1,1,1110,384,23.157749,"\text{Not used}","int((A + C*sin(e + f*x)^2)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(5/2),x)","\frac{\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{C\,c^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(m^4\,16{}\mathrm{i}+m^3\,128{}\mathrm{i}+m^2\,344{}\mathrm{i}+m\,352{}\mathrm{i}+105{}\mathrm{i}\right)}{8\,f\,\left(m^5\,32{}\mathrm{i}+m^4\,400{}\mathrm{i}+m^3\,1840{}\mathrm{i}+m^2\,3800{}\mathrm{i}+m\,3378{}\mathrm{i}+945{}\mathrm{i}\right)}+\frac{c^2\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(18900\,A+12285\,C+15648\,A\,m+648\,C\,m+5280\,A\,m^2+896\,A\,m^3+64\,A\,m^4+1416\,C\,m^2+224\,C\,m^3+16\,C\,m^4\right)}{4\,f\,\left(m^5\,32{}\mathrm{i}+m^4\,400{}\mathrm{i}+m^3\,1840{}\mathrm{i}+m^2\,3800{}\mathrm{i}+m\,3378{}\mathrm{i}+945{}\mathrm{i}\right)}+\frac{c^2\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(A\,18900{}\mathrm{i}+C\,12285{}\mathrm{i}+A\,m\,15648{}\mathrm{i}+C\,m\,648{}\mathrm{i}+A\,m^2\,5280{}\mathrm{i}+A\,m^3\,896{}\mathrm{i}+A\,m^4\,64{}\mathrm{i}+C\,m^2\,1416{}\mathrm{i}+C\,m^3\,224{}\mathrm{i}+C\,m^4\,16{}\mathrm{i}\right)}{4\,f\,\left(m^5\,32{}\mathrm{i}+m^4\,400{}\mathrm{i}+m^3\,1840{}\mathrm{i}+m^2\,3800{}\mathrm{i}+m\,3378{}\mathrm{i}+945{}\mathrm{i}\right)}+\frac{c^2\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\left(2\,m+1\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(1575\,A+1575\,C+1178\,A\,m+414\,C\,m+292\,A\,m^2+24\,A\,m^3+100\,C\,m^2+8\,C\,m^3\right)}{2\,f\,\left(m^5\,32{}\mathrm{i}+m^4\,400{}\mathrm{i}+m^3\,1840{}\mathrm{i}+m^2\,3800{}\mathrm{i}+m\,3378{}\mathrm{i}+945{}\mathrm{i}\right)}+\frac{c^2\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\left(2\,m+1\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(A\,1575{}\mathrm{i}+C\,1575{}\mathrm{i}+A\,m\,1178{}\mathrm{i}+C\,m\,414{}\mathrm{i}+A\,m^2\,292{}\mathrm{i}+A\,m^3\,24{}\mathrm{i}+C\,m^2\,100{}\mathrm{i}+C\,m^3\,8{}\mathrm{i}\right)}{2\,f\,\left(m^5\,32{}\mathrm{i}+m^4\,400{}\mathrm{i}+m^3\,1840{}\mathrm{i}+m^2\,3800{}\mathrm{i}+m\,3378{}\mathrm{i}+945{}\mathrm{i}\right)}+\frac{C\,c^2\,{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(16\,m^4+128\,m^3+344\,m^2+352\,m+105\right)}{8\,f\,\left(m^5\,32{}\mathrm{i}+m^4\,400{}\mathrm{i}+m^3\,1840{}\mathrm{i}+m^2\,3800{}\mathrm{i}+m\,3378{}\mathrm{i}+945{}\mathrm{i}\right)}-\frac{3\,C\,c^2\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(16\,m^4+192\,m^3+632\,m^2+720\,m+225\right)}{8\,f\,\left(m^5\,32{}\mathrm{i}+m^4\,400{}\mathrm{i}+m^3\,1840{}\mathrm{i}+m^2\,3800{}\mathrm{i}+m\,3378{}\mathrm{i}+945{}\mathrm{i}\right)}-\frac{3\,C\,c^2\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(m^4\,16{}\mathrm{i}+m^3\,192{}\mathrm{i}+m^2\,632{}\mathrm{i}+m\,720{}\mathrm{i}+225{}\mathrm{i}\right)}{8\,f\,\left(m^5\,32{}\mathrm{i}+m^4\,400{}\mathrm{i}+m^3\,1840{}\mathrm{i}+m^2\,3800{}\mathrm{i}+m\,3378{}\mathrm{i}+945{}\mathrm{i}\right)}-\frac{c^2\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(4\,m^2+8\,m+3\right)\,\left(63\,A+189\,C+32\,A\,m+44\,C\,m+4\,A\,m^2+4\,C\,m^2\right)}{2\,f\,\left(m^5\,32{}\mathrm{i}+m^4\,400{}\mathrm{i}+m^3\,1840{}\mathrm{i}+m^2\,3800{}\mathrm{i}+m\,3378{}\mathrm{i}+945{}\mathrm{i}\right)}-\frac{c^2\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(4\,m^2+8\,m+3\right)\,\left(A\,63{}\mathrm{i}+C\,189{}\mathrm{i}+A\,m\,32{}\mathrm{i}+C\,m\,44{}\mathrm{i}+A\,m^2\,4{}\mathrm{i}+C\,m^2\,4{}\mathrm{i}\right)}{2\,f\,\left(m^5\,32{}\mathrm{i}+m^4\,400{}\mathrm{i}+m^3\,1840{}\mathrm{i}+m^2\,3800{}\mathrm{i}+m\,3378{}\mathrm{i}+945{}\mathrm{i}\right)}\right)}{{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}+\frac{{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,\left(32\,m^5+400\,m^4+1840\,m^3+3800\,m^2+3378\,m+945\right)}{m^5\,32{}\mathrm{i}+m^4\,400{}\mathrm{i}+m^3\,1840{}\mathrm{i}+m^2\,3800{}\mathrm{i}+m\,3378{}\mathrm{i}+945{}\mathrm{i}}}","Not used",1,"((c - c*sin(e + f*x))^(1/2)*((C*c^2*(a + a*sin(e + f*x))^m*(m*352i + m^2*344i + m^3*128i + m^4*16i + 105i))/(8*f*(m*3378i + m^2*3800i + m^3*1840i + m^4*400i + m^5*32i + 945i)) + (c^2*exp(e*5i + f*x*5i)*(a + a*sin(e + f*x))^m*(18900*A + 12285*C + 15648*A*m + 648*C*m + 5280*A*m^2 + 896*A*m^3 + 64*A*m^4 + 1416*C*m^2 + 224*C*m^3 + 16*C*m^4))/(4*f*(m*3378i + m^2*3800i + m^3*1840i + m^4*400i + m^5*32i + 945i)) + (c^2*exp(e*4i + f*x*4i)*(a + a*sin(e + f*x))^m*(A*18900i + C*12285i + A*m*15648i + C*m*648i + A*m^2*5280i + A*m^3*896i + A*m^4*64i + C*m^2*1416i + C*m^3*224i + C*m^4*16i))/(4*f*(m*3378i + m^2*3800i + m^3*1840i + m^4*400i + m^5*32i + 945i)) + (c^2*exp(e*3i + f*x*3i)*(2*m + 1)*(a + a*sin(e + f*x))^m*(1575*A + 1575*C + 1178*A*m + 414*C*m + 292*A*m^2 + 24*A*m^3 + 100*C*m^2 + 8*C*m^3))/(2*f*(m*3378i + m^2*3800i + m^3*1840i + m^4*400i + m^5*32i + 945i)) + (c^2*exp(e*6i + f*x*6i)*(2*m + 1)*(a + a*sin(e + f*x))^m*(A*1575i + C*1575i + A*m*1178i + C*m*414i + A*m^2*292i + A*m^3*24i + C*m^2*100i + C*m^3*8i))/(2*f*(m*3378i + m^2*3800i + m^3*1840i + m^4*400i + m^5*32i + 945i)) + (C*c^2*exp(e*9i + f*x*9i)*(a + a*sin(e + f*x))^m*(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105))/(8*f*(m*3378i + m^2*3800i + m^3*1840i + m^4*400i + m^5*32i + 945i)) - (3*C*c^2*exp(e*1i + f*x*1i)*(a + a*sin(e + f*x))^m*(720*m + 632*m^2 + 192*m^3 + 16*m^4 + 225))/(8*f*(m*3378i + m^2*3800i + m^3*1840i + m^4*400i + m^5*32i + 945i)) - (3*C*c^2*exp(e*8i + f*x*8i)*(a + a*sin(e + f*x))^m*(m*720i + m^2*632i + m^3*192i + m^4*16i + 225i))/(8*f*(m*3378i + m^2*3800i + m^3*1840i + m^4*400i + m^5*32i + 945i)) - (c^2*exp(e*7i + f*x*7i)*(a + a*sin(e + f*x))^m*(8*m + 4*m^2 + 3)*(63*A + 189*C + 32*A*m + 44*C*m + 4*A*m^2 + 4*C*m^2))/(2*f*(m*3378i + m^2*3800i + m^3*1840i + m^4*400i + m^5*32i + 945i)) - (c^2*exp(e*2i + f*x*2i)*(a + a*sin(e + f*x))^m*(8*m + 4*m^2 + 3)*(A*63i + C*189i + A*m*32i + C*m*44i + A*m^2*4i + C*m^2*4i))/(2*f*(m*3378i + m^2*3800i + m^3*1840i + m^4*400i + m^5*32i + 945i))))/(exp(e*5i + f*x*5i) + (exp(e*4i + f*x*4i)*(3378*m + 3800*m^2 + 1840*m^3 + 400*m^4 + 32*m^5 + 945))/(m*3378i + m^2*3800i + m^3*1840i + m^4*400i + m^5*32i + 945i))","B"
2,1,714,285,20.659478,"\text{Not used}","int((A + C*sin(e + f*x)^2)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(3/2),x)","\frac{\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{C\,c\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(m^3\,8{}\mathrm{i}+m^2\,36{}\mathrm{i}+m\,46{}\mathrm{i}+15{}\mathrm{i}\right)}{4\,f\,\left(16\,m^4+128\,m^3+344\,m^2+352\,m+105\right)}+\frac{c\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(1260\,A+735\,C+1144\,A\,m-18\,C\,m+336\,A\,m^2+32\,A\,m^3+100\,C\,m^2+8\,C\,m^3\right)}{4\,f\,\left(16\,m^4+128\,m^3+344\,m^2+352\,m+105\right)}-\frac{c\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(A\,1260{}\mathrm{i}+C\,735{}\mathrm{i}+A\,m\,1144{}\mathrm{i}-C\,m\,18{}\mathrm{i}+A\,m^2\,336{}\mathrm{i}+A\,m^3\,32{}\mathrm{i}+C\,m^2\,100{}\mathrm{i}+C\,m^3\,8{}\mathrm{i}\right)}{4\,f\,\left(16\,m^4+128\,m^3+344\,m^2+352\,m+105\right)}-\frac{C\,c\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(8\,m^3+36\,m^2+46\,m+15\right)}{4\,f\,\left(16\,m^4+128\,m^3+344\,m^2+352\,m+105\right)}-\frac{C\,c\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(8\,m^3+100\,m^2+174\,m+63\right)}{4\,f\,\left(16\,m^4+128\,m^3+344\,m^2+352\,m+105\right)}+\frac{C\,c\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(m^3\,8{}\mathrm{i}+m^2\,100{}\mathrm{i}+m\,174{}\mathrm{i}+63{}\mathrm{i}\right)}{4\,f\,\left(16\,m^4+128\,m^3+344\,m^2+352\,m+105\right)}+\frac{c\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\left(2\,m+1\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(140\,A+175\,C+96\,A\,m+16\,C\,m+16\,A\,m^2+4\,C\,m^2\right)}{4\,f\,\left(16\,m^4+128\,m^3+344\,m^2+352\,m+105\right)}-\frac{c\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,\left(2\,m+1\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(A\,140{}\mathrm{i}+C\,175{}\mathrm{i}+A\,m\,96{}\mathrm{i}+C\,m\,16{}\mathrm{i}+A\,m^2\,16{}\mathrm{i}+C\,m^2\,4{}\mathrm{i}\right)}{4\,f\,\left(16\,m^4+128\,m^3+344\,m^2+352\,m+105\right)}\right)}{{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}-\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\left(m^4\,16{}\mathrm{i}+m^3\,128{}\mathrm{i}+m^2\,344{}\mathrm{i}+m\,352{}\mathrm{i}+105{}\mathrm{i}\right)}{16\,m^4+128\,m^3+344\,m^2+352\,m+105}}","Not used",1,"((c - c*sin(e + f*x))^(1/2)*((C*c*(a + a*sin(e + f*x))^m*(m*46i + m^2*36i + m^3*8i + 15i))/(4*f*(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105)) + (c*exp(e*3i + f*x*3i)*(a + a*sin(e + f*x))^m*(1260*A + 735*C + 1144*A*m - 18*C*m + 336*A*m^2 + 32*A*m^3 + 100*C*m^2 + 8*C*m^3))/(4*f*(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105)) - (c*exp(e*4i + f*x*4i)*(a + a*sin(e + f*x))^m*(A*1260i + C*735i + A*m*1144i - C*m*18i + A*m^2*336i + A*m^3*32i + C*m^2*100i + C*m^3*8i))/(4*f*(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105)) - (C*c*exp(e*7i + f*x*7i)*(a + a*sin(e + f*x))^m*(46*m + 36*m^2 + 8*m^3 + 15))/(4*f*(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105)) - (C*c*exp(e*1i + f*x*1i)*(a + a*sin(e + f*x))^m*(174*m + 100*m^2 + 8*m^3 + 63))/(4*f*(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105)) + (C*c*exp(e*6i + f*x*6i)*(a + a*sin(e + f*x))^m*(m*174i + m^2*100i + m^3*8i + 63i))/(4*f*(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105)) + (c*exp(e*5i + f*x*5i)*(2*m + 1)*(a + a*sin(e + f*x))^m*(140*A + 175*C + 96*A*m + 16*C*m + 16*A*m^2 + 4*C*m^2))/(4*f*(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105)) - (c*exp(e*2i + f*x*2i)*(2*m + 1)*(a + a*sin(e + f*x))^m*(A*140i + C*175i + A*m*96i + C*m*16i + A*m^2*16i + C*m^2*4i))/(4*f*(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105))))/(exp(e*4i + f*x*4i) - (exp(e*3i + f*x*3i)*(m*352i + m^2*344i + m^3*128i + m^4*16i + 105i))/(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105))","B"
