1,1,110,107,0.0601727,"\int F^{c (a+b x)} \sin ^n(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Sin[d + e*x]^n,x]","\frac{\left(1-e^{2 i (d+e x)}\right)^{-n} F^{c (a+b x)} \sin ^n(d+e x) \, _2F_1\left(-n,-\frac{i (b c \log (F)-i e n)}{2 e};1-\frac{i (b c \log (F)-i e n)}{2 e};e^{2 i (d+e x)}\right)}{b c \log (F)-i e n}","-\frac{\left(1-e^{2 i (d+e x)}\right)^{-n} F^{c (a+b x)} \sin ^n(d+e x) \, _2F_1\left(-n,-\frac{e n+i b c \log (F)}{2 e};\frac{1}{2} \left(-n-\frac{i b c \log (F)}{e}+2\right);e^{2 i (d+e x)}\right)}{-b c \log (F)+i e n}",1,"(F^(c*(a + b*x))*Hypergeometric2F1[-n, ((-1/2*I)*((-I)*e*n + b*c*Log[F]))/e, 1 - ((I/2)*((-I)*e*n + b*c*Log[F]))/e, E^((2*I)*(d + e*x))]*Sin[d + e*x]^n)/((1 - E^((2*I)*(d + e*x)))^n*((-I)*e*n + b*c*Log[F]))","A",1
2,1,154,199,0.7032422,"\int F^{c (a+b x)} \sin ^3(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Sin[d + e*x]^3,x]","\frac{F^{c (a+b x)} \left(3 \cos (3 (d+e x)) \left(b^2 c^2 e \log ^2(F)+e^3\right)-3 e \cos (d+e x) \left(b^2 c^2 \log ^2(F)+9 e^2\right)-2 b c \log (F) \sin (d+e x) \left(\cos (2 (d+e x)) \left(b^2 c^2 \log ^2(F)+e^2\right)-b^2 c^2 \log ^2(F)-13 e^2\right)\right)}{4 \left(b^4 c^4 \log ^4(F)+10 b^2 c^2 e^2 \log ^2(F)+9 e^4\right)}","\frac{b c \log (F) \sin ^3(d+e x) F^{c (a+b x)}}{b^2 c^2 \log ^2(F)+9 e^2}-\frac{3 e \sin ^2(d+e x) \cos (d+e x) F^{c (a+b x)}}{b^2 c^2 \log ^2(F)+9 e^2}+\frac{6 b c e^2 \log (F) \sin (d+e x) F^{c (a+b x)}}{b^4 c^4 \log ^4(F)+10 b^2 c^2 e^2 \log ^2(F)+9 e^4}-\frac{6 e^3 \cos (d+e x) F^{c (a+b x)}}{b^4 c^4 \log ^4(F)+10 b^2 c^2 e^2 \log ^2(F)+9 e^4}",1,"(F^(c*(a + b*x))*(-3*e*Cos[d + e*x]*(9*e^2 + b^2*c^2*Log[F]^2) + 3*Cos[3*(d + e*x)]*(e^3 + b^2*c^2*e*Log[F]^2) - 2*b*c*Log[F]*(-13*e^2 - b^2*c^2*Log[F]^2 + Cos[2*(d + e*x)]*(e^2 + b^2*c^2*Log[F]^2))*Sin[d + e*x]))/(4*(9*e^4 + 10*b^2*c^2*e^2*Log[F]^2 + b^4*c^4*Log[F]^4))","A",1
3,1,86,128,0.2248287,"\int F^{c (a+b x)} \sin ^2(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Sin[d + e*x]^2,x]","\frac{F^{c (a+b x)} \left(-b^2 c^2 \log ^2(F) \cos (2 (d+e x))+b^2 c^2 \log ^2(F)-2 b c e \log (F) \sin (2 (d+e x))+4 e^2\right)}{2 b^3 c^3 \log ^3(F)+8 b c e^2 \log (F)}","\frac{b c \log (F) \sin ^2(d+e x) F^{c (a+b x)}}{b^2 c^2 \log ^2(F)+4 e^2}-\frac{2 e \sin (d+e x) \cos (d+e x) F^{c (a+b x)}}{b^2 c^2 \log ^2(F)+4 e^2}+\frac{2 e^2 F^{c (a+b x)}}{b c \log (F) \left(b^2 c^2 \log ^2(F)+4 e^2\right)}",1,"(F^(c*(a + b*x))*(4*e^2 + b^2*c^2*Log[F]^2 - b^2*c^2*Cos[2*(d + e*x)]*Log[F]^2 - 2*b*c*e*Log[F]*Sin[2*(d + e*x)]))/(8*b*c*e^2*Log[F] + 2*b^3*c^3*Log[F]^3)","A",1
4,1,48,73,0.1249364,"\int F^{c (a+b x)} \sin (d+e x) \, dx","Integrate[F^(c*(a + b*x))*Sin[d + e*x],x]","\frac{F^{c (a+b x)} (b c \log (F) \sin (d+e x)-e \cos (d+e x))}{b^2 c^2 \log ^2(F)+e^2}","\frac{b c \log (F) \sin (d+e x) F^{c (a+b x)}}{b^2 c^2 \log ^2(F)+e^2}-\frac{e \cos (d+e x) F^{c (a+b x)}}{b^2 c^2 \log ^2(F)+e^2}",1,"(F^(c*(a + b*x))*(-(e*Cos[d + e*x]) + b*c*Log[F]*Sin[d + e*x]))/(e^2 + b^2*c^2*Log[F]^2)","A",1
5,1,114,81,1.7475586,"\int F^{c (a+b x)} \csc (d+e x) \, dx","Integrate[F^(c*(a + b*x))*Csc[d + e*x],x]","\frac{i F^{c (a+b x)} \left(\, _2F_1\left(1,-\frac{i b c \log (F)}{e};1-\frac{i b c \log (F)}{e};-\cos (d+e x)-i \sin (d+e x)\right)-\, _2F_1\left(1,-\frac{i b c \log (F)}{e};1-\frac{i b c \log (F)}{e};\cos (d+e x)+i \sin (d+e x)\right)\right)}{b c \log (F)}","-\frac{2 e^{i (d+e x)} F^{c (a+b x)} \, _2F_1\left(1,\frac{e-i b c \log (F)}{2 e};\frac{1}{2} \left(3-\frac{i b c \log (F)}{e}\right);e^{2 i (d+e x)}\right)}{e-i b c \log (F)}",1,"(I*F^(c*(a + b*x))*(Hypergeometric2F1[1, ((-I)*b*c*Log[F])/e, 1 - (I*b*c*Log[F])/e, -Cos[d + e*x] - I*Sin[d + e*x]] - Hypergeometric2F1[1, ((-I)*b*c*Log[F])/e, 1 - (I*b*c*Log[F])/e, Cos[d + e*x] + I*Sin[d + e*x]]))/(b*c*Log[F])","A",1
6,1,101,78,1.4815998,"\int F^{c (a+b x)} \csc ^2(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Csc[d + e*x]^2,x]","-\frac{2 i F^{c (a+b x)} \left(\left(-1+e^{2 i d}\right) \, _2F_1\left(1,-\frac{i b c \log (F)}{2 e};1-\frac{i b c \log (F)}{2 e};e^{2 i (d+e x)}\right)+\sin (d) \csc (d+e x) (\cos (e x)-i \sin (e x))\right)}{\left(-1+e^{2 i d}\right) e}","-\frac{4 e^{2 i (d+e x)} F^{c (a+b x)} \, _2F_1\left(2,1-\frac{i b c \log (F)}{2 e};2-\frac{i b c \log (F)}{2 e};e^{2 i (d+e x)}\right)}{b c \log (F)+2 i e}",1,"((-2*I)*F^(c*(a + b*x))*((-1 + E^((2*I)*d))*Hypergeometric2F1[1, ((-1/2*I)*b*c*Log[F])/e, 1 - ((I/2)*b*c*Log[F])/e, E^((2*I)*(d + e*x))] + Csc[d + e*x]*Sin[d]*(Cos[e*x] - I*Sin[e*x])))/(e*(-1 + E^((2*I)*d)))","A",1
7,1,334,137,7.6700054,"\int F^{c (a+b x)} \csc ^3(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Csc[d + e*x]^3,x]","\frac{F^{c (a+b x)} \left(-\frac{4 i \left(b^2 c^2 \log ^2(F)+e^2\right) \left(1+(i \sin (d)+\cos (d)-1) \, _2F_1\left(1,-\frac{i b c \log (F)}{e};1-\frac{i b c \log (F)}{e};\cos (d+e x)+i \sin (d+e x)\right)\right)}{b c \log (F) (i \sin (d)+\cos (d)-1)}-\frac{4 i \left(b^2 c^2 \log ^2(F)+e^2\right) \left(1-(i \sin (d)+\cos (d)+1) \, _2F_1\left(1,-\frac{i b c \log (F)}{e};1-\frac{i b c \log (F)}{e};-\cos (d+e x)-i \sin (d+e x)\right)\right)}{b c \log (F) (i \sin (d)+\cos (d)+1)}+\csc (d) \left(\frac{4 e^2}{b c \log (F)}+4 b c \log (F)\right)-2 b c \sec \left(\frac{d}{2}\right) \log (F) \sin \left(\frac{e x}{2}\right) \sec \left(\frac{1}{2} (d+e x)\right)+2 b c \csc \left(\frac{d}{2}\right) \log (F) \sin \left(\frac{e x}{2}\right) \csc \left(\frac{1}{2} (d+e x)\right)-4 b c \csc (d) \log (F)-e \csc ^2\left(\frac{1}{2} (d+e x)\right)+e \sec ^2\left(\frac{1}{2} (d+e x)\right)\right)}{8 e^2}","-\frac{e^{i (d+e x)} F^{c (a+b x)} (e+i b c \log (F)) \, _2F_1\left(1,\frac{e-i b c \log (F)}{2 e};\frac{1}{2} \left(3-\frac{i b c \log (F)}{e}\right);e^{2 i (d+e x)}\right)}{e^2}-\frac{b c \log (F) \csc (d+e x) F^{c (a+b x)}}{2 e^2}-\frac{\cot (d+e x) \csc (d+e x) F^{c (a+b x)}}{2 e}",1,"(F^(c*(a + b*x))*(-(e*Csc[(d + e*x)/2]^2) - 4*b*c*Csc[d]*Log[F] + Csc[d]*((4*e^2)/(b*c*Log[F]) + 4*b*c*Log[F]) + e*Sec[(d + e*x)/2]^2 - ((4*I)*(e^2 + b^2*c^2*Log[F]^2)*(1 + Hypergeometric2F1[1, ((-I)*b*c*Log[F])/e, 1 - (I*b*c*Log[F])/e, Cos[d + e*x] + I*Sin[d + e*x]]*(-1 + Cos[d] + I*Sin[d])))/(b*c*Log[F]*(-1 + Cos[d] + I*Sin[d])) - ((4*I)*(e^2 + b^2*c^2*Log[F]^2)*(1 - Hypergeometric2F1[1, ((-I)*b*c*Log[F])/e, 1 - (I*b*c*Log[F])/e, -Cos[d + e*x] - I*Sin[d + e*x]]*(1 + Cos[d] + I*Sin[d])))/(b*c*Log[F]*(1 + Cos[d] + I*Sin[d])) + 2*b*c*Csc[d/2]*Csc[(d + e*x)/2]*Log[F]*Sin[(e*x)/2] - 2*b*c*Log[F]*Sec[d/2]*Sec[(d + e*x)/2]*Sin[(e*x)/2]))/(8*e^2)","B",1
8,1,173,141,2.9573689,"\int F^{c (a+b x)} \csc ^4(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Csc[d + e*x]^4,x]","\frac{F^{c (a+b x)} \left(-\frac{2 i \left(b^2 c^2 \log ^2(F)+4 e^2\right) \left(1+\left(-1+e^{2 i d}\right) \, _2F_1\left(1,-\frac{i b c \log (F)}{2 e};1-\frac{i b c \log (F)}{2 e};e^{2 i (d+e x)}\right)\right)}{-1+e^{2 i d}}+\csc (d) \sin (e x) \csc (d+e x) \left(b^2 c^2 \log ^2(F)+4 e^2\right)-e \csc ^2(d+e x) (b c \log (F)+2 e \cot (d))+2 e^2 \csc (d) \sin (e x) \csc ^3(d+e x)\right)}{6 e^3}","\frac{2 e^{2 i (d+e x)} F^{c (a+b x)} (-b c \log (F)+2 i e) \, _2F_1\left(2,1-\frac{i b c \log (F)}{2 e};2-\frac{i b c \log (F)}{2 e};e^{2 i (d+e x)}\right)}{3 e^2}-\frac{b c \log (F) \csc ^2(d+e x) F^{c (a+b x)}}{6 e^2}-\frac{\cot (d+e x) \csc ^2(d+e x) F^{c (a+b x)}}{3 e}",1,"(F^(c*(a + b*x))*(-(e*Csc[d + e*x]^2*(2*e*Cot[d] + b*c*Log[F])) - ((2*I)*(1 + (-1 + E^((2*I)*d))*Hypergeometric2F1[1, ((-1/2*I)*b*c*Log[F])/e, 1 - ((I/2)*b*c*Log[F])/e, E^((2*I)*(d + e*x))])*(4*e^2 + b^2*c^2*Log[F]^2))/(-1 + E^((2*I)*d)) + 2*e^2*Csc[d]*Csc[d + e*x]^3*Sin[e*x] + Csc[d]*Csc[d + e*x]*(4*e^2 + b^2*c^2*Log[F]^2)*Sin[e*x]))/(6*e^3)","A",1
9,1,33,54,0.0415045,"\int e^x \sin ^4(x) \, dx","Integrate[E^x*Sin[x]^4,x]","\frac{1}{680} e^x (-136 \sin (2 x)+20 \sin (4 x)-68 \cos (2 x)+5 \cos (4 x)+255)","\frac{24 e^x}{85}+\frac{1}{17} e^x \sin ^4(x)+\frac{12}{85} e^x \sin ^2(x)-\frac{4}{17} e^x \sin ^3(x) \cos (x)-\frac{24}{85} e^x \sin (x) \cos (x)",1,"(E^x*(255 - 68*Cos[2*x] + 5*Cos[4*x] - 136*Sin[2*x] + 20*Sin[4*x]))/680","A",1
10,1,110,107,0.0563431,"\int F^{c (a+b x)} \cos ^n(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Cos[d + e*x]^n,x]","\frac{\left(1+e^{2 i (d+e x)}\right)^{-n} F^{c (a+b x)} \cos ^n(d+e x) \, _2F_1\left(-n,-\frac{i (b c \log (F)-i e n)}{2 e};1-\frac{i (b c \log (F)-i e n)}{2 e};-e^{2 i (d+e x)}\right)}{b c \log (F)-i e n}","-\frac{\left(1+e^{2 i (d+e x)}\right)^{-n} F^{c (a+b x)} \cos ^n(d+e x) \, _2F_1\left(-n,-\frac{e n+i b c \log (F)}{2 e};\frac{1}{2} \left(-n-\frac{i b c \log (F)}{e}+2\right);-e^{2 i (d+e x)}\right)}{-b c \log (F)+i e n}",1,"(F^(c*(a + b*x))*Cos[d + e*x]^n*Hypergeometric2F1[-n, ((-1/2*I)*((-I)*e*n + b*c*Log[F]))/e, 1 - ((I/2)*((-I)*e*n + b*c*Log[F]))/e, -E^((2*I)*(d + e*x))])/((1 + E^((2*I)*(d + e*x)))^n*((-I)*e*n + b*c*Log[F]))","A",1
11,1,155,199,0.6665116,"\int F^{c (a+b x)} \cos ^3(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Cos[d + e*x]^3,x]","\frac{F^{c (a+b x)} \left(b c \log (F) \cos (3 (d+e x)) \left(b^2 c^2 \log ^2(F)+e^2\right)+3 b c \log (F) \cos (d+e x) \left(b^2 c^2 \log ^2(F)+9 e^2\right)+6 e \sin (d+e x) \left(\cos (2 (d+e x)) \left(b^2 c^2 \log ^2(F)+e^2\right)+b^2 c^2 \log ^2(F)+5 e^2\right)\right)}{4 \left(b^4 c^4 \log ^4(F)+10 b^2 c^2 e^2 \log ^2(F)+9 e^4\right)}","\frac{b c \log (F) \cos ^3(d+e x) F^{c (a+b x)}}{b^2 c^2 \log ^2(F)+9 e^2}+\frac{3 e \sin (d+e x) \cos ^2(d+e x) F^{c (a+b x)}}{b^2 c^2 \log ^2(F)+9 e^2}+\frac{6 b c e^2 \log (F) \cos (d+e x) F^{c (a+b x)}}{b^4 c^4 \log ^4(F)+10 b^2 c^2 e^2 \log ^2(F)+9 e^4}+\frac{6 e^3 \sin (d+e x) F^{c (a+b x)}}{b^4 c^4 \log ^4(F)+10 b^2 c^2 e^2 \log ^2(F)+9 e^4}",1,"(F^(c*(a + b*x))*(b*c*Cos[3*(d + e*x)]*Log[F]*(e^2 + b^2*c^2*Log[F]^2) + 3*b*c*Cos[d + e*x]*Log[F]*(9*e^2 + b^2*c^2*Log[F]^2) + 6*e*(5*e^2 + b^2*c^2*Log[F]^2 + Cos[2*(d + e*x)]*(e^2 + b^2*c^2*Log[F]^2))*Sin[d + e*x]))/(4*(9*e^4 + 10*b^2*c^2*e^2*Log[F]^2 + b^4*c^4*Log[F]^4))","A",1
12,1,85,128,0.2136024,"\int F^{c (a+b x)} \cos ^2(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Cos[d + e*x]^2,x]","\frac{F^{c (a+b x)} \left(b^2 c^2 \log ^2(F) \cos (2 (d+e x))+b^2 c^2 \log ^2(F)+2 b c e \log (F) \sin (2 (d+e x))+4 e^2\right)}{2 b^3 c^3 \log ^3(F)+8 b c e^2 \log (F)}","\frac{b c \log (F) \cos ^2(d+e x) F^{c (a+b x)}}{b^2 c^2 \log ^2(F)+4 e^2}+\frac{2 e \sin (d+e x) \cos (d+e x) F^{c (a+b x)}}{b^2 c^2 \log ^2(F)+4 e^2}+\frac{2 e^2 F^{c (a+b x)}}{b c \log (F) \left(b^2 c^2 \log ^2(F)+4 e^2\right)}",1,"(F^(c*(a + b*x))*(4*e^2 + b^2*c^2*Log[F]^2 + b^2*c^2*Cos[2*(d + e*x)]*Log[F]^2 + 2*b*c*e*Log[F]*Sin[2*(d + e*x)]))/(8*b*c*e^2*Log[F] + 2*b^3*c^3*Log[F]^3)","A",1
13,1,47,72,0.109069,"\int F^{c (a+b x)} \cos (d+e x) \, dx","Integrate[F^(c*(a + b*x))*Cos[d + e*x],x]","\frac{F^{c (a+b x)} (b c \log (F) \cos (d+e x)+e \sin (d+e x))}{b^2 c^2 \log ^2(F)+e^2}","\frac{e \sin (d+e x) F^{c (a+b x)}}{b^2 c^2 \log ^2(F)+e^2}+\frac{b c \log (F) \cos (d+e x) F^{c (a+b x)}}{b^2 c^2 \log ^2(F)+e^2}",1,"(F^(c*(a + b*x))*(b*c*Cos[d + e*x]*Log[F] + e*Sin[d + e*x]))/(e^2 + b^2*c^2*Log[F]^2)","A",1
14,1,84,84,0.0194633,"\int F^{c (a+b x)} \sec (d+e x) \, dx","Integrate[F^(c*(a + b*x))*Sec[d + e*x],x]","\frac{2 e^{i (d+e x)} F^{c (a+b x)} \, _2F_1\left(1,\frac{1}{2}-\frac{i b c \log (F)}{2 e};\frac{3}{2}-\frac{i b c \log (F)}{2 e};-e^{2 i (d+e x)}\right)}{b c \log (F)+i e}","\frac{2 e^{i (d+e x)} F^{c (a+b x)} \, _2F_1\left(1,\frac{e-i b c \log (F)}{2 e};\frac{1}{2} \left(3-\frac{i b c \log (F)}{e}\right);-e^{2 i (d+e x)}\right)}{b c \log (F)+i e}",1,"(2*E^(I*(d + e*x))*F^(c*(a + b*x))*Hypergeometric2F1[1, 1/2 - ((I/2)*b*c*Log[F])/e, 3/2 - ((I/2)*b*c*Log[F])/e, -E^((2*I)*(d + e*x))])/(I*e + b*c*Log[F])","A",1
15,1,80,80,0.0149901,"\int F^{c (a+b x)} \sec ^2(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Sec[d + e*x]^2,x]","\frac{4 e^{2 i (d+e x)} F^{c (a+b x)} \, _2F_1\left(2,1-\frac{i b c \log (F)}{2 e};2-\frac{i b c \log (F)}{2 e};-e^{2 i (d+e x)}\right)}{b c \log (F)+2 i e}","\frac{4 e^{2 i (d+e x)} F^{c (a+b x)} \, _2F_1\left(2,1-\frac{i b c \log (F)}{2 e};2-\frac{i b c \log (F)}{2 e};-e^{2 i (d+e x)}\right)}{b c \log (F)+2 i e}",1,"(4*E^((2*I)*(d + e*x))*F^(c*(a + b*x))*Hypergeometric2F1[2, 1 - ((I/2)*b*c*Log[F])/e, 2 - ((I/2)*b*c*Log[F])/e, -E^((2*I)*(d + e*x))])/((2*I)*e + b*c*Log[F])","A",1
16,1,112,141,0.2908477,"\int F^{c (a+b x)} \sec ^3(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Sec[d + e*x]^3,x]","\frac{F^{c (a+b x)} \left(\sec (d+e x) (e \tan (d+e x)-b c \log (F))+2 e^{i (d+e x)} (b c \log (F)-i e) \, _2F_1\left(1,\frac{e-i b c \log (F)}{2 e};\frac{3}{2}-\frac{i b c \log (F)}{2 e};-e^{2 i (d+e x)}\right)\right)}{2 e^2}","-\frac{e^{i (d+e x)} F^{c (a+b x)} (-b c \log (F)+i e) \, _2F_1\left(1,\frac{e-i b c \log (F)}{2 e};\frac{1}{2} \left(3-\frac{i b c \log (F)}{e}\right);-e^{2 i (d+e x)}\right)}{e^2}-\frac{b c \log (F) \sec (d+e x) F^{c (a+b x)}}{2 e^2}+\frac{\tan (d+e x) \sec (d+e x) F^{c (a+b x)}}{2 e}",1,"(F^(c*(a + b*x))*(2*E^(I*(d + e*x))*Hypergeometric2F1[1, (e - I*b*c*Log[F])/(2*e), 3/2 - ((I/2)*b*c*Log[F])/e, -E^((2*I)*(d + e*x))]*((-I)*e + b*c*Log[F]) + Sec[d + e*x]*(-(b*c*Log[F]) + e*Tan[d + e*x])))/(2*e^2)","A",1
17,1,111,143,0.2149584,"\int F^{c (a+b x)} \sec ^4(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Sec[d + e*x]^4,x]","\frac{F^{c (a+b x)} \left(\sec ^2(d+e x) (2 e \tan (d+e x)-b c \log (F))+4 e^{2 i (d+e x)} (b c \log (F)-2 i e) \, _2F_1\left(2,1-\frac{i b c \log (F)}{2 e};2-\frac{i b c \log (F)}{2 e};-e^{2 i (d+e x)}\right)\right)}{6 e^2}","-\frac{2 e^{2 i (d+e x)} F^{c (a+b x)} (-b c \log (F)+2 i e) \, _2F_1\left(2,1-\frac{i b c \log (F)}{2 e};2-\frac{i b c \log (F)}{2 e};-e^{2 i (d+e x)}\right)}{3 e^2}-\frac{b c \log (F) \sec ^2(d+e x) F^{c (a+b x)}}{6 e^2}+\frac{\tan (d+e x) \sec ^2(d+e x) F^{c (a+b x)}}{3 e}",1,"(F^(c*(a + b*x))*(4*E^((2*I)*(d + e*x))*Hypergeometric2F1[2, 1 - ((I/2)*b*c*Log[F])/e, 2 - ((I/2)*b*c*Log[F])/e, -E^((2*I)*(d + e*x))]*((-2*I)*e + b*c*Log[F]) + Sec[d + e*x]^2*(-(b*c*Log[F]) + 2*e*Tan[d + e*x])))/(6*e^2)","A",1
18,1,33,54,0.02681,"\int e^x \cos ^4(x) \, dx","Integrate[E^x*Cos[x]^4,x]","\frac{1}{680} e^x (136 \sin (2 x)+20 \sin (4 x)+68 \cos (2 x)+5 \cos (4 x)+255)","\frac{24 e^x}{85}+\frac{1}{17} e^x \cos ^4(x)+\frac{12}{85} e^x \cos ^2(x)+\frac{4}{17} e^x \sin (x) \cos ^3(x)+\frac{24}{85} e^x \sin (x) \cos (x)",1,"(E^x*(255 + 68*Cos[2*x] + 5*Cos[4*x] + 136*Sin[2*x] + 20*Sin[4*x]))/680","A",1
19,1,212,194,2.1360627,"\int e^{c (a+b x)} \tan ^3(d+e x) \, dx","Integrate[E^(c*(a + b*x))*Tan[d + e*x]^3,x]","\frac{1}{2} e^{c (a+b x)} \left(\frac{2 e^{2 i d} \left(b^2 c^2-2 e^2\right) \left(b c e^{2 i e x} \, _2F_1\left(1,1-\frac{i b c}{2 e};2-\frac{i b c}{2 e};-e^{2 i (d+e x)}\right)-(b c+2 i e) \, _2F_1\left(1,-\frac{i b c}{2 e};1-\frac{i b c}{2 e};-e^{2 i (d+e x)}\right)\right)}{b c \left(1+e^{2 i d}\right) e^2 (-2 e+i b c)}-\frac{b c \sec (d) \sin (e x) \sec (d+e x)}{e^2}-\frac{2 \tan (d)}{b c}+\frac{\sec ^2(d+e x)}{e}\right)","-\frac{6 i e^{c (a+b x)} \, _2F_1\left(1,-\frac{i b c}{2 e};1-\frac{i b c}{2 e};-e^{2 i (d+e x)}\right)}{b c}+\frac{12 i e^{c (a+b x)} \, _2F_1\left(2,-\frac{i b c}{2 e};1-\frac{i b c}{2 e};-e^{2 i (d+e x)}\right)}{b c}-\frac{8 i e^{c (a+b x)} \, _2F_1\left(3,-\frac{i b c}{2 e};1-\frac{i b c}{2 e};-e^{2 i (d+e x)}\right)}{b c}+\frac{i e^{c (a+b x)}}{b c}",1,"(E^(c*(a + b*x))*((2*(b^2*c^2 - 2*e^2)*E^((2*I)*d)*(b*c*E^((2*I)*e*x)*Hypergeometric2F1[1, 1 - ((I/2)*b*c)/e, 2 - ((I/2)*b*c)/e, -E^((2*I)*(d + e*x))] - (b*c + (2*I)*e)*Hypergeometric2F1[1, ((-1/2*I)*b*c)/e, 1 - ((I/2)*b*c)/e, -E^((2*I)*(d + e*x))]))/(b*c*(I*b*c - 2*e)*e^2*(1 + E^((2*I)*d))) + Sec[d + e*x]^2/e - (b*c*Sec[d]*Sec[d + e*x]*Sin[e*x])/e^2 - (2*Tan[d])/(b*c)))/2","A",1
20,1,174,130,1.6742514,"\int e^{c (a+b x)} \tan ^2(d+e x) \, dx","Integrate[E^(c*(a + b*x))*Tan[d + e*x]^2,x]","e^{c (a+b x)} \left(\frac{2 i e^{2 i d} \left(b c e^{2 i e x} \, _2F_1\left(1,1-\frac{i b c}{2 e};2-\frac{i b c}{2 e};-e^{2 i (d+e x)}\right)-(b c+2 i e) \, _2F_1\left(1,-\frac{i b c}{2 e};1-\frac{i b c}{2 e};-e^{2 i (d+e x)}\right)\right)}{\left(1+e^{2 i d}\right) e (b c+2 i e)}-\frac{1}{b c}+\frac{\sec (d) \sin (e x) \sec (d+e x)}{e}\right)","\frac{4 e^{c (a+b x)} \, _2F_1\left(1,-\frac{i b c}{2 e};1-\frac{i b c}{2 e};-e^{2 i (d+e x)}\right)}{b c}-\frac{4 e^{c (a+b x)} \, _2F_1\left(2,-\frac{i b c}{2 e};1-\frac{i b c}{2 e};-e^{2 i (d+e x)}\right)}{b c}-\frac{e^{c (a+b x)}}{b c}",1,"E^(c*(a + b*x))*(-(1/(b*c)) + ((2*I)*E^((2*I)*d)*(b*c*E^((2*I)*e*x)*Hypergeometric2F1[1, 1 - ((I/2)*b*c)/e, 2 - ((I/2)*b*c)/e, -E^((2*I)*(d + e*x))] - (b*c + (2*I)*e)*Hypergeometric2F1[1, ((-1/2*I)*b*c)/e, 1 - ((I/2)*b*c)/e, -E^((2*I)*(d + e*x))]))/((b*c + (2*I)*e)*e*(1 + E^((2*I)*d))) + (Sec[d]*Sec[d + e*x]*Sin[e*x])/e)","A",1
