(x)^2),x)","\frac{2\,x-\sin\left(2\,x\right)}{4\,a}","Not used",1,"(2*x - sin(2*x))/(4*a)","B"
4,1,7,7,0.024023,"\text{Not used}","int(sin(x)^3/(a - a*cos(x)^2),x)","-\frac{\cos\left(x\right)}{a}","Not used",1,"-cos(x)/a","B"
5,1,5,5,2.049625,"\text{Not used}","int(sin(x)^2/(a - a*cos(x)^2),x)","\frac{x}{a}","Not used",1,"x/a","B"
6,1,8,8,2.112049,"\text{Not used}","int(sin(x)/(a - a*cos(x)^2),x)","-\frac{\mathrm{atanh}\left(\cos\left(x\right)\right)}{a}","Not used",1,"-atanh(cos(x))/a","B"
7,1,26,22,0.076626,"\text{Not used}","int(1/(sin(x)*(a - a*cos(x)^2)),x)","-\frac{\cos\left(x\right)}{2\,\left(a-a\,{\cos\left(x\right)}^2\right)}-\frac{\mathrm{atanh}\left(\cos\left(x\right)\right)}{2\,a}","Not used",1,"- cos(x)/(2*(a - a*cos(x)^2)) - atanh(cos(x))/(2*a)","B"
8,1,13,19,2.028752,"\text{Not used}","int(1/(sin(x)^2*(a - a*cos(x)^2)),x)","-\frac{\mathrm{cot}\left(x\right)\,\left({\mathrm{cot}\left(x\right)}^2+3\right)}{3\,a}","Not used",1,"-(cot(x)*(cot(x)^2 + 3))/(3*a)","B"
9,1,39,35,0.081786,"\text{Not used}","int(1/(sin(x)^3*(a - a*cos(x)^2)),x)","-\frac{3\,\mathrm{atanh}\left(\cos\left(x\right)\right)}{8\,a}-\frac{\frac{5\,\cos\left(x\right)}{8}-\frac{3\,{\cos\left(x\right)}^3}{8}}{a\,{\cos\left(x\right)}^4-2\,a\,{\cos\left(x\right)}^2+a}","Not used",1,"- (3*atanh(cos(x)))/(8*a) - ((5*cos(x))/8 - (3*cos(x)^3)/8)/(a - 2*a*cos(x)^2 + a*cos(x)^4)","B"
10,1,100,78,2.131719,"\text{Not used}","int(sin(x)^7/(a + b*cos(x)^2),x)","\cos\left(x\right)\,\left(\frac{3}{b}+\frac{a\,\left(\frac{a}{b^2}+\frac{3}{b}\right)}{b}\right)-{\cos\left(x\right)}^3\,\left(\frac{a}{3\,b^2}+\frac{1}{b}\right)+\frac{{\cos\left(x\right)}^5}{5\,b}-\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,\cos\left(x\right)\,{\left(a+b\right)}^3}{\sqrt{a}\,\left(a^3+3\,a^2\,b+3\,a\,b^2+b^3\right)}\right)\,{\left(a+b\right)}^3}{\sqrt{a}\,b^{7/2}}","Not used",1,"cos(x)*(3/b + (a*(a/b^2 + 3/b))/b) - cos(x)^3*(a/(3*b^2) + 1/b) + cos(x)^5/(5*b) - (atan((b^(1/2)*cos(x)*(a + b)^3)/(a^(1/2)*(3*a*b^2 + 3*a^2*b + a^3 + b^3)))*(a + b)^3)/(a^(1/2)*b^(7/2))","B"
11,1,65,54,0.096513,"\text{Not used}","int(sin(x)^5/(a + b*cos(x)^2),x)","\cos\left(x\right)\,\left(\frac{a}{b^2}+\frac{2}{b}\right)-\frac{{\cos\left(x\right)}^3}{3\,b}-\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,\cos\left(x\right)\,{\left(a+b\right)}^2}{\sqrt{a}\,\left(a^2+2\,a\,b+b^2\right)}\right)\,{\left(a+b\right)}^2}{\sqrt{a}\,b^{5/2}}","Not used",1,"cos(x)*(a/b^2 + 2/b) - cos(x)^3/(3*b) - (atan((b^(1/2)*cos(x)*(a + b)^2)/(a^(1/2)*(2*a*b + a^2 + b^2)))*(a + b)^2)/(a^(1/2)*b^(5/2))","B"
12,1,28,36,0.085438,"\text{Not used}","int(sin(x)^3/(a + b*cos(x)^2),x)","\frac{\cos\left(x\right)}{b}-\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,\cos\left(x\right)}{\sqrt{a}}\right)\,\left(a+b\right)}{\sqrt{a}\,b^{3/2}}","Not used",1,"cos(x)/b - (atan((b^(1/2)*cos(x))/a^(1/2))*(a + b))/(a^(1/2)*b^(3/2))","B"
13,1,18,26,2.226717,"\text{Not used}","int(sin(x)/(a + b*cos(x)^2),x)","-\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,\cos\left(x\right)}{\sqrt{a}}\right)}{\sqrt{a}\,\sqrt{b}}","Not used",1,"-atan((b^(1/2)*cos(x))/a^(1/2))/(a^(1/2)*b^(1/2))","B"
14,1,853,42,2.665991,"\text{Not used}","int(1/(sin(x)*(a + b*cos(x)^2)),x)","\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,a\,b^3+4\,b^4+4\,a^2\,b^2-\frac{\cos\left(x\right)\,\left(-8\,a^3\,b^2-8\,a^2\,b^3+8\,a\,b^4+8\,b^5\right)}{2\,\left(a+b\right)}}{2\,\left(a+b\right)}+4\,b^3\,\cos\left(x\right)\right)\,1{}\mathrm{i}}{2\,\left(a+b\right)}-\frac{\left(\frac{8\,a\,b^3+4\,b^4+4\,a^2\,b^2+\frac{\cos\left(x\right)\,\left(-8\,a^3\,b^2-8\,a^2\,b^3+8\,a\,b^4+8\,b^5\right)}{2\,\left(a+b\right)}}{2\,\left(a+b\right)}-4\,b^3\,\cos\left(x\right)\right)\,1{}\mathrm{i}}{2\,\left(a+b\right)}}{\frac{\frac{8\,a\,b^3+4\,b^4+4\,a^2\,b^2-\frac{\cos\left(x\right)\,\left(-8\,a^3\,b^2-8\,a^2\,b^3+8\,a\,b^4+8\,b^5\right)}{2\,\left(a+b\right)}}{2\,\left(a+b\right)}+4\,b^3\,\cos\left(x\right)}{2\,\left(a+b\right)}+\frac{\frac{8\,a\,b^3+4\,b^4+4\,a^2\,b^2+\frac{\cos\left(x\right)\,\left(-8\,a^3\,b^2-8\,a^2\,b^3+8\,a\,b^4+8\,b^5\right)}{2\,\left(a+b\right)}}{2\,\left(a+b\right)}-4\,b^3\,\cos\left(x\right)}{2\,\left(a+b\right)}}\right)\,1{}\mathrm{i}}{a+b}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-a\,b}\,\left(2\,b^3\,\cos\left(x\right)+\frac{\sqrt{-a\,b}\,\left(4\,a\,b^3+2\,b^4+2\,a^2\,b^2-\frac{\cos\left(x\right)\,\sqrt{-a\,b}\,\left(-8\,a^3\,b^2-8\,a^2\,b^3+8\,a\,b^4+8\,b^5\right)}{4\,\left(a^2+b\,a\right)}\right)}{2\,\left(a^2+b\,a\right)}\right)\,1{}\mathrm{i}}{a^2+b\,a}+\frac{\sqrt{-a\,b}\,\left(2\,b^3\,\cos\left(x\right)-\frac{\sqrt{-a\,b}\,\left(4\,a\,b^3+2\,b^4+2\,a^2\,b^2+\frac{\cos\left(x\right)\,\sqrt{-a\,b}\,\left(-8\,a^3\,b^2-8\,a^2\,b^3+8\,a\,b^4+8\,b^5\right)}{4\,\left(a^2+b\,a\right)}\right)}{2\,\left(a^2+b\,a\right)}\right)\,1{}\mathrm{i}}{a^2+b\,a}}{\frac{\sqrt{-a\,b}\,\left(2\,b^3\,\cos\left(x\right)+\frac{\sqrt{-a\,b}\,\left(4\,a\,b^3+2\,b^4+2\,a^2\,b^2-\frac{\cos\left(x\right)\,\sqrt{-a\,b}\,\left(-8\,a^3\,b^2-8\,a^2\,b^3+8\,a\,b^4+8\,b^5\right)}{4\,\left(a^2+b\,a\right)}\right)}{2\,\left(a^2+b\,a\right)}\right)}{a^2+b\,a}-\frac{\sqrt{-a\,b}\,\left(2\,b^3\,\cos\left(x\right)-\frac{\sqrt{-a\,b}\,\left(4\,a\,b^3+2\,b^4+2\,a^2\,b^2+\frac{\cos\left(x\right)\,\sqrt{-a\,b}\,\left(-8\,a^3\,b^2-8\,a^2\,b^3+8\,a\,b^4+8\,b^5\right)}{4\,\left(a^2+b\,a\right)}\right)}{2\,\left(a^2+b\,a\right)}\right)}{a^2+b\,a}}\right)\,\sqrt{-a\,b}\,1{}\mathrm{i}}{a\,\left(a+b\right)}","Not used",1,"(atan(((((8*a*b^3 + 4*b^4 + 4*a^2*b^2 - (cos(x)*(8*a*b^4 + 8*b^5 - 8*a^2*b^3 - 8*a^3*b^2))/(2*(a + b)))/(2*(a + b)) + 4*b^3*cos(x))*1i)/(2*(a + b)) - (((8*a*b^3 + 4*b^4 + 4*a^2*b^2 + (cos(x)*(8*a*b^4 + 8*b^5 - 8*a^2*b^3 - 8*a^3*b^2))/(2*(a + b)))/(2*(a + b)) - 4*b^3*cos(x))*1i)/(2*(a + b)))/(((8*a*b^3 + 4*b^4 + 4*a^2*b^2 - (cos(x)*(8*a*b^4 + 8*b^5 - 8*a^2*b^3 - 8*a^3*b^2))/(2*(a + b)))/(2*(a + b)) + 4*b^3*cos(x))/(2*(a + b)) + ((8*a*b^3 + 4*b^4 + 4*a^2*b^2 + (cos(x)*(8*a*b^4 + 8*b^5 - 8*a^2*b^3 - 8*a^3*b^2))/(2*(a + b)))/(2*(a + b)) - 4*b^3*cos(x))/(2*(a + b))))*1i)/(a + b) + (atan((((-a*b)^(1/2)*(2*b^3*cos(x) + ((-a*b)^(1/2)*(4*a*b^3 + 2*b^4 + 2*a^2*b^2 - (cos(x)*(-a*b)^(1/2)*(8*a*b^4 + 8*b^5 - 8*a^2*b^3 - 8*a^3*b^2))/(4*(a*b + a^2))))/(2*(a*b + a^2)))*1i)/(a*b + a^2) + ((-a*b)^(1/2)*(2*b^3*cos(x) - ((-a*b)^(1/2)*(4*a*b^3 + 2*b^4 + 2*a^2*b^2 + (cos(x)*(-a*b)^(1/2)*(8*a*b^4 + 8*b^5 - 8*a^2*b^3 - 8*a^3*b^2))/(4*(a*b + a^2))))/(2*(a*b + a^2)))*1i)/(a*b + a^2))/(((-a*b)^(1/2)*(2*b^3*cos(x) + ((-a*b)^(1/2)*(4*a*b^3 + 2*b^4 + 2*a^2*b^2 - (cos(x)*(-a*b)^(1/2)*(8*a*b^4 + 8*b^5 - 8*a^2*b^3 - 8*a^3*b^2))/(4*(a*b + a^2))))/(2*(a*b + a^2))))/(a*b + a^2) - ((-a*b)^(1/2)*(2*b^3*cos(x) - ((-a*b)^(1/2)*(4*a*b^3 + 2*b^4 + 2*a^2*b^2 + (cos(x)*(-a*b)^(1/2)*(8*a*b^4 + 8*b^5 - 8*a^2*b^3 - 8*a^3*b^2))/(4*(a*b + a^2))))/(2*(a*b + a^2))))/(a*b + a^2)))*(-a*b)^(1/2)*1i)/(a*(a + b))","B"
15,1,1138,62,2.588826,"\text{Not used}","int(1/(sin(x)^3*(a + b*cos(x)^2)),x)","\ln\left(\cos\left(x\right)-1\right)\,\left(\frac{b}{2\,{\left(a+b\right)}^2}+\frac{1}{4\,\left(a+b\right)}\right)-\frac{\cos\left(x\right)}{2\,{\sin\left(x\right)}^2\,\left(a+b\right)}-\frac{\ln\left(\cos\left(x\right)+1\right)\,\left(a+3\,b\right)}{4\,{\left(a+b\right)}^2}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-a\,b^3}\,\left(\frac{\cos\left(x\right)\,\left(a^2\,b^3+6\,a\,b^4+13\,b^5\right)}{4\,\left(a^2+2\,a\,b+b^2\right)}+\frac{\left(\frac{2\,a^5\,b^2+12\,a^4\,b^3+28\,a^3\,b^4+32\,a^2\,b^5+18\,a\,b^6+4\,b^7}{2\,\left(a^3+3\,a^2\,b+3\,a\,b^2+b^3\right)}-\frac{\cos\left(x\right)\,\sqrt{-a\,b^3}\,\left(-16\,a^5\,b^2-48\,a^4\,b^3-32\,a^3\,b^4+32\,a^2\,b^5+48\,a\,b^6+16\,b^7\right)}{8\,\left(a^2+2\,a\,b+b^2\right)\,\left(a^3+2\,a^2\,b+a\,b^2\right)}\right)\,\sqrt{-a\,b^3}}{2\,\left(a^3+2\,a^2\,b+a\,b^2\right)}\right)\,1{}\mathrm{i}}{a^3+2\,a^2\,b+a\,b^2}+\frac{\sqrt{-a\,b^3}\,\left(\frac{\cos\left(x\right)\,\left(a^2\,b^3+6\,a\,b^4+13\,b^5\right)}{4\,\left(a^2+2\,a\,b+b^2\right)}-\frac{\left(\frac{2\,a^5\,b^2+12\,a^4\,b^3+28\,a^3\,b^4+32\,a^2\,b^5+18\,a\,b^6+4\,b^7}{2\,\left(a^3+3\,a^2\,b+3\,a\,b^2+b^3\right)}+\frac{\cos\left(x\right)\,\sqrt{-a\,b^3}\,\left(-16\,a^5\,b^2-48\,a^4\,b^3-32\,a^3\,b^4+32\,a^2\,b^5+48\,a\,b^6+16\,b^7\right)}{8\,\left(a^2+2\,a\,b+b^2\right)\,\left(a^3+2\,a^2\,b+a\,b^2\right)}\right)\,\sqrt{-a\,b^3}}{2\,\left(a^3+2\,a^2\,b+a\,b^2\right)}\right)\,1{}\mathrm{i}}{a^3+2\,a^2\,b+a\,b^2}}{\frac{\frac{3\,b^5}{2}+\frac{a\,b^4}{2}}{a^3+3\,a^2\,b+3\,a\,b^2+b^3}-\frac{\sqrt{-a\,b^3}\,\left(\frac{\cos\left(x\right)\,\left(a^2\,b^3+6\,a\,b^4+13\,b^5\right)}{4\,\left(a^2+2\,a\,b+b^2\right)}+\frac{\left(\frac{2\,a^5\,b^2+12\,a^4\,b^3+28\,a^3\,b^4+32\,a^2\,b^5+18\,a\,b^6+4\,b^7}{2\,\left(a^3+3\,a^2\,b+3\,a\,b^2+b^3\right)}-\frac{\cos\left(x\right)\,\sqrt{-a\,b^3}\,\left(-16\,a^5\,b^2-48\,a^4\,b^3-32\,a^3\,b^4+32\,a^2\,b^5+48\,a\,b^6+16\,b^7\right)}{8\,\left(a^2+2\,a\,b+b^2\right)\,\left(a^3+2\,a^2\,b+a\,b^2\right)}\right)\,\sqrt{-a\,b^3}}{2\,\left(a^3+2\,a^2\,b+a\,b^2\right)}\right)}{a^3+2\,a^2\,b+a\,b^2}+\frac{\sqrt{-a\,b^3}\,\left(\frac{\cos\left(x\right)\,\left(a^2\,b^3+6\,a\,b^4+13\,b^5\right)}{4\,\left(a^2+2\,a\,b+b^2\right)}-\frac{\left(\frac{2\,a^5\,b^2+12\,a^4\,b^3+28\,a^3\,b^4+32\,a^2\,b^5+18\,a\,b^6+4\,b^7}{2\,\left(a^3+3\,a^2\,b+3\,a\,b^2+b^3\right)}+\frac{\cos\left(x\right)\,\sqrt{-a\,b^3}\,\left(-16\,a^5\,b^2-48\,a^4\,b^3-32\,a^3\,b^4+32\,a^2\,b^5+48\,a\,b^6+16\,b^7\right)}{8\,\left(a^2+2\,a\,b+b^2\right)\,\left(a^3+2\,a^2\,b+a\,b^2\right)}\right)\,\sqrt{-a\,b^3}}{2\,\left(a^3+2\,a^2\,b+a\,b^2\right)}\right)}{a^3+2\,a^2\,b+a\,b^2}}\right)\,\sqrt{-a\,b^3}\,1{}\mathrm{i}}{a^3+2\,a^2\,b+a\,b^2}","Not used",1,"log(cos(x) - 1)*(b/(2*(a + b)^2) + 1/(4*(a + b))) - cos(x)/(2*sin(x)^2*(a + b)) - (log(cos(x) + 1)*(a + 3*b))/(4*(a + b)^2) - (atan((((-a*b^3)^(1/2)*((cos(x)*(6*a*b^4 + 13*b^5 + a^2*b^3))/(4*(2*a*b + a^2 + b^2)) + (((18*a*b^6 + 4*b^7 + 32*a^2*b^5 + 28*a^3*b^4 + 12*a^4*b^3 + 2*a^5*b^2)/(2*(3*a*b^2 + 3*a^2*b + a^3 + b^3)) - (cos(x)*(-a*b^3)^(1/2)*(48*a*b^6 + 16*b^7 + 32*a^2*b^5 - 32*a^3*b^4 - 48*a^4*b^3 - 16*a^5*b^2))/(8*(2*a*b + a^2 + b^2)*(a*b^2 + 2*a^2*b + a^3)))*(-a*b^3)^(1/2))/(2*(a*b^2 + 2*a^2*b + a^3)))*1i)/(a*b^2 + 2*a^2*b + a^3) + ((-a*b^3)^(1/2)*((cos(x)*(6*a*b^4 + 13*b^5 + a^2*b^3))/(4*(2*a*b + a^2 + b^2)) - (((18*a*b^6 + 4*b^7 + 32*a^2*b^5 + 28*a^3*b^4 + 12*a^4*b^3 + 2*a^5*b^2)/(2*(3*a*b^2 + 3*a^2*b + a^3 + b^3)) + (cos(x)*(-a*b^3)^(1/2)*(48*a*b^6 + 16*b^7 + 32*a^2*b^5 - 32*a^3*b^4 - 48*a^4*b^3 - 16*a^5*b^2))/(8*(2*a*b + a^2 + b^2)*(a*b^2 + 2*a^2*b + a^3)))*(-a*b^3)^(1/2))/(2*(a*b^2 + 2*a^2*b + a^3)))*1i)/(a*b^2 + 2*a^2*b + a^3))/(((a*b^4)/2 + (3*b^5)/2)/(3*a*b^2 + 3*a^2*b + a^3 + b^3) - ((-a*b^3)^(1/2)*((cos(x)*(6*a*b^4 + 13*b^5 + a^2*b^3))/(4*(2*a*b + a^2 + b^2)) + (((18*a*b^6 + 4*b^7 + 32*a^2*b^5 + 28*a^3*b^4 + 12*a^4*b^3 + 2*a^5*b^2)/(2*(3*a*b^2 + 3*a^2*b + a^3 + b^3)) - (cos(x)*(-a*b^3)^(1/2)*(48*a*b^6 + 16*b^7 + 32*a^2*b^5 - 32*a^3*b^4 - 48*a^4*b^3 - 16*a^5*b^2))/(8*(2*a*b + a^2 + b^2)*(a*b^2 + 2*a^2*b + a^3)))*(-a*b^3)^(1/2))/(2*(a*b^2 + 2*a^2*b + a^3))))/(a*b^2 + 2*a^2*b + a^3) + ((-a*b^3)^(1/2)*((cos(x)*(6*a*b^4 + 13*b^5 + a^2*b^3))/(4*(2*a*b + a^2 + b^2)) - (((18*a*b^6 + 4*b^7 + 32*a^2*b^5 + 28*a^3*b^4 + 12*a^4*b^3 + 2*a^5*b^2)/(2*(3*a*b^2 + 3*a^2*b + a^3 + b^3)) + (cos(x)*(-a*b^3)^(1/2)*(48*a*b^6 + 16*b^7 + 32*a^2*b^5 - 32*a^3*b^4 - 48*a^4*b^3 - 16*a^5*b^2))/(8*(2*a*b + a^2 + b^2)*(a*b^2 + 2*a^2*b + a^3)))*(-a*b^3)^(1/2))/(2*(a*b^2 + 2*a^2*b + a^3))))/(a*b^2 + 2*a^2*b + a^3)))*(-a*b^3)^(1/2)*1i)/(a*b^2 + 2*a^2*b + a^3)","B"
