1,-1,0,0,0.000000," ","integrate(cot(e*x+d)^5/(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2,-1,0,0,0.000000," ","integrate(cot(e*x+d)^3/(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3,-1,0,0,0.000000," ","integrate(cot(e*x+d)/(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
4,-1,0,0,0.000000," ","integrate(tan(e*x+d)/(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
5,-1,0,0,0.000000," ","integrate(tan(e*x+d)^3/(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
6,-1,0,0,0.000000," ","integrate(cot(e*x+d)^5*(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
7,-1,0,0,0.000000," ","integrate(cot(e*x+d)^3*(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
8,-1,0,0,0.000000," ","integrate(cot(e*x+d)*(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
9,-1,0,0,0.000000," ","integrate((a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(1/2)*tan(e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
10,-1,0,0,0.000000," ","integrate((a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(1/2)*tan(e*x+d)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
11,-1,0,0,0.000000," ","integrate(cot(e*x+d)^7/(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
12,-1,0,0,0.000000," ","integrate(cot(e*x+d)^5/(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
13,-1,0,0,0.000000," ","integrate(cot(e*x+d)^3/(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
14,-1,0,0,0.000000," ","integrate(cot(e*x+d)/(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
15,-1,0,0,0.000000," ","integrate(tan(e*x+d)/(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
16,-1,0,0,0.000000," ","integrate(tan(e*x+d)^3/(a+b*cot(e*x+d)+c*cot(e*x+d)^2)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
17,1,2100,0,4.831793," ","integrate(cot(e*x+d)^5/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{a - b + c} c^{2} \log\left(2 \, {\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + 2 \, a^{2} - b^{2} + 2 \, c^{2} + 2 \, {\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{a - b + c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 4 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right) + {\left(a b - b^{2} + {\left(2 \, a - b\right)} c + 2 \, c^{2}\right)} \sqrt{c} \log\left(\frac{{\left(b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2} + 4 \, {\left({\left(b - 2 \, c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, b \cos\left(2 \, e x + 2 \, d\right) + b + 2 \, c\right)} \sqrt{c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 2 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}\right) - 4 \, {\left({\left(a - b\right)} c + c^{2}\right)} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{8 \, {\left({\left(a - b\right)} c^{2} + c^{3}\right)} e}, \frac{\sqrt{a - b + c} c^{2} \log\left(2 \, {\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + 2 \, a^{2} - b^{2} + 2 \, c^{2} + 2 \, {\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{a - b + c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 4 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right) + {\left(a b - b^{2} + {\left(2 \, a - b\right)} c + 2 \, c^{2}\right)} \sqrt{-c} \arctan\left(-\frac{{\left({\left(b - 2 \, c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, b \cos\left(2 \, e x + 2 \, d\right) + b + 2 \, c\right)} \sqrt{-c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{2 \, {\left({\left({\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + {\left(a + b\right)} c + c^{2} - 2 \, {\left(a c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)}}\right) - 2 \, {\left({\left(a - b\right)} c + c^{2}\right)} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{4 \, {\left({\left(a - b\right)} c^{2} + c^{3}\right)} e}, -\frac{4 \, \sqrt{-a + b - c} c^{2} \arctan\left(\frac{{\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{-a + b - c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{{\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + a^{2} - b^{2} + 2 \, a c + c^{2} - 2 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}\right) - {\left(a b - b^{2} + {\left(2 \, a - b\right)} c + 2 \, c^{2}\right)} \sqrt{c} \log\left(\frac{{\left(b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2} + 4 \, {\left({\left(b - 2 \, c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, b \cos\left(2 \, e x + 2 \, d\right) + b + 2 \, c\right)} \sqrt{c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 2 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}\right) + 4 \, {\left({\left(a - b\right)} c + c^{2}\right)} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{8 \, {\left({\left(a - b\right)} c^{2} + c^{3}\right)} e}, -\frac{2 \, \sqrt{-a + b - c} c^{2} \arctan\left(\frac{{\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{-a + b - c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{{\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + a^{2} - b^{2} + 2 \, a c + c^{2} - 2 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}\right) - {\left(a b - b^{2} + {\left(2 \, a - b\right)} c + 2 \, c^{2}\right)} \sqrt{-c} \arctan\left(-\frac{{\left({\left(b - 2 \, c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, b \cos\left(2 \, e x + 2 \, d\right) + b + 2 \, c\right)} \sqrt{-c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{2 \, {\left({\left({\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + {\left(a + b\right)} c + c^{2} - 2 \, {\left(a c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)}}\right) + 2 \, {\left({\left(a - b\right)} c + c^{2}\right)} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{4 \, {\left({\left(a - b\right)} c^{2} + c^{3}\right)} e}\right]"," ",0,"[1/8*(2*sqrt(a - b + c)*c^2*log(2*(a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + 2*a^2 - b^2 + 2*c^2 + 2*((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(a - b + c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 4*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d)) + (a*b - b^2 + (2*a - b)*c + 2*c^2)*sqrt(c)*log(((b^2 + 4*(a - 2*b)*c + 8*c^2)*cos(2*e*x + 2*d)^2 + b^2 + 4*(a + 2*b)*c + 8*c^2 + 4*((b - 2*c)*cos(2*e*x + 2*d)^2 - 2*b*cos(2*e*x + 2*d) + b + 2*c)*sqrt(c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 2*(b^2 + 4*a*c - 8*c^2)*cos(2*e*x + 2*d))/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 4*((a - b)*c + c^2)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/(((a - b)*c^2 + c^3)*e), 1/4*(sqrt(a - b + c)*c^2*log(2*(a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + 2*a^2 - b^2 + 2*c^2 + 2*((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(a - b + c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 4*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d)) + (a*b - b^2 + (2*a - b)*c + 2*c^2)*sqrt(-c)*arctan(-1/2*((b - 2*c)*cos(2*e*x + 2*d)^2 - 2*b*cos(2*e*x + 2*d) + b + 2*c)*sqrt(-c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/(((a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + (a + b)*c + c^2 - 2*(a*c - c^2)*cos(2*e*x + 2*d))) - 2*((a - b)*c + c^2)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/(((a - b)*c^2 + c^3)*e), -1/8*(4*sqrt(-a + b - c)*c^2*arctan(((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(-a + b - c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/((a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + a^2 - b^2 + 2*a*c + c^2 - 2*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d))) - (a*b - b^2 + (2*a - b)*c + 2*c^2)*sqrt(c)*log(((b^2 + 4*(a - 2*b)*c + 8*c^2)*cos(2*e*x + 2*d)^2 + b^2 + 4*(a + 2*b)*c + 8*c^2 + 4*((b - 2*c)*cos(2*e*x + 2*d)^2 - 2*b*cos(2*e*x + 2*d) + b + 2*c)*sqrt(c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 2*(b^2 + 4*a*c - 8*c^2)*cos(2*e*x + 2*d))/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) + 4*((a - b)*c + c^2)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/(((a - b)*c^2 + c^3)*e), -1/4*(2*sqrt(-a + b - c)*c^2*arctan(((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(-a + b - c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/((a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + a^2 - b^2 + 2*a*c + c^2 - 2*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d))) - (a*b - b^2 + (2*a - b)*c + 2*c^2)*sqrt(-c)*arctan(-1/2*((b - 2*c)*cos(2*e*x + 2*d)^2 - 2*b*cos(2*e*x + 2*d) + b + 2*c)*sqrt(-c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/(((a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + (a + b)*c + c^2 - 2*(a*c - c^2)*cos(2*e*x + 2*d))) + 2*((a - b)*c + c^2)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/(((a - b)*c^2 + c^3)*e)]","B",0
18,1,1695,0,3.972713," ","integrate(cot(e*x+d)^3/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a - b + c} c \log\left(2 \, {\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + 2 \, a^{2} - b^{2} + 2 \, c^{2} - 2 \, {\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{a - b + c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 4 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right) + {\left(a - b + c\right)} \sqrt{c} \log\left(\frac{{\left(b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2} - 4 \, {\left({\left(b - 2 \, c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, b \cos\left(2 \, e x + 2 \, d\right) + b + 2 \, c\right)} \sqrt{c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 2 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}\right)}{4 \, {\left({\left(a - b\right)} c + c^{2}\right)} e}, -\frac{2 \, {\left(a - b + c\right)} \sqrt{-c} \arctan\left(-\frac{{\left({\left(b - 2 \, c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, b \cos\left(2 \, e x + 2 \, d\right) + b + 2 \, c\right)} \sqrt{-c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{2 \, {\left({\left({\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + {\left(a + b\right)} c + c^{2} - 2 \, {\left(a c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)}}\right) - \sqrt{a - b + c} c \log\left(2 \, {\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + 2 \, a^{2} - b^{2} + 2 \, c^{2} - 2 \, {\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{a - b + c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 4 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)}{4 \, {\left({\left(a - b\right)} c + c^{2}\right)} e}, \frac{2 \, \sqrt{-a + b - c} c \arctan\left(\frac{{\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{-a + b - c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{{\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + a^{2} - b^{2} + 2 \, a c + c^{2} - 2 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}\right) + {\left(a - b + c\right)} \sqrt{c} \log\left(\frac{{\left(b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2} - 4 \, {\left({\left(b - 2 \, c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, b \cos\left(2 \, e x + 2 \, d\right) + b + 2 \, c\right)} \sqrt{c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 2 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}\right)}{4 \, {\left({\left(a - b\right)} c + c^{2}\right)} e}, \frac{\sqrt{-a + b - c} c \arctan\left(\frac{{\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{-a + b - c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{{\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + a^{2} - b^{2} + 2 \, a c + c^{2} - 2 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}\right) - {\left(a - b + c\right)} \sqrt{-c} \arctan\left(-\frac{{\left({\left(b - 2 \, c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, b \cos\left(2 \, e x + 2 \, d\right) + b + 2 \, c\right)} \sqrt{-c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{2 \, {\left({\left({\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + {\left(a + b\right)} c + c^{2} - 2 \, {\left(a c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)}}\right)}{2 \, {\left({\left(a - b\right)} c + c^{2}\right)} e}\right]"," ",0,"[1/4*(sqrt(a - b + c)*c*log(2*(a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + 2*a^2 - b^2 + 2*c^2 - 2*((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(a - b + c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 4*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d)) + (a - b + c)*sqrt(c)*log(((b^2 + 4*(a - 2*b)*c + 8*c^2)*cos(2*e*x + 2*d)^2 + b^2 + 4*(a + 2*b)*c + 8*c^2 - 4*((b - 2*c)*cos(2*e*x + 2*d)^2 - 2*b*cos(2*e*x + 2*d) + b + 2*c)*sqrt(c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 2*(b^2 + 4*a*c - 8*c^2)*cos(2*e*x + 2*d))/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/(((a - b)*c + c^2)*e), -1/4*(2*(a - b + c)*sqrt(-c)*arctan(-1/2*((b - 2*c)*cos(2*e*x + 2*d)^2 - 2*b*cos(2*e*x + 2*d) + b + 2*c)*sqrt(-c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/(((a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + (a + b)*c + c^2 - 2*(a*c - c^2)*cos(2*e*x + 2*d))) - sqrt(a - b + c)*c*log(2*(a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + 2*a^2 - b^2 + 2*c^2 - 2*((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(a - b + c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 4*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d)))/(((a - b)*c + c^2)*e), 1/4*(2*sqrt(-a + b - c)*c*arctan(((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(-a + b - c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/((a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + a^2 - b^2 + 2*a*c + c^2 - 2*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d))) + (a - b + c)*sqrt(c)*log(((b^2 + 4*(a - 2*b)*c + 8*c^2)*cos(2*e*x + 2*d)^2 + b^2 + 4*(a + 2*b)*c + 8*c^2 - 4*((b - 2*c)*cos(2*e*x + 2*d)^2 - 2*b*cos(2*e*x + 2*d) + b + 2*c)*sqrt(c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 2*(b^2 + 4*a*c - 8*c^2)*cos(2*e*x + 2*d))/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/(((a - b)*c + c^2)*e), 1/2*(sqrt(-a + b - c)*c*arctan(((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(-a + b - c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/((a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + a^2 - b^2 + 2*a*c + c^2 - 2*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d))) - (a - b + c)*sqrt(-c)*arctan(-1/2*((b - 2*c)*cos(2*e*x + 2*d)^2 - 2*b*cos(2*e*x + 2*d) + b + 2*c)*sqrt(-c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/(((a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + (a + b)*c + c^2 - 2*(a*c - c^2)*cos(2*e*x + 2*d))))/(((a - b)*c + c^2)*e)]","B",0
19,1,433,0,1.478800," ","integrate(cot(e*x+d)/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(2 \, {\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + 2 \, a^{2} - b^{2} + 2 \, c^{2} + 2 \, {\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{a - b + c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 4 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)}{4 \, \sqrt{a - b + c} e}, -\frac{\sqrt{-a + b - c} \arctan\left(\frac{{\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{-a + b - c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{{\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + a^{2} - b^{2} + 2 \, a c + c^{2} - 2 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}\right)}{2 \, {\left(a - b + c\right)} e}\right]"," ",0,"[1/4*log(2*(a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + 2*a^2 - b^2 + 2*c^2 + 2*((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(a - b + c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 4*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d))/(sqrt(a - b + c)*e), -1/2*sqrt(-a + b - c)*arctan(((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(-a + b - c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/((a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + a^2 - b^2 + 2*a*c + c^2 - 2*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d)))/((a - b + c)*e)]","B",0
20,1,1141,0,2.768522," ","integrate(tan(e*x+d)/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(a - b + c\right)} \sqrt{a} \log\left(8 \, a^{2} \tan\left(e x + d\right)^{4} + 8 \, a b \tan\left(e x + d\right)^{2} + b^{2} + 4 \, a c + 4 \, {\left(2 \, a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2}\right)} \sqrt{a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}\right) + \sqrt{a - b + c} a \log\left(\frac{{\left(8 \, a^{2} - 8 \, a b + b^{2} + 4 \, a c\right)} \tan\left(e x + d\right)^{4} + 2 \, {\left(4 \, a b - 3 \, b^{2} - 4 \, {\left(a - b\right)} c\right)} \tan\left(e x + d\right)^{2} + b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2} - 4 \, {\left({\left(2 \, a - b\right)} \tan\left(e x + d\right)^{4} + {\left(b - 2 \, c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{a - b + c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{\tan\left(e x + d\right)^{4} + 2 \, \tan\left(e x + d\right)^{2} + 1}\right)}{4 \, {\left(a^{2} - a b + a c\right)} e}, -\frac{2 \, \sqrt{-a} {\left(a - b + c\right)} \arctan\left(\frac{{\left(2 \, a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2}\right)} \sqrt{-a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{2 \, {\left(a^{2} \tan\left(e x + d\right)^{4} + a b \tan\left(e x + d\right)^{2} + a c\right)}}\right) - \sqrt{a - b + c} a \log\left(\frac{{\left(8 \, a^{2} - 8 \, a b + b^{2} + 4 \, a c\right)} \tan\left(e x + d\right)^{4} + 2 \, {\left(4 \, a b - 3 \, b^{2} - 4 \, {\left(a - b\right)} c\right)} \tan\left(e x + d\right)^{2} + b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2} - 4 \, {\left({\left(2 \, a - b\right)} \tan\left(e x + d\right)^{4} + {\left(b - 2 \, c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{a - b + c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{\tan\left(e x + d\right)^{4} + 2 \, \tan\left(e x + d\right)^{2} + 1}\right)}{4 \, {\left(a^{2} - a b + a c\right)} e}, -\frac{2 \, a \sqrt{-a + b - c} \arctan\left(-\frac{{\left({\left(2 \, a - b\right)} \tan\left(e x + d\right)^{4} + {\left(b - 2 \, c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{-a + b - c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{2 \, {\left({\left(a^{2} - a b + a c\right)} \tan\left(e x + d\right)^{4} + {\left(a b - b^{2} + b c\right)} \tan\left(e x + d\right)^{2} + {\left(a - b\right)} c + c^{2}\right)}}\right) - {\left(a - b + c\right)} \sqrt{a} \log\left(8 \, a^{2} \tan\left(e x + d\right)^{4} + 8 \, a b \tan\left(e x + d\right)^{2} + b^{2} + 4 \, a c + 4 \, {\left(2 \, a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2}\right)} \sqrt{a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}\right)}{4 \, {\left(a^{2} - a b + a c\right)} e}, -\frac{\sqrt{-a} {\left(a - b + c\right)} \arctan\left(\frac{{\left(2 \, a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2}\right)} \sqrt{-a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{2 \, {\left(a^{2} \tan\left(e x + d\right)^{4} + a b \tan\left(e x + d\right)^{2} + a c\right)}}\right) + a \sqrt{-a + b - c} \arctan\left(-\frac{{\left({\left(2 \, a - b\right)} \tan\left(e x + d\right)^{4} + {\left(b - 2 \, c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{-a + b - c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{2 \, {\left({\left(a^{2} - a b + a c\right)} \tan\left(e x + d\right)^{4} + {\left(a b - b^{2} + b c\right)} \tan\left(e x + d\right)^{2} + {\left(a - b\right)} c + c^{2}\right)}}\right)}{2 \, {\left(a^{2} - a b + a c\right)} e}\right]"," ",0,"[1/4*((a - b + c)*sqrt(a)*log(8*a^2*tan(e*x + d)^4 + 8*a*b*tan(e*x + d)^2 + b^2 + 4*a*c + 4*(2*a*tan(e*x + d)^4 + b*tan(e*x + d)^2)*sqrt(a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)) + sqrt(a - b + c)*a*log(((8*a^2 - 8*a*b + b^2 + 4*a*c)*tan(e*x + d)^4 + 2*(4*a*b - 3*b^2 - 4*(a - b)*c)*tan(e*x + d)^2 + b^2 + 4*(a - 2*b)*c + 8*c^2 - 4*((2*a - b)*tan(e*x + d)^4 + (b - 2*c)*tan(e*x + d)^2)*sqrt(a - b + c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4))/(tan(e*x + d)^4 + 2*tan(e*x + d)^2 + 1)))/((a^2 - a*b + a*c)*e), -1/4*(2*sqrt(-a)*(a - b + c)*arctan(1/2*(2*a*tan(e*x + d)^4 + b*tan(e*x + d)^2)*sqrt(-a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)/(a^2*tan(e*x + d)^4 + a*b*tan(e*x + d)^2 + a*c)) - sqrt(a - b + c)*a*log(((8*a^2 - 8*a*b + b^2 + 4*a*c)*tan(e*x + d)^4 + 2*(4*a*b - 3*b^2 - 4*(a - b)*c)*tan(e*x + d)^2 + b^2 + 4*(a - 2*b)*c + 8*c^2 - 4*((2*a - b)*tan(e*x + d)^4 + (b - 2*c)*tan(e*x + d)^2)*sqrt(a - b + c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4))/(tan(e*x + d)^4 + 2*tan(e*x + d)^2 + 1)))/((a^2 - a*b + a*c)*e), -1/4*(2*a*sqrt(-a + b - c)*arctan(-1/2*((2*a - b)*tan(e*x + d)^4 + (b - 2*c)*tan(e*x + d)^2)*sqrt(-a + b - c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)/((a^2 - a*b + a*c)*tan(e*x + d)^4 + (a*b - b^2 + b*c)*tan(e*x + d)^2 + (a - b)*c + c^2)) - (a - b + c)*sqrt(a)*log(8*a^2*tan(e*x + d)^4 + 8*a*b*tan(e*x + d)^2 + b^2 + 4*a*c + 4*(2*a*tan(e*x + d)^4 + b*tan(e*x + d)^2)*sqrt(a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)))/((a^2 - a*b + a*c)*e), -1/2*(sqrt(-a)*(a - b + c)*arctan(1/2*(2*a*tan(e*x + d)^4 + b*tan(e*x + d)^2)*sqrt(-a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)/(a^2*tan(e*x + d)^4 + a*b*tan(e*x + d)^2 + a*c)) + a*sqrt(-a + b - c)*arctan(-1/2*((2*a - b)*tan(e*x + d)^4 + (b - 2*c)*tan(e*x + d)^2)*sqrt(-a + b - c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)/((a^2 - a*b + a*c)*tan(e*x + d)^4 + (a*b - b^2 + b*c)*tan(e*x + d)^2 + (a - b)*c + c^2)))/((a^2 - a*b + a*c)*e)]","B",0