21,1,166,78,0.4696448,"\int e^{c (a+b x)} \tan (d+e x) \, dx","Integrate[E^(c*(a + b*x))*Tan[d + e*x],x]","\frac{e^{c (a+b x)} \left(2 b c e^{2 i (d+e x)} \, _2F_1\left(1,1-\frac{i b c}{2 e};2-\frac{i b c}{2 e};-e^{2 i (d+e x)}\right)-(b c+2 i e) \left(2 e^{2 i d} \, _2F_1\left(1,-\frac{i b c}{2 e};1-\frac{i b c}{2 e};-e^{2 i (d+e x)}\right)-e^{2 i d}+1\right)\right)}{b c \left(1+e^{2 i d}\right) (-2 e+i b c)}","\frac{2 i e^{c (a+b x)} \, _2F_1\left(1,-\frac{i b c}{2 e};1-\frac{i b c}{2 e};-e^{2 i (d+e x)}\right)}{b c}-\frac{i e^{c (a+b x)}}{b c}",1,"(E^(c*(a + b*x))*(2*b*c*E^((2*I)*(d + e*x))*Hypergeometric2F1[1, 1 - ((I/2)*b*c)/e, 2 - ((I/2)*b*c)/e, -E^((2*I)*(d + e*x))] - (b*c + (2*I)*e)*(1 - E^((2*I)*d) + 2*E^((2*I)*d)*Hypergeometric2F1[1, ((-1/2*I)*b*c)/e, 1 - ((I/2)*b*c)/e, -E^((2*I)*(d + e*x))])))/(b*c*(I*b*c - 2*e)*(1 + E^((2*I)*d)))","B",1
22,1,163,76,1.2321861,"\int e^{c (a+b x)} \cot (d+e x) \, dx","Integrate[E^(c*(a + b*x))*Cot[d + e*x],x]","\frac{e^{c (a+b x)} \left(2 i b c e^{2 i (d+e x)} \, _2F_1\left(1,1-\frac{i b c}{2 e};2-\frac{i b c}{2 e};e^{2 i (d+e x)}\right)+i (b c+2 i e) \left(-2 e^{2 i d} \, _2F_1\left(1,-\frac{i b c}{2 e};1-\frac{i b c}{2 e};e^{2 i (d+e x)}\right)+e^{2 i d}+1\right)\right)}{b c \left(-1+e^{2 i d}\right) (b c+2 i e)}","\frac{i e^{c (a+b x)}}{b c}-\frac{2 i e^{c (a+b x)} \, _2F_1\left(1,-\frac{i b c}{2 e};1-\frac{i b c}{2 e};e^{2 i (d+e x)}\right)}{b c}",1,"(E^(c*(a + b*x))*((2*I)*b*c*E^((2*I)*(d + e*x))*Hypergeometric2F1[1, 1 - ((I/2)*b*c)/e, 2 - ((I/2)*b*c)/e, E^((2*I)*(d + e*x))] + I*(b*c + (2*I)*e)*(1 + E^((2*I)*d) - 2*E^((2*I)*d)*Hypergeometric2F1[1, ((-1/2*I)*b*c)/e, 1 - ((I/2)*b*c)/e, E^((2*I)*(d + e*x))])))/(b*c*(b*c + (2*I)*e)*(-1 + E^((2*I)*d)))","B",1
23,1,170,126,1.6475809,"\int e^{c (a+b x)} \cot ^2(d+e x) \, dx","Integrate[E^(c*(a + b*x))*Cot[d + e*x]^2,x]","e^{c (a+b x)} \left(-\frac{2 i e^{2 i d} \left((b c+2 i e) \, _2F_1\left(1,-\frac{i b c}{2 e};1-\frac{i b c}{2 e};e^{2 i (d+e x)}\right)-b c e^{2 i e x} \, _2F_1\left(1,1-\frac{i b c}{2 e};2-\frac{i b c}{2 e};e^{2 i (d+e x)}\right)\right)}{\left(-1+e^{2 i d}\right) e (b c+2 i e)}-\frac{1}{b c}+\frac{\csc (d) \sin (e x) \csc (d+e x)}{e}\right)","\frac{4 e^{c (a+b x)} \, _2F_1\left(1,-\frac{i b c}{2 e};1-\frac{i b c}{2 e};e^{2 i (d+e x)}\right)}{b c}-\frac{4 e^{c (a+b x)} \, _2F_1\left(2,-\frac{i b c}{2 e};1-\frac{i b c}{2 e};e^{2 i (d+e x)}\right)}{b c}-\frac{e^{c (a+b x)}}{b c}",1,"E^(c*(a + b*x))*(-(1/(b*c)) - ((2*I)*E^((2*I)*d)*(-(b*c*E^((2*I)*e*x)*Hypergeometric2F1[1, 1 - ((I/2)*b*c)/e, 2 - ((I/2)*b*c)/e, E^((2*I)*(d + e*x))]) + (b*c + (2*I)*e)*Hypergeometric2F1[1, ((-1/2*I)*b*c)/e, 1 - ((I/2)*b*c)/e, E^((2*I)*(d + e*x))]))/((b*c + (2*I)*e)*e*(-1 + E^((2*I)*d))) + (Csc[d]*Csc[d + e*x]*Sin[e*x])/e)","A",1
24,1,210,188,2.1763406,"\int e^{c (a+b x)} \cot ^3(d+e x) \, dx","Integrate[E^(c*(a + b*x))*Cot[d + e*x]^3,x]","\frac{1}{2} e^{c (a+b x)} \left(\frac{2 e^{2 i d} \left(b^2 c^2-2 e^2\right) \left(i b c e^{2 i e x} \, _2F_1\left(1,1-\frac{i b c}{2 e};2-\frac{i b c}{2 e};e^{2 i (d+e x)}\right)+(2 e-i b c) \, _2F_1\left(1,-\frac{i b c}{2 e};1-\frac{i b c}{2 e};e^{2 i (d+e x)}\right)\right)}{b c \left(-1+e^{2 i d}\right) e^2 (b c+2 i e)}+\frac{b c \csc (d) \sin (e x) \csc (d+e x)}{e^2}-\frac{2 \cot (d)}{b c}-\frac{\csc ^2(d+e x)}{e}\right)","\frac{6 i e^{c (a+b x)} \, _2F_1\left(1,-\frac{i b c}{2 e};1-\frac{i b c}{2 e};e^{2 i (d+e x)}\right)}{b c}-\frac{12 i e^{c (a+b x)} \, _2F_1\left(2,-\frac{i b c}{2 e};1-\frac{i b c}{2 e};e^{2 i (d+e x)}\right)}{b c}+\frac{8 i e^{c (a+b x)} \, _2F_1\left(3,-\frac{i b c}{2 e};1-\frac{i b c}{2 e};e^{2 i (d+e x)}\right)}{b c}-\frac{i e^{c (a+b x)}}{b c}",1,"(E^(c*(a + b*x))*((-2*Cot[d])/(b*c) - Csc[d + e*x]^2/e + (2*(b^2*c^2 - 2*e^2)*E^((2*I)*d)*(I*b*c*E^((2*I)*e*x)*Hypergeometric2F1[1, 1 - ((I/2)*b*c)/e, 2 - ((I/2)*b*c)/e, E^((2*I)*(d + e*x))] + ((-I)*b*c + 2*e)*Hypergeometric2F1[1, ((-1/2*I)*b*c)/e, 1 - ((I/2)*b*c)/e, E^((2*I)*(d + e*x))]))/(b*c*(b*c + (2*I)*e)*e^2*(-1 + E^((2*I)*d))) + (b*c*Csc[d]*Csc[d + e*x]*Sin[e*x])/e^2))/2","A",1
25,1,133,76,0.3128557,"\int F^{a+b x} \tan \left(\frac{\pi }{4}+\frac{1}{2} (-c-d x)\right) \, dx","Integrate[F^(a + b*x)*Tan[Pi/4 + (-c - d*x)/2],x]","\frac{F^{a+b x} \left(b \log (F) e^{i (c+d x)} \, _2F_1\left(1,1-\frac{i b \log (F)}{d};2-\frac{i b \log (F)}{d};i e^{i (c+d x)}\right)+(d-i b \log (F)) \, _2F_1\left(1,-\frac{i b \log (F)}{d};1-\frac{i b \log (F)}{d};i e^{i (c+d x)}\right)\right)}{b \log (F) (b \log (F)+i d)}","\frac{i F^{a+b x}}{b \log (F)}-\frac{2 i F^{a+b x} \, _2F_1\left(1,-\frac{i b \log (F)}{d};1-\frac{i b \log (F)}{d};i e^{i (c+d x)}\right)}{b \log (F)}",1,"(F^(a + b*x)*(b*E^(I*(c + d*x))*Hypergeometric2F1[1, 1 - (I*b*Log[F])/d, 2 - (I*b*Log[F])/d, I*E^(I*(c + d*x))]*Log[F] + Hypergeometric2F1[1, ((-I)*b*Log[F])/d, 1 - (I*b*Log[F])/d, I*E^(I*(c + d*x))]*(d - I*b*Log[F])))/(b*Log[F]*(I*d + b*Log[F]))","A",1
26,1,102,100,0.0875163,"\int F^{c (a+b x)} \sec ^n(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Sec[d + e*x]^n,x]","-\frac{i \left(1+e^{2 i (d+e x)}\right)^n F^{c (a+b x)} \sec ^n(d+e x) \, _2F_1\left(n,\frac{e n-i b c \log (F)}{2 e};\frac{1}{2} \left(n-\frac{i b c \log (F)}{e}+2\right);-e^{2 i (d+e x)}\right)}{e n-i b c \log (F)}","\frac{\left(1+e^{2 i (d+e x)}\right)^n F^{a c+b c x} \sec ^n(d+e x) \, _2F_1\left(n,\frac{e n-i b c \log (F)}{2 e};\frac{1}{2} \left(n-\frac{i b c \log (F)}{e}+2\right);-e^{2 i (d+e x)}\right)}{b c \log (F)+i e n}",1,"((-I)*(1 + E^((2*I)*(d + e*x)))^n*F^(c*(a + b*x))*Hypergeometric2F1[n, (e*n - I*b*c*Log[F])/(2*e), (2 + n - (I*b*c*Log[F])/e)/2, -E^((2*I)*(d + e*x))]*Sec[d + e*x]^n)/(e*n - I*b*c*Log[F])","A",1
27,1,102,102,0.0983321,"\int F^{c (a+b x)} \csc ^n(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Csc[d + e*x]^n,x]","\frac{i \left(1-e^{-2 i (d+e x)}\right)^n F^{c (a+b x)} \csc ^n(d+e x) \, _2F_1\left(n,\frac{e n+i b c \log (F)}{2 e};\frac{1}{2} \left(n+\frac{i b c \log (F)}{e}+2\right);e^{-2 i (d+e x)}\right)}{e n+i b c \log (F)}","-\frac{\left(1-e^{-2 i (d+e x)}\right)^n F^{a c+b c x} \csc ^n(d+e x) \, _2F_1\left(n,\frac{e n+i b c \log (F)}{2 e};\frac{1}{2} \left(n+\frac{i b c \log (F)}{e}+2\right);e^{-2 i (d+e x)}\right)}{-b c \log (F)+i e n}",1,"(I*(1 - E^((-2*I)*(d + e*x)))^n*F^(c*(a + b*x))*Csc[d + e*x]^n*Hypergeometric2F1[n, (e*n + I*b*c*Log[F])/(2*e), (2 + n + (I*b*c*Log[F])/e)/2, E^((-2*I)*(d + e*x))])/(e*n + I*b*c*Log[F])","A",1
28,1,143,139,0.6150073,"\int F^{c (a+b x)} (f x)^m \sin (d+e x) \, dx","Integrate[F^(c*(a + b*x))*(f*x)^m*Sin[d + e*x],x]","\frac{1}{2} F^{a c} (f x)^m (x (-b c \log (F)-i e))^{-m} \left(-i x (\cos (d)-i \sin (d)) (-b c x \log (F)-i e x)^m (i x (e+i b c \log (F)))^{-m-1} \Gamma (m+1,i e x-b c x \log (F))-\frac{(\cos (d)+i \sin (d)) \Gamma (m+1,-i e x-b c \log (F) x)}{e-i b c \log (F)}\right)","-\frac{e^{i d} F^{a c} (f x)^m (-x (b c \log (F)+i e))^{-m} \Gamma (m+1,-x (i e+b c \log (F)))}{2 (e-i b c \log (F))}-\frac{e^{-i d} F^{a c} (f x)^m (x (-b c \log (F)+i e))^{-m} \Gamma (m+1,x (i e-b c \log (F)))}{2 (e+i b c \log (F))}",1,"(F^(a*c)*(f*x)^m*((-I)*x*Gamma[1 + m, I*e*x - b*c*x*Log[F]]*(I*x*(e + I*b*c*Log[F]))^(-1 - m)*((-I)*e*x - b*c*x*Log[F])^m*(Cos[d] - I*Sin[d]) - (Gamma[1 + m, (-I)*e*x - b*c*x*Log[F]]*(Cos[d] + I*Sin[d]))/(e - I*b*c*Log[F])))/(2*(x*((-I)*e - b*c*Log[F]))^m)","A",1
29,0,0,25,9.2018711,"\int F^{c (a+b x)} (f x)^m \csc (d+e x) \, dx","Integrate[F^(c*(a + b*x))*(f*x)^m*Csc[d + e*x],x]","\int F^{c (a+b x)} (f x)^m \csc (d+e x) \, dx","\text{Int}\left((f x)^m \csc (d+e x) F^{a c+b c x},x\right)",0,"Integrate[F^(c*(a + b*x))*(f*x)^m*Csc[d + e*x], x]","A",-1
30,0,0,27,10.7243676,"\int F^{c (a+b x)} (f x)^m \csc ^2(d+e x) \, dx","Integrate[F^(c*(a + b*x))*(f*x)^m*Csc[d + e*x]^2,x]","\int F^{c (a+b x)} (f x)^m \csc ^2(d+e x) \, dx","\text{Int}\left((f x)^m \csc ^2(d+e x) F^{a c+b c x},x\right)",0,"Integrate[F^(c*(a + b*x))*(f*x)^m*Csc[d + e*x]^2, x]","A",-1
31,1,26,24,1.3541827,"\int f F^{c (a+b x)} (f x)^{-2+m} (e x \cos (d+e x)+(-1+m+b c x \log (F)) \sin (d+e x)) \, dx","Integrate[f*F^(c*(a + b*x))*(f*x)^(-2 + m)*(e*x*Cos[d + e*x] + (-1 + m + b*c*x*Log[F])*Sin[d + e*x]),x]","f x (f x)^{m-2} \sin (d+e x) F^{a c+b c x}","(f x)^{m-1} \sin (d+e x) F^{a c+b c x}",1,"f*F^(a*c + b*c*x)*x*(f*x)^(-2 + m)*Sin[d + e*x]","A",1
32,1,23,23,0.9257648,"\int f F^{c (a+b x)} (f x)^m (e x \cos (d+e x)+(1+m+b c x \log (F)) \sin (d+e x)) \, dx","Integrate[f*F^(c*(a + b*x))*(f*x)^m*(e*x*Cos[d + e*x] + (1 + m + b*c*x*Log[F])*Sin[d + e*x]),x]","f x (f x)^m \sin (d+e x) F^{c (a+b x)}","f x (f x)^m \sin (d+e x) F^{c (a+b x)}",1,"f*F^(c*(a + b*x))*x*(f*x)^m*Sin[d + e*x]","A",1
33,1,22,22,0.8714524,"\int \frac{F^{c (a+b x)} (f x)^m (e x \cos (d+e x)+(m+b c x \log (F)) \sin (d+e x))}{x} \, dx","Integrate[(F^(c*(a + b*x))*(f*x)^m*(e*x*Cos[d + e*x] + (m + b*c*x*Log[F])*Sin[d + e*x]))/x,x]","(f x)^m \sin (d+e x) F^{a c+b c x}","(f x)^m \sin (d+e x) F^{a c+b c x}",1,"F^(a*c + b*c*x)*(f*x)^m*Sin[d + e*x]","A",1
34,1,17,17,0.406009,"\int F^{c (a+b x)} (e x \cos (d+e x)+(1+b c x \log (F)) \sin (d+e x)) \, dx","Integrate[F^(c*(a + b*x))*(e*x*Cos[d + e*x] + (1 + b*c*x*Log[F])*Sin[d + e*x]),x]","x \sin (d+e x) F^{c (a+b x)}","x \sin (d+e x) F^{c (a+b x)}",1,"F^(c*(a + b*x))*x*Sin[d + e*x]","A",1
35,1,16,16,0.0269708,"\int F^{c (a+b x)} (e \cos (d+e x)+b c \log (F) \sin (d+e x)) \, dx","Integrate[F^(c*(a + b*x))*(e*Cos[d + e*x] + b*c*Log[F]*Sin[d + e*x]),x]","\sin (d+e x) F^{c (a+b x)}","\sin (d+e x) F^{c (a+b x)}",1,"F^(c*(a + b*x))*Sin[d + e*x]","A",1
36,1,19,20,0.6118858,"\int \frac{F^{c (a+b x)} (e x \cos (d+e x)+(-1+b c x \log (F)) \sin (d+e x))}{x^2} \, dx","Integrate[(F^(c*(a + b*x))*(e*x*Cos[d + e*x] + (-1 + b*c*x*Log[F])*Sin[d + e*x]))/x^2,x]","\frac{\sin (d+e x) F^{c (a+b x)}}{x}","\frac{\sin (d+e x) F^{a c+b c x}}{x}",1,"(F^(c*(a + b*x))*Sin[d + e*x])/x","A",1
37,1,19,20,0.6490195,"\int \frac{F^{c (a+b x)} (e x \cos (d+e x)+(-2+b c x \log (F)) \sin (d+e x))}{x^3} \, dx","Integrate[(F^(c*(a + b*x))*(e*x*Cos[d + e*x] + (-2 + b*c*x*Log[F])*Sin[d + e*x]))/x^3,x]","\frac{\sin (d+e x) F^{c (a+b x)}}{x^2}","\frac{\sin (d+e x) F^{a c+b c x}}{x^2}",1,"(F^(c*(a + b*x))*Sin[d + e*x])/x^2","A",1
38,1,44,63,0.1549986,"\int e^{a+b x} \cos (c+d x) \sin (c+d x) \, dx","Integrate[E^(a + b*x)*Cos[c + d*x]*Sin[c + d*x],x]","\frac{e^{a+b x} (b \sin (2 (c+d x))-2 d \cos (2 (c+d x)))}{2 \left(b^2+4 d^2\right)}","\frac{b e^{a+b x} \sin (2 c+2 d x)}{2 \left(b^2+4 d^2\right)}-\frac{d e^{a+b x} \cos (2 c+2 d x)}{b^2+4 d^2}",1,"(E^(a + b*x)*(-2*d*Cos[2*(c + d*x)] + b*Sin[2*(c + d*x)]))/(2*(b^2 + 4*d^2))","A",1
39,1,74,119,0.6630869,"\int e^{a+b x} \cos (c+d x) \sin ^2(c+d x) \, dx","Integrate[E^(a + b*x)*Cos[c + d*x]*Sin[c + d*x]^2,x]","\frac{1}{4} e^{a+b x} \left(\frac{b \cos (c+d x)+d \sin (c+d x)}{b^2+d^2}-\frac{b \cos (3 (c+d x))+3 d \sin (3 (c+d x))}{b^2+9 d^2}\right)","\frac{d e^{a+b x} \sin (c+d x)}{4 \left(b^2+d^2\right)}-\frac{3 d e^{a+b x} \sin (3 c+3 d x)}{4 \left(b^2+9 d^2\right)}+\frac{b e^{a+b x} \cos (c+d x)}{4 \left(b^2+d^2\right)}-\frac{b e^{a+b x} \cos (3 c+3 d x)}{4 \left(b^2+9 d^2\right)}",1,"(E^(a + b*x)*((b*Cos[c + d*x] + d*Sin[c + d*x])/(b^2 + d^2) - (b*Cos[3*(c + d*x)] + 3*d*Sin[3*(c + d*x)])/(b^2 + 9*d^2)))/4","A",1
40,1,82,129,0.8955697,"\int e^{a+b x} \cos (c+d x) \sin ^3(c+d x) \, dx","Integrate[E^(a + b*x)*Cos[c + d*x]*Sin[c + d*x]^3,x]","\frac{1}{8} e^{a+b x} \left(\frac{2 (b \sin (2 (c+d x))-2 d \cos (2 (c+d x)))}{b^2+4 d^2}+\frac{4 d \cos (4 (c+d x))-b \sin (4 (c+d x))}{b^2+16 d^2}\right)","\frac{b e^{a+b x} \sin (2 c+2 d x)}{4 \left(b^2+4 d^2\right)}-\frac{b e^{a+b x} \sin (4 c+4 d x)}{8 \left(b^2+16 d^2\right)}-\frac{d e^{a+b x} \cos (2 c+2 d x)}{2 \left(b^2+4 d^2\right)}+\frac{d e^{a+b x} \cos (4 c+4 d x)}{2 \left(b^2+16 d^2\right)}",1,"(E^(a + b*x)*((2*(-2*d*Cos[2*(c + d*x)] + b*Sin[2*(c + d*x)]))/(b^2 + 4*d^2) + (4*d*Cos[4*(c + d*x)] - b*Sin[4*(c + d*x)])/(b^2 + 16*d^2)))/8","A",1
41,1,74,119,0.6724143,"\int e^{a+b x} \cos ^2(c+d x) \sin (c+d x) \, dx","Integrate[E^(a + b*x)*Cos[c + d*x]^2*Sin[c + d*x],x]","\frac{1}{4} e^{a+b x} \left(\frac{b \sin (c+d x)-d \cos (c+d x)}{b^2+d^2}+\frac{b \sin (3 (c+d x))-3 d \cos (3 (c+d x))}{b^2+9 d^2}\right)","\frac{b e^{a+b x} \sin (c+d x)}{4 \left(b^2+d^2\right)}+\frac{b e^{a+b x} \sin (3 c+3 d x)}{4 \left(b^2+9 d^2\right)}-\frac{d e^{a+b x} \cos (c+d x)}{4 \left(b^2+d^2\right)}-\frac{3 d e^{a+b x} \cos (3 c+3 d x)}{4 \left(b^2+9 d^2\right)}",1,"(E^(a + b*x)*((-(d*Cos[c + d*x]) + b*Sin[c + d*x])/(b^2 + d^2) + (-3*d*Cos[3*(c + d*x)] + b*Sin[3*(c + d*x)])/(b^2 + 9*d^2)))/4","A",1
42,1,57,79,0.3775961,"\int e^{a+b x} \cos ^2(c+d x) \sin ^2(c+d x) \, dx","Integrate[E^(a + b*x)*Cos[c + d*x]^2*Sin[c + d*x]^2,x]","\frac{e^{a+b x} \left(b^2 (-\cos (4 (c+d x)))+b^2-4 b d \sin (4 (c+d x))+16 d^2\right)}{8 \left(b^3+16 b d^2\right)}","-\frac{d e^{a+b x} \sin (4 c+4 d x)}{2 \left(b^2+16 d^2\right)}-\frac{b e^{a+b x} \cos (4 c+4 d x)}{8 \left(b^2+16 d^2\right)}+\frac{e^{a+b x}}{8 b}",1,"(E^(a + b*x)*(b^2 + 16*d^2 - b^2*Cos[4*(c + d*x)] - 4*b*d*Sin[4*(c + d*x)]))/(8*(b^3 + 16*b*d^2))","A",1
43,1,110,183,0.9215199,"\int e^{a+b x} \cos ^2(c+d x) \sin ^3(c+d x) \, dx","Integrate[E^(a + b*x)*Cos[c + d*x]^2*Sin[c + d*x]^3,x]","\frac{1}{16} e^{a+b x} \left(\frac{2 (b \sin (c+d x)-d \cos (c+d x))}{b^2+d^2}+\frac{b \sin (3 (c+d x))-3 d \cos (3 (c+d x))}{b^2+9 d^2}+\frac{5 d \cos (5 (c+d x))-b \sin (5 (c+d x))}{b^2+25 d^2}\right)","\frac{b e^{a+b x} \sin (c+d x)}{8 \left(b^2+d^2\right)}+\frac{b e^{a+b x} \sin (3 c+3 d x)}{16 \left(b^2+9 d^2\right)}-\frac{b e^{a+b x} \sin (5 c+5 d x)}{16 \left(b^2+25 d^2\right)}-\frac{d e^{a+b x} \cos (c+d x)}{8 \left(b^2+d^2\right)}-\frac{3 d e^{a+b x} \cos (3 c+3 d x)}{16 \left(b^2+9 d^2\right)}+\frac{5 d e^{a+b x} \cos (5 c+5 d x)}{16 \left(b^2+25 d^2\right)}",1,"(E^(a + b*x)*((2*(-(d*Cos[c + d*x]) + b*Sin[c + d*x]))/(b^2 + d^2) + (-3*d*Cos[3*(c + d*x)] + b*Sin[3*(c + d*x)])/(b^2 + 9*d^2) + (5*d*Cos[5*(c + d*x)] - b*Sin[5*(c + d*x)])/(b^2 + 25*d^2)))/16","A",1
44,1,81,129,0.677192,"\int e^{a+b x} \cos ^3(c+d x) \sin (c+d x) \, dx","Integrate[E^(a + b*x)*Cos[c + d*x]^3*Sin[c + d*x],x]","\frac{1}{8} e^{a+b x} \left(\frac{2 (b \sin (2 (c+d x))-2 d \cos (2 (c+d x)))}{b^2+4 d^2}+\frac{b \sin (4 (c+d x))-4 d \cos (4 (c+d x))}{b^2+16 d^2}\right)","\frac{b e^{a+b x} \sin (2 c+2 d x)}{4 \left(b^2+4 d^2\right)}+\frac{b e^{a+b x} \sin (4 c+4 d x)}{8 \left(b^2+16 d^2\right)}-\frac{d e^{a+b x} \cos (2 c+2 d x)}{2 \left(b^2+4 d^2\right)}-\frac{d e^{a+b x} \cos (4 c+4 d x)}{2 \left(b^2+16 d^2\right)}",1,"(E^(a + b*x)*((2*(-2*d*Cos[2*(c + d*x)] + b*Sin[2*(c + d*x)]))/(b^2 + 4*d^2) + (-4*d*Cos[4*(c + d*x)] + b*Sin[4*(c + d*x)])/(b^2 + 16*d^2)))/8","A",1
45,1,110,183,0.7793301,"\int e^{a+b x} \cos ^3(c+d x) \sin ^2(c+d x) \, dx","Integrate[E^(a + b*x)*Cos[c + d*x]^3*Sin[c + d*x]^2,x]","\frac{1}{16} e^{a+b x} \left(\frac{2 (b \cos (c+d x)+d \sin (c+d x))}{b^2+d^2}-\frac{b \cos (3 (c+d x))+3 d \sin (3 (c+d x))}{b^2+9 d^2}-\frac{b \cos (5 (c+d x))+5 d \sin (5 (c+d x))}{b^2+25 d^2}\right)","\frac{d e^{a+b x} \sin (c+d x)}{8 \left(b^2+d^2\right)}-\frac{3 d e^{a+b x} \sin (3 c+3 d x)}{16 \left(b^2+9 d^2\right)}-\frac{5 d e^{a+b x} \sin (5 c+5 d x)}{16 \left(b^2+25 d^2\right)}+\frac{b e^{a+b x} \cos (c+d x)}{8 \left(b^2+d^2\right)}-\frac{b e^{a+b x} \cos (3 c+3 d x)}{16 \left(b^2+9 d^2\right)}-\frac{b e^{a+b x} \cos (5 c+5 d x)}{16 \left(b^2+25 d^2\right)}",1,"(E^(a + b*x)*((2*(b*Cos[c + d*x] + d*Sin[c + d*x]))/(b^2 + d^2) - (b*Cos[3*(c + d*x)] + 3*d*Sin[3*(c + d*x)])/(b^2 + 9*d^2) - (b*Cos[5*(c + d*x)] + 5*d*Sin[5*(c + d*x)])/(b^2 + 25*d^2)))/16","A",1
46,1,111,129,0.9430721,"\int e^{a+b x} \cos ^3(c+d x) \sin ^3(c+d x) \, dx","Integrate[E^(a + b*x)*Cos[c + d*x]^3*Sin[c + d*x]^3,x]","\frac{e^{a+b x} \left(-6 d \left(b^2+36 d^2\right) \cos (2 (c+d x))+6 d \left(b^2+4 d^2\right) \cos (6 (c+d x))-2 b \sin (2 (c+d x)) \left(\left(b^2+4 d^2\right) \cos (4 (c+d x))-b^2-52 d^2\right)\right)}{32 \left(b^4+40 b^2 d^2+144 d^4\right)}","\frac{3 b e^{a+b x} \sin (2 c+2 d x)}{32 \left(b^2+4 d^2\right)}-\frac{b e^{a+b x} \sin (6 c+6 d x)}{32 \left(b^2+36 d^2\right)}-\frac{3 d e^{a+b x} \cos (2 c+2 d x)}{16 \left(b^2+4 d^2\right)}+\frac{3 d e^{a+b x} \cos (6 c+6 d x)}{16 \left(b^2+36 d^2\right)}",1,"(E^(a + b*x)*(-6*d*(b^2 + 36*d^2)*Cos[2*(c + d*x)] + 6*d*(b^2 + 4*d^2)*Cos[6*(c + d*x)] - 2*b*(-b^2 - 52*d^2 + (b^2 + 4*d^2)*Cos[4*(c + d*x)])*Sin[2*(c + d*x)]))/(32*(b^4 + 40*b^2*d^2 + 144*d^4))","A",1
47,1,19,30,0.0375813,"\int e^x x \sin (x) \, dx","Integrate[E^x*x*Sin[x],x]","\frac{1}{2} e^x (x \sin (x)-x \cos (x)+\cos (x))","\frac{1}{2} e^x x \sin (x)+\frac{1}{2} e^x \cos (x)-\frac{1}{2} e^x x \cos (x)",1,"(E^x*(Cos[x] - x*Cos[x] + x*Sin[x]))/2","A",1
48,1,25,50,0.0365299,"\int e^x x^2 \sin (x) \, dx","Integrate[E^x*x^2*Sin[x],x]","\frac{1}{2} e^x \left(\left(x^2-1\right) \sin (x)-(x-1)^2 \cos (x)\right)","\frac{1}{2} e^x x^2 \sin (x)-\frac{1}{2} e^x x^2 \cos (x)-\frac{1}{2} e^x \sin (x)+e^x x \cos (x)-\frac{1}{2} e^x \cos (x)",1,"(E^x*(-((-1 + x)^2*Cos[x]) + (-1 + x^2)*Sin[x]))/2","A",1
49,1,18,30,0.02705,"\int e^x x \cos (x) \, dx","Integrate[E^x*x*Cos[x],x]","\frac{1}{2} e^x ((x-1) \sin (x)+x \cos (x))","-\frac{1}{2} e^x \sin (x)+\frac{1}{2} e^x x \sin (x)+\frac{1}{2} e^x x \cos (x)",1,"(E^x*(x*Cos[x] + (-1 + x)*Sin[x]))/2","A",1
