1,1,203,0,0.3787536,"\int \frac{x}{a+b \sin ^2(x)} \, dx","Int[x/(a + b*Sin[x]^2),x]","-\frac{\text{PolyLog}\left(2,\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{\text{PolyLog}\left(2,\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}-\frac{i x \log \left(1-\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}+\frac{i x \log \left(1-\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}","-\frac{\text{PolyLog}\left(2,\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{\text{PolyLog}\left(2,\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}-\frac{i x \log \left(1-\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}+\frac{i x \log \left(1-\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}",1,"((-I/2)*x*Log[1 - (b*E^((2*I)*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b])])/(Sqrt[a]*Sqrt[a + b]) + ((I/2)*x*Log[1 - (b*E^((2*I)*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b])])/(Sqrt[a]*Sqrt[a + b]) - PolyLog[2, (b*E^((2*I)*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b])]/(4*Sqrt[a]*Sqrt[a + b]) + PolyLog[2, (b*E^((2*I)*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b])]/(4*Sqrt[a]*Sqrt[a + b])","A",9,6,12,0.5000,1,"{4585, 3321, 2264, 2190, 2279, 2391}"
2,1,309,0,0.5882762,"\int \frac{x^2}{a+b \sin ^2(x)} \, dx","Int[x^2/(a + b*Sin[x]^2),x]","-\frac{x \text{PolyLog}\left(2,\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}+\frac{x \text{PolyLog}\left(2,\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}-\frac{i \text{PolyLog}\left(3,\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{i \text{PolyLog}\left(3,\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}-\frac{i x^2 \log \left(1-\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}+\frac{i x^2 \log \left(1-\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}","-\frac{x \text{PolyLog}\left(2,\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}+\frac{x \text{PolyLog}\left(2,\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}-\frac{i \text{PolyLog}\left(3,\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{i \text{PolyLog}\left(3,\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}-\frac{i x^2 \log \left(1-\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}+\frac{i x^2 \log \left(1-\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}",1,"((-I/2)*x^2*Log[1 - (b*E^((2*I)*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b])])/(Sqrt[a]*Sqrt[a + b]) + ((I/2)*x^2*Log[1 - (b*E^((2*I)*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b])])/(Sqrt[a]*Sqrt[a + b]) - (x*PolyLog[2, (b*E^((2*I)*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b])])/(2*Sqrt[a]*Sqrt[a + b]) + (x*PolyLog[2, (b*E^((2*I)*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b])])/(2*Sqrt[a]*Sqrt[a + b]) - ((I/4)*PolyLog[3, (b*E^((2*I)*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b])])/(Sqrt[a]*Sqrt[a + b]) + ((I/4)*PolyLog[3, (b*E^((2*I)*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b])])/(Sqrt[a]*Sqrt[a + b])","A",11,7,14,0.5000,1,"{4585, 3321, 2264, 2190, 2531, 2282, 6589}"
3,1,411,0,0.6325061,"\int \frac{x^3}{a+b \sin ^2(x)} \, dx","Int[x^3/(a + b*Sin[x]^2),x]","-\frac{3 x^2 \text{PolyLog}\left(2,\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{3 x^2 \text{PolyLog}\left(2,\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}-\frac{3 i x \text{PolyLog}\left(3,\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{3 i x \text{PolyLog}\left(3,\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{3 \text{PolyLog}\left(4,\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{8 \sqrt{a} \sqrt{a+b}}-\frac{3 \text{PolyLog}\left(4,\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{8 \sqrt{a} \sqrt{a+b}}-\frac{i x^3 \log \left(1-\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}+\frac{i x^3 \log \left(1-\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}","-\frac{3 x^2 \text{PolyLog}\left(2,\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{3 x^2 \text{PolyLog}\left(2,\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}-\frac{3 i x \text{PolyLog}\left(3,\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{3 i x \text{PolyLog}\left(3,\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{3 \text{PolyLog}\left(4,\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{8 \sqrt{a} \sqrt{a+b}}-\frac{3 \text{PolyLog}\left(4,\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{8 \sqrt{a} \sqrt{a+b}}-\frac{i x^3 \log \left(1-\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}+\frac{i x^3 \log \left(1-\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}",1,"((-I/2)*x^3*Log[1 - (b*E^((2*I)*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b])])/(Sqrt[a]*Sqrt[a + b]) + ((I/2)*x^3*Log[1 - (b*E^((2*I)*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b])])/(Sqrt[a]*Sqrt[a + b]) - (3*x^2*PolyLog[2, (b*E^((2*I)*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b])])/(4*Sqrt[a]*Sqrt[a + b]) + (3*x^2*PolyLog[2, (b*E^((2*I)*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b])])/(4*Sqrt[a]*Sqrt[a + b]) - (((3*I)/4)*x*PolyLog[3, (b*E^((2*I)*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b])])/(Sqrt[a]*Sqrt[a + b]) + (((3*I)/4)*x*PolyLog[3, (b*E^((2*I)*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b])])/(Sqrt[a]*Sqrt[a + b]) + (3*PolyLog[4, (b*E^((2*I)*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b])])/(8*Sqrt[a]*Sqrt[a + b]) - (3*PolyLog[4, (b*E^((2*I)*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b])])/(8*Sqrt[a]*Sqrt[a + b])","A",13,8,14,0.5714,1,"{4585, 3321, 2264, 2190, 2531, 6609, 2282, 6589}"
4,1,329,0,0.6375926,"\int \frac{x}{\left(a+b \sin ^2(c+d x)\right)^2} \, dx","Int[x/(a + b*Sin[c + d*x]^2)^2,x]","-\frac{(2 a+b) \text{PolyLog}\left(2,\frac{b e^{2 i (c+d x)}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{8 a^{3/2} d^2 (a+b)^{3/2}}+\frac{(2 a+b) \text{PolyLog}\left(2,\frac{b e^{2 i (c+d x)}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{8 a^{3/2} d^2 (a+b)^{3/2}}-\frac{i x (2 a+b) \log \left(1-\frac{b e^{2 i (c+d x)}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 a^{3/2} d (a+b)^{3/2}}+\frac{i x (2 a+b) \log \left(1-\frac{b e^{2 i (c+d x)}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 a^{3/2} d (a+b)^{3/2}}-\frac{\log (2 a-b \cos (2 c+2 d x)+b)}{4 a d^2 (a+b)}+\frac{b x \sin (2 c+2 d x)}{2 a d (a+b) (2 a-b \cos (2 c+2 d x)+b)}","-\frac{(2 a+b) \text{PolyLog}\left(2,\frac{b e^{2 i (c+d x)}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{8 a^{3/2} d^2 (a+b)^{3/2}}+\frac{(2 a+b) \text{PolyLog}\left(2,\frac{b e^{2 i (c+d x)}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{8 a^{3/2} d^2 (a+b)^{3/2}}-\frac{i x (2 a+b) \log \left(1-\frac{b e^{2 i (c+d x)}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 a^{3/2} d (a+b)^{3/2}}+\frac{i x (2 a+b) \log \left(1-\frac{b e^{2 i (c+d x)}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 a^{3/2} d (a+b)^{3/2}}-\frac{\log (2 a-b \cos (2 c+2 d x)+b)}{4 a d^2 (a+b)}+\frac{b x \sin (2 c+2 d x)}{2 a d (a+b) (2 a-b \cos (2 c+2 d x)+b)}",1,"((-I/4)*(2*a + b)*x*Log[1 - (b*E^((2*I)*(c + d*x)))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b])])/(a^(3/2)*(a + b)^(3/2)*d) + ((I/4)*(2*a + b)*x*Log[1 - (b*E^((2*I)*(c + d*x)))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b])])/(a^(3/2)*(a + b)^(3/2)*d) - Log[2*a + b - b*Cos[2*c + 2*d*x]]/(4*a*(a + b)*d^2) - ((2*a + b)*PolyLog[2, (b*E^((2*I)*(c + d*x)))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b])])/(8*a^(3/2)*(a + b)^(3/2)*d^2) + ((2*a + b)*PolyLog[2, (b*E^((2*I)*(c + d*x)))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b])])/(8*a^(3/2)*(a + b)^(3/2)*d^2) + (b*x*Sin[2*c + 2*d*x])/(2*a*(a + b)*d*(2*a + b - b*Cos[2*c + 2*d*x]))","A",12,9,16,0.5625,1,"{4585, 3324, 3321, 2264, 2190, 2279, 2391, 2668, 31}"
5,1,22,0,0.0545788,"\int x \sqrt{\sin ^2(x)} \, dx","Int[x*Sqrt[Sin[x]^2],x]","\sqrt{\sin ^2(x)}-x \sqrt{\sin ^2(x)} \cot (x)","\sqrt{\sin ^2(x)}-x \sqrt{\sin ^2(x)} \cot (x)",1,"Sqrt[Sin[x]^2] - x*Cot[x]*Sqrt[Sin[x]^2]","A",3,3,10,0.3000,1,"{6720, 3296, 2637}"