3,1,185,180,17.164455,"\text{Not used}","int((A + C*sin(e + f*x)^2)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(1/2),x)","-\frac{{\left(a\,\left(\sin\left(e+f\,x\right)+1\right)\right)}^m\,\sqrt{-c\,\left(\sin\left(e+f\,x\right)-1\right)}\,\left(60\,A\,\cos\left(e+f\,x\right)+35\,C\,\cos\left(e+f\,x\right)-3\,C\,\cos\left(3\,e+3\,f\,x\right)-8\,C\,\sin\left(2\,e+2\,f\,x\right)-4\,C\,m^2\,\cos\left(3\,e+3\,f\,x\right)+64\,A\,m\,\cos\left(e+f\,x\right)+8\,C\,m\,\cos\left(e+f\,x\right)+16\,A\,m^2\,\cos\left(e+f\,x\right)-8\,C\,m\,\cos\left(3\,e+3\,f\,x\right)+4\,C\,m^2\,\cos\left(e+f\,x\right)-16\,C\,m\,\sin\left(2\,e+2\,f\,x\right)\right)}{2\,f\,\left(\sin\left(e+f\,x\right)-1\right)\,\left(8\,m^3+36\,m^2+46\,m+15\right)}","Not used",1,"-((a*(sin(e + f*x) + 1))^m*(-c*(sin(e + f*x) - 1))^(1/2)*(60*A*cos(e + f*x) + 35*C*cos(e + f*x) - 3*C*cos(3*e + 3*f*x) - 8*C*sin(2*e + 2*f*x) - 4*C*m^2*cos(3*e + 3*f*x) + 64*A*m*cos(e + f*x) + 8*C*m*cos(e + f*x) + 16*A*m^2*cos(e + f*x) - 8*C*m*cos(3*e + 3*f*x) + 4*C*m^2*cos(e + f*x) - 16*C*m*sin(2*e + 2*f*x)))/(2*f*(sin(e + f*x) - 1)*(46*m + 36*m^2 + 8*m^3 + 15))","B"
4,0,-1,123,0.000000,"\text{Not used}","int(((A + C*sin(e + f*x)^2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(1/2),x)","\int \frac{\left(C\,{\sin\left(e+f\,x\right)}^2+A\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((A + C*sin(e + f*x)^2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(1/2), x)","F"
5,0,-1,202,0.000000,"\text{Not used}","int(((A + C*sin(e + f*x)^2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{\left(C\,{\sin\left(e+f\,x\right)}^2+A\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*sin(e + f*x)^2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(3/2), x)","F"
6,0,-1,207,0.000000,"\text{Not used}","int(((A + C*sin(e + f*x)^2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{\left(C\,{\sin\left(e+f\,x\right)}^2+A\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((A + C*sin(e + f*x)^2)*(a + a*sin(e + f*x))^m)/(c - c*sin(e + f*x))^(5/2), x)","F"
7,0,-1,167,0.000000,"\text{Not used}","int((A + C*sin(e + f*x)^2)/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(3/2)),x)","\int \frac{C\,{\sin\left(e+f\,x\right)}^2+A}{\sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + C*sin(e + f*x)^2)/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(3/2)), x)","F"
8,0,-1,257,0.000000,"\text{Not used}","int((A + C*sin(e + f*x)^2)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n,x)","\int \left(C\,{\sin\left(e+f\,x\right)}^2+A\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((A + C*sin(e + f*x)^2)*(a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n, x)","F"
9,0,-1,366,0.000000,"\text{Not used}","int((A + C*sin(e + f*x)^2)*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^n,x)","\int \left(C\,{\sin\left(e+f\,x\right)}^2+A\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n \,d x","Not used",1,"int((A + C*sin(e + f*x)^2)*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^n, x)","F"
10,0,-1,392,0.000000,"\text{Not used}","int(((A + C*sin(e + f*x)^2)*(a + a*sin(e + f*x))^m)/(c + d*sin(e + f*x))^(m + 2),x)","\int \frac{\left(C\,{\sin\left(e+f\,x\right)}^2+A\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{m+2}} \,d x","Not used",1,"int(((A + C*sin(e + f*x)^2)*(a + a*sin(e + f*x))^m)/(c + d*sin(e + f*x))^(m + 2), x)","F"
11,0,-1,385,0.000000,"\text{Not used}","int((A + C*sin(e + f*x)^2)*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^(3/2),x)","\int \left(C\,{\sin\left(e+f\,x\right)}^2+A\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2} \,d x","Not used",1,"int((A + C*sin(e + f*x)^2)*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^(3/2), x)","F"
12,0,-1,375,0.000000,"\text{Not used}","int((A + C*sin(e + f*x)^2)*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^(1/2),x)","\int \left(C\,{\sin\left(e+f\,x\right)}^2+A\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\sqrt{c+d\,\sin\left(e+f\,x\right)} \,d x","Not used",1,"int((A + C*sin(e + f*x)^2)*(a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^(1/2), x)","F"