50,1,23,51,0.0342857,"\int e^x x^2 \cos (x) \, dx","Integrate[E^x*x^2*Cos[x],x]","\frac{1}{2} e^x (x-1) ((x-1) \sin (x)+(x+1) \cos (x))","\frac{1}{2} e^x x^2 \sin (x)+\frac{1}{2} e^x x^2 \cos (x)-e^x x \sin (x)+\frac{1}{2} e^x \sin (x)-\frac{1}{2} e^x \cos (x)",1,"(E^x*(-1 + x)*((1 + x)*Cos[x] + (-1 + x)*Sin[x]))/2","A",1
51,1,22,27,0.0917775,"\int e^{3 x} (-5 \cos (4 x)+2 \sin (4 x)) \, dx","Integrate[E^(3*x)*(-5*Cos[4*x] + 2*Sin[4*x]),x]","-\frac{1}{25} e^{3 x} (14 \sin (4 x)+23 \cos (4 x))","-\frac{14}{25} e^{3 x} \sin (4 x)-\frac{23}{25} e^{3 x} \cos (4 x)",1,"-1/25*(E^(3*x)*(23*Cos[4*x] + 14*Sin[4*x]))","A",1
52,1,33,41,0.0650696,"\int \left(e^{-x} \sin (x)+e^x \sin (x)\right) \, dx","Integrate[Sin[x]/E^x + E^x*Sin[x],x]","-\frac{1}{2} e^x \left(e^{-2 x}-1\right) \sin (x)-\frac{1}{2} e^x \left(e^{-2 x}+1\right) \cos (x)","-\frac{1}{2} e^{-x} \sin (x)+\frac{1}{2} e^x \sin (x)-\frac{1}{2} e^{-x} \cos (x)-\frac{1}{2} e^x \cos (x)",1,"-1/2*(E^x*(1 + E^(-2*x))*Cos[x]) - (E^x*(-1 + E^(-2*x))*Sin[x])/2","A",1
53,1,64,82,2.546138,"\int \frac{F^{a+b x} \cos (c+d x)}{e+e \sin (c+d x)} \, dx","Integrate[(F^(a + b*x)*Cos[c + d*x])/(e + e*Sin[c + d*x]),x]","-\frac{i F^{a+b x} \left(-1+2 \, _2F_1\left(1,-\frac{i b \log (F)}{d};1-\frac{i b \log (F)}{d};i e^{i (c+d x)}\right)\right)}{b e \log (F)}","\frac{i F^{a+b x}}{b e \log (F)}-\frac{2 i F^{a+b x} \, _2F_1\left(1,-\frac{i b \log (F)}{d};1-\frac{i b \log (F)}{d};i e^{i (c+d x)}\right)}{b e \log (F)}",1,"((-I)*F^(a + b*x)*(-1 + 2*Hypergeometric2F1[1, ((-I)*b*Log[F])/d, 1 - (I*b*Log[F])/d, I*E^(I*(c + d*x))]))/(b*e*Log[F])","A",1
54,1,64,82,2.6352392,"\int \frac{F^{a+b x} \cos (c+d x)}{e-e \sin (c+d x)} \, dx","Integrate[(F^(a + b*x)*Cos[c + d*x])/(e - e*Sin[c + d*x]),x]","\frac{i F^{a+b x} \left(-1+2 \, _2F_1\left(1,-\frac{i b \log (F)}{d};1-\frac{i b \log (F)}{d};-i e^{i (c+d x)}\right)\right)}{b e \log (F)}","\frac{2 i F^{a+b x} \, _2F_1\left(1,-\frac{i b \log (F)}{d};1-\frac{i b \log (F)}{d};-i e^{i (c+d x)}\right)}{b e \log (F)}-\frac{i F^{a+b x}}{b e \log (F)}",1,"(I*F^(a + b*x)*(-1 + 2*Hypergeometric2F1[1, ((-I)*b*Log[F])/d, 1 - (I*b*Log[F])/d, (-I)*E^(I*(c + d*x))]))/(b*e*Log[F])","A",1
55,1,68,80,0.671543,"\int \frac{F^{a+b x} \sin (c+d x)}{e+e \cos (c+d x)} \, dx","Integrate[(F^(a + b*x)*Sin[c + d*x])/(e + e*Cos[c + d*x]),x]","\frac{i F^{a+b x} \left(-1+2 \, _2F_1\left(1,-\frac{i b \log (F)}{d};1-\frac{i b \log (F)}{d};-\cos (c+d x)-i \sin (c+d x)\right)\right)}{b e \log (F)}","\frac{2 i F^{a+b x} \, _2F_1\left(1,-\frac{i b \log (F)}{d};1-\frac{i b \log (F)}{d};-e^{i (c+d x)}\right)}{b e \log (F)}-\frac{i F^{a+b x}}{b e \log (F)}",1,"(I*F^(a + b*x)*(-1 + 2*Hypergeometric2F1[1, ((-I)*b*Log[F])/d, 1 - (I*b*Log[F])/d, -Cos[c + d*x] - I*Sin[c + d*x]]))/(b*e*Log[F])","A",1
56,1,66,78,0.6342867,"\int \frac{F^{a+b x} \sin (c+d x)}{e-e \cos (c+d x)} \, dx","Integrate[(F^(a + b*x)*Sin[c + d*x])/(e - e*Cos[c + d*x]),x]","-\frac{i F^{a+b x} \left(-1+2 \, _2F_1\left(1,-\frac{i b \log (F)}{d};1-\frac{i b \log (F)}{d};\cos (c+d x)+i \sin (c+d x)\right)\right)}{b e \log (F)}","\frac{i F^{a+b x}}{b e \log (F)}-\frac{2 i F^{a+b x} \, _2F_1\left(1,-\frac{i b \log (F)}{d};1-\frac{i b \log (F)}{d};e^{i (c+d x)}\right)}{b e \log (F)}",1,"((-I)*F^(a + b*x)*(-1 + 2*Hypergeometric2F1[1, ((-I)*b*Log[F])/d, 1 - (I*b*Log[F])/d, Cos[c + d*x] + I*Sin[c + d*x]]))/(b*e*Log[F])","A",1
57,1,43,69,0.0253918,"\int e^{x^2} \sin (b x) \, dx","Integrate[E^x^2*Sin[b*x],x]","\frac{1}{4} \sqrt{\pi } e^{\frac{b^2}{4}} \left(\text{erf}\left(\frac{b}{2}-i x\right)+\text{erf}\left(\frac{b}{2}+i x\right)\right)","\frac{1}{4} i \sqrt{\pi } e^{\frac{b^2}{4}} \text{erfi}\left(\frac{1}{2} (2 x-i b)\right)-\frac{1}{4} i \sqrt{\pi } e^{\frac{b^2}{4}} \text{erfi}\left(\frac{1}{2} (2 x+i b)\right)",1,"(E^(b^2/4)*Sqrt[Pi]*(Erf[b/2 - I*x] + Erf[b/2 + I*x]))/4","A",1
58,1,47,65,0.0184048,"\int e^{x^2} \cos (b x) \, dx","Integrate[E^x^2*Cos[b*x],x]","\frac{1}{4} \sqrt{\pi } e^{\frac{b^2}{4}} \left(\text{erfi}\left(\frac{1}{2} (2 x-i b)\right)+\text{erfi}\left(\frac{1}{2} (2 x+i b)\right)\right)","\frac{1}{4} \sqrt{\pi } e^{\frac{b^2}{4}} \text{erfi}\left(\frac{1}{2} (2 x-i b)\right)+\frac{1}{4} \sqrt{\pi } e^{\frac{b^2}{4}} \text{erfi}\left(\frac{1}{2} (2 x+i b)\right)",1,"(E^(b^2/4)*Sqrt[Pi]*(Erfi[((-I)*b + 2*x)/2] + Erfi[(I*b + 2*x)/2]))/4","A",1
59,1,81,81,0.0817104,"\int e^{x^2} \sin (a+b x) \, dx","Integrate[E^x^2*Sin[a + b*x],x]","\frac{1}{4} \sqrt{\pi } e^{\frac{b^2}{4}} \left(\cos (a) \text{erf}\left(\frac{b}{2}-i x\right)+\cos (a) \text{erf}\left(\frac{b}{2}+i x\right)+\sin (a) \left(\text{erfi}\left(\frac{1}{2} (2 x-i b)\right)+\text{erfi}\left(\frac{1}{2} (2 x+i b)\right)\right)\right)","\frac{1}{4} i \sqrt{\pi } e^{\frac{b^2}{4}-i a} \text{erfi}\left(\frac{1}{2} (2 x-i b)\right)-\frac{1}{4} i \sqrt{\pi } e^{\frac{b^2}{4}+i a} \text{erfi}\left(\frac{1}{2} (2 x+i b)\right)",1,"(E^(b^2/4)*Sqrt[Pi]*(Cos[a]*Erf[b/2 - I*x] + Cos[a]*Erf[b/2 + I*x] + (Erfi[((-I)*b + 2*x)/2] + Erfi[(I*b + 2*x)/2])*Sin[a]))/4","A",1
60,1,82,77,0.0830353,"\int e^{x^2} \cos (a+b x) \, dx","Integrate[E^x^2*Cos[a + b*x],x]","\frac{1}{4} \sqrt{\pi } e^{\frac{b^2}{4}} \left(-\sin (a) \left(\text{erf}\left(\frac{b}{2}-i x\right)+\text{erf}\left(\frac{b}{2}+i x\right)\right)+\cos (a) \text{erfi}\left(\frac{1}{2} (2 x-i b)\right)+\cos (a) \text{erfi}\left(\frac{1}{2} (2 x+i b)\right)\right)","\frac{1}{4} \sqrt{\pi } e^{\frac{b^2}{4}-i a} \text{erfi}\left(\frac{1}{2} (2 x-i b)\right)+\frac{1}{4} \sqrt{\pi } e^{\frac{b^2}{4}+i a} \text{erfi}\left(\frac{1}{2} (2 x+i b)\right)",1,"(E^(b^2/4)*Sqrt[Pi]*(Cos[a]*Erfi[((-I)*b + 2*x)/2] + Cos[a]*Erfi[(I*b + 2*x)/2] - (Erf[b/2 - I*x] + Erf[b/2 + I*x])*Sin[a]))/4","A",1
61,1,24,35,0.0369419,"\int e^{2 x^2} x \cos \left(2 x^2\right) \, dx","Integrate[E^(2*x^2)*x*Cos[2*x^2],x]","\frac{1}{8} e^{2 x^2} \left(\sin \left(2 x^2\right)+\cos \left(2 x^2\right)\right)","\frac{1}{8} e^{2 x^2} \sin \left(2 x^2\right)+\frac{1}{8} e^{2 x^2} \cos \left(2 x^2\right)",1,"(E^(2*x^2)*(Cos[2*x^2] + Sin[2*x^2]))/8","A",1
62,1,6,6,0.0091642,"\int e^x \sin \left(e^x\right) \, dx","Integrate[E^x*Sin[E^x],x]","-\cos \left(e^x\right)","-\cos \left(e^x\right)",1,"-Cos[E^x]","A",1
63,1,21,5,0.017355,"\int e^x \csc \left(e^x\right) \sec \left(e^x\right) \, dx","Integrate[E^x*Csc[E^x]*Sec[E^x],x]","2 \left(\frac{1}{2} \log \left(\sin \left(e^x\right)\right)-\frac{1}{2} \log \left(\cos \left(e^x\right)\right)\right)","\log \left(\tan \left(e^x\right)\right)",1,"2*(-1/2*Log[Cos[E^x]] + Log[Sin[E^x]]/2)","B",1
64,1,4,4,0.0095463,"\int e^x \cos \left(e^x\right) \, dx","Integrate[E^x*Cos[E^x],x]","\sin \left(e^x\right)","\sin \left(e^x\right)",1,"Sin[E^x]","A",1
65,1,10,10,0.0098965,"\int e^{2 x} \cos \left(e^{2 x}\right) \, dx","Integrate[E^(2*x)*Cos[E^(2*x)],x]","\frac{1}{2} \sin \left(e^{2 x}\right)","\frac{1}{2} \sin \left(e^{2 x}\right)",1,"Sin[E^(2*x)]/2","A",1
66,1,10,10,0.0108982,"\int e^{-2 x} \cos \left(e^{-2 x}\right) \, dx","Integrate[Cos[E^(-2*x)]/E^(2*x),x]","-\frac{1}{2} \sin \left(e^{-2 x}\right)","-\frac{1}{2} \sin \left(e^{-2 x}\right)",1,"-1/2*Sin[E^(-2*x)]","A",1
67,1,13,13,0.0156006,"\int e^{2 x} \cos \left(e^x\right) \, dx","Integrate[E^(2*x)*Cos[E^x],x]","e^x \sin \left(e^x\right)+\cos \left(e^x\right)","e^x \sin \left(e^x\right)+\cos \left(e^x\right)",1,"Cos[E^x] + E^x*Sin[E^x]","A",1
68,1,30,30,0.0631568,"\int e^{-1+3 x} \cos \left(e^{-1+3 x}\right) \sin \left(1+e^{-1+3 x}\right) \, dx","Integrate[E^(-1 + 3*x)*Cos[E^(-1 + 3*x)]*Sin[1 + E^(-1 + 3*x)],x]","\frac{1}{6} e^{3 x-1} \sin (1)-\frac{1}{12} \cos \left(2 e^{3 x-1}+1\right)","\frac{1}{6} e^{3 x-1} \sin (1)-\frac{1}{12} \cos \left(2 e^{3 x-1}+1\right)",1,"-1/12*Cos[1 + 2*E^(-1 + 3*x)] + (E^(-1 + 3*x)*Sin[1])/6","A",1
69,1,7,7,0.0081474,"\int e^x \tan \left(e^x\right) \, dx","Integrate[E^x*Tan[E^x],x]","-\log \left(\cos \left(e^x\right)\right)","-\log \left(\cos \left(e^x\right)\right)",1,"-Log[Cos[E^x]]","A",1
70,1,5,5,0.0051759,"\int e^x \sec \left(e^x\right) \, dx","Integrate[E^x*Sec[E^x],x]","\tanh ^{-1}\left(\sin \left(e^x\right)\right)","\tanh ^{-1}\left(\sin \left(e^x\right)\right)",1,"ArcTanh[Sin[E^x]]","A",1
71,1,4,4,0.0096375,"\int e^x \sec \left(e^x\right) \tan \left(e^x\right) \, dx","Integrate[E^x*Sec[E^x]*Tan[E^x],x]","\sec \left(e^x\right)","\sec \left(e^x\right)",1,"Sec[E^x]","A",1
72,1,6,6,0.016501,"\int e^x \csc ^2\left(e^x\right) \, dx","Integrate[E^x*Csc[E^x]^2,x]","-\cot \left(e^x\right)","-\cot \left(e^x\right)",1,"-Cot[E^x]","A",1
73,1,27,37,0.0623542,"\int e^x \sin (a+b x) \, dx","Integrate[E^x*Sin[a + b*x],x]","\frac{e^x (\sin (a+b x)-b \cos (a+b x))}{b^2+1}","\frac{e^x \sin (a+b x)}{b^2+1}-\frac{b e^x \cos (a+b x)}{b^2+1}",1,"(E^x*(-(b*Cos[a + b*x]) + Sin[a + b*x]))/(1 + b^2)","A",1
74,1,108,115,0.1621106,"\int e^x \sin \left(a+c x^2\right) \, dx","Integrate[E^x*Sin[a + c*x^2],x]","-\frac{\sqrt[4]{-1} \sqrt{\pi } e^{\left.-\frac{i}{4}\right/c} \left(e^{\left.\frac{i}{2}\right/c} (\cos (a)+i \sin (a)) \text{erfi}\left(\frac{\sqrt[4]{-1} (2 c x-i)}{2 \sqrt{c}}\right)+(\sin (a)+i \cos (a)) \text{erfi}\left(\frac{(-1)^{3/4} (2 c x+i)}{2 \sqrt{c}}\right)\right)}{4 \sqrt{c}}","\frac{(-1)^{3/4} \sqrt{\pi } e^{\frac{1}{4} i \left(4 a+\frac{1}{c}\right)} \text{erf}\left(\frac{\sqrt[4]{-1} (1+2 i c x)}{2 \sqrt{c}}\right)}{4 \sqrt{c}}+\frac{(-1)^{3/4} \sqrt{\pi } e^{-\frac{1}{4} i \left(4 a+\frac{1}{c}\right)} \text{erfi}\left(\frac{\sqrt[4]{-1} (1-2 i c x)}{2 \sqrt{c}}\right)}{4 \sqrt{c}}",1,"-1/4*((-1)^(1/4)*Sqrt[Pi]*(E^((I/2)/c)*Erfi[((-1)^(1/4)*(-I + 2*c*x))/(2*Sqrt[c])]*(Cos[a] + I*Sin[a]) + Erfi[((-1)^(3/4)*(I + 2*c*x))/(2*Sqrt[c])]*(I*Cos[a] + Sin[a])))/(Sqrt[c]*E^((I/4)/c))","A",1
75,1,134,144,0.2575858,"\int e^x \sin \left(a+b x+c x^2\right) \, dx","Integrate[E^x*Sin[a + b*x + c*x^2],x]","-\frac{\sqrt[4]{-1} \sqrt{\pi } e^{-\frac{i \left(b^2-2 i b+1\right)}{4 c}} \left(e^{\frac{i b^2}{2 c}} (\sin (a)+i \cos (a)) \text{erfi}\left(\frac{(-1)^{3/4} (b+2 c x+i)}{2 \sqrt{c}}\right)+e^{\left.\frac{i}{2}\right/c} (\cos (a)+i \sin (a)) \text{erfi}\left(\frac{\sqrt[4]{-1} (b+2 c x-i)}{2 \sqrt{c}}\right)\right)}{4 \sqrt{c}}","\frac{(-1)^{3/4} \sqrt{\pi } e^{\frac{1}{4} i \left(4 a+\frac{(1+i b)^2}{c}\right)} \text{erf}\left(\frac{\sqrt[4]{-1} (i b+2 i c x+1)}{2 \sqrt{c}}\right)}{4 \sqrt{c}}+\frac{(-1)^{3/4} \sqrt{\pi } e^{\frac{i (b+i)^2}{4 c}-i a} \text{erfi}\left(\frac{\sqrt[4]{-1} (-i b-2 i c x+1)}{2 \sqrt{c}}\right)}{4 \sqrt{c}}",1,"-1/4*((-1)^(1/4)*Sqrt[Pi]*(E^((I/2)/c)*Erfi[((-1)^(1/4)*(-I + b + 2*c*x))/(2*Sqrt[c])]*(Cos[a] + I*Sin[a]) + E^(((I/2)*b^2)/c)*Erfi[((-1)^(3/4)*(I + b + 2*c*x))/(2*Sqrt[c])]*(I*Cos[a] + Sin[a])))/(Sqrt[c]*E^(((I/4)*(1 - (2*I)*b + b^2))/c))","A",1
76,1,81,81,0.0210297,"\int e^{x^2} \sin (a+b x) \, dx","Integrate[E^x^2*Sin[a + b*x],x]","\frac{1}{4} \sqrt{\pi } e^{\frac{b^2}{4}} \left(\cos (a) \text{erf}\left(\frac{b}{2}-i x\right)+\cos (a) \text{erf}\left(\frac{b}{2}+i x\right)+\sin (a) \left(\text{erfi}\left(\frac{1}{2} (2 x-i b)\right)+\text{erfi}\left(\frac{1}{2} (2 x+i b)\right)\right)\right)","\frac{1}{4} i \sqrt{\pi } e^{\frac{b^2}{4}-i a} \text{erfi}\left(\frac{1}{2} (2 x-i b)\right)-\frac{1}{4} i \sqrt{\pi } e^{\frac{b^2}{4}+i a} \text{erfi}\left(\frac{1}{2} (2 x+i b)\right)",1,"(E^(b^2/4)*Sqrt[Pi]*(Cos[a]*Erf[b/2 - I*x] + Cos[a]*Erf[b/2 + I*x] + (Erfi[((-I)*b + 2*x)/2] + Erfi[(I*b + 2*x)/2])*Sin[a]))/4","A",1
77,1,129,87,0.2359322,"\int e^{x^2} \sin \left(a+c x^2\right) \, dx","Integrate[E^x^2*Sin[a + c*x^2],x]","-\frac{\sqrt[4]{-1} \sqrt{\pi } \left(\sqrt{c+i} \left(\sin (a) \text{erf}\left(\frac{(1+i) \sqrt{c+i} x}{\sqrt{2}}\right)+\text{erfi}\left((-1)^{3/4} \sqrt{c+i} x\right) (c \sin (a)+i c \cos (a)+\cos (a))\right)+\sqrt{c-i} (c+i) (\cos (a)+i \sin (a)) \text{erfi}\left(\sqrt[4]{-1} \sqrt{c-i} x\right)\right)}{4 \left(c^2+1\right)}","\frac{i \sqrt{\pi } e^{-i a} \text{erfi}\left(\sqrt{1-i c} x\right)}{4 \sqrt{1-i c}}-\frac{i \sqrt{\pi } e^{i a} \text{erfi}\left(\sqrt{1+i c} x\right)}{4 \sqrt{1+i c}}",1,"-1/4*((-1)^(1/4)*Sqrt[Pi]*(Sqrt[-I + c]*(I + c)*Erfi[(-1)^(1/4)*Sqrt[-I + c]*x]*(Cos[a] + I*Sin[a]) + Sqrt[I + c]*(Erf[((1 + I)*Sqrt[I + c]*x)/Sqrt[2]]*Sin[a] + Erfi[(-1)^(3/4)*Sqrt[I + c]*x]*(Cos[a] + I*c*Cos[a] + c*Sin[a]))))/(1 + c^2)","A",1
78,1,165,155,0.5815522,"\int e^{x^2} \sin \left(a+b x+c x^2\right) \, dx","Integrate[E^x^2*Sin[a + b*x + c*x^2],x]","-\frac{(-1)^{3/4} \sqrt{\pi } e^{\frac{i b^2}{-4 c+4 i}} \left((c-i) \sqrt{c+i} e^{\frac{i b^2 c}{2 c^2+2}} (\cos (a)-i \sin (a)) \text{erfi}\left(\frac{(-1)^{3/4} (b+2 (c+i) x)}{2 \sqrt{c+i}}\right)+\sqrt{c-i} (c+i) (\sin (a)-i \cos (a)) \text{erfi}\left(\frac{\sqrt[4]{-1} (b+2 (c-i) x)}{2 \sqrt{c-i}}\right)\right)}{4 \left(c^2+1\right)}","-\frac{i \sqrt{\pi } e^{-i \left(a-\frac{b^2}{4 c+4 i}\right)} \text{erfi}\left(\frac{i b-2 (1-i c) x}{2 \sqrt{1-i c}}\right)}{4 \sqrt{1-i c}}-\frac{i \sqrt{\pi } e^{i a+\frac{b^2}{4 (1+i c)}} \text{erfi}\left(\frac{i b+2 (1+i c) x}{2 \sqrt{1+i c}}\right)}{4 \sqrt{1+i c}}",1,"-1/4*((-1)^(3/4)*E^((I*b^2)/(4*I - 4*c))*Sqrt[Pi]*((-I + c)*Sqrt[I + c]*E^((I*b^2*c)/(2 + 2*c^2))*Erfi[((-1)^(3/4)*(b + 2*(I + c)*x))/(2*Sqrt[I + c])]*(Cos[a] - I*Sin[a]) + Sqrt[-I + c]*(I + c)*Erfi[((-1)^(1/4)*(b + 2*(-I + c)*x))/(2*Sqrt[-I + c])]*((-I)*Cos[a] + Sin[a])))/(1 + c^2)","A",1
79,1,132,142,0.2268079,"\int f^{a+b x} \sin \left(d+f x^2\right) \, dx","Integrate[f^(a + b*x)*Sin[d + f*x^2],x]","-\frac{1}{4} \sqrt[4]{-1} \sqrt{\pi } f^{a-\frac{1}{2}} e^{-\frac{i b^2 \log ^2(f)}{4 f}} \left(e^{\frac{i b^2 \log ^2(f)}{2 f}} (\cos (d)+i \sin (d)) \text{erfi}\left(\frac{\sqrt[4]{-1} (2 f x-i b \log (f))}{2 \sqrt{f}}\right)+(\sin (d)+i \cos (d)) \text{erfi}\left(\frac{(-1)^{3/4} (2 f x+i b \log (f))}{2 \sqrt{f}}\right)\right)","\frac{1}{4} (-1)^{3/4} \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{1}{4} i \left(\frac{b^2 \log ^2(f)}{f}+4 d\right)} \text{erf}\left(\frac{\sqrt[4]{-1} (b \log (f)+2 i f x)}{2 \sqrt{f}}\right)-\frac{1}{4} (-1)^{3/4} \sqrt{\pi } f^{a-\frac{1}{2}} e^{-\frac{1}{4} i \left(\frac{b^2 \log ^2(f)}{f}+4 d\right)} \text{erfi}\left(\frac{\sqrt[4]{-1} (-b \log (f)+2 i f x)}{2 \sqrt{f}}\right)",1,"-1/4*((-1)^(1/4)*f^(-1/2 + a)*Sqrt[Pi]*(E^(((I/2)*b^2*Log[f]^2)/f)*Erfi[((-1)^(1/4)*(2*f*x - I*b*Log[f]))/(2*Sqrt[f])]*(Cos[d] + I*Sin[d]) + Erfi[((-1)^(3/4)*(2*f*x + I*b*Log[f]))/(2*Sqrt[f])]*(I*Cos[d] + Sin[d])))/E^(((I/4)*b^2*Log[f]^2)/f)","A",1
80,1,156,157,1.0362792,"\int f^{a+b x} \sin ^2\left(d+f x^2\right) \, dx","Integrate[f^(a + b*x)*Sin[d + f*x^2]^2,x]","\frac{1}{16} f^a \left(-\frac{(1-i) \sqrt{\pi } e^{-\frac{i b^2 \log ^2(f)}{8 f}} (\cos (d)-i \sin (d))^2 \text{erf}\left(\frac{(4+4 i) f x-(1-i) b \log (f)}{4 \sqrt{f}}\right)}{\sqrt{f}}-\frac{(1-i) \sqrt{\pi } e^{\frac{i b^2 \log ^2(f)}{8 f}} (\cos (d)+i \sin (d))^2 \text{erfi}\left(\frac{(1-i) b \log (f)+(4+4 i) f x}{4 \sqrt{f}}\right)}{\sqrt{f}}+\frac{8 f^{b x}}{b \log (f)}\right)","\left(\frac{1}{16}+\frac{i}{16}\right) \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{i b^2 \log ^2(f)}{8 f}+2 i d} \text{erf}\left(\frac{\left(\frac{1}{4}+\frac{i}{4}\right) (b \log (f)+4 i f x)}{\sqrt{f}}\right)+\left(\frac{1}{16}+\frac{i}{16}\right) \sqrt{\pi } f^{a-\frac{1}{2}} e^{-\frac{1}{8} i \left(\frac{b^2 \log ^2(f)}{f}+16 d\right)} \text{erfi}\left(\frac{\left(\frac{1}{4}+\frac{i}{4}\right) (-b \log (f)+4 i f x)}{\sqrt{f}}\right)+\frac{f^{a+b x}}{2 b \log (f)}",1,"(f^a*((8*f^(b*x))/(b*Log[f]) - ((1 - I)*Sqrt[Pi]*Erf[((4 + 4*I)*f*x - (1 - I)*b*Log[f])/(4*Sqrt[f])]*(Cos[d] - I*Sin[d])^2)/(E^(((I/8)*b^2*Log[f]^2)/f)*Sqrt[f]) - ((1 - I)*E^(((I/8)*b^2*Log[f]^2)/f)*Sqrt[Pi]*Erfi[((4 + 4*I)*f*x + (1 - I)*b*Log[f])/(4*Sqrt[f])]*(Cos[d] + I*Sin[d])^2)/Sqrt[f]))/16","A",1
81,1,268,298,0.8124868,"\int f^{a+b x} \sin ^3\left(d+f x^2\right) \, dx","Integrate[f^(a + b*x)*Sin[d + f*x^2]^3,x]","\frac{1}{48} (-1)^{3/4} \sqrt{\pi } f^{a-\frac{1}{2}} e^{-\frac{i b^2 \log ^2(f)}{4 f}} \left(9 i e^{\frac{i b^2 \log ^2(f)}{2 f}} (\cos (d)+i \sin (d)) \text{erfi}\left(\frac{\sqrt[4]{-1} (2 f x-i b \log (f))}{2 \sqrt{f}}\right)+\sqrt{3} e^{\frac{i b^2 \log ^2(f)}{6 f}} \left(e^{\frac{i b^2 \log ^2(f)}{6 f}} (\sin (3 d)-i \cos (3 d)) \text{erfi}\left(\frac{(1-i) b \log (f)+(6+6 i) f x}{2 \sqrt{6} \sqrt{f}}\right)+(\cos (3 d)-i \sin (3 d)) \text{erfi}\left(\frac{(-1)^{3/4} (6 f x+i b \log (f))}{2 \sqrt{3} \sqrt{f}}\right)\right)-9 (\cos (d)-i \sin (d)) \text{erfi}\left(\frac{(-1)^{3/4} (2 f x+i b \log (f))}{2 \sqrt{f}}\right)\right)","\frac{3}{16} (-1)^{3/4} \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{1}{4} i \left(\frac{b^2 \log ^2(f)}{f}+4 d\right)} \text{erf}\left(\frac{\sqrt[4]{-1} (b \log (f)+2 i f x)}{2 \sqrt{f}}\right)+\left(\frac{1}{16}-\frac{i}{16}\right) \sqrt{\frac{\pi }{6}} f^{a-\frac{1}{2}} e^{\frac{i b^2 \log ^2(f)}{12 f}+3 i d} \text{erf}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (b \log (f)+6 i f x)}{\sqrt{6} \sqrt{f}}\right)-\frac{3}{16} (-1)^{3/4} \sqrt{\pi } f^{a-\frac{1}{2}} e^{-\frac{1}{4} i \left(\frac{b^2 \log ^2(f)}{f}+4 d\right)} \text{erfi}\left(\frac{\sqrt[4]{-1} (-b \log (f)+2 i f x)}{2 \sqrt{f}}\right)-\left(\frac{1}{16}-\frac{i}{16}\right) \sqrt{\frac{\pi }{6}} f^{a-\frac{1}{2}} e^{-\frac{1}{12} i \left(\frac{b^2 \log ^2(f)}{f}+36 d\right)} \text{erfi}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (-b \log (f)+6 i f x)}{\sqrt{6} \sqrt{f}}\right)",1,"((-1)^(3/4)*f^(-1/2 + a)*Sqrt[Pi]*(-9*Erfi[((-1)^(3/4)*(2*f*x + I*b*Log[f]))/(2*Sqrt[f])]*(Cos[d] - I*Sin[d]) + (9*I)*E^(((I/2)*b^2*Log[f]^2)/f)*Erfi[((-1)^(1/4)*(2*f*x - I*b*Log[f]))/(2*Sqrt[f])]*(Cos[d] + I*Sin[d]) + Sqrt[3]*E^(((I/6)*b^2*Log[f]^2)/f)*(Erfi[((-1)^(3/4)*(6*f*x + I*b*Log[f]))/(2*Sqrt[3]*Sqrt[f])]*(Cos[3*d] - I*Sin[3*d]) + E^(((I/6)*b^2*Log[f]^2)/f)*Erfi[((6 + 6*I)*f*x + (1 - I)*b*Log[f])/(2*Sqrt[6]*Sqrt[f])]*((-I)*Cos[3*d] + Sin[3*d]))))/(48*E^(((I/4)*b^2*Log[f]^2)/f))","A",1