6,1,203,0,0.3338434,"\int \frac{x}{a+b \cos ^2(x)} \, dx","Int[x/(a + b*Cos[x]^2),x]","-\frac{\text{PolyLog}\left(2,-\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{\text{PolyLog}\left(2,-\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}-\frac{i x \log \left(1+\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}+\frac{i x \log \left(1+\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}","-\frac{\text{PolyLog}\left(2,-\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{\text{PolyLog}\left(2,-\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}-\frac{i x \log \left(1+\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}+\frac{i x \log \left(1+\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}",1,"((-I/2)*x*Log[1 + (b*E^((2*I)*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b])])/(Sqrt[a]*Sqrt[a + b]) + ((I/2)*x*Log[1 + (b*E^((2*I)*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b])])/(Sqrt[a]*Sqrt[a + b]) - PolyLog[2, -((b*E^((2*I)*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b]))]/(4*Sqrt[a]*Sqrt[a + b]) + PolyLog[2, -((b*E^((2*I)*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b]))]/(4*Sqrt[a]*Sqrt[a + b])","A",9,6,12,0.5000,1,"{4586, 3321, 2264, 2190, 2279, 2391}"
7,1,311,0,0.5648514,"\int \frac{x^2}{a+b \cos ^2(x)} \, dx","Int[x^2/(a + b*Cos[x]^2),x]","-\frac{x \text{PolyLog}\left(2,-\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}+\frac{x \text{PolyLog}\left(2,-\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}-\frac{i \text{PolyLog}\left(3,-\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{i \text{PolyLog}\left(3,-\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}-\frac{i x^2 \log \left(1+\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}+\frac{i x^2 \log \left(1+\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}","-\frac{x \text{PolyLog}\left(2,-\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}+\frac{x \text{PolyLog}\left(2,-\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}-\frac{i \text{PolyLog}\left(3,-\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{i \text{PolyLog}\left(3,-\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}-\frac{i x^2 \log \left(1+\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}+\frac{i x^2 \log \left(1+\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}",1,"((-I/2)*x^2*Log[1 + (b*E^((2*I)*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b])])/(Sqrt[a]*Sqrt[a + b]) + ((I/2)*x^2*Log[1 + (b*E^((2*I)*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b])])/(Sqrt[a]*Sqrt[a + b]) - (x*PolyLog[2, -((b*E^((2*I)*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b]))])/(2*Sqrt[a]*Sqrt[a + b]) + (x*PolyLog[2, -((b*E^((2*I)*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b]))])/(2*Sqrt[a]*Sqrt[a + b]) - ((I/4)*PolyLog[3, -((b*E^((2*I)*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b]))])/(Sqrt[a]*Sqrt[a + b]) + ((I/4)*PolyLog[3, -((b*E^((2*I)*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b]))])/(Sqrt[a]*Sqrt[a + b])","A",11,7,14,0.5000,1,"{4586, 3321, 2264, 2190, 2531, 2282, 6589}"
8,1,415,0,0.6234744,"\int \frac{x^3}{a+b \cos ^2(x)} \, dx","Int[x^3/(a + b*Cos[x]^2),x]","-\frac{3 x^2 \text{PolyLog}\left(2,-\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{3 x^2 \text{PolyLog}\left(2,-\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}-\frac{3 i x \text{PolyLog}\left(3,-\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{3 i x \text{PolyLog}\left(3,-\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{3 \text{PolyLog}\left(4,-\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{8 \sqrt{a} \sqrt{a+b}}-\frac{3 \text{PolyLog}\left(4,-\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{8 \sqrt{a} \sqrt{a+b}}-\frac{i x^3 \log \left(1+\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}+\frac{i x^3 \log \left(1+\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}","-\frac{3 