13,0,-1,365,0.000000,"\text{Not used}","int(((A + C*sin(e + f*x)^2)*(a + a*sin(e + f*x))^m)/(c + d*sin(e + f*x))^(1/2),x)","\int \frac{\left(C\,{\sin\left(e+f\,x\right)}^2+A\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((A + C*sin(e + f*x)^2)*(a + a*sin(e + f*x))^m)/(c + d*sin(e + f*x))^(1/2), x)","F"
14,0,-1,413,0.000000,"\text{Not used}","int(((A + C*sin(e + f*x)^2)*(a + a*sin(e + f*x))^m)/(c + d*sin(e + f*x))^(3/2),x)","\int \frac{\left(C\,{\sin\left(e+f\,x\right)}^2+A\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((A + C*sin(e + f*x)^2)*(a + a*sin(e + f*x))^m)/(c + d*sin(e + f*x))^(3/2), x)","F"
15,0,-1,424,0.000000,"\text{Not used}","int(((A + C*sin(e + f*x)^2)*(a + a*sin(e + f*x))^m)/(c + d*sin(e + f*x))^(5/2),x)","\int \frac{\left(C\,{\sin\left(e+f\,x\right)}^2+A\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((A + C*sin(e + f*x)^2)*(a + a*sin(e + f*x))^m)/(c + d*sin(e + f*x))^(5/2), x)","F"
16,0,-1,174,0.000000,"\text{Not used}","int((A + B*sin(e + f*x) + C*sin(e + f*x)^2)/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(3/2)),x)","\int \frac{C\,{\sin\left(e+f\,x\right)}^2+B\,\sin\left(e+f\,x\right)+A}{\sqrt{a+a\,\sin\left(e+f\,x\right)}\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int((A + B*sin(e + f*x) + C*sin(e + f*x)^2)/((a + a*sin(e + f*x))^(1/2)*(c - c*sin(e + f*x))^(3/2)), x)","F"
17,0,-1,269,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n*(A + B*sin(e + f*x) + C*sin(e + f*x)^2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c-c\,\sin\left(e+f\,x\right)\right)}^n\,\left(C\,{\sin\left(e+f\,x\right)}^2+B\,\sin\left(e+f\,x\right)+A\right) \,d x","Not used",1,"int((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^n*(A + B*sin(e + f*x) + C*sin(e + f*x)^2), x)","F"
18,1,1253,435,22.847140,"\text{Not used}","int((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(5/2)*(A + B*sin(e + f*x) + C*sin(e + f*x)^2),x)","\frac{\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{C\,c^2\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(m^4\,16{}\mathrm{i}+m^3\,128{}\mathrm{i}+m^2\,344{}\mathrm{i}+m\,352{}\mathrm{i}+105{}\mathrm{i}\right)}{8\,f\,\left(m^5\,32{}\mathrm{i}+m^4\,400{}\mathrm{i}+m^3\,1840{}\mathrm{i}+m^2\,3800{}\mathrm{i}+m\,3378{}\mathrm{i}+945{}\mathrm{i}\right)}+\frac{c^2\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(18900\,A-14175\,B+12285\,C+15648\,A\,m-4140\,B\,m+648\,C\,m+5280\,A\,m^2+896\,A\,m^3+64\,A\,m^4-832\,B\,m^2-208\,B\,m^3-16\,B\,m^4+1416\,C\,m^2+224\,C\,m^3+16\,C\,m^4\right)}{4\,f\,\left(m^5\,32{}\mathrm{i}+m^4\,400{}\mathrm{i}+m^3\,1840{}\mathrm{i}+m^2\,3800{}\mathrm{i}+m\,3378{}\mathrm{i}+945{}\mathrm{i}\right)}+\frac{c^2\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(A\,18900{}\mathrm{i}-B\,14175{}\mathrm{i}+C\,12285{}\mathrm{i}+A\,m\,15648{}\mathrm{i}-B\,m\,4140{}\mathrm{i}+C\,m\,648{}\mathrm{i}+A\,m^2\,5280{}\mathrm{i}+A\,m^3\,896{}\mathrm{i}+A\,m^4\,64{}\mathrm{i}-B\,m^2\,832{}\mathrm{i}-B\,m^3\,208{}\mathrm{i}-B\,m^4\,16{}\mathrm{i}+C\,m^2\,1416{}\mathrm{i}+C\,m^3\,224{}\mathrm{i}+C\,m^4\,16{}\mathrm{i}\right)}{4\,f\,\left(m^5\,32{}\mathrm{i}+m^4\,400{}\mathrm{i}+m^3\,1840{}\mathrm{i}+m^2\,3800{}\mathrm{i}+m\,3378{}\mathrm{i}+945{}\mathrm{i}\right)}+\frac{C\,c^2\,{\mathrm{e}}^{e\,9{}\mathrm{i}+f\,x\,9{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(16\,m^4+128\,m^3+344\,m^2+352\,m+105\right)}{8\,f\,\left(m^5\,32{}\mathrm{i}+m^4\,400{}\mathrm{i}+m^3\,1840{}\mathrm{i}+m^2\,3800{}\mathrm{i}+m\,3378{}\mathrm{i}+945{}\mathrm{i}\right)}-\frac{c^2\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(4\,m^2+8\,m+3\right)\,\left(126\,A-315\,B+378\,C+64\,A\,m-124\,B\,m+88\,C\,m+8\,A\,m^2-12\,B\,m^2+8\,C\,m^2\right)}{4\,f\,\left(m^5\,32{}\mathrm{i}+m^4\,400{}\mathrm{i}+m^3\,1840{}\mathrm{i}+m^2\,3800{}\mathrm{i}+m\,3378{}\mathrm{i}+945{}\mathrm{i}\right)}-\frac{c^2\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(4\,m^2+8\,m+3\right)\,\left(A\,126{}\mathrm{i}-B\,315{}\mathrm{i}+C\,378{}\mathrm{i}+A\,m\,64{}\mathrm{i}-B\,m\,124{}\mathrm{i}+C\,m\,88{}\mathrm{i}+A\,m^2\,8{}\mathrm{i}-B\,m^2\,12{}\mathrm{i}+C\,m^2\,8{}\mathrm{i}\right)}{4\,f\,\left(m^5\,32{}\mathrm{i}+m^4\,400{}\mathrm{i}+m^3\,1840{}\mathrm{i}+m^2\,3800{}\mathrm{i}+m\,3378{}\mathrm{i}+945{}\mathrm{i}\right)}+\frac{c^2\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\left(2\,m+1\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(3150\,A-3465\,B+3150\,C+2356\,A\,m-1706\,B\,m+828\,C\,m+584\,A\,m^2+48\,A\,m^3-316\,