16,1,833,94,5.276898,"\text{Not used}","int(1/(sin(x)^5*(a + b*cos(x)^2)),x)","-\frac{3\,a^3\,\mathrm{atanh}\left(\cos\left(x\right)\right)-3\,a^3\,{\cos\left(x\right)}^3+5\,a^3\,\cos\left(x\right)+9\,a\,b^2\,\cos\left(x\right)+14\,a^2\,b\,\cos\left(x\right)-6\,a^3\,\mathrm{atanh}\left(\cos\left(x\right)\right)\,{\cos\left(x\right)}^2+3\,a^3\,\mathrm{atanh}\left(\cos\left(x\right)\right)\,{\cos\left(x\right)}^4-7\,a\,b^2\,{\cos\left(x\right)}^3-10\,a^2\,b\,{\cos\left(x\right)}^3+15\,a\,b^2\,\mathrm{atanh}\left(\cos\left(x\right)\right)+10\,a^2\,b\,\mathrm{atanh}\left(\cos\left(x\right)\right)-30\,a\,b^2\,\mathrm{atanh}\left(\cos\left(x\right)\right)\,{\cos\left(x\right)}^2-20\,a^2\,b\,\mathrm{atanh}\left(\cos\left(x\right)\right)\,{\cos\left(x\right)}^2+15\,a\,b^2\,\mathrm{atanh}\left(\cos\left(x\right)\right)\,{\cos\left(x\right)}^4+10\,a^2\,b\,\mathrm{atanh}\left(\cos\left(x\right)\right)\,{\cos\left(x\right)}^4+\mathrm{atan}\left(\frac{a\,\cos\left(x\right)\,{\left(-a\,b^5\right)}^{3/2}\,64{}\mathrm{i}-b\,\cos\left(x\right)\,{\left(-a\,b^5\right)}^{3/2}\,64{}\mathrm{i}+a^6\,b\,\cos\left(x\right)\,\sqrt{-a\,b^5}\,9{}\mathrm{i}+a^2\,b^5\,\cos\left(x\right)\,\sqrt{-a\,b^5}\,289{}\mathrm{i}+a^3\,b^4\,\cos\left(x\right)\,\sqrt{-a\,b^5}\,300{}\mathrm{i}+a^4\,b^3\,\cos\left(x\right)\,\sqrt{-a\,b^5}\,190{}\mathrm{i}+a^5\,b^2\,\cos\left(x\right)\,\sqrt{-a\,b^5}\,60{}\mathrm{i}}{9\,a^7\,b^3+60\,a^6\,b^4+190\,a^5\,b^5+300\,a^4\,b^6+225\,a^3\,b^7+64\,a^2\,b^8}\right)\,\sqrt{-a\,b^5}\,8{}\mathrm{i}-\mathrm{atan}\left(\frac{a\,\cos\left(x\right)\,{\left(-a\,b^5\right)}^{3/2}\,64{}\mathrm{i}-b\,\cos\left(x\right)\,{\left(-a\,b^5\right)}^{3/2}\,64{}\mathrm{i}+a^6\,b\,\cos\left(x\right)\,\sqrt{-a\,b^5}\,9{}\mathrm{i}+a^2\,b^5\,\cos\left(x\right)\,\sqrt{-a\,b^5}\,289{}\mathrm{i}+a^3\,b^4\,\cos\left(x\right)\,\sqrt{-a\,b^5}\,300{}\mathrm{i}+a^4\,b^3\,\cos\left(x\right)\,\sqrt{-a\,b^5}\,190{}\mathrm{i}+a^5\,b^2\,\cos\left(x\right)\,\sqrt{-a\,b^5}\,60{}\mathrm{i}}{9\,a^7\,b^3+60\,a^6\,b^4+190\,a^5\,b^5+300\,a^4\,b^6+225\,a^3\,b^7+64\,a^2\,b^8}\right)\,{\cos\left(x\right)}^2\,\sqrt{-a\,b^5}\,16{}\mathrm{i}+\mathrm{atan}\left(\frac{a\,\cos\left(x\right)\,{\left(-a\,b^5\right)}^{3/2}\,64{}\mathrm{i}-b\,\cos\left(x\right)\,{\left(-a\,b^5\right)}^{3/2}\,64{}\mathrm{i}+a^6\,b\,\cos\left(x\right)\,\sqrt{-a\,b^5}\,9{}\mathrm{i}+a^2\,b^5\,\cos\left(x\right)\,\sqrt{-a\,b^5}\,289{}\mathrm{i}+a^3\,b^4\,\cos\left(x\right)\,\sqrt{-a\,b^5}\,300{}\mathrm{i}+a^4\,b^3\,\cos\left(x\right)\,\sqrt{-a\,b^5}\,190{}\mathrm{i}+a^5\,b^2\,\cos\left(x\right)\,\sqrt{-a\,b^5}\,60{}\mathrm{i}}{9\,a^7\,b^3+60\,a^6\,b^4+190\,a^5\,b^5+300\,a^4\,b^6+225\,a^3\,b^7+64\,a^2\,b^8}\right)\,{\cos\left(x\right)}^4\,\sqrt{-a\,b^5}\,8{}\mathrm{i}}{8\,a^4\,{\cos\left(x\right)}^4-16\,a^4\,{\cos\left(x\right)}^2+8\,a^4+24\,a^3\,b\,{\cos\left(x\right)}^4-48\,a^3\,b\,{\cos\left(x\right)}^2+24\,a^3\,b+24\,a^2\,b^2\,{\cos\left(x\right)}^4-48\,a^2\,b^2\,{\cos\left(x\right)}^2+24\,a^2\,b^2+8\,a\,b^3\,{\cos\left(x\right)}^4-16\,a\,b^3\,{\cos\left(x\right)}^2+8\,a\,b^3}","Not used",1,"-(atan((a*cos(x)*(-a*b^5)^(3/2)*64i - b*cos(x)*(-a*b^5)^(3/2)*64i + a^6*b*cos(x)*(-a*b^5)^(1/2)*9i + a^2*b^5*cos(x)*(-a*b^5)^(1/2)*289i + a^3*b^4*cos(x)*(-a*b^5)^(1/2)*300i + a^4*b^3*cos(x)*(-a*b^5)^(1/2)*190i + a^5*b^2*cos(x)*(-a*b^5)^(1/2)*60i)/(64*a^2*b^8 + 225*a^3*b^7 + 300*a^4*b^6 + 190*a^5*b^5 + 60*a^6*b^4 + 9*a^7*b^3))*(-a*b^5)^(1/2)*8i - 3*a^3*cos(x)^3 + 3*a^3*atanh(cos(x)) + 5*a^3*cos(x) - atan((a*cos(x)*(-a*b^5)^(3/2)*64i - b*cos(x)*(-a*b^5)^(3/2)*64i + a^6*b*cos(x)*(-a*b^5)^(1/2)*9i + a^2*b^5*cos(x)*(-a*b^5)^(1/2)*289i + a^3*b^4*cos(x)*(-a*b^5)^(1/2)*300i + a^4*b^3*cos(x)*(-a*b^5)^(1/2)*190i + a^5*b^2*cos(x)*(-a*b^5)^(1/2)*60i)/(64*a^2*b^8 + 225*a^3*b^7 + 300*a^4*b^6 + 190*a^5*b^5 + 60*a^6*b^4 + 9*a^7*b^3))*cos(x)^2*(-a*b^5)^(1/2)*16i + atan((a*cos(x)*(-a*b^5)^(3/2)*64i - b*cos(x)*(-a*b^5)^(3/2)*64i + a^6*b*cos(x)*(-a*b^5)^(1/2)*9i + a^2*b^5*cos(x)*(-a*b^5)^(1/2)*289i + a^3*b^4*cos(x)*(-a*b^5)^(1/2)*300i + a^4*b^3*cos(x)*(-a*b^5)^(1/2)*190i + a^5*b^2*cos(x)*(-a*b^5)^(1/2)*60i)/(64*a^2*b^8 + 225*a^3*b^7 + 300*a^4*b^6 + 190*a^5*b^5 + 60*a^6*b^4 + 9*a^7*b^3))*cos(x)^4*(-a*b^5)^(1/2)*8i + 9*a*b^2*cos(x) + 14*a^2*b*cos(x) - 6*a^3*atanh(cos(x))*cos(x)^2 + 3*a^3*atanh(cos(x))*cos(x)^4 - 7*a*b^2*cos(x)^3 - 10*a^2*b*cos(x)^3 + 15*a*b^2*atanh(cos(x)) + 10*a^2*b*atanh(cos(x)) - 30*a*b^2*atanh(cos(x))*cos(x)^2 - 20*a^2*b*atanh(cos(x))*cos(x)^2 + 15*a*b^2*atanh(cos(x))*cos(x)^4 + 10*a^2*b*atanh(cos(x))*cos(x)^4)/(8*a^4*cos(x)^4 - 16*a^4*cos(x)^2 + 8*a*b^3 + 24*a^3*b + 8*a^4 + 24*a^2*b^2 - 48*a^2*b^2*cos(x)^2 + 24*a^2*b^2*cos(x)^4 - 16*a*b^3*cos(x)^2 - 48*a^3*b*cos(x)^2 + 8*a*b^3*cos(x)^4 + 24*a^3*b*cos(x)^4)","B"
17,1,681,88,2.682798,"\text{Not used}","int(sin(x)^6/(a + b*cos(x)^2),x)","\frac{\frac{{\mathrm{tan}\left(x\right)}^3\,\left(4\,a+9\,b\right)}{8\,b^2}+\frac{\mathrm{tan}\left(x\right)\,\left(4\,a+7\,b\right)}{8\,b^2}}{{\mathrm{tan}\left(x\right)}^4+2\,{\mathrm{tan}\left(x\right)}^2+1}-\frac{\mathrm{atanh}\left(\frac{95\,a^2\,\mathrm{tan}\left(x\right)\,\sqrt{-a^6-5\,a^5\,b-10\,a^4\,b^2-10\,a^3\,b^3-5\,a^2\,b^4-a\,b^5}}{32\,\left(2\,a\,b^4+\frac{469\,a^4\,b}{32}+\frac{215\,a^5}{32}+\frac{287\,a^2\,b^3}{32}+\frac{517\,a^3\,b^2}{32}+\frac{5\,a^6}{4\,b}\right)}+\frac{5\,a^3\,\mathrm{tan}\left(x\right)\,\sqrt{-a^6-5\,a^5\,b-10\,a^4\,b^2-10\,a^3\,b^3-5\,a^2\,b^4-a\,b^5}}{4\,\left(\frac{5\,a^6}{4}+\frac{215\,a^5\,b}{32}+\frac{469\,a^4\,b^2}{32}+\frac{517\,a^3\,b^3}{32}+\frac{287\,a^2\,b^4}{32}+2\,a\,b^5\right)}+\frac{2\,a\,\mathrm{tan}\left(x\right)\,\sqrt{-a^6-5\,a^5\,b-10\,a^4\,b^2-10\,a^3\,b^3-5\,a^2\,b^4-a\,b^5}}{2\,a\,b^3+\frac{517\,a^3\,b}{32}+\frac{469\,a^4}{32}+\frac{287\,a^2\,b^2}{32}+\frac{215\,a^5}{32\,b}+\frac{5\,a^6}{4\,b^2}}\right)\,\sqrt{-a\,{\left(a+b\right)}^5}}{a\,b^3}+\frac{\mathrm{atan}\left(\frac{5717\,a^3\,\mathrm{tan}\left(x\right)}{256\,\left(\frac{15\,a\,b^2}{4}+\frac{3665\,a^2\,b}{256}+\frac{5717\,a^3}{256}+\frac{1143\,a^4}{64\,b}+\frac{235\,a^5}{32\,b^2}+\frac{5\,a^6}{4\,b^3}\right)}+\frac{3665\,a^2\,\mathrm{tan}\left(x\right)}{256\,\left(\frac{15\,a\,b}{4}+\frac{3665\,a^2}{256}+\frac{5717\,a^3}{256\,b}+\frac{1143\,a^4}{64\,b^2}+\frac{235\,a^5}{32\,b^3}+\frac{5\,a^6}{4\,b^4}\right)}+\frac{1143\,a^4\,\mathrm{tan}\left(x\right)}{64\,\left(\frac{15\,a\,b^3}{4}+\frac{5717\,a^3\,b}{256}+\frac{1143\,a^4}{64}+\frac{3665\,a^2\,b^2}{256}+\frac{235\,a^5}{32\,b}+\frac{5\,a^6}{4\,b^2}\right)}+\frac{235\,a^5\,\mathrm{tan}\left(x\right)}{32\,\left(\frac{15\,a\,b^4}{4}+\frac{1143\,a^4\,b}{64}+\frac{235\,a^5}{32}+\frac{3665\,a^2\,b^3}{256}+\frac{5717\,a^3\,b^2}{256}+\frac{5\,a^6}{4\,b}\right)}+\frac{5\,a^6\,\mathrm{tan}\left(x\right)}{4\,\left(\frac{5\,a^6}{4}+\frac{235\,a^5\,b}{32}+\frac{1143\,a^4\,b^2}{64}+\frac{5717\,a^3\,b^3}{256}+\frac{3665\,a^2\,b^4}{256}+\frac{15\,a\,b^5}{4}\right)}+\frac{15\,a\,b\,\mathrm{tan}\left(x\right)}{4\,\left(\frac{15\,a\,b}{4}+\frac{3665\,a^2}{256}+\frac{5717\,a^3}{256\,b}+\frac{1143\,a^4}{64\,b^2}+\frac{235\,a^5}{32\,b^3}+\frac{5\,a^6}{4\,b^4}\right)}\right)\,\left(a^2\,8{}\mathrm{i}+a\,b\,20{}\mathrm{i}+b^2\,15{}\mathrm{i}\right)\,1{}\mathrm{i}}{8\,b^3}","Not used",1,"((tan(x)^3*(4*a + 9*b))/(8*b^2) + (tan(x)*(4*a + 7*b))/(8*b^2))/(2*tan(x)^2 + tan(x)^4 + 1) + (atan((5717*a^3*tan(x))/(256*((15*a*b^2)/4 + (3665*a^2*b)/256 + (5717*a^3)/256 + (1143*a^4)/(64*b) + (235*a^5)/(32*b^2) + (5*a^6)/(4*b^3))) + (3665*a^2*tan(x))/(256*((15*a*b)/4 + (3665*a^2)/256 + (5717*a^3)/(256*b) + (1143*a^4)/(64*b^2) + (235*a^5)/(32*b^3) + (5*a^6)/(4*b^4))) + (1143*a^4*tan(x))/(64*((15*a*b^3)/4 + (5717*a^3*b)/256 + (1143*a^4)/64 + (3665*a^2*b^2)/256 + (235*a^5)/(32*b) + (5*a^6)/(4*b^2))) + (235*a^5*tan(x))/(32*((15*a*b^4)/4 + (1143*a^4*b)/64 + (235*a^5)/32 + (3665*a^2*b^3)/256 + (5717*a^3*b^2)/256 + (5*a^6)/(4*b))) + (5*a^6*tan(x))/(4*((15*a*b^5)/4 + (235*a^5*b)/32 + (5*a^6)/4 + (3665*a^2*b^4)/256 + (5717*a^3*b^3)/256 + (1143*a^4*b^2)/64)) + (15*a*b*tan(x))/(4*((15*a*b)/4 + (3665*a^2)/256 + (5717*a^3)/(256*b) + (1143*a^4)/(64*b^2) + (235*a^5)/(32*b^3) + (5*a^6)/(4*b^4))))*(a*b*20i + a^2*8i + b^2*15i)*1i)/(8*b^3) - (atanh((95*a^2*tan(x)*(- a*b^5 - 5*a^5*b - a^6 - 5*a^2*b^4 - 10*a^3*b^3 - 10*a^4*b^2)^(1/2))/(32*(2*a*b^4 + (469*a^4*b)/32 + (215*a^5)/32 + (287*a^2*b^3)/32 + (517*a^3*b^2)/32 + (5*a^6)/(4*b))) + (5*a^3*tan(x)*(- a*b^5 - 5*a^5*b - a^6 - 5*a^2*b^4 - 10*a^3*b^3 - 10*a^4*b^2)^(1/2))/(4*(2*a*b^5 + (215*a^5*b)/32 + (5*a^6)/4 + (287*a^2*b^4)/32 + (517*a^3*b^3)/32 + (469*a^4*b^2)/32)) + (2*a*tan(x)*(- a*b^5 - 5*a^5*b - a^6 - 5*a^2*b^4 - 10*a^3*b^3 - 10*a^4*b^2)^(1/2))/(2*a*b^3 + (517*a^3*b)/32 + (469*a^4)/32 + (287*a^2*b^2)/32 + (215*a^5)/(32*b) + (5*a^6)/(4*b^2)))*(-a*(a + b)^5)^(1/2))/(a*b^3)","B"
18,1,126,60,2.453051,"\text{Not used}","int(sin(x)^4/(a + b*cos(x)^2),x)","\frac{\cos\left(x\right)\,\sin\left(x\right)}{2\,b}-\frac{a\,\mathrm{atan}\left(\frac{\sin\left(x\right)}{\cos\left(x\right)}\right)}{b^2}-\frac{3\,\mathrm{atan}\left(\frac{\sin\left(x\right)}{\cos\left(x\right)}\right)}{2\,b}-\frac{\mathrm{atanh}\left(\frac{\sin\left(x\right)\,\sqrt{-a^4-3\,a^3\,b-3\,a^2\,b^2-a\,b^3}}{\cos\left(x\right)\,a^2+2\,\cos\left(x\right)\,a\,b+\cos\left(x\right)\,b^2}\right)\,\sqrt{-a^4-3\,a^3\,b-3\,a^2\,b^2-a\,b^3}}{a\,b^2}","Not used",1,"(cos(x)*sin(x))/(2*b) - (a*atan(sin(x)/cos(x)))/b^2 - (3*atan(sin(x)/cos(x)))/(2*b) - (atanh((sin(x)*(- a*b^3 - 3*a^3*b - a^4 - 3*a^2*b^2)^(1/2))/(a^2*cos(x) + b^2*cos(x) + 2*a*b*cos(x)))*(- a*b^3 - 3*a^3*b - a^4 - 3*a^2*b^2)^(1/2))/(a*b^2)","B"
19,1,108,40,2.369671,"\text{Not used}","int(sin(x)^2/(a + b*cos(x)^2),x)","-\frac{\mathrm{atan}\left(\frac{2\,a\,b^2\,\mathrm{tan}\left(x\right)}{2\,a^2\,b+2\,a\,b^2}+\frac{2\,a^2\,b\,\mathrm{tan}\left(x\right)}{2\,a^2\,b+2\,a\,b^2}\right)}{b}-\frac{\mathrm{atanh}\left(\frac{2\,a^2\,b\,\mathrm{tan}\left(x\right)\,\sqrt{-a^2-b\,a}}{2\,a^3\,b+2\,a^2\,b^2}\right)\,\sqrt{-a\,\left(a+b\right)}}{a\,b}","Not used",1,"- atan((2*a*b^2*tan(x))/(2*a*b^2 + 2*a^2*b) + (2*a^2*b*tan(x))/(2*a*b^2 + 2*a^2*b))/b - (atanh((2*a^2*b*tan(x)*(- a*b - a^2)^(1/2))/(2*a^3*b + 2*a^2*b^2))*(-a*(a + b))^(1/2))/(a*b)","B"
20,1,24,30,2.384207,"\text{Not used}","int(1/(a + b*cos(x)^2),x)","\frac{\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(x\right)}{\sqrt{a^2+b\,a}}\right)}{\sqrt{a^2+b\,a}}","Not used",1,"atan((a*tan(x))/(a*b + a^2)^(1/2))/(a*b + a^2)^(1/2)","B"
21,1,34,41,2.301904,"\text{Not used}","int(1/(sin(x)^2*(a + b*cos(x)^2)),x)","\frac{b\,\mathrm{atan}\left(\frac{\sqrt{a}\,\mathrm{tan}\left(x\right)}{\sqrt{a+b}}\right)}{\sqrt{a}\,{\left(a+b\right)}^{3/2}}-\frac{1}{\mathrm{tan}\left(x\right)\,\left(a+b\right)}","Not used",1,"(b*atan((a^(1/2)*tan(x))/(a + b)^(1/2)))/(a^(1/2)*(a + b)^(3/2)) - 1/(tan(x)*(a + b))","B"
22,1,67,61,2.335081,"\text{Not used}","int(1/(sin(x)^4*(a + b*cos(x)^2)),x)","\frac{b^2\,\mathrm{atan}\left(\frac{\sqrt{a}\,\mathrm{tan}\left(x\right)\,\left(a^2+2\,a\,b+b^2\right)}{{\left(a+b\right)}^{5/2}}\right)}{\sqrt{a}\,{\left(a+b\right)}^{5/2}}-\frac{\frac{1}{3\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(x\right)}^2\,\left(a+2\,b\right)}{{\left(a+b\right)}^2}}{{\mathrm{tan}\left(x\right)}^3}","Not used",1,"(b^2*atan((a^(1/2)*tan(x)*(2*a*b + a^2 + b^2))/(a + b)^(5/2)))/(a^(1/2)*(a + b)^(5/2)) - (1/(3*(a + b)) + (tan(x)^2*(a + 2*b))/(a + b)^2)/tan(x)^3","B"
23,1,101,89,2.366624,"\text{Not used}","int(1/(sin(x)^6*(a + b*cos(x)^2)),x)","\frac{b^3\,\mathrm{atan}\left(\frac{\sqrt{a}\,\mathrm{tan}\left(x\right)\,\left(a^3+3\,a^2\,b+3\,a\,b^2+b^3\right)}{{\left(a+b\right)}^{7/2}}\right)}{\sqrt{a}\,{\left(a+b\right)}^{7/2}}-\frac{\frac{1}{5\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(x\right)}^2\,\left(2\,a+3\,b\right)}{3\,{\left(a+b\right)}^2}+\frac{{\mathrm{tan}\left(x\right)}^4\,\left(a^2+3\,a\,b+3\,b^2\right)}{{\left(a+b\right)}^3}}{{\mathrm{tan}\left(x\right)}^5}","Not used",1,"(b^3*atan((a^(1/2)*tan(x)*(3*a*b^2 + 3*a^2*b + a^3 + b^3))/(a + b)^(7/2)))/(a^(1/2)*(a + b)^(7/2)) - (1/(5*(a + b)) + (tan(x)^2*(2*a + 3*b))/(3*(a + b)^2) + (tan(x)^4*(3*a*b + a^2 + 3*b^2))/(a + b)^3)/tan(x)^5","B"
24,1,75,98,0.307413,"\text{Not used}","int(-sin(x)/(3*cos(x)^3 - 4),x)","\frac{6^{2/3}\,\ln\left(\cos\left(x\right)-\frac{6^{2/3}}{3}\right)}{36}+\frac{6^{2/3}\,\ln\left(\cos\left(x\right)-\frac{6^{2/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{6}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{72}-\frac{6^{2/3}\,\ln\left(\cos\left(x\right)+\frac{6^{2/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{6}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{72}","Not used",1,"(6^(2/3)*log(cos(x) - 6^(2/3)/3))/36 + (6^(2/3)*log(cos(x) - (6^(2/3)*(3^(1/2)*1i - 1))/6)*(3^(1/2)*1i - 1))/72 - (6^(2/3)*log(cos(x) + (6^(2/3)*(3^(1/2)*1i + 1))/6)*(3^(1/2)*1i + 1))/72","B"
25,1,4,4,2.244127,"\text{Not used}","int(-1/(cos(x)^2 - 1),x)","-\mathrm{cot}\left(x\right)","Not used",1,"-cot(x)","B"
26,1,10,13,2.248724,"\text{Not used}","int(1/(cos(x)^2 - 1)^2,x)","-\frac{\mathrm{cot}\left(x\right)\,\left({\mathrm{cot}\left(x\right)}^2+3\right)}{3}","Not used",1,"-(cot(x)*(cot(x)^2 + 3))/3","B"
27,1,17,21,2.236806,"\text{Not used}","int(-1/(cos(x)^2 - 1)^3,x)","-\frac{{\mathrm{cot}\left(x\right)}^5}{5}-\frac{2\,{\mathrm{cot}\left(x\right)}^3}{3}-\mathrm{cot}\left(x\right)","Not used",1,"- cot(x) - (2*cot(x)^3)/3 - cot(x)^5/5","B"
28,1,86,78,0.133735,"\text{Not used}","int(cos(x)^7/(a + b*cos(x)^2),x)","\frac{{\sin\left(x\right)}^5}{5\,b}+{\sin\left(x\right)}^3\,\left(\frac{a+b}{3\,b^2}-\frac{1}{b}\right)+\sin\left(x\right)\,\left(\frac{3}{b}+\frac{\left(a+b\right)\,\left(\frac{a+b}{b^2}-\frac{3}{b}\right)}{b}\right)+\frac{a^3\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sin\left(x\right)\,1{}\mathrm{i}}{\sqrt{a+b}}\right)\,1{}\mathrm{i}}{b^{7/2}\,\sqrt{a+b}}","Not used",1,"sin(x)^5/(5*b) + sin(x)^3*((a + b)/(3*b^2) - 1/b) + sin(x)*(3/b + ((a + b)*((a + b)/b^2 - 3/b))/b) + (a^3*atan((b^(1/2)*sin(x)*1i)/(a + b)^(1/2))*1i)/(b^(7/2)*(a + b)^(1/2))","B"
29,1,51,56,2.311883,"\text{Not used}","int(cos(x)^5/(a + b*cos(x)^2),x)","\frac{a^2\,\mathrm{atanh}\left(\frac{\sqrt{b}\,\sin\left(x\right)}{\sqrt{a+b}}\right)}{b^{5/2}\,\sqrt{a+b}}-\frac{{\sin\left(x\right)}^3}{3\,b}-\sin\left(x\right)\,\left(\frac{a+b}{b^2}-\frac{2}{b}\right)","Not used",1,"(a^2*atanh((b^(1/2)*sin(x))/(a + b)^(1/2)))/(b^(5/2)*(a + b)^(1/2)) - sin(x)^3/(3*b) - sin(x)*((a + b)/b^2 - 2/b)","B"
