1,1,892,0,0.882489," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(5/2)*(A+C*sin(f*x+e)^2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{{\left({\left(4 \, m^{2} + 24 \, m + 43\right)} a^{m} c^{\frac{5}{2}} - \frac{{\left(12 \, m^{2} + 40 \, m - 15\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, {\left(4 \, m^{2} + 8 \, m + 35\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2 \, {\left(4 \, m^{2} + 8 \, m + 35\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{{\left(12 \, m^{2} + 40 \, m - 15\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{{\left(4 \, m^{2} + 24 \, m + 43\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} A e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(8 \, m^{3} + 36 \, m^{2} + 46 \, m + 15\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{5}{2}}} + \frac{4 \, {\left(2 \, {\left(4 \, m^{2} + 56 \, m + 219\right)} a^{m} c^{\frac{5}{2}} - \frac{4 \, {\left(4 \, m^{3} + 56 \, m^{2} + 219 \, m\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{{\left(16 \, m^{4} + 240 \, m^{3} + 1136 \, m^{2} + 1380 \, m + 1971\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{{\left(48 \, m^{4} + 496 \, m^{3} + 1568 \, m^{2} + 3108 \, m - 315\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{4 \, {\left(8 \, m^{4} + 68 \, m^{3} + 290 \, m^{2} + 111 \, m + 567\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{4 \, {\left(8 \, m^{4} + 68 \, m^{3} + 290 \, m^{2} + 111 \, m + 567\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{{\left(48 \, m^{4} + 496 \, m^{3} + 1568 \, m^{2} + 3108 \, m - 315\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{{\left(16 \, m^{4} + 240 \, m^{3} + 1136 \, m^{2} + 1380 \, m + 1971\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{4 \, {\left(4 \, m^{3} + 56 \, m^{2} + 219 \, m\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{2 \, {\left(4 \, m^{2} + 56 \, m + 219\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}\right)} C e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(32 \, m^{5} + 400 \, m^{4} + 1840 \, m^{3} + 3800 \, m^{2} + 3378 \, m + \frac{2 \, {\left(32 \, m^{5} + 400 \, m^{4} + 1840 \, m^{3} + 3800 \, m^{2} + 3378 \, m + 945\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{{\left(32 \, m^{5} + 400 \, m^{4} + 1840 \, m^{3} + 3800 \, m^{2} + 3378 \, m + 945\right)} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 945\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{5}{2}}}\right)}}{f}"," ",0,"-2*(((4*m^2 + 24*m + 43)*a^m*c^(5/2) - (12*m^2 + 40*m - 15)*a^m*c^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 2*(4*m^2 + 8*m + 35)*a^m*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2*(4*m^2 + 8*m + 35)*a^m*c^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - (12*m^2 + 40*m - 15)*a^m*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + (4*m^2 + 24*m + 43)*a^m*c^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*A*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((8*m^3 + 36*m^2 + 46*m + 15)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(5/2)) + 4*(2*(4*m^2 + 56*m + 219)*a^m*c^(5/2) - 4*(4*m^3 + 56*m^2 + 219*m)*a^m*c^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + (16*m^4 + 240*m^3 + 1136*m^2 + 1380*m + 1971)*a^m*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - (48*m^4 + 496*m^3 + 1568*m^2 + 3108*m - 315)*a^m*c^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 4*(8*m^4 + 68*m^3 + 290*m^2 + 111*m + 567)*a^m*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 4*(8*m^4 + 68*m^3 + 290*m^2 + 111*m + 567)*a^m*c^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - (48*m^4 + 496*m^3 + 1568*m^2 + 3108*m - 315)*a^m*c^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + (16*m^4 + 240*m^3 + 1136*m^2 + 1380*m + 1971)*a^m*c^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 4*(4*m^3 + 56*m^2 + 219*m)*a^m*c^(5/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 2*(4*m^2 + 56*m + 219)*a^m*c^(5/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9)*C*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((32*m^5 + 400*m^4 + 1840*m^3 + 3800*m^2 + 3378*m + 2*(32*m^5 + 400*m^4 + 1840*m^3 + 3800*m^2 + 3378*m + 945)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + (32*m^5 + 400*m^4 + 1840*m^3 + 3800*m^2 + 3378*m + 945)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 945)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(5/2)))/f","B",0