B\,m^2-24\,B\,m^3+200\,C\,m^2+16\,C\,m^3\right)}{4\,f\,\left(m^5\,32{}\mathrm{i}+m^4\,400{}\mathrm{i}+m^3\,1840{}\mathrm{i}+m^2\,3800{}\mathrm{i}+m\,3378{}\mathrm{i}+945{}\mathrm{i}\right)}+\frac{c^2\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,\left(2\,m+1\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(A\,3150{}\mathrm{i}-B\,3465{}\mathrm{i}+C\,3150{}\mathrm{i}+A\,m\,2356{}\mathrm{i}-B\,m\,1706{}\mathrm{i}+C\,m\,828{}\mathrm{i}+A\,m^2\,584{}\mathrm{i}+A\,m^3\,48{}\mathrm{i}-B\,m^2\,316{}\mathrm{i}-B\,m^3\,24{}\mathrm{i}+C\,m^2\,200{}\mathrm{i}+C\,m^3\,16{}\mathrm{i}\right)}{4\,f\,\left(m^5\,32{}\mathrm{i}+m^4\,400{}\mathrm{i}+m^3\,1840{}\mathrm{i}+m^2\,3800{}\mathrm{i}+m\,3378{}\mathrm{i}+945{}\mathrm{i}\right)}+\frac{c^2\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(8\,m^3+36\,m^2+46\,m+15\right)\,\left(18\,B-45\,C+4\,B\,m-6\,C\,m\right)}{8\,f\,\left(m^5\,32{}\mathrm{i}+m^4\,400{}\mathrm{i}+m^3\,1840{}\mathrm{i}+m^2\,3800{}\mathrm{i}+m\,3378{}\mathrm{i}+945{}\mathrm{i}\right)}+\frac{c^2\,{\mathrm{e}}^{e\,8{}\mathrm{i}+f\,x\,8{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(8\,m^3+36\,m^2+46\,m+15\right)\,\left(B\,18{}\mathrm{i}-C\,45{}\mathrm{i}+B\,m\,4{}\mathrm{i}-C\,m\,6{}\mathrm{i}\right)}{8\,f\,\left(m^5\,32{}\mathrm{i}+m^4\,400{}\mathrm{i}+m^3\,1840{}\mathrm{i}+m^2\,3800{}\mathrm{i}+m\,3378{}\mathrm{i}+945{}\mathrm{i}\right)}\right)}{{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}+\frac{{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,\left(32\,m^5+400\,m^4+1840\,m^3+3800\,m^2+3378\,m+945\right)}{m^5\,32{}\mathrm{i}+m^4\,400{}\mathrm{i}+m^3\,1840{}\mathrm{i}+m^2\,3800{}\mathrm{i}+m\,3378{}\mathrm{i}+945{}\mathrm{i}}}","Not used",1,"((c - c*sin(e + f*x))^(1/2)*((C*c^2*(a + a*sin(e + f*x))^m*(m*352i + m^2*344i + m^3*128i + m^4*16i + 105i))/(8*f*(m*3378i + m^2*3800i + m^3*1840i + m^4*400i + m^5*32i + 945i)) + (c^2*exp(e*5i + f*x*5i)*(a + a*sin(e + f*x))^m*(18900*A - 14175*B + 12285*C + 15648*A*m - 4140*B*m + 648*C*m + 5280*A*m^2 + 896*A*m^3 + 64*A*m^4 - 832*B*m^2 - 208*B*m^3 - 16*B*m^4 + 1416*C*m^2 + 224*C*m^3 + 16*C*m^4))/(4*f*(m*3378i + m^2*3800i + m^3*1840i + m^4*400i + m^5*32i + 945i)) + (c^2*exp(e*4i + f*x*4i)*(a + a*sin(e + f*x))^m*(A*18900i - B*14175i + C*12285i + A*m*15648i - B*m*4140i + C*m*648i + A*m^2*5280i + A*m^3*896i + A*m^4*64i - B*m^2*832i - B*m^3*208i - B*m^4*16i + C*m^2*1416i + C*m^3*224i + C*m^4*16i))/(4*f*(m*3378i + m^2*3800i + m^3*1840i + m^4*400i + m^5*32i + 945i)) + (C*c^2*exp(e*9i + f*x*9i)*(a + a*sin(e + f*x))^m*(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105))/(8*f*(m*3378i + m^2*3800i + m^3*1840i + m^4*400i + m^5*32i + 945i)) - (c^2*exp(e*7i + f*x*7i)*(a + a*sin(e + f*x))^m*(8*m + 4*m^2 + 3)*(126*A - 315*B + 378*C + 64*A*m - 124*B*m + 88*C*m + 8*A*m^2 - 12*B*m^2 + 8*C*m^2))/(4*f*(m*3378i + m^2*3800i + m^3*1840i + m^4*400i + m^5*32i + 945i)) - (c^2*exp(e*2i + f*x*2i)*(a + a*sin(e + f*x))^m*(8*m + 4*m^2 + 3)*(A*126i - B*315i + C*378i + A*m*64i - B*m*124i + C*m*88i + A*m^2*8i - B*m^2*12i + C*m^2*8i))/(4*f*(m*3378i + m^2*3800i + m^3*1840i + m^4*400i + m^5*32i + 945i)) + (c^2*exp(e*3i + f*x*3i)*(2*m + 1)*(a + a*sin(e + f*x))^m*(3150*A - 3465*B + 3150*C + 2356*A*m - 1706*B*m + 828*C*m + 584*A*m^2 + 48*A*m^3 - 316*B*m^2 - 24*B*m^3 + 200*C*m^2 + 16*C*m^3))/(4*f*(m*3378i + m^2*3800i + m^3*1840i + m^4*400i + m^5*32i + 945i)) + (c^2*exp(e*6i + f*x*6i)*(2*m + 1)*(a + a*sin(e + f*x))^m*(A*3150i - B*3465i + C*3150i + A*m*2356i - B*m*1706i + C*m*828i + A*m^2*584i + A*m^3*48i - B*m^2*316i - B*m^3*24i + C*m^2*200i + C*m^3*16i))/(4*f*(m*3378i + m^2*3800i + m^3*1840i + m^4*400i + m^5*32i + 945i)) + (c^2*exp(e*1i + f*x*1i)*(a + a*sin(e + f*x))^m*(46*m + 36*m^2 + 8*m^3 + 15)*(18*B - 45*C + 4*B*m - 6*C*m))/(8*f*(m*3378i + m^2*3800i + m^3*1840i + m^4*400i + m^5*32i + 945i)) + (c^2*exp(e*8i + f*x*8i)*(a + a*sin(e + f*x))^m*(46*m + 36*m^2 + 8*m^3 + 15)*(B*18i - C*45i + B*m*4i - C*m*6i))/(8*f*(m*3378i + m^2*3800i + m^3*1840i + m^4*400i + m^5*32i + 945i))))/(exp(e*5i + f*x*5i) + (exp(e*4i + f*x*4i)*(3378*m + 3800*m^2 + 1840*m^3 + 400*m^4 + 32*m^5 + 945))/(m*3378i + m^2*3800i + m^3*1840i + m^4*400i + m^5*32i + 945i))","B"