21,1,1444,0,3.469292," ","integrate(tan(e*x+d)^3/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{a - b + c} a^{2} \log\left(\frac{{\left(8 \, a^{2} - 8 \, a b + b^{2} + 4 \, a c\right)} \tan\left(e x + d\right)^{4} + 2 \, {\left(4 \, a b - 3 \, b^{2} - 4 \, {\left(a - b\right)} c\right)} \tan\left(e x + d\right)^{2} + b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2} + 4 \, {\left({\left(2 \, a - b\right)} \tan\left(e x + d\right)^{4} + {\left(b - 2 \, c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{a - b + c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{\tan\left(e x + d\right)^{4} + 2 \, \tan\left(e x + d\right)^{2} + 1}\right) + 4 \, {\left(a^{2} - a b + a c\right)} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}} \tan\left(e x + d\right)^{2} + {\left(2 \, a^{2} - a b - b^{2} + {\left(2 \, a + b\right)} c\right)} \sqrt{a} \log\left(8 \, a^{2} \tan\left(e x + d\right)^{4} + 8 \, a b \tan\left(e x + d\right)^{2} + b^{2} + 4 \, a c - 4 \, {\left(2 \, a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2}\right)} \sqrt{a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}\right)}{8 \, {\left(a^{3} - a^{2} b + a^{2} c\right)} e}, \frac{\sqrt{a - b + c} a^{2} \log\left(\frac{{\left(8 \, a^{2} - 8 \, a b + b^{2} + 4 \, a c\right)} \tan\left(e x + d\right)^{4} + 2 \, {\left(4 \, a b - 3 \, b^{2} - 4 \, {\left(a - b\right)} c\right)} \tan\left(e x + d\right)^{2} + b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2} + 4 \, {\left({\left(2 \, a - b\right)} \tan\left(e x + d\right)^{4} + {\left(b - 2 \, c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{a - b + c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{\tan\left(e x + d\right)^{4} + 2 \, \tan\left(e x + d\right)^{2} + 1}\right) + 2 \, {\left(a^{2} - a b + a c\right)} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}} \tan\left(e x + d\right)^{2} + {\left(2 \, a^{2} - a b - b^{2} + {\left(2 \, a + b\right)} c\right)} \sqrt{-a} \arctan\left(\frac{{\left(2 \, a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2}\right)} \sqrt{-a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{2 \, {\left(a^{2} \tan\left(e x + d\right)^{4} + a b \tan\left(e x + d\right)^{2} + a c\right)}}\right)}{4 \, {\left(a^{3} - a^{2} b + a^{2} c\right)} e}, \frac{4 \, a^{2} \sqrt{-a + b - c} \arctan\left(-\frac{{\left({\left(2 \, a - b\right)} \tan\left(e x + d\right)^{4} + {\left(b - 2 \, c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{-a + b - c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{2 \, {\left({\left(a^{2} - a b + a c\right)} \tan\left(e x + d\right)^{4} + {\left(a b - b^{2} + b c\right)} \tan\left(e x + d\right)^{2} + {\left(a - b\right)} c + c^{2}\right)}}\right) + 4 \, {\left(a^{2} - a b + a c\right)} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}} \tan\left(e x + d\right)^{2} + {\left(2 \, a^{2} - a b - b^{2} + {\left(2 \, a + b\right)} c\right)} \sqrt{a} \log\left(8 \, a^{2} \tan\left(e x + d\right)^{4} + 8 \, a b \tan\left(e x + d\right)^{2} + b^{2} + 4 \, a c - 4 \, {\left(2 \, a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2}\right)} \sqrt{a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}\right)}{8 \, {\left(a^{3} - a^{2} b + a^{2} c\right)} e}, \frac{2 \, a^{2} \sqrt{-a + b - c} \arctan\left(-\frac{{\left({\left(2 \, a - b\right)} \tan\left(e x + d\right)^{4} + {\left(b - 2 \, c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{-a + b - c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{2 \, {\left({\left(a^{2} - a b + a c\right)} \tan\left(e x + d\right)^{4} + {\left(a b - b^{2} + b c\right)} \tan\left(e x + d\right)^{2} + {\left(a - b\right)} c + c^{2}\right)}}\right) + 2 \, {\left(a^{2} - a b + a c\right)} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}} \tan\left(e x + d\right)^{2} + {\left(2 \, a^{2} - a b - b^{2} + {\left(2 \, a + b\right)} c\right)} \sqrt{-a} \arctan\left(\frac{{\left(2 \, a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2}\right)} \sqrt{-a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{2 \, {\left(a^{2} \tan\left(e x + d\right)^{4} + a b \tan\left(e x + d\right)^{2} + a c\right)}}\right)}{4 \, {\left(a^{3} - a^{2} b + a^{2} c\right)} e}\right]"," ",0,"[1/8*(2*sqrt(a - b + c)*a^2*log(((8*a^2 - 8*a*b + b^2 + 4*a*c)*tan(e*x + d)^4 + 2*(4*a*b - 3*b^2 - 4*(a - b)*c)*tan(e*x + d)^2 + b^2 + 4*(a - 2*b)*c + 8*c^2 + 4*((2*a - b)*tan(e*x + d)^4 + (b - 2*c)*tan(e*x + d)^2)*sqrt(a - b + c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4))/(tan(e*x + d)^4 + 2*tan(e*x + d)^2 + 1)) + 4*(a^2 - a*b + a*c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)*tan(e*x + d)^2 + (2*a^2 - a*b - b^2 + (2*a + b)*c)*sqrt(a)*log(8*a^2*tan(e*x + d)^4 + 8*a*b*tan(e*x + d)^2 + b^2 + 4*a*c - 4*(2*a*tan(e*x + d)^4 + b*tan(e*x + d)^2)*sqrt(a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)))/((a^3 - a^2*b + a^2*c)*e), 1/4*(sqrt(a - b + c)*a^2*log(((8*a^2 - 8*a*b + b^2 + 4*a*c)*tan(e*x + d)^4 + 2*(4*a*b - 3*b^2 - 4*(a - b)*c)*tan(e*x + d)^2 + b^2 + 4*(a - 2*b)*c + 8*c^2 + 4*((2*a - b)*tan(e*x + d)^4 + (b - 2*c)*tan(e*x + d)^2)*sqrt(a - b + c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4))/(tan(e*x + d)^4 + 2*tan(e*x + d)^2 + 1)) + 2*(a^2 - a*b + a*c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)*tan(e*x + d)^2 + (2*a^2 - a*b - b^2 + (2*a + b)*c)*sqrt(-a)*arctan(1/2*(2*a*tan(e*x + d)^4 + b*tan(e*x + d)^2)*sqrt(-a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)/(a^2*tan(e*x + d)^4 + a*b*tan(e*x + d)^2 + a*c)))/((a^3 - a^2*b + a^2*c)*e), 1/8*(4*a^2*sqrt(-a + b - c)*arctan(-1/2*((2*a - b)*tan(e*x + d)^4 + (b - 2*c)*tan(e*x + d)^2)*sqrt(-a + b - c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)/((a^2 - a*b + a*c)*tan(e*x + d)^4 + (a*b - b^2 + b*c)*tan(e*x + d)^2 + (a - b)*c + c^2)) + 4*(a^2 - a*b + a*c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)*tan(e*x + d)^2 + (2*a^2 - a*b - b^2 + (2*a + b)*c)*sqrt(a)*log(8*a^2*tan(e*x + d)^4 + 8*a*b*tan(e*x + d)^2 + b^2 + 4*a*c - 4*(2*a*tan(e*x + d)^4 + b*tan(e*x + d)^2)*sqrt(a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)))/((a^3 - a^2*b + a^2*c)*e), 1/4*(2*a^2*sqrt(-a + b - c)*arctan(-1/2*((2*a - b)*tan(e*x + d)^4 + (b - 2*c)*tan(e*x + d)^2)*sqrt(-a + b - c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)/((a^2 - a*b + a*c)*tan(e*x + d)^4 + (a*b - b^2 + b*c)*tan(e*x + d)^2 + (a - b)*c + c^2)) + 2*(a^2 - a*b + a*c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)*tan(e*x + d)^2 + (2*a^2 - a*b - b^2 + (2*a + b)*c)*sqrt(-a)*arctan(1/2*(2*a*tan(e*x + d)^4 + b*tan(e*x + d)^2)*sqrt(-a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)/(a^2*tan(e*x + d)^4 + a*b*tan(e*x + d)^2 + a*c)))/((a^3 - a^2*b + a^2*c)*e)]","A",0
22,1,3019,0,6.434656," ","integrate(cot(e*x+d)^5*(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2),x, algorithm=""fricas"")","\left[\frac{48 \, {\left(c^{3} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, c^{3} \cos\left(2 \, e x + 2 \, d\right) + c^{3}\right)} \sqrt{a - b + c} \log\left(2 \, {\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + 2 \, a^{2} - b^{2} + 2 \, c^{2} + 2 \, {\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{a - b + c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 4 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right) - 3 \, {\left(b^{3} - 8 \, {\left(a - b\right)} c^{2} - 16 \, c^{3} + {\left(b^{3} - 8 \, {\left(a - b\right)} c^{2} - 16 \, c^{3} - 2 \, {\left(2 \, a b - b^{2}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(2 \, a b - b^{2}\right)} c - 2 \, {\left(b^{3} - 8 \, {\left(a - b\right)} c^{2} - 16 \, c^{3} - 2 \, {\left(2 \, a b - b^{2}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{c} \log\left(\frac{{\left(b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2} + 4 \, {\left({\left(b - 2 \, c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, b \cos\left(2 \, e x + 2 \, d\right) + b + 2 \, c\right)} \sqrt{c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 2 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}\right) + 4 \, {\left(3 \, b^{2} c - 4 \, {\left(2 \, a - b\right)} c^{2} - 20 \, c^{3} + {\left(3 \, b^{2} c - 8 \, {\left(a - b\right)} c^{2} - 44 \, c^{3}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(3 \, b^{2} c - 2 \, {\left(4 \, a - 3 \, b\right)} c^{2} - 16 \, c^{3}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{192 \, {\left(c^{3} e \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, c^{3} e \cos\left(2 \, e x + 2 \, d\right) + c^{3} e\right)}}, -\frac{3 \, {\left(b^{3} - 8 \, {\left(a - b\right)} c^{2} - 16 \, c^{3} + {\left(b^{3} - 8 \, {\left(a - b\right)} c^{2} - 16 \, c^{3} - 2 \, {\left(2 \, a b - b^{2}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(2 \, a b - b^{2}\right)} c - 2 \, {\left(b^{3} - 8 \, {\left(a - b\right)} c^{2} - 16 \, c^{3} - 2 \, {\left(2 \, a b - b^{2}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{-c} \arctan\left(-\frac{{\left({\left(b - 2 \, c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, b \cos\left(2 \, e x + 2 \, d\right) + b + 2 \, c\right)} \sqrt{-c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{2 \, {\left({\left({\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + {\left(a + b\right)} c + c^{2} - 2 \, {\left(a c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)}}\right) - 24 \, {\left(c^{3} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, c^{3} \cos\left(2 \, e x + 2 \, d\right) + c^{3}\right)} \sqrt{a - b + c} \log\left(2 \, {\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + 2 \, a^{2} - b^{2} + 2 \, c^{2} + 2 \, {\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{a - b + c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 4 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right) - 2 \, {\left(3 \, b^{2} c - 4 \, {\left(2 \, a - b\right)} c^{2} - 20 \, c^{3} + {\left(3 \, b^{2} c - 8 \, {\left(a - b\right)} c^{2} - 44 \, c^{3}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(3 \, b^{2} c - 2 \, {\left(4 \, a - 3 \, b\right)} c^{2} - 16 \, c^{3}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{96 \, {\left(c^{3} e \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, c^{3} e \cos\left(2 \, e x + 2 \, d\right) + c^{3} e\right)}}, -\frac{96 \, {\left(c^{3} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, c^{3} \cos\left(2 \, e x + 2 \, d\right) + c^{3}\right)} \sqrt{-a + b - c} \arctan\left(\frac{{\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{-a + b - c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{{\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + a^{2} - b^{2} + 2 \, a c + c^{2} - 2 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}\right) + 3 \, {\left(b^{3} - 8 \, {\left(a - b\right)} c^{2} - 16 \, c^{3} + {\left(b^{3} - 8 \, {\left(a - b\right)} c^{2} - 16 \, c^{3} - 2 \, {\left(2 \, a b - b^{2}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(2 \, a b - b^{2}\right)} c - 2 \, {\left(b^{3} - 8 \, {\left(a - b\right)} c^{2} - 16 \, c^{3} - 2 \, {\left(2 \, a b - b^{2}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{c} \log\left(\frac{{\left(b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2} + 4 \, {\left({\left(b - 2 \, c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, b \cos\left(2 \, e x + 2 \, d\right) + b + 2 \, c\right)} \sqrt{c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 2 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}\right) - 4 \, {\left(3 \, b^{2} c - 4 \, {\left(2 \, a - b\right)} c^{2} - 20 \, c^{3} + {\left(3 \, b^{2} c - 8 \, {\left(a - b\right)} c^{2} - 44 \, c^{3}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(3 \, b^{2} c - 2 \, {\left(4 \, a - 3 \, b\right)} c^{2} - 16 \, c^{3}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{192 \, {\left(c^{3} e \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, c^{3} e \cos\left(2 \, e x + 2 \, d\right) + c^{3} e\right)}}, -\frac{48 \, {\left(c^{3} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, c^{3} \cos\left(2 \, e x + 2 \, d\right) + c^{3}\right)} \sqrt{-a + b - c} \arctan\left(\frac{{\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{-a + b - c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{{\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + a^{2} - b^{2} + 2 \, a c + c^{2} - 2 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}\right) + 3 \, {\left(b^{3} - 8 \, {\left(a - b\right)} c^{2} - 16 \, c^{3} + {\left(b^{3} - 8 \, {\left(a - b\right)} c^{2} - 16 \, c^{3} - 2 \, {\left(2 \, a b - b^{2}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(2 \, a b - b^{2}\right)} c - 2 \, {\left(b^{3} - 8 \, {\left(a - b\right)} c^{2} - 16 \, c^{3} - 2 \, {\left(2 \, a b - b^{2}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{-c} \arctan\left(-\frac{{\left({\left(b - 2 \, c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, b \cos\left(2 \, e x + 2 \, d\right) + b + 2 \, c\right)} \sqrt{-c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{2 \, {\left({\left({\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + {\left(a + b\right)} c + c^{2} - 2 \, {\left(a c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)}}\right) - 2 \, {\left(3 \, b^{2} c - 4 \, {\left(2 \, a - b\right)} c^{2} - 20 \, c^{3} + {\left(3 \, b^{2} c - 8 \, {\left(a - b\right)} c^{2} - 44 \, c^{3}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(3 \, b^{2} c - 2 \, {\left(4 \, a - 3 \, b\right)} c^{2} - 16 \, c^{3}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{96 \, {\left(c^{3} e \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, c^{3} e \cos\left(2 \, e x + 2 \, d\right) + c^{3} e\right)}}\right]"," ",0,"[1/192*(48*(c^3*cos(2*e*x + 2*d)^2 - 2*c^3*cos(2*e*x + 2*d) + c^3)*sqrt(a - b + c)*log(2*(a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + 2*a^2 - b^2 + 2*c^2 + 2*((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(a - b + c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 4*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d)) - 3*(b^3 - 8*(a - b)*c^2 - 16*c^3 + (b^3 - 8*(a - b)*c^2 - 16*c^3 - 2*(2*a*b - b^2)*c)*cos(2*e*x + 2*d)^2 - 2*(2*a*b - b^2)*c - 2*(b^3 - 8*(a - b)*c^2 - 16*c^3 - 2*(2*a*b - b^2)*c)*cos(2*e*x + 2*d))*sqrt(c)*log(((b^2 + 4*(a - 2*b)*c + 8*c^2)*cos(2*e*x + 2*d)^2 + b^2 + 4*(a + 2*b)*c + 8*c^2 + 4*((b - 2*c)*cos(2*e*x + 2*d)^2 - 2*b*cos(2*e*x + 2*d) + b + 2*c)*sqrt(c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 2*(b^2 + 4*a*c - 8*c^2)*cos(2*e*x + 2*d))/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) + 4*(3*b^2*c - 4*(2*a - b)*c^2 - 20*c^3 + (3*b^2*c - 8*(a - b)*c^2 - 44*c^3)*cos(2*e*x + 2*d)^2 - 2*(3*b^2*c - 2*(4*a - 3*b)*c^2 - 16*c^3)*cos(2*e*x + 2*d))*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/(c^3*e*cos(2*e*x + 2*d)^2 - 2*c^3*e*cos(2*e*x + 2*d) + c^3*e), -1/96*(3*(b^3 - 8*(a - b)*c^2 - 16*c^3 + (b^3 - 8*(a - b)*c^2 - 16*c^3 - 2*(2*a*b - b^2)*c)*cos(2*e*x + 2*d)^2 - 2*(2*a*b - b^2)*c - 2*(b^3 - 8*(a - b)*c^2 - 16*c^3 - 2*(2*a*b - b^2)*c)*cos(2*e*x + 2*d))*sqrt(-c)*arctan(-1/2*((b - 2*c)*cos(2*e*x + 2*d)^2 - 2*b*cos(2*e*x + 2*d) + b + 2*c)*sqrt(-c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/(((a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + (a + b)*c + c^2 - 2*(a*c - c^2)*cos(2*e*x + 2*d))) - 24*(c^3*cos(2*e*x + 2*d)^2 - 2*c^3*cos(2*e*x + 2*d) + c^3)*sqrt(a - b + c)*log(2*(a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + 2*a^2 - b^2 + 2*c^2 + 2*((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(a - b + c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 4*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d)) - 2*(3*b^2*c - 4*(2*a - b)*c^2 - 20*c^3 + (3*b^2*c - 8*(a - b)*c^2 - 44*c^3)*cos(2*e*x + 2*d)^2 - 2*(3*b^2*c - 2*(4*a - 3*b)*c^2 - 16*c^3)*cos(2*e*x + 2*d))*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/(c^3*e*cos(2*e*x + 2*d)^2 - 2*c^3*e*cos(2*e*x + 2*d) + c^3*e), -1/192*(96*(c^3*cos(2*e*x + 2*d)^2 - 2*c^3*cos(2*e*x + 2*d) + c^3)*sqrt(-a + b - c)*arctan(((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(-a + b - c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/((a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + a^2 - b^2 + 2*a*c + c^2 - 2*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d))) + 3*(b^3 - 8*(a - b)*c^2 - 16*c^3 + (b^3 - 8*(a - b)*c^2 - 16*c^3 - 2*(2*a*b - b^2)*c)*cos(2*e*x + 2*d)^2 - 2*(2*a*b - b^2)*c - 2*(b^3 - 8*(a - b)*c^2 - 16*c^3 - 2*(2*a*b - b^2)*c)*cos(2*e*x + 2*d))*sqrt(c)*log(((b^2 + 4*(a - 2*b)*c + 8*c^2)*cos(2*e*x + 2*d)^2 + b^2 + 4*(a + 2*b)*c + 8*c^2 + 4*((b - 2*c)*cos(2*e*x + 2*d)^2 - 2*b*cos(2*e*x + 2*d) + b + 2*c)*sqrt(c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 2*(b^2 + 4*a*c - 8*c^2)*cos(2*e*x + 2*d))/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 4*(3*b^2*c - 4*(2*a - b)*c^2 - 20*c^3 + (3*b^2*c - 8*(a - b)*c^2 - 44*c^3)*cos(2*e*x + 2*d)^2 - 2*(3*b^2*c - 2*(4*a - 3*b)*c^2 - 16*c^3)*cos(2*e*x + 2*d))*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/(c^3*e*cos(2*e*x + 2*d)^2 - 2*c^3*e*cos(2*e*x + 2*d) + c^3*e), -1/96*(48*(c^3*cos(2*e*x + 2*d)^2 - 2*c^3*cos(2*e*x + 2*d) + c^3)*sqrt(-a + b - c)*arctan(((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(-a + b - c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/((a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + a^2 - b^2 + 2*a*c + c^2 - 2*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d))) + 3*(b^3 - 8*(a - b)*c^2 - 16*c^3 + (b^3 - 8*(a - b)*c^2 - 16*c^3 - 2*(2*a*b - b^2)*c)*cos(2*e*x + 2*d)^2 - 2*(2*a*b - b^2)*c - 2*(b^3 - 8*(a - b)*c^2 - 16*c^3 - 2*(2*a*b - b^2)*c)*cos(2*e*x + 2*d))*sqrt(-c)*arctan(-1/2*((b - 2*c)*cos(2*e*x + 2*d)^2 - 2*b*cos(2*e*x + 2*d) + b + 2*c)*sqrt(-c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/(((a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + (a + b)*c + c^2 - 2*(a*c - c^2)*cos(2*e*x + 2*d))) - 2*(3*b^2*c - 4*(2*a - b)*c^2 - 20*c^3 + (3*b^2*c - 8*(a - b)*c^2 - 44*c^3)*cos(2*e*x + 2*d)^2 - 2*(3*b^2*c - 2*(4*a - 3*b)*c^2 - 16*c^3)*cos(2*e*x + 2*d))*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/(c^3*e*cos(2*e*x + 2*d)^2 - 2*c^3*e*cos(2*e*x + 2*d) + c^3*e)]","B",0