30,1,30,38,0.101197,"\text{Not used}","int(cos(x)^3/(a + b*cos(x)^2),x)","\frac{\sin\left(x\right)}{b}-\frac{a\,\mathrm{atanh}\left(\frac{\sqrt{b}\,\sin\left(x\right)}{\sqrt{a+b}}\right)}{b^{3/2}\,\sqrt{a+b}}","Not used",1,"sin(x)/b - (a*atanh((b^(1/2)*sin(x))/(a + b)^(1/2)))/(b^(3/2)*(a + b)^(1/2))","B"
31,1,21,29,0.090782,"\text{Not used}","int(cos(x)/(a + b*cos(x)^2),x)","\frac{\mathrm{atanh}\left(\frac{\sqrt{b}\,\sin\left(x\right)}{\sqrt{a+b}}\right)}{\sqrt{b}\,\sqrt{a+b}}","Not used",1,"atanh((b^(1/2)*sin(x))/(a + b)^(1/2))/(b^(1/2)*(a + b)^(1/2))","B"
32,1,414,41,2.500409,"\text{Not used}","int(1/(cos(x)*(a + b*cos(x)^2)),x)","\frac{\mathrm{atanh}\left(\sin\left(x\right)\right)}{a}+\frac{\mathrm{atan}\left(\frac{\frac{\left(2\,b^3\,\sin\left(x\right)+\frac{\left(2\,a^2\,b^2-\frac{\sin\left(x\right)\,\left(8\,a^3\,b^2+16\,a^2\,b^3\right)\,\sqrt{b\,\left(a+b\right)}}{4\,\left(a^2+b\,a\right)}\right)\,\sqrt{b\,\left(a+b\right)}}{2\,\left(a^2+b\,a\right)}\right)\,\sqrt{b\,\left(a+b\right)}\,1{}\mathrm{i}}{a^2+b\,a}+\frac{\left(2\,b^3\,\sin\left(x\right)-\frac{\left(2\,a^2\,b^2+\frac{\sin\left(x\right)\,\left(8\,a^3\,b^2+16\,a^2\,b^3\right)\,\sqrt{b\,\left(a+b\right)}}{4\,\left(a^2+b\,a\right)}\right)\,\sqrt{b\,\left(a+b\right)}}{2\,\left(a^2+b\,a\right)}\right)\,\sqrt{b\,\left(a+b\right)}\,1{}\mathrm{i}}{a^2+b\,a}}{\frac{\left(2\,b^3\,\sin\left(x\right)+\frac{\left(2\,a^2\,b^2-\frac{\sin\left(x\right)\,\left(8\,a^3\,b^2+16\,a^2\,b^3\right)\,\sqrt{b\,\left(a+b\right)}}{4\,\left(a^2+b\,a\right)}\right)\,\sqrt{b\,\left(a+b\right)}}{2\,\left(a^2+b\,a\right)}\right)\,\sqrt{b\,\left(a+b\right)}}{a^2+b\,a}-\frac{\left(2\,b^3\,\sin\left(x\right)-\frac{\left(2\,a^2\,b^2+\frac{\sin\left(x\right)\,\left(8\,a^3\,b^2+16\,a^2\,b^3\right)\,\sqrt{b\,\left(a+b\right)}}{4\,\left(a^2+b\,a\right)}\right)\,\sqrt{b\,\left(a+b\right)}}{2\,\left(a^2+b\,a\right)}\right)\,\sqrt{b\,\left(a+b\right)}}{a^2+b\,a}}\right)\,\sqrt{b\,\left(a+b\right)}\,1{}\mathrm{i}}{a^2+b\,a}","Not used",1,"atanh(sin(x))/a + (atan((((2*b^3*sin(x) + ((2*a^2*b^2 - (sin(x)*(16*a^2*b^3 + 8*a^3*b^2)*(b*(a + b))^(1/2))/(4*(a*b + a^2)))*(b*(a + b))^(1/2))/(2*(a*b + a^2)))*(b*(a + b))^(1/2)*1i)/(a*b + a^2) + ((2*b^3*sin(x) - ((2*a^2*b^2 + (sin(x)*(16*a^2*b^3 + 8*a^3*b^2)*(b*(a + b))^(1/2))/(4*(a*b + a^2)))*(b*(a + b))^(1/2))/(2*(a*b + a^2)))*(b*(a + b))^(1/2)*1i)/(a*b + a^2))/(((2*b^3*sin(x) + ((2*a^2*b^2 - (sin(x)*(16*a^2*b^3 + 8*a^3*b^2)*(b*(a + b))^(1/2))/(4*(a*b + a^2)))*(b*(a + b))^(1/2))/(2*(a*b + a^2)))*(b*(a + b))^(1/2))/(a*b + a^2) - ((2*b^3*sin(x) - ((2*a^2*b^2 + (sin(x)*(16*a^2*b^3 + 8*a^3*b^2)*(b*(a + b))^(1/2))/(4*(a*b + a^2)))*(b*(a + b))^(1/2))/(2*(a*b + a^2)))*(b*(a + b))^(1/2))/(a*b + a^2)))*(b*(a + b))^(1/2)*1i)/(a*b + a^2)","B"
33,1,483,59,2.526867,"\text{Not used}","int(1/(cos(x)^3*(a + b*cos(x)^2)),x)","-\frac{a^2\,\sin\left(x\right)+a^2\,\mathrm{atanh}\left(\sin\left(x\right)\right)-2\,b^2\,\mathrm{atanh}\left(\sin\left(x\right)\right)+a\,b\,\sin\left(x\right)-a\,b\,\mathrm{atanh}\left(\sin\left(x\right)\right)-a^2\,\mathrm{atanh}\left(\sin\left(x\right)\right)\,{\sin\left(x\right)}^2+2\,b^2\,\mathrm{atanh}\left(\sin\left(x\right)\right)\,{\sin\left(x\right)}^2+a\,b\,\mathrm{atanh}\left(\sin\left(x\right)\right)\,{\sin\left(x\right)}^2+\mathrm{atan}\left(\frac{b^5\,\sin\left(x\right)\,\sqrt{b^4+a\,b^3}\,8{}\mathrm{i}-a\,\sin\left(x\right)\,{\left(b^4+a\,b^3\right)}^{3/2}\,4{}\mathrm{i}-b\,\sin\left(x\right)\,{\left(b^4+a\,b^3\right)}^{3/2}\,8{}\mathrm{i}+a\,b^4\,\sin\left(x\right)\,\sqrt{b^4+a\,b^3}\,12{}\mathrm{i}+a^4\,b\,\sin\left(x\right)\,\sqrt{b^4+a\,b^3}\,1{}\mathrm{i}+a^2\,b^3\,\sin\left(x\right)\,\sqrt{b^4+a\,b^3}\,1{}\mathrm{i}-a^3\,b^2\,\sin\left(x\right)\,\sqrt{b^4+a\,b^3}\,2{}\mathrm{i}}{-a^5\,b^2+a^4\,b^3+5\,a^3\,b^4+3\,a^2\,b^5}\right)\,\sqrt{b^4+a\,b^3}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{b^5\,\sin\left(x\right)\,\sqrt{b^4+a\,b^3}\,8{}\mathrm{i}-a\,\sin\left(x\right)\,{\left(b^4+a\,b^3\right)}^{3/2}\,4{}\mathrm{i}-b\,\sin\left(x\right)\,{\left(b^4+a\,b^3\right)}^{3/2}\,8{}\mathrm{i}+a\,b^4\,\sin\left(x\right)\,\sqrt{b^4+a\,b^3}\,12{}\mathrm{i}+a^4\,b\,\sin\left(x\right)\,\sqrt{b^4+a\,b^3}\,1{}\mathrm{i}+a^2\,b^3\,\sin\left(x\right)\,\sqrt{b^4+a\,b^3}\,1{}\mathrm{i}-a^3\,b^2\,\sin\left(x\right)\,\sqrt{b^4+a\,b^3}\,2{}\mathrm{i}}{-a^5\,b^2+a^4\,b^3+5\,a^3\,b^4+3\,a^2\,b^5}\right)\,{\sin\left(x\right)}^2\,\sqrt{b^4+a\,b^3}\,2{}\mathrm{i}}{2\,a^3\,{\sin\left(x\right)}^2-2\,a^3+2\,b\,a^2\,{\sin\left(x\right)}^2-2\,b\,a^2}","Not used",1,"-(a^2*sin(x) + a^2*atanh(sin(x)) - 2*b^2*atanh(sin(x)) + atan((b^5*sin(x)*(a*b^3 + b^4)^(1/2)*8i - a*sin(x)*(a*b^3 + b^4)^(3/2)*4i - b*sin(x)*(a*b^3 + b^4)^(3/2)*8i + a*b^4*sin(x)*(a*b^3 + b^4)^(1/2)*12i + a^4*b*sin(x)*(a*b^3 + b^4)^(1/2)*1i + a^2*b^3*sin(x)*(a*b^3 + b^4)^(1/2)*1i - a^3*b^2*sin(x)*(a*b^3 + b^4)^(1/2)*2i)/(3*a^2*b^5 + 5*a^3*b^4 + a^4*b^3 - a^5*b^2))*(a*b^3 + b^4)^(1/2)*2i + a*b*sin(x) - a*b*atanh(sin(x)) - a^2*atanh(sin(x))*sin(x)^2 + 2*b^2*atanh(sin(x))*sin(x)^2 - atan((b^5*sin(x)*(a*b^3 + b^4)^(1/2)*8i - a*sin(x)*(a*b^3 + b^4)^(3/2)*4i - b*sin(x)*(a*b^3 + b^4)^(3/2)*8i + a*b^4*sin(x)*(a*b^3 + b^4)^(1/2)*12i + a^4*b*sin(x)*(a*b^3 + b^4)^(1/2)*1i + a^2*b^3*sin(x)*(a*b^3 + b^4)^(1/2)*1i - a^3*b^2*sin(x)*(a*b^3 + b^4)^(1/2)*2i)/(3*a^2*b^5 + 5*a^3*b^4 + a^4*b^3 - a^5*b^2))*sin(x)^2*(a*b^3 + b^4)^(1/2)*2i + a*b*atanh(sin(x))*sin(x)^2)/(2*a^3*sin(x)^2 - 2*a^2*b - 2*a^3 + 2*a^2*b*sin(x)^2)","B"
34,1,969,90,2.639251,"\text{Not used}","int(1/(cos(x)^5*(a + b*cos(x)^2)),x)","\frac{5\,a^3\,\sin\left(x\right)-3\,a^3\,{\sin\left(x\right)}^3+3\,a^3\,\mathrm{atanh}\left(\sin\left(x\right)\right)+8\,b^3\,\mathrm{atanh}\left(\sin\left(x\right)\right)-4\,a\,b^2\,\sin\left(x\right)+a^2\,b\,\sin\left(x\right)-6\,a^3\,\mathrm{atanh}\left(\sin\left(x\right)\right)\,{\sin\left(x\right)}^2+3\,a^3\,\mathrm{atanh}\left(\sin\left(x\right)\right)\,{\sin\left(x\right)}^4-16\,b^3\,\mathrm{atanh}\left(\sin\left(x\right)\right)\,{\sin\left(x\right)}^2+8\,b^3\,\mathrm{atanh}\left(\sin\left(x\right)\right)\,{\sin\left(x\right)}^4+4\,a\,b^2\,{\sin\left(x\right)}^3+a^2\,b\,{\sin\left(x\right)}^3+4\,a\,b^2\,\mathrm{atanh}\left(\sin\left(x\right)\right)-a^2\,b\,\mathrm{atanh}\left(\sin\left(x\right)\right)-8\,a\,b^2\,\mathrm{atanh}\left(\sin\left(x\right)\right)\,{\sin\left(x\right)}^2+2\,a^2\,b\,\mathrm{atanh}\left(\sin\left(x\right)\right)\,{\sin\left(x\right)}^2+4\,a\,b^2\,\mathrm{atanh}\left(\sin\left(x\right)\right)\,{\sin\left(x\right)}^4-a^2\,b\,\mathrm{atanh}\left(\sin\left(x\right)\right)\,{\sin\left(x\right)}^4+\mathrm{atan}\left(\frac{b^7\,\sin\left(x\right)\,\sqrt{b^6+a\,b^5}\,128{}\mathrm{i}-a\,\sin\left(x\right)\,{\left(b^6+a\,b^5\right)}^{3/2}\,64{}\mathrm{i}-b\,\sin\left(x\right)\,{\left(b^6+a\,b^5\right)}^{3/2}\,128{}\mathrm{i}+a\,b^6\,\sin\left(x\right)\,\sqrt{b^6+a\,b^5}\,192{}\mathrm{i}+a^6\,b\,\sin\left(x\right)\,\sqrt{b^6+a\,b^5}\,9{}\mathrm{i}+a^2\,b^5\,\sin\left(x\right)\,\sqrt{b^6+a\,b^5}\,64{}\mathrm{i}+a^3\,b^4\,\sin\left(x\right)\,\sqrt{b^6+a\,b^5}\,40{}\mathrm{i}+a^4\,b^3\,\sin\left(x\right)\,\sqrt{b^6+a\,b^5}\,25{}\mathrm{i}-a^5\,b^2\,\sin\left(x\right)\,\sqrt{b^6+a\,b^5}\,6{}\mathrm{i}}{9\,a^7\,b^3+3\,a^6\,b^4+19\,a^5\,b^5+65\,a^4\,b^6+40\,a^3\,b^7}\right)\,\sqrt{b^6+a\,b^5}\,8{}\mathrm{i}-\mathrm{atan}\left(\frac{b^7\,\sin\left(x\right)\,\sqrt{b^6+a\,b^5}\,128{}\mathrm{i}-a\,\sin\left(x\right)\,{\left(b^6+a\,b^5\right)}^{3/2}\,64{}\mathrm{i}-b\,\sin\left(x\right)\,{\left(b^6+a\,b^5\right)}^{3/2}\,128{}\mathrm{i}+a\,b^6\,\sin\left(x\right)\,\sqrt{b^6+a\,b^5}\,192{}\mathrm{i}+a^6\,b\,\sin\left(x\right)\,\sqrt{b^6+a\,b^5}\,9{}\mathrm{i}+a^2\,b^5\,\sin\left(x\right)\,\sqrt{b^6+a\,b^5}\,64{}\mathrm{i}+a^3\,b^4\,\sin\left(x\right)\,\sqrt{b^6+a\,b^5}\,40{}\mathrm{i}+a^4\,b^3\,\sin\left(x\right)\,\sqrt{b^6+a\,b^5}\,25{}\mathrm{i}-a^5\,b^2\,\sin\left(x\right)\,\sqrt{b^6+a\,b^5}\,6{}\mathrm{i}}{9\,a^7\,b^3+3\,a^6\,b^4+19\,a^5\,b^5+65\,a^4\,b^6+40\,a^3\,b^7}\right)\,{\sin\left(x\right)}^2\,\sqrt{b^6+a\,b^5}\,16{}\mathrm{i}+\mathrm{atan}\left(\frac{b^7\,\sin\left(x\right)\,\sqrt{b^6+a\,b^5}\,128{}\mathrm{i}-a\,\sin\left(x\right)\,{\left(b^6+a\,b^5\right)}^{3/2}\,64{}\mathrm{i}-b\,\sin\left(x\right)\,{\left(b^6+a\,b^5\right)}^{3/2}\,128{}\mathrm{i}+a\,b^6\,\sin\left(x\right)\,\sqrt{b^6+a\,b^5}\,192{}\mathrm{i}+a^6\,b\,\sin\left(x\right)\,\sqrt{b^6+a\,b^5}\,9{}\mathrm{i}+a^2\,b^5\,\sin\left(x\right)\,\sqrt{b^6+a\,b^5}\,64{}\mathrm{i}+a^3\,b^4\,\sin\left(x\right)\,\sqrt{b^6+a\,b^5}\,40{}\mathrm{i}+a^4\,b^3\,\sin\left(x\right)\,\sqrt{b^6+a\,b^5}\,25{}\mathrm{i}-a^5\,b^2\,\sin\left(x\right)\,\sqrt{b^6+a\,b^5}\,6{}\mathrm{i}}{9\,a^7\,b^3+3\,a^6\,b^4+19\,a^5\,b^5+65\,a^4\,b^6+40\,a^3\,b^7}\right)\,{\sin\left(x\right)}^4\,\sqrt{b^6+a\,b^5}\,8{}\mathrm{i}}{8\,a^4\,{\sin\left(x\right)}^4-16\,a^4\,{\sin\left(x\right)}^2+8\,a^4+8\,b\,a^3\,{\sin\left(x\right)}^4-16\,b\,a^3\,{\sin\left(x\right)}^2+8\,b\,a^3}","Not used",1,"(5*a^3*sin(x) + atan((b^7*sin(x)*(a*b^5 + b^6)^(1/2)*128i - a*sin(x)*(a*b^5 + b^6)^(3/2)*64i - b*sin(x)*(a*b^5 + b^6)^(3/2)*128i + a*b^6*sin(x)*(a*b^5 + b^6)^(1/2)*192i + a^6*b*sin(x)*(a*b^5 + b^6)^(1/2)*9i + a^2*b^5*sin(x)*(a*b^5 + b^6)^(1/2)*64i + a^3*b^4*sin(x)*(a*b^5 + b^6)^(1/2)*40i + a^4*b^3*sin(x)*(a*b^5 + b^6)^(1/2)*25i - a^5*b^2*sin(x)*(a*b^5 + b^6)^(1/2)*6i)/(40*a^3*b^7 + 65*a^4*b^6 + 19*a^5*b^5 + 3*a^6*b^4 + 9*a^7*b^3))*(a*b^5 + b^6)^(1/2)*8i - 3*a^3*sin(x)^3 + 3*a^3*atanh(sin(x)) + 8*b^3*atanh(sin(x)) - 4*a*b^2*sin(x) + a^2*b*sin(x) - atan((b^7*sin(x)*(a*b^5 + b^6)^(1/2)*128i - a*sin(x)*(a*b^5 + b^6)^(3/2)*64i - b*sin(x)*(a*b^5 + b^6)^(3/2)*128i + a*b^6*sin(x)*(a*b^5 + b^6)^(1/2)*192i + a^6*b*sin(x)*(a*b^5 + b^6)^(1/2)*9i + a^2*b^5*sin(x)*(a*b^5 + b^6)^(1/2)*64i + a^3*b^4*sin(x)*(a*b^5 + b^6)^(1/2)*40i + a^4*b^3*sin(x)*(a*b^5 + b^6)^(1/2)*25i - a^5*b^2*sin(x)*(a*b^5 + b^6)^(1/2)*6i)/(40*a^3*b^7 + 65*a^4*b^6 + 19*a^5*b^5 + 3*a^6*b^4 + 9*a^7*b^3))*sin(x)^2*(a*b^5 + b^6)^(1/2)*16i + atan((b^7*sin(x)*(a*b^5 + b^6)^(1/2)*128i - a*sin(x)*(a*b^5 + b^6)^(3/2)*64i - b*sin(x)*(a*b^5 + b^6)^(3/2)*128i + a*b^6*sin(x)*(a*b^5 + b^6)^(1/2)*192i + a^6*b*sin(x)*(a*b^5 + b^6)^(1/2)*9i + a^2*b^5*sin(x)*(a*b^5 + b^6)^(1/2)*64i + a^3*b^4*sin(x)*(a*b^5 + b^6)^(1/2)*40i + a^4*b^3*sin(x)*(a*b^5 + b^6)^(1/2)*25i - a^5*b^2*sin(x)*(a*b^5 + b^6)^(1/2)*6i)/(40*a^3*b^7 + 65*a^4*b^6 + 19*a^5*b^5 + 3*a^6*b^4 + 9*a^7*b^3))*sin(x)^4*(a*b^5 + b^6)^(1/2)*8i - 6*a^3*atanh(sin(x))*sin(x)^2 + 3*a^3*atanh(sin(x))*sin(x)^4 - 16*b^3*atanh(sin(x))*sin(x)^2 + 8*b^3*atanh(sin(x))*sin(x)^4 + 4*a*b^2*sin(x)^3 + a^2*b*sin(x)^3 + 4*a*b^2*atanh(sin(x)) - a^2*b*atanh(sin(x)) - 8*a*b^2*atanh(sin(x))*sin(x)^2 + 2*a^2*b*atanh(sin(x))*sin(x)^2 + 4*a*b^2*atanh(sin(x))*sin(x)^4 - a^2*b*atanh(sin(x))*sin(x)^4)/(8*a^4*sin(x)^4 - 16*a^4*sin(x)^2 + 8*a^3*b + 8*a^4 - 16*a^3*b*sin(x)^2 + 8*a^3*b*sin(x)^4)","B"
35,1,1036,87,2.693766,"\text{Not used}","int(cos(x)^6/(a + b*cos(x)^2),x)","-\frac{\frac{{\mathrm{tan}\left(x\right)}^3\,\left(4\,a-3\,b\right)}{8\,b^2}+\frac{\mathrm{tan}\left(x\right)\,\left(4\,a-5\,b\right)}{8\,b^2}}{{\mathrm{tan}\left(x\right)}^4+2\,{\mathrm{tan}\left(x\right)}^2+1}-\frac{\mathrm{atan}\left(\frac{63\,a^4\,\mathrm{tan}\left(x\right)}{64\,\left(\frac{63\,a^4}{64}-\frac{81\,a^3\,b}{256}+\frac{27\,a^2\,b^2}{256}-\frac{35\,a^5}{32\,b}+\frac{5\,a^6}{4\,b^2}\right)}-\frac{81\,a^3\,\mathrm{tan}\left(x\right)}{256\,\left(\frac{27\,a^2\,b}{256}-\frac{81\,a^3}{256}+\frac{63\,a^4}{64\,b}-\frac{35\,a^5}{32\,b^2}+\frac{5\,a^6}{4\,b^3}\right)}-\frac{35\,a^5\,\mathrm{tan}\left(x\right)}{32\,\left(\frac{63\,a^4\,b}{64}-\frac{35\,a^5}{32}+\frac{27\,a^2\,b^3}{256}-\frac{81\,a^3\,b^2}{256}+\frac{5\,a^6}{4\,b}\right)}+\frac{5\,a^6\,\mathrm{tan}\left(x\right)}{4\,\left(\frac{5\,a^6}{4}-\frac{35\,a^5\,b}{32}+\frac{63\,a^4\,b^2}{64}-\frac{81\,a^3\,b^3}{256}+\frac{27\,a^2\,b^4}{256}\right)}+\frac{27\,a^2\,\mathrm{tan}\left(x\right)}{256\,\left(\frac{27\,a^2}{256}-\frac{81\,a^3}{256\,b}+\frac{63\,a^4}{64\,b^2}-\frac{35\,a^5}{32\,b^3}+\frac{5\,a^6}{4\,b^4}\right)}\right)\,\left(a^2\,8{}\mathrm{i}-a\,b\,4{}\mathrm{i}+b^2\,3{}\mathrm{i}\right)\,1{}\mathrm{i}}{8\,b^3}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-a^5\,\left(a+b\right)}\,\left(\frac{\sqrt{-a^5\,\left(a+b\right)}\,\left(\frac{2\,a^4\,b^6-\frac{a^3\,b^7}{2}+\frac{3\,a^2\,b^8}{2}}{2\,b^6}-\frac{\mathrm{tan}\left(x\right)\,\left(512\,a^3\,b^6+256\,a^2\,b^7\right)\,\sqrt{-a^5\,\left(a+b\right)}}{128\,b^4\,\left(b^4+a\,b^3\right)}\right)}{2\,\left(b^4+a\,b^3\right)}-\frac{\mathrm{tan}\left(x\right)\,\left(128\,a^7-64\,a^6\,b+64\,a^5\,b^2-24\,a^4\,b^3+9\,a^3\,b^4\right)}{64\,b^4}\right)\,1{}\mathrm{i}}{b^4+a\,b^3}-\frac{\sqrt{-a^5\,\left(a+b\right)}\,\left(\frac{\sqrt{-a^5\,\left(a+b\right)}\,\left(\frac{2\,a^4\,b^6-\frac{a^3\,b^7}{2}+\frac{3\,a^2\,b^8}{2}}{2\,b^6}+\frac{\mathrm{tan}\left(x\right)\,\left(512\,a^3\,b^6+256\,a^2\,b^7\right)\,\sqrt{-a^5\,\left(a+b\right)}}{128\,b^4\,\left(b^4+a\,b^3\right)}\right)}{2\,\left(b^4+a\,b^3\right)}+\frac{\mathrm{tan}\left(x\right)\,\left(128\,a^7-64\,a^6\,b+64\,a^5\,b^2-24\,a^4\,b^3+9\,a^3\,b^4\right)}{64\,b^4}\right)\,1{}\mathrm{i}}{b^4+a\,b^3}}{\frac{\sqrt{-a^5\,\left(a+b\right)}\,\left(\frac{\sqrt{-a^5\,\left(a+b\right)}\,\left(\frac{2\,a^4\,b^6-\frac{a^3\,b^7}{2}+\frac{3\,a^2\,b^8}{2}}{2\,b^6}-\frac{\mathrm{tan}\left(x\right)\,\left(512\,a^3\,b^6+256\,a^2\,b^7\right)\,\sqrt{-a^5\,\left(a+b\right)}}{128\,b^4\,\left(b^4+a\,b^3\right)}\right)}{2\,\left(b^4+a\,b^3\right)}-\frac{\mathrm{tan}\left(x\right)\,\left(128\,a^7-64\,a^6\,b+64\,a^5\,b^2-24\,a^4\,b^3+9\,a^3\,b^4\right)}{64\,b^4}\right)}{b^4+a\,b^3}-\frac{-a^8+\frac{5\,a^7\,b}{4}-\frac{3\,a^6\,b^2}{4}+\frac{9\,a^5\,b^3}{32}}{b^6}+\frac{\sqrt{-a^5\,\left(a+b\right)}\,\left(\frac{\sqrt{-a^5\,\left(a+b\right)}\,\left(\frac{2\,a^4\,b^6-\frac{a^3\,b^7}{2}+\frac{3\,a^2\,b^8}{2}}{2\,b^6}+\frac{\mathrm{tan}\left(x\right)\,\left(512\,a^3\,b^6+256\,a^2\,b^7\right)\,\sqrt{-a^5\,\left(a+b\right)}}{128\,b^4\,\left(b^4+a\,b^3\right)}\right)}{2\,\left(b^4+a\,b^3\right)}+\frac{\mathrm{tan}\left(x\right)\,\left(128\,a^7-64\,a^6\,b+64\,a^5\,b^2-24\,a^4\,b^3+9\,a^3\,b^4\right)}{64\,b^4}\right)}{b^4+a\,b^3}}\right)\,\sqrt{-a^5\,\left(a+b\right)}\,1{}\mathrm{i}}{b^4+a\,b^3}","Not