2,1,648,0,0.717935," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(3/2)*(A+C*sin(f*x+e)^2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{{\left(a^{m} c^{\frac{3}{2}} {\left(2 \, m + 5\right)} - \frac{a^{m} c^{\frac{3}{2}} {\left(2 \, m - 3\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{a^{m} c^{\frac{3}{2}} {\left(2 \, m - 3\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{m} c^{\frac{3}{2}} {\left(2 \, m + 5\right)} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)} A e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(4 \, m^{2} + 8 \, m + 3\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{3}{2}}} + \frac{4 \, {\left(2 \, a^{m} c^{\frac{3}{2}} {\left(2 \, m + 13\right)} - \frac{4 \, {\left(2 \, m^{2} + 13 \, m\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{{\left(8 \, m^{3} + 60 \, m^{2} + 66 \, m + 91\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{{\left(8 \, m^{3} + 20 \, m^{2} + 82 \, m - 35\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{{\left(8 \, m^{3} + 20 \, m^{2} + 82 \, m - 35\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{{\left(8 \, m^{3} + 60 \, m^{2} + 66 \, m + 91\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{4 \, {\left(2 \, m^{2} + 13 \, m\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{2 \, a^{m} c^{\frac{3}{2}} {\left(2 \, m + 13\right)} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}\right)} C e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(16 \, m^{4} + 128 \, m^{3} + 344 \, m^{2} + 352 \, m + \frac{2 \, {\left(16 \, m^{4} + 128 \, m^{3} + 344 \, m^{2} + 352 \, m + 105\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{{\left(16 \, m^{4} + 128 \, m^{3} + 344 \, m^{2} + 352 \, m + 105\right)} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 105\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{3}{2}}}\right)}}{f}"," ",0,"-2*((a^m*c^(3/2)*(2*m + 5) - a^m*c^(3/2)*(2*m - 3)*sin(f*x + e)/(cos(f*x + e) + 1) - a^m*c^(3/2)*(2*m - 3)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^m*c^(3/2)*(2*m + 5)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)*A*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((4*m^2 + 8*m + 3)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(3/2)) + 4*(2*a^m*c^(3/2)*(2*m + 13) - 4*(2*m^2 + 13*m)*a^m*c^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + (8*m^3 + 60*m^2 + 66*m + 91)*a^m*c^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - (8*m^3 + 20*m^2 + 82*m - 35)*a^m*c^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - (8*m^3 + 20*m^2 + 82*m - 35)*a^m*c^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + (8*m^3 + 60*m^2 + 66*m + 91)*a^m*c^(3/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 4*(2*m^2 + 13*m)*a^m*c^(3/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 2*a^m*c^(3/2)*(2*m + 13)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7)*C*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((16*m^4 + 128*m^3 + 344*m^2 + 352*m + 2*(16*m^4 + 128*m^3 + 344*m^2 + 352*m + 105)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + (16*m^4 + 128*m^3 + 344*m^2 + 352*m + 105)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 105)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(3/2)))/f","B",0
3,1,441,0,0.827933," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1/2)*(A+C*sin(f*x+e)^2),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{4 \, {\left(\frac{4 \, a^{m} \sqrt{c} m \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{{\left(4 \, m^{2} + 4 \, m + 5\right)} a^{m} \sqrt{c} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{{\left(4 \, m^{2} + 4 \, m + 5\right)} a^{m} \sqrt{c} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{4 \, a^{m} \sqrt{c} m \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 2 \, a^{m} \sqrt{c} - \frac{2 \, a^{m} \sqrt{c} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} C e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(8 \, m^{3} + 36 \, m^{2} + 46 \, m + \frac{2 \, {\left(8 \, m^{3} + 36 \, m^{2} + 46 \, m + 15\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{{\left(8 \, m^{3} + 36 \, m^{2} + 46 \, m + 15\right)} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 15\right)} \sqrt{\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1}} - \frac{{\left(a^{m} \sqrt{c} + \frac{a^{m} \sqrt{c} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)} A e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(2 \, m + 1\right)} \sqrt{\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1}}\right)}}{f}"," ",0,"2*(4*(4*a^m*sqrt(c)*m*sin(f*x + e)/(cos(f*x + e) + 1) - (4*m^2 + 4*m + 5)*a^m*sqrt(c)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - (4*m^2 + 4*m + 5)*a^m*sqrt(c)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 4*a^m*sqrt(c)*m*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 2*a^m*sqrt(c) - 2*a^m*sqrt(c)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*C*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((8*m^3 + 36*m^2 + 46*m + 2*(8*m^3 + 36*m^2 + 46*m + 15)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + (8*m^3 + 36*m^2 + 46*m + 15)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 15)*sqrt(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)) - (a^m*sqrt(c) + a^m*sqrt(c)*sin(f*x + e)/(cos(f*x + e) + 1))*A*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((2*m + 1)*sqrt(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)))/f","B",0
