1,1,23,40,0.0124313,"\int \frac{(-5+3 x)^2}{(-1+2 x)^{7/2}} \, dx","Integrate[(-5 + 3*x)^2/(-1 + 2*x)^(7/2),x]","\frac{-45 x^2+80 x-41}{5 (2 x-1)^{5/2}}","-\frac{9}{4 \sqrt{2 x-1}}+\frac{7}{2 (2 x-1)^{3/2}}-\frac{49}{20 (2 x-1)^{5/2}}",1,"(-41 + 80*x - 45*x^2)/(5*(-1 + 2*x)^(5/2))","A",1
2,1,24,24,0.0106322,"\int \frac{1}{-5 e^{-m x}+2 e^{m x}} \, dx","Integrate[(-5/E^(m*x) + 2*E^(m*x))^(-1),x]","-\frac{\tanh ^{-1}\left(\sqrt{\frac{2}{5}} e^{m x}\right)}{\sqrt{10} m}","-\frac{\tanh ^{-1}\left(\sqrt{\frac{2}{5}} e^{m x}\right)}{\sqrt{10} m}",1,"-(ArcTanh[Sqrt[2/5]*E^(m*x)]/(Sqrt[10]*m))","A",1
3,1,41,42,0.0330093,"\int \frac{1}{a+b \cos (x)} \, dx","Integrate[(a + b*Cos[x])^(-1),x]","-\frac{2 \tanh ^{-1}\left(\frac{(a-b) \tan \left(\frac{x}{2}\right)}{\sqrt{b^2-a^2}}\right)}{\sqrt{b^2-a^2}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{a-b} \tan \left(\frac{x}{2}\right)}{\sqrt{a+b}}\right)}{\sqrt{a-b} \sqrt{a+b}}",1,"(-2*ArcTanh[((a - b)*Tan[x/2])/Sqrt[-a^2 + b^2]])/Sqrt[-a^2 + b^2]","A",1
4,1,34,15,0.0188957,"\int \frac{1}{3+3 \cos (x)+4 \sin (x)} \, dx","Integrate[(3 + 3*Cos[x] + 4*Sin[x])^(-1),x]","\frac{1}{4} \log \left(4 \sin \left(\frac{x}{2}\right)+3 \cos \left(\frac{x}{2}\right)\right)-\frac{1}{4} \log \left(\cos \left(\frac{x}{2}\right)\right)","\frac{1}{4} \log \left(4 \tan \left(\frac{x}{2}\right)+3\right)",1,"-1/4*Log[Cos[x/2]] + Log[3*Cos[x/2] + 4*Sin[x/2]]/4","B",1
5,1,39,21,0.0171,"\int \frac{1}{4+3 \cos (x)+4 \sin (x)} \, dx","Integrate[(4 + 3*Cos[x] + 4*Sin[x])^(-1),x]","\frac{1}{3} \log \left(\sin \left(\frac{x}{2}\right)+\cos \left(\frac{x}{2}\right)\right)-\frac{1}{3} \log \left(\sin \left(\frac{x}{2}\right)+7 \cos \left(\frac{x}{2}\right)\right)","-\frac{1}{3} \log \left(3 \cot \left(\frac{x}{2}+\frac{\pi }{4}\right)+4\right)",1,"Log[Cos[x/2] + Sin[x/2]]/3 - Log[7*Cos[x/2] + Sin[x/2]]/3","A",1
6,1,26,12,0.0330626,"\int \frac{1}{5+3 \cos (x)+4 \sin (x)} \, dx","Integrate[(5 + 3*Cos[x] + 4*Sin[x])^(-1),x]","\frac{\sin \left(\frac{x}{2}\right)}{2 \sin \left(\frac{x}{2}\right)+4 \cos \left(\frac{x}{2}\right)}","-\frac{1}{\tan \left(\frac{x}{2}\right)+2}",1,"Sin[x/2]/(4*Cos[x/2] + 2*Sin[x/2])","B",1
7,1,24,43,0.0267852,"\int \frac{1}{6+3 \cos (x)+4 \sin (x)} \, dx","Integrate[(6 + 3*Cos[x] + 4*Sin[x])^(-1),x]","\frac{2 \tan ^{-1}\left(\frac{3 \tan \left(\frac{x}{2}\right)+4}{\sqrt{11}}\right)}{\sqrt{11}}","\frac{x}{\sqrt{11}}+\frac{2 \tan ^{-1}\left(\frac{4 \cos (x)-3 \sin (x)}{4 \sin (x)+3 \cos (x)+\sqrt{11}+6}\right)}{\sqrt{11}}",1,"(2*ArcTan[(4 + 3*Tan[x/2])/Sqrt[11]])/Sqrt[11]","A",1
8,1,31,30,0.0045114,"\int \frac{1}{2} \log \left(\left(-a^2+x^2\right)^2\right) \, dx","Integrate[Log[(-a^2 + x^2)^2]/2,x]","\frac{1}{2} \left(x \log \left(\left(a^2-x^2\right)^2\right)+4 a \tanh ^{-1}\left(\frac{x}{a}\right)-4 x\right)","\frac{1}{2} x \log \left(\left(x^2-a^2\right)^2\right)+2 a \tanh ^{-1}\left(\frac{x}{a}\right)-2 x",1,"(-4*x + 4*a*ArcTanh[x/a] + x*Log[(a^2 - x^2)^2])/2","A",1