used",1,"- ((tan(x)^3*(4*a - 3*b))/(8*b^2) + (tan(x)*(4*a - 5*b))/(8*b^2))/(2*tan(x)^2 + tan(x)^4 + 1) - (atan((63*a^4*tan(x))/(64*((63*a^4)/64 - (81*a^3*b)/256 + (27*a^2*b^2)/256 - (35*a^5)/(32*b) + (5*a^6)/(4*b^2))) - (81*a^3*tan(x))/(256*((27*a^2*b)/256 - (81*a^3)/256 + (63*a^4)/(64*b) - (35*a^5)/(32*b^2) + (5*a^6)/(4*b^3))) - (35*a^5*tan(x))/(32*((63*a^4*b)/64 - (35*a^5)/32 + (27*a^2*b^3)/256 - (81*a^3*b^2)/256 + (5*a^6)/(4*b))) + (5*a^6*tan(x))/(4*((5*a^6)/4 - (35*a^5*b)/32 + (27*a^2*b^4)/256 - (81*a^3*b^3)/256 + (63*a^4*b^2)/64)) + (27*a^2*tan(x))/(256*((27*a^2)/256 - (81*a^3)/(256*b) + (63*a^4)/(64*b^2) - (35*a^5)/(32*b^3) + (5*a^6)/(4*b^4))))*(a^2*8i - a*b*4i + b^2*3i)*1i)/(8*b^3) - (atan((((-a^5*(a + b))^(1/2)*(((-a^5*(a + b))^(1/2)*(((3*a^2*b^8)/2 - (a^3*b^7)/2 + 2*a^4*b^6)/(2*b^6) - (tan(x)*(256*a^2*b^7 + 512*a^3*b^6)*(-a^5*(a + b))^(1/2))/(128*b^4*(a*b^3 + b^4))))/(2*(a*b^3 + b^4)) - (tan(x)*(128*a^7 - 64*a^6*b + 9*a^3*b^4 - 24*a^4*b^3 + 64*a^5*b^2))/(64*b^4))*1i)/(a*b^3 + b^4) - ((-a^5*(a + b))^(1/2)*(((-a^5*(a + b))^(1/2)*(((3*a^2*b^8)/2 - (a^3*b^7)/2 + 2*a^4*b^6)/(2*b^6) + (tan(x)*(256*a^2*b^7 + 512*a^3*b^6)*(-a^5*(a + b))^(1/2))/(128*b^4*(a*b^3 + b^4))))/(2*(a*b^3 + b^4)) + (tan(x)*(128*a^7 - 64*a^6*b + 9*a^3*b^4 - 24*a^4*b^3 + 64*a^5*b^2))/(64*b^4))*1i)/(a*b^3 + b^4))/(((-a^5*(a + b))^(1/2)*(((-a^5*(a + b))^(1/2)*(((3*a^2*b^8)/2 - (a^3*b^7)/2 + 2*a^4*b^6)/(2*b^6) - (tan(x)*(256*a^2*b^7 + 512*a^3*b^6)*(-a^5*(a + b))^(1/2))/(128*b^4*(a*b^3 + b^4))))/(2*(a*b^3 + b^4)) - (tan(x)*(128*a^7 - 64*a^6*b + 9*a^3*b^4 - 24*a^4*b^3 + 64*a^5*b^2))/(64*b^4)))/(a*b^3 + b^4) - ((5*a^7*b)/4 - a^8 + (9*a^5*b^3)/32 - (3*a^6*b^2)/4)/b^6 + ((-a^5*(a + b))^(1/2)*(((-a^5*(a + b))^(1/2)*(((3*a^2*b^8)/2 - (a^3*b^7)/2 + 2*a^4*b^6)/(2*b^6) + (tan(x)*(256*a^2*b^7 + 512*a^3*b^6)*(-a^5*(a + b))^(1/2))/(128*b^4*(a*b^3 + b^4))))/(2*(a*b^3 + b^4)) + (tan(x)*(128*a^7 - 64*a^6*b + 9*a^3*b^4 - 24*a^4*b^3 + 64*a^5*b^2))/(64*b^4)))/(a*b^3 + b^4)))*(-a^5*(a + b))^(1/2)*1i)/(a*b^3 + b^4)","B"
36,1,291,60,2.612131,"\text{Not used}","int(cos(x)^4/(a + b*cos(x)^2),x)","-\frac{2\,a^2\,\mathrm{atan}\left(\frac{\sin\left(x\right)}{\cos\left(x\right)}\right)-b^2\,\mathrm{atan}\left(\frac{\sin\left(x\right)}{\cos\left(x\right)}\right)-\frac{b^2\,\sin\left(2\,x\right)}{2}+a\,b\,\mathrm{atan}\left(\frac{\sin\left(x\right)}{\cos\left(x\right)}\right)-\frac{a\,b\,\sin\left(2\,x\right)}{2}+\mathrm{atan}\left(\frac{a\,\sin\left(x\right)\,{\left(-a^4-b\,a^3\right)}^{3/2}\,8{}\mathrm{i}+b\,\sin\left(x\right)\,{\left(-a^4-b\,a^3\right)}^{3/2}\,4{}\mathrm{i}+a^5\,\sin\left(x\right)\,\sqrt{-a^4-b\,a^3}\,8{}\mathrm{i}-a^2\,b^3\,\sin\left(x\right)\,\sqrt{-a^4-b\,a^3}\,2{}\mathrm{i}+a^3\,b^2\,\sin\left(x\right)\,\sqrt{-a^4-b\,a^3}\,1{}\mathrm{i}+a\,b^4\,\sin\left(x\right)\,\sqrt{-a^4-b\,a^3}\,1{}\mathrm{i}+a^4\,b\,\sin\left(x\right)\,\sqrt{-a^4-b\,a^3}\,12{}\mathrm{i}}{3\,\cos\left(x\right)\,a^5\,b^2+5\,\cos\left(x\right)\,a^4\,b^3+\cos\left(x\right)\,a^3\,b^4-\cos\left(x\right)\,a^2\,b^5}\right)\,\sqrt{-a^4-b\,a^3}\,2{}\mathrm{i}}{2\,b^3+2\,a\,b^2}","Not used",1,"-(2*a^2*atan(sin(x)/cos(x)) - b^2*atan(sin(x)/cos(x)) + atan((a*sin(x)*(- a^3*b - a^4)^(3/2)*8i + b*sin(x)*(- a^3*b - a^4)^(3/2)*4i + a^5*sin(x)*(- a^3*b - a^4)^(1/2)*8i - a^2*b^3*sin(x)*(- a^3*b - a^4)^(1/2)*2i + a^3*b^2*sin(x)*(- a^3*b - a^4)^(1/2)*1i + a*b^4*sin(x)*(- a^3*b - a^4)^(1/2)*1i + a^4*b*sin(x)*(- a^3*b - a^4)^(1/2)*12i)/(a^3*b^4*cos(x) - a^2*b^5*cos(x) + 5*a^4*b^3*cos(x) + 3*a^5*b^2*cos(x)))*(- a^3*b - a^4)^(1/2)*2i - (b^2*sin(2*x))/2 + a*b*atan(sin(x)/cos(x)) - (a*b*sin(2*x))/2)/(2*a*b^2 + 2*b^3)","B"
37,1,425,38,2.549233,"\text{Not used}","int(cos(x)^2/(a + b*cos(x)^2),x)","\frac{x}{b}-\frac{\mathrm{atan}\left(\frac{\frac{\left(2\,a^3\,\mathrm{tan}\left(x\right)-\frac{\left(2\,a^2\,b^2-\frac{\mathrm{tan}\left(x\right)\,\left(16\,a^3\,b^2+8\,a^2\,b^3\right)\,\sqrt{-a\,\left(a+b\right)}}{4\,\left(b^2+a\,b\right)}\right)\,\sqrt{-a\,\left(a+b\right)}}{2\,\left(b^2+a\,b\right)}\right)\,\sqrt{-a\,\left(a+b\right)}\,1{}\mathrm{i}}{b^2+a\,b}+\frac{\left(2\,a^3\,\mathrm{tan}\left(x\right)+\frac{\left(2\,a^2\,b^2+\frac{\mathrm{tan}\left(x\right)\,\left(16\,a^3\,b^2+8\,a^2\,b^3\right)\,\sqrt{-a\,\left(a+b\right)}}{4\,\left(b^2+a\,b\right)}\right)\,\sqrt{-a\,\left(a+b\right)}}{2\,\left(b^2+a\,b\right)}\right)\,\sqrt{-a\,\left(a+b\right)}\,1{}\mathrm{i}}{b^2+a\,b}}{\frac{\left(2\,a^3\,\mathrm{tan}\left(x\right)-\frac{\left(2\,a^2\,b^2-\frac{\mathrm{tan}\left(x\right)\,\left(16\,a^3\,b^2+8\,a^2\,b^3\right)\,\sqrt{-a\,\left(a+b\right)}}{4\,\left(b^2+a\,b\right)}\right)\,\sqrt{-a\,\left(a+b\right)}}{2\,\left(b^2+a\,b\right)}\right)\,\sqrt{-a\,\left(a+b\right)}}{b^2+a\,b}-\frac{\left(2\,a^3\,\mathrm{tan}\left(x\right)+\frac{\left(2\,a^2\,b^2+\frac{\mathrm{tan}\left(x\right)\,\left(16\,a^3\,b^2+8\,a^2\,b^3\right)\,\sqrt{-a\,\left(a+b\right)}}{4\,\left(b^2+a\,b\right)}\right)\,\sqrt{-a\,\left(a+b\right)}}{2\,\left(b^2+a\,b\right)}\right)\,\sqrt{-a\,\left(a+b\right)}}{b^2+a\,b}}\right)\,\sqrt{-a\,\left(a+b\right)}\,1{}\mathrm{i}}{b^2+a\,b}","Not used",1,"x/b - (atan((((2*a^3*tan(x) - ((2*a^2*b^2 - (tan(x)*(8*a^2*b^3 + 16*a^3*b^2)*(-a*(a + b))^(1/2))/(4*(a*b + b^2)))*(-a*(a + b))^(1/2))/(2*(a*b + b^2)))*(-a*(a + b))^(1/2)*1i)/(a*b + b^2) + ((2*a^3*tan(x) + ((2*a^2*b^2 + (tan(x)*(8*a^2*b^3 + 16*a^3*b^2)*(-a*(a + b))^(1/2))/(4*(a*b + b^2)))*(-a*(a + b))^(1/2))/(2*(a*b + b^2)))*(-a*(a + b))^(1/2)*1i)/(a*b + b^2))/(((2*a^3*tan(x) - ((2*a^2*b^2 - (tan(x)*(8*a^2*b^3 + 16*a^3*b^2)*(-a*(a + b))^(1/2))/(4*(a*b + b^2)))*(-a*(a + b))^(1/2))/(2*(a*b + b^2)))*(-a*(a + b))^(1/2))/(a*b + b^2) - ((2*a^3*tan(x) + ((2*a^2*b^2 + (tan(x)*(8*a^2*b^3 + 16*a^3*b^2)*(-a*(a + b))^(1/2))/(4*(a*b + b^2)))*(-a*(a + b))^(1/2))/(2*(a*b + b^2)))*(-a*(a + b))^(1/2))/(a*b + b^2)))*(-a*(a + b))^(1/2)*1i)/(a*b + b^2)","B"
38,1,24,30,0.002161,"\text{Not used}","int(1/(a + b*cos(x)^2),x)","\frac{\mathrm{atan}\left(\frac{a\,\mathrm{tan}\left(x\right)}{\sqrt{a^2+b\,a}}\right)}{\sqrt{a^2+b\,a}}","Not used",1,"atan((a*tan(x))/(a*b + a^2)^(1/2))/(a*b + a^2)^(1/2)","B"
39,1,30,37,2.378915,"\text{Not used}","int(1/(cos(x)^2*(a + b*cos(x)^2)),x)","\frac{\mathrm{tan}\left(x\right)}{a}-\frac{b\,\mathrm{atan}\left(\frac{\sqrt{a}\,\mathrm{tan}\left(x\right)}{\sqrt{a+b}}\right)}{a^{3/2}\,\sqrt{a+b}}","Not used",1,"tan(x)/a - (b*atan((a^(1/2)*tan(x))/(a + b)^(1/2)))/(a^(3/2)*(a + b)^(1/2))","B"
40,1,51,56,2.308975,"\text{Not used}","int(1/(cos(x)^4*(a + b*cos(x)^2)),x)","\frac{{\mathrm{tan}\left(x\right)}^3}{3\,a}-\mathrm{tan}\left(x\right)\,\left(\frac{a+b}{a^2}-\frac{2}{a}\right)+\frac{b^2\,\mathrm{atan}\left(\frac{\sqrt{a}\,\mathrm{tan}\left(x\right)}{\sqrt{a+b}}\right)}{a^{5/2}\,\sqrt{a+b}}","Not used",1,"tan(x)^3/(3*a) - tan(x)*((a + b)/a^2 - 2/a) + (b^2*atan((a^(1/2)*tan(x))/(a + b)^(1/2)))/(a^(5/2)*(a + b)^(1/2))","B"
41,1,84,79,2.304262,"\text{Not used}","int(1/(cos(x)^6*(a + b*cos(x)^2)),x)","\frac{{\mathrm{tan}\left(x\right)}^5}{5\,a}-{\mathrm{tan}\left(x\right)}^3\,\left(\frac{a+b}{3\,a^2}-\frac{1}{a}\right)+\mathrm{tan}\left(x\right)\,\left(\frac{3}{a}+\frac{\left(a+b\right)\,\left(\frac{a+b}{a^2}-\frac{3}{a}\right)}{a}\right)-\frac{b^3\,\mathrm{atan}\left(\frac{\sqrt{a}\,\mathrm{tan}\left(x\right)}{\sqrt{a+b}}\right)}{a^{7/2}\,\sqrt{a+b}}","Not used",1,"tan(x)^5/(5*a) - tan(x)^3*((a + b)/(3*a^2) - 1/a) + tan(x)*(3/a + ((a + b)*((a + b)/a^2 - 3/a))/a) - (b^3*atan((a^(1/2)*tan(x))/(a + b)^(1/2)))/(a^(7/2)*(a + b)^(1/2))","B"
42,1,52,65,2.340984,"\text{Not used}","int(1/(a + b*cos(x)^2)^2,x)","\frac{\mathrm{atan}\left(\frac{\sqrt{a}\,\mathrm{tan}\left(x\right)}{\sqrt{a+b}}\right)\,\left(2\,a+b\right)}{2\,a^{3/2}\,{\left(a+b\right)}^{3/2}}-\frac{b\,\mathrm{tan}\left(x\right)}{2\,a\,\left(a+b\right)\,\left(a\,{\mathrm{tan}\left(x\right)}^2+a+b\right)}","Not used",1,"(atan((a^(1/2)*tan(x))/(a + b)^(1/2))*(2*a + b))/(2*a^(3/2)*(a + b)^(3/2)) - (b*tan(x))/(2*a*(a + b)*(a + b + a*tan(x)^2))","B"
43,1,123,107,2.439917,"\text{Not used}","int(1/(a + b*cos(x)^2)^3,x)","\frac{\mathrm{atan}\left(\frac{\sqrt{a}\,\mathrm{tan}\left(x\right)}{\sqrt{a+b}}\right)\,\left(8\,a^2+8\,a\,b+3\,b^2\right)}{8\,a^{5/2}\,{\left(a+b\right)}^{5/2}}-\frac{\frac{\mathrm{tan}\left(x\right)\,\left(3\,b^2+8\,a\,b\right)}{8\,a^2\,\left(a+b\right)}+\frac{{\mathrm{tan}\left(x\right)}^3\,\left(5\,b^2+8\,a\,b\right)}{8\,a\,{\left(a+b\right)}^2}}{2\,a\,b+{\mathrm{tan}\left(x\right)}^2\,\left(2\,a^2+2\,b\,a\right)+a^2\,{\mathrm{tan}\left(x\right)}^4+a^2+b^2}","Not used",1,"(atan((a^(1/2)*tan(x))/(a + b)^(1/2))*(8*a*b + 8*a^2 + 3*b^2))/(8*a^(5/2)*(a + b)^(5/2)) - ((tan(x)*(8*a*b + 3*b^2))/(8*a^2*(a + b)) + (tan(x)^3*(8*a*b + 5*b^2))/(8*a*(a + b)^2))/(2*a*b + tan(x)^2*(2*a*b + 2*a^2) + a^2*tan(x)^4 + a^2 + b^2)","B"
44,1,26,34,2.324637,"\text{Not used}","int(1/(cos(x)^2 + 1),x)","\frac{\sqrt{2}\,\left(x-\mathrm{atan}\left(\mathrm{tan}\left(x\right)\right)\right)}{2}+\frac{\sqrt{2}\,\mathrm{atan}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)}{2}\right)}{2}","Not used",1,"(2^(1/2)*(x - atan(tan(x))))/2 + (2^(1/2)*atan((2^(1/2)*tan(x))/2))/2","B"
45,1,40,55,2.169798,"\text{Not used}","int(1/(cos(x)^2 + 1)^2,x)","\frac{3\,\sqrt{2}\,\left(x-\mathrm{atan}\left(\mathrm{tan}\left(x\right)\right)\right)}{8}-\frac{\mathrm{tan}\left(x\right)}{4\,\left({\mathrm{tan}\left(x\right)}^2+2\right)}+\frac{3\,\sqrt{2}\,\mathrm{atan}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)}{2}\right)}{8}","Not used",1,"(3*2^(1/2)*(x - atan(tan(x))))/8 - tan(x)/(4*(tan(x)^2 + 2)) + (3*2^(1/2)*atan((2^(1/2)*tan(x))/2))/8","B"
46,1,53,71,2.148548,"\text{Not used}","int(1/(cos(x)^2 + 1)^3,x)","\frac{19\,\sqrt{2}\,\left(x-\mathrm{atan}\left(\mathrm{tan}\left(x\right)\right)\right)}{64}-\frac{\frac{13\,{\mathrm{tan}\left(x\right)}^3}{32}+\frac{11\,\mathrm{tan}\left(x\right)}{16}}{{\mathrm{tan}\left(x\right)}^4+4\,{\mathrm{tan}\left(x\right)}^2+4}+\frac{19\,\sqrt{2}\,\mathrm{atan}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)}{2}\right)}{64}","Not used",1,"(19*2^(1/2)*(x - atan(tan(x))))/64 - ((11*tan(x))/16 + (13*tan(x)^3)/32)/(4*tan(x)^2 + tan(x)^4 + 4) + (19*2^(1/2)*atan((2^(1/2)*tan(x))/2))/64","B"
47,1,10,12,0.034538,"\text{Not used}","int((1 - cos(x)^2)^(1/2),x)","-\mathrm{cot}\left(x\right)\,\sqrt{{\sin\left(x\right)}^2}","Not used",1,"-cot(x)*(sin(x)^2)^(1/2)","B"
48,1,39,14,2.294593,"\text{Not used}","int((cos(x)^2 - 1)^(1/2),x)","-\frac{\sqrt{-4\,{\sin\left(x\right)}^2}\,\left(-{\sin\left(x\right)}^2+\frac{\sin\left(2\,x\right)\,1{}\mathrm{i}}{2}+1\right)}{{\sin\left(x\right)}^2\,2{}\mathrm{i}+\sin\left(2\,x\right)}","Not used",1,"-((-4*sin(x)^2)^(1/2)*((sin(2*x)*1i)/2 - sin(x)^2 + 1))/(sin(2*x) + sin(x)^2*2i)","B"
49,0,-1,29,0.000000,"\text{Not used}","int((1 - cos(x)^2)^(3/2),x)","\int {\left(1-{\cos\left(x\right)}^2\right)}^{3/2} \,d x","Not used",1,"int((1 - cos(x)^2)^(3/2), x)","F"
50,0,-1,33,0.000000,"\text{Not used}","int((cos(x)^2 - 1)^(3/2),x)","\int {\left({\cos\left(x\right)}^2-1\right)}^{3/2} \,d x","Not used",1,"int((cos(x)^2 - 1)^(3/2), x)","F"
51,0,-1,15,0.000000,"\text{Not used}","int(1/(1 - cos(x)^2)^(1/2),x)","\int \frac{1}{\sqrt{1-{\cos\left(x\right)}^2}} \,d x","Not used",1,"int(1/(1 - cos(x)^2)^(1/2), x)","F"
52,0,-1,17,0.000000,"\text{Not used}","int(1/(cos(x)^2 - 1)^(1/2),x)","\int \frac{1}{\sqrt{{\cos\left(x\right)}^2-1}} \,d x","Not used",1,"int(1/(cos(x)^2 - 1)^(1/2), x)","F"
53,0,-1,32,0.000000,"\text{Not used}","int(1/(1 - cos(x)^2)^(3/2),x)","\int \frac{1}{{\left(1-{\cos\left(x\right)}^2\right)}^{3/2}} \,d x","Not used",1,"int(1/(1 - cos(x)^2)^(3/2), x)","F"
54,0,-1,36,0.000000,"\text{Not used}","int(1/(cos(x)^2 - 1)^(3/2),x)","\int \frac{1}{{\left({\cos\left(x\right)}^2-1\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(x)^2 - 1)^(3/2), x)","F"
55,1,7,9,0.008545,"\text{Not used}","int((cos(x)^2 + 1)^(1/2),x)","\sqrt{2}\,\mathrm{E}\left(x\middle|\frac{1}{2}\right)","Not used",1,"2^(1/2)*ellipticE(x, 1/2)","B"