19,1,790,322,23.158798,"\text{Not used}","int((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(3/2)*(A + B*sin(e + f*x) + C*sin(e + f*x)^2),x)","\frac{\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(\frac{C\,c\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(m^3\,8{}\mathrm{i}+m^2\,36{}\mathrm{i}+m\,46{}\mathrm{i}+15{}\mathrm{i}\right)}{4\,f\,\left(16\,m^4+128\,m^3+344\,m^2+352\,m+105\right)}+\frac{c\,{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(1260\,A-840\,B+735\,C+1144\,A\,m-128\,B\,m-18\,C\,m+336\,A\,m^2+32\,A\,m^3+32\,B\,m^2+100\,C\,m^2+8\,C\,m^3\right)}{4\,f\,\left(16\,m^4+128\,m^3+344\,m^2+352\,m+105\right)}-\frac{c\,{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(A\,1260{}\mathrm{i}-B\,840{}\mathrm{i}+C\,735{}\mathrm{i}+A\,m\,1144{}\mathrm{i}-B\,m\,128{}\mathrm{i}-C\,m\,18{}\mathrm{i}+A\,m^2\,336{}\mathrm{i}+A\,m^3\,32{}\mathrm{i}+B\,m^2\,32{}\mathrm{i}+C\,m^2\,100{}\mathrm{i}+C\,m^3\,8{}\mathrm{i}\right)}{4\,f\,\left(16\,m^4+128\,m^3+344\,m^2+352\,m+105\right)}+\frac{c\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,\left(2\,m+1\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(140\,A-210\,B+175\,C+96\,A\,m-88\,B\,m+16\,C\,m+16\,A\,m^2-8\,B\,m^2+4\,C\,m^2\right)}{4\,f\,\left(16\,m^4+128\,m^3+344\,m^2+352\,m+105\right)}-\frac{c\,{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,\left(2\,m+1\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(A\,140{}\mathrm{i}-B\,210{}\mathrm{i}+C\,175{}\mathrm{i}+A\,m\,96{}\mathrm{i}-B\,m\,88{}\mathrm{i}+C\,m\,16{}\mathrm{i}+A\,m^2\,16{}\mathrm{i}-B\,m^2\,8{}\mathrm{i}+C\,m^2\,4{}\mathrm{i}\right)}{4\,f\,\left(16\,m^4+128\,m^3+344\,m^2+352\,m+105\right)}+\frac{c\,{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(4\,m^2+8\,m+3\right)\,\left(14\,B-21\,C+4\,B\,m-2\,C\,m\right)}{4\,f\,\left(16\,m^4+128\,m^3+344\,m^2+352\,m+105\right)}-\frac{c\,{\mathrm{e}}^{e\,6{}\mathrm{i}+f\,x\,6{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(4\,m^2+8\,m+3\right)\,\left(B\,14{}\mathrm{i}-C\,21{}\mathrm{i}+B\,m\,4{}\mathrm{i}-C\,m\,2{}\mathrm{i}\right)}{4\,f\,\left(16\,m^4+128\,m^3+344\,m^2+352\,m+105\right)}-\frac{C\,c\,{\mathrm{e}}^{e\,7{}\mathrm{i}+f\,x\,7{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(8\,m^3+36\,m^2+46\,m+15\right)}{4\,f\,\left(16\,m^4+128\,m^3+344\,m^2+352\,m+105\right)}\right)}{{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}-\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,\left(m^4\,16{}\mathrm{i}+m^3\,128{}\mathrm{i}+m^2\,344{}\mathrm{i}+m\,352{}\mathrm{i}+105{}\mathrm{i}\right)}{16\,m^4+128\,m^3+344\,m^2+352\,m+105}}","Not used",1,"((c - c*sin(e + f*x))^(1/2)*((C*c*(a + a*sin(e + f*x))^m*(m*46i + m^2*36i + m^3*8i + 15i))/(4*f*(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105)) + (c*exp(e*3i + f*x*3i)*(a + a*sin(e + f*x))^m*(1260*A - 840*B + 735*C + 1144*A*m - 128*B*m - 18*C*m + 336*A*m^2 + 32*A*m^3 + 32*B*m^2 + 100*C*m^2 + 8*C*m^3))/(4*f*(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105)) - (c*exp(e*4i + f*x*4i)*(a + a*sin(e + f*x))^m*(A*1260i - B*840i + C*735i + A*m*1144i - B*m*128i - C*m*18i + A*m^2*336i + A*m^3*32i + B*m^2*32i + C*m^2*100i + C*m^3*8i))/(4*f*(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105)) + (c*exp(e*5i + f*x*5i)*(2*m + 1)*(a + a*sin(e + f*x))^m*(140*A - 210*B + 175*C + 96*A*m - 88*B*m + 16*C*m + 16*A*m^2 - 8*B*m^2 + 4*C*m^2))/(4*f*(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105)) - (c*exp(e*2i + f*x*2i)*(2*m + 1)*(a + a*sin(e + f*x))^m*(A*140i - B*210i + C*175i + A*m*96i - B*m*88i + C*m*16i + A*m^2*16i - B*m^2*8i + C*m^2*4i))/(4*f*(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105)) + (c*exp(e*1i + f*x*1i)*(a + a*sin(e + f*x))^m*(8*m + 4*m^2 + 3)*(14*B - 21*C + 4*B*m - 2*C*m))/(4*f*(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105)) - (c*exp(e*6i + f*x*6i)*(a + a*sin(e + f*x))^m*(8*m + 4*m^2 + 3)*(B*14i - C*21i + B*m*4i - C*m*2i))/(4*f*(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105)) - (C*c*exp(e*7i + f*x*7i)*(a + a*sin(e + f*x))^m*(46*m + 36*m^2 + 8*m^3 + 15))/(4*f*(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105))))/(exp(e*4i + f*x*4i) - (exp(e*3i + f*x*3i)*(m*352i + m^2*344i + m^3*128i + m^4*16i + 105i))/(352*m + 344*m^2 + 128*m^3 + 16*m^4 + 105))","B"
20,1,510,197,19.421628,"\text{Not used}","int((a + a*sin(e + f*x))^m*(c - c*sin(e + f*x))^(1/2)*(A + B*sin(e + f*x) + C*sin(e + f*x)^2),x)","-\frac{\sqrt{c-c\,\sin\left(e+f\,x\right)}\,\left(-\frac{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(30\,A-15\,B+15\,C+32\,A\,m+4\,B\,m+8\,A\,m^2+4\,B\,m^2+4\,C\,m^2\right)}{f\,\left(m^3\,8{}\mathrm{i}+m^2\,36{}\mathrm{i}+m\,46{}\mathrm{i}+15{}\mathrm{i}\right)}-\frac{{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(A\,30{}\mathrm{i}-B\,15{}\mathrm{i}+C\,15{}\mathrm{i}+A\,m\,32{}\mathrm{i}+B\,m\,4{}\mathrm{i}+A\,m^2\,8{}\mathrm{i}+B\,m^2\,4{}\mathrm{i}+C\,m^2\,4{}\mathrm{i}\right)}{f\,\left(m^3\,8{}\mathrm{i}+m^2\,36{}\mathrm{i}+m\,46{}\mathrm{i}+15{}\mathrm{i}\right)}+\frac{C\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(m^2\,4{}\mathrm{i}+m\,8{}\mathrm{i}+3{}\mathrm{i}\right)}{2\,f\,\left(m^3\,8{}\mathrm{i}+m^2\,36{}\mathrm{i}+m\,46{}\mathrm{i}+15{}\mathrm{i}\right)}+\frac{C\,{\mathrm{e}}^{e\,5{}\mathrm{i}+f\,x\,5{}\mathrm{i}}\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(4\,m^2+8\,m+3\right)}{2\,f\,\left(m^3\,8{}\mathrm{i}+m^2\,36{}\mathrm{i}+m\,46{}\mathrm{i}+15{}\mathrm{i}\right)}+\frac{{\mathrm{e}}^{e\,1{}\mathrm{i}+f\,x\,1{}\mathrm{i}}\,\left(2\,m+1\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(10\,B-5\,C+4\,B\,m+2\,C\,m\right)}{2\,f\,\left(m^3\,8{}\mathrm{i}+m^2\,36{}\mathrm{i}+m\,46{}\mathrm{i}+15{}\mathrm{i}\right)}+\frac{{\mathrm{e}}^{e\,4{}\mathrm{i}+f\,x\,4{}\mathrm{i}}\,\left(2\,m+1\right)\,{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(B\,10{}\mathrm{i}-C\,5{}\mathrm{i}+B\,m\,4{}\mathrm{i}+C\,m\,2{}\mathrm{i}\right)}{2\,f\,\left(m^3\,8{}\mathrm{i}+m^2\,36{}\mathrm{i}+m\,46{}\mathrm{i}+15{}\mathrm{i}\right)}\right)}{{\mathrm{e}}^{e\,3{}\mathrm{i}+f\,x\,3{}\mathrm{i}}+\frac{{\mathrm{e}}^{e\,2{}\mathrm{i}+f\,x\,2{}\mathrm{i}}\,\left(8\,m^3+36\,m^2+46\,m+15\right)}{m^3\,8{}\mathrm{i}+m^2\,36{}\mathrm{i}+m\,46{}\mathrm{i}+15{}\mathrm{i}}}","Not used",1,"-((c - c*sin(e + f*x))^(1/2)*((C*(a + a*sin(e + f*x))^m*(m*8i + m^2*4i + 3i))/(2*f*(m*46i + m^2*36i + m^3*8i + 15i)) - (exp(e*2i + f*x*2i)*(a + a*sin(e + f*x))^m*(A*30i - B*15i + C*15i + A*m*32i + B*m*4i + A*m^2*8i + B*m^2*4i + C*m^2*4i))/(f*(m*46i + m^2*36i + m^3*8i + 15i)) - (exp(e*3i + f*x*3i)*(a + a*sin(e + f*x))^m*(30*A - 15*B + 15*C + 32*A*m + 4*B*m + 8*A*m^2 + 4*B*m^2 + 4*C*m^2))/(f*(m*46i + m^2*36i + m^3*8i + 15i)) + (C*exp(e*5i + f*x*5i)*(a + a*sin(e + f*x))^m*(8*m + 4*m^2 + 3))/(2*f*(m*46i + m^2*36i + m^3*8i + 15i)) + (exp(e*1i + f*x*1i)*(2*m + 1)*(a + a*sin(e + f*x))^m*(10*B - 5*C + 4*B*m + 2*C*m))/(2*f*(m*46i + m^2*36i + m^3*8i + 15i)) + (exp(e*4i + f*x*4i)*(2*m + 1)*(a + a*sin(e + f*x))^m*(B*10i - C*5i + B*m*4i + C*m*2i))/(2*f*(m*46i + m^2*36i + m^3*8i + 15i))))/(exp(e*3i + f*x*3i) + (exp(e*2i + f*x*2i)*(46*m + 36*m^2 + 8*m^3 + 15))/(m*46i + m^2*36i + m^3*8i + 15i))","B"
21,0,-1,170,0.000000,"\text{Not used}","int(((a + a*sin(e + f*x))^m*(A + B*sin(e + f*x) + C*sin(e + f*x)^2))/(c - c*sin(e + f*x))^(1/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(C\,{\sin\left(e+f\,x\right)}^2+B\,\sin\left(e+f\,x\right)+A\right)}{\sqrt{c-c\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((a + a*sin(e + f*x))^m*(A + B*sin(e + f*x) + C*sin(e + f*x)^2))/(c - c*sin(e + f*x))^(1/2), x)","F"
22,0,-1,216,0.000000,"\text{Not used}","int(((a + a*sin(e + f*x))^m*(A + B*sin(e + f*x) + C*sin(e + f*x)^2))/(c - c*sin(e + f*x))^(3/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(C\,{\sin\left(e+f\,x\right)}^2+B\,\sin\left(e+f\,x\right)+A\right)}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((a + a*sin(e + f*x))^m*(A + B*sin(e + f*x) + C*sin(e + f*x)^2))/(c - c*sin(e + f*x))^(3/2), x)","F"
23,0,-1,230,0.000000,"\text{Not used}","int(((a + a*sin(e + f*x))^m*(A + B*sin(e + f*x) + C*sin(e + f*x)^2))/(c - c*sin(e + f*x))^(5/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(C\,{\sin\left(e+f\,x\right)}^2+B\,\sin\left(e+f\,x\right)+A\right)}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((a + a*sin(e + f*x))^m*(A + B*sin(e + f*x) + C*sin(e + f*x)^2))/(c - c*sin(e + f*x))^(5/2), x)","F"
24,0,-1,232,0.000000,"\text{Not used}","int(((a + a*sin(e + f*x))^m*(A + B*sin(e + f*x) + C*sin(e + f*x)^2))/(c - c*sin(e + f*x))^(m + 2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(C\,{\sin\left(e+f\,x\right)}^2+B\,\sin\left(e+f\,x\right)+A\right)}{{\left(c-c\,\sin\left(e+f\,x\right)\right)}^{m+2}} \,d x","Not used",1,"int(((a + a*sin(e + f*x))^m*(A + B*sin(e + f*x) + C*sin(e + f*x)^2))/(c - c*sin(e + f*x))^(m + 2), x)","F"
25,0,-1,383,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^n*(A + B*sin(e + f*x) + C*sin(e + f*x)^2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n\,\left(C\,{\sin\left(e+f\,x\right)}^2+B\,\sin\left(e+f\,x\right)+A\right) \,d x","Not used",1,"int((a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^n*(A + B*sin(e + f*x) + C*sin(e + f*x)^2), x)","F"
26,0,-1,410,0.000000,"\text{Not used}","int(((a + a*sin(e + f*x))^m*(A + B*sin(e + f*x) + C*sin(e + f*x)^2))/(c + d*sin(e + f*x))^(m + 2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(C\,{\sin\left(e+f\,x\right)}^2+B\,\sin\left(e+f\,x\right)+A\right)}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{m+2}} \,d x","Not used",1,"int(((a + a*sin(e + f*x))^m*(A + B*sin(e + f*x) + C*sin(e + f*x)^2))/(c + d*sin(e + f*x))^(m + 2), x)","F"
