1,1,116,0,1.391127," ","integrate((-5+3*x)**2/(-1+2*x)**(7/2),x)","- \frac{45 x^{2}}{20 x^{2} \sqrt{2 x - 1} - 20 x \sqrt{2 x - 1} + 5 \sqrt{2 x - 1}} + \frac{80 x}{20 x^{2} \sqrt{2 x - 1} - 20 x \sqrt{2 x - 1} + 5 \sqrt{2 x - 1}} - \frac{41}{20 x^{2} \sqrt{2 x - 1} - 20 x \sqrt{2 x - 1} + 5 \sqrt{2 x - 1}}"," ",0,"-45*x**2/(20*x**2*sqrt(2*x - 1) - 20*x*sqrt(2*x - 1) + 5*sqrt(2*x - 1)) + 80*x/(20*x**2*sqrt(2*x - 1) - 20*x*sqrt(2*x - 1) + 5*sqrt(2*x - 1)) - 41/(20*x**2*sqrt(2*x - 1) - 20*x*sqrt(2*x - 1) + 5*sqrt(2*x - 1))","B",0
2,1,19,0,0.146724," ","integrate(1/(-5/exp(m*x)+2*exp(m*x)),x)","\frac{\operatorname{RootSum} {\left(40 z^{2} - 1, \left( i \mapsto i \log{\left(- 10 i + e^{m x} \right)} \right)\right)}}{m}"," ",0,"RootSum(40*_z**2 - 1, Lambda(_i, _i*log(-10*_i + exp(m*x))))/m","A",0
3,1,144,0,4.297380," ","integrate(1/(a+b*cos(x)),x)","\begin{cases} \tilde{\infty} \left(- \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} + \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{1}{b \tan{\left(\frac{x}{2} \right)}} & \text{for}\: a = - b \\\frac{\tan{\left(\frac{x}{2} \right)}}{b} & \text{for}\: a = b \\\frac{\log{\left(- \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{a \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} - \frac{\log{\left(\sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} + \tan{\left(\frac{x}{2} \right)} \right)}}{a \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}} - b \sqrt{- \frac{a}{a - b} - \frac{b}{a - b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(-log(tan(x/2) - 1) + log(tan(x/2) + 1)), Eq(a, 0) & Eq(b, 0)), (1/(b*tan(x/2)), Eq(a, -b)), (tan(x/2)/b, Eq(a, b)), (log(-sqrt(-a/(a - b) - b/(a - b)) + tan(x/2))/(a*sqrt(-a/(a - b) - b/(a - b)) - b*sqrt(-a/(a - b) - b/(a - b))) - log(sqrt(-a/(a - b) - b/(a - b)) + tan(x/2))/(a*sqrt(-a/(a - b) - b/(a - b)) - b*sqrt(-a/(a - b) - b/(a - b))), True))","A",0
4,1,10,0,0.263491," ","integrate(1/(3+3*cos(x)+4*sin(x)),x)","\frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{3}{4} \right)}}{4}"," ",0,"log(tan(x/2) + 3/4)/4","A",0
5,1,19,0,0.272918," ","integrate(1/(4+3*cos(x)+4*sin(x)),x)","\frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{3} - \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 7 \right)}}{3}"," ",0,"log(tan(x/2) + 1)/3 - log(tan(x/2) + 7)/3","A",0
6,1,8,0,0.434148," ","integrate(1/(5+3*cos(x)+4*sin(x)),x)","- \frac{1}{\tan{\left(\frac{x}{2} \right)} + 2}"," ",0,"-1/(tan(x/2) + 2)","A",0
7,1,42,0,0.522212," ","integrate(1/(6+3*cos(x)+4*sin(x)),x)","\frac{2 \sqrt{11} \left(\operatorname{atan}{\left(\frac{3 \sqrt{11} \tan{\left(\frac{x}{2} \right)}}{11} + \frac{4 \sqrt{11}}{11} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{11}"," ",0,"2*sqrt(11)*(atan(3*sqrt(11)*tan(x/2)/11 + 4*sqrt(11)/11) + pi*floor((x/2 - pi/2)/pi))/11","A",0
8,1,32,0,0.177696," ","integrate(1/2*ln((-a**2+x**2)**2),x)","- 2 a \left(\frac{\log{\left(- a + x \right)}}{2} - \frac{\log{\left(a + x \right)}}{2}\right) + \frac{x \log{\left(\left(- a^{2} + x^{2}\right)^{2} \right)}}{2} - 2 x"," ",0,"-2*a*(log(-a + x)/2 - log(a + x)/2) + x*log((-a**2 + x**2)**2)/2 - 2*x","A",0