23,1,2344,0,6.183769," ","integrate(cot(e*x+d)^3*(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2),x, algorithm=""fricas"")","\left[\frac{8 \, {\left(c^{2} \cos\left(2 \, e x + 2 \, d\right) - c^{2}\right)} \sqrt{a - b + c} \log\left(2 \, {\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + 2 \, a^{2} - b^{2} + 2 \, c^{2} - 2 \, {\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{a - b + c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 4 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right) + {\left(b^{2} - 4 \, {\left(a - b\right)} c - 8 \, c^{2} - {\left(b^{2} - 4 \, {\left(a - b\right)} c - 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{c} \log\left(\frac{{\left(b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2} - 4 \, {\left({\left(b - 2 \, c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, b \cos\left(2 \, e x + 2 \, d\right) + b + 2 \, c\right)} \sqrt{c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 2 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}\right) + 4 \, {\left(b c - 2 \, c^{2} - {\left(b c - 6 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{32 \, {\left(c^{2} e \cos\left(2 \, e x + 2 \, d\right) - c^{2} e\right)}}, -\frac{{\left(b^{2} - 4 \, {\left(a - b\right)} c - 8 \, c^{2} - {\left(b^{2} - 4 \, {\left(a - b\right)} c - 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{-c} \arctan\left(-\frac{{\left({\left(b - 2 \, c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, b \cos\left(2 \, e x + 2 \, d\right) + b + 2 \, c\right)} \sqrt{-c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{2 \, {\left({\left({\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + {\left(a + b\right)} c + c^{2} - 2 \, {\left(a c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)}}\right) - 4 \, {\left(c^{2} \cos\left(2 \, e x + 2 \, d\right) - c^{2}\right)} \sqrt{a - b + c} \log\left(2 \, {\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + 2 \, a^{2} - b^{2} + 2 \, c^{2} - 2 \, {\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{a - b + c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 4 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right) - 2 \, {\left(b c - 2 \, c^{2} - {\left(b c - 6 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{16 \, {\left(c^{2} e \cos\left(2 \, e x + 2 \, d\right) - c^{2} e\right)}}, \frac{16 \, {\left(c^{2} \cos\left(2 \, e x + 2 \, d\right) - c^{2}\right)} \sqrt{-a + b - c} \arctan\left(\frac{{\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{-a + b - c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{{\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + a^{2} - b^{2} + 2 \, a c + c^{2} - 2 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}\right) + {\left(b^{2} - 4 \, {\left(a - b\right)} c - 8 \, c^{2} - {\left(b^{2} - 4 \, {\left(a - b\right)} c - 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{c} \log\left(\frac{{\left(b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2} - 4 \, {\left({\left(b - 2 \, c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, b \cos\left(2 \, e x + 2 \, d\right) + b + 2 \, c\right)} \sqrt{c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 2 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}\right) + 4 \, {\left(b c - 2 \, c^{2} - {\left(b c - 6 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{32 \, {\left(c^{2} e \cos\left(2 \, e x + 2 \, d\right) - c^{2} e\right)}}, \frac{8 \, {\left(c^{2} \cos\left(2 \, e x + 2 \, d\right) - c^{2}\right)} \sqrt{-a + b - c} \arctan\left(\frac{{\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{-a + b - c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{{\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + a^{2} - b^{2} + 2 \, a c + c^{2} - 2 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}\right) - {\left(b^{2} - 4 \, {\left(a - b\right)} c - 8 \, c^{2} - {\left(b^{2} - 4 \, {\left(a - b\right)} c - 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{-c} \arctan\left(-\frac{{\left({\left(b - 2 \, c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, b \cos\left(2 \, e x + 2 \, d\right) + b + 2 \, c\right)} \sqrt{-c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{2 \, {\left({\left({\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + {\left(a + b\right)} c + c^{2} - 2 \, {\left(a c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)}}\right) + 2 \, {\left(b c - 2 \, c^{2} - {\left(b c - 6 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{16 \, {\left(c^{2} e \cos\left(2 \, e x + 2 \, d\right) - c^{2} e\right)}}\right]"," ",0,"[1/32*(8*(c^2*cos(2*e*x + 2*d) - c^2)*sqrt(a - b + c)*log(2*(a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + 2*a^2 - b^2 + 2*c^2 - 2*((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(a - b + c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 4*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d)) + (b^2 - 4*(a - b)*c - 8*c^2 - (b^2 - 4*(a - b)*c - 8*c^2)*cos(2*e*x + 2*d))*sqrt(c)*log(((b^2 + 4*(a - 2*b)*c + 8*c^2)*cos(2*e*x + 2*d)^2 + b^2 + 4*(a + 2*b)*c + 8*c^2 - 4*((b - 2*c)*cos(2*e*x + 2*d)^2 - 2*b*cos(2*e*x + 2*d) + b + 2*c)*sqrt(c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 2*(b^2 + 4*a*c - 8*c^2)*cos(2*e*x + 2*d))/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) + 4*(b*c - 2*c^2 - (b*c - 6*c^2)*cos(2*e*x + 2*d))*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/(c^2*e*cos(2*e*x + 2*d) - c^2*e), -1/16*((b^2 - 4*(a - b)*c - 8*c^2 - (b^2 - 4*(a - b)*c - 8*c^2)*cos(2*e*x + 2*d))*sqrt(-c)*arctan(-1/2*((b - 2*c)*cos(2*e*x + 2*d)^2 - 2*b*cos(2*e*x + 2*d) + b + 2*c)*sqrt(-c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/(((a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + (a + b)*c + c^2 - 2*(a*c - c^2)*cos(2*e*x + 2*d))) - 4*(c^2*cos(2*e*x + 2*d) - c^2)*sqrt(a - b + c)*log(2*(a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + 2*a^2 - b^2 + 2*c^2 - 2*((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(a - b + c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 4*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d)) - 2*(b*c - 2*c^2 - (b*c - 6*c^2)*cos(2*e*x + 2*d))*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/(c^2*e*cos(2*e*x + 2*d) - c^2*e), 1/32*(16*(c^2*cos(2*e*x + 2*d) - c^2)*sqrt(-a + b - c)*arctan(((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(-a + b - c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/((a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + a^2 - b^2 + 2*a*c + c^2 - 2*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d))) + (b^2 - 4*(a - b)*c - 8*c^2 - (b^2 - 4*(a - b)*c - 8*c^2)*cos(2*e*x + 2*d))*sqrt(c)*log(((b^2 + 4*(a - 2*b)*c + 8*c^2)*cos(2*e*x + 2*d)^2 + b^2 + 4*(a + 2*b)*c + 8*c^2 - 4*((b - 2*c)*cos(2*e*x + 2*d)^2 - 2*b*cos(2*e*x + 2*d) + b + 2*c)*sqrt(c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 2*(b^2 + 4*a*c - 8*c^2)*cos(2*e*x + 2*d))/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) + 4*(b*c - 2*c^2 - (b*c - 6*c^2)*cos(2*e*x + 2*d))*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/(c^2*e*cos(2*e*x + 2*d) - c^2*e), 1/16*(8*(c^2*cos(2*e*x + 2*d) - c^2)*sqrt(-a + b - c)*arctan(((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(-a + b - c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/((a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + a^2 - b^2 + 2*a*c + c^2 - 2*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d))) - (b^2 - 4*(a - b)*c - 8*c^2 - (b^2 - 4*(a - b)*c - 8*c^2)*cos(2*e*x + 2*d))*sqrt(-c)*arctan(-1/2*((b - 2*c)*cos(2*e*x + 2*d)^2 - 2*b*cos(2*e*x + 2*d) + b + 2*c)*sqrt(-c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/(((a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + (a + b)*c + c^2 - 2*(a*c - c^2)*cos(2*e*x + 2*d))) + 2*(b*c - 2*c^2 - (b*c - 6*c^2)*cos(2*e*x + 2*d))*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/(c^2*e*cos(2*e*x + 2*d) - c^2*e)]","B",0
24,1,1932,0,4.526549," ","integrate(cot(e*x+d)*(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{a - b + c} c \log\left(2 \, {\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + 2 \, a^{2} - b^{2} + 2 \, c^{2} + 2 \, {\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{a - b + c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 4 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right) - {\left(b - 2 \, c\right)} \sqrt{c} \log\left(\frac{{\left(b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2} + 4 \, {\left({\left(b - 2 \, c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, b \cos\left(2 \, e x + 2 \, d\right) + b + 2 \, c\right)} \sqrt{c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 2 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}\right) - 4 \, c \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{8 \, c e}, -\frac{{\left(b - 2 \, c\right)} \sqrt{-c} \arctan\left(-\frac{{\left({\left(b - 2 \, c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, b \cos\left(2 \, e x + 2 \, d\right) + b + 2 \, c\right)} \sqrt{-c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{2 \, {\left({\left({\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + {\left(a + b\right)} c + c^{2} - 2 \, {\left(a c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)}}\right) - \sqrt{a - b + c} c \log\left(2 \, {\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + 2 \, a^{2} - b^{2} + 2 \, c^{2} + 2 \, {\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{a - b + c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 4 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right) + 2 \, c \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{4 \, c e}, -\frac{4 \, \sqrt{-a + b - c} c \arctan\left(\frac{{\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{-a + b - c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{{\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + a^{2} - b^{2} + 2 \, a c + c^{2} - 2 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}\right) + {\left(b - 2 \, c\right)} \sqrt{c} \log\left(\frac{{\left(b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2} + 4 \, {\left({\left(b - 2 \, c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, b \cos\left(2 \, e x + 2 \, d\right) + b + 2 \, c\right)} \sqrt{c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 2 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}\right) + 4 \, c \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{8 \, c e}, -\frac{2 \, \sqrt{-a + b - c} c \arctan\left(\frac{{\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{-a + b - c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{{\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + a^{2} - b^{2} + 2 \, a c + c^{2} - 2 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}\right) + {\left(b - 2 \, c\right)} \sqrt{-c} \arctan\left(-\frac{{\left({\left(b - 2 \, c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, b \cos\left(2 \, e x + 2 \, d\right) + b + 2 \, c\right)} \sqrt{-c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{2 \, {\left({\left({\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + {\left(a + b\right)} c + c^{2} - 2 \, {\left(a c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)}}\right) + 2 \, c \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{4 \, c e}\right]"," ",0,"[1/8*(2*sqrt(a - b + c)*c*log(2*(a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + 2*a^2 - b^2 + 2*c^2 + 2*((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(a - b + c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 4*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d)) - (b - 2*c)*sqrt(c)*log(((b^2 + 4*(a - 2*b)*c + 8*c^2)*cos(2*e*x + 2*d)^2 + b^2 + 4*(a + 2*b)*c + 8*c^2 + 4*((b - 2*c)*cos(2*e*x + 2*d)^2 - 2*b*cos(2*e*x + 2*d) + b + 2*c)*sqrt(c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 2*(b^2 + 4*a*c - 8*c^2)*cos(2*e*x + 2*d))/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 4*c*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/(c*e), -1/4*((b - 2*c)*sqrt(-c)*arctan(-1/2*((b - 2*c)*cos(2*e*x + 2*d)^2 - 2*b*cos(2*e*x + 2*d) + b + 2*c)*sqrt(-c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/(((a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + (a + b)*c + c^2 - 2*(a*c - c^2)*cos(2*e*x + 2*d))) - sqrt(a - b + c)*c*log(2*(a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + 2*a^2 - b^2 + 2*c^2 + 2*((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(a - b + c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 4*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d)) + 2*c*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/(c*e), -1/8*(4*sqrt(-a + b - c)*c*arctan(((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(-a + b - c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/((a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + a^2 - b^2 + 2*a*c + c^2 - 2*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d))) + (b - 2*c)*sqrt(c)*log(((b^2 + 4*(a - 2*b)*c + 8*c^2)*cos(2*e*x + 2*d)^2 + b^2 + 4*(a + 2*b)*c + 8*c^2 + 4*((b - 2*c)*cos(2*e*x + 2*d)^2 - 2*b*cos(2*e*x + 2*d) + b + 2*c)*sqrt(c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 2*(b^2 + 4*a*c - 8*c^2)*cos(2*e*x + 2*d))/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) + 4*c*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/(c*e), -1/4*(2*sqrt(-a + b - c)*c*arctan(((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(-a + b - c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/((a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + a^2 - b^2 + 2*a*c + c^2 - 2*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d))) + (b - 2*c)*sqrt(-c)*arctan(-1/2*((b - 2*c)*cos(2*e*x + 2*d)^2 - 2*b*cos(2*e*x + 2*d) + b + 2*c)*sqrt(-c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/(((a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + (a + b)*c + c^2 - 2*(a*c - c^2)*cos(2*e*x + 2*d))) + 2*c*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/(c*e)]","B",0
25,1,2522,0,1.982797," ","integrate((a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)*tan(e*x+d),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} \log\left(8 \, a^{2} \tan\left(e x + d\right)^{4} + 8 \, a b \tan\left(e x + d\right)^{2} + b^{2} + 4 \, a c + 4 \, {\left(2 \, a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2}\right)} \sqrt{a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}\right) + \sqrt{a - b + c} \log\left(\frac{{\left(8 \, a^{2} - 8 \, a b + b^{2} + 4 \, a c\right)} \tan\left(e x + d\right)^{4} + 2 \, {\left(4 \, a b - 3 \, b^{2} - 4 \, {\left(a - b\right)} c\right)} \tan\left(e x + d\right)^{2} + b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2} - 4 \, {\left({\left(2 \, a - b\right)} \tan\left(e x + d\right)^{4} + {\left(b - 2 \, c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{a - b + c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{\tan\left(e x + d\right)^{4} + 2 \, \tan\left(e x + d\right)^{2} + 1}\right) + \sqrt{c} \log\left(\frac{{\left(b^{2} + 4 \, a c\right)} \tan\left(e x + d\right)^{4} + 8 \, b c \tan\left(e x + d\right)^{2} + 8 \, c^{2} - 4 \, {\left(b \tan\left(e x + d\right)^{4} + 2 \, c \tan\left(e x + d\right)^{2}\right)} \sqrt{c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{\tan\left(e x + d\right)^{4}}\right)}{4 \, e}, \frac{2 \, \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{-c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}} \tan\left(e x + d\right)^{2}}{b \tan\left(e x + d\right)^{2} + 2 \, c}\right) + \sqrt{a} \log\left(8 \, a^{2} \tan\left(e x + d\right)^{4} + 8 \, a b \tan\left(e x + d\right)^{2} + b^{2} + 4 \, a c + 4 \, {\left(2 \, a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2}\right)} \sqrt{a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}\right) + \sqrt{a - b + c} \log\left(\frac{{\left(8 \, a^{2} - 8 \, a b + b^{2} + 4 \, a c\right)} \tan\left(e x + d\right)^{4} + 2 \, {\left(4 \, a b - 3 \, b^{2} - 4 \, {\left(a - b\right)} c\right)} \tan\left(e x + d\right)^{2} + b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2} - 4 \, {\left({\left(2 \, a - b\right)} \tan\left(e x + d\right)^{4} + {\left(b - 2 \, c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{a - b + c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{\tan\left(e x + d\right)^{4} + 2 \, \tan\left(e x + d\right)^{2} + 1}\right)}{4 \, e}, -\frac{2 \, \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}} \tan\left(e x + d\right)^{2}}{2 \, a \tan\left(e x + d\right)^{2} + b}\right) - \sqrt{a - b + c} \log\left(\frac{{\left(8 \, a^{2} - 8 \, a b + b^{2} + 4 \, a c\right)} \tan\left(e x + d\right)^{4} + 2 \, {\left(4 \, a b - 3 \, b^{2} - 4 \, {\left(a - b\right)} c\right)} \tan\left(e x + d\right)^{2} + b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2} - 4 \, {\left({\left(2 \, a - b\right)} \tan\left(e x + d\right)^{4} + {\left(b - 2 \, c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{a - b + c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{\tan\left(e x + d\right)^{4} + 2 \, \tan\left(e x + d\right)^{2} + 1}\right) - \sqrt{c} \log\left(\frac{{\left(b^{2} + 4 \, a c\right)} \tan\left(e x + d\right)^{4} + 8 \, b c \tan\left(e x + d\right)^{2} + 8 \, c^{2} - 4 \, {\left(b \tan\left(e x + d\right)^{4} + 2 \, c \tan\left(e x + d\right)^{2}\right)} \sqrt{c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{\tan\left(e x + d\right)^{4}}\right)}{4 \, e}, -\frac{2 \, \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}} \tan\left(e x + d\right)^{2}}{2 \, a \tan\left(e x + d\right)^{2} + b}\right) - 2 \, \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{-c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}} \tan\left(e x + d\right)^{2}}{b \tan\left(e x + d\right)^{2} + 2 \, c}\right) - \sqrt{a - b + c} \log\left(\frac{{\left(8 \, a^{2} - 8 \, a b + b^{2} + 4 \, a c\right)} \tan\left(e x + d\right)^{4} + 2 \, {\left(4 \, a b - 3 \, b^{2} - 4 \, {\left(a - b\right)} c\right)} \tan\left(e x + d\right)^{2} + b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2} - 4 \, {\left({\left(2 \, a - b\right)} \tan\left(e x + d\right)^{4} + {\left(b - 2 \, c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{a - b + c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{\tan\left(e x + d\right)^{4} + 2 \, \tan\left(e x + d\right)^{2} + 1}\right)}{4 \, e}, -\frac{2 \, \sqrt{-a + b - c} \arctan\left(-\frac{2 \, \sqrt{-a + b - c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}} \tan\left(e x + d\right)^{2}}{{\left(2 \, a - b\right)} \tan\left(e x + d\right)^{2} + b - 2 \, c}\right) - \sqrt{a} \log\left(8 \, a^{2} \tan\left(e x + d\right)^{4} + 8 \, a b \tan\left(e x + d\right)^{2} + b^{2} + 4 \, a c + 4 \, {\left(2 \, a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2}\right)} \sqrt{a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}\right) - \sqrt{c} \log\left(\frac{{\left(b^{2} + 4 \, a c\right)} \tan\left(e x + d\right)^{4} + 8 \, b c \tan\left(e x + d\right)^{2} + 8 \, c^{2} - 4 \, {\left(b \tan\left(e x + d\right)^{4} + 2 \, c \tan\left(e x + d\right)^{2}\right)} \sqrt{c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{\tan\left(e x + d\right)^{4}}\right)}{4 \, e}, -\frac{2 \, \sqrt{-a + b - c} \arctan\left(-\frac{2 \, \sqrt{-a + b - c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}} \tan\left(e x + d\right)^{2}}{{\left(2 \, a - b\right)} \tan\left(e x + d\right)^{2} + b - 2 \, c}\right) - 2 \, \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{-c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}} \tan\left(e x + d\right)^{2}}{b \tan\left(e x + d\right)^{2} + 2 \, c}\right) - \sqrt{a} \log\left(8 \, a^{2} \tan\left(e x + d\right)^{4} + 8 \, a b \tan\left(e x + d\right)^{2} + b^{2} + 4 \, a c + 4 \, {\left(2 \, a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2}\right)} \sqrt{a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}\right)}{4 \, e}, -\frac{2 \, \sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}} \tan\left(e x + d\right)^{2}}{2 \, a \tan\left(e x + d\right)^{2} + b}\right) + 2 \, \sqrt{-a + b - c} \arctan\left(-\frac{2 \, \sqrt{-a + b - c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}} \tan\left(e x + d\right)^{2}}{{\left(2 \, a - b\right)} \tan\left(e x + d\right)^{2} + b - 2 \, c}\right) - \sqrt{c} \log\left(\frac{{\left(b^{2} + 4 \, a c\right)} \tan\left(e x + d\right)^{4} + 8 \, b c \tan\left(e x + d\right)^{2} + 8 \, c^{2} - 4 \, {\left(b \tan\left(e x + d\right)^{4} + 2 \, c \tan\left(e x + d\right)^{2}\right)} \sqrt{c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{\tan\left(e x + d\right)^{4}}\right)}{4 \, e}, -\frac{\sqrt{-a} \arctan\left(\frac{2 \, \sqrt{-a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}} \tan\left(e x + d\right)^{2}}{2 \, a \tan\left(e x + d\right)^{2} + b}\right) + \sqrt{-a + b - c} \arctan\left(-\frac{2 \, \sqrt{-a + b - c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}} \tan\left(e x + d\right)^{2}}{{\left(2 \, a - b\right)} \tan\left(e x + d\right)^{2} + b - 2 \, c}\right) - \sqrt{-c} \arctan\left(\frac{2 \, \sqrt{-c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}} \tan\left(e x + d\right)^{2}}{b \tan\left(e x + d\right)^{2} + 2 \, c}\right)}{2 \, e}\right]"," ",0,"[1/4*(sqrt(a)*log(8*a^2*tan(e*x + d)^4 + 8*a*b*tan(e*x + d)^2 + b^2 + 4*a*c + 4*(2*a*tan(e*x + d)^4 + b*tan(e*x + d)^2)*sqrt(a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)) + sqrt(a - b + c)*log(((8*a^2 - 8*a*b + b^2 + 4*a*c)*tan(e*x + d)^4 + 2*(4*a*b - 3*b^2 - 4*(a - b)*c)*tan(e*x + d)^2 + b^2 + 4*(a - 2*b)*c + 8*c^2 - 4*((2*a - b)*tan(e*x + d)^4 + (b - 2*c)*tan(e*x + d)^2)*sqrt(a - b + c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4))/(tan(e*x + d)^4 + 2*tan(e*x + d)^2 + 1)) + sqrt(c)*log(((b^2 + 4*a*c)*tan(e*x + d)^4 + 8*b*c*tan(e*x + d)^2 + 8*c^2 - 4*(b*tan(e*x + d)^4 + 2*c*tan(e*x + d)^2)*sqrt(c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4))/tan(e*x + d)^4))/e, 1/4*(2*sqrt(-c)*arctan(2*sqrt(-c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)*tan(e*x + d)^2/(b*tan(e*x + d)^2 + 2*c)) + sqrt(a)*log(8*a^2*tan(e*x + d)^4 + 8*a*b*tan(e*x + d)^2 + b^2 + 4*a*c + 4*(2*a*tan(e*x + d)^4 + b*tan(e*x + d)^2)*sqrt(a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)) + sqrt(a - b + c)*log(((8*a^2 - 8*a*b + b^2 + 4*a*c)*tan(e*x + d)^4 + 2*(4*a*b - 3*b^2 - 4*(a - b)*c)*tan(e*x + d)^2 + b^2 + 4*(a - 2*b)*c + 8*c^2 - 4*((2*a - b)*tan(e*x + d)^4 + (b - 2*c)*tan(e*x + d)^2)*sqrt(a - b + c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4))/(tan(e*x + d)^4 + 2*tan(e*x + d)^2 + 1)))/e, -1/4*(2*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)*tan(e*x + d)^2/(2*a*tan(e*x + d)^2 + b)) - sqrt(a - b + c)*log(((8*a^2 - 8*a*b + b^2 + 4*a*c)*tan(e*x + d)^4 + 2*(4*a*b - 3*b^2 - 4*(a - b)*c)*tan(e*x + d)^2 + b^2 + 4*(a - 2*b)*c + 8*c^2 - 4*((2*a - b)*tan(e*x + d)^4 + (b - 2*c)*tan(e*x + d)^2)*sqrt(a - b + c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4))/(tan(e*x + d)^4 + 2*tan(e*x + d)^2 + 1)) - sqrt(c)*log(((b^2 + 4*a*c)*tan(e*x + d)^4 + 8*b*c*tan(e*x + d)^2 + 8*c^2 - 4*(b*tan(e*x + d)^4 + 2*c*tan(e*x + d)^2)*sqrt(c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4))/tan(e*x + d)^4))/e, -1/4*(2*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)*tan(e*x + d)^2/(2*a*tan(e*x + d)^2 + b)) - 2*sqrt(-c)*arctan(2*sqrt(-c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)*tan(e*x + d)^2/(b*tan(e*x + d)^2 + 2*c)) - sqrt(a - b + c)*log(((8*a^2 - 8*a*b + b^2 + 4*a*c)*tan(e*x + d)^4 + 2*(4*a*b - 3*b^2 - 4*(a - b)*c)*tan(e*x + d)^2 + b^2 + 4*(a - 2*b)*c + 8*c^2 - 4*((2*a - b)*tan(e*x + d)^4 + (b - 2*c)*tan(e*x + d)^2)*sqrt(a - b + c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4))/(tan(e*x + d)^4 + 2*tan(e*x + d)^2 + 1)))/e, -1/4*(2*sqrt(-a + b - c)*arctan(-2*sqrt(-a + b - c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)*tan(e*x + d)^2/((2*a - b)*tan(e*x + d)^2 + b - 2*c)) - sqrt(a)*log(8*a^2*tan(e*x + d)^4 + 8*a*b*tan(e*x + d)^2 + b^2 + 4*a*c + 4*(2*a*tan(e*x + d)^4 + b*tan(e*x + d)^2)*sqrt(a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)) - sqrt(c)*log(((b^2 + 4*a*c)*tan(e*x + d)^4 + 8*b*c*tan(e*x + d)^2 + 8*c^2 - 4*(b*tan(e*x + d)^4 + 2*c*tan(e*x + d)^2)*sqrt(c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4))/tan(e*x + d)^4))/e, -1/4*(2*sqrt(-a + b - c)*arctan(-2*sqrt(-a + b - c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)*tan(e*x + d)^2/((2*a - b)*tan(e*x + d)^2 + b - 2*c)) - 2*sqrt(-c)*arctan(2*sqrt(-c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)*tan(e*x + d)^2/(b*tan(e*x + d)^2 + 2*c)) - sqrt(a)*log(8*a^2*tan(e*x + d)^4 + 8*a*b*tan(e*x + d)^2 + b^2 + 4*a*c + 4*(2*a*tan(e*x + d)^4 + b*tan(e*x + d)^2)*sqrt(a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)))/e, -1/4*(2*sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)*tan(e*x + d)^2/(2*a*tan(e*x + d)^2 + b)) + 2*sqrt(-a + b - c)*arctan(-2*sqrt(-a + b - c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)*tan(e*x + d)^2/((2*a - b)*tan(e*x + d)^2 + b - 2*c)) - sqrt(c)*log(((b^2 + 4*a*c)*tan(e*x + d)^4 + 8*b*c*tan(e*x + d)^2 + 8*c^2 - 4*(b*tan(e*x + d)^4 + 2*c*tan(e*x + d)^2)*sqrt(c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4))/tan(e*x + d)^4))/e, -1/2*(sqrt(-a)*arctan(2*sqrt(-a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)*tan(e*x + d)^2/(2*a*tan(e*x + d)^2 + b)) + sqrt(-a + b - c)*arctan(-2*sqrt(-a + b - c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)*tan(e*x + d)^2/((2*a - b)*tan(e*x + d)^2 + b - 2*c)) - sqrt(-c)*arctan(2*sqrt(-c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)*tan(e*x + d)^2/(b*tan(e*x + d)^2 + 2*c)))/e]","A",0
26,1,1282,0,4.313939," ","integrate((a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(1/2)*tan(e*x+d)^3,x, algorithm=""fricas"")","\left[\frac{4 \, a \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}} \tan\left(e x + d\right)^{2} - {\left(2 \, a - b\right)} \sqrt{a} \log\left(8 \, a^{2} \tan\left(e x + d\right)^{4} + 8 \, a b \tan\left(e x + d\right)^{2} + b^{2} + 4 \, a c + 4 \, {\left(2 \, a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2}\right)} \sqrt{a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}\right) + 2 \, \sqrt{a - b + c} a \log\left(\frac{{\left(8 \, a^{2} - 8 \, a b + b^{2} + 4 \, a c\right)} \tan\left(e x + d\right)^{4} + 2 \, {\left(4 \, a b - 3 \, b^{2} - 4 \, {\left(a - b\right)} c\right)} \tan\left(e x + d\right)^{2} + b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2} + 4 \, {\left({\left(2 \, a - b\right)} \tan\left(e x + d\right)^{4} + {\left(b - 2 \, c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{a - b + c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{\tan\left(e x + d\right)^{4} + 2 \, \tan\left(e x + d\right)^{2} + 1}\right)}{8 \, a e}, \frac{4 \, a \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}} \tan\left(e x + d\right)^{2} + 4 \, a \sqrt{-a + b - c} \arctan\left(-\frac{{\left({\left(2 \, a - b\right)} \tan\left(e x + d\right)^{4} + {\left(b - 2 \, c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{-a + b - c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{2 \, {\left({\left(a^{2} - a b + a c\right)} \tan\left(e x + d\right)^{4} + {\left(a b - b^{2} + b c\right)} \tan\left(e x + d\right)^{2} + {\left(a - b\right)} c + c^{2}\right)}}\right) - {\left(2 \, a - b\right)} \sqrt{a} \log\left(8 \, a^{2} \tan\left(e x + d\right)^{4} + 8 \, a b \tan\left(e x + d\right)^{2} + b^{2} + 4 \, a c + 4 \, {\left(2 \, a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2}\right)} \sqrt{a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}\right)}{8 \, a e}, \frac{2 \, a \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}} \tan\left(e x + d\right)^{2} + \sqrt{-a} {\left(2 \, a - b\right)} \arctan\left(\frac{{\left(2 \, a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2}\right)} \sqrt{-a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{2 \, {\left(a^{2} \tan\left(e x + d\right)^{4} + a b \tan\left(e x + d\right)^{2} + a c\right)}}\right) + \sqrt{a - b + c} a \log\left(\frac{{\left(8 \, a^{2} - 8 \, a b + b^{2} + 4 \, a c\right)} \tan\left(e x + d\right)^{4} + 2 \, {\left(4 \, a b - 3 \, b^{2} - 4 \, {\left(a - b\right)} c\right)} \tan\left(e x + d\right)^{2} + b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2} + 4 \, {\left({\left(2 \, a - b\right)} \tan\left(e x + d\right)^{4} + {\left(b - 2 \, c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{a - b + c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{\tan\left(e x + d\right)^{4} + 2 \, \tan\left(e x + d\right)^{2} + 1}\right)}{4 \, a e}, \frac{2 \, a \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}} \tan\left(e x + d\right)^{2} + \sqrt{-a} {\left(2 \, a - b\right)} \arctan\left(\frac{{\left(2 \, a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2}\right)} \sqrt{-a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{2 \, {\left(a^{2} \tan\left(e x + d\right)^{4} + a b \tan\left(e x + d\right)^{2} + a c\right)}}\right) + 2 \, a \sqrt{-a + b - c} \arctan\left(-\frac{{\left({\left(2 \, a - b\right)} \tan\left(e x + d\right)^{4} + {\left(b - 2 \, c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{-a + b - c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{2 \, {\left({\left(a^{2} - a b + a c\right)} \tan\left(e x + d\right)^{4} + {\left(a b - b^{2} + b c\right)} \tan\left(e x + d\right)^{2} + {\left(a - b\right)} c + c^{2}\right)}}\right)}{4 \, a e}\right]"," ",0,"[1/8*(4*a*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)*tan(e*x + d)^2 - (2*a - b)*sqrt(a)*log(8*a^2*tan(e*x + d)^4 + 8*a*b*tan(e*x + d)^2 + b^2 + 4*a*c + 4*(2*a*tan(e*x + d)^4 + b*tan(e*x + d)^2)*sqrt(a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)) + 2*sqrt(a - b + c)*a*log(((8*a^2 - 8*a*b + b^2 + 4*a*c)*tan(e*x + d)^4 + 2*(4*a*b - 3*b^2 - 4*(a - b)*c)*tan(e*x + d)^2 + b^2 + 4*(a - 2*b)*c + 8*c^2 + 4*((2*a - b)*tan(e*x + d)^4 + (b - 2*c)*tan(e*x + d)^2)*sqrt(a - b + c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4))/(tan(e*x + d)^4 + 2*tan(e*x + d)^2 + 1)))/(a*e), 1/8*(4*a*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)*tan(e*x + d)^2 + 4*a*sqrt(-a + b - c)*arctan(-1/2*((2*a - b)*tan(e*x + d)^4 + (b - 2*c)*tan(e*x + d)^2)*sqrt(-a + b - c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)/((a^2 - a*b + a*c)*tan(e*x + d)^4 + (a*b - b^2 + b*c)*tan(e*x + d)^2 + (a - b)*c + c^2)) - (2*a - b)*sqrt(a)*log(8*a^2*tan(e*x + d)^4 + 8*a*b*tan(e*x + d)^2 + b^2 + 4*a*c + 4*(2*a*tan(e*x + d)^4 + b*tan(e*x + d)^2)*sqrt(a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)))/(a*e), 1/4*(2*a*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)*tan(e*x + d)^2 + sqrt(-a)*(2*a - b)*arctan(1/2*(2*a*tan(e*x + d)^4 + b*tan(e*x + d)^2)*sqrt(-a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)/(a^2*tan(e*x + d)^4 + a*b*tan(e*x + d)^2 + a*c)) + sqrt(a - b + c)*a*log(((8*a^2 - 8*a*b + b^2 + 4*a*c)*tan(e*x + d)^4 + 2*(4*a*b - 3*b^2 - 4*(a - b)*c)*tan(e*x + d)^2 + b^2 + 4*(a - 2*b)*c + 8*c^2 + 4*((2*a - b)*tan(e*x + d)^4 + (b - 2*c)*tan(e*x + d)^2)*sqrt(a - b + c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4))/(tan(e*x + d)^4 + 2*tan(e*x + d)^2 + 1)))/(a*e), 1/4*(2*a*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)*tan(e*x + d)^2 + sqrt(-a)*(2*a - b)*arctan(1/2*(2*a*tan(e*x + d)^4 + b*tan(e*x + d)^2)*sqrt(-a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)/(a^2*tan(e*x + d)^4 + a*b*tan(e*x + d)^2 + a*c)) + 2*a*sqrt(-a + b - c)*arctan(-1/2*((2*a - b)*tan(e*x + d)^4 + (b - 2*c)*tan(e*x + d)^2)*sqrt(-a + b - c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)/((a^2 - a*b + a*c)*tan(e*x + d)^4 + (a*b - b^2 + b*c)*tan(e*x + d)^2 + (a - b)*c + c^2)))/(a*e)]","A",0
27,1,6011,0,5.971560," ","integrate(cot(e*x+d)^7/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(4 \, a c^{4} + {\left(4 \, a^{2} + 4 \, a b - b^{2}\right)} c^{3} - {\left(a b^{2} + b^{3}\right)} c^{2} + {\left(4 \, a c^{4} + {\left(4 \, a^{2} - 4 \, a b - b^{2}\right)} c^{3} - {\left(a b^{2} - b^{3}\right)} c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + 2 \, {\left(a b^{2} c^{2} + 4 \, a c^{4} - {\left(4 \, a^{2} + b^{2}\right)} c^{3}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{a - b + c} \log\left(2 \, {\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + 2 \, a^{2} - b^{2} + 2 \, c^{2} - 2 \, {\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{a - b + c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 4 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right) - {\left(a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5} - 4 \, a c^{4} - {\left(12 \, a^{2} - 4 \, a b - b^{2}\right)} c^{3} - {\left(12 \, a^{3} - 8 \, a^{2} b - 7 \, a b^{2} + b^{3}\right)} c^{2} + {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5} - 4 \, a c^{4} - {\left(12 \, a^{2} - 12 \, a b - b^{2}\right)} c^{3} - 3 \, {\left(4 \, a^{3} - 8 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 12 \, a^{3} b + 9 \, a^{2} b^{2} + 2 \, a b^{3} - 3 \, b^{4}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(4 \, a^{4} - 4 \, a^{3} b - 7 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4}\right)} c - 2 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + 4 \, a c^{4} + {\left(4 \, a^{2} - 8 \, a b - b^{2}\right)} c^{3} - {\left(4 \, a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2} + b^{4}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{c} \log\left(\frac{{\left(b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2} - 4 \, {\left({\left(b - 2 \, c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, b \cos\left(2 \, e x + 2 \, d\right) + b + 2 \, c\right)} \sqrt{c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 2 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}\right) - 4 \, {\left(3 \, a b c^{3} + {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} c^{2} + {\left({\left(4 \, a^{2} - 3 \, a b\right)} c^{3} + {\left(4 \, a^{3} - 6 \, a^{2} b + a b^{2} + b^{3}\right)} c^{2} + {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + {\left(a^{3} b - a^{2} b^{2} - a b^{3} + b^{4}\right)} c - 2 \, {\left(2 \, a^{2} c^{3} + {\left(2 \, a^{3} - a^{2} b - a b^{2}\right)} c^{2} + {\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{4 \, {\left({\left(4 \, a c^{6} + {\left(12 \, a^{2} - 12 \, a b - b^{2}\right)} c^{5} + 3 \, {\left(4 \, a^{3} - 8 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c^{4} + {\left(4 \, a^{4} - 12 \, a^{3} b + 9 \, a^{2} b^{2} + 2 \, a b^{3} - 3 \, b^{4}\right)} c^{3} - {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} c^{2}\right)} e \cos\left(2 \, e x + 2 \, d\right)^{2} + 2 \, {\left(4 \, a c^{6} + {\left(4 \, a^{2} - 8 \, a b - b^{2}\right)} c^{5} - {\left(4 \, a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} c^{4} - {\left(4 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2} + b^{4}\right)} c^{3} + {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} c^{2}\right)} e \cos\left(2 \, e x + 2 \, d\right) + {\left(4 \, a c^{6} + {\left(12 \, a^{2} - 4 \, a b - b^{2}\right)} c^{5} + {\left(12 \, a^{3} - 8 \, a^{2} b - 7 \, a b^{2} + b^{3}\right)} c^{4} + {\left(4 \, a^{4} - 4 \, a^{3} b - 7 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4}\right)} c^{3} - {\left(a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5}\right)} c^{2}\right)} e\right)}}, \frac{2 \, {\left(a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5} - 4 \, a c^{4} - {\left(12 \, a^{2} - 4 \, a b - b^{2}\right)} c^{3} - {\left(12 \, a^{3} - 8 \, a^{2} b - 7 \, a b^{2} + b^{3}\right)} c^{2} + {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5} - 4 \, a c^{4} - {\left(12 \, a^{2} - 12 \, a b - b^{2}\right)} c^{3} - 3 \, {\left(4 \, a^{3} - 8 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 12 \, a^{3} b + 9 \, a^{2} b^{2} + 2 \, a b^{3} - 3 \, b^{4}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(4 \, a^{4} - 4 \, a^{3} b - 7 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4}\right)} c - 2 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + 4 \, a c^{4} + {\left(4 \, a^{2} - 8 \, a b - b^{2}\right)} c^{3} - {\left(4 \, a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2} + b^{4}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{-c} \arctan\left(-\frac{{\left({\left(b - 2 \, c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, b \cos\left(2 \, e x + 2 \, d\right) + b + 2 \, c\right)} \sqrt{-c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{2 \, {\left({\left({\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + {\left(a + b\right)} c + c^{2} - 2 \, {\left(a c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)}}\right) + {\left(4 \, a c^{4} + {\left(4 \, a^{2} + 4 \, a b - b^{2}\right)} c^{3} - {\left(a b^{2} + b^{3}\right)} c^{2} + {\left(4 \, a c^{4} + {\left(4 \, a^{2} - 4 \, a b - b^{2}\right)} c^{3} - {\left(a b^{2} - b^{3}\right)} c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + 2 \, {\left(a b^{2} c^{2} + 4 \, a c^{4} - {\left(4 \, a^{2} + b^{2}\right)} c^{3}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{a - b + c} \log\left(2 \, {\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + 2 \, a^{2} - b^{2} + 2 \, c^{2} - 2 \, {\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{a - b + c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 4 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right) - 4 \, {\left(3 \, a b c^{3} + {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} c^{2} + {\left({\left(4 \, a^{2} - 3 \, a b\right)} c^{3} + {\left(4 \, a^{3} - 6 \, a^{2} b + a b^{2} + b^{3}\right)} c^{2} + {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + {\left(a^{3} b - a^{2} b^{2} - a b^{3} + b^{4}\right)} c - 2 \, {\left(2 \, a^{2} c^{3} + {\left(2 \, a^{3} - a^{2} b - a b^{2}\right)} c^{2} + {\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{4 \, {\left({\left(4 \, a c^{6} + {\left(12 \, a^{2} - 12 \, a b - b^{2}\right)} c^{5} + 3 \, {\left(4 \, a^{3} - 8 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c^{4} + {\left(4 \, a^{4} - 12 \, a^{3} b + 9 \, a^{2} b^{2} + 2 \, a b^{3} - 3 \, b^{4}\right)} c^{3} - {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} c^{2}\right)} e \cos\left(2 \, e x + 2 \, d\right)^{2} + 2 \, {\left(4 \, a c^{6} + {\left(4 \, a^{2} - 8 \, a b - b^{2}\right)} c^{5} - {\left(4 \, a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} c^{4} - {\left(4 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2} + b^{4}\right)} c^{3} + {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} c^{2}\right)} e \cos\left(2 \, e x + 2 \, d\right) + {\left(4 \, a c^{6} + {\left(12 \, a^{2} - 4 \, a b - b^{2}\right)} c^{5} + {\left(12 \, a^{3} - 8 \, a^{2} b - 7 \, a b^{2} + b^{3}\right)} c^{4} + {\left(4 \, a^{4} - 4 \, a^{3} b - 7 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4}\right)} c^{3} - {\left(a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5}\right)} c^{2}\right)} e\right)}}, \frac{2 \, {\left(4 \, a c^{4} + {\left(4 \, a^{2} + 4 \, a