82,1,162,162,0.3782505,"\int f^{a+b x} \sin \left(d+e x+f x^2\right) \, dx","Integrate[f^(a + b*x)*Sin[d + e*x + f*x^2],x]","-\frac{1}{4} \sqrt[4]{-1} \sqrt{\pi } f^{a-\frac{b e+f}{2 f}} e^{-\frac{i \left(b^2 \log ^2(f)+e^2\right)}{4 f}} \left(e^{\frac{i b^2 \log ^2(f)}{2 f}} (\cos (d)+i \sin (d)) \text{erfi}\left(\frac{\sqrt[4]{-1} (-i b \log (f)+e+2 f x)}{2 \sqrt{f}}\right)+e^{\frac{i e^2}{2 f}} (\sin (d)+i \cos (d)) \text{erfi}\left(\frac{(-1)^{3/4} (i b \log (f)+e+2 f x)}{2 \sqrt{f}}\right)\right)","\frac{1}{4} (-1)^{3/4} \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{1}{4} i \left(4 d+\frac{(b \log (f)+i e)^2}{f}\right)} \text{erf}\left(\frac{\sqrt[4]{-1} (b \log (f)+i e+2 i f x)}{2 \sqrt{f}}\right)-\frac{1}{4} (-1)^{3/4} \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{i (e+i b \log (f))^2}{4 f}-i d} \text{erfi}\left(\frac{\sqrt[4]{-1} (-b \log (f)+i e+2 i f x)}{2 \sqrt{f}}\right)",1,"-1/4*((-1)^(1/4)*f^(a - (b*e + f)/(2*f))*Sqrt[Pi]*(E^(((I/2)*b^2*Log[f]^2)/f)*Erfi[((-1)^(1/4)*(e + 2*f*x - I*b*Log[f]))/(2*Sqrt[f])]*(Cos[d] + I*Sin[d]) + E^(((I/2)*e^2)/f)*Erfi[((-1)^(3/4)*(e + 2*f*x + I*b*Log[f]))/(2*Sqrt[f])]*(I*Cos[d] + Sin[d])))/E^(((I/4)*(e^2 + b^2*Log[f]^2))/f)","A",1
83,1,244,179,1.0805869,"\int f^{a+b x} \sin ^2\left(d+e x+f x^2\right) \, dx","Integrate[f^(a + b*x)*Sin[d + e*x + f*x^2]^2,x]","\frac{f^{a-\frac{b e+f}{2 f}} e^{-\frac{i \left(b^2 \log ^2(f)+4 e^2\right)}{8 f}} \left(\sqrt[4]{-1} \sqrt{2 \pi } b \log (f) e^{\frac{i b^2 \log ^2(f)}{4 f}} (\cos (2 d)+i \sin (2 d)) \text{erf}\left(\frac{\left(\frac{1}{4}+\frac{i}{4}\right) (b \log (f)+2 i (e+2 f x))}{\sqrt{f}}\right)+8 f^{b \left(\frac{e}{2 f}+x\right)+\frac{1}{2}} e^{\frac{i \left(b^2 \log ^2(f)+4 e^2\right)}{8 f}}+\sqrt[4]{-1} \sqrt{2 \pi } b e^{\frac{i e^2}{f}} \log (f) (\sin (2 d)+i \cos (2 d)) \text{erf}\left(\frac{\left(\frac{1}{4}+\frac{i}{4}\right) (i b \log (f)+2 e+4 f x)}{\sqrt{f}}\right)\right)}{16 b \log (f)}","\left(\frac{1}{16}+\frac{i}{16}\right) \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{i (b \log (f)+2 i e)^2}{8 f}+2 i d} \text{erf}\left(\frac{\left(\frac{1}{4}+\frac{i}{4}\right) (b \log (f)+2 i e+4 i f x)}{\sqrt{f}}\right)+\left(\frac{1}{16}+\frac{i}{16}\right) \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{i (2 e+i b \log (f))^2}{8 f}-2 i d} \text{erfi}\left(\frac{\left(\frac{1}{4}+\frac{i}{4}\right) (-b \log (f)+2 i e+4 i f x)}{\sqrt{f}}\right)+\frac{f^{a+b x}}{2 b \log (f)}",1,"(f^(a - (b*e + f)/(2*f))*(8*E^(((I/8)*(4*e^2 + b^2*Log[f]^2))/f)*f^(1/2 + b*(e/(2*f) + x)) + (-1)^(1/4)*b*E^(((I/4)*b^2*Log[f]^2)/f)*Sqrt[2*Pi]*Erf[((1/4 + I/4)*((2*I)*(e + 2*f*x) + b*Log[f]))/Sqrt[f]]*Log[f]*(Cos[2*d] + I*Sin[2*d]) + (-1)^(1/4)*b*E^((I*e^2)/f)*Sqrt[2*Pi]*Erf[((1/4 + I/4)*(2*e + 4*f*x + I*b*Log[f]))/Sqrt[f]]*Log[f]*(I*Cos[2*d] + Sin[2*d])))/(16*b*E^(((I/8)*(4*e^2 + b^2*Log[f]^2))/f)*Log[f])","A",1
84,1,323,340,1.4969984,"\int f^{a+b x} \sin ^3\left(d+e x+f x^2\right) \, dx","Integrate[f^(a + b*x)*Sin[d + e*x + f*x^2]^3,x]","\frac{1}{48} (-1)^{3/4} \sqrt{\pi } f^{a-\frac{b e+f}{2 f}} e^{-\frac{i \left(b^2 \log ^2(f)+3 e^2\right)}{4 f}} \left(9 i (\cos (d)+i \sin (d)) e^{\frac{i \left(b^2 \log ^2(f)+e^2\right)}{2 f}} \text{erfi}\left(\frac{\sqrt[4]{-1} (-i b \log (f)+e+2 f x)}{2 \sqrt{f}}\right)+e^{\frac{i e^2}{f}} \left(\sqrt{3} (\cos (3 d)-i \sin (3 d)) e^{\frac{i \left(b^2 \log ^2(f)+3 e^2\right)}{6 f}} \text{erfi}\left(\frac{(-1)^{3/4} (i b \log (f)+3 e+6 f x)}{2 \sqrt{3} \sqrt{f}}\right)-9 (\cos (d)-i \sin (d)) \text{erfi}\left(\frac{(-1)^{3/4} (i b \log (f)+e+2 f x)}{2 \sqrt{f}}\right)\right)+\sqrt{3} e^{\frac{i b^2 \log ^2(f)}{3 f}} (\sin (3 d)-i \cos (3 d)) \text{erfi}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (-i b \log (f)+3 e+6 f x)}{\sqrt{6} \sqrt{f}}\right)\right)","\frac{3}{16} (-1)^{3/4} \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{1}{4} i \left(4 d+\frac{(b \log (f)+i e)^2}{f}\right)} \text{erf}\left(\frac{\sqrt[4]{-1} (b \log (f)+i e+2 i f x)}{2 \sqrt{f}}\right)+\left(\frac{1}{16}-\frac{i}{16}\right) \sqrt{\frac{\pi }{6}} f^{a-\frac{1}{2}} e^{\frac{i (b \log (f)+3 i e)^2}{12 f}+3 i d} \text{erf}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (b \log (f)+3 i e+6 i f x)}{\sqrt{6} \sqrt{f}}\right)-\frac{3}{16} (-1)^{3/4} \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{i (e+i b \log (f))^2}{4 f}-i d} \text{erfi}\left(\frac{\sqrt[4]{-1} (-b \log (f)+i e+2 i f x)}{2 \sqrt{f}}\right)-\left(\frac{1}{16}-\frac{i}{16}\right) \sqrt{\frac{\pi }{6}} f^{a-\frac{1}{2}} e^{\frac{i (3 e+i b \log (f))^2}{12 f}-3 i d} \text{erfi}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (-b \log (f)+3 i e+6 i f x)}{\sqrt{6} \sqrt{f}}\right)",1,"((-1)^(3/4)*f^(a - (b*e + f)/(2*f))*Sqrt[Pi]*((9*I)*E^(((I/2)*(e^2 + b^2*Log[f]^2))/f)*Erfi[((-1)^(1/4)*(e + 2*f*x - I*b*Log[f]))/(2*Sqrt[f])]*(Cos[d] + I*Sin[d]) + E^((I*e^2)/f)*(-9*Erfi[((-1)^(3/4)*(e + 2*f*x + I*b*Log[f]))/(2*Sqrt[f])]*(Cos[d] - I*Sin[d]) + Sqrt[3]*E^(((I/6)*(3*e^2 + b^2*Log[f]^2))/f)*Erfi[((-1)^(3/4)*(3*e + 6*f*x + I*b*Log[f]))/(2*Sqrt[3]*Sqrt[f])]*(Cos[3*d] - I*Sin[3*d])) + Sqrt[3]*E^(((I/3)*b^2*Log[f]^2)/f)*Erfi[((1/2 + I/2)*(3*e + 6*f*x - I*b*Log[f]))/(Sqrt[6]*Sqrt[f])]*((-I)*Cos[3*d] + Sin[3*d])))/(48*E^(((I/4)*(3*e^2 + b^2*Log[f]^2))/f))","A",1
85,1,119,151,0.1528507,"\int f^{a+c x^2} \sin (d+e x) \, dx","Integrate[f^(a + c*x^2)*Sin[d + e*x],x]","\frac{\sqrt{\pi } f^a e^{\frac{e^2}{4 c \log (f)}} \left(i (\cos (d)+i \sin (d)) \text{erfi}\left(\frac{-2 c x \log (f)-i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+(\sin (d)+i \cos (d)) \text{erfi}\left(\frac{2 c x \log (f)-i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)\right)}{4 \sqrt{c} \sqrt{\log (f)}}","-\frac{i \sqrt{\pi } f^a e^{\frac{e^2}{4 c \log (f)}-i d} \text{erfi}\left(\frac{-2 c x \log (f)+i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}-\frac{i \sqrt{\pi } f^a e^{\frac{e^2}{4 c \log (f)}+i d} \text{erfi}\left(\frac{2 c x \log (f)+i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}",1,"(E^(e^2/(4*c*Log[f]))*f^a*Sqrt[Pi]*(I*Erfi[((-I)*e - 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cos[d] + I*Sin[d]) + Erfi[((-I)*e + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(I*Cos[d] + Sin[d])))/(4*Sqrt[c]*Sqrt[Log[f]])","A",1
86,1,132,171,0.2465246,"\int f^{a+c x^2} \sin ^2(d+e x) \, dx","Integrate[f^(a + c*x^2)*Sin[d + e*x]^2,x]","\frac{\sqrt{\pi } f^a \left(2 \text{erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)-e^{\frac{e^2}{c \log (f)}} \left((\cos (2 d)-i \sin (2 d)) \text{erfi}\left(\frac{c x \log (f)-i e}{\sqrt{c} \sqrt{\log (f)}}\right)+(\cos (2 d)+i \sin (2 d)) \text{erfi}\left(\frac{c x \log (f)+i e}{\sqrt{c} \sqrt{\log (f)}}\right)\right)\right)}{8 \sqrt{c} \sqrt{\log (f)}}","\frac{\sqrt{\pi } f^a e^{\frac{e^2}{c \log (f)}-2 i d} \text{erfi}\left(\frac{-c x \log (f)+i e}{\sqrt{c} \sqrt{\log (f)}}\right)}{8 \sqrt{c} \sqrt{\log (f)}}-\frac{\sqrt{\pi } f^a e^{\frac{e^2}{c \log (f)}+2 i d} \text{erfi}\left(\frac{c x \log (f)+i e}{\sqrt{c} \sqrt{\log (f)}}\right)}{8 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a \text{erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)}{4 \sqrt{c} \sqrt{\log (f)}}",1,"(f^a*Sqrt[Pi]*(2*Erfi[Sqrt[c]*x*Sqrt[Log[f]]] - E^(e^2/(c*Log[f]))*(Erfi[((-I)*e + c*x*Log[f])/(Sqrt[c]*Sqrt[Log[f]])]*(Cos[2*d] - I*Sin[2*d]) + Erfi[(I*e + c*x*Log[f])/(Sqrt[c]*Sqrt[Log[f]])]*(Cos[2*d] + I*Sin[2*d]))))/(8*Sqrt[c]*Sqrt[Log[f]])","A",1
87,1,224,301,0.4239674,"\int f^{a+c x^2} \sin ^3(d+e x) \, dx","Integrate[f^(a + c*x^2)*Sin[d + e*x]^3,x]","\frac{\sqrt{\pi } f^a e^{\frac{e^2}{4 c \log (f)}} \left(-i e^{\frac{2 e^2}{c \log (f)}} \left((\cos (3 d)-i \sin (3 d)) \text{erfi}\left(\frac{2 c x \log (f)-3 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)-(\cos (3 d)+i \sin (3 d)) \text{erfi}\left(\frac{2 c x \log (f)+3 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)\right)+3 i (\cos (d)+i \sin (d)) \text{erfi}\left(\frac{-2 c x \log (f)-i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+3 (\sin (d)+i \cos (d)) \text{erfi}\left(\frac{2 c x \log (f)-i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)\right)}{16 \sqrt{c} \sqrt{\log (f)}}","-\frac{3 i \sqrt{\pi } f^a e^{\frac{e^2}{4 c \log (f)}-i d} \text{erfi}\left(\frac{-2 c x \log (f)+i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}+\frac{i \sqrt{\pi } f^a e^{\frac{9 e^2}{4 c \log (f)}-3 i d} \text{erfi}\left(\frac{-2 c x \log (f)+3 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}-\frac{3 i \sqrt{\pi } f^a e^{\frac{e^2}{4 c \log (f)}+i d} \text{erfi}\left(\frac{2 c x \log (f)+i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}+\frac{i \sqrt{\pi } f^a e^{\frac{9 e^2}{4 c \log (f)}+3 i d} \text{erfi}\left(\frac{2 c x \log (f)+3 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}",1,"(E^(e^2/(4*c*Log[f]))*f^a*Sqrt[Pi]*((3*I)*Erfi[((-I)*e - 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cos[d] + I*Sin[d]) + 3*Erfi[((-I)*e + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(I*Cos[d] + Sin[d]) - I*E^((2*e^2)/(c*Log[f]))*(Erfi[((-3*I)*e + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cos[3*d] - I*Sin[3*d]) - Erfi[((3*I)*e + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cos[3*d] + I*Sin[3*d]))))/(16*Sqrt[c]*Sqrt[Log[f]])","A",1
88,1,170,107,0.4774522,"\int f^{a+c x^2} \sin \left(d+f x^2\right) \, dx","Integrate[f^(a + c*x^2)*Sin[d + f*x^2],x]","-\frac{\sqrt[4]{-1} \sqrt{\pi } f^a \left(\sqrt{f+i c \log (f)} \left(c \sin (d) \log (f) \text{erf}\left(\frac{(1+i) x \sqrt{f+i c \log (f)}}{\sqrt{2}}\right)+\text{erfi}\left((-1)^{3/4} x \sqrt{f+i c \log (f)}\right) (f \sin (d)+\cos (d) (c \log (f)+i f))\right)+\sqrt{f-i c \log (f)} (f+i c \log (f)) (\cos (d)+i \sin (d)) \text{erfi}\left(\sqrt[4]{-1} x \sqrt{f-i c \log (f)}\right)\right)}{4 \left(c^2 \log ^2(f)+f^2\right)}","\frac{i \sqrt{\pi } e^{-i d} f^a \text{erf}\left(x \sqrt{-c \log (f)+i f}\right)}{4 \sqrt{-c \log (f)+i f}}-\frac{i \sqrt{\pi } e^{i d} f^a \text{erfi}\left(x \sqrt{c \log (f)+i f}\right)}{4 \sqrt{c \log (f)+i f}}",1,"-1/4*((-1)^(1/4)*f^a*Sqrt[Pi]*(Erfi[(-1)^(1/4)*x*Sqrt[f - I*c*Log[f]]]*Sqrt[f - I*c*Log[f]]*(f + I*c*Log[f])*(Cos[d] + I*Sin[d]) + Sqrt[f + I*c*Log[f]]*(c*Erf[((1 + I)*x*Sqrt[f + I*c*Log[f]])/Sqrt[2]]*Log[f]*Sin[d] + Erfi[(-1)^(3/4)*x*Sqrt[f + I*c*Log[f]]]*(Cos[d]*(I*f + c*Log[f]) + f*Sin[d]))))/(f^2 + c^2*Log[f]^2)","A",1
89,1,188,140,0.8165228,"\int f^{a+c x^2} \sin ^2\left(d+f x^2\right) \, dx","Integrate[f^(a + c*x^2)*Sin[d + f*x^2]^2,x]","\frac{1}{8} \sqrt{\pi } f^a \left(\frac{2 \text{erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)}{\sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt[4]{-1} \left(\sqrt{2 f+i c \log (f)} (c \log (f)+2 i f) (\cos (2 d)-i \sin (2 d)) \text{erf}\left(\sqrt[4]{-1} x \sqrt{2 f+i c \log (f)}\right)+\sqrt{2 f-i c \log (f)} (2 f+i c \log (f)) (\cos (2 d)+i \sin (2 d)) \text{erf}\left((-1)^{3/4} x \sqrt{2 f-i c \log (f)}\right)\right)}{c^2 \log ^2(f)+4 f^2}\right)","-\frac{\sqrt{\pi } e^{-2 i d} f^a \text{erf}\left(x \sqrt{-c \log (f)+2 i f}\right)}{8 \sqrt{-c \log (f)+2 i f}}-\frac{\sqrt{\pi } e^{2 i d} f^a \text{erfi}\left(x \sqrt{c \log (f)+2 i f}\right)}{8 \sqrt{c \log (f)+2 i f}}+\frac{\sqrt{\pi } f^a \text{erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)}{4 \sqrt{c} \sqrt{\log (f)}}",1,"(f^a*Sqrt[Pi]*((2*Erfi[Sqrt[c]*x*Sqrt[Log[f]]])/(Sqrt[c]*Sqrt[Log[f]]) + ((-1)^(1/4)*(Erf[(-1)^(1/4)*x*Sqrt[2*f + I*c*Log[f]]]*Sqrt[2*f + I*c*Log[f]]*((2*I)*f + c*Log[f])*(Cos[2*d] - I*Sin[2*d]) + Erf[(-1)^(3/4)*x*Sqrt[2*f - I*c*Log[f]]]*Sqrt[2*f - I*c*Log[f]]*(2*f + I*c*Log[f])*(Cos[2*d] + I*Sin[2*d])))/(4*f^2 + c^2*Log[f]^2)))/8","A",1
90,1,386,213,2.3145668,"\int f^{a+c x^2} \sin ^3\left(d+f x^2\right) \, dx","Integrate[f^(a + c*x^2)*Sin[d + f*x^2]^3,x]","\frac{\sqrt[4]{-1} \sqrt{\pi } f^a \left((f-i c \log (f)) \left(\sqrt{3 f-i c \log (f)} \left(-c^2 \log ^2(f)+4 i c f \log (f)+3 f^2\right) (\cos (3 d)+i \sin (3 d)) \text{erfi}\left(\sqrt[4]{-1} x \sqrt{3 f-i c \log (f)}\right)+(3 f-i c \log (f)) \left(3 \sqrt{f+i c \log (f)} \text{erf}\left(\frac{(1+i) x \sqrt{f+i c \log (f)}}{\sqrt{2}}\right) (c \sin (d) \log (f)+3 f \cos (d))+3 \sqrt{f+i c \log (f)} \text{erfi}\left((-1)^{3/4} x \sqrt{f+i c \log (f)}\right) (c \cos (d) \log (f)-3 f \sin (d))+(f+i c \log (f)) \sqrt{3 f+i c \log (f)} (\sin (3 d)+i \cos (3 d)) \text{erfi}\left((-1)^{3/4} x \sqrt{3 f+i c \log (f)}\right)\right)\right)-3 \sqrt{f-i c \log (f)} \left(i c^3 \log ^3(f)+c^2 f \log ^2(f)+9 i c f^2 \log (f)+9 f^3\right) (\cos (d)+i \sin (d)) \text{erfi}\left(\sqrt[4]{-1} x \sqrt{f-i c \log (f)}\right)\right)}{16 \left(c^4 \log ^4(f)+10 c^2 f^2 \log ^2(f)+9 f^4\right)}","\frac{3 i \sqrt{\pi } e^{-i d} f^a \text{erf}\left(x \sqrt{-c \log (f)+i f}\right)}{16 \sqrt{-c \log (f)+i f}}-\frac{i \sqrt{\pi } e^{-3 i d} f^a \text{erf}\left(x \sqrt{-c \log (f)+3 i f}\right)}{16 \sqrt{-c \log (f)+3 i f}}-\frac{3 i \sqrt{\pi } e^{i d} f^a \text{erfi}\left(x \sqrt{c \log (f)+i f}\right)}{16 \sqrt{c \log (f)+i f}}+\frac{i \sqrt{\pi } e^{3 i d} f^a \text{erfi}\left(x \sqrt{c \log (f)+3 i f}\right)}{16 \sqrt{c \log (f)+3 i f}}",1,"((-1)^(1/4)*f^a*Sqrt[Pi]*(-3*Erfi[(-1)^(1/4)*x*Sqrt[f - I*c*Log[f]]]*Sqrt[f - I*c*Log[f]]*(9*f^3 + (9*I)*c*f^2*Log[f] + c^2*f*Log[f]^2 + I*c^3*Log[f]^3)*(Cos[d] + I*Sin[d]) + (f - I*c*Log[f])*(Erfi[(-1)^(1/4)*x*Sqrt[3*f - I*c*Log[f]]]*Sqrt[3*f - I*c*Log[f]]*(3*f^2 + (4*I)*c*f*Log[f] - c^2*Log[f]^2)*(Cos[3*d] + I*Sin[3*d]) + (3*f - I*c*Log[f])*(3*Erfi[(-1)^(3/4)*x*Sqrt[f + I*c*Log[f]]]*Sqrt[f + I*c*Log[f]]*(c*Cos[d]*Log[f] - 3*f*Sin[d]) + 3*Erf[((1 + I)*x*Sqrt[f + I*c*Log[f]])/Sqrt[2]]*Sqrt[f + I*c*Log[f]]*(3*f*Cos[d] + c*Log[f]*Sin[d]) + Erfi[(-1)^(3/4)*x*Sqrt[3*f + I*c*Log[f]]]*(f + I*c*Log[f])*Sqrt[3*f + I*c*Log[f]]*(I*Cos[3*d] + Sin[3*d])))))/(16*(9*f^4 + 10*c^2*f^2*Log[f]^2 + c^4*Log[f]^4))","A",1
91,1,216,187,0.9569118,"\int f^{a+c x^2} \sin \left(d+e x+f x^2\right) \, dx","Integrate[f^(a + c*x^2)*Sin[d + e*x + f*x^2],x]","-\frac{(-1)^{3/4} \sqrt{\pi } f^a e^{\frac{e^2}{4 c \log (f)+4 i f}} \left((f-i c \log (f)) \sqrt{f+i c \log (f)} (\cos (d)-i \sin (d)) e^{\frac{i e^2 f}{2 \left(c^2 \log ^2(f)+f^2\right)}} \text{erfi}\left(\frac{(-1)^{3/4} (2 i c x \log (f)+e+2 f x)}{2 \sqrt{f+i c \log (f)}}\right)+\sqrt{f-i c \log (f)} (c \log (f)-i f) (\cos (d)+i \sin (d)) \text{erfi}\left(\frac{\sqrt[4]{-1} (-2 i c x \log (f)+e+2 f x)}{2 \sqrt{f-i c \log (f)}}\right)\right)}{4 \left(c^2 \log ^2(f)+f^2\right)}","\frac{i \sqrt{\pi } f^a e^{-\frac{e^2}{-4 c \log (f)+4 i f}-i d} \text{erf}\left(\frac{2 x (-c \log (f)+i f)+i e}{2 \sqrt{-c \log (f)+i f}}\right)}{4 \sqrt{-c \log (f)+i f}}-\frac{i \sqrt{\pi } f^a e^{\frac{e^2}{4 c \log (f)+4 i f}+i d} \text{erfi}\left(\frac{2 x (c \log (f)+i f)+i e}{2 \sqrt{c \log (f)+i f}}\right)}{4 \sqrt{c \log (f)+i f}}",1,"-1/4*((-1)^(3/4)*E^(e^2/((4*I)*f + 4*c*Log[f]))*f^a*Sqrt[Pi]*(E^(((I/2)*e^2*f)/(f^2 + c^2*Log[f]^2))*Erfi[((-1)^(3/4)*(e + 2*f*x + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*(f - I*c*Log[f])*Sqrt[f + I*c*Log[f]]*(Cos[d] - I*Sin[d]) + Erfi[((-1)^(1/4)*(e + 2*f*x - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Sqrt[f - I*c*Log[f]]*((-I)*f + c*Log[f])*(Cos[d] + I*Sin[d])))/(f^2 + c^2*Log[f]^2)","A",0
92,1,251,211,2.2485259,"\int f^{a+c x^2} \sin ^2\left(d+e x+f x^2\right) \, dx","Integrate[f^(a + c*x^2)*Sin[d + e*x + f*x^2]^2,x]","\frac{1}{8} \sqrt{\pi } f^a \left(\frac{2 \text{erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)}{\sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt[4]{-1} \left(\sqrt{2 f-i c \log (f)} (2 f+i c \log (f)) (\cos (2 d)+i \sin (2 d)) e^{\frac{e^2}{c \log (f)+2 i f}} \text{erf}\left(\frac{(-1)^{3/4} (-i c x \log (f)+e+2 f x)}{\sqrt{2 f-i c \log (f)}}\right)+(2 f-i c \log (f)) \sqrt{2 f+i c \log (f)} (\sin (2 d)+i \cos (2 d)) e^{\frac{e^2}{c \log (f)-2 i f}} \text{erf}\left(\frac{\sqrt[4]{-1} (i c x \log (f)+e+2 f x)}{\sqrt{2 f+i c \log (f)}}\right)\right)}{c^2 \log ^2(f)+4 f^2}\right)","-\frac{\sqrt{\pi } f^a e^{-\frac{e^2}{-c \log (f)+2 i f}-2 i d} \text{erf}\left(\frac{x (-c \log (f)+2 i f)+i e}{\sqrt{-c \log (f)+2 i f}}\right)}{8 \sqrt{-c \log (f)+2 i f}}-\frac{\sqrt{\pi } f^a e^{\frac{e^2}{c \log (f)+2 i f}+2 i d} \text{erfi}\left(\frac{x (c \log (f)+2 i f)+i e}{\sqrt{c \log (f)+2 i f}}\right)}{8 \sqrt{c \log (f)+2 i f}}+\frac{\sqrt{\pi } f^a \text{erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)}{4 \sqrt{c} \sqrt{\log (f)}}",1,"(f^a*Sqrt[Pi]*((2*Erfi[Sqrt[c]*x*Sqrt[Log[f]]])/(Sqrt[c]*Sqrt[Log[f]]) + ((-1)^(1/4)*(E^(e^2/((2*I)*f + c*Log[f]))*Erf[((-1)^(3/4)*(e + 2*f*x - I*c*x*Log[f]))/Sqrt[2*f - I*c*Log[f]]]*Sqrt[2*f - I*c*Log[f]]*(2*f + I*c*Log[f])*(Cos[2*d] + I*Sin[2*d]) + E^(e^2/((-2*I)*f + c*Log[f]))*Erf[((-1)^(1/4)*(e + 2*f*x + I*c*x*Log[f]))/Sqrt[2*f + I*c*Log[f]]]*(2*f - I*c*Log[f])*Sqrt[2*f + I*c*Log[f]]*(I*Cos[2*d] + Sin[2*d])))/(4*f^2 + c^2*Log[f]^2)))/8","A",0