56,0,-1,32,0.000000,"\text{Not used}","int((- cos(x)^2 - 1)^(1/2),x)","\int \sqrt{-{\cos\left(x\right)}^2-1} \,d x","Not used",1,"int((- cos(x)^2 - 1)^(1/2), x)","F"
57,0,-1,42,0.000000,"\text{Not used}","int((a + b*cos(x)^2)^(1/2),x)","\int \sqrt{b\,{\cos\left(x\right)}^2+a} \,d x","Not used",1,"int((a + b*cos(x)^2)^(1/2), x)","F"
58,0,-1,43,0.000000,"\text{Not used}","int((cos(x)^2 + 1)^(3/2),x)","\int {\left({\cos\left(x\right)}^2+1\right)}^{3/2} \,d x","Not used",1,"int((cos(x)^2 + 1)^(3/2), x)","F"
59,0,-1,89,0.000000,"\text{Not used}","int((- cos(x)^2 - 1)^(3/2),x)","\int {\left(-{\cos\left(x\right)}^2-1\right)}^{3/2} \,d x","Not used",1,"int((- cos(x)^2 - 1)^(3/2), x)","F"
60,0,-1,121,0.000000,"\text{Not used}","int((a + b*cos(x)^2)^(3/2),x)","\int {\left(b\,{\cos\left(x\right)}^2+a\right)}^{3/2} \,d x","Not used",1,"int((a + b*cos(x)^2)^(3/2), x)","F"
61,0,-1,9,0.000000,"\text{Not used}","int(1/(cos(x)^2 + 1)^(1/2),x)","\int \frac{1}{\sqrt{{\cos\left(x\right)}^2+1}} \,d x","Not used",1,"int(1/(cos(x)^2 + 1)^(1/2), x)","F"
62,0,-1,32,0.000000,"\text{Not used}","int(1/(- cos(x)^2 - 1)^(1/2),x)","\int \frac{1}{\sqrt{-{\cos\left(x\right)}^2-1}} \,d x","Not used",1,"int(1/(- cos(x)^2 - 1)^(1/2), x)","F"
63,0,-1,42,0.000000,"\text{Not used}","int(1/(a + b*cos(x)^2)^(1/2),x)","\int \frac{1}{\sqrt{b\,{\cos\left(x\right)}^2+a}} \,d x","Not used",1,"int(1/(a + b*cos(x)^2)^(1/2), x)","F"
64,0,-1,32,0.000000,"\text{Not used}","int(1/(cos(x)^2 + 1)^(3/2),x)","\int \frac{1}{{\left({\cos\left(x\right)}^2+1\right)}^{3/2}} \,d x","Not used",1,"int(1/(cos(x)^2 + 1)^(3/2), x)","F"
65,0,-1,56,0.000000,"\text{Not used}","int(1/(- cos(x)^2 - 1)^(3/2),x)","\int \frac{1}{{\left(-{\cos\left(x\right)}^2-1\right)}^{3/2}} \,d x","Not used",1,"int(1/(- cos(x)^2 - 1)^(3/2), x)","F"
66,0,-1,78,0.000000,"\text{Not used}","int(1/(a + b*cos(x)^2)^(3/2),x)","\int \frac{1}{{\left(b\,{\cos\left(x\right)}^2+a\right)}^{3/2}} \,d x","Not used",1,"int(1/(a + b*cos(x)^2)^(3/2), x)","F"
67,0,-1,9,0.000000,"\text{Not used}","int(cos(x)/(cos(x)^2 + 1)^(1/2),x)","\int \frac{\cos\left(x\right)}{\sqrt{{\cos\left(x\right)}^2+1}} \,d x","Not used",1,"int(cos(x)/(cos(x)^2 + 1)^(1/2), x)","F"
68,0,-1,15,0.000000,"\text{Not used}","int(cos(3*x + 5)/(cos(3*x + 5)^2 + 3)^(1/2),x)","\int \frac{\cos\left(3\,x+5\right)}{\sqrt{{\cos\left(3\,x+5\right)}^2+3}} \,d x","Not used",1,"int(cos(3*x + 5)/(cos(3*x + 5)^2 + 3)^(1/2), x)","F"
69,0,-1,9,0.000000,"\text{Not used}","int(cos(x)/(4 - cos(x)^2)^(1/2),x)","\int \frac{\cos\left(x\right)}{\sqrt{4-{\cos\left(x\right)}^2}} \,d x","Not used",1,"int(cos(x)/(4 - cos(x)^2)^(1/2), x)","F"
70,1,926,487,2.655481,"\text{Not used}","int(1/(a + b*cos(x)^4),x)","-2\,\mathrm{atanh}\left(\frac{8\,a^6\,b\,\mathrm{tan}\left(x\right)\,\sqrt{-\frac{a^2}{16\,\left(a^4+b\,a^3\right)}-\frac{\sqrt{-a^3\,b}}{16\,\left(a^4+b\,a^3\right)}}}{\frac{2\,a^9\,b}{a^4+b\,a^3}-2\,a^4\,b^2-2\,a^5\,b+\frac{2\,a^8\,b^2}{a^4+b\,a^3}+\frac{2\,a^7\,b\,\sqrt{-a^3\,b}}{a^4+b\,a^3}+\frac{2\,a^6\,b^2\,\sqrt{-a^3\,b}}{a^4+b\,a^3}}-\frac{8\,a^2\,b\,\mathrm{tan}\left(x\right)\,\sqrt{-\frac{a^2}{16\,\left(a^4+b\,a^3\right)}-\frac{\sqrt{-a^3\,b}}{16\,\left(a^4+b\,a^3\right)}}}{\frac{2\,a^5\,b}{a^4+b\,a^3}-2\,a\,b+\frac{2\,a^3\,b\,\sqrt{-a^3\,b}}{a^4+b\,a^3}}+\frac{8\,a^4\,b\,\mathrm{tan}\left(x\right)\,\sqrt{-a^3\,b}\,\sqrt{-\frac{a^2}{16\,\left(a^4+b\,a^3\right)}-\frac{\sqrt{-a^3\,b}}{16\,\left(a^4+b\,a^3\right)}}}{\frac{2\,a^9\,b}{a^4+b\,a^3}-2\,a^4\,b^2-2\,a^5\,b+\frac{2\,a^8\,b^2}{a^4+b\,a^3}+\frac{2\,a^7\,b\,\sqrt{-a^3\,b}}{a^4+b\,a^3}+\frac{2\,a^6\,b^2\,\sqrt{-a^3\,b}}{a^4+b\,a^3}}\right)\,\sqrt{-\frac{a^2+\sqrt{-a^3\,b}}{16\,\left(a^4+b\,a^3\right)}}-2\,\mathrm{atanh}\left(\frac{8\,a^2\,b\,\mathrm{tan}\left(x\right)\,\sqrt{\frac{\sqrt{-a^3\,b}}{16\,\left(a^4+b\,a^3\right)}-\frac{a^2}{16\,\left(a^4+b\,a^3\right)}}}{2\,a\,b-\frac{2\,a^5\,b}{a^4+b\,a^3}+\frac{2\,a^3\,b\,\sqrt{-a^3\,b}}{a^4+b\,a^3}}-\frac{8\,a^6\,b\,\mathrm{tan}\left(x\right)\,\sqrt{\frac{\sqrt{-a^3\,b}}{16\,\left(a^4+b\,a^3\right)}-\frac{a^2}{16\,\left(a^4+b\,a^3\right)}}}{2\,a^5\,b+2\,a^4\,b^2-\frac{2\,a^9\,b}{a^4+b\,a^3}-\frac{2\,a^8\,b^2}{a^4+b\,a^3}+\frac{2\,a^7\,b\,\sqrt{-a^3\,b}}{a^4+b\,a^3}+\frac{2\,a^6\,b^2\,\sqrt{-a^3\,b}}{a^4+b\,a^3}}+\frac{8\,a^4\,b\,\mathrm{tan}\left(x\right)\,\sqrt{-a^3\,b}\,\sqrt{\frac{\sqrt{-a^3\,b}}{16\,\left(a^4+b\,a^3\right)}-\frac{a^2}{16\,\left(a^4+b\,a^3\right)}}}{2\,a^5\,b+2\,a^4\,b^2-\frac{2\,a^9\,b}{a^4+b\,a^3}-\frac{2\,a^8\,b^2}{a^4+b\,a^3}+\frac{2\,a^7\,b\,\sqrt{-a^3\,b}}{a^4+b\,a^3}+\frac{2\,a^6\,b^2\,\sqrt{-a^3\,b}}{a^4+b\,a^3}}\right)\,\sqrt{-\frac{a^2-\sqrt{-a^3\,b}}{16\,\left(a^4+b\,a^3\right)}}","Not used",1,"- 2*atanh((8*a^6*b*tan(x)*(- a^2/(16*(a^3*b + a^4)) - (-a^3*b)^(1/2)/(16*(a^3*b + a^4)))^(1/2))/((2*a^9*b)/(a^3*b + a^4) - 2*a^4*b^2 - 2*a^5*b + (2*a^8*b^2)/(a^3*b + a^4) + (2*a^7*b*(-a^3*b)^(1/2))/(a^3*b + a^4) + (2*a^6*b^2*(-a^3*b)^(1/2))/(a^3*b + a^4)) - (8*a^2*b*tan(x)*(- a^2/(16*(a^3*b + a^4)) - (-a^3*b)^(1/2)/(16*(a^3*b + a^4)))^(1/2))/((2*a^5*b)/(a^3*b + a^4) - 2*a*b + (2*a^3*b*(-a^3*b)^(1/2))/(a^3*b + a^4)) + (8*a^4*b*tan(x)*(-a^3*b)^(1/2)*(- a^2/(16*(a^3*b + a^4)) - (-a^3*b)^(1/2)/(16*(a^3*b + a^4)))^(1/2))/((2*a^9*b)/(a^3*b + a^4) - 2*a^4*b^2 - 2*a^5*b + (2*a^8*b^2)/(a^3*b + a^4) + (2*a^7*b*(-a^3*b)^(1/2))/(a^3*b + a^4) + (2*a^6*b^2*(-a^3*b)^(1/2))/(a^3*b + a^4)))*(-(a^2 + (-a^3*b)^(1/2))/(16*(a^3*b + a^4)))^(1/2) - 2*atanh((8*a^2*b*tan(x)*((-a^3*b)^(1/2)/(16*(a^3*b + a^4)) - a^2/(16*(a^3*b + a^4)))^(1/2))/(2*a*b - (2*a^5*b)/(a^3*b + a^4) + (2*a^3*b*(-a^3*b)^(1/2))/(a^3*b + a^4)) - (8*a^6*b*tan(x)*((-a^3*b)^(1/2)/(16*(a^3*b + a^4)) - a^2/(16*(a^3*b + a^4)))^(1/2))/(2*a^5*b + 2*a^4*b^2 - (2*a^9*b)/(a^3*b + a^4) - (2*a^8*b^2)/(a^3*b + a^4) + (2*a^7*b*(-a^3*b)^(1/2))/(a^3*b + a^4) + (2*a^6*b^2*(-a^3*b)^(1/2))/(a^3*b + a^4)) + (8*a^4*b*tan(x)*(-a^3*b)^(1/2)*((-a^3*b)^(1/2)/(16*(a^3*b + a^4)) - a^2/(16*(a^3*b + a^4)))^(1/2))/(2*a^5*b + 2*a^4*b^2 - (2*a^9*b)/(a^3*b + a^4) - (2*a^8*b^2)/(a^3*b + a^4) + (2*a^7*b*(-a^3*b)^(1/2))/(a^3*b + a^4) + (2*a^6*b^2*(-a^3*b)^(1/2))/(a^3*b + a^4)))*(-(a^2 - (-a^3*b)^(1/2))/(16*(a^3*b + a^4)))^(1/2)","B"
71,1,938,101,2.596093,"\text{Not used}","int(1/(a - b*cos(x)^4),x)","2\,\mathrm{atanh}\left(\frac{8\,a^6\,b\,\mathrm{tan}\left(x\right)\,\sqrt{\frac{a^2}{16\,\left(a^3\,b-a^4\right)}+\frac{\sqrt{a^3\,b}}{16\,\left(a^3\,b-a^4\right)}}}{2\,a^5\,b-2\,a^4\,b^2-\frac{2\,a^8\,b^2}{a^3\,b-a^4}+\frac{2\,a^9\,b}{a^3\,b-a^4}-\frac{2\,a^6\,b^2\,\sqrt{a^3\,b}}{a^3\,b-a^4}+\frac{2\,a^7\,b\,\sqrt{a^3\,b}}{a^3\,b-a^4}}-\frac{8\,a^2\,b\,\mathrm{tan}\left(x\right)\,\sqrt{\frac{a^2}{16\,\left(a^3\,b-a^4\right)}+\frac{\sqrt{a^3\,b}}{16\,\left(a^3\,b-a^4\right)}}}{2\,a\,b+\frac{2\,a^5\,b}{a^3\,b-a^4}+\frac{2\,a^3\,b\,\sqrt{a^3\,b}}{a^3\,b-a^4}}+\frac{8\,a^4\,b\,\mathrm{tan}\left(x\right)\,\sqrt{\frac{a^2}{16\,\left(a^3\,b-a^4\right)}+\frac{\sqrt{a^3\,b}}{16\,\left(a^3\,b-a^4\right)}}\,\sqrt{a^3\,b}}{2\,a^5\,b-2\,a^4\,b^2-\frac{2\,a^8\,b^2}{a^3\,b-a^4}+\frac{2\,a^9\,b}{a^3\,b-a^4}-\frac{2\,a^6\,b^2\,\sqrt{a^3\,b}}{a^3\,b-a^4}+\frac{2\,a^7\,b\,\sqrt{a^3\,b}}{a^3\,b-a^4}}\right)\,\sqrt{\frac{a^2+\sqrt{a^3\,b}}{16\,\left(a^3\,b-a^4\right)}}-2\,\mathrm{atanh}\left(\frac{8\,a^2\,b\,\mathrm{tan}\left(x\right)\,\sqrt{\frac{a^2}{16\,\left(a^3\,b-a^4\right)}-\frac{\sqrt{a^3\,b}}{16\,\left(a^3\,b-a^4\right)}}}{2\,a\,b+\frac{2\,a^5\,b}{a^3\,b-a^4}-\frac{2\,a^3\,b\,\sqrt{a^3\,b}}{a^3\,b-a^4}}-\frac{8\,a^6\,b\,\mathrm{tan}\left(x\right)\,\sqrt{\frac{a^2}{16\,\left(a^3\,b-a^4\right)}-\frac{\sqrt{a^3\,b}}{16\,\left(a^3\,b-a^4\right)}}}{2\,a^5\,b-2\,a^4\,b^2-\frac{2\,a^8\,b^2}{a^3\,b-a^4}+\frac{2\,a^9\,b}{a^3\,b-a^4}+\frac{2\,a^6\,b^2\,\sqrt{a^3\,b}}{a^3\,b-a^4}-\frac{2\,a^7\,b\,\sqrt{a^3\,b}}{a^3\,b-a^4}}+\frac{8\,a^4\,b\,\mathrm{tan}\left(x\right)\,\sqrt{\frac{a^2}{16\,\left(a^3\,b-a^4\right)}-\frac{\sqrt{a^3\,b}}{16\,\left(a^3\,b-a^4\right)}}\,\sqrt{a^3\,b}}{2\,a^5\,b-2\,a^4\,b^2-\frac{2\,a^8\,b^2}{a^3\,b-a^4}+\frac{2\,a^9\,b}{a^3\,b-a^4}+\frac{2\,a^6\,b^2\,\sqrt{a^3\,b}}{a^3\,b-a^4}-\frac{2\,a^7\,b\,\sqrt{a^3\,b}}{a^3\,b-a^4}}\right)\,\sqrt{\frac{a^2-\sqrt{a^3\,b}}{16\,\left(a^3\,b-a^4\right)}}","Not used",1,"2*atanh((8*a^6*b*tan(x)*(a^2/(16*(a^3*b - a^4)) + (a^3*b)^(1/2)/(16*(a^3*b - a^4)))^(1/2))/(2*a^5*b - 2*a^4*b^2 - (2*a^8*b^2)/(a^3*b - a^4) + (2*a^9*b)/(a^3*b - a^4) - (2*a^6*b^2*(a^3*b)^(1/2))/(a^3*b - a^4) + (2*a^7*b*(a^3*b)^(1/2))/(a^3*b - a^4)) - (8*a^2*b*tan(x)*(a^2/(16*(a^3*b - a^4)) + (a^3*b)^(1/2)/(16*(a^3*b - a^4)))^(1/2))/(2*a*b + (2*a^5*b)/(a^3*b - a^4) + (2*a^3*b*(a^3*b)^(1/2))/(a^3*b - a^4)) + (8*a^4*b*tan(x)*(a^2/(16*(a^3*b - a^4)) + (a^3*b)^(1/2)/(16*(a^3*b - a^4)))^(1/2)*(a^3*b)^(1/2))/(2*a^5*b - 2*a^4*b^2 - (2*a^8*b^2)/(a^3*b - a^4) + (2*a^9*b)/(a^3*b - a^4) - (2*a^6*b^2*(a^3*b)^(1/2))/(a^3*b - a^4) + (2*a^7*b*(a^3*b)^(1/2))/(a^3*b - a^4)))*((a^2 + (a^3*b)^(1/2))/(16*(a^3*b - a^4)))^(1/2) - 2*atanh((8*a^2*b*tan(x)*(a^2/(16*(a^3*b - a^4)) - (a^3*b)^(1/2)/(16*(a^3*b - a^4)))^(1/2))/(2*a*b + (2*a^5*b)/(a^3*b - a^4) - (2*a^3*b*(a^3*b)^(1/2))/(a^3*b - a^4)) - (8*a^6*b*tan(x)*(a^2/(16*(a^3*b - a^4)) - (a^3*b)^(1/2)/(16*(a^3*b - a^4)))^(1/2))/(2*a^5*b - 2*a^4*b^2 - (2*a^8*b^2)/(a^3*b - a^4) + (2*a^9*b)/(a^3*b - a^4) + (2*a^6*b^2*(a^3*b)^(1/2))/(a^3*b - a^4) - (2*a^7*b*(a^3*b)^(1/2))/(a^3*b - a^4)) + (8*a^4*b*tan(x)*(a^2/(16*(a^3*b - a^4)) - (a^3*b)^(1/2)/(16*(a^3*b - a^4)))^(1/2)*(a^3*b)^(1/2))/(2*a^5*b - 2*a^4*b^2 - (2*a^8*b^2)/(a^3*b - a^4) + (2*a^9*b)/(a^3*b - a^4) + (2*a^6*b^2*(a^3*b)^(1/2))/(a^3*b - a^4) - (2*a^7*b*(a^3*b)^(1/2))/(a^3*b - a^4)))*((a^2 - (a^3*b)^(1/2))/(16*(a^3*b - a^4)))^(1/2)","B"
72,1,214,292,2.729877,"\text{Not used}","int(1/(cos(x)^4 + 1),x)","\mathrm{atanh}\left(\frac{4\,\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{-\frac{\sqrt{2}}{64}-\frac{1}{64}}}{64\,\sqrt{\frac{\sqrt{2}}{64}-\frac{1}{64}}\,\sqrt{-\frac{\sqrt{2}}{64}-\frac{1}{64}}-1}+\frac{4\,\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{\frac{\sqrt{2}}{64}-\frac{1}{64}}}{64\,\sqrt{\frac{\sqrt{2}}{64}-\frac{1}{64}}\,\sqrt{-\frac{\sqrt{2}}{64}-\frac{1}{64}}-1}\right)\,\left(2\,\sqrt{-\frac{\sqrt{2}}{64}-\frac{1}{64}}-2\,\sqrt{\frac{\sqrt{2}}{64}-\frac{1}{64}}\right)-\mathrm{atanh}\left(\frac{4\,\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{-\frac{\sqrt{2}}{64}-\frac{1}{64}}}{64\,\sqrt{\frac{\sqrt{2}}{64}-\frac{1}{64}}\,\sqrt{-\frac{\sqrt{2}}{64}-\frac{1}{64}}+1}-\frac{4\,\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{\frac{\sqrt{2}}{64}-\frac{1}{64}}}{64\,\sqrt{\frac{\sqrt{2}}{64}-\frac{1}{64}}\,\sqrt{-\frac{\sqrt{2}}{64}-\frac{1}{64}}+1}\right)\,\left(2\,\sqrt{-\frac{\sqrt{2}}{64}-\frac{1}{64}}+2\,\sqrt{\frac{\sqrt{2}}{64}-\frac{1}{64}}\right)","Not used",1,"atanh((4*2^(1/2)*tan(x)*(- 2^(1/2)/64 - 1/64)^(1/2))/(64*(2^(1/2)/64 - 1/64)^(1/2)*(- 2^(1/2)/64 - 1/64)^(1/2) - 1) + (4*2^(1/2)*tan(x)*(2^(1/2)/64 - 1/64)^(1/2))/(64*(2^(1/2)/64 - 1/64)^(1/2)*(- 2^(1/2)/64 - 1/64)^(1/2) - 1))*(2*(- 2^(1/2)/64 - 1/64)^(1/2) - 2*(2^(1/2)/64 - 1/64)^(1/2)) - atanh((4*2^(1/2)*tan(x)*(- 2^(1/2)/64 - 1/64)^(1/2))/(64*(2^(1/2)/64 - 1/64)^(1/2)*(- 2^(1/2)/64 - 1/64)^(1/2) + 1) - (4*2^(1/2)*tan(x)*(2^(1/2)/64 - 1/64)^(1/2))/(64*(2^(1/2)/64 - 1/64)^(1/2)*(- 2^(1/2)/64 - 1/64)^(1/2) + 1))*(2*(- 2^(1/2)/64 - 1/64)^(1/2) + 2*(2^(1/2)/64 - 1/64)^(1/2))","B"
73,1,20,45,2.163938,"\text{Not used}","int(-1/(cos(x)^4 - 1),x)","\frac{\sqrt{2}\,\mathrm{atan}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)}{2}\right)}{4}-\frac{1}{2\,\mathrm{tan}\left(x\right)}","Not used",1,"(2^(1/2)*atan((2^(1/2)*tan(x))/2))/4 - 1/(2*tan(x))","B"