b - b^{2}\right)} c^{3} - {\left(a b^{2} + b^{3}\right)} c^{2} + {\left(4 \, a c^{4} + {\left(4 \, a^{2} - 4 \, a b - b^{2}\right)} c^{3} - {\left(a b^{2} - b^{3}\right)} c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + 2 \, {\left(a b^{2} c^{2} + 4 \, a c^{4} - {\left(4 \, a^{2} + b^{2}\right)} c^{3}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{-a + b - c} \arctan\left(\frac{{\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{-a + b - c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{{\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + a^{2} - b^{2} + 2 \, a c + c^{2} - 2 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}\right) - {\left(a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5} - 4 \, a c^{4} - {\left(12 \, a^{2} - 4 \, a b - b^{2}\right)} c^{3} - {\left(12 \, a^{3} - 8 \, a^{2} b - 7 \, a b^{2} + b^{3}\right)} c^{2} + {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5} - 4 \, a c^{4} - {\left(12 \, a^{2} - 12 \, a b - b^{2}\right)} c^{3} - 3 \, {\left(4 \, a^{3} - 8 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 12 \, a^{3} b + 9 \, a^{2} b^{2} + 2 \, a b^{3} - 3 \, b^{4}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(4 \, a^{4} - 4 \, a^{3} b - 7 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4}\right)} c - 2 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + 4 \, a c^{4} + {\left(4 \, a^{2} - 8 \, a b - b^{2}\right)} c^{3} - {\left(4 \, a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2} + b^{4}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{c} \log\left(\frac{{\left(b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2} - 4 \, {\left({\left(b - 2 \, c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, b \cos\left(2 \, e x + 2 \, d\right) + b + 2 \, c\right)} \sqrt{c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 2 \, {\left(b^{2} + 4 \, a c - 8 \, c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}\right) - 4 \, {\left(3 \, a b c^{3} + {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} c^{2} + {\left({\left(4 \, a^{2} - 3 \, a b\right)} c^{3} + {\left(4 \, a^{3} - 6 \, a^{2} b + a b^{2} + b^{3}\right)} c^{2} + {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + {\left(a^{3} b - a^{2} b^{2} - a b^{3} + b^{4}\right)} c - 2 \, {\left(2 \, a^{2} c^{3} + {\left(2 \, a^{3} - a^{2} b - a b^{2}\right)} c^{2} + {\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{4 \, {\left({\left(4 \, a c^{6} + {\left(12 \, a^{2} - 12 \, a b - b^{2}\right)} c^{5} + 3 \, {\left(4 \, a^{3} - 8 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c^{4} + {\left(4 \, a^{4} - 12 \, a^{3} b + 9 \, a^{2} b^{2} + 2 \, a b^{3} - 3 \, b^{4}\right)} c^{3} - {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} c^{2}\right)} e \cos\left(2 \, e x + 2 \, d\right)^{2} + 2 \, {\left(4 \, a c^{6} + {\left(4 \, a^{2} - 8 \, a b - b^{2}\right)} c^{5} - {\left(4 \, a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} c^{4} - {\left(4 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2} + b^{4}\right)} c^{3} + {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} c^{2}\right)} e \cos\left(2 \, e x + 2 \, d\right) + {\left(4 \, a c^{6} + {\left(12 \, a^{2} - 4 \, a b - b^{2}\right)} c^{5} + {\left(12 \, a^{3} - 8 \, a^{2} b - 7 \, a b^{2} + b^{3}\right)} c^{4} + {\left(4 \, a^{4} - 4 \, a^{3} b - 7 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4}\right)} c^{3} - {\left(a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5}\right)} c^{2}\right)} e\right)}}, \frac{{\left(4 \, a c^{4} + {\left(4 \, a^{2} + 4 \, a b - b^{2}\right)} c^{3} - {\left(a b^{2} + b^{3}\right)} c^{2} + {\left(4 \, a c^{4} + {\left(4 \, a^{2} - 4 \, a b - b^{2}\right)} c^{3} - {\left(a b^{2} - b^{3}\right)} c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + 2 \, {\left(a b^{2} c^{2} + 4 \, a c^{4} - {\left(4 \, a^{2} + b^{2}\right)} c^{3}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{-a + b - c} \arctan\left(\frac{{\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{-a + b - c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{{\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + a^{2} - b^{2} + 2 \, a c + c^{2} - 2 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}\right) + {\left(a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5} - 4 \, a c^{4} - {\left(12 \, a^{2} - 4 \, a b - b^{2}\right)} c^{3} - {\left(12 \, a^{3} - 8 \, a^{2} b - 7 \, a b^{2} + b^{3}\right)} c^{2} + {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5} - 4 \, a c^{4} - {\left(12 \, a^{2} - 12 \, a b - b^{2}\right)} c^{3} - 3 \, {\left(4 \, a^{3} - 8 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 12 \, a^{3} b + 9 \, a^{2} b^{2} + 2 \, a b^{3} - 3 \, b^{4}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(4 \, a^{4} - 4 \, a^{3} b - 7 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4}\right)} c - 2 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + 4 \, a c^{4} + {\left(4 \, a^{2} - 8 \, a b - b^{2}\right)} c^{3} - {\left(4 \, a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2} + b^{4}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{-c} \arctan\left(-\frac{{\left({\left(b - 2 \, c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, b \cos\left(2 \, e x + 2 \, d\right) + b + 2 \, c\right)} \sqrt{-c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{2 \, {\left({\left({\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + {\left(a + b\right)} c + c^{2} - 2 \, {\left(a c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right)}}\right) - 2 \, {\left(3 \, a b c^{3} + {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} c^{2} + {\left({\left(4 \, a^{2} - 3 \, a b\right)} c^{3} + {\left(4 \, a^{3} - 6 \, a^{2} b + a b^{2} + b^{3}\right)} c^{2} + {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + {\left(a^{3} b - a^{2} b^{2} - a b^{3} + b^{4}\right)} c - 2 \, {\left(2 \, a^{2} c^{3} + {\left(2 \, a^{3} - a^{2} b - a b^{2}\right)} c^{2} + {\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{2 \, {\left({\left(4 \, a c^{6} + {\left(12 \, a^{2} - 12 \, a b - b^{2}\right)} c^{5} + 3 \, {\left(4 \, a^{3} - 8 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c^{4} + {\left(4 \, a^{4} - 12 \, a^{3} b + 9 \, a^{2} b^{2} + 2 \, a b^{3} - 3 \, b^{4}\right)} c^{3} - {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} c^{2}\right)} e \cos\left(2 \, e x + 2 \, d\right)^{2} + 2 \, {\left(4 \, a c^{6} + {\left(4 \, a^{2} - 8 \, a b - b^{2}\right)} c^{5} - {\left(4 \, a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} c^{4} - {\left(4 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2} + b^{4}\right)} c^{3} + {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} c^{2}\right)} e \cos\left(2 \, e x + 2 \, d\right) + {\left(4 \, a c^{6} + {\left(12 \, a^{2} - 4 \, a b - b^{2}\right)} c^{5} + {\left(12 \, a^{3} - 8 \, a^{2} b - 7 \, a b^{2} + b^{3}\right)} c^{4} + {\left(4 \, a^{4} - 4 \, a^{3} b - 7 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4}\right)} c^{3} - {\left(a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5}\right)} c^{2}\right)} e\right)}}\right]"," ",0,"[1/4*((4*a*c^4 + (4*a^2 + 4*a*b - b^2)*c^3 - (a*b^2 + b^3)*c^2 + (4*a*c^4 + (4*a^2 - 4*a*b - b^2)*c^3 - (a*b^2 - b^3)*c^2)*cos(2*e*x + 2*d)^2 + 2*(a*b^2*c^2 + 4*a*c^4 - (4*a^2 + b^2)*c^3)*cos(2*e*x + 2*d))*sqrt(a - b + c)*log(2*(a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + 2*a^2 - b^2 + 2*c^2 - 2*((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(a - b + c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 4*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d)) - (a^3*b^2 - a^2*b^3 - a*b^4 + b^5 - 4*a*c^4 - (12*a^2 - 4*a*b - b^2)*c^3 - (12*a^3 - 8*a^2*b - 7*a*b^2 + b^3)*c^2 + (a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5 - 4*a*c^4 - (12*a^2 - 12*a*b - b^2)*c^3 - 3*(4*a^3 - 8*a^2*b + 3*a*b^2 + b^3)*c^2 - (4*a^4 - 12*a^3*b + 9*a^2*b^2 + 2*a*b^3 - 3*b^4)*c)*cos(2*e*x + 2*d)^2 - (4*a^4 - 4*a^3*b - 7*a^2*b^2 + 6*a*b^3 + b^4)*c - 2*(a^3*b^2 - 2*a^2*b^3 + a*b^4 + 4*a*c^4 + (4*a^2 - 8*a*b - b^2)*c^3 - (4*a^3 - 3*a*b^2 - 2*b^3)*c^2 - (4*a^4 - 8*a^3*b + 3*a^2*b^2 + b^4)*c)*cos(2*e*x + 2*d))*sqrt(c)*log(((b^2 + 4*(a - 2*b)*c + 8*c^2)*cos(2*e*x + 2*d)^2 + b^2 + 4*(a + 2*b)*c + 8*c^2 - 4*((b - 2*c)*cos(2*e*x + 2*d)^2 - 2*b*cos(2*e*x + 2*d) + b + 2*c)*sqrt(c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 2*(b^2 + 4*a*c - 8*c^2)*cos(2*e*x + 2*d))/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 4*(3*a*b*c^3 + (4*a^2*b - 3*a*b^2 - b^3)*c^2 + ((4*a^2 - 3*a*b)*c^3 + (4*a^3 - 6*a^2*b + a*b^2 + b^3)*c^2 + (a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*c)*cos(2*e*x + 2*d)^2 + (a^3*b - a^2*b^2 - a*b^3 + b^4)*c - 2*(2*a^2*c^3 + (2*a^3 - a^2*b - a*b^2)*c^2 + (a^3*b - 2*a^2*b^2 + a*b^3)*c)*cos(2*e*x + 2*d))*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/((4*a*c^6 + (12*a^2 - 12*a*b - b^2)*c^5 + 3*(4*a^3 - 8*a^2*b + 3*a*b^2 + b^3)*c^4 + (4*a^4 - 12*a^3*b + 9*a^2*b^2 + 2*a*b^3 - 3*b^4)*c^3 - (a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*c^2)*e*cos(2*e*x + 2*d)^2 + 2*(4*a*c^6 + (4*a^2 - 8*a*b - b^2)*c^5 - (4*a^3 - 3*a*b^2 - 2*b^3)*c^4 - (4*a^4 - 8*a^3*b + 3*a^2*b^2 + b^4)*c^3 + (a^3*b^2 - 2*a^2*b^3 + a*b^4)*c^2)*e*cos(2*e*x + 2*d) + (4*a*c^6 + (12*a^2 - 4*a*b - b^2)*c^5 + (12*a^3 - 8*a^2*b - 7*a*b^2 + b^3)*c^4 + (4*a^4 - 4*a^3*b - 7*a^2*b^2 + 6*a*b^3 + b^4)*c^3 - (a^3*b^2 - a^2*b^3 - a*b^4 + b^5)*c^2)*e), 1/4*(2*(a^3*b^2 - a^2*b^3 - a*b^4 + b^5 - 4*a*c^4 - (12*a^2 - 4*a*b - b^2)*c^3 - (12*a^3 - 8*a^2*b - 7*a*b^2 + b^3)*c^2 + (a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5 - 4*a*c^4 - (12*a^2 - 12*a*b - b^2)*c^3 - 3*(4*a^3 - 8*a^2*b + 3*a*b^2 + b^3)*c^2 - (4*a^4 - 12*a^3*b + 9*a^2*b^2 + 2*a*b^3 - 3*b^4)*c)*cos(2*e*x + 2*d)^2 - (4*a^4 - 4*a^3*b - 7*a^2*b^2 + 6*a*b^3 + b^4)*c - 2*(a^3*b^2 - 2*a^2*b^3 + a*b^4 + 4*a*c^4 + (4*a^2 - 8*a*b - b^2)*c^3 - (4*a^3 - 3*a*b^2 - 2*b^3)*c^2 - (4*a^4 - 8*a^3*b + 3*a^2*b^2 + b^4)*c)*cos(2*e*x + 2*d))*sqrt(-c)*arctan(-1/2*((b - 2*c)*cos(2*e*x + 2*d)^2 - 2*b*cos(2*e*x + 2*d) + b + 2*c)*sqrt(-c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/(((a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + (a + b)*c + c^2 - 2*(a*c - c^2)*cos(2*e*x + 2*d))) + (4*a*c^4 + (4*a^2 + 4*a*b - b^2)*c^3 - (a*b^2 + b^3)*c^2 + (4*a*c^4 + (4*a^2 - 4*a*b - b^2)*c^3 - (a*b^2 - b^3)*c^2)*cos(2*e*x + 2*d)^2 + 2*(a*b^2*c^2 + 4*a*c^4 - (4*a^2 + b^2)*c^3)*cos(2*e*x + 2*d))*sqrt(a - b + c)*log(2*(a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + 2*a^2 - b^2 + 2*c^2 - 2*((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(a - b + c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 4*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d)) - 4*(3*a*b*c^3 + (4*a^2*b - 3*a*b^2 - b^3)*c^2 + ((4*a^2 - 3*a*b)*c^3 + (4*a^3 - 6*a^2*b + a*b^2 + b^3)*c^2 + (a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*c)*cos(2*e*x + 2*d)^2 + (a^3*b - a^2*b^2 - a*b^3 + b^4)*c - 2*(2*a^2*c^3 + (2*a^3 - a^2*b - a*b^2)*c^2 + (a^3*b - 2*a^2*b^2 + a*b^3)*c)*cos(2*e*x + 2*d))*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/((4*a*c^6 + (12*a^2 - 12*a*b - b^2)*c^5 + 3*(4*a^3 - 8*a^2*b + 3*a*b^2 + b^3)*c^4 + (4*a^4 - 12*a^3*b + 9*a^2*b^2 + 2*a*b^3 - 3*b^4)*c^3 - (a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*c^2)*e*cos(2*e*x + 2*d)^2 + 2*(4*a*c^6 + (4*a^2 - 8*a*b - b^2)*c^5 - (4*a^3 - 3*a*b^2 - 2*b^3)*c^4 - (4*a^4 - 8*a^3*b + 3*a^2*b^2 + b^4)*c^3 + (a^3*b^2 - 2*a^2*b^3 + a*b^4)*c^2)*e*cos(2*e*x + 2*d) + (4*a*c^6 + (12*a^2 - 4*a*b - b^2)*c^5 + (12*a^3 - 8*a^2*b - 7*a*b^2 + b^3)*c^4 + (4*a^4 - 4*a^3*b - 7*a^2*b^2 + 6*a*b^3 + b^4)*c^3 - (a^3*b^2 - a^2*b^3 - a*b^4 + b^5)*c^2)*e), 1/4*(2*(4*a*c^4 + (4*a^2 + 4*a*b - b^2)*c^3 - (a*b^2 + b^3)*c^2 + (4*a*c^4 + (4*a^2 - 4*a*b - b^2)*c^3 - (a*b^2 - b^3)*c^2)*cos(2*e*x + 2*d)^2 + 2*(a*b^2*c^2 + 4*a*c^4 - (4*a^2 + b^2)*c^3)*cos(2*e*x + 2*d))*sqrt(-a + b - c)*arctan(((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(-a + b - c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/((a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + a^2 - b^2 + 2*a*c + c^2 - 2*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d))) - (a^3*b^2 - a^2*b^3 - a*b^4 + b^5 - 4*a*c^4 - (12*a^2 - 4*a*b - b^2)*c^3 - (12*a^3 - 8*a^2*b - 7*a*b^2 + b^3)*c^2 + (a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5 - 4*a*c^4 - (12*a^2 - 12*a*b - b^2)*c^3 - 3*(4*a^3 - 8*a^2*b + 3*a*b^2 + b^3)*c^2 - (4*a^4 - 12*a^3*b + 9*a^2*b^2 + 2*a*b^3 - 3*b^4)*c)*cos(2*e*x + 2*d)^2 - (4*a^4 - 4*a^3*b - 7*a^2*b^2 + 6*a*b^3 + b^4)*c - 2*(a^3*b^2 - 2*a^2*b^3 + a*b^4 + 4*a*c^4 + (4*a^2 - 8*a*b - b^2)*c^3 - (4*a^3 - 3*a*b^2 - 2*b^3)*c^2 - (4*a^4 - 8*a^3*b + 3*a^2*b^2 + b^4)*c)*cos(2*e*x + 2*d))*sqrt(c)*log(((b^2 + 4*(a - 2*b)*c + 8*c^2)*cos(2*e*x + 2*d)^2 + b^2 + 4*(a + 2*b)*c + 8*c^2 - 4*((b - 2*c)*cos(2*e*x + 2*d)^2 - 2*b*cos(2*e*x + 2*d) + b + 2*c)*sqrt(c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 2*(b^2 + 4*a*c - 8*c^2)*cos(2*e*x + 2*d))/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 4*(3*a*b*c^3 + (4*a^2*b - 3*a*b^2 - b^3)*c^2 + ((4*a^2 - 3*a*b)*c^3 + (4*a^3 - 6*a^2*b + a*b^2 + b^3)*c^2 + (a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*c)*cos(2*e*x + 2*d)^2 + (a^3*b - a^2*b^2 - a*b^3 + b^4)*c - 2*(2*a^2*c^3 + (2*a^3 - a^2*b - a*b^2)*c^2 + (a^3*b - 2*a^2*b^2 + a*b^3)*c)*cos(2*e*x + 2*d))*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/((4*a*c^6 + (12*a^2 - 12*a*b - b^2)*c^5 + 3*(4*a^3 - 8*a^2*b + 3*a*b^2 + b^3)*c^4 + (4*a^4 - 12*a^3*b + 9*a^2*b^2 + 2*a*b^3 - 3*b^4)*c^3 - (a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*c^2)*e*cos(2*e*x + 2*d)^2 + 2*(4*a*c^6 + (4*a^2 - 8*a*b - b^2)*c^5 - (4*a^3 - 3*a*b^2 - 2*b^3)*c^4 - (4*a^4 - 8*a^3*b + 3*a^2*b^2 + b^4)*c^3 + (a^3*b^2 - 2*a^2*b^3 + a*b^4)*c^2)*e*cos(2*e*x + 2*d) + (4*a*c^6 + (12*a^2 - 4*a*b - b^2)*c^5 + (12*a^3 - 8*a^2*b - 7*a*b^2 + b^3)*c^4 + (4*a^4 - 4*a^3*b - 7*a^2*b^2 + 6*a*b^3 + b^4)*c^3 - (a^3*b^2 - a^2*b^3 - a*b^4 + b^5)*c^2)*e), 1/2*((4*a*c^4 + (4*a^2 + 4*a*b - b^2)*c^3 - (a*b^2 + b^3)*c^2 + (4*a*c^4 + (4*a^2 - 4*a*b - b^2)*c^3 - (a*b^2 - b^3)*c^2)*cos(2*e*x + 2*d)^2 + 2*(a*b^2*c^2 + 4*a*c^4 - (4*a^2 + b^2)*c^3)*cos(2*e*x + 2*d))*sqrt(-a + b - c)*arctan(((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(-a + b - c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/((a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + a^2 - b^2 + 2*a*c + c^2 - 2*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d))) + (a^3*b^2 - a^2*b^3 - a*b^4 + b^5 - 4*a*c^4 - (12*a^2 - 4*a*b - b^2)*c^3 - (12*a^3 - 8*a^2*b - 7*a*b^2 + b^3)*c^2 + (a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5 - 4*a*c^4 - (12*a^2 - 12*a*b - b^2)*c^3 - 3*(4*a^3 - 8*a^2*b + 3*a*b^2 + b^3)*c^2 - (4*a^4 - 12*a^3*b + 9*a^2*b^2 + 2*a*b^3 - 3*b^4)*c)*cos(2*e*x + 2*d)^2 - (4*a^4 - 4*a^3*b - 7*a^2*b^2 + 6*a*b^3 + b^4)*c - 2*(a^3*b^2 - 2*a^2*b^3 + a*b^4 + 4*a*c^4 + (4*a^2 - 8*a*b - b^2)*c^3 - (4*a^3 - 3*a*b^2 - 2*b^3)*c^2 - (4*a^4 - 8*a^3*b + 3*a^2*b^2 + b^4)*c)*cos(2*e*x + 2*d))*sqrt(-c)*arctan(-1/2*((b - 2*c)*cos(2*e*x + 2*d)^2 - 2*b*cos(2*e*x + 2*d) + b + 2*c)*sqrt(-c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/(((a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + (a + b)*c + c^2 - 2*(a*c - c^2)*cos(2*e*x + 2*d))) - 2*(3*a*b*c^3 + (4*a^2*b - 3*a*b^2 - b^3)*c^2 + ((4*a^2 - 3*a*b)*c^3 + (4*a^3 - 6*a^2*b + a*b^2 + b^3)*c^2 + (a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*c)*cos(2*e*x + 2*d)^2 + (a^3*b - a^2*b^2 - a*b^3 + b^4)*c - 2*(2*a^2*c^3 + (2*a^3 - a^2*b - a*b^2)*c^2 + (a^3*b - 2*a^2*b^2 + a*b^3)*c)*cos(2*e*x + 2*d))*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/((4*a*c^6 + (12*a^2 - 12*a*b - b^2)*c^5 + 3*(4*a^3 - 8*a^2*b + 3*a*b^2 + b^3)*c^4 + (4*a^4 - 12*a^3*b + 9*a^2*b^2 + 2*a*b^3 - 3*b^4)*c^3 - (a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*c^2)*e*cos(2*e*x + 2*d)^2 + 2*(4*a*c^6 + (4*a^2 - 8*a*b - b^2)*c^5 - (4*a^3 - 3*a*b^2 - 2*b^3)*c^4 - (4*a^4 - 8*a^3*b + 3*a^2*b^2 + b^4)*c^3 + (a^3*b^2 - 2*a^2*b^3 + a*b^4)*c^2)*e*cos(2*e*x + 2*d) + (4*a*c^6 + (12*a^2 - 4*a*b - b^2)*c^5 + (12*a^3 - 8*a^2*b - 7*a*b^2 + b^3)*c^4 + (4*a^4 - 4*a^3*b - 7*a^2*b^2 + 6*a*b^3 + b^4)*c^3 - (a^3*b^2 - a^2*b^3 - a*b^4 + b^5)*c^2)*e)]","B",0
28,1,1743,0,1.206133," ","integrate(cot(e*x+d)^5/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a b^{2} + b^{3} - 4 \, a c^{2} + {\left(a b^{2} - b^{3} - 4 \, a c^{2} - {\left(4 \, a^{2} - 4 \, a b - b^{2}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(4 \, a^{2} + 4 \, a b - b^{2}\right)} c - 2 \, {\left(a b^{2} + 4 \, a c^{2} - {\left(4 \, a^{2} + b^{2}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{a - b + c} \log\left(2 \, {\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + 2 \, a^{2} - b^{2} + 2 \, c^{2} + 2 \, {\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{a - b + c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 4 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right) - 4 \, {\left(2 \, a^{3} - 2 \, a^{2} b - a b^{2} + b^{3} + 2 \, a c^{2} + {\left(2 \, a^{3} - 4 \, a^{2} b + 3 \, a b^{2} - b^{3} + b^{2} c - 2 \, a c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + {\left(4 \, a^{2} - 2 \, a b - b^{2}\right)} c - 2 \, {\left(2 \, a^{3} - 3 \, a^{2} b + a b^{2} + {\left(2 \, a^{2} - a b\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{4 \, {\left({\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5} - 4 \, a c^{4} - {\left(12 \, a^{2} - 12 \, a b - b^{2}\right)} c^{3} - 3 \, {\left(4 \, a^{3} - 8 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 12 \, a^{3} b + 9 \, a^{2} b^{2} + 2 \, a b^{3} - 3 \, b^{4}\right)} c\right)} e \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + 4 \, a c^{4} + {\left(4 \, a^{2} - 8 \, a b - b^{2}\right)} c^{3} - {\left(4 \, a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2} + b^{4}\right)} c\right)} e \cos\left(2 \, e x + 2 \, d\right) + {\left(a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5} - 4 \, a c^{4} - {\left(12 \, a^{2} - 4 \, a b - b^{2}\right)} c^{3} - {\left(12 \, a^{3} - 8 \, a^{2} b - 7 \, a b^{2} + b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 4 \, a^{3} b - 7 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4}\right)} c\right)} e\right)}}, -\frac{{\left(a b^{2} + b^{3} - 4 \, a c^{2} + {\left(a b^{2} - b^{3} - 4 \, a c^{2} - {\left(4 \, a^{2} - 4 \, a b - b^{2}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(4 \, a^{2} + 4 \, a b - b^{2}\right)} c - 2 \, {\left(a b^{2} + 4 \, a c^{2} - {\left(4 \, a^{2} + b^{2}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{-a + b - c} \arctan\left(\frac{{\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{-a + b - c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{{\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + a^{2} - b^{2} + 2 \, a c + c^{2} - 2 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}\right) + 2 \, {\left(2 \, a^{3} - 2 \, a^{2} b - a b^{2} + b^{3} + 2 \, a c^{2} + {\left(2 \, a^{3} - 4 \, a^{2} b + 3 \, a b^{2} - b^{3} + b^{2} c - 2 \, a c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + {\left(4 \, a^{2} - 2 \, a b - b^{2}\right)} c - 2 \, {\left(2 \, a^{3} - 3 \, a^{2} b + a b^{2} + {\left(2 \, a^{2} - a b\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{2 \, {\left({\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5} - 4 \, a c^{4} - {\left(12 \, a^{2} - 12 \, a b - b^{2}\right)} c^{3} - 3 \, {\left(4 \, a^{3} - 8 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 12 \, a^{3} b + 9 \, a^{2} b^{2} + 2 \, a b^{3} - 3 \, b^{4}\right)} c\right)} e \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + 4 \, a c^{4} + {\left(4 \, a^{2} - 8 \, a b - b^{2}\right)} c^{3} - {\left(4 \, a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2} + b^{4}\right)} c\right)} e \cos\left(2 \, e x + 2 \, d\right) + {\left(a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5} - 4 \, a c^{4} - {\left(12 \, a^{2} - 4 \, a b - b^{2}\right)} c^{3} - {\left(12 \, a^{3} - 8 \, a^{2} b - 7 \, a b^{2} + b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 4 \, a^{3} b - 7 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4}\right)} c\right)} e\right)}}\right]"," ",0,"[1/4*((a*b^2 + b^3 - 4*a*c^2 + (a*b^2 - b^3 - 4*a*c^2 - (4*a^2 - 4*a*b - b^2)*c)*cos(2*e*x + 2*d)^2 - (4*a^2 + 4*a*b - b^2)*c - 2*(a*b^2 + 4*a*c^2 - (4*a^2 + b^2)*c)*cos(2*e*x + 2*d))*sqrt(a - b + c)*log(2*(a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + 2*a^2 - b^2 + 2*c^2 + 2*((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(a - b + c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 4*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d)) - 4*(2*a^3 - 2*a^2*b - a*b^2 + b^3 + 2*a*c^2 + (2*a^3 - 4*a^2*b + 3*a*b^2 - b^3 + b^2*c - 2*a*c^2)*cos(2*e*x + 2*d)^2 + (4*a^2 - 2*a*b - b^2)*c - 2*(2*a^3 - 3*a^2*b + a*b^2 + (2*a^2 - a*b)*c)*cos(2*e*x + 2*d))*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/((a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5 - 4*a*c^4 - (12*a^2 - 12*a*b - b^2)*c^3 - 3*(4*a^3 - 8*a^2*b + 3*a*b^2 + b^3)*c^2 - (4*a^4 - 12*a^3*b + 9*a^2*b^2 + 2*a*b^3 - 3*b^4)*c)*e*cos(2*e*x + 2*d)^2 - 2*(a^3*b^2 - 2*a^2*b^3 + a*b^4 + 4*a*c^4 + (4*a^2 - 8*a*b - b^2)*c^3 - (4*a^3 - 3*a*b^2 - 2*b^3)*c^2 - (4*a^4 - 8*a^3*b + 3*a^2*b^2 + b^4)*c)*e*cos(2*e*x + 2*d) + (a^3*b^2 - a^2*b^3 - a*b^4 + b^5 - 4*a*c^4 - (12*a^2 - 4*a*b - b^2)*c^3 - (12*a^3 - 8*a^2*b - 7*a*b^2 + b^3)*c^2 - (4*a^4 - 4*a^3*b - 7*a^2*b^2 + 6*a*b^3 + b^4)*c)*e), -1/2*((a*b^2 + b^3 - 4*a*c^2 + (a*b^2 - b^3 - 4*a*c^2 - (4*a^2 - 4*a*b - b^2)*c)*cos(2*e*x + 2*d)^2 - (4*a^2 + 4*a*b - b^2)*c - 2*(a*b^2 + 4*a*c^2 - (4*a^2 + b^2)*c)*cos(2*e*x + 2*d))*sqrt(-a + b - c)*arctan(((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(-a + b - c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/((a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + a^2 - b^2 + 2*a*c + c^2 - 2*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d))) + 2*(2*a^3 - 2*a^2*b - a*b^2 + b^3 + 2*a*c^2 + (2*a^3 - 4*a^2*b + 3*a*b^2 - b^3 + b^2*c - 2*a*c^2)*cos(2*e*x + 2*d)^2 + (4*a^2 - 2*a*b - b^2)*c - 2*(2*a^3 - 3*a^2*b + a*b^2 + (2*a^2 - a*b)*c)*cos(2*e*x + 2*d))*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/((a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5 - 4*a*c^4 - (12*a^2 - 12*a*b - b^2)*c^3 - 3*(4*a^3 - 8*a^2*b + 3*a*b^2 + b^3)*c^2 - (4*a^4 - 12*a^3*b + 9*a^2*b^2 + 2*a*b^3 - 3*b^4)*c)*e*cos(2*e*x + 2*d)^2 - 2*(a^3*b^2 - 2*a^2*b^3 + a*b^4 + 4*a*c^4 + (4*a^2 - 8*a*b - b^2)*c^3 - (4*a^3 - 3*a*b^2 - 2*b^3)*c^2 - (4*a^4 - 8*a^3*b + 3*a^2*b^2 + b^4)*c)*e*cos(2*e*x + 2*d) + (a^3*b^2 - a^2*b^3 - a*b^4 + b^5 - 4*a*c^4 - (12*a^2 - 4*a*b - b^2)*c^3 - (12*a^3 - 8*a^2*b - 7*a*b^2 + b^3)*c^2 - (4*a^4 - 4*a^3*b - 7*a^2*b^2 + 6*a*b^3 + b^4)*c)*e)]","B",0
29,1,1717,0,1.826224," ","integrate(cot(e*x+d)^3/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a b^{2} + b^{3} - 4 \, a c^{2} + {\left(a b^{2} - b^{3} - 4 \, a c^{2} - {\left(4 \, a^{2} - 4 \, a b - b^{2}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(4 \, a^{2} + 4 \, a b - b^{2}\right)} c - 2 \, {\left(a b^{2} + 4 \, a c^{2} - {\left(4 \, a^{2} + b^{2}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{a - b + c} \log\left(2 \, {\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + 2 \, a^{2} - b^{2} + 2 \, c^{2} - 2 \, {\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{a - b + c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 4 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right) + 4 \, {\left(a^{2} b - a b^{2} + b^{2} c - b c^{2} + {\left(a^{2} b - a b^{2} - {\left(4 \, a - b\right)} c^{2} - {\left(4 \, a^{2} - 6 \, a b + b^{2}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a^{2} b - a b^{2} - 2 \, a c^{2} - {\left(2 \, a^{2} - 3 \, a b\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{4 \, {\left({\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5} - 4 \, a c^{4} - {\left(12 \, a^{2} - 12 \, a b - b^{2}\right)} c^{3} - 3 \, {\left(4 \, a^{3} - 8 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 12 \, a^{3} b + 9 \, a^{2} b^{2} + 2 \, a b^{3} - 3 \, b^{4}\right)} c\right)} e \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + 4 \, a c^{4} + {\left(4 \, a^{2} - 8 \, a b - b^{2}\right)} c^{3} - {\left(4 \, a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2} + b^{4}\right)} c\right)} e \cos\left(2 \, e x + 2 \, d\right) + {\left(a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5} - 4 \, a c^{4} - {\left(12 \, a^{2} - 4 \, a b - b^{2}\right)} c^{3} - {\left(12 \, a^{3} - 8 \, a^{2} b - 7 \, a b^{2} + b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 4 \, a^{3} b - 7 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4}\right)} c\right)} e\right)}}, \frac{{\left(a b^{2} + b^{3} - 4 \, a c^{2} + {\left(a b^{2} - b^{3} - 4 \, a c^{2} - {\left(4 \, a^{2} - 4 \, a b - b^{2}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(4 \, a^{2} + 4 \, a b - b^{2}\right)} c - 2 \, {\left(a b^{2} + 4 \, a c^{2} - {\left(4 \, a^{2} + b^{2}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{-a + b - c} \arctan\left(\frac{{\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{-a + b - c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{{\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + a^{2} - b^{2} + 2 \, a c + c^{2} - 2 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}\right) + 2 \, {\left(a^{2} b - a b^{2} + b^{2} c - b c^{2} + {\left(a^{2} b - a b^{2} - {\left(4 \, a - b\right)} c^{2} - {\left(4 \, a^{2} - 6 \, a b + b^{2}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a^{2} b - a b^{2} - 2 \, a c^{2} - {\left(2 \, a^{2} - 3 \, a b\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{2 \, {\left({\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5} - 4 \, a c^{4} - {\left(12 \, a^{2} - 12 \, a b - b^{2}\right)} c^{3} - 3 \, {\left(4 \, a^{3} - 8 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 12 \, a^{3} b + 9 \, a^{2} b^{2} + 2 \, a b^{3} - 3 \, b^{4}\right)} c\right)} e \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + 4 \, a c^{4} + {\left(4 \, a^{2} - 8 \, a b - b^{2}\right)} c^{3} - {\left(4 \, a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2} + b^{4}\right)} c\right)} e \cos\left(2 \, e x + 2 \, d\right) + {\left(a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5} - 4 \, a c^{4} - {\left(12 \, a^{2} - 4 \, a b - b^{2}\right)} c^{3} - {\left(12 \, a^{3} - 8 \, a^{2} b - 7 \, a b^{2} + b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 4 \, a^{3} b - 7 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4}\right)} c\right)} e\right)}}\right]"," ",0,"[1/4*((a*b^2 + b^3 - 4*a*c^2 + (a*b^2 - b^3 - 4*a*c^2 - (4*a^2 - 4*a*b - b^2)*c)*cos(2*e*x + 2*d)^2 - (4*a^2 + 4*a*b - b^2)*c - 2*(a*b^2 + 4*a*c^2 - (4*a^2 + b^2)*c)*cos(2*e*x + 2*d))*sqrt(a - b + c)*log(2*(a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + 2*a^2 - b^2 + 2*c^2 - 2*((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(a - b + c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 4*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d)) + 4*(a^2*b - a*b^2 + b^2*c - b*c^2 + (a^2*b - a*b^2 - (4*a - b)*c^2 - (4*a^2 - 6*a*b + b^2)*c)*cos(2*e*x + 2*d)^2 - 2*(a^2*b - a*b^2 - 2*a*c^2 - (2*a^2 - 3*a*b)*c)*cos(2*e*x + 2*d))*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/((a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5 - 4*a*c^4 - (12*a^2 - 12*a*b - b^2)*c^3 - 3*(4*a^3 - 8*a^2*b + 3*a*b^2 + b^3)*c^2 - (4*a^4 - 12*a^3*b + 9*a^2*b^2 + 2*a*b^3 - 3*b^4)*c)*e*cos(2*e*x + 2*d)^2 - 2*(a^3*b^2 - 2*a^2*b^3 + a*b^4 + 4*a*c^4 + (4*a^2 - 8*a*b - b^2)*c^3 - (4*a^3 - 3*a*b^2 - 2*b^3)*c^2 - (4*a^4 - 8*a^3*b + 3*a^2*b^2 + b^4)*c)*e*cos(2*e*x + 2*d) + (a^3*b^2 - a^2*b^3 - a*b^4 + b^5 - 4*a*c^4 - (12*a^2 - 4*a*b - b^2)*c^3 - (12*a^3 - 8*a^2*b - 7*a*b^2 + b^3)*c^2 - (4*a^4 - 4*a^3*b - 7*a^2*b^2 + 6*a*b^3 + b^4)*c)*e), 1/2*((a*b^2 + b^3 - 4*a*c^2 + (a*b^2 - b^3 - 4*a*c^2 - (4*a^2 - 4*a*b - b^2)*c)*cos(2*e*x + 2*d)^2 - (4*a^2 + 4*a*b - b^2)*c - 2*(a*b^2 + 4*a*c^2 - (4*a^2 + b^2)*c)*cos(2*e*x + 2*d))*sqrt(-a + b - c)*arctan(((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(-a + b - c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/((a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + a^2 - b^2 + 2*a*c + c^2 - 2*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d))) + 2*(a^2*b - a*b^2 + b^2*c - b*c^2 + (a^2*b - a*b^2 - (4*a - b)*c^2 - (4*a^2 - 6*a*b + b^2)*c)*cos(2*e*x + 2*d)^2 - 2*(a^2*b - a*b^2 - 2*a*c^2 - (2*a^2 - 3*a*b)*c)*cos(2*e*x + 2*d))*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/((a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5 - 4*a*c^4 - (12*a^2 - 12*a*b - b^2)*c^3 - 3*(4*a^3 - 8*a^2*b + 3*a*b^2 + b^3)*c^2 - (4*a^4 - 12*a^3*b + 9*a^2*b^2 + 2*a*b^3 - 3*b^4)*c)*e*cos(2*e*x + 2*d)^2 - 2*(a^3*b^2 - 2*a^2*b^3 + a*b^4 + 4*a*c^4 + (4*a^2 - 8*a*b - b^2)*c^3 - (4*a^3 - 3*a*b^2 - 2*b^3)*c^2 - (4*a^4 - 8*a^3*b + 3*a^2*b^2 + b^4)*c)*e*cos(2*e*x + 2*d) + (a^3*b^2 - a^2*b^3 - a*b^4 + b^5 - 4*a*c^4 - (12*a^2 - 4*a*b - b^2)*c^3 - (12*a^3 - 8*a^2*b - 7*a*b^2 + b^3)*c^2 - (4*a^4 - 4*a^3*b - 7*a^2*b^2 + 6*a*b^3 + b^4)*c)*e)]","B",0
30,1,1771,0,1.797818," ","integrate(cot(e*x+d)/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a b^{2} + b^{3} - 4 \, a c^{2} + {\left(a b^{2} - b^{3} - 4 \, a c^{2} - {\left(4 \, a^{2} - 4 \, a b - b^{2}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(4 \, a^{2} + 4 \, a b - b^{2}\right)} c - 2 \, {\left(a b^{2} + 4 \, a c^{2} - {\left(4 \, a^{2} + b^{2}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{a - b + c} \log\left(2 \, {\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + 2 \, a^{2} - b^{2} + 2 \, c^{2} + 2 \, {\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{a - b + c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}} - 4 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)\right) - 4 \, {\left(a b^{2} - b^{3} - 2 \, {\left(2 \, a - b\right)} c^{2} - 2 \, c^{3} + {\left(a b^{2} - b^{3} - 4 \, b c^{2} + 2 \, c^{3} - {\left(2 \, a^{2} - 3 \, b^{2}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a^{2} - 2 \, a b - b^{2}\right)} c - 2 \, {\left(a b^{2} - b^{3} - {\left(2 \, a + b\right)} c^{2} - {\left(2 \, a^{2} - a b - 2 \, b^{2}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{4 \, {\left({\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5} - 4 \, a c^{4} - {\left(12 \, a^{2} - 12 \, a b - b^{2}\right)} c^{3} - 3 \, {\left(4 \, a^{3} - 8 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 12 \, a^{3} b + 9 \, a^{2} b^{2} + 2 \, a b^{3} - 3 \, b^{4}\right)} c\right)} e \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + 4 \, a c^{4} + {\left(4 \, a^{2} - 8 \, a b - b^{2}\right)} c^{3} - {\left(4 \, a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2} + b^{4}\right)} c\right)} e \cos\left(2 \, e x + 2 \, d\right) + {\left(a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5} - 4 \, a c^{4} - {\left(12 \, a^{2} - 4 \, a b - b^{2}\right)} c^{3} - {\left(12 \, a^{3} - 8 \, a^{2} b - 7 \, a b^{2} + b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 4 \, a^{3} b - 7 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4}\right)} c\right)} e\right)}}, -\frac{{\left(a b^{2} + b^{3} - 4 \, a c^{2} + {\left(a b^{2} - b^{3} - 4 \, a c^{2} - {\left(4 \, a^{2} - 4 \, a b - b^{2}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(4 \, a^{2} + 4 \, a b - b^{2}\right)} c - 2 \, {\left(a b^{2} + 4 \, a c^{2} - {\left(4 \, a^{2} + b^{2}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{-a + b - c} \arctan\left(\frac{{\left({\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a - b\right)} \cos\left(2 \, e x + 2 \, d\right) + a - c\right)} \sqrt{-a + b - c} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{{\left(a^{2} - 2 \, a b + b^{2} + 2 \, {\left(a - b\right)} c + c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} + a^{2} - b^{2} + 2 \, a c + c^{2} - 2 \, {\left(a^{2} - a b + b c - c^{2}\right)} \cos\left(2 \, e x + 2 \, d\right)}\right) + 2 \, {\left(a b^{2} - b^{3} - 2 \, {\left(2 \, a - b\right)} c^{2} - 2 \, c^{3} + {\left(a b^{2} - b^{3} - 4 \, b c^{2} + 2 \, c^{3} - {\left(2 \, a^{2} - 3 \, b^{2}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - {\left(2 \, a^{2} - 2 \, a b - b^{2}\right)} c - 2 \, {\left(a b^{2} - b^{3} - {\left(2 \, a + b\right)} c^{2} - {\left(2 \, a^{2} - a b - 2 \, b^{2}\right)} c\right)} \cos\left(2 \, e x + 2 \, d\right)\right)} \sqrt{\frac{{\left(a - b + c\right)} \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a - c\right)} \cos\left(2 \, e x + 2 \, d\right) + a + b + c}{\cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, \cos\left(2 \, e x + 2 \, d\right) + 1}}}{2 \, {\left({\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5} - 4 \, a c^{4} - {\left(12 \, a^{2} - 12 \, a b - b^{2}\right)} c^{3} - 3 \, {\left(4 \, a^{3} - 8 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 12 \, a^{3} b + 9 \, a^{2} b^{2} + 2 \, a b^{3} - 3 \, b^{4}\right)} c\right)} e \cos\left(2 \, e x + 2 \, d\right)^{2} - 2 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + 4 \, a c^{4} + {\left(4 \, a^{2} - 8 \, a b - b^{2}\right)} c^{3} - {\left(4 \, a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2} + b^{4}\right)} c\right)} e \cos\left(2 \, e x + 2 \, d\right) + {\left(a^{3} b^{2} - a^{2} b^{3} - a b^{4} + b^{5} - 4 \, a c^{4} - {\left(12 \, a^{2} - 4 \, a b - b^{2}\right)} c^{3} - {\left(12 \, a^{3} - 8 \, a^{2} b - 7 \, a b^{2} + b^{3}\right)} c^{2} - {\left(4 \, a^{4} - 4 \, a^{3} b - 7 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4}\right)} c\right)} e\right)}}\right]"," ",0,"[1/4*((a*b^2 + b^3 - 4*a*c^2 + (a*b^2 - b^3 - 4*a*c^2 - (4*a^2 - 4*a*b - b^2)*c)*cos(2*e*x + 2*d)^2 - (4*a^2 + 4*a*b - b^2)*c - 2*(a*b^2 + 4*a*c^2 - (4*a^2 + b^2)*c)*cos(2*e*x + 2*d))*sqrt(a - b + c)*log(2*(a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + 2*a^2 - b^2 + 2*c^2 + 2*((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(a - b + c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)) - 4*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d)) - 4*(a*b^2 - b^3 - 2*(2*a - b)*c^2 - 2*c^3 + (a*b^2 - b^3 - 4*b*c^2 + 2*c^3 - (2*a^2 - 3*b^2)*c)*cos(2*e*x + 2*d)^2 - (2*a^2 - 2*a*b - b^2)*c - 2*(a*b^2 - b^3 - (2*a + b)*c^2 - (2*a^2 - a*b - 2*b^2)*c)*cos(2*e*x + 2*d))*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/((a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5 - 4*a*c^4 - (12*a^2 - 12*a*b - b^2)*c^3 - 3*(4*a^3 - 8*a^2*b + 3*a*b^2 + b^3)*c^2 - (4*a^4 - 12*a^3*b + 9*a^2*b^2 + 2*a*b^3 - 3*b^4)*c)*e*cos(2*e*x + 2*d)^2 - 2*(a^3*b^2 - 2*a^2*b^3 + a*b^4 + 4*a*c^4 + (4*a^2 - 8*a*b - b^2)*c^3 - (4*a^3 - 3*a*b^2 - 2*b^3)*c^2 - (4*a^4 - 8*a^3*b + 3*a^2*b^2 + b^4)*c)*e*cos(2*e*x + 2*d) + (a^3*b^2 - a^2*b^3 - a*b^4 + b^5 - 4*a*c^4 - (12*a^2 - 4*a*b - b^2)*c^3 - (12*a^3 - 8*a^2*b - 7*a*b^2 + b^3)*c^2 - (4*a^4 - 4*a^3*b - 7*a^2*b^2 + 6*a*b^3 + b^4)*c)*e), -1/2*((a*b^2 + b^3 - 4*a*c^2 + (a*b^2 - b^3 - 4*a*c^2 - (4*a^2 - 4*a*b - b^2)*c)*cos(2*e*x + 2*d)^2 - (4*a^2 + 4*a*b - b^2)*c - 2*(a*b^2 + 4*a*c^2 - (4*a^2 + b^2)*c)*cos(2*e*x + 2*d))*sqrt(-a + b - c)*arctan(((a - b + c)*cos(2*e*x + 2*d)^2 - (2*a - b)*cos(2*e*x + 2*d) + a - c)*sqrt(-a + b - c)*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1))/((a^2 - 2*a*b + b^2 + 2*(a - b)*c + c^2)*cos(2*e*x + 2*d)^2 + a^2 - b^2 + 2*a*c + c^2 - 2*(a^2 - a*b + b*c - c^2)*cos(2*e*x + 2*d))) + 2*(a*b^2 - b^3 - 2*(2*a - b)*c^2 - 2*c^3 + (a*b^2 - b^3 - 4*b*c^2 + 2*c^3 - (2*a^2 - 3*b^2)*c)*cos(2*e*x + 2*d)^2 - (2*a^2 - 2*a*b - b^2)*c - 2*(a*b^2 - b^3 - (2*a + b)*c^2 - (2*a^2 - a*b - 2*b^2)*c)*cos(2*e*x + 2*d))*sqrt(((a - b + c)*cos(2*e*x + 2*d)^2 - 2*(a - c)*cos(2*e*x + 2*d) + a + b + c)/(cos(2*e*x + 2*d)^2 - 2*cos(2*e*x + 2*d) + 1)))/((a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5 - 4*a*c^4 - (12*a^2 - 12*a*b - b^2)*c^3 - 3*(4*a^3 - 8*a^2*b + 3*a*b^2 + b^3)*c^2 - (4*a^4 - 12*a^3*b + 9*a^2*b^2 + 2*a*b^3 - 3*b^4)*c)*e*cos(2*e*x + 2*d)^2 - 2*(a^3*b^2 - 2*a^2*b^3 + a*b^4 + 4*a*c^4 + (4*a^2 - 8*a*b - b^2)*c^3 - (4*a^3 - 3*a*b^2 - 2*b^3)*c^2 - (4*a^4 - 8*a^3*b + 3*a^2*b^2 + b^4)*c)*e*cos(2*e*x + 2*d) + (a^3*b^2 - a^2*b^3 - a*b^4 + b^5 - 4*a*c^4 - (12*a^2 - 4*a*b - b^2)*c^3 - (12*a^3 - 8*a^2*b - 7*a*b^2 + b^3)*c^2 - (4*a^4 - 4*a^3*b - 7*a^2*b^2 + 6*a*b^3 + b^4)*c)*e)]","B",0