93,1,490,377,6.6843454,"\int f^{a+c x^2} \sin ^3\left(d+e x+f x^2\right) \, dx","Integrate[f^(a + c*x^2)*Sin[d + e*x + f*x^2]^3,x]","\frac{\sqrt[4]{-1} \sqrt{\pi } f^a \left((f-i c \log (f)) \left(\sqrt{3 f-i c \log (f)} \left(-c^2 \log ^2(f)+4 i c f \log (f)+3 f^2\right) (\cos (3 d)+i \sin (3 d)) e^{\frac{9 e^2}{4 (c \log (f)+3 i f)}} \text{erfi}\left(\frac{\sqrt[4]{-1} (-2 i c x \log (f)+3 e+6 f x)}{2 \sqrt{3 f-i c \log (f)}}\right)+(3 f-i c \log (f)) \left(3 \sqrt{f+i c \log (f)} (c \log (f)-3 i f) (\cos (d)-i \sin (d)) e^{\frac{e^2}{4 c \log (f)-4 i f}} \text{erfi}\left(\frac{(-1)^{3/4} (2 i c x \log (f)+e+2 f x)}{2 \sqrt{f+i c \log (f)}}\right)+(f+i c \log (f)) \sqrt{3 f+i c \log (f)} (\sin (3 d)+i \cos (3 d)) e^{\frac{9 e^2}{4 (c \log (f)-3 i f)}} \text{erfi}\left(\frac{(-1)^{3/4} (2 i c x \log (f)+3 e+6 f x)}{2 \sqrt{3 f+i c \log (f)}}\right)\right)\right)-3 \sqrt{f-i c \log (f)} \left(i c^3 \log ^3(f)+c^2 f \log ^2(f)+9 i c f^2 \log (f)+9 f^3\right) (\cos (d)+i \sin (d)) e^{\frac{e^2}{4 c \log (f)+4 i f}} \text{erfi}\left(\frac{\sqrt[4]{-1} (-2 i c x \log (f)+e+2 f x)}{2 \sqrt{f-i c \log (f)}}\right)\right)}{16 \left(c^4 \log ^4(f)+10 c^2 f^2 \log ^2(f)+9 f^4\right)}","-\frac{i \sqrt{\pi } f^a \exp \left(-\frac{9 e^2}{4 (-c \log (f)+3 i f)}-3 i d\right) \text{erf}\left(\frac{2 x (-c \log (f)+3 i f)+3 i e}{2 \sqrt{-c \log (f)+3 i f}}\right)}{16 \sqrt{-c \log (f)+3 i f}}+\frac{3 i \sqrt{\pi } f^a e^{-\frac{e^2}{-4 c \log (f)+4 i f}-i d} \text{erf}\left(\frac{2 x (-c \log (f)+i f)+i e}{2 \sqrt{-c \log (f)+i f}}\right)}{16 \sqrt{-c \log (f)+i f}}-\frac{3 i \sqrt{\pi } f^a e^{\frac{e^2}{4 c \log (f)+4 i f}+i d} \text{erfi}\left(\frac{2 x (c \log (f)+i f)+i e}{2 \sqrt{c \log (f)+i f}}\right)}{16 \sqrt{c \log (f)+i f}}+\frac{i \sqrt{\pi } f^a e^{\frac{9 e^2}{4 (c \log (f)+3 i f)}+3 i d} \text{erfi}\left(\frac{2 x (c \log (f)+3 i f)+3 i e}{2 \sqrt{c \log (f)+3 i f}}\right)}{16 \sqrt{c \log (f)+3 i f}}",1,"((-1)^(1/4)*f^a*Sqrt[Pi]*(-3*E^(e^2/((4*I)*f + 4*c*Log[f]))*Erfi[((-1)^(1/4)*(e + 2*f*x - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Sqrt[f - I*c*Log[f]]*(9*f^3 + (9*I)*c*f^2*Log[f] + c^2*f*Log[f]^2 + I*c^3*Log[f]^3)*(Cos[d] + I*Sin[d]) + (f - I*c*Log[f])*(E^((9*e^2)/(4*((3*I)*f + c*Log[f])))*Erfi[((-1)^(1/4)*(3*e + 6*f*x - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Sqrt[3*f - I*c*Log[f]]*(3*f^2 + (4*I)*c*f*Log[f] - c^2*Log[f]^2)*(Cos[3*d] + I*Sin[3*d]) + (3*f - I*c*Log[f])*(3*E^(e^2/((-4*I)*f + 4*c*Log[f]))*Erfi[((-1)^(3/4)*(e + 2*f*x + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Sqrt[f + I*c*Log[f]]*((-3*I)*f + c*Log[f])*(Cos[d] - I*Sin[d]) + E^((9*e^2)/(4*((-3*I)*f + c*Log[f])))*Erfi[((-1)^(3/4)*(3*e + 6*f*x + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*(f + I*c*Log[f])*Sqrt[3*f + I*c*Log[f]]*(I*Cos[3*d] + Sin[3*d])))))/(16*(9*f^4 + 10*c^2*f^2*Log[f]^2 + c^4*Log[f]^4))","A",0
94,1,155,176,0.3375705,"\int f^{a+b x+c x^2} \sin (d+e x) \, dx","Integrate[f^(a + b*x + c*x^2)*Sin[d + e*x],x]","\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} e^{\frac{e (e-2 i b \log (f))}{4 c \log (f)}} \left(i (\cos (d)+i \sin (d)) \text{erfi}\left(\frac{-\log (f) (b+2 c x)-i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+e^{\frac{i b e}{c}} (\sin (d)+i \cos (d)) \text{erfi}\left(\frac{\log (f) (b+2 c x)-i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)\right)}{4 \sqrt{c} \sqrt{\log (f)}}","-\frac{i \sqrt{\pi } f^a e^{\frac{(e+i b \log (f))^2}{4 c \log (f)}-i d} \text{erfi}\left(\frac{-b \log (f)-2 c x \log (f)+i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}-\frac{i \sqrt{\pi } f^a e^{\frac{(e-i b \log (f))^2}{4 c \log (f)}+i d} \text{erfi}\left(\frac{b \log (f)+2 c x \log (f)+i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}",1,"(E^((e*(e - (2*I)*b*Log[f]))/(4*c*Log[f]))*f^(a - b^2/(4*c))*Sqrt[Pi]*(I*Erfi[((-I)*e - (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cos[d] + I*Sin[d]) + E^((I*b*e)/c)*Erfi[((-I)*e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(I*Cos[d] + Sin[d])))/(4*Sqrt[c]*Sqrt[Log[f]])","A",1
95,1,204,231,0.6937783,"\int f^{a+b x+c x^2} \sin ^2(d+e x) \, dx","Integrate[f^(a + b*x + c*x^2)*Sin[d + e*x]^2,x]","-\frac{\sqrt{\pi } e^{-\frac{i b e}{c}} f^{a-\frac{b^2}{4 c}} \left((\cos (2 d)+i \sin (2 d)) e^{\frac{e^2}{c \log (f)}} \text{erfi}\left(\frac{\log (f) (b+2 c x)+2 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+(\cos (2 d)-i \sin (2 d)) e^{\frac{e (e+2 i b \log (f))}{c \log (f)}} \text{erfi}\left(\frac{\log (f) (b+2 c x)-2 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)-2 e^{\frac{i b e}{c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)\right)}{8 \sqrt{c} \sqrt{\log (f)}}","\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a e^{\frac{(2 e+i b \log (f))^2}{4 c \log (f)}-2 i d} \text{erfi}\left(\frac{-b \log (f)-2 c x \log (f)+2 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{8 \sqrt{c} \sqrt{\log (f)}}-\frac{\sqrt{\pi } f^a e^{2 i d-\frac{(b \log (f)+2 i e)^2}{4 c \log (f)}} \text{erfi}\left(\frac{b \log (f)+2 c x \log (f)+2 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{8 \sqrt{c} \sqrt{\log (f)}}",1,"-1/8*(f^(a - b^2/(4*c))*Sqrt[Pi]*(-2*E^((I*b*e)/c)*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])] + E^((e*(e + (2*I)*b*Log[f]))/(c*Log[f]))*Erfi[((-2*I)*e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cos[2*d] - I*Sin[2*d]) + E^(e^2/(c*Log[f]))*Erfi[((2*I)*e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cos[2*d] + I*Sin[2*d])))/(Sqrt[c]*E^((I*b*e)/c)*Sqrt[Log[f]])","A",1
96,1,391,354,0.9849715,"\int f^{a+b x+c x^2} \sin ^3(d+e x) \, dx","Integrate[f^(a + b*x + c*x^2)*Sin[d + e*x]^3,x]","\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} e^{\frac{e (e-6 i b \log (f))}{4 c \log (f)}} \left(-\sin (3 d) e^{\frac{2 e^2}{c \log (f)}} \text{erfi}\left(\frac{\log (f) (b+2 c x)+3 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+i \cos (3 d) e^{\frac{2 e^2}{c \log (f)}} \text{erfi}\left(\frac{\log (f) (b+2 c x)+3 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)-\sin (3 d) e^{\frac{e (2 e+3 i b \log (f))}{c \log (f)}} \text{erfi}\left(\frac{\log (f) (b+2 c x)-3 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)-i \cos (3 d) e^{\frac{e (2 e+3 i b \log (f))}{c \log (f)}} \text{erfi}\left(\frac{\log (f) (b+2 c x)-3 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+3 i e^{\frac{i b e}{c}} (\cos (d)+i \sin (d)) \text{erfi}\left(\frac{-\log (f) (b+2 c x)-i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+3 e^{\frac{2 i b e}{c}} (\sin (d)+i \cos (d)) \text{erfi}\left(\frac{\log (f) (b+2 c x)-i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)\right)}{16 \sqrt{c} \sqrt{\log (f)}}","-\frac{3 i \sqrt{\pi } f^a e^{\frac{(e+i b \log (f))^2}{4 c \log (f)}-i d} \text{erfi}\left(\frac{-b \log (f)-2 c x \log (f)+i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}+\frac{i \sqrt{\pi } f^a e^{\frac{(3 e+i b \log (f))^2}{4 c \log (f)}-3 i d} \text{erfi}\left(\frac{-b \log (f)-2 c x \log (f)+3 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}-\frac{3 i \sqrt{\pi } f^a e^{\frac{(e-i b \log (f))^2}{4 c \log (f)}+i d} \text{erfi}\left(\frac{b \log (f)+2 c x \log (f)+i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}+\frac{i \sqrt{\pi } f^a e^{3 i d-\frac{(b \log (f)+3 i e)^2}{4 c \log (f)}} \text{erfi}\left(\frac{b \log (f)+2 c x \log (f)+3 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}",1,"(E^((e*(e - (6*I)*b*Log[f]))/(4*c*Log[f]))*f^(a - b^2/(4*c))*Sqrt[Pi]*((-I)*E^((e*(2*e + (3*I)*b*Log[f]))/(c*Log[f]))*Cos[3*d]*Erfi[((-3*I)*e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])] + I*E^((2*e^2)/(c*Log[f]))*Cos[3*d]*Erfi[((3*I)*e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])] + (3*I)*E^((I*b*e)/c)*Erfi[((-I)*e - (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cos[d] + I*Sin[d]) + 3*E^(((2*I)*b*e)/c)*Erfi[((-I)*e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(I*Cos[d] + Sin[d]) - E^((e*(2*e + (3*I)*b*Log[f]))/(c*Log[f]))*Erfi[((-3*I)*e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*Sin[3*d] - E^((2*e^2)/(c*Log[f]))*Erfi[((3*I)*e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*Sin[3*d]))/(16*Sqrt[c]*Sqrt[Log[f]])","A",1
97,1,230,193,0.9880321,"\int f^{a+b x+c x^2} \sin \left(d+f x^2\right) \, dx","Integrate[f^(a + b*x + c*x^2)*Sin[d + f*x^2],x]","-\frac{\sqrt[4]{-1} \sqrt{\pi } f^a e^{\frac{b^2 \log ^2(f)}{-4 c \log (f)+4 i f}} \left(\sqrt{f-i c \log (f)} (f+i c \log (f)) (\cos (d)+i \sin (d)) e^{\frac{i b^2 f \log ^2(f)}{2 \left(c^2 \log ^2(f)+f^2\right)}} \text{erfi}\left(\frac{\sqrt[4]{-1} (2 f x-i \log (f) (b+2 c x))}{2 \sqrt{f-i c \log (f)}}\right)+\sqrt{f+i c \log (f)} (c \log (f)+i f) (\cos (d)-i \sin (d)) \text{erfi}\left(\frac{(-1)^{3/4} (2 f x+i \log (f) (b+2 c x))}{2 \sqrt{f+i c \log (f)}}\right)\right)}{4 \left(c^2 \log ^2(f)+f^2\right)}","-\frac{i \sqrt{\pi } f^a e^{\frac{b^2 \log ^2(f)}{-4 c \log (f)+4 i f}-i d} \text{erf}\left(\frac{b \log (f)-2 x (-c \log (f)+i f)}{2 \sqrt{-c \log (f)+i f}}\right)}{4 \sqrt{-c \log (f)+i f}}-\frac{i \sqrt{\pi } f^a e^{i d-\frac{b^2 \log ^2(f)}{4 c \log (f)+4 i f}} \text{erfi}\left(\frac{b \log (f)+2 x (c \log (f)+i f)}{2 \sqrt{c \log (f)+i f}}\right)}{4 \sqrt{c \log (f)+i f}}",1,"-1/4*((-1)^(1/4)*E^((b^2*Log[f]^2)/((4*I)*f - 4*c*Log[f]))*f^a*Sqrt[Pi]*(Erfi[((-1)^(3/4)*(2*f*x + I*(b + 2*c*x)*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Sqrt[f + I*c*Log[f]]*(I*f + c*Log[f])*(Cos[d] - I*Sin[d]) + E^(((I/2)*b^2*f*Log[f]^2)/(f^2 + c^2*Log[f]^2))*Erfi[((-1)^(1/4)*(2*f*x - I*(b + 2*c*x)*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Sqrt[f - I*c*Log[f]]*(f + I*c*Log[f])*(Cos[d] + I*Sin[d])))/(f^2 + c^2*Log[f]^2)","A",1
98,1,299,245,3.0906914,"\int f^{a+b x+c x^2} \sin ^2\left(d+f x^2\right) \, dx","Integrate[f^(a + b*x + c*x^2)*Sin[d + f*x^2]^2,x]","\frac{1}{8} \sqrt{\pi } f^a \left(\frac{2 f^{-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{\sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt[4]{-1} e^{\frac{b^2 \log ^2(f)}{-4 c \log (f)+8 i f}} \left(\sqrt{2 f-i c \log (f)} (2 f+i c \log (f)) (\cos (2 d)+i \sin (2 d)) e^{\frac{i b^2 f \log ^2(f)}{c^2 \log ^2(f)+4 f^2}} \text{erf}\left(\frac{(-1)^{3/4} (4 f x-i \log (f) (b+2 c x))}{2 \sqrt{2 f-i c \log (f)}}\right)+\sqrt{2 f+i c \log (f)} (c \log (f)+2 i f) (\cos (2 d)-i \sin (2 d)) \text{erf}\left(\frac{\sqrt[4]{-1} (4 f x+i \log (f) (b+2 c x))}{2 \sqrt{2 f+i c \log (f)}}\right)\right)}{c^2 \log ^2(f)+4 f^2}\right)","\frac{\sqrt{\pi } f^a e^{\frac{b^2 \log ^2(f)}{-4 c \log (f)+8 i f}-2 i d} \text{erf}\left(\frac{b \log (f)-2 x (-c \log (f)+2 i f)}{2 \sqrt{-c \log (f)+2 i f}}\right)}{8 \sqrt{-c \log (f)+2 i f}}-\frac{\sqrt{\pi } f^a e^{2 i d-\frac{b^2 \log ^2(f)}{4 c \log (f)+8 i f}} \text{erfi}\left(\frac{b \log (f)+2 x (c \log (f)+2 i f)}{2 \sqrt{c \log (f)+2 i f}}\right)}{8 \sqrt{c \log (f)+2 i f}}+\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}",1,"(f^a*Sqrt[Pi]*((2*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])])/(Sqrt[c]*f^(b^2/(4*c))*Sqrt[Log[f]]) + ((-1)^(1/4)*E^((b^2*Log[f]^2)/((8*I)*f - 4*c*Log[f]))*(Erf[((-1)^(1/4)*(4*f*x + I*(b + 2*c*x)*Log[f]))/(2*Sqrt[2*f + I*c*Log[f]])]*Sqrt[2*f + I*c*Log[f]]*((2*I)*f + c*Log[f])*(Cos[2*d] - I*Sin[2*d]) + E^((I*b^2*f*Log[f]^2)/(4*f^2 + c^2*Log[f]^2))*Erf[((-1)^(3/4)*(4*f*x - I*(b + 2*c*x)*Log[f]))/(2*Sqrt[2*f - I*c*Log[f]])]*Sqrt[2*f - I*c*Log[f]]*(2*f + I*c*Log[f])*(Cos[2*d] + I*Sin[2*d])))/(4*f^2 + c^2*Log[f]^2)))/8","A",0
99,1,3291,386,7.0381777,"\int f^{a+b x+c x^2} \sin ^3\left(d+f x^2\right) \, dx","Integrate[f^(a + b*x + c*x^2)*Sin[d + f*x^2]^3,x]","\text{Result too large to show}","-\frac{3 i \sqrt{\pi } f^a e^{\frac{b^2 \log ^2(f)}{-4 c \log (f)+4 i f}-i d} \text{erf}\left(\frac{b \log (f)-2 x (-c \log (f)+i f)}{2 \sqrt{-c \log (f)+i f}}\right)}{16 \sqrt{-c \log (f)+i f}}+\frac{i \sqrt{\pi } f^a e^{\frac{b^2 \log ^2(f)}{-4 c \log (f)+12 i f}-3 i d} \text{erf}\left(\frac{b \log (f)-2 x (-c \log (f)+3 i f)}{2 \sqrt{-c \log (f)+3 i f}}\right)}{16 \sqrt{-c \log (f)+3 i f}}+\frac{i \sqrt{\pi } f^a \exp \left(3 i d-\frac{b^2 \log ^2(f)}{4 (c \log (f)+3 i f)}\right) \text{erfi}\left(\frac{b \log (f)+2 x (c \log (f)+3 i f)}{2 \sqrt{c \log (f)+3 i f}}\right)}{16 \sqrt{c \log (f)+3 i f}}-\frac{3 i \sqrt{\pi } f^a e^{i d-\frac{b^2 \log ^2(f)}{4 c \log (f)+4 i f}} \text{erfi}\left(\frac{b \log (f)+2 x (c \log (f)+i f)}{2 \sqrt{c \log (f)+i f}}\right)}{16 \sqrt{c \log (f)+i f}}",1,"(f^a*Sqrt[Pi]*(-27*(-1)^(3/4)*E^(((I/4)*b^2*Log[f]^2)/(f - I*c*Log[f]))*f^3*Cos[d]*Erfi[((-1)^(1/4)*(2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Sqrt[f - I*c*Log[f]] + 27*(-1)^(1/4)*c*E^(((I/4)*b^2*Log[f]^2)/(f - I*c*Log[f]))*f^2*Cos[d]*Erfi[((-1)^(1/4)*(2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]*Sqrt[f - I*c*Log[f]] - 3*(-1)^(3/4)*c^2*E^(((I/4)*b^2*Log[f]^2)/(f - I*c*Log[f]))*f*Cos[d]*Erfi[((-1)^(1/4)*(2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]^2*Sqrt[f - I*c*Log[f]] + 3*(-1)^(1/4)*c^3*E^(((I/4)*b^2*Log[f]^2)/(f - I*c*Log[f]))*Cos[d]*Erfi[((-1)^(1/4)*(2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]^3*Sqrt[f - I*c*Log[f]] + 3*(-1)^(3/4)*E^(((I/4)*b^2*Log[f]^2)/(3*f - I*c*Log[f]))*f^3*Cos[3*d]*Erfi[((-1)^(1/4)*(6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Sqrt[3*f - I*c*Log[f]] - (-1)^(1/4)*c*E^(((I/4)*b^2*Log[f]^2)/(3*f - I*c*Log[f]))*f^2*Cos[3*d]*Erfi[((-1)^(1/4)*(6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]*Sqrt[3*f - I*c*Log[f]] + 3*(-1)^(3/4)*c^2*E^(((I/4)*b^2*Log[f]^2)/(3*f - I*c*Log[f]))*f*Cos[3*d]*Erfi[((-1)^(1/4)*(6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]^2*Sqrt[3*f - I*c*Log[f]] - (-1)^(1/4)*c^3*E^(((I/4)*b^2*Log[f]^2)/(3*f - I*c*Log[f]))*Cos[3*d]*Erfi[((-1)^(1/4)*(6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]^3*Sqrt[3*f - I*c*Log[f]] + (27*(-1)^(1/4)*f^3*Cos[d]*Erfi[((-1)^(3/4)*(2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Sqrt[f + I*c*Log[f]])/E^(((I/4)*b^2*Log[f]^2)/(f + I*c*Log[f])) - (27*(-1)^(3/4)*c*f^2*Cos[d]*Erfi[((-1)^(3/4)*(2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]*Sqrt[f + I*c*Log[f]])/E^(((I/4)*b^2*Log[f]^2)/(f + I*c*Log[f])) + (3*(-1)^(1/4)*c^2*f*Cos[d]*Erfi[((-1)^(3/4)*(2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]^2*Sqrt[f + I*c*Log[f]])/E^(((I/4)*b^2*Log[f]^2)/(f + I*c*Log[f])) - (3*(-1)^(3/4)*c^3*Cos[d]*Erfi[((-1)^(3/4)*(2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]^3*Sqrt[f + I*c*Log[f]])/E^(((I/4)*b^2*Log[f]^2)/(f + I*c*Log[f])) - (3*(-1)^(1/4)*f^3*Cos[3*d]*Erfi[((-1)^(3/4)*(6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Sqrt[3*f + I*c*Log[f]])/E^(((I/4)*b^2*Log[f]^2)/(3*f + I*c*Log[f])) + ((-1)^(3/4)*c*f^2*Cos[3*d]*Erfi[((-1)^(3/4)*(6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]*Sqrt[3*f + I*c*Log[f]])/E^(((I/4)*b^2*Log[f]^2)/(3*f + I*c*Log[f])) - (3*(-1)^(1/4)*c^2*f*Cos[3*d]*Erfi[((-1)^(3/4)*(6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]^2*Sqrt[3*f + I*c*Log[f]])/E^(((I/4)*b^2*Log[f]^2)/(3*f + I*c*Log[f])) + ((-1)^(3/4)*c^3*Cos[3*d]*Erfi[((-1)^(3/4)*(6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]^3*Sqrt[3*f + I*c*Log[f]])/E^(((I/4)*b^2*Log[f]^2)/(3*f + I*c*Log[f])) + 27*(-1)^(1/4)*E^(((I/4)*b^2*Log[f]^2)/(f - I*c*Log[f]))*f^3*Erfi[((-1)^(1/4)*(2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Sqrt[f - I*c*Log[f]]*Sin[d] + 27*(-1)^(3/4)*c*E^(((I/4)*b^2*Log[f]^2)/(f - I*c*Log[f]))*f^2*Erfi[((-1)^(1/4)*(2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]*Sqrt[f - I*c*Log[f]]*Sin[d] + 3*(-1)^(1/4)*c^2*E^(((I/4)*b^2*Log[f]^2)/(f - I*c*Log[f]))*f*Erfi[((-1)^(1/4)*(2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]^2*Sqrt[f - I*c*Log[f]]*Sin[d] + 3*(-1)^(3/4)*c^3*E^(((I/4)*b^2*Log[f]^2)/(f - I*c*Log[f]))*Erfi[((-1)^(1/4)*(2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]^3*Sqrt[f - I*c*Log[f]]*Sin[d] - (27*(-1)^(3/4)*f^3*Erfi[((-1)^(3/4)*(2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Sqrt[f + I*c*Log[f]]*Sin[d])/E^(((I/4)*b^2*Log[f]^2)/(f + I*c*Log[f])) - (27*(-1)^(1/4)*c*f^2*Erfi[((-1)^(3/4)*(2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]*Sqrt[f + I*c*Log[f]]*Sin[d])/E^(((I/4)*b^2*Log[f]^2)/(f + I*c*Log[f])) - (3*(-1)^(3/4)*c^2*f*Erfi[((-1)^(3/4)*(2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]^2*Sqrt[f + I*c*Log[f]]*Sin[d])/E^(((I/4)*b^2*Log[f]^2)/(f + I*c*Log[f])) - (3*(-1)^(1/4)*c^3*Erfi[((-1)^(3/4)*(2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]^3*Sqrt[f + I*c*Log[f]]*Sin[d])/E^(((I/4)*b^2*Log[f]^2)/(f + I*c*Log[f])) - 3*(-1)^(1/4)*E^(((I/4)*b^2*Log[f]^2)/(3*f - I*c*Log[f]))*f^3*Erfi[((-1)^(1/4)*(6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Sqrt[3*f - I*c*Log[f]]*Sin[3*d] - (-1)^(3/4)*c*E^(((I/4)*b^2*Log[f]^2)/(3*f - I*c*Log[f]))*f^2*Erfi[((-1)^(1/4)*(6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]*Sqrt[3*f - I*c*Log[f]]*Sin[3*d] - 3*(-1)^(1/4)*c^2*E^(((I/4)*b^2*Log[f]^2)/(3*f - I*c*Log[f]))*f*Erfi[((-1)^(1/4)*(6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]^2*Sqrt[3*f - I*c*Log[f]]*Sin[3*d] - (-1)^(3/4)*c^3*E^(((I/4)*b^2*Log[f]^2)/(3*f - I*c*Log[f]))*Erfi[((-1)^(1/4)*(6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]^3*Sqrt[3*f - I*c*Log[f]]*Sin[3*d] + (3*(-1)^(3/4)*f^3*Erfi[((-1)^(3/4)*(6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Sqrt[3*f + I*c*Log[f]]*Sin[3*d])/E^(((I/4)*b^2*Log[f]^2)/(3*f + I*c*Log[f])) + ((-1)^(1/4)*c*f^2*Erfi[((-1)^(3/4)*(6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]*Sqrt[3*f + I*c*Log[f]]*Sin[3*d])/E^(((I/4)*b^2*Log[f]^2)/(3*f + I*c*Log[f])) + (3*(-1)^(3/4)*c^2*f*Erfi[((-1)^(3/4)*(6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]^2*Sqrt[3*f + I*c*Log[f]]*Sin[3*d])/E^(((I/4)*b^2*Log[f]^2)/(3*f + I*c*Log[f])) + ((-1)^(1/4)*c^3*Erfi[((-1)^(3/4)*(6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]^3*Sqrt[3*f + I*c*Log[f]]*Sin[3*d])/E^(((I/4)*b^2*Log[f]^2)/(3*f + I*c*Log[f]))))/(16*(I*f - c*Log[f])*(f - I*c*Log[f])*(3*f - I*c*Log[f])*(3*f + I*c*Log[f]))","B",1