x^2 \text{PolyLog}\left(2,-\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{3 x^2 \text{PolyLog}\left(2,-\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}-\frac{3 i x \text{PolyLog}\left(3,-\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{3 i x \text{PolyLog}\left(3,-\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 \sqrt{a} \sqrt{a+b}}+\frac{3 \text{PolyLog}\left(4,-\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{8 \sqrt{a} \sqrt{a+b}}-\frac{3 \text{PolyLog}\left(4,-\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{8 \sqrt{a} \sqrt{a+b}}-\frac{i x^3 \log \left(1+\frac{b e^{2 i x}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}+\frac{i x^3 \log \left(1+\frac{b e^{2 i x}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{2 \sqrt{a} \sqrt{a+b}}",1,"((-I/2)*x^3*Log[1 + (b*E^((2*I)*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b])])/(Sqrt[a]*Sqrt[a + b]) + ((I/2)*x^3*Log[1 + (b*E^((2*I)*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b])])/(Sqrt[a]*Sqrt[a + b]) - (3*x^2*PolyLog[2, -((b*E^((2*I)*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b]))])/(4*Sqrt[a]*Sqrt[a + b]) + (3*x^2*PolyLog[2, -((b*E^((2*I)*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b]))])/(4*Sqrt[a]*Sqrt[a + b]) - (((3*I)/4)*x*PolyLog[3, -((b*E^((2*I)*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b]))])/(Sqrt[a]*Sqrt[a + b]) + (((3*I)/4)*x*PolyLog[3, -((b*E^((2*I)*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b]))])/(Sqrt[a]*Sqrt[a + b]) + (3*PolyLog[4, -((b*E^((2*I)*x))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b]))])/(8*Sqrt[a]*Sqrt[a + b]) - (3*PolyLog[4, -((b*E^((2*I)*x))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b]))])/(8*Sqrt[a]*Sqrt[a + b])","A",13,8,14,0.5714,1,"{4586, 3321, 2264, 2190, 2531, 6609, 2282, 6589}"
9,1,327,0,0.5865293,"\int \frac{x}{\left(a+b \cos ^2(c+d x)\right)^2} \, dx","Int[x/(a + b*Cos[c + d*x]^2)^2,x]","-\frac{(2 a+b) \text{PolyLog}\left(2,-\frac{b e^{2 i (c+d x)}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{8 a^{3/2} d^2 (a+b)^{3/2}}+\frac{(2 a+b) \text{PolyLog}\left(2,-\frac{b e^{2 i (c+d x)}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{8 a^{3/2} d^2 (a+b)^{3/2}}-\frac{i x (2 a+b) \log \left(1+\frac{b e^{2 i (c+d x)}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 a^{3/2} d (a+b)^{3/2}}+\frac{i x (2 a+b) \log \left(1+\frac{b e^{2 i (c+d x)}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 a^{3/2} d (a+b)^{3/2}}-\frac{\log (2 a+b \cos (2 c+2 d x)+b)}{4 a d^2 (a+b)}-\frac{b x \sin (2 c+2 d x)}{2 a d (a+b) (2 a+b \cos (2 c+2 d x)+b)}","-\frac{(2 a+b) \text{PolyLog}\left(2,-\frac{b e^{2 i (c+d x)}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{8 a^{3/2} d^2 (a+b)^{3/2}}+\frac{(2 a+b) \text{PolyLog}\left(2,-\frac{b e^{2 i (c+d x)}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{8 a^{3/2} d^2 (a+b)^{3/2}}-\frac{i x (2 a+b) \log \left(1+\frac{b e^{2 i (c+d x)}}{-2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 a^{3/2} d (a+b)^{3/2}}+\frac{i x (2 a+b) \log \left(1+\frac{b e^{2 i (c+d x)}}{2 \sqrt{a} \sqrt{a+b}+2 a+b}\right)}{4 a^{3/2} d (a+b)^{3/2}}-\frac{\log (2 a+b \cos (2 c+2 d x)+b)}{4 a d^2 (a+b)}-\frac{b x \sin (2 c+2 d x)}{2 a d (a+b) (2 a+b \cos (2 c+2 d x)+b)}",1,"((-I/4)*(2*a + b)*x*Log[1 + (b*E^((2*I)*(c + d*x)))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b])])/(a^(3/2)*(a + b)^(3/2)*d) + ((I/4)*(2*a + b)*x*Log[1 + (b*E^((2*I)*(c + d*x)))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b])])/(a^(3/2)*(a + b)^(3/2)*d) - Log[2*a + b + b*Cos[2*c + 2*d*x]]/(4*a*(a + b)*d^2) - ((2*a + b)*PolyLog[2, -((b*E^((2*I)*(c + d*x)))/(2*a + b - 2*Sqrt[a]*Sqrt[a + b]))])/(8*a^(3/2)*(a + b)^(3/2)*d^2) + ((2*a + b)*PolyLog[2, -((b*E^((2*I)*(c + d*x)))/(2*a + b + 2*Sqrt[a]*Sqrt[a + b]))])/(8*a^(3/2)*(a + b)^(3/2)*d^2) - (b*x*Sin[2*c + 2*d*x])/(2*a*(a + b)*d*(2*a + b + b*Cos[2*c + 2*d*x]))","A",12,9,16,0.5625,1,"{4586, 3324, 3321, 2264, 2190, 2279, 2391, 2668, 31}"