31,1,4153,0,8.353479," ","integrate(tan(e*x+d)/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, a c^{4} - {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} - 4 \, a^{2} c^{3} - {\left(8 \, a^{3} - 8 \, a^{2} b - a b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{4} - 4 \, a^{3} b + a^{2} b^{2} + a b^{3}\right)} c\right)} \tan\left(e x + d\right)^{4} + {\left(8 \, a^{2} - 8 \, a b - b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{3} - 4 \, a^{2} b + a b^{2} + b^{3}\right)} c^{2} - {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5} - 4 \, a b c^{3} - {\left(8 \, a^{2} b - 8 \, a b^{2} - b^{3}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b - 4 \, a^{2} b^{2} + a b^{3} + b^{4}\right)} c\right)} \tan\left(e x + d\right)^{2} - {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} c\right)} \sqrt{a} \log\left(8 \, a^{2} \tan\left(e x + d\right)^{4} + 8 \, a b \tan\left(e x + d\right)^{2} + b^{2} + 4 \, a c + 4 \, {\left(2 \, a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2}\right)} \sqrt{a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}\right) - {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \tan\left(e x + d\right)^{4} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{a - b + c} \log\left(\frac{{\left(8 \, a^{2} - 8 \, a b + b^{2} + 4 \, a c\right)} \tan\left(e x + d\right)^{4} + 2 \, {\left(4 \, a b - 3 \, b^{2} - 4 \, {\left(a - b\right)} c\right)} \tan\left(e x + d\right)^{2} + b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2} - 4 \, {\left({\left(2 \, a - b\right)} \tan\left(e x + d\right)^{4} + {\left(b - 2 \, c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{a - b + c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{\tan\left(e x + d\right)^{4} + 2 \, \tan\left(e x + d\right)^{2} + 1}\right) - 4 \, {\left({\left(a^{2} b^{3} - a b^{4} + 2 \, a^{2} c^{3} + {\left(2 \, a^{3} - 5 \, a^{2} b - a b^{2}\right)} c^{2} - {\left(3 \, a^{3} b - 2 \, a^{2} b^{2} - 2 \, a b^{3}\right)} c\right)} \tan\left(e x + d\right)^{4} - {\left({\left(2 \, a^{2} + a b\right)} c^{3} + {\left(2 \, a^{3} - a^{2} b - 2 \, a b^{2}\right)} c^{2} - {\left(a^{2} b^{2} - a b^{3}\right)} c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{4 \, {\left({\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4} - 4 \, a^{4} c^{3} - {\left(8 \, a^{5} - 8 \, a^{4} b - a^{3} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{6} - 4 \, a^{5} b + a^{4} b^{2} + a^{3} b^{3}\right)} c\right)} e \tan\left(e x + d\right)^{4} + {\left(a^{4} b^{3} - 2 \, a^{3} b^{4} + a^{2} b^{5} - 4 \, a^{3} b c^{3} - {\left(8 \, a^{4} b - 8 \, a^{3} b^{2} - a^{2} b^{3}\right)} c^{2} - 2 \, {\left(2 \, a^{5} b - 4 \, a^{4} b^{2} + a^{3} b^{3} + a^{2} b^{4}\right)} c\right)} e \tan\left(e x + d\right)^{2} - {\left(4 \, a^{3} c^{4} + {\left(8 \, a^{4} - 8 \, a^{3} b - a^{2} b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{5} - 4 \, a^{4} b + a^{3} b^{2} + a^{2} b^{3}\right)} c^{2} - {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} c\right)} e\right)}}, \frac{2 \, {\left(4 \, a c^{4} - {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} - 4 \, a^{2} c^{3} - {\left(8 \, a^{3} - 8 \, a^{2} b - a b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{4} - 4 \, a^{3} b + a^{2} b^{2} + a b^{3}\right)} c\right)} \tan\left(e x + d\right)^{4} + {\left(8 \, a^{2} - 8 \, a b - b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{3} - 4 \, a^{2} b + a b^{2} + b^{3}\right)} c^{2} - {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5} - 4 \, a b c^{3} - {\left(8 \, a^{2} b - 8 \, a b^{2} - b^{3}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b - 4 \, a^{2} b^{2} + a b^{3} + b^{4}\right)} c\right)} \tan\left(e x + d\right)^{2} - {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} c\right)} \sqrt{-a} \arctan\left(\frac{{\left(2 \, a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2}\right)} \sqrt{-a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{2 \, {\left(a^{2} \tan\left(e x + d\right)^{4} + a b \tan\left(e x + d\right)^{2} + a c\right)}}\right) + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \tan\left(e x + d\right)^{4} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{a - b + c} \log\left(\frac{{\left(8 \, a^{2} - 8 \, a b + b^{2} + 4 \, a c\right)} \tan\left(e x + d\right)^{4} + 2 \, {\left(4 \, a b - 3 \, b^{2} - 4 \, {\left(a - b\right)} c\right)} \tan\left(e x + d\right)^{2} + b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2} - 4 \, {\left({\left(2 \, a - b\right)} \tan\left(e x + d\right)^{4} + {\left(b - 2 \, c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{a - b + c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{\tan\left(e x + d\right)^{4} + 2 \, \tan\left(e x + d\right)^{2} + 1}\right) + 4 \, {\left({\left(a^{2} b^{3} - a b^{4} + 2 \, a^{2} c^{3} + {\left(2 \, a^{3} - 5 \, a^{2} b - a b^{2}\right)} c^{2} - {\left(3 \, a^{3} b - 2 \, a^{2} b^{2} - 2 \, a b^{3}\right)} c\right)} \tan\left(e x + d\right)^{4} - {\left({\left(2 \, a^{2} + a b\right)} c^{3} + {\left(2 \, a^{3} - a^{2} b - 2 \, a b^{2}\right)} c^{2} - {\left(a^{2} b^{2} - a b^{3}\right)} c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{4 \, {\left({\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4} - 4 \, a^{4} c^{3} - {\left(8 \, a^{5} - 8 \, a^{4} b - a^{3} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{6} - 4 \, a^{5} b + a^{4} b^{2} + a^{3} b^{3}\right)} c\right)} e \tan\left(e x + d\right)^{4} + {\left(a^{4} b^{3} - 2 \, a^{3} b^{4} + a^{2} b^{5} - 4 \, a^{3} b c^{3} - {\left(8 \, a^{4} b - 8 \, a^{3} b^{2} - a^{2} b^{3}\right)} c^{2} - 2 \, {\left(2 \, a^{5} b - 4 \, a^{4} b^{2} + a^{3} b^{3} + a^{2} b^{4}\right)} c\right)} e \tan\left(e x + d\right)^{2} - {\left(4 \, a^{3} c^{4} + {\left(8 \, a^{4} - 8 \, a^{3} b - a^{2} b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{5} - 4 \, a^{4} b + a^{3} b^{2} + a^{2} b^{3}\right)} c^{2} - {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} c\right)} e\right)}}, -\frac{2 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \tan\left(e x + d\right)^{4} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{-a + b - c} \arctan\left(-\frac{{\left({\left(2 \, a - b\right)} \tan\left(e x + d\right)^{4} + {\left(b - 2 \, c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{-a + b - c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{2 \, {\left({\left(a^{2} - a b + a c\right)} \tan\left(e x + d\right)^{4} + {\left(a b - b^{2} + b c\right)} \tan\left(e x + d\right)^{2} + {\left(a - b\right)} c + c^{2}\right)}}\right) + {\left(4 \, a c^{4} - {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} - 4 \, a^{2} c^{3} - {\left(8 \, a^{3} - 8 \, a^{2} b - a b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{4} - 4 \, a^{3} b + a^{2} b^{2} + a b^{3}\right)} c\right)} \tan\left(e x + d\right)^{4} + {\left(8 \, a^{2} - 8 \, a b - b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{3} - 4 \, a^{2} b + a b^{2} + b^{3}\right)} c^{2} - {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5} - 4 \, a b c^{3} - {\left(8 \, a^{2} b - 8 \, a b^{2} - b^{3}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b - 4 \, a^{2} b^{2} + a b^{3} + b^{4}\right)} c\right)} \tan\left(e x + d\right)^{2} - {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} c\right)} \sqrt{a} \log\left(8 \, a^{2} \tan\left(e x + d\right)^{4} + 8 \, a b \tan\left(e x + d\right)^{2} + b^{2} + 4 \, a c + 4 \, {\left(2 \, a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2}\right)} \sqrt{a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}\right) - 4 \, {\left({\left(a^{2} b^{3} - a b^{4} + 2 \, a^{2} c^{3} + {\left(2 \, a^{3} - 5 \, a^{2} b - a b^{2}\right)} c^{2} - {\left(3 \, a^{3} b - 2 \, a^{2} b^{2} - 2 \, a b^{3}\right)} c\right)} \tan\left(e x + d\right)^{4} - {\left({\left(2 \, a^{2} + a b\right)} c^{3} + {\left(2 \, a^{3} - a^{2} b - 2 \, a b^{2}\right)} c^{2} - {\left(a^{2} b^{2} - a b^{3}\right)} c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{4 \, {\left({\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4} - 4 \, a^{4} c^{3} - {\left(8 \, a^{5} - 8 \, a^{4} b - a^{3} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{6} - 4 \, a^{5} b + a^{4} b^{2} + a^{3} b^{3}\right)} c\right)} e \tan\left(e x + d\right)^{4} + {\left(a^{4} b^{3} - 2 \, a^{3} b^{4} + a^{2} b^{5} - 4 \, a^{3} b c^{3} - {\left(8 \, a^{4} b - 8 \, a^{3} b^{2} - a^{2} b^{3}\right)} c^{2} - 2 \, {\left(2 \, a^{5} b - 4 \, a^{4} b^{2} + a^{3} b^{3} + a^{2} b^{4}\right)} c\right)} e \tan\left(e x + d\right)^{2} - {\left(4 \, a^{3} c^{4} + {\left(8 \, a^{4} - 8 \, a^{3} b - a^{2} b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{5} - 4 \, a^{4} b + a^{3} b^{2} + a^{2} b^{3}\right)} c^{2} - {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} c\right)} e\right)}}, \frac{{\left(4 \, a c^{4} - {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} - 4 \, a^{2} c^{3} - {\left(8 \, a^{3} - 8 \, a^{2} b - a b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{4} - 4 \, a^{3} b + a^{2} b^{2} + a b^{3}\right)} c\right)} \tan\left(e x + d\right)^{4} + {\left(8 \, a^{2} - 8 \, a b - b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{3} - 4 \, a^{2} b + a b^{2} + b^{3}\right)} c^{2} - {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5} - 4 \, a b c^{3} - {\left(8 \, a^{2} b - 8 \, a b^{2} - b^{3}\right)} c^{2} - 2 \, {\left(2 \, a^{3} b - 4 \, a^{2} b^{2} + a b^{3} + b^{4}\right)} c\right)} \tan\left(e x + d\right)^{2} - {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} c\right)} \sqrt{-a} \arctan\left(\frac{{\left(2 \, a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2}\right)} \sqrt{-a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{2 \, {\left(a^{2} \tan\left(e x + d\right)^{4} + a b \tan\left(e x + d\right)^{2} + a c\right)}}\right) - {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \tan\left(e x + d\right)^{4} + {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{-a + b - c} \arctan\left(-\frac{{\left({\left(2 \, a - b\right)} \tan\left(e x + d\right)^{4} + {\left(b - 2 \, c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{-a + b - c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{2 \, {\left({\left(a^{2} - a b + a c\right)} \tan\left(e x + d\right)^{4} + {\left(a b - b^{2} + b c\right)} \tan\left(e x + d\right)^{2} + {\left(a - b\right)} c + c^{2}\right)}}\right) + 2 \, {\left({\left(a^{2} b^{3} - a b^{4} + 2 \, a^{2} c^{3} + {\left(2 \, a^{3} - 5 \, a^{2} b - a b^{2}\right)} c^{2} - {\left(3 \, a^{3} b - 2 \, a^{2} b^{2} - 2 \, a b^{3}\right)} c\right)} \tan\left(e x + d\right)^{4} - {\left({\left(2 \, a^{2} + a b\right)} c^{3} + {\left(2 \, a^{3} - a^{2} b - 2 \, a b^{2}\right)} c^{2} - {\left(a^{2} b^{2} - a b^{3}\right)} c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{2 \, {\left({\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4} - 4 \, a^{4} c^{3} - {\left(8 \, a^{5} - 8 \, a^{4} b - a^{3} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{6} - 4 \, a^{5} b + a^{4} b^{2} + a^{3} b^{3}\right)} c\right)} e \tan\left(e x + d\right)^{4} + {\left(a^{4} b^{3} - 2 \, a^{3} b^{4} + a^{2} b^{5} - 4 \, a^{3} b c^{3} - {\left(8 \, a^{4} b - 8 \, a^{3} b^{2} - a^{2} b^{3}\right)} c^{2} - 2 \, {\left(2 \, a^{5} b - 4 \, a^{4} b^{2} + a^{3} b^{3} + a^{2} b^{4}\right)} c\right)} e \tan\left(e x + d\right)^{2} - {\left(4 \, a^{3} c^{4} + {\left(8 \, a^{4} - 8 \, a^{3} b - a^{2} b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{5} - 4 \, a^{4} b + a^{3} b^{2} + a^{2} b^{3}\right)} c^{2} - {\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4}\right)} c\right)} e\right)}}\right]"," ",0,"[-1/4*((4*a*c^4 - (a^3*b^2 - 2*a^2*b^3 + a*b^4 - 4*a^2*c^3 - (8*a^3 - 8*a^2*b - a*b^2)*c^2 - 2*(2*a^4 - 4*a^3*b + a^2*b^2 + a*b^3)*c)*tan(e*x + d)^4 + (8*a^2 - 8*a*b - b^2)*c^3 + 2*(2*a^3 - 4*a^2*b + a*b^2 + b^3)*c^2 - (a^2*b^3 - 2*a*b^4 + b^5 - 4*a*b*c^3 - (8*a^2*b - 8*a*b^2 - b^3)*c^2 - 2*(2*a^3*b - 4*a^2*b^2 + a*b^3 + b^4)*c)*tan(e*x + d)^2 - (a^2*b^2 - 2*a*b^3 + b^4)*c)*sqrt(a)*log(8*a^2*tan(e*x + d)^4 + 8*a*b*tan(e*x + d)^2 + b^2 + 4*a*c + 4*(2*a*tan(e*x + d)^4 + b*tan(e*x + d)^2)*sqrt(a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)) - (a^2*b^2*c - 4*a^3*c^2 + (a^3*b^2 - 4*a^4*c)*tan(e*x + d)^4 + (a^2*b^3 - 4*a^3*b*c)*tan(e*x + d)^2)*sqrt(a - b + c)*log(((8*a^2 - 8*a*b + b^2 + 4*a*c)*tan(e*x + d)^4 + 2*(4*a*b - 3*b^2 - 4*(a - b)*c)*tan(e*x + d)^2 + b^2 + 4*(a - 2*b)*c + 8*c^2 - 4*((2*a - b)*tan(e*x + d)^4 + (b - 2*c)*tan(e*x + d)^2)*sqrt(a - b + c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4))/(tan(e*x + d)^4 + 2*tan(e*x + d)^2 + 1)) - 4*((a^2*b^3 - a*b^4 + 2*a^2*c^3 + (2*a^3 - 5*a^2*b - a*b^2)*c^2 - (3*a^3*b - 2*a^2*b^2 - 2*a*b^3)*c)*tan(e*x + d)^4 - ((2*a^2 + a*b)*c^3 + (2*a^3 - a^2*b - 2*a*b^2)*c^2 - (a^2*b^2 - a*b^3)*c)*tan(e*x + d)^2)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4))/((a^5*b^2 - 2*a^4*b^3 + a^3*b^4 - 4*a^4*c^3 - (8*a^5 - 8*a^4*b - a^3*b^2)*c^2 - 2*(2*a^6 - 4*a^5*b + a^4*b^2 + a^3*b^3)*c)*e*tan(e*x + d)^4 + (a^4*b^3 - 2*a^3*b^4 + a^2*b^5 - 4*a^3*b*c^3 - (8*a^4*b - 8*a^3*b^2 - a^2*b^3)*c^2 - 2*(2*a^5*b - 4*a^4*b^2 + a^3*b^3 + a^2*b^4)*c)*e*tan(e*x + d)^2 - (4*a^3*c^4 + (8*a^4 - 8*a^3*b - a^2*b^2)*c^3 + 2*(2*a^5 - 4*a^4*b + a^3*b^2 + a^2*b^3)*c^2 - (a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*c)*e), 1/4*(2*(4*a*c^4 - (a^3*b^2 - 2*a^2*b^3 + a*b^4 - 4*a^2*c^3 - (8*a^3 - 8*a^2*b - a*b^2)*c^2 - 2*(2*a^4 - 4*a^3*b + a^2*b^2 + a*b^3)*c)*tan(e*x + d)^4 + (8*a^2 - 8*a*b - b^2)*c^3 + 2*(2*a^3 - 4*a^2*b + a*b^2 + b^3)*c^2 - (a^2*b^3 - 2*a*b^4 + b^5 - 4*a*b*c^3 - (8*a^2*b - 8*a*b^2 - b^3)*c^2 - 2*(2*a^3*b - 4*a^2*b^2 + a*b^3 + b^4)*c)*tan(e*x + d)^2 - (a^2*b^2 - 2*a*b^3 + b^4)*c)*sqrt(-a)*arctan(1/2*(2*a*tan(e*x + d)^4 + b*tan(e*x + d)^2)*sqrt(-a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)/(a^2*tan(e*x + d)^4 + a*b*tan(e*x + d)^2 + a*c)) + (a^2*b^2*c - 4*a^3*c^2 + (a^3*b^2 - 4*a^4*c)*tan(e*x + d)^4 + (a^2*b^3 - 4*a^3*b*c)*tan(e*x + d)^2)*sqrt(a - b + c)*log(((8*a^2 - 8*a*b + b^2 + 4*a*c)*tan(e*x + d)^4 + 2*(4*a*b - 3*b^2 - 4*(a - b)*c)*tan(e*x + d)^2 + b^2 + 4*(a - 2*b)*c + 8*c^2 - 4*((2*a - b)*tan(e*x + d)^4 + (b - 2*c)*tan(e*x + d)^2)*sqrt(a - b + c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4))/(tan(e*x + d)^4 + 2*tan(e*x + d)^2 + 1)) + 4*((a^2*b^3 - a*b^4 + 2*a^2*c^3 + (2*a^3 - 5*a^2*b - a*b^2)*c^2 - (3*a^3*b - 2*a^2*b^2 - 2*a*b^3)*c)*tan(e*x + d)^4 - ((2*a^2 + a*b)*c^3 + (2*a^3 - a^2*b - 2*a*b^2)*c^2 - (a^2*b^2 - a*b^3)*c)*tan(e*x + d)^2)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4))/((a^5*b^2 - 2*a^4*b^3 + a^3*b^4 - 4*a^4*c^3 - (8*a^5 - 8*a^4*b - a^3*b^2)*c^2 - 2*(2*a^6 - 4*a^5*b + a^4*b^2 + a^3*b^3)*c)*e*tan(e*x + d)^4 + (a^4*b^3 - 2*a^3*b^4 + a^2*b^5 - 4*a^3*b*c^3 - (8*a^4*b - 8*a^3*b^2 - a^2*b^3)*c^2 - 2*(2*a^5*b - 4*a^4*b^2 + a^3*b^3 + a^2*b^4)*c)*e*tan(e*x + d)^2 - (4*a^3*c^4 + (8*a^4 - 8*a^3*b - a^2*b^2)*c^3 + 2*(2*a^5 - 4*a^4*b + a^3*b^2 + a^2*b^3)*c^2 - (a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*c)*e), -1/4*(2*(a^2*b^2*c - 4*a^3*c^2 + (a^3*b^2 - 4*a^4*c)*tan(e*x + d)^4 + (a^2*b^3 - 4*a^3*b*c)*tan(e*x + d)^2)*sqrt(-a + b - c)*arctan(-1/2*((2*a - b)*tan(e*x + d)^4 + (b - 2*c)*tan(e*x + d)^2)*sqrt(-a + b - c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)/((a^2 - a*b + a*c)*tan(e*x + d)^4 + (a*b - b^2 + b*c)*tan(e*x + d)^2 + (a - b)*c + c^2)) + (4*a*c^4 - (a^3*b^2 - 2*a^2*b^3 + a*b^4 - 4*a^2*c^3 - (8*a^3 - 8*a^2*b - a*b^2)*c^2 - 2*(2*a^4 - 4*a^3*b + a^2*b^2 + a*b^3)*c)*tan(e*x + d)^4 + (8*a^2 - 8*a*b - b^2)*c^3 + 2*(2*a^3 - 4*a^2*b + a*b^2 + b^3)*c^2 - (a^2*b^3 - 2*a*b^4 + b^5 - 4*a*b*c^3 - (8*a^2*b - 8*a*b^2 - b^3)*c^2 - 2*(2*a^3*b - 4*a^2*b^2 + a*b^3 + b^4)*c)*tan(e*x + d)^2 - (a^2*b^2 - 2*a*b^3 + b^4)*c)*sqrt(a)*log(8*a^2*tan(e*x + d)^4 + 8*a*b*tan(e*x + d)^2 + b^2 + 4*a*c + 4*(2*a*tan(e*x + d)^4 + b*tan(e*x + d)^2)*sqrt(a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)) - 4*((a^2*b^3 - a*b^4 + 2*a^2*c^3 + (2*a^3 - 5*a^2*b - a*b^2)*c^2 - (3*a^3*b - 2*a^2*b^2 - 2*a*b^3)*c)*tan(e*x + d)^4 - ((2*a^2 + a*b)*c^3 + (2*a^3 - a^2*b - 2*a*b^2)*c^2 - (a^2*b^2 - a*b^3)*c)*tan(e*x + d)^2)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4))/((a^5*b^2 - 2*a^4*b^3 + a^3*b^4 - 4*a^4*c^3 - (8*a^5 - 8*a^4*b - a^3*b^2)*c^2 - 2*(2*a^6 - 4*a^5*b + a^4*b^2 + a^3*b^3)*c)*e*tan(e*x + d)^4 + (a^4*b^3 - 2*a^3*b^4 + a^2*b^5 - 4*a^3*b*c^3 - (8*a^4*b - 8*a^3*b^2 - a^2*b^3)*c^2 - 2*(2*a^5*b - 4*a^4*b^2 + a^3*b^3 + a^2*b^4)*c)*e*tan(e*x + d)^2 - (4*a^3*c^4 + (8*a^4 - 8*a^3*b - a^2*b^2)*c^3 + 2*(2*a^5 - 4*a^4*b + a^3*b^2 + a^2*b^3)*c^2 - (a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*c)*e), 1/2*((4*a*c^4 - (a^3*b^2 - 2*a^2*b^3 + a*b^4 - 4*a^2*c^3 - (8*a^3 - 8*a^2*b - a*b^2)*c^2 - 2*(2*a^4 - 4*a^3*b + a^2*b^2 + a*b^3)*c)*tan(e*x + d)^4 + (8*a^2 - 8*a*b - b^2)*c^3 + 2*(2*a^3 - 4*a^2*b + a*b^2 + b^3)*c^2 - (a^2*b^3 - 2*a*b^4 + b^5 - 4*a*b*c^3 - (8*a^2*b - 8*a*b^2 - b^3)*c^2 - 2*(2*a^3*b - 4*a^2*b^2 + a*b^3 + b^4)*c)*tan(e*x + d)^2 - (a^2*b^2 - 2*a*b^3 + b^4)*c)*sqrt(-a)*arctan(1/2*(2*a*tan(e*x + d)^4 + b*tan(e*x + d)^2)*sqrt(-a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)/(a^2*tan(e*x + d)^4 + a*b*tan(e*x + d)^2 + a*c)) - (a^2*b^2*c - 4*a^3*c^2 + (a^3*b^2 - 4*a^4*c)*tan(e*x + d)^4 + (a^2*b^3 - 4*a^3*b*c)*tan(e*x + d)^2)*sqrt(-a + b - c)*arctan(-1/2*((2*a - b)*tan(e*x + d)^4 + (b - 2*c)*tan(e*x + d)^2)*sqrt(-a + b - c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)/((a^2 - a*b + a*c)*tan(e*x + d)^4 + (a*b - b^2 + b*c)*tan(e*x + d)^2 + (a - b)*c + c^2)) + 2*((a^2*b^3 - a*b^4 + 2*a^2*c^3 + (2*a^3 - 5*a^2*b - a*b^2)*c^2 - (3*a^3*b - 2*a^2*b^2 - 2*a*b^3)*c)*tan(e*x + d)^4 - ((2*a^2 + a*b)*c^3 + (2*a^3 - a^2*b - 2*a*b^2)*c^2 - (a^2*b^2 - a*b^3)*c)*tan(e*x + d)^2)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4))/((a^5*b^2 - 2*a^4*b^3 + a^3*b^4 - 4*a^4*c^3 - (8*a^5 - 8*a^4*b - a^3*b^2)*c^2 - 2*(2*a^6 - 4*a^5*b + a^4*b^2 + a^3*b^3)*c)*e*tan(e*x + d)^4 + (a^4*b^3 - 2*a^3*b^4 + a^2*b^5 - 4*a^3*b*c^3 - (8*a^4*b - 8*a^3*b^2 - a^2*b^3)*c^2 - 2*(2*a^5*b - 4*a^4*b^2 + a^3*b^3 + a^2*b^4)*c)*e*tan(e*x + d)^2 - (4*a^3*c^4 + (8*a^4 - 8*a^3*b - a^2*b^2)*c^3 + 2*(2*a^5 - 4*a^4*b + a^3*b^2 + a^2*b^3)*c^2 - (a^4*b^2 - 2*a^3*b^3 + a^2*b^4)*c)*e)]","B",0
32,1,5274,0,8.129662," ","integrate(tan(e*x+d)^3/(a+b*cot(e*x+d)^2+c*cot(e*x+d)^4)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(4 \, {\left(2 \, a^{2} + 3 \, a b\right)} c^{4} - {\left(2 \, a^{4} b^{2} - a^{3} b^{3} - 4 \, a^{2} b^{4} + 3 \, a b^{5} - 4 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} c^{3} - {\left(16 \, a^{4} + 8 \, a^{3} b - 26 \, a^{2} b^{2} - 3 \, a b^{3}\right)} c^{2} - 2 \, {\left(4 \, a^{5} - 2 \, a^{4} b - 10 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 3 \, a b^{4}\right)} c\right)} \tan\left(e x + d\right)^{4} + {\left(16 \, a^{3} + 8 \, a^{2} b - 26 \, a b^{2} - 3 \, b^{3}\right)} c^{3} + 2 \, {\left(4 \, a^{4} - 2 \, a^{3} b - 10 \, a^{2} b^{2} + 5 \, a b^{3} + 3 \, b^{4}\right)} c^{2} - {\left(2 \, a^{3} b^{3} - a^{2} b^{4} - 4 \, a b^{5} + 3 \, b^{6} - 4 \, {\left(2 \, a^{2} b + 3 \, a b^{2}\right)} c^{3} - {\left(16 \, a^{3} b + 8 \, a^{2} b^{2} - 26 \, a b^{3} - 3 \, b^{4}\right)} c^{2} - 2 \, {\left(4 \, a^{4} b - 2 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} + 3 \, b^{5}\right)} c\right)} \tan\left(e x + d\right)^{2} - {\left(2 \, a^{3} b^{2} - a^{2} b^{3} - 4 \, a b^{4} + 3 \, b^{5}\right)} c\right)} \sqrt{a} \log\left(8 \, a^{2} \tan\left(e x + d\right)^{4} + 8 \, a b \tan\left(e x + d\right)^{2} + b^{2} + 4 \, a c - 4 \, {\left(2 \, a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2}\right)} \sqrt{a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}\right) - 2 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \tan\left(e x + d\right)^{4} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{a - b + c} \log\left(\frac{{\left(8 \, a^{2} - 8 \, a b + b^{2} + 4 \, a c\right)} \tan\left(e x + d\right)^{4} + 2 \, {\left(4 \, a b - 3 \, b^{2} - 4 \, {\left(a - b\right)} c\right)} \tan\left(e x + d\right)^{2} + b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2} + 4 \, {\left({\left(2 \, a - b\right)} \tan\left(e x + d\right)^{4} + {\left(b - 2 \, c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{a - b + c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{\tan\left(e x + d\right)^{4} + 2 \, \tan\left(e x + d\right)^{2} + 1}\right) - 4 \, {\left({\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4} - 4 \, a^{3} c^{3} - {\left(8 \, a^{4} - 8 \, a^{3} b - a^{2} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{5} - 4 \, a^{4} b + a^{3} b^{2} + a^{2} b^{3}\right)} c\right)} \tan\left(e x + d\right)^{6} + {\left(a^{3} b^{3} - 4 \, a^{2} b^{4} + 3 \, a b^{5} - 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b\right)} c^{3} - {\left(4 \, a^{4} + 10 \, a^{3} b - 22 \, a^{2} b^{2} - 3 \, a b^{3}\right)} c^{2} - 2 \, {\left(2 \, a^{4} b - 8 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 3 \, a b^{4}\right)} c\right)} \tan\left(e x + d\right)^{4} - {\left(8 \, a^{2} c^{4} + 3 \, {\left(4 \, a^{3} - 6 \, a^{2} b - a b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{4} - 7 \, a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3}\right)} c^{2} - {\left(a^{3} b^{2} - 4 \, a^{2} b^{3} + 3 \, a b^{4}\right)} c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{8 \, {\left({\left(a^{6} b^{2} - 2 \, a^{5} b^{3} + a^{4} b^{4} - 4 \, a^{5} c^{3} - {\left(8 \, a^{6} - 8 \, a^{5} b - a^{4} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{7} - 4 \, a^{6} b + a^{5} b^{2} + a^{4} b^{3}\right)} c\right)} e \tan\left(e x + d\right)^{4} + {\left(a^{5} b^{3} - 2 \, a^{4} b^{4} + a^{3} b^{5} - 4 \, a^{4} b c^{3} - {\left(8 \, a^{5} b - 8 \, a^{4} b^{2} - a^{3} b^{3}\right)} c^{2} - 2 \, {\left(2 \, a^{6} b - 4 \, a^{5} b^{2} + a^{4} b^{3} + a^{3} b^{4}\right)} c\right)} e \tan\left(e x + d\right)^{2} - {\left(4 \, a^{4} c^{4} + {\left(8 \, a^{5} - 8 \, a^{4} b - a^{3} b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{6} - 4 \, a^{5} b + a^{4} b^{2} + a^{3} b^{3}\right)} c^{2} - {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} c\right)} e\right)}}, -\frac{{\left(4 \, {\left(2 \, a^{2} + 3 \, a b\right)} c^{4} - {\left(2 \, a^{4} b^{2} - a^{3} b^{3} - 4 \, a^{2} b^{4} + 3 \, a b^{5} - 4 