4,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+C*sin(f*x+e)^2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sin\left(f x + e\right)^{2} + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((C*sin(f*x + e)^2 + A)*(a*sin(f*x + e) + a)^m/sqrt(-c*sin(f*x + e) + c), x)","F",0
5,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+C*sin(f*x+e)^2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sin\left(f x + e\right)^{2} + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sin(f*x + e)^2 + A)*(a*sin(f*x + e) + a)^m/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
6,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+C*sin(f*x+e)^2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sin\left(f x + e\right)^{2} + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sin(f*x + e)^2 + A)*(a*sin(f*x + e) + a)^m/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
7,0,0,0,0.000000," ","integrate((A+C*sin(f*x+e)^2)/(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{C \sin\left(f x + e\right)^{2} + A}{\sqrt{a \sin\left(f x + e\right) + a} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sin(f*x + e)^2 + A)/(sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(3/2)), x)","F",0
8,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n*(A+C*sin(f*x+e)^2),x, algorithm=""maxima"")","\int {\left(C \sin\left(f x + e\right)^{2} + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((C*sin(f*x + e)^2 + A)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n, x)","F",0
9,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n*(A+C*sin(f*x+e)^2),x, algorithm=""maxima"")","\int {\left(C \sin\left(f x + e\right)^{2} + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((C*sin(f*x + e)^2 + A)*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n, x)","F",0
10,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(-2-m)*(A+C*sin(f*x+e)^2),x, algorithm=""maxima"")","\int {\left(C \sin\left(f x + e\right)^{2} + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{-m - 2}\,{d x}"," ",0,"integrate((C*sin(f*x + e)^2 + A)*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^(-m - 2), x)","F",0
11,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(3/2)*(A+C*sin(f*x+e)^2),x, algorithm=""maxima"")","\int {\left(C \sin\left(f x + e\right)^{2} + A\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((C*sin(f*x + e)^2 + A)*(d*sin(f*x + e) + c)^(3/2)*(a*sin(f*x + e) + a)^m, x)","F",0
12,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(1/2)*(A+C*sin(f*x+e)^2),x, algorithm=""maxima"")","\int {\left(C \sin\left(f x + e\right)^{2} + A\right)} \sqrt{d \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((C*sin(f*x + e)^2 + A)*sqrt(d*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m, x)","F",0
13,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+C*sin(f*x+e)^2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sin\left(f x + e\right)^{2} + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((C*sin(f*x + e)^2 + A)*(a*sin(f*x + e) + a)^m/sqrt(d*sin(f*x + e) + c), x)","F",0
14,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+C*sin(f*x+e)^2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sin\left(f x + e\right)^{2} + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sin(f*x + e)^2 + A)*(a*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c)^(3/2), x)","F",0
15,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+C*sin(f*x+e)^2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sin\left(f x + e\right)^{2} + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sin(f*x + e)^2 + A)*(a*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c)^(5/2), x)","F",0
16,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e)+C*sin(f*x+e)^2)/(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{C \sin\left(f x + e\right)^{2} + B \sin\left(f x + e\right) + A}{\sqrt{a \sin\left(f x + e\right) + a} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sin(f*x + e)^2 + B*sin(f*x + e) + A)/(sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(3/2)), x)","F",0
17,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n*(A+B*sin(f*x+e)+C*sin(f*x+e)^2),x, algorithm=""maxima"")","\int {\left(C \sin\left(f x + e\right)^{2} + B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((C*sin(f*x + e)^2 + B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n, x)","F",0