74,1,1520,494,8.818040,"\text{Not used}","int(1/(a + b*cos(x)^5),x)","\sum _{k=1}^{10}\ln\left(-\frac{b^7\,\left(a-b\right)\,\left(7\,\mathrm{cot}\left(\frac{x}{2}\right)-\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)\,a\,56+\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)\,b-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^3\,a^3\,5800-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^5\,a^5\,225000-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^7\,a^7\,3875000-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^9\,a^9\,25000000+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^2\,a^2\,\mathrm{cot}\left(\frac{x}{2}\right)\,735+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^4\,a^4\,\mathrm{cot}\left(\frac{x}{2}\right)\,28875+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^6\,a^6\,\mathrm{cot}\left(\frac{x}{2}\right)\,503125+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^8\,a^8\,\mathrm{cot}\left(\frac{x}{2}\right)\,3281250+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^3\,a^2\,b\,800+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^5\,a^4\,b\,100000+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^7\,a^6\,b\,4000000+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^9\,a^8\,b\,50000000-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^7\,a^5\,b^2\,125000-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^9\,a^7\,b^2\,25000000-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^2\,a\,b\,\mathrm{cot}\left(\frac{x}{2}\right)\,35-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^4\,a^3\,b\,\mathrm{cot}\left(\frac{x}{2}\right)\,7000-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^6\,a^5\,b\,\mathrm{cot}\left(\frac{x}{2}\right)\,350000-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^8\,a^7\,b\,\mathrm{cot}\left(\frac{x}{2}\right)\,5000000+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^6\,a^4\,b^2\,\mathrm{cot}\left(\frac{x}{2}\right)\,3125+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^8\,a^6\,b^2\,\mathrm{cot}\left(\frac{x}{2}\right)\,1718750\right)\,10995116277760}{\mathrm{cot}\left(\frac{x}{2}\right)}\right)\,\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)","Not used",1,"symsum(log(-(10995116277760*b^7*(a - b)*(7*cot(x/2) - 56*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)*a + root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)*b - 5800*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^3*a^3 - 225000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^5*a^5 - 3875000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^7*a^7 - 25000000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^9*a^9 + 735*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^2*a^2*cot(x/2) + 28875*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^4*a^4*cot(x/2) + 503125*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^6*a^6*cot(x/2) + 3281250*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^8*a^8*cot(x/2) + 800*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^3*a^2*b + 100000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^5*a^4*b + 4000000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^7*a^6*b + 50000000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^9*a^8*b - 125000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^7*a^5*b^2 - 25000000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^9*a^7*b^2 - 35*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^2*a*b*cot(x/2) - 7000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^4*a^3*b*cot(x/2) - 350000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^6*a^5*b*cot(x/2) - 5000000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^8*a^7*b*cot(x/2) + 3125*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^6*a^4*b^2*cot(x/2) + 1718750*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^8*a^6*b^2*cot(x/2)))/cot(x/2))*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k), k, 1, 10)","B"
75,1,184,171,3.080837,"\text{Not used}","int(1/(a + b*cos(x)^6),x)","\sum _{k=1}^6\ln\left({\mathrm{root}\left(46656\,a^5\,b\,d^6+46656\,a^6\,d^6+3888\,a^4\,d^4+108\,a^2\,d^2+1,d,k\right)}^2\,a^3\,b^3\,\left({\mathrm{root}\left(46656\,a^5\,b\,d^6+46656\,a^6\,d^6+3888\,a^4\,d^4+108\,a^2\,d^2+1,d,k\right)}^2\,a^2\,36+1\right)\,\left(\mathrm{root}\left(46656\,a^5\,b\,d^6+46656\,a^6\,d^6+3888\,a^4\,d^4+108\,a^2\,d^2+1,d,k\right)\,a\,\mathrm{tan}\left(x\right)\,6-1\right)\,36\right)\,\mathrm{root}\left(46656\,a^5\,b\,d^6+46656\,a^6\,d^6+3888\,a^4\,d^4+108\,a^2\,d^2+1,d,k\right)","Not used",1,"symsum(log(36*root(46656*a^5*b*d^6 + 46656*a^6*d^6 + 3888*a^4*d^4 + 108*a^2*d^2 + 1, d, k)^2*a^3*b^3*(36*root(46656*a^5*b*d^6 + 46656*a^6*d^6 + 3888*a^4*d^4 + 108*a^2*d^2 + 1, d, k)^2*a^2 + 1)*(6*root(46656*a^5*b*d^6 + 46656*a^6*d^6 + 3888*a^4*d^4 + 108*a^2*d^2 + 1, d, k)*a*tan(x) - 1))*root(46656*a^5*b*d^6 + 46656*a^6*d^6 + 3888*a^4*d^4 + 108*a^2*d^2 + 1, d, k), k, 1, 6)","B"
76,1,216,245,3.420714,"\text{Not used}","int(1/(a + b*cos(x)^8),x)","\sum _{k=1}^8\ln\left({\mathrm{root}\left(16777216\,a^7\,b\,d^8+16777216\,a^8\,d^8+1048576\,a^6\,d^6+24576\,a^4\,d^4+256\,a^2\,d^2+1,d,k\right)}^4\,a^5\,b^5\,\left({\mathrm{root}\left(16777216\,a^7\,b\,d^8+16777216\,a^8\,d^8+1048576\,a^6\,d^6+24576\,a^4\,d^4+256\,a^2\,d^2+1,d,k\right)}^2\,a^2\,64+1\right)\,\left(\mathrm{root}\left(16777216\,a^7\,b\,d^8+16777216\,a^8\,d^8+1048576\,a^6\,d^6+24576\,a^4\,d^4+256\,a^2\,d^2+1,d,k\right)\,a\,\mathrm{tan}\left(x\right)\,8-1\right)\,4096\right)\,\mathrm{root}\left(16777216\,a^7\,b\,d^8+16777216\,a^8\,d^8+1048576\,a^6\,d^6+24576\,a^4\,d^4+256\,a^2\,d^2+1,d,k\right)","Not used",1,"symsum(log(4096*root(16777216*a^7*b*d^8 + 16777216*a^8*d^8 + 1048576*a^6*d^6 + 24576*a^4*d^4 + 256*a^2*d^2 + 1, d, k)^4*a^5*b^5*(64*root(16777216*a^7*b*d^8 + 16777216*a^8*d^8 + 1048576*a^6*d^6 + 24576*a^4*d^4 + 256*a^2*d^2 + 1, d, k)^2*a^2 + 1)*(8*root(16777216*a^7*b*d^8 + 16777216*a^8*d^8 + 1048576*a^6*d^6 + 24576*a^4*d^4 + 256*a^2*d^2 + 1, d, k)*a*tan(x) - 1))*root(16777216*a^7*b*d^8 + 16777216*a^8*d^8 + 1048576*a^6*d^6 + 24576*a^4*d^4 + 256*a^2*d^2 + 1, d, k), k, 1, 8)","B"
77,1,1518,494,7.832136,"\text{Not used}","int(1/(a - b*cos(x)^5),x)","\sum _{k=1}^{10}\ln\left(-\frac{b^7\,\left(a+b\right)\,\left(-7\,\mathrm{cot}\left(\frac{x}{2}\right)+\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)\,a\,56+\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)\,b+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^3\,a^3\,5800+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^5\,a^5\,225000+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^7\,a^7\,3875000+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^9\,a^9\,25000000-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^2\,a^2\,\mathrm{cot}\left(\frac{x}{2}\right)\,735-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^4\,a^4\,\mathrm{cot}\left(\frac{x}{2}\right)\,28875-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^6\,a^6\,\mathrm{cot}\left(\frac{x}{2}\right)\,503125-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^8\,a^8\,\mathrm{cot}\left(\frac{x}{2}\right)\,3281250+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^3\,a^2\,b\,800+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^5\,a^4\,b\,100000+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^7\,a^6\,b\,4000000+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^9\,a^8\,b\,50000000+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^7\,a^5\,b^2\,125000+{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^9\,a^7\,b^2\,25000000-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^2\,a\,b\,\mathrm{cot}\left(\frac{x}{2}\right)\,35-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^4\,a^3\,b\,\mathrm{cot}\left(\frac{x}{2}\right)\,7000-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^6\,a^5\,b\,\mathrm{cot}\left(\frac{x}{2}\right)\,350000-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^8\,a^7\,b\,\mathrm{cot}\left(\frac{x}{2}\right)\,5000000-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^6\,a^4\,b^2\,\mathrm{cot}\left(\frac{x}{2}\right)\,3125-{\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)}^8\,a^6\,b^2\,\mathrm{cot}\left(\frac{x}{2}\right)\,1718750\right)\,10995116277760}{\mathrm{cot}\left(\frac{x}{2}\right)}\right)\,\mathrm{root}\left(9765625\,a^8\,b^2\,d^{10}-9765625\,a^{10}\,d^{10}-1953125\,a^8\,d^8-156250\,a^6\,d^6-6250\,a^4\,d^4-125\,a^2\,d^2-1,d,k\right)","Not used",1,"symsum(log(-(10995116277760*b^7*(a + b)*(56*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)*a - 7*cot(x/2) + root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)*b + 5800*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^3*a^3 + 225000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^5*a^5 + 3875000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^7*a^7 + 25000000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^9*a^9 - 735*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^2*a^2*cot(x/2) - 28875*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^4*a^4*cot(x/2) - 503125*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^6*a^6*cot(x/2) - 3281250*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^8*a^8*cot(x/2) + 800*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^3*a^2*b + 100000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^5*a^4*b + 4000000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^7*a^6*b + 50000000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^9*a^8*b + 125000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^7*a^5*b^2 + 25000000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^9*a^7*b^2 - 35*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^2*a*b*cot(x/2) - 7000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^4*a^3*b*cot(x/2) - 350000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^6*a^5*b*cot(x/2) - 5000000*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^8*a^7*b*cot(x/2) - 3125*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^6*a^4*b^2*cot(x/2) - 1718750*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k)^8*a^6*b^2*cot(x/2)))/cot(x/2))*root(9765625*a^8*b^2*d^10 - 9765625*a^10*d^10 - 1953125*a^8*d^8 - 156250*a^6*d^6 - 6250*a^4*d^4 - 125*a^2*d^2 - 1, d, k), k, 1, 10)","B"
78,1,184,175,3.119972,"\text{Not used}","int(1/(a - b*cos(x)^6),x)","\sum _{k=1}^6\ln\left(-{\mathrm{root}\left(46656\,a^5\,b\,d^6-46656\,a^6\,d^6-3888\,a^4\,d^4-108\,a^2\,d^2-1,d,k\right)}^2\,a^3\,b^3\,\left({\mathrm{root}\left(46656\,a^5\,b\,d^6-46656\,a^6\,d^6-3888\,a^4\,d^4-108\,a^2\,d^2-1,d,k\right)}^2\,a^2\,36+1\right)\,\left(\mathrm{root}\left(46656\,a^5\,b\,d^6-46656\,a^6\,d^6-3888\,a^4\,d^4-108\,a^2\,d^2-1,d,k\right)\,a\,\mathrm{tan}\left(x\right)\,6-1\right)\,36\right)\,\mathrm{root}\left(46656\,a^5\,b\,d^6-46656\,a^6\,d^6-3888\,a^4\,d^4-108\,a^2\,d^2-1,d,k\right)","Not used",1,"symsum(log(-36*root(46656*a^5*b*d^6 - 46656*a^6*d^6 - 3888*a^4*d^4 - 108*a^2*d^2 - 1, d, k)^2*a^3*b^3*(36*root(46656*a^5*b*d^6 - 46656*a^6*d^6 - 3888*a^4*d^4 - 108*a^2*d^2 - 1, d, k)^2*a^2 + 1)*(6*root(46656*a^5*b*d^6 - 46656*a^6*d^6 - 3888*a^4*d^4 - 108*a^2*d^2 - 1, d, k)*a*tan(x) - 1))*root(46656*a^5*b*d^6 - 46656*a^6*d^6 - 3888*a^4*d^4 - 108*a^2*d^2 - 1, d, k), k, 1, 6)","B"
79,1,216,213,3.416480,"\text{Not used}","int(1/(a - b*cos(x)^8),x)","\sum _{k=1}^8\ln\left(-{\mathrm{root}\left(16777216\,a^7\,b\,d^8-16777216\,a^8\,d^8-1048576\,a^6\,d^6-24576\,a^4\,d^4-256\,a^2\,d^2-1,d,k\right)}^4\,a^5\,b^5\,\left({\mathrm{root}\left(16777216\,a^7\,b\,d^8-16777216\,a^8\,d^8-1048576\,a^6\,d^6-24576\,a^4\,d^4-256\,a^2\,d^2-1,d,k\right)}^2\,a^2\,64+1\right)\,\left(\mathrm{root}\left(16777216\,a^7\,b\,d^8-16777216\,a^8\,d^8-1048576\,a^6\,d^6-24576\,a^4\,d^4-256\,a^2\,d^2-1,d,k\right)\,a\,\mathrm{tan}\left(x\right)\,8-1\right)\,4096\right)\,\mathrm{root}\left(16777216\,a^7\,b\,d^8-16777216\,a^8\,d^8-1048576\,a^6\,d^6-24576\,a^4\,d^4-256\,a^2\,d^2-1,d,k\right)","Not used",1,"symsum(log(-4096*root(16777216*a^7*b*d^8 - 16777216*a^8*d^8 - 1048576*a^6*d^6 - 24576*a^4*d^4 - 256*a^2*d^2 - 1, d, k)^4*a^5*b^5*(64*root(16777216*a^7*b*d^8 - 16777216*a^8*d^8 - 1048576*a^6*d^6 - 24576*a^4*d^4 - 256*a^2*d^2 - 1, d, k)^2*a^2 + 1)*(8*root(16777216*a^7*b*d^8 - 16777216*a^8*d^8 - 1048576*a^6*d^6 - 24576*a^4*d^4 - 256*a^2*d^2 - 1, d, k)*a*tan(x) - 1))*root(16777216*a^7*b*d^8 - 16777216*a^8*d^8 - 1048576*a^6*d^6 - 24576*a^4*d^4 - 256*a^2*d^2 - 1, d, k), k, 1, 8)","B"