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} c^{3} - {\left(16 \, a^{4} + 8 \, a^{3} b - 26 \, a^{2} b^{2} - 3 \, a b^{3}\right)} c^{2} - 2 \, {\left(4 \, a^{5} - 2 \, a^{4} b - 10 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 3 \, a b^{4}\right)} c\right)} \tan\left(e x + d\right)^{4} + {\left(16 \, a^{3} + 8 \, a^{2} b - 26 \, a b^{2} - 3 \, b^{3}\right)} c^{3} + 2 \, {\left(4 \, a^{4} - 2 \, a^{3} b - 10 \, a^{2} b^{2} + 5 \, a b^{3} + 3 \, b^{4}\right)} c^{2} - {\left(2 \, a^{3} b^{3} - a^{2} b^{4} - 4 \, a b^{5} + 3 \, b^{6} - 4 \, {\left(2 \, a^{2} b + 3 \, a b^{2}\right)} c^{3} - {\left(16 \, a^{3} b + 8 \, a^{2} b^{2} - 26 \, a b^{3} - 3 \, b^{4}\right)} c^{2} - 2 \, {\left(4 \, a^{4} b - 2 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} + 3 \, b^{5}\right)} c\right)} \tan\left(e x + d\right)^{2} - {\left(2 \, a^{3} b^{2} - a^{2} b^{3} - 4 \, a b^{4} + 3 \, b^{5}\right)} c\right)} \sqrt{-a} \arctan\left(\frac{{\left(2 \, a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2}\right)} \sqrt{-a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{2 \, {\left(a^{2} \tan\left(e x + d\right)^{4} + a b \tan\left(e x + d\right)^{2} + a c\right)}}\right) - {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \tan\left(e x + d\right)^{4} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{a - b + c} \log\left(\frac{{\left(8 \, a^{2} - 8 \, a b + b^{2} + 4 \, a c\right)} \tan\left(e x + d\right)^{4} + 2 \, {\left(4 \, a b - 3 \, b^{2} - 4 \, {\left(a - b\right)} c\right)} \tan\left(e x + d\right)^{2} + b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2} + 4 \, {\left({\left(2 \, a - b\right)} \tan\left(e x + d\right)^{4} + {\left(b - 2 \, c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{a - b + c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{\tan\left(e x + d\right)^{4} + 2 \, \tan\left(e x + d\right)^{2} + 1}\right) - 2 \, {\left({\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4} - 4 \, a^{3} c^{3} - {\left(8 \, a^{4} - 8 \, a^{3} b - a^{2} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{5} - 4 \, a^{4} b + a^{3} b^{2} + a^{2} b^{3}\right)} c\right)} \tan\left(e x + d\right)^{6} + {\left(a^{3} b^{3} - 4 \, a^{2} b^{4} + 3 \, a b^{5} - 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b\right)} c^{3} - {\left(4 \, a^{4} + 10 \, a^{3} b - 22 \, a^{2} b^{2} - 3 \, a b^{3}\right)} c^{2} - 2 \, {\left(2 \, a^{4} b - 8 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 3 \, a b^{4}\right)} c\right)} \tan\left(e x + d\right)^{4} - {\left(8 \, a^{2} c^{4} + 3 \, {\left(4 \, a^{3} - 6 \, a^{2} b - a b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{4} - 7 \, a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3}\right)} c^{2} - {\left(a^{3} b^{2} - 4 \, a^{2} b^{3} + 3 \, a b^{4}\right)} c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{4 \, {\left({\left(a^{6} b^{2} - 2 \, a^{5} b^{3} + a^{4} b^{4} - 4 \, a^{5} c^{3} - {\left(8 \, a^{6} - 8 \, a^{5} b - a^{4} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{7} - 4 \, a^{6} b + a^{5} b^{2} + a^{4} b^{3}\right)} c\right)} e \tan\left(e x + d\right)^{4} + {\left(a^{5} b^{3} - 2 \, a^{4} b^{4} + a^{3} b^{5} - 4 \, a^{4} b c^{3} - {\left(8 \, a^{5} b - 8 \, a^{4} b^{2} - a^{3} b^{3}\right)} c^{2} - 2 \, {\left(2 \, a^{6} b - 4 \, a^{5} b^{2} + a^{4} b^{3} + a^{3} b^{4}\right)} c\right)} e \tan\left(e x + d\right)^{2} - {\left(4 \, a^{4} c^{4} + {\left(8 \, a^{5} - 8 \, a^{4} b - a^{3} b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{6} - 4 \, a^{5} b + a^{4} b^{2} + a^{3} b^{3}\right)} c^{2} - {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} c\right)} e\right)}}, \frac{4 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \tan\left(e x + d\right)^{4} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{-a + b - c} \arctan\left(-\frac{{\left({\left(2 \, a - b\right)} \tan\left(e x + d\right)^{4} + {\left(b - 2 \, c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{-a + b - c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{2 \, {\left({\left(a^{2} - a b + a c\right)} \tan\left(e x + d\right)^{4} + {\left(a b - b^{2} + b c\right)} \tan\left(e x + d\right)^{2} + {\left(a - b\right)} c + c^{2}\right)}}\right) - {\left(4 \, {\left(2 \, a^{2} + 3 \, a b\right)} c^{4} - {\left(2 \, a^{4} b^{2} - a^{3} b^{3} - 4 \, a^{2} b^{4} + 3 \, a b^{5} - 4 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} c^{3} - {\left(16 \, a^{4} + 8 \, a^{3} b - 26 \, a^{2} b^{2} - 3 \, a b^{3}\right)} c^{2} - 2 \, {\left(4 \, a^{5} - 2 \, a^{4} b - 10 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 3 \, a b^{4}\right)} c\right)} \tan\left(e x + d\right)^{4} + {\left(16 \, a^{3} + 8 \, a^{2} b - 26 \, a b^{2} - 3 \, b^{3}\right)} c^{3} + 2 \, {\left(4 \, a^{4} - 2 \, a^{3} b - 10 \, a^{2} b^{2} + 5 \, a b^{3} + 3 \, b^{4}\right)} c^{2} - {\left(2 \, a^{3} b^{3} - a^{2} b^{4} - 4 \, a b^{5} + 3 \, b^{6} - 4 \, {\left(2 \, a^{2} b + 3 \, a b^{2}\right)} c^{3} - {\left(16 \, a^{3} b + 8 \, a^{2} b^{2} - 26 \, a b^{3} - 3 \, b^{4}\right)} c^{2} - 2 \, {\left(4 \, a^{4} b - 2 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} + 3 \, b^{5}\right)} c\right)} \tan\left(e x + d\right)^{2} - {\left(2 \, a^{3} b^{2} - a^{2} b^{3} - 4 \, a b^{4} + 3 \, b^{5}\right)} c\right)} \sqrt{a} \log\left(8 \, a^{2} \tan\left(e x + d\right)^{4} + 8 \, a b \tan\left(e x + d\right)^{2} + b^{2} + 4 \, a c - 4 \, {\left(2 \, a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2}\right)} \sqrt{a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}\right) + 4 \, {\left({\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4} - 4 \, a^{3} c^{3} - {\left(8 \, a^{4} - 8 \, a^{3} b - a^{2} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{5} - 4 \, a^{4} b + a^{3} b^{2} + a^{2} b^{3}\right)} c\right)} \tan\left(e x + d\right)^{6} + {\left(a^{3} b^{3} - 4 \, a^{2} b^{4} + 3 \, a b^{5} - 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b\right)} c^{3} - {\left(4 \, a^{4} + 10 \, a^{3} b - 22 \, a^{2} b^{2} - 3 \, a b^{3}\right)} c^{2} - 2 \, {\left(2 \, a^{4} b - 8 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 3 \, a b^{4}\right)} c\right)} \tan\left(e x + d\right)^{4} - {\left(8 \, a^{2} c^{4} + 3 \, {\left(4 \, a^{3} - 6 \, a^{2} b - a b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{4} - 7 \, a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3}\right)} c^{2} - {\left(a^{3} b^{2} - 4 \, a^{2} b^{3} + 3 \, a b^{4}\right)} c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{8 \, {\left({\left(a^{6} b^{2} - 2 \, a^{5} b^{3} + a^{4} b^{4} - 4 \, a^{5} c^{3} - {\left(8 \, a^{6} - 8 \, a^{5} b - a^{4} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{7} - 4 \, a^{6} b + a^{5} b^{2} + a^{4} b^{3}\right)} c\right)} e \tan\left(e x + d\right)^{4} + {\left(a^{5} b^{3} - 2 \, a^{4} b^{4} + a^{3} b^{5} - 4 \, a^{4} b c^{3} - {\left(8 \, a^{5} b - 8 \, a^{4} b^{2} - a^{3} b^{3}\right)} c^{2} - 2 \, {\left(2 \, a^{6} b - 4 \, a^{5} b^{2} + a^{4} b^{3} + a^{3} b^{4}\right)} c\right)} e \tan\left(e x + d\right)^{2} - {\left(4 \, a^{4} c^{4} + {\left(8 \, a^{5} - 8 \, a^{4} b - a^{3} b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{6} - 4 \, a^{5} b + a^{4} b^{2} + a^{3} b^{3}\right)} c^{2} - {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} c\right)} e\right)}}, -\frac{{\left(4 \, {\left(2 \, a^{2} + 3 \, a b\right)} c^{4} - {\left(2 \, a^{4} b^{2} - a^{3} b^{3} - 4 \, a^{2} b^{4} + 3 \, a b^{5} - 4 \, {\left(2 \, a^{3} + 3 \, a^{2} b\right)} c^{3} - {\left(16 \, a^{4} + 8 \, a^{3} b - 26 \, a^{2} b^{2} - 3 \, a b^{3}\right)} c^{2} - 2 \, {\left(4 \, a^{5} - 2 \, a^{4} b - 10 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + 3 \, a b^{4}\right)} c\right)} \tan\left(e x + d\right)^{4} + {\left(16 \, a^{3} + 8 \, a^{2} b - 26 \, a b^{2} - 3 \, b^{3}\right)} c^{3} + 2 \, {\left(4 \, a^{4} - 2 \, a^{3} b - 10 \, a^{2} b^{2} + 5 \, a b^{3} + 3 \, b^{4}\right)} c^{2} - {\left(2 \, a^{3} b^{3} - a^{2} b^{4} - 4 \, a b^{5} + 3 \, b^{6} - 4 \, {\left(2 \, a^{2} b + 3 \, a b^{2}\right)} c^{3} - {\left(16 \, a^{3} b + 8 \, a^{2} b^{2} - 26 \, a b^{3} - 3 \, b^{4}\right)} c^{2} - 2 \, {\left(4 \, a^{4} b - 2 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} + 3 \, b^{5}\right)} c\right)} \tan\left(e x + d\right)^{2} - {\left(2 \, a^{3} b^{2} - a^{2} b^{3} - 4 \, a b^{4} + 3 \, b^{5}\right)} c\right)} \sqrt{-a} \arctan\left(\frac{{\left(2 \, a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2}\right)} \sqrt{-a} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{2 \, {\left(a^{2} \tan\left(e x + d\right)^{4} + a b \tan\left(e x + d\right)^{2} + a c\right)}}\right) - 2 \, {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} \tan\left(e x + d\right)^{4} + {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{-a + b - c} \arctan\left(-\frac{{\left({\left(2 \, a - b\right)} \tan\left(e x + d\right)^{4} + {\left(b - 2 \, c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{-a + b - c} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{2 \, {\left({\left(a^{2} - a b + a c\right)} \tan\left(e x + d\right)^{4} + {\left(a b - b^{2} + b c\right)} \tan\left(e x + d\right)^{2} + {\left(a - b\right)} c + c^{2}\right)}}\right) - 2 \, {\left({\left(a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4} - 4 \, a^{3} c^{3} - {\left(8 \, a^{4} - 8 \, a^{3} b - a^{2} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{5} - 4 \, a^{4} b + a^{3} b^{2} + a^{2} b^{3}\right)} c\right)} \tan\left(e x + d\right)^{6} + {\left(a^{3} b^{3} - 4 \, a^{2} b^{4} + 3 \, a b^{5} - 2 \, {\left(2 \, a^{3} + 5 \, a^{2} b\right)} c^{3} - {\left(4 \, a^{4} + 10 \, a^{3} b - 22 \, a^{2} b^{2} - 3 \, a b^{3}\right)} c^{2} - 2 \, {\left(2 \, a^{4} b - 8 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + 3 \, a b^{4}\right)} c\right)} \tan\left(e x + d\right)^{4} - {\left(8 \, a^{2} c^{4} + 3 \, {\left(4 \, a^{3} - 6 \, a^{2} b - a b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{4} - 7 \, a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3}\right)} c^{2} - {\left(a^{3} b^{2} - 4 \, a^{2} b^{3} + 3 \, a b^{4}\right)} c\right)} \tan\left(e x + d\right)^{2}\right)} \sqrt{\frac{a \tan\left(e x + d\right)^{4} + b \tan\left(e x + d\right)^{2} + c}{\tan\left(e x + d\right)^{4}}}}{4 \, {\left({\left(a^{6} b^{2} - 2 \, a^{5} b^{3} + a^{4} b^{4} - 4 \, a^{5} c^{3} - {\left(8 \, a^{6} - 8 \, a^{5} b - a^{4} b^{2}\right)} c^{2} - 2 \, {\left(2 \, a^{7} - 4 \, a^{6} b + a^{5} b^{2} + a^{4} b^{3}\right)} c\right)} e \tan\left(e x + d\right)^{4} + {\left(a^{5} b^{3} - 2 \, a^{4} b^{4} + a^{3} b^{5} - 4 \, a^{4} b c^{3} - {\left(8 \, a^{5} b - 8 \, a^{4} b^{2} - a^{3} b^{3}\right)} c^{2} - 2 \, {\left(2 \, a^{6} b - 4 \, a^{5} b^{2} + a^{4} b^{3} + a^{3} b^{4}\right)} c\right)} e \tan\left(e x + d\right)^{2} - {\left(4 \, a^{4} c^{4} + {\left(8 \, a^{5} - 8 \, a^{4} b - a^{3} b^{2}\right)} c^{3} + 2 \, {\left(2 \, a^{6} - 4 \, a^{5} b + a^{4} b^{2} + a^{3} b^{3}\right)} c^{2} - {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} c\right)} e\right)}}\right]"," ",0,"[-1/8*((4*(2*a^2 + 3*a*b)*c^4 - (2*a^4*b^2 - a^3*b^3 - 4*a^2*b^4 + 3*a*b^5 - 4*(2*a^3 + 3*a^2*b)*c^3 - (16*a^4 + 8*a^3*b - 26*a^2*b^2 - 3*a*b^3)*c^2 - 2*(4*a^5 - 2*a^4*b - 10*a^3*b^2 + 5*a^2*b^3 + 3*a*b^4)*c)*tan(e*x + d)^4 + (16*a^3 + 8*a^2*b - 26*a*b^2 - 3*b^3)*c^3 + 2*(4*a^4 - 2*a^3*b - 10*a^2*b^2 + 5*a*b^3 + 3*b^4)*c^2 - (2*a^3*b^3 - a^2*b^4 - 4*a*b^5 + 3*b^6 - 4*(2*a^2*b + 3*a*b^2)*c^3 - (16*a^3*b + 8*a^2*b^2 - 26*a*b^3 - 3*b^4)*c^2 - 2*(4*a^4*b - 2*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 + 3*b^5)*c)*tan(e*x + d)^2 - (2*a^3*b^2 - a^2*b^3 - 4*a*b^4 + 3*b^5)*c)*sqrt(a)*log(8*a^2*tan(e*x + d)^4 + 8*a*b*tan(e*x + d)^2 + b^2 + 4*a*c - 4*(2*a*tan(e*x + d)^4 + b*tan(e*x + d)^2)*sqrt(a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)) - 2*(a^3*b^2*c - 4*a^4*c^2 + (a^4*b^2 - 4*a^5*c)*tan(e*x + d)^4 + (a^3*b^3 - 4*a^4*b*c)*tan(e*x + d)^2)*sqrt(a - b + c)*log(((8*a^2 - 8*a*b + b^2 + 4*a*c)*tan(e*x + d)^4 + 2*(4*a*b - 3*b^2 - 4*(a - b)*c)*tan(e*x + d)^2 + b^2 + 4*(a - 2*b)*c + 8*c^2 + 4*((2*a - b)*tan(e*x + d)^4 + (b - 2*c)*tan(e*x + d)^2)*sqrt(a - b + c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4))/(tan(e*x + d)^4 + 2*tan(e*x + d)^2 + 1)) - 4*((a^4*b^2 - 2*a^3*b^3 + a^2*b^4 - 4*a^3*c^3 - (8*a^4 - 8*a^3*b - a^2*b^2)*c^2 - 2*(2*a^5 - 4*a^4*b + a^3*b^2 + a^2*b^3)*c)*tan(e*x + d)^6 + (a^3*b^3 - 4*a^2*b^4 + 3*a*b^5 - 2*(2*a^3 + 5*a^2*b)*c^3 - (4*a^4 + 10*a^3*b - 22*a^2*b^2 - 3*a*b^3)*c^2 - 2*(2*a^4*b - 8*a^3*b^2 + 4*a^2*b^3 + 3*a*b^4)*c)*tan(e*x + d)^4 - (8*a^2*c^4 + 3*(4*a^3 - 6*a^2*b - a*b^2)*c^3 + 2*(2*a^4 - 7*a^3*b + 3*a^2*b^2 + 3*a*b^3)*c^2 - (a^3*b^2 - 4*a^2*b^3 + 3*a*b^4)*c)*tan(e*x + d)^2)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4))/((a^6*b^2 - 2*a^5*b^3 + a^4*b^4 - 4*a^5*c^3 - (8*a^6 - 8*a^5*b - a^4*b^2)*c^2 - 2*(2*a^7 - 4*a^6*b + a^5*b^2 + a^4*b^3)*c)*e*tan(e*x + d)^4 + (a^5*b^3 - 2*a^4*b^4 + a^3*b^5 - 4*a^4*b*c^3 - (8*a^5*b - 8*a^4*b^2 - a^3*b^3)*c^2 - 2*(2*a^6*b - 4*a^5*b^2 + a^4*b^3 + a^3*b^4)*c)*e*tan(e*x + d)^2 - (4*a^4*c^4 + (8*a^5 - 8*a^4*b - a^3*b^2)*c^3 + 2*(2*a^6 - 4*a^5*b + a^4*b^2 + a^3*b^3)*c^2 - (a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*c)*e), -1/4*((4*(2*a^2 + 3*a*b)*c^4 - (2*a^4*b^2 - a^3*b^3 - 4*a^2*b^4 + 3*a*b^5 - 4*(2*a^3 + 3*a^2*b)*c^3 - (16*a^4 + 8*a^3*b - 26*a^2*b^2 - 3*a*b^3)*c^2 - 2*(4*a^5 - 2*a^4*b - 10*a^3*b^2 + 5*a^2*b^3 + 3*a*b^4)*c)*tan(e*x + d)^4 + (16*a^3 + 8*a^2*b - 26*a*b^2 - 3*b^3)*c^3 + 2*(4*a^4 - 2*a^3*b - 10*a^2*b^2 + 5*a*b^3 + 3*b^4)*c^2 - (2*a^3*b^3 - a^2*b^4 - 4*a*b^5 + 3*b^6 - 4*(2*a^2*b + 3*a*b^2)*c^3 - (16*a^3*b + 8*a^2*b^2 - 26*a*b^3 - 3*b^4)*c^2 - 2*(4*a^4*b - 2*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 + 3*b^5)*c)*tan(e*x + d)^2 - (2*a^3*b^2 - a^2*b^3 - 4*a*b^4 + 3*b^5)*c)*sqrt(-a)*arctan(1/2*(2*a*tan(e*x + d)^4 + b*tan(e*x + d)^2)*sqrt(-a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)/(a^2*tan(e*x + d)^4 + a*b*tan(e*x + d)^2 + a*c)) - (a^3*b^2*c - 4*a^4*c^2 + (a^4*b^2 - 4*a^5*c)*tan(e*x + d)^4 + (a^3*b^3 - 4*a^4*b*c)*tan(e*x + d)^2)*sqrt(a - b + c)*log(((8*a^2 - 8*a*b + b^2 + 4*a*c)*tan(e*x + d)^4 + 2*(4*a*b - 3*b^2 - 4*(a - b)*c)*tan(e*x + d)^2 + b^2 + 4*(a - 2*b)*c + 8*c^2 + 4*((2*a - b)*tan(e*x + d)^4 + (b - 2*c)*tan(e*x + d)^2)*sqrt(a - b + c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4))/(tan(e*x + d)^4 + 2*tan(e*x + d)^2 + 1)) - 2*((a^4*b^2 - 2*a^3*b^3 + a^2*b^4 - 4*a^3*c^3 - (8*a^4 - 8*a^3*b - a^2*b^2)*c^2 - 2*(2*a^5 - 4*a^4*b + a^3*b^2 + a^2*b^3)*c)*tan(e*x + d)^6 + (a^3*b^3 - 4*a^2*b^4 + 3*a*b^5 - 2*(2*a^3 + 5*a^2*b)*c^3 - (4*a^4 + 10*a^3*b - 22*a^2*b^2 - 3*a*b^3)*c^2 - 2*(2*a^4*b - 8*a^3*b^2 + 4*a^2*b^3 + 3*a*b^4)*c)*tan(e*x + d)^4 - (8*a^2*c^4 + 3*(4*a^3 - 6*a^2*b - a*b^2)*c^3 + 2*(2*a^4 - 7*a^3*b + 3*a^2*b^2 + 3*a*b^3)*c^2 - (a^3*b^2 - 4*a^2*b^3 + 3*a*b^4)*c)*tan(e*x + d)^2)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4))/((a^6*b^2 - 2*a^5*b^3 + a^4*b^4 - 4*a^5*c^3 - (8*a^6 - 8*a^5*b - a^4*b^2)*c^2 - 2*(2*a^7 - 4*a^6*b + a^5*b^2 + a^4*b^3)*c)*e*tan(e*x + d)^4 + (a^5*b^3 - 2*a^4*b^4 + a^3*b^5 - 4*a^4*b*c^3 - (8*a^5*b - 8*a^4*b^2 - a^3*b^3)*c^2 - 2*(2*a^6*b - 4*a^5*b^2 + a^4*b^3 + a^3*b^4)*c)*e*tan(e*x + d)^2 - (4*a^4*c^4 + (8*a^5 - 8*a^4*b - a^3*b^2)*c^3 + 2*(2*a^6 - 4*a^5*b + a^4*b^2 + a^3*b^3)*c^2 - (a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*c)*e), 1/8*(4*(a^3*b^2*c - 4*a^4*c^2 + (a^4*b^2 - 4*a^5*c)*tan(e*x + d)^4 + (a^3*b^3 - 4*a^4*b*c)*tan(e*x + d)^2)*sqrt(-a + b - c)*arctan(-1/2*((2*a - b)*tan(e*x + d)^4 + (b - 2*c)*tan(e*x + d)^2)*sqrt(-a + b - c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)/((a^2 - a*b + a*c)*tan(e*x + d)^4 + (a*b - b^2 + b*c)*tan(e*x + d)^2 + (a - b)*c + c^2)) - (4*(2*a^2 + 3*a*b)*c^4 - (2*a^4*b^2 - a^3*b^3 - 4*a^2*b^4 + 3*a*b^5 - 4*(2*a^3 + 3*a^2*b)*c^3 - (16*a^4 + 8*a^3*b - 26*a^2*b^2 - 3*a*b^3)*c^2 - 2*(4*a^5 - 2*a^4*b - 10*a^3*b^2 + 5*a^2*b^3 + 3*a*b^4)*c)*tan(e*x + d)^4 + (16*a^3 + 8*a^2*b - 26*a*b^2 - 3*b^3)*c^3 + 2*(4*a^4 - 2*a^3*b - 10*a^2*b^2 + 5*a*b^3 + 3*b^4)*c^2 - (2*a^3*b^3 - a^2*b^4 - 4*a*b^5 + 3*b^6 - 4*(2*a^2*b + 3*a*b^2)*c^3 - (16*a^3*b + 8*a^2*b^2 - 26*a*b^3 - 3*b^4)*c^2 - 2*(4*a^4*b - 2*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 + 3*b^5)*c)*tan(e*x + d)^2 - (2*a^3*b^2 - a^2*b^3 - 4*a*b^4 + 3*b^5)*c)*sqrt(a)*log(8*a^2*tan(e*x + d)^4 + 8*a*b*tan(e*x + d)^2 + b^2 + 4*a*c - 4*(2*a*tan(e*x + d)^4 + b*tan(e*x + d)^2)*sqrt(a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)) + 4*((a^4*b^2 - 2*a^3*b^3 + a^2*b^4 - 4*a^3*c^3 - (8*a^4 - 8*a^3*b - a^2*b^2)*c^2 - 2*(2*a^5 - 4*a^4*b + a^3*b^2 + a^2*b^3)*c)*tan(e*x + d)^6 + (a^3*b^3 - 4*a^2*b^4 + 3*a*b^5 - 2*(2*a^3 + 5*a^2*b)*c^3 - (4*a^4 + 10*a^3*b - 22*a^2*b^2 - 3*a*b^3)*c^2 - 2*(2*a^4*b - 8*a^3*b^2 + 4*a^2*b^3 + 3*a*b^4)*c)*tan(e*x + d)^4 - (8*a^2*c^4 + 3*(4*a^3 - 6*a^2*b - a*b^2)*c^3 + 2*(2*a^4 - 7*a^3*b + 3*a^2*b^2 + 3*a*b^3)*c^2 - (a^3*b^2 - 4*a^2*b^3 + 3*a*b^4)*c)*tan(e*x + d)^2)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4))/((a^6*b^2 - 2*a^5*b^3 + a^4*b^4 - 4*a^5*c^3 - (8*a^6 - 8*a^5*b - a^4*b^2)*c^2 - 2*(2*a^7 - 4*a^6*b + a^5*b^2 + a^4*b^3)*c)*e*tan(e*x + d)^4 + (a^5*b^3 - 2*a^4*b^4 + a^3*b^5 - 4*a^4*b*c^3 - (8*a^5*b - 8*a^4*b^2 - a^3*b^3)*c^2 - 2*(2*a^6*b - 4*a^5*b^2 + a^4*b^3 + a^3*b^4)*c)*e*tan(e*x + d)^2 - (4*a^4*c^4 + (8*a^5 - 8*a^4*b - a^3*b^2)*c^3 + 2*(2*a^6 - 4*a^5*b + a^4*b^2 + a^3*b^3)*c^2 - (a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*c)*e), -1/4*((4*(2*a^2 + 3*a*b)*c^4 - (2*a^4*b^2 - a^3*b^3 - 4*a^2*b^4 + 3*a*b^5 - 4*(2*a^3 + 3*a^2*b)*c^3 - (16*a^4 + 8*a^3*b - 26*a^2*b^2 - 3*a*b^3)*c^2 - 2*(4*a^5 - 2*a^4*b - 10*a^3*b^2 + 5*a^2*b^3 + 3*a*b^4)*c)*tan(e*x + d)^4 + (16*a^3 + 8*a^2*b - 26*a*b^2 - 3*b^3)*c^3 + 2*(4*a^4 - 2*a^3*b - 10*a^2*b^2 + 5*a*b^3 + 3*b^4)*c^2 - (2*a^3*b^3 - a^2*b^4 - 4*a*b^5 + 3*b^6 - 4*(2*a^2*b + 3*a*b^2)*c^3 - (16*a^3*b + 8*a^2*b^2 - 26*a*b^3 - 3*b^4)*c^2 - 2*(4*a^4*b - 2*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 + 3*b^5)*c)*tan(e*x + d)^2 - (2*a^3*b^2 - a^2*b^3 - 4*a*b^4 + 3*b^5)*c)*sqrt(-a)*arctan(1/2*(2*a*tan(e*x + d)^4 + b*tan(e*x + d)^2)*sqrt(-a)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)/(a^2*tan(e*x + d)^4 + a*b*tan(e*x + d)^2 + a*c)) - 2*(a^3*b^2*c - 4*a^4*c^2 + (a^4*b^2 - 4*a^5*c)*tan(e*x + d)^4 + (a^3*b^3 - 4*a^4*b*c)*tan(e*x + d)^2)*sqrt(-a + b - c)*arctan(-1/2*((2*a - b)*tan(e*x + d)^4 + (b - 2*c)*tan(e*x + d)^2)*sqrt(-a + b - c)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4)/((a^2 - a*b + a*c)*tan(e*x + d)^4 + (a*b - b^2 + b*c)*tan(e*x + d)^2 + (a - b)*c + c^2)) - 2*((a^4*b^2 - 2*a^3*b^3 + a^2*b^4 - 4*a^3*c^3 - (8*a^4 - 8*a^3*b - a^2*b^2)*c^2 - 2*(2*a^5 - 4*a^4*b + a^3*b^2 + a^2*b^3)*c)*tan(e*x + d)^6 + (a^3*b^3 - 4*a^2*b^4 + 3*a*b^5 - 2*(2*a^3 + 5*a^2*b)*c^3 - (4*a^4 + 10*a^3*b - 22*a^2*b^2 - 3*a*b^3)*c^2 - 2*(2*a^4*b - 8*a^3*b^2 + 4*a^2*b^3 + 3*a*b^4)*c)*tan(e*x + d)^4 - (8*a^2*c^4 + 3*(4*a^3 - 6*a^2*b - a*b^2)*c^3 + 2*(2*a^4 - 7*a^3*b + 3*a^2*b^2 + 3*a*b^3)*c^2 - (a^3*b^2 - 4*a^2*b^3 + 3*a*b^4)*c)*tan(e*x + d)^2)*sqrt((a*tan(e*x + d)^4 + b*tan(e*x + d)^2 + c)/tan(e*x + d)^4))/((a^6*b^2 - 2*a^5*b^3 + a^4*b^4 - 4*a^5*c^3 - (8*a^6 - 8*a^5*b - a^4*b^2)*c^2 - 2*(2*a^7 - 4*a^6*b + a^5*b^2 + a^4*b^3)*c)*e*tan(e*x + d)^4 + (a^5*b^3 - 2*a^4*b^4 + a^3*b^5 - 4*a^4*b*c^3 - (8*a^5*b - 8*a^4*b^2 - a^3*b^3)*c^2 - 2*(2*a^6*b - 4*a^5*b^2 + a^4*b^3 + a^3*b^4)*c)*e*tan(e*x + d)^2 - (4*a^4*c^4 + (8*a^5 - 8*a^4*b - a^3*b^2)*c^3 + 2*(2*a^6 - 4*a^5*b + a^4*b^2 + a^3*b^3)*c^2 - (a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*c)*e)]","B",0