100,1,347,212,2.2028703,"\int f^{a+b x+c x^2} \sin \left(d+e x+f x^2\right) \, dx","Integrate[f^(a + b*x + c*x^2)*Sin[d + e*x + f*x^2],x]","-\frac{\sqrt[4]{-1} \sqrt{\pi } f^{\frac{f (a f-b e)+a c^2 \log ^2(f)}{c^2 \log ^2(f)+f^2}} \exp \left(-\frac{1}{4} i \left(\frac{b^2 \log ^2(f)}{f+i c \log (f)}+\frac{e^2}{f-i c \log (f)}\right)\right) \left(\sqrt{f-i c \log (f)} (f+i c \log (f)) (\cos (d)+i \sin (d)) e^{\frac{i b^2 f \log ^2(f)}{2 \left(c^2 \log ^2(f)+f^2\right)}} f^{\frac{b e}{2 f+2 i c \log (f)}} \text{erfi}\left(\frac{\sqrt[4]{-1} (-i \log (f) (b+2 c x)+e+2 f x)}{2 \sqrt{f-i c \log (f)}}\right)+(f-i c \log (f)) \sqrt{f+i c \log (f)} (\sin (d)+i \cos (d)) e^{\frac{i e^2 f}{2 \left(c^2 \log ^2(f)+f^2\right)}} f^{\frac{b e}{2 f-2 i c \log (f)}} \text{erfi}\left(\frac{(-1)^{3/4} (i \log (f) (b+2 c x)+e+2 f x)}{2 \sqrt{f+i c \log (f)}}\right)\right)}{4 \left(c^2 \log ^2(f)+f^2\right)}","\frac{i \sqrt{\pi } f^a \exp \left(-\frac{(e+i b \log (f))^2}{-4 c \log (f)+4 i f}-i d\right) \text{erf}\left(\frac{-b \log (f)+2 x (-c \log (f)+i f)+i e}{2 \sqrt{-c \log (f)+i f}}\right)}{4 \sqrt{-c \log (f)+i f}}-\frac{i \sqrt{\pi } f^a \exp \left(\frac{(e-i b \log (f))^2}{4 c \log (f)+4 i f}+i d\right) \text{erfi}\left(\frac{b \log (f)+2 x (c \log (f)+i f)+i e}{2 \sqrt{c \log (f)+i f}}\right)}{4 \sqrt{c \log (f)+i f}}",1,"-1/4*((-1)^(1/4)*f^((f*(-(b*e) + a*f) + a*c^2*Log[f]^2)/(f^2 + c^2*Log[f]^2))*Sqrt[Pi]*(E^(((I/2)*b^2*f*Log[f]^2)/(f^2 + c^2*Log[f]^2))*f^((b*e)/(2*f + (2*I)*c*Log[f]))*Erfi[((-1)^(1/4)*(e + 2*f*x - I*(b + 2*c*x)*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Sqrt[f - I*c*Log[f]]*(f + I*c*Log[f])*(Cos[d] + I*Sin[d]) + E^(((I/2)*e^2*f)/(f^2 + c^2*Log[f]^2))*f^((b*e)/(2*f - (2*I)*c*Log[f]))*Erfi[((-1)^(3/4)*(e + 2*f*x + I*(b + 2*c*x)*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*(f - I*c*Log[f])*Sqrt[f + I*c*Log[f]]*(I*Cos[d] + Sin[d])))/(E^((I/4)*(e^2/(f - I*c*Log[f]) + (b^2*Log[f]^2)/(f + I*c*Log[f])))*(f^2 + c^2*Log[f]^2))","A",0
101,1,1120,268,6.7280264,"\int f^{a+b x+c x^2} \sin ^2\left(d+e x+f x^2\right) \, dx","Integrate[f^(a + b*x + c*x^2)*Sin[d + e*x + f*x^2]^2,x]","\frac{f^a \sqrt{\pi } \left(8 \sqrt{c} \text{erfi}\left(\frac{(b+2 c x) \sqrt{\log (f)}}{2 \sqrt{c}}\right) \sqrt{\log (f)} f^{2-\frac{b^2}{4 c}}+2 c^{5/2} \text{erfi}\left(\frac{(b+2 c x) \sqrt{\log (f)}}{2 \sqrt{c}}\right) \log ^{\frac{5}{2}}(f) f^{-\frac{b^2}{4 c}}+2 (-1)^{3/4} c e^{\frac{i \left(-4 e^2+4 i b \log (f) e+b^2 \log ^2(f)\right)}{4 (2 f-i c \log (f))}} \text{erf}\left(\frac{(-1)^{3/4} (2 e+4 f x-i b \log (f)-2 i c x \log (f))}{2 \sqrt{2 f-i c \log (f)}}\right) \log (f) \sqrt{2 f-i c \log (f)} \sin (2 d) f+2 \sqrt[4]{-1} c e^{-\frac{i \left(-4 e^2-4 i b \log (f) e+b^2 \log ^2(f)\right)}{4 (2 f+i c \log (f))}} \text{erf}\left(\frac{\sqrt[4]{-1} (2 e+4 f x+i b \log (f)+2 i c x \log (f))}{2 \sqrt{2 f+i c \log (f)}}\right) \log (f) \sqrt{2 f+i c \log (f)} \sin (2 d) f+2 \sqrt[4]{-1} c e^{\frac{i \left(-4 e^2+4 i b \log (f) e+b^2 \log ^2(f)\right)}{4 (2 f-i c \log (f))}} \cos (2 d) \text{erf}\left(\frac{(-1)^{3/4} (2 e+4 f x-i b \log (f)-2 i c x \log (f))}{2 \sqrt{2 f-i c \log (f)}}\right) \log (f) \sqrt{2 f-i c \log (f)} f+2 (-1)^{3/4} c e^{-\frac{i \left(-4 e^2-4 i b \log (f) e+b^2 \log ^2(f)\right)}{4 (2 f+i c \log (f))}} \cos (2 d) \text{erf}\left(\frac{\sqrt[4]{-1} (2 e+4 f x+i b \log (f)+2 i c x \log (f))}{2 \sqrt{2 f+i c \log (f)}}\right) \log (f) \sqrt{2 f+i c \log (f)} f-\sqrt[4]{-1} c^2 e^{\frac{i \left(-4 e^2+4 i b \log (f) e+b^2 \log ^2(f)\right)}{4 (2 f-i c \log (f))}} \text{erf}\left(\frac{(-1)^{3/4} (2 e+4 f x-i b \log (f)-2 i c x \log (f))}{2 \sqrt{2 f-i c \log (f)}}\right) \log ^2(f) \sqrt{2 f-i c \log (f)} \sin (2 d)-(-1)^{3/4} c^2 e^{-\frac{i \left(-4 e^2-4 i b \log (f) e+b^2 \log ^2(f)\right)}{4 (2 f+i c \log (f))}} \text{erf}\left(\frac{\sqrt[4]{-1} (2 e+4 f x+i b \log (f)+2 i c x \log (f))}{2 \sqrt{2 f+i c \log (f)}}\right) \log ^2(f) \sqrt{2 f+i c \log (f)} \sin (2 d)+(-1)^{3/4} c^2 e^{\frac{i \left(-4 e^2+4 i b \log (f) e+b^2 \log ^2(f)\right)}{4 (2 f-i c \log (f))}} \cos (2 d) \text{erf}\left(\frac{(-1)^{3/4} (2 e+4 f x-i b \log (f)-2 i c x \log (f))}{2 \sqrt{2 f-i c \log (f)}}\right) \log ^2(f) \sqrt{2 f-i c \log (f)}+\sqrt[4]{-1} c^2 e^{-\frac{i \left(-4 e^2-4 i b \log (f) e+b^2 \log ^2(f)\right)}{4 (2 f+i c \log (f))}} \cos (2 d) \text{erf}\left(\frac{\sqrt[4]{-1} (2 e+4 f x+i b \log (f)+2 i c x \log (f))}{2 \sqrt{2 f+i c \log (f)}}\right) \log ^2(f) \sqrt{2 f+i c \log (f)}\right)}{8 c \log (f) (2 f-i c \log (f)) (2 f+i c \log (f))}","\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}-\frac{\sqrt{\pi } f^a \exp \left(-\frac{(2 e+i b \log (f))^2}{-4 c \log (f)+8 i f}-2 i d\right) \text{erf}\left(\frac{-b \log (f)+2 x (-c \log (f)+2 i f)+2 i e}{2 \sqrt{-c \log (f)+2 i f}}\right)}{8 \sqrt{-c \log (f)+2 i f}}-\frac{\sqrt{\pi } f^a \exp \left(\frac{(2 e-i b \log (f))^2}{4 c \log (f)+8 i f}+2 i d\right) \text{erfi}\left(\frac{b \log (f)+2 x (c \log (f)+2 i f)+2 i e}{2 \sqrt{c \log (f)+2 i f}}\right)}{8 \sqrt{c \log (f)+2 i f}}",1,"(f^a*Sqrt[Pi]*(8*Sqrt[c]*f^(2 - b^2/(4*c))*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])]*Sqrt[Log[f]] + (2*c^(5/2)*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])]*Log[f]^(5/2))/f^(b^2/(4*c)) + 2*(-1)^(1/4)*c*E^(((I/4)*(-4*e^2 + (4*I)*b*e*Log[f] + b^2*Log[f]^2))/(2*f - I*c*Log[f]))*f*Cos[2*d]*Erf[((-1)^(3/4)*(2*e + 4*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[2*f - I*c*Log[f]])]*Log[f]*Sqrt[2*f - I*c*Log[f]] + (-1)^(3/4)*c^2*E^(((I/4)*(-4*e^2 + (4*I)*b*e*Log[f] + b^2*Log[f]^2))/(2*f - I*c*Log[f]))*Cos[2*d]*Erf[((-1)^(3/4)*(2*e + 4*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[2*f - I*c*Log[f]])]*Log[f]^2*Sqrt[2*f - I*c*Log[f]] + (2*(-1)^(3/4)*c*f*Cos[2*d]*Erf[((-1)^(1/4)*(2*e + 4*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[2*f + I*c*Log[f]])]*Log[f]*Sqrt[2*f + I*c*Log[f]])/E^(((I/4)*(-4*e^2 - (4*I)*b*e*Log[f] + b^2*Log[f]^2))/(2*f + I*c*Log[f])) + ((-1)^(1/4)*c^2*Cos[2*d]*Erf[((-1)^(1/4)*(2*e + 4*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[2*f + I*c*Log[f]])]*Log[f]^2*Sqrt[2*f + I*c*Log[f]])/E^(((I/4)*(-4*e^2 - (4*I)*b*e*Log[f] + b^2*Log[f]^2))/(2*f + I*c*Log[f])) + 2*(-1)^(3/4)*c*E^(((I/4)*(-4*e^2 + (4*I)*b*e*Log[f] + b^2*Log[f]^2))/(2*f - I*c*Log[f]))*f*Erf[((-1)^(3/4)*(2*e + 4*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[2*f - I*c*Log[f]])]*Log[f]*Sqrt[2*f - I*c*Log[f]]*Sin[2*d] - (-1)^(1/4)*c^2*E^(((I/4)*(-4*e^2 + (4*I)*b*e*Log[f] + b^2*Log[f]^2))/(2*f - I*c*Log[f]))*Erf[((-1)^(3/4)*(2*e + 4*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[2*f - I*c*Log[f]])]*Log[f]^2*Sqrt[2*f - I*c*Log[f]]*Sin[2*d] + (2*(-1)^(1/4)*c*f*Erf[((-1)^(1/4)*(2*e + 4*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[2*f + I*c*Log[f]])]*Log[f]*Sqrt[2*f + I*c*Log[f]]*Sin[2*d])/E^(((I/4)*(-4*e^2 - (4*I)*b*e*Log[f] + b^2*Log[f]^2))/(2*f + I*c*Log[f])) - ((-1)^(3/4)*c^2*Erf[((-1)^(1/4)*(2*e + 4*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[2*f + I*c*Log[f]])]*Log[f]^2*Sqrt[2*f + I*c*Log[f]]*Sin[2*d])/E^(((I/4)*(-4*e^2 - (4*I)*b*e*Log[f] + b^2*Log[f]^2))/(2*f + I*c*Log[f]))))/(8*c*Log[f]*(2*f - I*c*Log[f])*(2*f + I*c*Log[f]))","B",0
102,1,3835,430,7.2610606,"\int f^{a+b x+c x^2} \sin ^3\left(d+e x+f x^2\right) \, dx","Integrate[f^(a + b*x + c*x^2)*Sin[d + e*x + f*x^2]^3,x]","\text{Result too large to show}","\frac{3 i \sqrt{\pi } f^a \exp \left(-\frac{(e+i b \log (f))^2}{-4 c \log (f)+4 i f}-i d\right) \text{erf}\left(\frac{-b \log (f)+2 x (-c \log (f)+i f)+i e}{2 \sqrt{-c \log (f)+i f}}\right)}{16 \sqrt{-c \log (f)+i f}}-\frac{i \sqrt{\pi } f^a \exp \left(-\frac{(3 e+i b \log (f))^2}{4 (-c \log (f)+3 i f)}-3 i d\right) \text{erf}\left(\frac{-b \log (f)+2 x (-c \log (f)+3 i f)+3 i e}{2 \sqrt{-c \log (f)+3 i f}}\right)}{16 \sqrt{-c \log (f)+3 i f}}-\frac{3 i \sqrt{\pi } f^a \exp \left(\frac{(e-i b \log (f))^2}{4 c \log (f)+4 i f}+i d\right) \text{erfi}\left(\frac{b \log (f)+2 x (c \log (f)+i f)+i e}{2 \sqrt{c \log (f)+i f}}\right)}{16 \sqrt{c \log (f)+i f}}+\frac{i \sqrt{\pi } f^a \exp \left(3 i d-\frac{(b \log (f)+3 i e)^2}{4 (c \log (f)+3 i f)}\right) \text{erfi}\left(\frac{b \log (f)+2 x (c \log (f)+3 i f)+3 i e}{2 \sqrt{c \log (f)+3 i f}}\right)}{16 \sqrt{c \log (f)+3 i f}}",1,"(f^a*Sqrt[Pi]*(-27*(-1)^(3/4)*E^(((I/4)*(-e^2 + (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f - I*c*Log[f]))*f^3*Cos[d]*Erfi[((-1)^(1/4)*(e + 2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Sqrt[f - I*c*Log[f]] + 27*(-1)^(1/4)*c*E^(((I/4)*(-e^2 + (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f - I*c*Log[f]))*f^2*Cos[d]*Erfi[((-1)^(1/4)*(e + 2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]*Sqrt[f - I*c*Log[f]] - 3*(-1)^(3/4)*c^2*E^(((I/4)*(-e^2 + (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f - I*c*Log[f]))*f*Cos[d]*Erfi[((-1)^(1/4)*(e + 2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]^2*Sqrt[f - I*c*Log[f]] + 3*(-1)^(1/4)*c^3*E^(((I/4)*(-e^2 + (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f - I*c*Log[f]))*Cos[d]*Erfi[((-1)^(1/4)*(e + 2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]^3*Sqrt[f - I*c*Log[f]] + 3*(-1)^(3/4)*E^(((I/4)*(-9*e^2 + (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f - I*c*Log[f]))*f^3*Cos[3*d]*Erfi[((-1)^(1/4)*(3*e + 6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Sqrt[3*f - I*c*Log[f]] - (-1)^(1/4)*c*E^(((I/4)*(-9*e^2 + (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f - I*c*Log[f]))*f^2*Cos[3*d]*Erfi[((-1)^(1/4)*(3*e + 6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]*Sqrt[3*f - I*c*Log[f]] + 3*(-1)^(3/4)*c^2*E^(((I/4)*(-9*e^2 + (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f - I*c*Log[f]))*f*Cos[3*d]*Erfi[((-1)^(1/4)*(3*e + 6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]^2*Sqrt[3*f - I*c*Log[f]] - (-1)^(1/4)*c^3*E^(((I/4)*(-9*e^2 + (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f - I*c*Log[f]))*Cos[3*d]*Erfi[((-1)^(1/4)*(3*e + 6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]^3*Sqrt[3*f - I*c*Log[f]] + (27*(-1)^(1/4)*f^3*Cos[d]*Erfi[((-1)^(3/4)*(e + 2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Sqrt[f + I*c*Log[f]])/E^(((I/4)*(-e^2 - (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f + I*c*Log[f])) - (27*(-1)^(3/4)*c*f^2*Cos[d]*Erfi[((-1)^(3/4)*(e + 2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]*Sqrt[f + I*c*Log[f]])/E^(((I/4)*(-e^2 - (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f + I*c*Log[f])) + (3*(-1)^(1/4)*c^2*f*Cos[d]*Erfi[((-1)^(3/4)*(e + 2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]^2*Sqrt[f + I*c*Log[f]])/E^(((I/4)*(-e^2 - (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f + I*c*Log[f])) - (3*(-1)^(3/4)*c^3*Cos[d]*Erfi[((-1)^(3/4)*(e + 2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]^3*Sqrt[f + I*c*Log[f]])/E^(((I/4)*(-e^2 - (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f + I*c*Log[f])) - (3*(-1)^(1/4)*f^3*Cos[3*d]*Erfi[((-1)^(3/4)*(3*e + 6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Sqrt[3*f + I*c*Log[f]])/E^(((I/4)*(-9*e^2 - (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f + I*c*Log[f])) + ((-1)^(3/4)*c*f^2*Cos[3*d]*Erfi[((-1)^(3/4)*(3*e + 6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]*Sqrt[3*f + I*c*Log[f]])/E^(((I/4)*(-9*e^2 - (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f + I*c*Log[f])) - (3*(-1)^(1/4)*c^2*f*Cos[3*d]*Erfi[((-1)^(3/4)*(3*e + 6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]^2*Sqrt[3*f + I*c*Log[f]])/E^(((I/4)*(-9*e^2 - (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f + I*c*Log[f])) + ((-1)^(3/4)*c^3*Cos[3*d]*Erfi[((-1)^(3/4)*(3*e + 6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]^3*Sqrt[3*f + I*c*Log[f]])/E^(((I/4)*(-9*e^2 - (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f + I*c*Log[f])) + 27*(-1)^(1/4)*E^(((I/4)*(-e^2 + (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f - I*c*Log[f]))*f^3*Erfi[((-1)^(1/4)*(e + 2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Sqrt[f - I*c*Log[f]]*Sin[d] + 27*(-1)^(3/4)*c*E^(((I/4)*(-e^2 + (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f - I*c*Log[f]))*f^2*Erfi[((-1)^(1/4)*(e + 2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]*Sqrt[f - I*c*Log[f]]*Sin[d] + 3*(-1)^(1/4)*c^2*E^(((I/4)*(-e^2 + (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f - I*c*Log[f]))*f*Erfi[((-1)^(1/4)*(e + 2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]^2*Sqrt[f - I*c*Log[f]]*Sin[d] + 3*(-1)^(3/4)*c^3*E^(((I/4)*(-e^2 + (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f - I*c*Log[f]))*Erfi[((-1)^(1/4)*(e + 2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]^3*Sqrt[f - I*c*Log[f]]*Sin[d] - (27*(-1)^(3/4)*f^3*Erfi[((-1)^(3/4)*(e + 2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Sqrt[f + I*c*Log[f]]*Sin[d])/E^(((I/4)*(-e^2 - (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f + I*c*Log[f])) - (27*(-1)^(1/4)*c*f^2*Erfi[((-1)^(3/4)*(e + 2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]*Sqrt[f + I*c*Log[f]]*Sin[d])/E^(((I/4)*(-e^2 - (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f + I*c*Log[f])) - (3*(-1)^(3/4)*c^2*f*Erfi[((-1)^(3/4)*(e + 2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]^2*Sqrt[f + I*c*Log[f]]*Sin[d])/E^(((I/4)*(-e^2 - (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f + I*c*Log[f])) - (3*(-1)^(1/4)*c^3*Erfi[((-1)^(3/4)*(e + 2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]^3*Sqrt[f + I*c*Log[f]]*Sin[d])/E^(((I/4)*(-e^2 - (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f + I*c*Log[f])) - 3*(-1)^(1/4)*E^(((I/4)*(-9*e^2 + (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f - I*c*Log[f]))*f^3*Erfi[((-1)^(1/4)*(3*e + 6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Sqrt[3*f - I*c*Log[f]]*Sin[3*d] - (-1)^(3/4)*c*E^(((I/4)*(-9*e^2 + (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f - I*c*Log[f]))*f^2*Erfi[((-1)^(1/4)*(3*e + 6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]*Sqrt[3*f - I*c*Log[f]]*Sin[3*d] - 3*(-1)^(1/4)*c^2*E^(((I/4)*(-9*e^2 + (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f - I*c*Log[f]))*f*Erfi[((-1)^(1/4)*(3*e + 6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]^2*Sqrt[3*f - I*c*Log[f]]*Sin[3*d] - (-1)^(3/4)*c^3*E^(((I/4)*(-9*e^2 + (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f - I*c*Log[f]))*Erfi[((-1)^(1/4)*(3*e + 6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]^3*Sqrt[3*f - I*c*Log[f]]*Sin[3*d] + (3*(-1)^(3/4)*f^3*Erfi[((-1)^(3/4)*(3*e + 6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Sqrt[3*f + I*c*Log[f]]*Sin[3*d])/E^(((I/4)*(-9*e^2 - (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f + I*c*Log[f])) + ((-1)^(1/4)*c*f^2*Erfi[((-1)^(3/4)*(3*e + 6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]*Sqrt[3*f + I*c*Log[f]]*Sin[3*d])/E^(((I/4)*(-9*e^2 - (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f + I*c*Log[f])) + (3*(-1)^(3/4)*c^2*f*Erfi[((-1)^(3/4)*(3*e + 6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]^2*Sqrt[3*f + I*c*Log[f]]*Sin[3*d])/E^(((I/4)*(-9*e^2 - (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f + I*c*Log[f])) + ((-1)^(1/4)*c^3*Erfi[((-1)^(3/4)*(3*e + 6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]^3*Sqrt[3*f + I*c*Log[f]]*Sin[3*d])/E^(((I/4)*(-9*e^2 - (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f + I*c*Log[f]))))/(16*(I*f - c*Log[f])*(f - I*c*Log[f])*(3*f - I*c*Log[f])*(3*f + I*c*Log[f]))","B",0