18,1,1324,0,0.722607," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e)+C*sin(f*x+e)^2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{{\left({\left(4 \, m^{2} + 24 \, m + 43\right)} a^{m} c^{\frac{5}{2}} - \frac{{\left(12 \, m^{2} + 40 \, m - 15\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, {\left(4 \, m^{2} + 8 \, m + 35\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2 \, {\left(4 \, m^{2} + 8 \, m + 35\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{{\left(12 \, m^{2} + 40 \, m - 15\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{{\left(4 \, m^{2} + 24 \, m + 43\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} A e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(8 \, m^{3} + 36 \, m^{2} + 46 \, m + 15\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{5}{2}}} - \frac{2 \, {\left({\left(4 \, m^{2} + 40 \, m + 115\right)} a^{m} c^{\frac{5}{2}} - \frac{2 \, {\left(4 \, m^{3} + 40 \, m^{2} + 115 \, m\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, {\left(12 \, m^{3} + 76 \, m^{2} + 97 \, m + 175\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{{\left(16 \, m^{3} + 76 \, m^{2} + 260 \, m - 175\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{{\left(16 \, m^{3} + 76 \, m^{2} + 260 \, m - 175\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{2 \, {\left(12 \, m^{3} + 76 \, m^{2} + 97 \, m + 175\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{2 \, {\left(4 \, m^{3} + 40 \, m^{2} + 115 \, m\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{{\left(4 \, m^{2} + 40 \, m + 115\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}\right)} B e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(16 \, m^{4} + 128 \, m^{3} + 344 \, m^{2} + 352 \, m + \frac{{\left(16 \, m^{4} + 128 \, m^{3} + 344 \, m^{2} + 352 \, m + 105\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 105\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{5}{2}}} + \frac{4 \, {\left(2 \, {\left(4 \, m^{2} + 56 \, m + 219\right)} a^{m} c^{\frac{5}{2}} - \frac{4 \, {\left(4 \, m^{3} + 56 \, m^{2} + 219 \, m\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{{\left(16 \, m^{4} + 240 \, m^{3} + 1136 \, m^{2} + 1380 \, m + 1971\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{{\left(48 \, m^{4} + 496 \, m^{3} + 1568 \, m^{2} + 3108 \, m - 315\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{4 \, {\left(8 \, m^{4} + 68 \, m^{3} + 290 \, m^{2} + 111 \, m + 567\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{4 \, {\left(8 \, m^{4} + 68 \, m^{3} + 290 \, m^{2} + 111 \, m + 567\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{{\left(48 \, m^{4} + 496 \, m^{3} + 1568 \, m^{2} + 3108 \, m - 315\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{{\left(16 \, m^{4} + 240 \, m^{3} + 1136 \, m^{2} + 1380 \, m + 1971\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{4 \, {\left(4 \, m^{3} + 56 \, m^{2} + 219 \, m\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{2 \, {\left(4 \, m^{2} + 56 \, m + 219\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}\right)} C e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(32 \, m^{5} + 400 \, m^{4} + 1840 \, m^{3} + 3800 \, m^{2} + 3378 \, m + \frac{2 \, {\left(32 \, m^{5} + 400 \, m^{4} + 1840 \, m^{3} + 3800 \, m^{2} + 3378 \, m + 945\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{{\left(32 \, m^{5} + 400 \, m^{4} + 1840 \, m^{3} + 3800 \, m^{2} + 3378 \, m + 945\right)} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 945\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{5}{2}}}\right)}}{f}"," ",0,"-2*(((4*m^2 + 24*m + 43)*a^m*c^(5/2) - (12*m^2 + 40*m - 15)*a^m*c^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 2*(4*m^2 + 8*m + 35)*a^m*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2*(4*m^2 + 8*m + 35)*a^m*c^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - (12*m^2 + 40*m - 15)*a^m*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + (4*m^2 + 24*m + 43)*a^m*c^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*A*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((8*m^3 + 36*m^2 + 46*m + 15)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(5/2)) - 2*((4*m^2 + 40*m + 115)*a^m*c^(5/2) - 2*(4*m^3 + 40*m^2 + 115*m)*a^m*c^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 2*(12*m^3 + 76*m^2 + 97*m + 175)*a^m*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - (16*m^3 + 76*m^2 + 260*m - 175)*a^m*c^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - (16*m^3 + 76*m^2 + 260*m - 175)*a^m*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 2*(12*m^3 + 76*m^2 + 97*m + 175)*a^m*c^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 2*(4*m^3 + 40*m^2 + 115*m)*a^m*c^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + (4*m^2 + 40*m + 