80,1,535,223,2.778015,"\text{Not used}","int(1/(cos(x)^5 + 1),x)","\frac{\mathrm{tan}\left(\frac{x}{2}\right)}{5}+2\,\mathrm{atanh}\left(\frac{603979776\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{244140625\,\left(\frac{33554432\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{1220703125}-\frac{134217728\,\sqrt{5}}{1220703125}+\frac{67108864\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{1220703125}-\frac{301989888}{1220703125}\right)}+\frac{268435456\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{244140625\,\left(\frac{33554432\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{1220703125}-\frac{134217728\,\sqrt{5}}{1220703125}+\frac{67108864\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{1220703125}-\frac{301989888}{1220703125}\right)}\right)\,\sqrt{-\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}-2\,\mathrm{atanh}\left(\frac{603979776\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{244140625\,\left(\frac{33554432\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{1220703125}+\frac{134217728\,\sqrt{5}}{1220703125}+\frac{67108864\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{1220703125}+\frac{301989888}{1220703125}\right)}+\frac{268435456\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{244140625\,\left(\frac{33554432\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{1220703125}+\frac{134217728\,\sqrt{5}}{1220703125}+\frac{67108864\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{1220703125}+\frac{301989888}{1220703125}\right)}\right)\,\sqrt{\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}-2\,\mathrm{atanh}\left(\frac{603979776\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{244140625\,\left(\frac{33554432\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{1220703125}-\frac{134217728\,\sqrt{5}}{1220703125}-\frac{67108864\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{1220703125}+\frac{301989888}{1220703125}\right)}-\frac{268435456\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{244140625\,\left(\frac{33554432\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{1220703125}-\frac{134217728\,\sqrt{5}}{1220703125}-\frac{67108864\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{1220703125}+\frac{301989888}{1220703125}\right)}\right)\,\sqrt{-\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}+2\,\mathrm{atanh}\left(\frac{603979776\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{244140625\,\left(\frac{33554432\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{1220703125}+\frac{134217728\,\sqrt{5}}{1220703125}-\frac{67108864\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{1220703125}-\frac{301989888}{1220703125}\right)}-\frac{268435456\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{244140625\,\left(\frac{33554432\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{1220703125}+\frac{134217728\,\sqrt{5}}{1220703125}-\frac{67108864\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{1220703125}-\frac{301989888}{1220703125}\right)}\right)\,\sqrt{\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}","Not used",1,"tan(x/2)/5 + 2*atanh((603979776*tan(x/2)*(- (- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(244140625*((33554432*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/1220703125 - (134217728*5^(1/2))/1220703125 + (67108864*(- (2*5^(1/2))/5 - 1)^(1/2))/1220703125 - 301989888/1220703125)) + (268435456*5^(1/2)*tan(x/2)*(- (- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(244140625*((33554432*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/1220703125 - (134217728*5^(1/2))/1220703125 + (67108864*(- (2*5^(1/2))/5 - 1)^(1/2))/1220703125 - 301989888/1220703125)))*(- (- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2) - 2*atanh((603979776*tan(x/2)*((- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(244140625*((33554432*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/1220703125 + (134217728*5^(1/2))/1220703125 + (67108864*(- (2*5^(1/2))/5 - 1)^(1/2))/1220703125 + 301989888/1220703125)) + (268435456*5^(1/2)*tan(x/2)*((- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(244140625*((33554432*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2))/1220703125 + (134217728*5^(1/2))/1220703125 + (67108864*(- (2*5^(1/2))/5 - 1)^(1/2))/1220703125 + 301989888/1220703125)))*((- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2) - 2*atanh((603979776*tan(x/2)*(- ((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(244140625*((33554432*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/1220703125 - (134217728*5^(1/2))/1220703125 - (67108864*((2*5^(1/2))/5 - 1)^(1/2))/1220703125 + 301989888/1220703125)) - (268435456*5^(1/2)*tan(x/2)*(- ((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(244140625*((33554432*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/1220703125 - (134217728*5^(1/2))/1220703125 - (67108864*((2*5^(1/2))/5 - 1)^(1/2))/1220703125 + 301989888/1220703125)))*(- ((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2) + 2*atanh((603979776*tan(x/2)*(((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(244140625*((33554432*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/1220703125 + (134217728*5^(1/2))/1220703125 - (67108864*((2*5^(1/2))/5 - 1)^(1/2))/1220703125 - 301989888/1220703125)) - (268435456*5^(1/2)*tan(x/2)*(((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(244140625*((33554432*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2))/1220703125 + (134217728*5^(1/2))/1220703125 - (67108864*((2*5^(1/2))/5 - 1)^(1/2))/1220703125 - 301989888/1220703125)))*(((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2)","B"
81,1,99,83,2.388572,"\text{Not used}","int(1/(cos(x)^6 + 1),x)","\frac{\sqrt{2}\,\mathrm{atan}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)}{2}\right)}{6}+\mathrm{atan}\left(\frac{\sqrt{3}\,\mathrm{tan}\left(x\right)}{2}+\frac{\mathrm{tan}\left(x\right)\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\sqrt{3}}{6}+\frac{1}{6}{}\mathrm{i}\right)-\mathrm{atan}\left(-\frac{\sqrt{3}\,\mathrm{tan}\left(x\right)}{2}+\frac{\mathrm{tan}\left(x\right)\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\sqrt{3}}{6}-\frac{1}{6}{}\mathrm{i}\right)+\frac{\left(x-\mathrm{atan}\left(\mathrm{tan}\left(x\right)\right)\right)\,\left(\frac{\pi \,\sqrt{2}}{6}+\pi \,\left(\frac{\sqrt{3}}{6}-\frac{1}{6}{}\mathrm{i}\right)+\pi \,\left(\frac{\sqrt{3}}{6}+\frac{1}{6}{}\mathrm{i}\right)\right)}{\pi }","Not used",1,"atan((tan(x)*1i)/2 + (3^(1/2)*tan(x))/2)*(3^(1/2)/6 + 1i/6) - atan((tan(x)*1i)/2 - (3^(1/2)*tan(x))/2)*(3^(1/2)/6 - 1i/6) + (2^(1/2)*atan((2^(1/2)*tan(x))/2))/6 + ((x - atan(tan(x)))*((2^(1/2)*pi)/6 + pi*(3^(1/2)/6 - 1i/6) + pi*(3^(1/2)/6 + 1i/6)))/pi","B"
82,1,1025,129,3.107901,"\text{Not used}","int(1/(cos(x)^8 + 1),x)","-\mathrm{atan}\left(\frac{\mathrm{tan}\left(x\right)\,\sqrt{-\frac{\sqrt{2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,8{}\mathrm{i}}{\frac{\sqrt{2}\,\sqrt{2\,\sqrt{2}-3}}{2}+\frac{\sqrt{2}}{2}-\sqrt{2\,\sqrt{2}-3}-1}-\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{-\frac{\sqrt{2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,4{}\mathrm{i}}{\frac{\sqrt{2}\,\sqrt{2\,\sqrt{2}-3}}{2}+\frac{\sqrt{2}}{2}-\sqrt{2\,\sqrt{2}-3}-1}+\frac{\mathrm{tan}\left(x\right)\,\sqrt{2\,\sqrt{2}-3}\,\sqrt{-\frac{\sqrt{2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,8{}\mathrm{i}}{\frac{\sqrt{2}\,\sqrt{2\,\sqrt{2}-3}}{2}+\frac{\sqrt{2}}{2}-\sqrt{2\,\sqrt{2}-3}-1}-\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{2\,\sqrt{2}-3}\,\sqrt{-\frac{\sqrt{2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,4{}\mathrm{i}}{\frac{\sqrt{2}\,\sqrt{2\,\sqrt{2}-3}}{2}+\frac{\sqrt{2}}{2}-\sqrt{2\,\sqrt{2}-3}-1}\right)\,\sqrt{-\frac{\sqrt{2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\mathrm{tan}\left(x\right)\,\sqrt{\frac{\sqrt{2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,8{}\mathrm{i}}{\frac{\sqrt{2}\,\sqrt{2\,\sqrt{2}-3}}{2}-\frac{\sqrt{2}}{2}-\sqrt{2\,\sqrt{2}-3}+1}-\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{\frac{\sqrt{2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,4{}\mathrm{i}}{\frac{\sqrt{2}\,\sqrt{2\,\sqrt{2}-3}}{2}-\frac{\sqrt{2}}{2}-\sqrt{2\,\sqrt{2}-3}+1}-\frac{\mathrm{tan}\left(x\right)\,\sqrt{2\,\sqrt{2}-3}\,\sqrt{\frac{\sqrt{2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,8{}\mathrm{i}}{\frac{\sqrt{2}\,\sqrt{2\,\sqrt{2}-3}}{2}-\frac{\sqrt{2}}{2}-\sqrt{2\,\sqrt{2}-3}+1}+\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{2\,\sqrt{2}-3}\,\sqrt{\frac{\sqrt{2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,4{}\mathrm{i}}{\frac{\sqrt{2}\,\sqrt{2\,\sqrt{2}-3}}{2}-\frac{\sqrt{2}}{2}-\sqrt{2\,\sqrt{2}-3}+1}\right)\,\sqrt{\frac{\sqrt{2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\mathrm{tan}\left(x\right)\,\sqrt{-\frac{\sqrt{-2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,8{}\mathrm{i}}{\frac{\sqrt{2}\,\sqrt{-2\,\sqrt{2}-3}}{2}+\frac{\sqrt{2}}{2}+\sqrt{-2\,\sqrt{2}-3}+1}+\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{-\frac{\sqrt{-2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,4{}\mathrm{i}}{\frac{\sqrt{2}\,\sqrt{-2\,\sqrt{2}-3}}{2}+\frac{\sqrt{2}}{2}+\sqrt{-2\,\sqrt{2}-3}+1}+\frac{\mathrm{tan}\left(x\right)\,\sqrt{-2\,\sqrt{2}-3}\,\sqrt{-\frac{\sqrt{-2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,8{}\mathrm{i}}{\frac{\sqrt{2}\,\sqrt{-2\,\sqrt{2}-3}}{2}+\frac{\sqrt{2}}{2}+\sqrt{-2\,\sqrt{2}-3}+1}+\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{-2\,\sqrt{2}-3}\,\sqrt{-\frac{\sqrt{-2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,4{}\mathrm{i}}{\frac{\sqrt{2}\,\sqrt{-2\,\sqrt{2}-3}}{2}+\frac{\sqrt{2}}{2}+\sqrt{-2\,\sqrt{2}-3}+1}\right)\,\sqrt{-\frac{\sqrt{-2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\mathrm{tan}\left(x\right)\,\sqrt{\frac{\sqrt{-2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,8{}\mathrm{i}}{\frac{\sqrt{2}\,\sqrt{-2\,\sqrt{2}-3}}{2}-\frac{\sqrt{2}}{2}+\sqrt{-2\,\sqrt{2}-3}-1}+\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{\frac{\sqrt{-2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,4{}\mathrm{i}}{\frac{\sqrt{2}\,\sqrt{-2\,\sqrt{2}-3}}{2}-\frac{\sqrt{2}}{2}+\sqrt{-2\,\sqrt{2}-3}-1}-\frac{\mathrm{tan}\left(x\right)\,\sqrt{-2\,\sqrt{2}-3}\,\sqrt{\frac{\sqrt{-2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,8{}\mathrm{i}}{\frac{\sqrt{2}\,\sqrt{-2\,\sqrt{2}-3}}{2}-\frac{\sqrt{2}}{2}+\sqrt{-2\,\sqrt{2}-3}-1}-\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{-2\,\sqrt{2}-3}\,\sqrt{\frac{\sqrt{-2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,4{}\mathrm{i}}{\frac{\sqrt{2}\,\sqrt{-2\,\sqrt{2}-3}}{2}-\frac{\sqrt{2}}{2}+\sqrt{-2\,\sqrt{2}-3}-1}\right)\,\sqrt{\frac{\sqrt{-2\,\sqrt{2}-3}}{128}-\frac{1}{128}}\,2{}\mathrm{i}","Not used",1,"atan((tan(x)*((2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*8i)/((2^(1/2)*(2*2^(1/2) - 3)^(1/2))/2 - 2^(1/2)/2 - (2*2^(1/2) - 3)^(1/2) + 1) - (2^(1/2)*tan(x)*((2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*4i)/((2^(1/2)*(2*2^(1/2) - 3)^(1/2))/2 - 2^(1/2)/2 - (2*2^(1/2) - 3)^(1/2) + 1) - (tan(x)*(2*2^(1/2) - 3)^(1/2)*((2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*8i)/((2^(1/2)*(2*2^(1/2) - 3)^(1/2))/2 - 2^(1/2)/2 - (2*2^(1/2) - 3)^(1/2) + 1) + (2^(1/2)*tan(x)*(2*2^(1/2) - 3)^(1/2)*((2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*4i)/((2^(1/2)*(2*2^(1/2) - 3)^(1/2))/2 - 2^(1/2)/2 - (2*2^(1/2) - 3)^(1/2) + 1))*((2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*2i - atan((tan(x)*(- (2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*8i)/((2^(1/2)*(2*2^(1/2) - 3)^(1/2))/2 + 2^(1/2)/2 - (2*2^(1/2) - 3)^(1/2) - 1) - (2^(1/2)*tan(x)*(- (2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*4i)/((2^(1/2)*(2*2^(1/2) - 3)^(1/2))/2 + 2^(1/2)/2 - (2*2^(1/2) - 3)^(1/2) - 1) + (tan(x)*(2*2^(1/2) - 3)^(1/2)*(- (2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*8i)/((2^(1/2)*(2*2^(1/2) - 3)^(1/2))/2 + 2^(1/2)/2 - (2*2^(1/2) - 3)^(1/2) - 1) - (2^(1/2)*tan(x)*(2*2^(1/2) - 3)^(1/2)*(- (2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*4i)/((2^(1/2)*(2*2^(1/2) - 3)^(1/2))/2 + 2^(1/2)/2 - (2*2^(1/2) - 3)^(1/2) - 1))*(- (2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*2i + atan((tan(x)*(- (- 2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*8i)/((2^(1/2)*(- 2*2^(1/2) - 3)^(1/2))/2 + 2^(1/2)/2 + (- 2*2^(1/2) - 3)^(1/2) + 1) + (2^(1/2)*tan(x)*(- (- 2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*4i)/((2^(1/2)*(- 2*2^(1/2) - 3)^(1/2))/2 + 2^(1/2)/2 + (- 2*2^(1/2) - 3)^(1/2) + 1) + (tan(x)*(- 2*2^(1/2) - 3)^(1/2)*(- (- 2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*8i)/((2^(1/2)*(- 2*2^(1/2) - 3)^(1/2))/2 + 2^(1/2)/2 + (- 2*2^(1/2) - 3)^(1/2) + 1) + (2^(1/2)*tan(x)*(- 2*2^(1/2) - 3)^(1/2)*(- (- 2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*4i)/((2^(1/2)*(- 2*2^(1/2) - 3)^(1/2))/2 + 2^(1/2)/2 + (- 2*2^(1/2) - 3)^(1/2) + 1))*(- (- 2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*2i - atan((tan(x)*((- 2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*8i)/((2^(1/2)*(- 2*2^(1/2) - 3)^(1/2))/2 - 2^(1/2)/2 + (- 2*2^(1/2) - 3)^(1/2) - 1) + (2^(1/2)*tan(x)*((- 2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*4i)/((2^(1/2)*(- 2*2^(1/2) - 3)^(1/2))/2 - 2^(1/2)/2 + (- 2*2^(1/2) - 3)^(1/2) - 1) - (tan(x)*(- 2*2^(1/2) - 3)^(1/2)*((- 2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*8i)/((2^(1/2)*(- 2*2^(1/2) - 3)^(1/2))/2 - 2^(1/2)/2 + (- 2*2^(1/2) - 3)^(1/2) - 1) - (2^(1/2)*tan(x)*(- 2*2^(1/2) - 3)^(1/2)*((- 2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*4i)/((2^(1/2)*(- 2*2^(1/2) - 3)^(1/2))/2 - 2^(1/2)/2 + (- 2*2^(1/2) - 3)^(1/2) - 1))*((- 2*2^(1/2) - 3)^(1/2)/128 - 1/128)^(1/2)*2i","B"