103,1,324,213,1.8474736,"\int f^{a+b x+c x^2} \sin \left(a+b x+e x^2\right) \, dx","Integrate[f^(a + b*x + c*x^2)*Sin[a + b*x + e*x^2],x]","\frac{\sqrt{\pi } e^{-\frac{b^2 c \log ^3(f)}{2 \left(c^2 \log ^2(f)+e^2\right)}} f^{a-\frac{b^2}{2 (e-i c \log (f))}} \left((\cos (a)+i \sin (a)) (e+i c \log (f)) \sqrt{c \log (f)+i e} \exp \left(\frac{1}{4} b^2 \left(\frac{\log ^2(f)}{c \log (f)-i e}+\frac{1}{c \log (f)+i e}\right)\right) \text{erfi}\left(\frac{-\log (f) (b+2 c x)-i (b+2 e x)}{2 \sqrt{c \log (f)+i e}}\right)-(\cos (a)-i \sin (a)) (e-i c \log (f)) \sqrt{c \log (f)-i e} f^{\frac{i b^2 c \log (f)}{c^2 \log ^2(f)+e^2}} \exp \left(\frac{1}{4} b^2 \left(\frac{\log ^2(f)}{c \log (f)+i e}+\frac{1}{c \log (f)-i e}\right)\right) \text{erfi}\left(\frac{\log (f) (b+2 c x)-i (b+2 e x)}{2 \sqrt{c \log (f)-i e}}\right)\right)}{4 \left(c^2 \log ^2(f)+e^2\right)}","\frac{i \sqrt{\pi } \exp \left(-\left((-\log (f)+i) \left(a-\frac{b^2 (-\log (f)+i)}{-4 c \log (f)+4 i e}\right)\right)\right) \text{erf}\left(\frac{b (-\log (f)+i)+2 x (-c \log (f)+i e)}{2 \sqrt{-c \log (f)+i e}}\right)}{4 \sqrt{-c \log (f)+i e}}-\frac{i \sqrt{\pi } \exp \left((\log (f)+i) \left(a-\frac{b^2 (\log (f)+i)}{4 c \log (f)+4 i e}\right)\right) \text{erfi}\left(\frac{b (\log (f)+i)+2 x (c \log (f)+i e)}{2 \sqrt{c \log (f)+i e}}\right)}{4 \sqrt{c \log (f)+i e}}",1,"(f^(a - b^2/(2*(e - I*c*Log[f])))*Sqrt[Pi]*(-(E^((b^2*(((-I)*e + c*Log[f])^(-1) + Log[f]^2/(I*e + c*Log[f])))/4)*f^((I*b^2*c*Log[f])/(e^2 + c^2*Log[f]^2))*Erfi[((-I)*(b + 2*e*x) + (b + 2*c*x)*Log[f])/(2*Sqrt[(-I)*e + c*Log[f]])]*(e - I*c*Log[f])*Sqrt[(-I)*e + c*Log[f]]*(Cos[a] - I*Sin[a])) + E^((b^2*(Log[f]^2/((-I)*e + c*Log[f]) + (I*e + c*Log[f])^(-1)))/4)*Erfi[((-I)*(b + 2*e*x) - (b + 2*c*x)*Log[f])/(2*Sqrt[I*e + c*Log[f]])]*(e + I*c*Log[f])*Sqrt[I*e + c*Log[f]]*(Cos[a] + I*Sin[a])))/(4*E^((b^2*c*Log[f]^3)/(2*(e^2 + c^2*Log[f]^2)))*(e^2 + c^2*Log[f]^2))","A",0
104,1,26,36,0.0584079,"\int e^x \cos (a+b x) \, dx","Integrate[E^x*Cos[a + b*x],x]","\frac{e^x (b \sin (a+b x)+\cos (a+b x))}{b^2+1}","\frac{b e^x \sin (a+b x)}{b^2+1}+\frac{e^x \cos (a+b x)}{b^2+1}",1,"(E^x*(Cos[a + b*x] + b*Sin[a + b*x]))/(1 + b^2)","A",1
105,1,109,115,0.1657117,"\int e^x \cos \left(a+c x^2\right) \, dx","Integrate[E^x*Cos[a + c*x^2],x]","\frac{\sqrt[4]{-1} \sqrt{\pi } e^{\left.-\frac{i}{4}\right/c} \left(e^{\left.\frac{i}{2}\right/c} (\sin (a)-i \cos (a)) \text{erfi}\left(\frac{\sqrt[4]{-1} (2 c x-i)}{2 \sqrt{c}}\right)-(\cos (a)-i \sin (a)) \text{erfi}\left(\frac{(-1)^{3/4} (2 c x+i)}{2 \sqrt{c}}\right)\right)}{4 \sqrt{c}}","\frac{\sqrt[4]{-1} \sqrt{\pi } e^{-\frac{1}{4} i \left(4 a+\frac{1}{c}\right)} \text{erfi}\left(\frac{\sqrt[4]{-1} (1-2 i c x)}{2 \sqrt{c}}\right)}{4 \sqrt{c}}-\frac{\sqrt[4]{-1} \sqrt{\pi } e^{\frac{1}{4} i \left(4 a+\frac{1}{c}\right)} \text{erf}\left(\frac{\sqrt[4]{-1} (1+2 i c x)}{2 \sqrt{c}}\right)}{4 \sqrt{c}}",1,"((-1)^(1/4)*Sqrt[Pi]*(-(Erfi[((-1)^(3/4)*(I + 2*c*x))/(2*Sqrt[c])]*(Cos[a] - I*Sin[a])) + E^((I/2)/c)*Erfi[((-1)^(1/4)*(-I + 2*c*x))/(2*Sqrt[c])]*((-I)*Cos[a] + Sin[a])))/(4*Sqrt[c]*E^((I/4)/c))","A",1
106,1,135,144,0.2581894,"\int e^x \cos \left(a+b x+c x^2\right) \, dx","Integrate[E^x*Cos[a + b*x + c*x^2],x]","\frac{\sqrt[4]{-1} \sqrt{\pi } e^{-\frac{i \left(b^2-2 i b+1\right)}{4 c}} \left(e^{\left.\frac{i}{2}\right/c} (\sin (a)-i \cos (a)) \text{erfi}\left(\frac{\sqrt[4]{-1} (b+2 c x-i)}{2 \sqrt{c}}\right)-e^{\frac{i b^2}{2 c}} (\cos (a)-i \sin (a)) \text{erfi}\left(\frac{(-1)^{3/4} (b+2 c x+i)}{2 \sqrt{c}}\right)\right)}{4 \sqrt{c}}","\frac{\sqrt[4]{-1} \sqrt{\pi } e^{\frac{i (b+i)^2}{4 c}-i a} \text{erfi}\left(\frac{\sqrt[4]{-1} (-i b-2 i c x+1)}{2 \sqrt{c}}\right)}{4 \sqrt{c}}-\frac{\sqrt[4]{-1} \sqrt{\pi } e^{\frac{1}{4} i \left(4 a+\frac{(1+i b)^2}{c}\right)} \text{erf}\left(\frac{\sqrt[4]{-1} (i b+2 i c x+1)}{2 \sqrt{c}}\right)}{4 \sqrt{c}}",1,"((-1)^(1/4)*Sqrt[Pi]*(-(E^(((I/2)*b^2)/c)*Erfi[((-1)^(3/4)*(I + b + 2*c*x))/(2*Sqrt[c])]*(Cos[a] - I*Sin[a])) + E^((I/2)/c)*Erfi[((-1)^(1/4)*(-I + b + 2*c*x))/(2*Sqrt[c])]*((-I)*Cos[a] + Sin[a])))/(4*Sqrt[c]*E^(((I/4)*(1 - (2*I)*b + b^2))/c))","A",1
107,1,82,77,0.0831497,"\int e^{x^2} \cos (a+b x) \, dx","Integrate[E^x^2*Cos[a + b*x],x]","\frac{1}{4} \sqrt{\pi } e^{\frac{b^2}{4}} \left(-\sin (a) \left(\text{erf}\left(\frac{b}{2}-i x\right)+\text{erf}\left(\frac{b}{2}+i x\right)\right)+\cos (a) \text{erfi}\left(\frac{1}{2} (2 x-i b)\right)+\cos (a) \text{erfi}\left(\frac{1}{2} (2 x+i b)\right)\right)","\frac{1}{4} \sqrt{\pi } e^{\frac{b^2}{4}-i a} \text{erfi}\left(\frac{1}{2} (2 x-i b)\right)+\frac{1}{4} \sqrt{\pi } e^{\frac{b^2}{4}+i a} \text{erfi}\left(\frac{1}{2} (2 x+i b)\right)",1,"(E^(b^2/4)*Sqrt[Pi]*(Cos[a]*Erfi[((-I)*b + 2*x)/2] + Cos[a]*Erfi[(I*b + 2*x)/2] - (Erf[b/2 - I*x] + Erf[b/2 + I*x])*Sin[a]))/4","A",1
108,1,107,83,0.2031538,"\int e^{x^2} \cos \left(a+c x^2\right) \, dx","Integrate[E^x^2*Cos[a + c*x^2],x]","\frac{\sqrt[4]{-1} \sqrt{\pi } \left((1-i c) \sqrt{c-i} (\cos (a)+i \sin (a)) \text{erfi}\left(\sqrt[4]{-1} \sqrt{c-i} x\right)-(c-i) \sqrt{c+i} (\cos (a)-i \sin (a)) \text{erfi}\left((-1)^{3/4} \sqrt{c+i} x\right)\right)}{4 \left(c^2+1\right)}","\frac{\sqrt{\pi } e^{-i a} \text{erfi}\left(\sqrt{1-i c} x\right)}{4 \sqrt{1-i c}}+\frac{\sqrt{\pi } e^{i a} \text{erfi}\left(\sqrt{1+i c} x\right)}{4 \sqrt{1+i c}}",1,"((-1)^(1/4)*Sqrt[Pi]*(-((-I + c)*Sqrt[I + c]*Erfi[(-1)^(3/4)*Sqrt[I + c]*x]*(Cos[a] - I*Sin[a])) + (1 - I*c)*Sqrt[-I + c]*Erfi[(-1)^(1/4)*Sqrt[-I + c]*x]*(Cos[a] + I*Sin[a])))/(4*(1 + c^2))","A",1
109,1,166,151,0.6037301,"\int e^{x^2} \cos \left(a+b x+c x^2\right) \, dx","Integrate[E^x^2*Cos[a + b*x + c*x^2],x]","\frac{\sqrt[4]{-1} \sqrt{\pi } e^{\frac{i b^2}{-4 c+4 i}} \left(\sqrt{c-i} (c+i) (\sin (a)-i \cos (a)) \text{erfi}\left(\frac{\sqrt[4]{-1} (b+2 (c-i) x)}{2 \sqrt{c-i}}\right)-(c-i) \sqrt{c+i} e^{\frac{i b^2 c}{2 c^2+2}} (\cos (a)-i \sin (a)) \text{erfi}\left(\frac{(-1)^{3/4} (b+2 (c+i) x)}{2 \sqrt{c+i}}\right)\right)}{4 \left(c^2+1\right)}","\frac{\sqrt{\pi } e^{i a+\frac{b^2}{4 (1+i c)}} \text{erfi}\left(\frac{i b+2 (1+i c) x}{2 \sqrt{1+i c}}\right)}{4 \sqrt{1+i c}}-\frac{\sqrt{\pi } e^{-i \left(a-\frac{b^2}{4 c+4 i}\right)} \text{erfi}\left(\frac{i b-2 (1-i c) x}{2 \sqrt{1-i c}}\right)}{4 \sqrt{1-i c}}",1,"((-1)^(1/4)*E^((I*b^2)/(4*I - 4*c))*Sqrt[Pi]*(-((-I + c)*Sqrt[I + c]*E^((I*b^2*c)/(2 + 2*c^2))*Erfi[((-1)^(3/4)*(b + 2*(I + c)*x))/(2*Sqrt[I + c])]*(Cos[a] - I*Sin[a])) + Sqrt[-I + c]*(I + c)*Erfi[((-1)^(1/4)*(b + 2*(-I + c)*x))/(2*Sqrt[-I + c])]*((-I)*Cos[a] + Sin[a])))/(4*(1 + c^2))","A",1
110,1,133,142,0.2319416,"\int f^{a+b x} \cos \left(d+f x^2\right) \, dx","Integrate[f^(a + b*x)*Cos[d + f*x^2],x]","\frac{1}{4} \sqrt[4]{-1} \sqrt{\pi } f^{a-\frac{1}{2}} e^{-\frac{i b^2 \log ^2(f)}{4 f}} \left(e^{\frac{i b^2 \log ^2(f)}{2 f}} (\sin (d)-i \cos (d)) \text{erfi}\left(\frac{\sqrt[4]{-1} (2 f x-i b \log (f))}{2 \sqrt{f}}\right)-(\cos (d)-i \sin (d)) \text{erfi}\left(\frac{(-1)^{3/4} (2 f x+i b \log (f))}{2 \sqrt{f}}\right)\right)","-\frac{1}{4} \sqrt[4]{-1} \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{1}{4} i \left(\frac{b^2 \log ^2(f)}{f}+4 d\right)} \text{erf}\left(\frac{\sqrt[4]{-1} (b \log (f)+2 i f x)}{2 \sqrt{f}}\right)-\frac{1}{4} \sqrt[4]{-1} \sqrt{\pi } f^{a-\frac{1}{2}} e^{-\frac{1}{4} i \left(\frac{b^2 \log ^2(f)}{f}+4 d\right)} \text{erfi}\left(\frac{\sqrt[4]{-1} (-b \log (f)+2 i f x)}{2 \sqrt{f}}\right)",1,"((-1)^(1/4)*f^(-1/2 + a)*Sqrt[Pi]*(-(Erfi[((-1)^(3/4)*(2*f*x + I*b*Log[f]))/(2*Sqrt[f])]*(Cos[d] - I*Sin[d])) + E^(((I/2)*b^2*Log[f]^2)/f)*Erfi[((-1)^(1/4)*(2*f*x - I*b*Log[f]))/(2*Sqrt[f])]*((-I)*Cos[d] + Sin[d])))/(4*E^(((I/4)*b^2*Log[f]^2)/f))","A",1
111,1,158,157,1.0353705,"\int f^{a+b x} \cos ^2\left(d+f x^2\right) \, dx","Integrate[f^(a + b*x)*Cos[d + f*x^2]^2,x]","\frac{1}{16} f^a \left(\frac{(1-i) \sqrt{\pi } e^{-\frac{i b^2 \log ^2(f)}{8 f}} (\cos (d)-i \sin (d))^2 \text{erf}\left(\frac{(4+4 i) f x-(1-i) b \log (f)}{4 \sqrt{f}}\right)}{\sqrt{f}}+\frac{(1+i) \sqrt{\pi } e^{\frac{i b^2 \log ^2(f)}{8 f}} (\sin (2 d)-i \cos (2 d)) \text{erfi}\left(\frac{(1-i) b \log (f)+(4+4 i) f x}{4 \sqrt{f}}\right)}{\sqrt{f}}+\frac{8 f^{b x}}{b \log (f)}\right)","\left(-\frac{1}{16}-\frac{i}{16}\right) \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{i b^2 \log ^2(f)}{8 f}+2 i d} \text{erf}\left(\frac{\left(\frac{1}{4}+\frac{i}{4}\right) (b \log (f)+4 i f x)}{\sqrt{f}}\right)-\left(\frac{1}{16}+\frac{i}{16}\right) \sqrt{\pi } f^{a-\frac{1}{2}} e^{-\frac{1}{8} i \left(\frac{b^2 \log ^2(f)}{f}+16 d\right)} \text{erfi}\left(\frac{\left(\frac{1}{4}+\frac{i}{4}\right) (-b \log (f)+4 i f x)}{\sqrt{f}}\right)+\frac{f^{a+b x}}{2 b \log (f)}",1,"(f^a*((8*f^(b*x))/(b*Log[f]) + ((1 - I)*Sqrt[Pi]*Erf[((4 + 4*I)*f*x - (1 - I)*b*Log[f])/(4*Sqrt[f])]*(Cos[d] - I*Sin[d])^2)/(E^(((I/8)*b^2*Log[f]^2)/f)*Sqrt[f]) + ((1 + I)*E^(((I/8)*b^2*Log[f]^2)/f)*Sqrt[Pi]*Erfi[((4 + 4*I)*f*x + (1 - I)*b*Log[f])/(4*Sqrt[f])]*((-I)*Cos[2*d] + Sin[2*d]))/Sqrt[f]))/16","A",1
112,1,267,298,0.8773987,"\int f^{a+b x} \cos ^3\left(d+f x^2\right) \, dx","Integrate[f^(a + b*x)*Cos[d + f*x^2]^3,x]","\frac{1}{48} \sqrt[4]{-1} \sqrt{\pi } f^{a-\frac{1}{2}} e^{-\frac{i b^2 \log ^2(f)}{4 f}} \left(9 e^{\frac{i b^2 \log ^2(f)}{2 f}} (\sin (d)-i \cos (d)) \text{erfi}\left(\frac{\sqrt[4]{-1} (2 f x-i b \log (f))}{2 \sqrt{f}}\right)+\sqrt{3} e^{\frac{i b^2 \log ^2(f)}{6 f}} \left(e^{\frac{i b^2 \log ^2(f)}{6 f}} (\sin (3 d)-i \cos (3 d)) \text{erfi}\left(\frac{(1-i) b \log (f)+(6+6 i) f x}{2 \sqrt{6} \sqrt{f}}\right)-(\cos (3 d)-i \sin (3 d)) \text{erfi}\left(\frac{(-1)^{3/4} (6 f x+i b \log (f))}{2 \sqrt{3} \sqrt{f}}\right)\right)-9 (\cos (d)-i \sin (d)) \text{erfi}\left(\frac{(-1)^{3/4} (2 f x+i b \log (f))}{2 \sqrt{f}}\right)\right)","-\frac{3}{16} \sqrt[4]{-1} \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{1}{4} i \left(\frac{b^2 \log ^2(f)}{f}+4 d\right)} \text{erf}\left(\frac{\sqrt[4]{-1} (b \log (f)+2 i f x)}{2 \sqrt{f}}\right)-\left(\frac{1}{16}+\frac{i}{16}\right) \sqrt{\frac{\pi }{6}} f^{a-\frac{1}{2}} e^{\frac{i b^2 \log ^2(f)}{12 f}+3 i d} \text{erf}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (b \log (f)+6 i f x)}{\sqrt{6} \sqrt{f}}\right)-\frac{3}{16} \sqrt[4]{-1} \sqrt{\pi } f^{a-\frac{1}{2}} e^{-\frac{1}{4} i \left(\frac{b^2 \log ^2(f)}{f}+4 d\right)} \text{erfi}\left(\frac{\sqrt[4]{-1} (-b \log (f)+2 i f x)}{2 \sqrt{f}}\right)-\left(\frac{1}{16}+\frac{i}{16}\right) \sqrt{\frac{\pi }{6}} f^{a-\frac{1}{2}} e^{-\frac{1}{12} i \left(\frac{b^2 \log ^2(f)}{f}+36 d\right)} \text{erfi}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (-b \log (f)+6 i f x)}{\sqrt{6} \sqrt{f}}\right)",1,"((-1)^(1/4)*f^(-1/2 + a)*Sqrt[Pi]*(-9*Erfi[((-1)^(3/4)*(2*f*x + I*b*Log[f]))/(2*Sqrt[f])]*(Cos[d] - I*Sin[d]) + 9*E^(((I/2)*b^2*Log[f]^2)/f)*Erfi[((-1)^(1/4)*(2*f*x - I*b*Log[f]))/(2*Sqrt[f])]*((-I)*Cos[d] + Sin[d]) + Sqrt[3]*E^(((I/6)*b^2*Log[f]^2)/f)*(-(Erfi[((-1)^(3/4)*(6*f*x + I*b*Log[f]))/(2*Sqrt[3]*Sqrt[f])]*(Cos[3*d] - I*Sin[3*d])) + E^(((I/6)*b^2*Log[f]^2)/f)*Erfi[((6 + 6*I)*f*x + (1 - I)*b*Log[f])/(2*Sqrt[6]*Sqrt[f])]*((-I)*Cos[3*d] + Sin[3*d]))))/(48*E^(((I/4)*b^2*Log[f]^2)/f))","A",1
113,1,163,162,0.3859505,"\int f^{a+b x} \cos \left(d+e x+f x^2\right) \, dx","Integrate[f^(a + b*x)*Cos[d + e*x + f*x^2],x]","\frac{1}{4} \sqrt[4]{-1} \sqrt{\pi } f^{a-\frac{b e+f}{2 f}} e^{-\frac{i \left(b^2 \log ^2(f)+e^2\right)}{4 f}} \left(e^{\frac{i b^2 \log ^2(f)}{2 f}} (\sin (d)-i \cos (d)) \text{erfi}\left(\frac{\sqrt[4]{-1} (-i b \log (f)+e+2 f x)}{2 \sqrt{f}}\right)-e^{\frac{i e^2}{2 f}} (\cos (d)-i \sin (d)) \text{erfi}\left(\frac{(-1)^{3/4} (i b \log (f)+e+2 f x)}{2 \sqrt{f}}\right)\right)","-\frac{1}{4} \sqrt[4]{-1} \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{1}{4} i \left(4 d+\frac{(b \log (f)+i e)^2}{f}\right)} \text{erf}\left(\frac{\sqrt[4]{-1} (b \log (f)+i e+2 i f x)}{2 \sqrt{f}}\right)-\frac{1}{4} \sqrt[4]{-1} \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{i (e+i b \log (f))^2}{4 f}-i d} \text{erfi}\left(\frac{\sqrt[4]{-1} (-b \log (f)+i e+2 i f x)}{2 \sqrt{f}}\right)",1,"((-1)^(1/4)*f^(a - (b*e + f)/(2*f))*Sqrt[Pi]*(-(E^(((I/2)*e^2)/f)*Erfi[((-1)^(3/4)*(e + 2*f*x + I*b*Log[f]))/(2*Sqrt[f])]*(Cos[d] - I*Sin[d])) + E^(((I/2)*b^2*Log[f]^2)/f)*Erfi[((-1)^(1/4)*(e + 2*f*x - I*b*Log[f]))/(2*Sqrt[f])]*((-I)*Cos[d] + Sin[d])))/(4*E^(((I/4)*(e^2 + b^2*Log[f]^2))/f))","A",1
114,1,245,179,1.0848968,"\int f^{a+b x} \cos ^2\left(d+e x+f x^2\right) \, dx","Integrate[f^(a + b*x)*Cos[d + e*x + f*x^2]^2,x]","\frac{f^{a-\frac{b e+f}{2 f}} e^{-\frac{i \left(b^2 \log ^2(f)+4 e^2\right)}{8 f}} \left(\sqrt[4]{-1} \sqrt{2 \pi } b \log (f) e^{\frac{i b^2 \log ^2(f)}{4 f}} (\sin (2 d)-i \cos (2 d)) \text{erfi}\left(\frac{\left(\frac{1}{4}+\frac{i}{4}\right) (-i b \log (f)+2 e+4 f x)}{\sqrt{f}}\right)+8 f^{b \left(\frac{e}{2 f}+x\right)+\frac{1}{2}} e^{\frac{i \left(b^2 \log ^2(f)+4 e^2\right)}{8 f}}-\sqrt[4]{-1} \sqrt{2 \pi } b e^{\frac{i e^2}{f}} \log (f) (\sin (2 d)+i \cos (2 d)) \text{erf}\left(\frac{\left(\frac{1}{4}+\frac{i}{4}\right) (i b \log (f)+2 e+4 f x)}{\sqrt{f}}\right)\right)}{16 b \log (f)}","\left(-\frac{1}{16}-\frac{i}{16}\right) \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{i (b \log (f)+2 i e)^2}{8 f}+2 i d} \text{erf}\left(\frac{\left(\frac{1}{4}+\frac{i}{4}\right) (b \log (f)+2 i e+4 i f x)}{\sqrt{f}}\right)-\left(\frac{1}{16}+\frac{i}{16}\right) \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{i (2 e+i b \log (f))^2}{8 f}-2 i d} \text{erfi}\left(\frac{\left(\frac{1}{4}+\frac{i}{4}\right) (-b \log (f)+2 i e+4 i f x)}{\sqrt{f}}\right)+\frac{f^{a+b x}}{2 b \log (f)}",1,"(f^(a - (b*e + f)/(2*f))*(8*E^(((I/8)*(4*e^2 + b^2*Log[f]^2))/f)*f^(1/2 + b*(e/(2*f) + x)) + (-1)^(1/4)*b*E^(((I/4)*b^2*Log[f]^2)/f)*Sqrt[2*Pi]*Erfi[((1/4 + I/4)*(2*e + 4*f*x - I*b*Log[f]))/Sqrt[f]]*Log[f]*((-I)*Cos[2*d] + Sin[2*d]) - (-1)^(1/4)*b*E^((I*e^2)/f)*Sqrt[2*Pi]*Erf[((1/4 + I/4)*(2*e + 4*f*x + I*b*Log[f]))/Sqrt[f]]*Log[f]*(I*Cos[2*d] + Sin[2*d])))/(16*b*E^(((I/8)*(4*e^2 + b^2*Log[f]^2))/f)*Log[f])","A",1
115,1,322,340,1.5730032,"\int f^{a+b x} \cos ^3\left(d+e x+f x^2\right) \, dx","Integrate[f^(a + b*x)*Cos[d + e*x + f*x^2]^3,x]","\frac{1}{48} \sqrt[4]{-1} \sqrt{\pi } f^{a-\frac{b e+f}{2 f}} e^{-\frac{i \left(b^2 \log ^2(f)+3 e^2\right)}{4 f}} \left(9 (\sin (d)-i \cos (d)) e^{\frac{i \left(b^2 \log ^2(f)+e^2\right)}{2 f}} \text{erfi}\left(\frac{\sqrt[4]{-1} (-i b \log (f)+e+2 f x)}{2 \sqrt{f}}\right)+e^{\frac{i e^2}{f}} \left(-\sqrt{3} (\cos (3 d)-i \sin (3 d)) e^{\frac{i \left(b^2 \log ^2(f)+3 e^2\right)}{6 f}} \text{erfi}\left(\frac{(-1)^{3/4} (i b \log (f)+3 e+6 f x)}{2 \sqrt{3} \sqrt{f}}\right)-9 (\cos (d)-i \sin (d)) \text{erfi}\left(\frac{(-1)^{3/4} (i b \log (f)+e+2 f x)}{2 \sqrt{f}}\right)\right)+\sqrt{3} e^{\frac{i b^2 \log ^2(f)}{3 f}} (\sin (3 d)-i \cos (3 d)) \text{erfi}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (-i b \log (f)+3 e+6 f x)}{\sqrt{6} \sqrt{f}}\right)\right)","-\frac{3}{16} \sqrt[4]{-1} \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{1}{4} i \left(4 d+\frac{(b \log (f)+i e)^2}{f}\right)} \text{erf}\left(\frac{\sqrt[4]{-1} (b \log (f)+i e+2 i f x)}{2 \sqrt{f}}\right)-\left(\frac{1}{16}+\frac{i}{16}\right) \sqrt{\frac{\pi }{6}} f^{a-\frac{1}{2}} e^{\frac{i (b \log (f)+3 i e)^2}{12 f}+3 i d} \text{erf}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (b \log (f)+3 i e+6 i f x)}{\sqrt{6} \sqrt{f}}\right)-\frac{3}{16} \sqrt[4]{-1} \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{i (e+i b \log (f))^2}{4 f}-i d} \text{erfi}\left(\frac{\sqrt[4]{-1} (-b \log (f)+i e+2 i f x)}{2 \sqrt{f}}\right)-\left(\frac{1}{16}+\frac{i}{16}\right) \sqrt{\frac{\pi }{6}} f^{a-\frac{1}{2}} e^{\frac{i (3 e+i b \log (f))^2}{12 f}-3 i d} \text{erfi}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) (-b \log (f)+3 i e+6 i f x)}{\sqrt{6} \sqrt{f}}\right)",1,"((-1)^(1/4)*f^(a - (b*e + f)/(2*f))*Sqrt[Pi]*(9*E^(((I/2)*(e^2 + b^2*Log[f]^2))/f)*Erfi[((-1)^(1/4)*(e + 2*f*x - I*b*Log[f]))/(2*Sqrt[f])]*((-I)*Cos[d] + Sin[d]) + E^((I*e^2)/f)*(-9*Erfi[((-1)^(3/4)*(e + 2*f*x + I*b*Log[f]))/(2*Sqrt[f])]*(Cos[d] - I*Sin[d]) - Sqrt[3]*E^(((I/6)*(3*e^2 + b^2*Log[f]^2))/f)*Erfi[((-1)^(3/4)*(3*e + 6*f*x + I*b*Log[f]))/(2*Sqrt[3]*Sqrt[f])]*(Cos[3*d] - I*Sin[3*d])) + Sqrt[3]*E^(((I/3)*b^2*Log[f]^2)/f)*Erfi[((1/2 + I/2)*(3*e + 6*f*x - I*b*Log[f]))/(Sqrt[6]*Sqrt[f])]*((-I)*Cos[3*d] + Sin[3*d])))/(48*E^(((I/4)*(3*e^2 + b^2*Log[f]^2))/f))","A",1
116,1,116,147,0.1556792,"\int f^{a+c x^2} \cos (d+e x) \, dx","Integrate[f^(a + c*x^2)*Cos[d + e*x],x]","\frac{\sqrt{\pi } f^a e^{\frac{e^2}{4 c \log (f)}} \left((\cos (d)-i \sin (d)) \text{erfi}\left(\frac{2 c x \log (f)-i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+(\cos (d)+i \sin (d)) \text{erfi}\left(\frac{2 c x \log (f)+i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)\right)}{4 \sqrt{c} \sqrt{\log (f)}}","\frac{\sqrt{\pi } f^a e^{\frac{e^2}{4 c \log (f)}+i d} \text{erfi}\left(\frac{2 c x \log (f)+i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}-\frac{\sqrt{\pi } f^a e^{\frac{e^2}{4 c \log (f)}-i d} \text{erfi}\left(\frac{-2 c x \log (f)+i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}",1,"(E^(e^2/(4*c*Log[f]))*f^a*Sqrt[Pi]*(Erfi[((-I)*e + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cos[d] - I*Sin[d]) + Erfi[(I*e + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cos[d] + I*Sin[d])))/(4*Sqrt[c]*Sqrt[Log[f]])","A",1