115)*a^m*c^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7)*B*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((16*m^4 + 128*m^3 + 344*m^2 + 352*m + (16*m^4 + 128*m^3 + 344*m^2 + 352*m + 105)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 105)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(5/2)) + 4*(2*(4*m^2 + 56*m + 219)*a^m*c^(5/2) - 4*(4*m^3 + 56*m^2 + 219*m)*a^m*c^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + (16*m^4 + 240*m^3 + 1136*m^2 + 1380*m + 1971)*a^m*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - (48*m^4 + 496*m^3 + 1568*m^2 + 3108*m - 315)*a^m*c^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 4*(8*m^4 + 68*m^3 + 290*m^2 + 111*m + 567)*a^m*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 4*(8*m^4 + 68*m^3 + 290*m^2 + 111*m + 567)*a^m*c^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - (48*m^4 + 496*m^3 + 1568*m^2 + 3108*m - 315)*a^m*c^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + (16*m^4 + 240*m^3 + 1136*m^2 + 1380*m + 1971)*a^m*c^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 4*(4*m^3 + 56*m^2 + 219*m)*a^m*c^(5/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 2*(4*m^2 + 56*m + 219)*a^m*c^(5/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9)*C*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((32*m^5 + 400*m^4 + 1840*m^3 + 3800*m^2 + 3378*m + 2*(32*m^5 + 400*m^4 + 1840*m^3 + 3800*m^2 + 3378*m + 945)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + (32*m^5 + 400*m^4 + 1840*m^3 + 3800*m^2 + 3378*m + 945)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 945)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(5/2)))/f","B",0
19,1,950,0,0.587152," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e)+C*sin(f*x+e)^2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{{\left(a^{m} c^{\frac{3}{2}} {\left(2 \, m + 5\right)} - \frac{a^{m} c^{\frac{3}{2}} {\left(2 \, m - 3\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{a^{m} c^{\frac{3}{2}} {\left(2 \, m - 3\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{m} c^{\frac{3}{2}} {\left(2 \, m + 5\right)} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)} A e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(4 \, m^{2} + 8 \, m + 3\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(a^{m} c^{\frac{3}{2}} {\left(2 \, m + 9\right)} - \frac{2 \, {\left(2 \, m^{2} + 9 \, m\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{{\left(4 \, m^{2} + 15\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{{\left(4 \, m^{2} + 15\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{2 \, {\left(2 \, m^{2} + 9 \, m\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{m} c^{\frac{3}{2}} {\left(2 \, m + 9\right)} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} B e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(8 \, m^{3} + 36 \, m^{2} + 46 \, m + \frac{{\left(8 \, m^{3} + 36 \, m^{2} + 46 \, m + 15\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 15\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{3}{2}}} + \frac{4 \, {\left(2 \, a^{m} c^{\frac{3}{2}} {\left(2 \, m + 13\right)} - \frac{4 \, {\left(2 \, m^{2} + 13 \, m\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{{\left(8 \, m^{3} + 60 \, m^{2} + 66 \, m + 91\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{{\left(8 \, m^{3} + 20 \, m^{2} + 82 \, m - 35\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{{\left(8 \, m^{3} + 20 \, m^{2} + 82 \, m - 35\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{{\left(8 \, m^{3} + 60 \, m^{2} + 66 \, m + 91\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{4 \, {\left(2 \, m^{2} + 13 \, m\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{2 \, a^{m} c^{\frac{3}{2}} {\left(2 \, m + 13\right)} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}\right)} C e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(16 \, m^{4} + 128 \, m^{3} + 344 \, m^{2} + 352 \, m + \frac{2 \, {\left(16 \, m^{4} + 128 \, m^{3} + 344 \, m^{2} + 352 \, m + 105\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{{\left(16 \, m^{4} + 128 \, m^{3} + 344 \, m^{2} + 352 \, m + 105\right)} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 105\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{3}{2}}}\right)}}{f}"," ",0,"-2*((a^m*c^(3/2)*(2*m + 5) - a^m*c^(3/2)*(2*m - 3)*sin(f*x + e)/(cos(f*x + e) + 1) - a^m*c^(3/2)*(2*m - 3)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^m*c^(3/2)*(2*m + 5)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)*A*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((4*m^2 + 8*m + 3)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(3/2)) - 2*(a^m*c^(3/2)*(2*m + 9) - 2*(2*m^2 + 9*m)*a^m*c^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + (4*m^2 + 15)*a^m*c^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + (4*m^2 + 15)*a^m*c^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 2*(2*m^2 + 9*m)*a^m*c^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^m*c^(3/2)*(2*m + 9)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*B*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((8*m^3 + 36*m^2 + 46*m + (8*m^3 + 36*m^2 + 46*m + 15)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 15)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(3/2)) + 4*(2*a^m*c^(3/2)*(2*m + 13) - 4*(2*m^2 + 13*m)*a^m*c^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + (8*m^3 + 60*m^2 + 66*m + 91)*a^m*c^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - (8*m^3 + 20*m^2 + 82*m - 35)*a^m*c^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - (8*m^3 + 20*m^2 + 82*m - 35)*a^m*c^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + (8*m^3 + 60*m^2 + 66*m + 91)*a^m*c^(3/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 4*(2*m^2 + 13*m)*a^m*c^(3/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 2*a^m*c^(3/2)*(2*m + 13)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7)*C*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((16*m^4 + 128*m^3 + 344*m^2 + 352*m + 2*(16*m^4 + 128*m^3 + 344*m^2 + 352*m + 105)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + (16*m^4 + 128*m^3 + 344*m^2 + 352*m + 105)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 105)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(3/2)))/f","B",0
20,1,644,0,0.686714," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1/2)*(A+B*sin(f*x+e)+C*sin(f*x+e)^2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{2 \, {\left(\frac{2 \, a^{m} \sqrt{c} m \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, a^{m} \sqrt{c} m \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - a^{m} \sqrt{c} - \frac{a^{m} \sqrt{c} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)} B e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(4 \, m^{2} + 8 \, m + \frac{{\left(4 \, m^{2} + 8 \, m + 3\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 3\right)} \sqrt{\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1}} - \frac{4 \, {\left(\frac{4 \, a^{m} \sqrt{c} m \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{{\left(4 \, m^{2} + 4 \, m + 5\right)} a^{m} \sqrt{c} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{{\left(4 \, m^{2} + 4 \, m + 5\right)} a^{m} \sqrt{c} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{4 \, a^{m} \sqrt{c} m \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 2 \, a^{m} \sqrt{c} - \frac{2 \, a^{m} \sqrt{c} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} C e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(8 \, m^{3} + 36 \, m^{2} + 46 \, m + \frac{2 \, {\left(8 \, m^{3} + 36 \, m^{2} + 46 \, m + 15\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{{\left(8 \, m^{3} + 36 \, m^{2} + 46 \, m + 15\right)} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 15\right)} \sqrt{\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1}} + \frac{{\left(a^{m} \sqrt{c} + \frac{a^{m} \sqrt{c} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)} A e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(2 \, m + 1\right)} \sqrt{\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1}}\right)}}{f}"," ",0,"-2*(2*(2*a^m*sqrt(c)*m*sin(f*x + e)/(cos(f*x + e) + 1) + 2*a^m*sqrt(c)*m*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - a^m*sqrt(c) - a^m*sqrt(c)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)*B*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((4*m^2 + 8*m + (4*m^2 + 8*m + 3)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3)*sqrt(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)) - 4*(4*a^m*sqrt(c)*m*sin(f*x + e)/(cos(f*x + e) + 1) - (4*m^2 + 4*m + 5)*a^m*sqrt(c)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - (4*m^2 + 4*m + 5)*a^m*sqrt(c)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 4*a^m*sqrt(c)*m*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 2*a^m*sqrt(c) - 2*a^m*sqrt(c)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*C*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((8*m^3 + 36*m^2 + 46*m + 2*(8*m^3 + 36*m^2 + 46*m + 15)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + (8*m^3 + 36*m^2 + 46*m + 15)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 15)*sqrt(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)) + (a^m*sqrt(c) + a^m*sqrt(c)*sin(f*x + e)/(cos(f*x + e) + 1))*A*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((2*m + 1)*sqrt(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)))/f","B",0