83,1,403,205,2.447271,"\text{Not used}","int(-1/(cos(x)^5 - 1),x)","2\,\mathrm{atanh}\left(\frac{50\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}-20\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}+2\,\sqrt{5}-10\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}-5}\right)\,\sqrt{\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}-2\,\mathrm{atanh}\left(\frac{50\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}-20\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\sqrt{5}\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}-2\,\sqrt{5}-10\,\sqrt{-\frac{2\,\sqrt{5}}{5}-1}+5}\right)\,\sqrt{-\frac{\sqrt{-\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}-\frac{\mathrm{cot}\left(\frac{x}{2}\right)}{5}+2\,\mathrm{atanh}\left(\frac{50\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}+20\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{-\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}-2\,\sqrt{5}+10\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}-5}\right)\,\sqrt{-\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}-2\,\mathrm{atanh}\left(\frac{50\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}+20\,\sqrt{5}\,\mathrm{tan}\left(\frac{x}{2}\right)\,\sqrt{\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}}{5\,\sqrt{5}\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}+2\,\sqrt{5}+10\,\sqrt{\frac{2\,\sqrt{5}}{5}-1}+5}\right)\,\sqrt{\frac{\sqrt{\frac{2\,\sqrt{5}}{5}-1}}{50}-\frac{1}{50}}","Not used",1,"2*atanh((50*tan(x/2)*((- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2) - 20*5^(1/2)*tan(x/2)*((- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2) + 2*5^(1/2) - 10*(- (2*5^(1/2))/5 - 1)^(1/2) - 5))*((- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2) - 2*atanh((50*tan(x/2)*(- (- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2) - 20*5^(1/2)*tan(x/2)*(- (- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*5^(1/2)*(- (2*5^(1/2))/5 - 1)^(1/2) - 2*5^(1/2) - 10*(- (2*5^(1/2))/5 - 1)^(1/2) + 5))*(- (- (2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2) - cot(x/2)/5 + 2*atanh((50*tan(x/2)*(- ((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2) + 20*5^(1/2)*tan(x/2)*(- ((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2) - 2*5^(1/2) + 10*((2*5^(1/2))/5 - 1)^(1/2) - 5))*(- ((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2) - 2*atanh((50*tan(x/2)*(((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2) + 20*5^(1/2)*tan(x/2)*(((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2))/(5*5^(1/2)*((2*5^(1/2))/5 - 1)^(1/2) + 2*5^(1/2) + 10*((2*5^(1/2))/5 - 1)^(1/2) + 5))*(((2*5^(1/2))/5 - 1)^(1/2)/50 - 1/50)^(1/2)","B"
84,1,95,71,2.292541,"\text{Not used}","int(-1/(cos(x)^6 - 1),x)","-\frac{1}{3\,\mathrm{tan}\left(x\right)}+\frac{\sqrt{6}\,\mathrm{atan}\left(\frac{3^{1/4}\,\sqrt{6}\,\mathrm{tan}\left(x\right)\,\left(\frac{1}{27}-\frac{1}{27}{}\mathrm{i}\right)}{-\frac{1}{9}+\frac{\sqrt{3}\,1{}\mathrm{i}}{9}}\right)\,\left(3^{1/4}\,\left(1+1{}\mathrm{i}\right)+3^{3/4}\,\left(-1+1{}\mathrm{i}\right)\right)\,1{}\mathrm{i}}{36}+\frac{\sqrt{6}\,\mathrm{atan}\left(\frac{3^{1/4}\,\sqrt{6}\,\mathrm{tan}\left(x\right)\,\left(\frac{1}{27}+\frac{1}{27}{}\mathrm{i}\right)}{\frac{1}{9}+\frac{\sqrt{3}\,1{}\mathrm{i}}{9}}\right)\,\left(3^{1/4}\,\left(1-\mathrm{i}\right)+3^{3/4}\,\left(-1-\mathrm{i}\right)\right)\,1{}\mathrm{i}}{36}","Not used",1,"(6^(1/2)*atan((3^(1/4)*6^(1/2)*tan(x)*(1/27 - 1i/27))/((3^(1/2)*1i)/9 - 1/9))*(3^(1/4)*(1 + 1i) - 3^(3/4)*(1 - 1i))*1i)/36 - 1/(3*tan(x)) + (6^(1/2)*atan((3^(1/4)*6^(1/2)*tan(x)*(1/27 + 1i/27))/((3^(1/2)*1i)/9 + 1/9))*(3^(1/4)*(1 - 1i) - 3^(3/4)*(1 + 1i))*1i)/36","B"
85,1,241,89,2.267041,"\text{Not used}","int(-1/(cos(x)^8 - 1),x)","\frac{\sqrt{2}\,\mathrm{atan}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)}{2}\right)}{8}-\mathrm{atan}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{-\frac{\sqrt{2}}{256}-\frac{1}{256}}\,1{}\mathrm{i}}{2\,\left(16\,\sqrt{\frac{\sqrt{2}}{256}-\frac{1}{256}}\,\sqrt{-\frac{\sqrt{2}}{256}-\frac{1}{256}}-\frac{1}{16}\right)}+\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{\frac{\sqrt{2}}{256}-\frac{1}{256}}\,1{}\mathrm{i}}{2\,\left(16\,\sqrt{\frac{\sqrt{2}}{256}-\frac{1}{256}}\,\sqrt{-\frac{\sqrt{2}}{256}-\frac{1}{256}}-\frac{1}{16}\right)}\right)\,\left(\sqrt{-\frac{\sqrt{2}}{256}-\frac{1}{256}}\,2{}\mathrm{i}-\sqrt{\frac{\sqrt{2}}{256}-\frac{1}{256}}\,2{}\mathrm{i}\right)+\mathrm{atan}\left(\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{-\frac{\sqrt{2}}{256}-\frac{1}{256}}\,1{}\mathrm{i}}{2\,\left(16\,\sqrt{\frac{\sqrt{2}}{256}-\frac{1}{256}}\,\sqrt{-\frac{\sqrt{2}}{256}-\frac{1}{256}}+\frac{1}{16}\right)}-\frac{\sqrt{2}\,\mathrm{tan}\left(x\right)\,\sqrt{\frac{\sqrt{2}}{256}-\frac{1}{256}}\,1{}\mathrm{i}}{2\,\left(16\,\sqrt{\frac{\sqrt{2}}{256}-\frac{1}{256}}\,\sqrt{-\frac{\sqrt{2}}{256}-\frac{1}{256}}+\frac{1}{16}\right)}\right)\,\left(\sqrt{-\frac{\sqrt{2}}{256}-\frac{1}{256}}\,2{}\mathrm{i}+\sqrt{\frac{\sqrt{2}}{256}-\frac{1}{256}}\,2{}\mathrm{i}\right)-\frac{1}{4\,\mathrm{tan}\left(x\right)}","Not used",1,"atan((2^(1/2)*tan(x)*(- 2^(1/2)/256 - 1/256)^(1/2)*1i)/(2*(16*(2^(1/2)/256 - 1/256)^(1/2)*(- 2^(1/2)/256 - 1/256)^(1/2) + 1/16)) - (2^(1/2)*tan(x)*(2^(1/2)/256 - 1/256)^(1/2)*1i)/(2*(16*(2^(1/2)/256 - 1/256)^(1/2)*(- 2^(1/2)/256 - 1/256)^(1/2) + 1/16)))*((- 2^(1/2)/256 - 1/256)^(1/2)*2i + (2^(1/2)/256 - 1/256)^(1/2)*2i) - atan((2^(1/2)*tan(x)*(- 2^(1/2)/256 - 1/256)^(1/2)*1i)/(2*(16*(2^(1/2)/256 - 1/256)^(1/2)*(- 2^(1/2)/256 - 1/256)^(1/2) - 1/16)) + (2^(1/2)*tan(x)*(2^(1/2)/256 - 1/256)^(1/2)*1i)/(2*(16*(2^(1/2)/256 - 1/256)^(1/2)*(- 2^(1/2)/256 - 1/256)^(1/2) - 1/16)))*((- 2^(1/2)/256 - 1/256)^(1/2)*2i - (2^(1/2)/256 - 1/256)^(1/2)*2i) - 1/(4*tan(x)) + (2^(1/2)*atan((2^(1/2)*tan(x))/2))/8","B"
86,1,9,17,2.162551,"\text{Not used}","int(tan(x)/(cos(x)^2 + 1),x)","\frac{\ln\left({\mathrm{tan}\left(x\right)}^2+2\right)}{2}","Not used",1,"log(tan(x)^2 + 2)/2","B"
87,0,-1,40,0.000000,"\text{Not used}","int(tan(x)*(a + b*cos(x)^2)^(1/2),x)","\int \mathrm{tan}\left(x\right)\,\sqrt{b\,{\cos\left(x\right)}^2+a} \,d x","Not used",1,"int(tan(x)*(a + b*cos(x)^2)^(1/2), x)","F"
88,0,-1,20,0.000000,"\text{Not used}","int(tan(x)*(1 - cos(x)^2)^(1/2),x)","\int \mathrm{tan}\left(x\right)\,\sqrt{1-{\cos\left(x\right)}^2} \,d x","Not used",1,"int(tan(x)*(1 - cos(x)^2)^(1/2), x)","F"
89,0,-1,25,0.000000,"\text{Not used}","int(tan(x)/(a + b*cos(x)^2)^(1/2),x)","\int \frac{\mathrm{tan}\left(x\right)}{\sqrt{b\,{\cos\left(x\right)}^2+a}} \,d x","Not used",1,"int(tan(x)/(a + b*cos(x)^2)^(1/2), x)","F"
90,0,-1,11,0.000000,"\text{Not used}","int(tan(x)/(cos(x)^2 + 1)^(1/2),x)","\int \frac{\mathrm{tan}\left(x\right)}{\sqrt{{\cos\left(x\right)}^2+1}} \,d x","Not used",1,"int(tan(x)/(cos(x)^2 + 1)^(1/2), x)","F"
91,0,-1,9,0.000000,"\text{Not used}","int(tan(x)/(1 - cos(x)^2)^(1/2),x)","\int \frac{\mathrm{tan}\left(x\right)}{\sqrt{1-{\cos\left(x\right)}^2}} \,d x","Not used",1,"int(tan(x)/(1 - cos(x)^2)^(1/2), x)","F"
92,1,1281,153,5.210716,"\text{Not used}","int(tan(x)^3/(a + b*cos(x)^3),x)","\frac{2\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2}{a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^4-2\,a\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2+a}+\frac{\ln\left({\mathrm{tan}\left(\frac{x}{2}\right)}^2-1\right)}{a}+\left(\sum _{k=1}^3\ln\left(\frac{262144\,\left(-16\,a^9\,b^2+72\,a^8\,b^3-121\,a^7\,b^4+73\,a^6\,b^5+43\,a^5\,b^6-107\,a^4\,b^7+85\,a^3\,b^8-37\,a^2\,b^9+9\,a\,b^{10}-b^{11}\right)}{a^6}+\mathrm{root}\left(27\,a^5\,z^3+27\,a^4\,z^2+9\,a^3\,z+a^2-b^2,z,k\right)\,\left(\mathrm{root}\left(27\,a^5\,z^3+27\,a^4\,z^2+9\,a^3\,z+a^2-b^2,z,k\right)\,\left(\mathrm{root}\left(27\,a^5\,z^3+27\,a^4\,z^2+9\,a^3\,z+a^2-b^2,z,k\right)\,\left(\frac{262144\,\left(-192\,a^{12}\,b^2-2112\,a^{11}\,b^3+3972\,a^{10}\,b^4+612\,a^9\,b^5-3684\,a^8\,b^6+1428\,a^7\,b^7-96\,a^6\,b^8+72\,a^5\,b^9\right)}{a^6}+\mathrm{root}\left(27\,a^5\,z^3+27\,a^4\,z^2+9\,a^3\,z+a^2-b^2,z,k\right)\,\left(\mathrm{root}\left(27\,a^5\,z^3+27\,a^4\,z^2+9\,a^3\,z+a^2-b^2,z,k\right)\,\left(-\mathrm{root}\left(27\,a^5\,z^3+27\,a^4\,z^2+9\,a^3\,z+a^2-b^2,z,k\right)\,\left(\frac{262144\,\left(1296\,a^{15}\,b^2-3888\,a^{14}\,b^3+2592\,a^{13}\,b^4+2592\,a^{12}\,b^5-3888\,a^{11}\,b^6+1296\,a^{10}\,b^7\right)}{a^6}-\frac{262144\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(-1944\,a^{15}\,b^2+12960\,a^{14}\,b^3-28512\,a^{13}\,b^4+27216\,a^{12}\,b^5-11016\,a^{11}\,b^6+1296\,a^{10}\,b^7\right)}{a^6}\right)+\frac{262144\,\left(864\,a^{14}\,b^2+1296\,a^{13}\,b^3-6048\,a^{12}\,b^4+1728\,a^{11}\,b^5+5184\,a^{10}\,b^6-3024\,a^9\,b^7\right)}{a^6}+\frac{262144\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(1296\,a^{14}\,b^2-5292\,a^{13}\,b^3-1836\,a^{12}\,b^4+18468\,a^{11}\,b^5-16740\,a^{10}\,b^6+4104\,a^9\,b^7\right)}{a^6}\right)+\frac{262144\,\left(1296\,a^{13}\,b^2-4248\,a^{12}\,b^3+108\,a^{11}\,b^4+6084\,a^{10}\,b^5-1692\,a^9\,b^6-1836\,a^8\,b^7+288\,a^7\,b^8\right)}{a^6}+\frac{262144\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(1944\,a^{13}\,b^2-15354\,a^{12}\,b^3+35946\,a^{11}\,b^4-29934\,a^{10}\,b^5+3366\,a^9\,b^6+4392\,a^8\,b^7-360\,a^7\,b^8\right)}{a^6}\right)-\frac{262144\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(288\,a^{12}\,b^2+432\,a^{11}\,b^3-14526\,a^{10}\,b^4+30276\,a^9\,b^5-20160\,a^8\,b^6+3780\,a^7\,b^7-162\,a^6\,b^8+72\,a^5\,b^9\right)}{a^6}\right)+\frac{262144\,\left(-496\,a^{11}\,b^2+608\,a^{10}\,b^3+987\,a^9\,b^4-1579\,a^8\,b^5-55\,a^7\,b^6+903\,a^6\,b^7-436\,a^5\,b^8+68\,a^4\,b^9\right)}{a^6}-\frac{262144\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(744\,a^{11}\,b^2-5604\,a^{10}\,b^3+8919\,a^9\,b^4-1311\,a^8\,b^5-5925\,a^7\,b^6+3753\,a^6\,b^7-666\,a^5\,b^8+90\,a^4\,b^9\right)}{a^6}\right)-\frac{262144\,\left(160\,a^{10}\,b^2-496\,a^9\,b^3+402\,a^8\,b^4+230\,a^7\,b^5-540\,a^6\,b^6+292\,a^5\,b^7-30\,a^4\,b^8-26\,a^3\,b^9+8\,a^2\,b^{10}\right)}{a^6}+\frac{262144\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(-240\,a^{10}\,b^2+2252\,a^9\,b^3-6168\,a^8\,b^4+7442\,a^7\,b^5-4214\,a^6\,b^6+920\,a^5\,b^7+52\,a^4\,b^8-54\,a^3\,b^9+10\,a^2\,b^{10}\right)}{a^6}\right)-\frac{262144\,{\mathrm{tan}\left(\frac{x}{2}\right)}^2\,\left(24\,a^9\,b^2-262\,a^8\,b^3+941\,a^7\,b^4-1677\,a^6\,b^5+1705\,a^5\,b^6-1045\,a^4\,b^7+391\,a^3\,b^8-87\,a^2\,b^9+11\,a\,b^{10}-b^{11}\right)}{a^6}\right)\,\mathrm{root}\left(27\,a^5\,z^3+27\,a^4\,z^2+9\,a^3\,z+a^2-b^2,z,k\right)\right)","Not used",1,"(2*tan(x/2)^2)/(a - 2*a*tan(x/2)^2 + a*tan(x/2)^4) + log(tan(x/2)^2 - 1)/a + symsum(log((262144*(9*a*b^10 - b^11 - 37*a^2*b^9 + 85*a^3*b^8 - 107*a^4*b^7 + 43*a^5*b^6 + 73*a^6*b^5 - 121*a^7*b^4 + 72*a^8*b^3 - 16*a^9*b^2))/a^6 + root(27*a^5*z^3 + 27*a^4*z^2 + 9*a^3*z + a^2 - b^2, z, k)*(root(27*a^5*z^3 + 27*a^4*z^2 + 9*a^3*z + a^2 - b^2, z, k)*(root(27*a^5*z^3 + 27*a^4*z^2 + 9*a^3*z + a^2 - b^2, z, k)*((262144*(72*a^5*b^9 - 96*a^6*b^8 + 1428*a^7*b^7 - 3684*a^8*b^6 + 612*a^9*b^5 + 3972*a^10*b^4 - 2112*a^11*b^3 - 192*a^12*b^2))/a^6 + root(27*a^5*z^3 + 27*a^4*z^2 + 9*a^3*z + a^2 - b^2, z, k)*(root(27*a^5*z^3 + 27*a^4*z^2 + 9*a^3*z + a^2 - b^2, z, k)*((262144*(5184*a^10*b^6 - 3024*a^9*b^7 + 1728*a^11*b^5 - 6048*a^12*b^4 + 1296*a^13*b^3 + 864*a^14*b^2))/a^6 - root(27*a^5*z^3 + 27*a^4*z^2 + 9*a^3*z + a^2 - b^2, z, k)*((262144*(1296*a^10*b^7 - 3888*a^11*b^6 + 2592*a^12*b^5 + 2592*a^13*b^4 - 3888*a^14*b^3 + 1296*a^15*b^2))/a^6 - (262144*tan(x/2)^2*(1296*a^10*b^7 - 11016*a^11*b^6 + 27216*a^12*b^5 - 28512*a^13*b^4 + 12960*a^14*b^3 - 1944*a^15*b^2))/a^6) + (262144*tan(x/2)^2*(4104*a^9*b^7 - 16740*a^10*b^6 + 18468*a^11*b^5 - 1836*a^12*b^4 - 5292*a^13*b^3 + 1296*a^14*b^2))/a^6) + (262144*(288*a^7*b^8 - 1836*a^8*b^7 - 1692*a^9*b^6 + 6084*a^10*b^5 + 108*a^11*b^4 - 4248*a^12*b^3 + 1296*a^13*b^2))/a^6 + (262144*tan(x/2)^2*(4392*a^8*b^7 - 360*a^7*b^8 + 3366*a^9*b^6 - 29934*a^10*b^5 + 35946*a^11*b^4 - 15354*a^12*b^3 + 1944*a^13*b^2))/a^6) - (262144*tan(x/2)^2*(72*a^5*b^9 - 162*a^6*b^8 + 3780*a^7*b^7 - 20160*a^8*b^6 + 30276*a^9*b^5 - 14526*a^10*b^4 + 432*a^11*b^3 + 288*a^12*b^2))/a^6) + (262144*(68*a^4*b^9 - 436*a^5*b^8 + 903*a^6*b^7 - 55*a^7*b^6 - 1579*a^8*b^5 + 987*a^9*b^4 + 608*a^10*b^3 - 496*a^11*b^2))/a^6 - (262144*tan(x/2)^2*(90*a^4*b^9 - 666*a^5*b^8 + 3753*a^6*b^7 - 5925*a^7*b^6 - 1311*a^8*b^5 + 8919*a^9*b^4 - 5604*a^10*b^3 + 744*a^11*b^2))/a^6) - (262144*(8*a^2*b^10 - 26*a^3*b^9 - 30*a^4*b^8 + 292*a^5*b^7 - 540*a^6*b^6 + 230*a^7*b^5 + 402*a^8*b^4 - 496*a^9*b^3 + 160*a^10*b^2))/a^6 + (262144*tan(x/2)^2*(10*a^2*b^10 - 54*a^3*b^9 + 52*a^4*b^8 + 920*a^5*b^7 - 4214*a^6*b^6 + 7442*a^7*b^5 - 6168*a^8*b^4 + 2252*a^9*b^3 - 240*a^10*b^2))/a^6) - (262144*tan(x/2)^2*(11*a*b^10 - b^11 - 87*a^2*b^9 + 391*a^3*b^8 - 1045*a^4*b^7 + 1705*a^5*b^6 - 1677*a^6*b^5 + 941*a^7*b^4 - 262*a^8*b^3 + 24*a^9*b^2))/a^6)*root(27*a^5*z^3 + 27*a^4*z^2 + 9*a^3*z + a^2 - b^2, z, k), k, 1, 3)","B"
93,0,-1,45,0.000000,"\text{Not used}","int(tan(x)*(a + b*cos(x)^3)^(1/2),x)","\int \mathrm{tan}\left(x\right)\,\sqrt{b\,{\cos\left(x\right)}^3+a} \,d x","Not used",1,"int(tan(x)*(a + b*cos(x)^3)^(1/2), x)","F"
94,0,-1,28,0.000000,"\text{Not used}","int(tan(x)/(a + b*cos(x)^3)^(1/2),x)","\int \frac{\mathrm{tan}\left(x\right)}{\sqrt{b\,{\cos\left(x\right)}^3+a}} \,d x","Not used",1,"int(tan(x)/(a + b*cos(x)^3)^(1/2), x)","F"
95,0,-1,45,0.000000,"\text{Not used}","int(tan(x)*(a + b*cos(x)^4)^(1/2),x)","\int \mathrm{tan}\left(x\right)\,\sqrt{b\,{\cos\left(x\right)}^4+a} \,d x","Not used",1,"int(tan(x)*(a + b*cos(x)^4)^(1/2), x)","F"
96,0,-1,28,0.000000,"\text{Not used}","int(tan(x)/(a + b*cos(x)^4)^(1/2),x)","\int \frac{\mathrm{tan}\left(x\right)}{\sqrt{b\,{\cos\left(x\right)}^4+a}} \,d x","Not used",1,"int(tan(x)/(a + b*cos(x)^4)^(1/2), x)","F"
97,0,-1,47,0.000000,"\text{Not used}","int(tan(x)*(a + b*cos(x)^n)^(1/2),x)","\int \mathrm{tan}\left(x\right)\,\sqrt{a+b\,{\cos\left(x\right)}^n} \,d x","Not used",1,"int(tan(x)*(a + b*cos(x)^n)^(1/2), x)","F"
98,0,-1,29,0.000000,"\text{Not used}","int(tan(x)/(a + b*cos(x)^n)^(1/2),x)","\int \frac{\mathrm{tan}\left(x\right)}{\sqrt{a+b\,{\cos\left(x\right)}^n}} \,d x","Not used",1,"int(tan(x)/(a + b*cos(x)^n)^(1/2), x)","F"