27,0,-1,406,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^(3/2)*(A + B*sin(e + f*x) + C*sin(e + f*x)^2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}\,\left(C\,{\sin\left(e+f\,x\right)}^2+B\,\sin\left(e+f\,x\right)+A\right) \,d x","Not used",1,"int((a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^(3/2)*(A + B*sin(e + f*x) + C*sin(e + f*x)^2), x)","F"
28,0,-1,396,0.000000,"\text{Not used}","int((a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^(1/2)*(A + B*sin(e + f*x) + C*sin(e + f*x)^2),x)","\int {\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\sqrt{c+d\,\sin\left(e+f\,x\right)}\,\left(C\,{\sin\left(e+f\,x\right)}^2+B\,\sin\left(e+f\,x\right)+A\right) \,d x","Not used",1,"int((a + a*sin(e + f*x))^m*(c + d*sin(e + f*x))^(1/2)*(A + B*sin(e + f*x) + C*sin(e + f*x)^2), x)","F"
29,0,-1,389,0.000000,"\text{Not used}","int(((a + a*sin(e + f*x))^m*(A + B*sin(e + f*x) + C*sin(e + f*x)^2))/(c + d*sin(e + f*x))^(1/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(C\,{\sin\left(e+f\,x\right)}^2+B\,\sin\left(e+f\,x\right)+A\right)}{\sqrt{c+d\,\sin\left(e+f\,x\right)}} \,d x","Not used",1,"int(((a + a*sin(e + f*x))^m*(A + B*sin(e + f*x) + C*sin(e + f*x)^2))/(c + d*sin(e + f*x))^(1/2), x)","F"
30,0,-1,433,0.000000,"\text{Not used}","int(((a + a*sin(e + f*x))^m*(A + B*sin(e + f*x) + C*sin(e + f*x)^2))/(c + d*sin(e + f*x))^(3/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(C\,{\sin\left(e+f\,x\right)}^2+B\,\sin\left(e+f\,x\right)+A\right)}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{3/2}} \,d x","Not used",1,"int(((a + a*sin(e + f*x))^m*(A + B*sin(e + f*x) + C*sin(e + f*x)^2))/(c + d*sin(e + f*x))^(3/2), x)","F"
31,0,-1,451,0.000000,"\text{Not used}","int(((a + a*sin(e + f*x))^m*(A + B*sin(e + f*x) + C*sin(e + f*x)^2))/(c + d*sin(e + f*x))^(5/2),x)","\int \frac{{\left(a+a\,\sin\left(e+f\,x\right)\right)}^m\,\left(C\,{\sin\left(e+f\,x\right)}^2+B\,\sin\left(e+f\,x\right)+A\right)}{{\left(c+d\,\sin\left(e+f\,x\right)\right)}^{5/2}} \,d x","Not used",1,"int(((a + a*sin(e + f*x))^m*(A + B*sin(e + f*x) + C*sin(e + f*x)^2))/(c + d*sin(e + f*x))^(5/2), x)","F"
32,1,93,81,13.757696,"\text{Not used}","int((a + b*sin(c + d*x))*(A + B*sin(c + d*x) + C*sin(c + d*x)^2),x)","-\frac{6\,A\,b\,\cos\left(c+d\,x\right)+6\,B\,a\,\cos\left(c+d\,x\right)+\frac{9\,C\,b\,\cos\left(c+d\,x\right)}{2}-\frac{C\,b\,\cos\left(3\,c+3\,d\,x\right)}{2}+\frac{3\,B\,b\,\sin\left(2\,c+2\,d\,x\right)}{2}+\frac{3\,C\,a\,\sin\left(2\,c+2\,d\,x\right)}{2}-6\,A\,a\,d\,x-3\,B\,b\,d\,x-3\,C\,a\,d\,x}{6\,d}","Not used",1,"-(6*A*b*cos(c + d*x) + 6*B*a*cos(c + d*x) + (9*C*b*cos(c + d*x))/2 - (C*b*cos(3*c + 3*d*x))/2 + (3*B*b*sin(2*c + 2*d*x))/2 + (3*C*a*sin(2*c + 2*d*x))/2 - 6*A*a*d*x - 3*B*b*d*x - 3*C*a*d*x)/(6*d)","B"
33,1,169,117,14.847208,"\text{Not used}","int(((a + b*sin(e + f*x))*(A + B*sin(e + f*x) + C*sin(e + f*x)^2))/sin(e + f*x)^(3/2),x)","\frac{2\,B\,b\,\mathrm{E}\left(\frac{e}{2}-\frac{\pi }{4}+\frac{f\,x}{2}\middle|2\right)}{f}-\frac{2\,B\,a\,\mathrm{F}\left(\frac{\pi }{4}-\frac{e}{2}-\frac{f\,x}{2}\middle|2\right)}{f}-\frac{2\,A\,b\,\mathrm{F}\left(\frac{\pi }{4}-\frac{e}{2}-\frac{f\,x}{2}\middle|2\right)}{f}+\frac{2\,C\,a\,\mathrm{E}\left(\frac{e}{2}-\frac{\pi }{4}+\frac{f\,x}{2}\middle|2\right)}{f}-\frac{A\,a\,\cos\left(e+f\,x\right)\,{\left({\sin\left(e+f\,x\right)}^2\right)}^{1/4}\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{2},\frac{5}{4};\ \frac{3}{2};\ {\cos\left(e+f\,x\right)}^2\right)}{f\,\sqrt{\sin\left(e+f\,x\right)}}-\frac{C\,b\,\cos\left(e+f\,x\right)\,{\sin\left(e+f\,x\right)}^{5/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{4},\frac{1}{2};\ \frac{3}{2};\ {\cos\left(e+f\,x\right)}^2\right)}{f\,{\left({\sin\left(e+f\,x\right)}^2\right)}^{5/4}}","Not used",1,"(2*B*b*ellipticE(e/2 - pi/4 + (f*x)/2, 2))/f - (2*B*a*ellipticF(pi/4 - e/2 - (f*x)/2, 2))/f - (2*A*b*ellipticF(pi/4 - e/2 - (f*x)/2, 2))/f + (2*C*a*ellipticE(e/2 - pi/4 + (f*x)/2, 2))/f - (A*a*cos(e + f*x)*(sin(e + f*x)^2)^(1/4)*hypergeom([1/2, 5/4], 3/2, cos(e + f*x)^2))/(f*sin(e + f*x)^(1/2)) - (C*b*cos(e + f*x)*sin(e + f*x)^(5/2)*hypergeom([-1/4, 1/2], 3/2, cos(e + f*x)^2))/(f*(sin(e + f*x)^2)^(5/4))","B"
34,0,-1,48,0.000000,"\text{Not used}","int((a + b*sin(e + f*x))^m*(c + d*sin(e + f*x))^n*(A + B*sin(e + f*x) + C*sin(e + f*x)^2),x)","\int {\left(a+b\,\sin\left(e+f\,x\right)\right)}^m\,{\left(c+d\,\sin\left(e+f\,x\right)\right)}^n\,\left(C\,{\sin\left(e+f\,x\right)}^2+B\,\sin\left(e+f\,x\right)+A\right) \,d x","Not used",0,"int((a + b*sin(e + f*x))^m*(c + d*sin(e + f*x))^n*(A + B*sin(e + f*x) + C*sin(e + f*x)^2), x)","F"