21,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)+C*sin(f*x+e)^2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sin\left(f x + e\right)^{2} + B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((C*sin(f*x + e)^2 + B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/sqrt(-c*sin(f*x + e) + c), x)","F",0
22,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)+C*sin(f*x+e)^2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sin\left(f x + e\right)^{2} + B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sin(f*x + e)^2 + B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
23,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)+C*sin(f*x+e)^2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sin\left(f x + e\right)^{2} + B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sin(f*x + e)^2 + B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
24,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2-m)*(A+B*sin(f*x+e)+C*sin(f*x+e)^2),x, algorithm=""maxima"")","\int {\left(C \sin\left(f x + e\right)^{2} + B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 2}\,{d x}"," ",0,"integrate((C*sin(f*x + e)^2 + B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 2), x)","F",0
25,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n*(A+B*sin(f*x+e)+C*sin(f*x+e)^2),x, algorithm=""maxima"")","\int {\left(C \sin\left(f x + e\right)^{2} + B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((C*sin(f*x + e)^2 + B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n, x)","F",0
26,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(-2-m)*(A+B*sin(f*x+e)+C*sin(f*x+e)^2),x, algorithm=""maxima"")","\int {\left(C \sin\left(f x + e\right)^{2} + B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{-m - 2}\,{d x}"," ",0,"integrate((C*sin(f*x + e)^2 + B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^(-m - 2), x)","F",0
27,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e)+C*sin(f*x+e)^2),x, algorithm=""maxima"")","\int {\left(C \sin\left(f x + e\right)^{2} + B \sin\left(f x + e\right) + A\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((C*sin(f*x + e)^2 + B*sin(f*x + e) + A)*(d*sin(f*x + e) + c)^(3/2)*(a*sin(f*x + e) + a)^m, x)","F",0
28,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(1/2)*(A+B*sin(f*x+e)+C*sin(f*x+e)^2),x, algorithm=""maxima"")","\int {\left(C \sin\left(f x + e\right)^{2} + B \sin\left(f x + e\right) + A\right)} \sqrt{d \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((C*sin(f*x + e)^2 + B*sin(f*x + e) + A)*sqrt(d*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m, x)","F",0
29,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)+C*sin(f*x+e)^2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sin\left(f x + e\right)^{2} + B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{\sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((C*sin(f*x + e)^2 + B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/sqrt(d*sin(f*x + e) + c), x)","F",0
30,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)+C*sin(f*x+e)^2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sin\left(f x + e\right)^{2} + B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sin(f*x + e)^2 + B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c)^(3/2), x)","F",0
31,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)+C*sin(f*x+e)^2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sin\left(f x + e\right)^{2} + B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((C*sin(f*x + e)^2 + B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c)^(5/2), x)","F",0
32,1,102,0,0.333132," ","integrate((a+b*sin(d*x+c))*(A+B*sin(d*x+c)+C*sin(d*x+c)^2),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} A a + 3 \, {\left(2 \, d x + 2 \, c - \sin\left(2 \, d x + 2 \, c\right)\right)} C a + 3 \, {\left(2 \, d x + 2 \, c - \sin\left(2 \, d x + 2 \, c\right)\right)} B b + 4 \, {\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} C b - 12 \, B a \cos\left(d x + c\right) - 12 \, A b \cos\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(12*(d*x + c)*A*a + 3*(2*d*x + 2*c - sin(2*d*x + 2*c))*C*a + 3*(2*d*x + 2*c - sin(2*d*x + 2*c))*B*b + 4*(cos(d*x + c)^3 - 3*cos(d*x + c))*C*b - 12*B*a*cos(d*x + c) - 12*A*b*cos(d*x + c))/d","A",0
33,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))*(A+B*sin(f*x+e)+C*sin(f*x+e)^2)/sin(f*x+e)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(C \sin\left(f x + e\right)^{2} + B \sin\left(f x + e\right) + A\right)} {\left(b \sin\left(f x + e\right) + a\right)}}{\sin\left(f x + e\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((C*sin(f*x + e)^2 + B*sin(f*x + e) + A)*(b*sin(f*x + e) + a)/sin(f*x + e)^(3/2), x)","F",0
34,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^n*(A+B*sin(f*x+e)+C*sin(f*x+e)^2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