117,1,131,171,0.2512732,"\int f^{a+c x^2} \cos ^2(d+e x) \, dx","Integrate[f^(a + c*x^2)*Cos[d + e*x]^2,x]","\frac{\sqrt{\pi } f^a \left(2 \text{erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)+e^{\frac{e^2}{c \log (f)}} \left((\cos (2 d)-i \sin (2 d)) \text{erfi}\left(\frac{c x \log (f)-i e}{\sqrt{c} \sqrt{\log (f)}}\right)+(\cos (2 d)+i \sin (2 d)) \text{erfi}\left(\frac{c x \log (f)+i e}{\sqrt{c} \sqrt{\log (f)}}\right)\right)\right)}{8 \sqrt{c} \sqrt{\log (f)}}","-\frac{\sqrt{\pi } f^a e^{\frac{e^2}{c \log (f)}-2 i d} \text{erfi}\left(\frac{-c x \log (f)+i e}{\sqrt{c} \sqrt{\log (f)}}\right)}{8 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a e^{\frac{e^2}{c \log (f)}+2 i d} \text{erfi}\left(\frac{c x \log (f)+i e}{\sqrt{c} \sqrt{\log (f)}}\right)}{8 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a \text{erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)}{4 \sqrt{c} \sqrt{\log (f)}}",1,"(f^a*Sqrt[Pi]*(2*Erfi[Sqrt[c]*x*Sqrt[Log[f]]] + E^(e^2/(c*Log[f]))*(Erfi[((-I)*e + c*x*Log[f])/(Sqrt[c]*Sqrt[Log[f]])]*(Cos[2*d] - I*Sin[2*d]) + Erfi[(I*e + c*x*Log[f])/(Sqrt[c]*Sqrt[Log[f]])]*(Cos[2*d] + I*Sin[2*d]))))/(8*Sqrt[c]*Sqrt[Log[f]])","A",1
118,1,218,293,0.4175906,"\int f^{a+c x^2} \cos ^3(d+e x) \, dx","Integrate[f^(a + c*x^2)*Cos[d + e*x]^3,x]","\frac{\sqrt{\pi } f^a e^{\frac{e^2}{4 c \log (f)}} \left(e^{\frac{2 e^2}{c \log (f)}} \left((\cos (3 d)-i \sin (3 d)) \text{erfi}\left(\frac{2 c x \log (f)-3 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+(\cos (3 d)+i \sin (3 d)) \text{erfi}\left(\frac{2 c x \log (f)+3 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)\right)+3 (\cos (d)-i \sin (d)) \text{erfi}\left(\frac{2 c x \log (f)-i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+3 (\cos (d)+i \sin (d)) \text{erfi}\left(\frac{2 c x \log (f)+i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)\right)}{16 \sqrt{c} \sqrt{\log (f)}}","-\frac{3 \sqrt{\pi } f^a e^{\frac{e^2}{4 c \log (f)}-i d} \text{erfi}\left(\frac{-2 c x \log (f)+i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}-\frac{\sqrt{\pi } f^a e^{\frac{9 e^2}{4 c \log (f)}-3 i d} \text{erfi}\left(\frac{-2 c x \log (f)+3 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}+\frac{3 \sqrt{\pi } f^a e^{\frac{e^2}{4 c \log (f)}+i d} \text{erfi}\left(\frac{2 c x \log (f)+i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a e^{\frac{9 e^2}{4 c \log (f)}+3 i d} \text{erfi}\left(\frac{2 c x \log (f)+3 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}",1,"(E^(e^2/(4*c*Log[f]))*f^a*Sqrt[Pi]*(3*Erfi[((-I)*e + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cos[d] - I*Sin[d]) + 3*Erfi[(I*e + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cos[d] + I*Sin[d]) + E^((2*e^2)/(c*Log[f]))*(Erfi[((-3*I)*e + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cos[3*d] - I*Sin[3*d]) + Erfi[((3*I)*e + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cos[3*d] + I*Sin[3*d]))))/(16*Sqrt[c]*Sqrt[Log[f]])","A",1
119,1,170,103,0.4853853,"\int f^{a+c x^2} \cos \left(d+f x^2\right) \, dx","Integrate[f^(a + c*x^2)*Cos[d + f*x^2],x]","-\frac{(-1)^{3/4} \sqrt{\pi } f^a \left(\sqrt{f+i c \log (f)} \left(f \cos (d) \text{erf}\left(\frac{(1+i) x \sqrt{f+i c \log (f)}}{\sqrt{2}}\right)-\text{erfi}\left((-1)^{3/4} x \sqrt{f+i c \log (f)}\right) (c \cos (d) \log (f)+\sin (d) (f-i c \log (f)))\right)+\sqrt{f-i c \log (f)} (f+i c \log (f)) (\cos (d)+i \sin (d)) \text{erfi}\left(\sqrt[4]{-1} x \sqrt{f-i c \log (f)}\right)\right)}{4 \left(c^2 \log ^2(f)+f^2\right)}","\frac{\sqrt{\pi } e^{-i d} f^a \text{erf}\left(x \sqrt{-c \log (f)+i f}\right)}{4 \sqrt{-c \log (f)+i f}}+\frac{\sqrt{\pi } e^{i d} f^a \text{erfi}\left(x \sqrt{c \log (f)+i f}\right)}{4 \sqrt{c \log (f)+i f}}",1,"-1/4*((-1)^(3/4)*f^a*Sqrt[Pi]*(Erfi[(-1)^(1/4)*x*Sqrt[f - I*c*Log[f]]]*Sqrt[f - I*c*Log[f]]*(f + I*c*Log[f])*(Cos[d] + I*Sin[d]) + Sqrt[f + I*c*Log[f]]*(f*Cos[d]*Erf[((1 + I)*x*Sqrt[f + I*c*Log[f]])/Sqrt[2]] - Erfi[(-1)^(3/4)*x*Sqrt[f + I*c*Log[f]]]*(c*Cos[d]*Log[f] + (f - I*c*Log[f])*Sin[d]))))/(f^2 + c^2*Log[f]^2)","A",1
120,1,189,140,0.8257227,"\int f^{a+c x^2} \cos ^2\left(d+f x^2\right) \, dx","Integrate[f^(a + c*x^2)*Cos[d + f*x^2]^2,x]","\frac{1}{8} \sqrt{\pi } f^a \left(\frac{2 \text{erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)}{\sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt[4]{-1} \left(\sqrt{2 f-i c \log (f)} (c \log (f)-2 i f) (\cos (2 d)+i \sin (2 d)) \text{erfi}\left(\sqrt[4]{-1} x \sqrt{2 f-i c \log (f)}\right)-(2 f-i c \log (f)) \sqrt{2 f+i c \log (f)} (\cos (2 d)-i \sin (2 d)) \text{erfi}\left((-1)^{3/4} x \sqrt{2 f+i c \log (f)}\right)\right)}{c^2 \log ^2(f)+4 f^2}\right)","\frac{\sqrt{\pi } e^{-2 i d} f^a \text{erf}\left(x \sqrt{-c \log (f)+2 i f}\right)}{8 \sqrt{-c \log (f)+2 i f}}+\frac{\sqrt{\pi } e^{2 i d} f^a \text{erfi}\left(x \sqrt{c \log (f)+2 i f}\right)}{8 \sqrt{c \log (f)+2 i f}}+\frac{\sqrt{\pi } f^a \text{erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)}{4 \sqrt{c} \sqrt{\log (f)}}",1,"(f^a*Sqrt[Pi]*((2*Erfi[Sqrt[c]*x*Sqrt[Log[f]]])/(Sqrt[c]*Sqrt[Log[f]]) + ((-1)^(1/4)*(-(Erfi[(-1)^(3/4)*x*Sqrt[2*f + I*c*Log[f]]]*(2*f - I*c*Log[f])*Sqrt[2*f + I*c*Log[f]]*(Cos[2*d] - I*Sin[2*d])) + Erfi[(-1)^(1/4)*x*Sqrt[2*f - I*c*Log[f]]]*Sqrt[2*f - I*c*Log[f]]*((-2*I)*f + c*Log[f])*(Cos[2*d] + I*Sin[2*d])))/(4*f^2 + c^2*Log[f]^2)))/8","A",1
121,1,389,205,2.1872651,"\int f^{a+c x^2} \cos ^3\left(d+f x^2\right) \, dx","Integrate[f^(a + c*x^2)*Cos[d + f*x^2]^3,x]","\frac{\sqrt[4]{-1} \sqrt{\pi } f^a \left((f-i c \log (f)) \left(\sqrt{3 f-i c \log (f)} \left(i c^2 \log ^2(f)+4 c f \log (f)-3 i f^2\right) (\cos (3 d)+i \sin (3 d)) \text{erfi}\left(\sqrt[4]{-1} x \sqrt{3 f-i c \log (f)}\right)-(3 f-i c \log (f)) \left(9 f \sin (d) \sqrt{f+i c \log (f)} \text{erf}\left(\frac{(1+i) x \sqrt{f+i c \log (f)}}{\sqrt{2}}\right)+3 \sqrt{f+i c \log (f)} \text{erfi}\left((-1)^{3/4} x \sqrt{f+i c \log (f)}\right) (c \sin (d) \log (f)+\cos (d) (3 f+i c \log (f)))+(f+i c \log (f)) \sqrt{3 f+i c \log (f)} (\cos (3 d)-i \sin (3 d)) \text{erfi}\left((-1)^{3/4} x \sqrt{3 f+i c \log (f)}\right)\right)\right)+3 \sqrt{f-i c \log (f)} \left(c^3 \log ^3(f)-i c^2 f \log ^2(f)+9 c f^2 \log (f)-9 i f^3\right) (\cos (d)+i \sin (d)) \text{erfi}\left(\sqrt[4]{-1} x \sqrt{f-i c \log (f)}\right)\right)}{16 \left(c^4 \log ^4(f)+10 c^2 f^2 \log ^2(f)+9 f^4\right)}","\frac{3 \sqrt{\pi } e^{-i d} f^a \text{erf}\left(x \sqrt{-c \log (f)+i f}\right)}{16 \sqrt{-c \log (f)+i f}}+\frac{\sqrt{\pi } e^{-3 i d} f^a \text{erf}\left(x \sqrt{-c \log (f)+3 i f}\right)}{16 \sqrt{-c \log (f)+3 i f}}+\frac{3 \sqrt{\pi } e^{i d} f^a \text{erfi}\left(x \sqrt{c \log (f)+i f}\right)}{16 \sqrt{c \log (f)+i f}}+\frac{\sqrt{\pi } e^{3 i d} f^a \text{erfi}\left(x \sqrt{c \log (f)+3 i f}\right)}{16 \sqrt{c \log (f)+3 i f}}",1,"((-1)^(1/4)*f^a*Sqrt[Pi]*(3*Erfi[(-1)^(1/4)*x*Sqrt[f - I*c*Log[f]]]*Sqrt[f - I*c*Log[f]]*((-9*I)*f^3 + 9*c*f^2*Log[f] - I*c^2*f*Log[f]^2 + c^3*Log[f]^3)*(Cos[d] + I*Sin[d]) + (f - I*c*Log[f])*(-((3*f - I*c*Log[f])*(9*f*Erf[((1 + I)*x*Sqrt[f + I*c*Log[f]])/Sqrt[2]]*Sqrt[f + I*c*Log[f]]*Sin[d] + 3*Erfi[(-1)^(3/4)*x*Sqrt[f + I*c*Log[f]]]*Sqrt[f + I*c*Log[f]]*(Cos[d]*(3*f + I*c*Log[f]) + c*Log[f]*Sin[d]) + Erfi[(-1)^(3/4)*x*Sqrt[3*f + I*c*Log[f]]]*(f + I*c*Log[f])*Sqrt[3*f + I*c*Log[f]]*(Cos[3*d] - I*Sin[3*d]))) + Erfi[(-1)^(1/4)*x*Sqrt[3*f - I*c*Log[f]]]*Sqrt[3*f - I*c*Log[f]]*((-3*I)*f^2 + 4*c*f*Log[f] + I*c^2*Log[f]^2)*(Cos[3*d] + I*Sin[3*d]))))/(16*(9*f^4 + 10*c^2*f^2*Log[f]^2 + c^4*Log[f]^4))","A",1
122,1,217,183,0.9548868,"\int f^{a+c x^2} \cos \left(d+e x+f x^2\right) \, dx","Integrate[f^(a + c*x^2)*Cos[d + e*x + f*x^2],x]","\frac{\sqrt[4]{-1} \sqrt{\pi } f^a e^{\frac{e^2}{4 c \log (f)+4 i f}} \left(\sqrt{f-i c \log (f)} (c \log (f)-i f) (\cos (d)+i \sin (d)) \text{erfi}\left(\frac{\sqrt[4]{-1} (-2 i c x \log (f)+e+2 f x)}{2 \sqrt{f-i c \log (f)}}\right)-(f-i c \log (f)) \sqrt{f+i c \log (f)} (\cos (d)-i \sin (d)) e^{\frac{i e^2 f}{2 \left(c^2 \log ^2(f)+f^2\right)}} \text{erfi}\left(\frac{(-1)^{3/4} (2 i c x \log (f)+e+2 f x)}{2 \sqrt{f+i c \log (f)}}\right)\right)}{4 \left(c^2 \log ^2(f)+f^2\right)}","\frac{\sqrt{\pi } f^a e^{-\frac{e^2}{-4 c \log (f)+4 i f}-i d} \text{erf}\left(\frac{2 x (-c \log (f)+i f)+i e}{2 \sqrt{-c \log (f)+i f}}\right)}{4 \sqrt{-c \log (f)+i f}}+\frac{\sqrt{\pi } f^a e^{\frac{e^2}{4 c \log (f)+4 i f}+i d} \text{erfi}\left(\frac{2 x (c \log (f)+i f)+i e}{2 \sqrt{c \log (f)+i f}}\right)}{4 \sqrt{c \log (f)+i f}}",1,"((-1)^(1/4)*E^(e^2/((4*I)*f + 4*c*Log[f]))*f^a*Sqrt[Pi]*(-(E^(((I/2)*e^2*f)/(f^2 + c^2*Log[f]^2))*Erfi[((-1)^(3/4)*(e + 2*f*x + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*(f - I*c*Log[f])*Sqrt[f + I*c*Log[f]]*(Cos[d] - I*Sin[d])) + Erfi[((-1)^(1/4)*(e + 2*f*x - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Sqrt[f - I*c*Log[f]]*((-I)*f + c*Log[f])*(Cos[d] + I*Sin[d])))/(4*(f^2 + c^2*Log[f]^2))","A",0
123,1,252,211,2.3210975,"\int f^{a+c x^2} \cos ^2\left(d+e x+f x^2\right) \, dx","Integrate[f^(a + c*x^2)*Cos[d + e*x + f*x^2]^2,x]","\frac{1}{8} \sqrt{\pi } f^a \left(\frac{2 \text{erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)}{\sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt[4]{-1} \left(\sqrt{2 f-i c \log (f)} (2 f+i c \log (f)) (\sin (2 d)-i \cos (2 d)) e^{\frac{e^2}{c \log (f)+2 i f}} \text{erfi}\left(\frac{\sqrt[4]{-1} (-i c x \log (f)+e+2 f x)}{\sqrt{2 f-i c \log (f)}}\right)-(2 f-i c \log (f)) \sqrt{2 f+i c \log (f)} (\cos (2 d)-i \sin (2 d)) e^{\frac{e^2}{c \log (f)-2 i f}} \text{erfi}\left(\frac{(-1)^{3/4} (i c x \log (f)+e+2 f x)}{\sqrt{2 f+i c \log (f)}}\right)\right)}{c^2 \log ^2(f)+4 f^2}\right)","\frac{\sqrt{\pi } f^a e^{-\frac{e^2}{-c \log (f)+2 i f}-2 i d} \text{erf}\left(\frac{x (-c \log (f)+2 i f)+i e}{\sqrt{-c \log (f)+2 i f}}\right)}{8 \sqrt{-c \log (f)+2 i f}}+\frac{\sqrt{\pi } f^a e^{\frac{e^2}{c \log (f)+2 i f}+2 i d} \text{erfi}\left(\frac{x (c \log (f)+2 i f)+i e}{\sqrt{c \log (f)+2 i f}}\right)}{8 \sqrt{c \log (f)+2 i f}}+\frac{\sqrt{\pi } f^a \text{erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)}{4 \sqrt{c} \sqrt{\log (f)}}",1,"(f^a*Sqrt[Pi]*((2*Erfi[Sqrt[c]*x*Sqrt[Log[f]]])/(Sqrt[c]*Sqrt[Log[f]]) + ((-1)^(1/4)*(-(E^(e^2/((-2*I)*f + c*Log[f]))*Erfi[((-1)^(3/4)*(e + 2*f*x + I*c*x*Log[f]))/Sqrt[2*f + I*c*Log[f]]]*(2*f - I*c*Log[f])*Sqrt[2*f + I*c*Log[f]]*(Cos[2*d] - I*Sin[2*d])) + E^(e^2/((2*I)*f + c*Log[f]))*Erfi[((-1)^(1/4)*(e + 2*f*x - I*c*x*Log[f]))/Sqrt[2*f - I*c*Log[f]]]*Sqrt[2*f - I*c*Log[f]]*(2*f + I*c*Log[f])*((-I)*Cos[2*d] + Sin[2*d])))/(4*f^2 + c^2*Log[f]^2)))/8","A",0
124,1,2997,369,6.953748,"\int f^{a+c x^2} \cos ^3\left(d+e x+f x^2\right) \, dx","Integrate[f^(a + c*x^2)*Cos[d + e*x + f*x^2]^3,x]","\text{Result too large to show}","\frac{\sqrt{\pi } f^a \exp \left(-\frac{9 e^2}{4 (-c \log (f)+3 i f)}-3 i d\right) \text{erf}\left(\frac{2 x (-c \log (f)+3 i f)+3 i e}{2 \sqrt{-c \log (f)+3 i f}}\right)}{16 \sqrt{-c \log (f)+3 i f}}+\frac{3 \sqrt{\pi } f^a e^{-\frac{e^2}{-4 c \log (f)+4 i f}-i d} \text{erf}\left(\frac{2 x (-c \log (f)+i f)+i e}{2 \sqrt{-c \log (f)+i f}}\right)}{16 \sqrt{-c \log (f)+i f}}+\frac{3 \sqrt{\pi } f^a e^{\frac{e^2}{4 c \log (f)+4 i f}+i d} \text{erfi}\left(\frac{2 x (c \log (f)+i f)+i e}{2 \sqrt{c \log (f)+i f}}\right)}{16 \sqrt{c \log (f)+i f}}+\frac{\sqrt{\pi } f^a e^{\frac{9 e^2}{4 (c \log (f)+3 i f)}+3 i d} \text{erfi}\left(\frac{2 x (c \log (f)+3 i f)+3 i e}{2 \sqrt{c \log (f)+3 i f}}\right)}{16 \sqrt{c \log (f)+3 i f}}",1,"(f^a*Sqrt[Pi]*((-27*(-1)^(3/4)*f^3*Cos[d]*Erfi[((-1)^(1/4)*(e + 2*f*x - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Sqrt[f - I*c*Log[f]])/E^(((I/4)*e^2)/(f - I*c*Log[f])) + (27*(-1)^(1/4)*c*f^2*Cos[d]*Erfi[((-1)^(1/4)*(e + 2*f*x - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]*Sqrt[f - I*c*Log[f]])/E^(((I/4)*e^2)/(f - I*c*Log[f])) - (3*(-1)^(3/4)*c^2*f*Cos[d]*Erfi[((-1)^(1/4)*(e + 2*f*x - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]^2*Sqrt[f - I*c*Log[f]])/E^(((I/4)*e^2)/(f - I*c*Log[f])) + (3*(-1)^(1/4)*c^3*Cos[d]*Erfi[((-1)^(1/4)*(e + 2*f*x - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]^3*Sqrt[f - I*c*Log[f]])/E^(((I/4)*e^2)/(f - I*c*Log[f])) - (3*(-1)^(3/4)*f^3*Cos[3*d]*Erfi[((-1)^(1/4)*(3*e + 6*f*x - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Sqrt[3*f - I*c*Log[f]])/E^((((9*I)/4)*e^2)/(3*f - I*c*Log[f])) + ((-1)^(1/4)*c*f^2*Cos[3*d]*Erfi[((-1)^(1/4)*(3*e + 6*f*x - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]*Sqrt[3*f - I*c*Log[f]])/E^((((9*I)/4)*e^2)/(3*f - I*c*Log[f])) - (3*(-1)^(3/4)*c^2*f*Cos[3*d]*Erfi[((-1)^(1/4)*(3*e + 6*f*x - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]^2*Sqrt[3*f - I*c*Log[f]])/E^((((9*I)/4)*e^2)/(3*f - I*c*Log[f])) + ((-1)^(1/4)*c^3*Cos[3*d]*Erfi[((-1)^(1/4)*(3*e + 6*f*x - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]^3*Sqrt[3*f - I*c*Log[f]])/E^((((9*I)/4)*e^2)/(3*f - I*c*Log[f])) - 27*(-1)^(1/4)*E^(((I/4)*e^2)/(f + I*c*Log[f]))*f^3*Cos[d]*Erfi[((-1)^(3/4)*(e + 2*f*x + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Sqrt[f + I*c*Log[f]] + 27*(-1)^(3/4)*c*E^(((I/4)*e^2)/(f + I*c*Log[f]))*f^2*Cos[d]*Erfi[((-1)^(3/4)*(e + 2*f*x + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]*Sqrt[f + I*c*Log[f]] - 3*(-1)^(1/4)*c^2*E^(((I/4)*e^2)/(f + I*c*Log[f]))*f*Cos[d]*Erfi[((-1)^(3/4)*(e + 2*f*x + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]^2*Sqrt[f + I*c*Log[f]] + 3*(-1)^(3/4)*c^3*E^(((I/4)*e^2)/(f + I*c*Log[f]))*Cos[d]*Erfi[((-1)^(3/4)*(e + 2*f*x + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]^3*Sqrt[f + I*c*Log[f]] - 3*(-1)^(1/4)*E^((((9*I)/4)*e^2)/(3*f + I*c*Log[f]))*f^3*Cos[3*d]*Erfi[((-1)^(3/4)*(3*e + 6*f*x + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Sqrt[3*f + I*c*Log[f]] + (-1)^(3/4)*c*E^((((9*I)/4)*e^2)/(3*f + I*c*Log[f]))*f^2*Cos[3*d]*Erfi[((-1)^(3/4)*(3*e + 6*f*x + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]*Sqrt[3*f + I*c*Log[f]] - 3*(-1)^(1/4)*c^2*E^((((9*I)/4)*e^2)/(3*f + I*c*Log[f]))*f*Cos[3*d]*Erfi[((-1)^(3/4)*(3*e + 6*f*x + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]^2*Sqrt[3*f + I*c*Log[f]] + (-1)^(3/4)*c^3*E^((((9*I)/4)*e^2)/(3*f + I*c*Log[f]))*Cos[3*d]*Erfi[((-1)^(3/4)*(3*e + 6*f*x + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]^3*Sqrt[3*f + I*c*Log[f]] + (27*(-1)^(1/4)*f^3*Erfi[((-1)^(1/4)*(e + 2*f*x - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Sqrt[f - I*c*Log[f]]*Sin[d])/E^(((I/4)*e^2)/(f - I*c*Log[f])) + (27*(-1)^(3/4)*c*f^2*Erfi[((-1)^(1/4)*(e + 2*f*x - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]*Sqrt[f - I*c*Log[f]]*Sin[d])/E^(((I/4)*e^2)/(f - I*c*Log[f])) + (3*(-1)^(1/4)*c^2*f*Erfi[((-1)^(1/4)*(e + 2*f*x - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]^2*Sqrt[f - I*c*Log[f]]*Sin[d])/E^(((I/4)*e^2)/(f - I*c*Log[f])) + (3*(-1)^(3/4)*c^3*Erfi[((-1)^(1/4)*(e + 2*f*x - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]^3*Sqrt[f - I*c*Log[f]]*Sin[d])/E^(((I/4)*e^2)/(f - I*c*Log[f])) + 27*(-1)^(3/4)*E^(((I/4)*e^2)/(f + I*c*Log[f]))*f^3*Erfi[((-1)^(3/4)*(e + 2*f*x + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Sqrt[f + I*c*Log[f]]*Sin[d] + 27*(-1)^(1/4)*c*E^(((I/4)*e^2)/(f + I*c*Log[f]))*f^2*Erfi[((-1)^(3/4)*(e + 2*f*x + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]*Sqrt[f + I*c*Log[f]]*Sin[d] + 3*(-1)^(3/4)*c^2*E^(((I/4)*e^2)/(f + I*c*Log[f]))*f*Erfi[((-1)^(3/4)*(e + 2*f*x + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]^2*Sqrt[f + I*c*Log[f]]*Sin[d] + 3*(-1)^(1/4)*c^3*E^(((I/4)*e^2)/(f + I*c*Log[f]))*Erfi[((-1)^(3/4)*(e + 2*f*x + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]^3*Sqrt[f + I*c*Log[f]]*Sin[d] + (3*(-1)^(1/4)*f^3*Erfi[((-1)^(1/4)*(3*e + 6*f*x - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Sqrt[3*f - I*c*Log[f]]*Sin[3*d])/E^((((9*I)/4)*e^2)/(3*f - I*c*Log[f])) + ((-1)^(3/4)*c*f^2*Erfi[((-1)^(1/4)*(3*e + 6*f*x - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]*Sqrt[3*f - I*c*Log[f]]*Sin[3*d])/E^((((9*I)/4)*e^2)/(3*f - I*c*Log[f])) + (3*(-1)^(1/4)*c^2*f*Erfi[((-1)^(1/4)*(3*e + 6*f*x - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]^2*Sqrt[3*f - I*c*Log[f]]*Sin[3*d])/E^((((9*I)/4)*e^2)/(3*f - I*c*Log[f])) + ((-1)^(3/4)*c^3*Erfi[((-1)^(1/4)*(3*e + 6*f*x - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]^3*Sqrt[3*f - I*c*Log[f]]*Sin[3*d])/E^((((9*I)/4)*e^2)/(3*f - I*c*Log[f])) + 3*(-1)^(3/4)*E^((((9*I)/4)*e^2)/(3*f + I*c*Log[f]))*f^3*Erfi[((-1)^(3/4)*(3*e + 6*f*x + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Sqrt[3*f + I*c*Log[f]]*Sin[3*d] + (-1)^(1/4)*c*E^((((9*I)/4)*e^2)/(3*f + I*c*Log[f]))*f^2*Erfi[((-1)^(3/4)*(3*e + 6*f*x + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]*Sqrt[3*f + I*c*Log[f]]*Sin[3*d] + 3*(-1)^(3/4)*c^2*E^((((9*I)/4)*e^2)/(3*f + I*c*Log[f]))*f*Erfi[((-1)^(3/4)*(3*e + 6*f*x + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]^2*Sqrt[3*f + I*c*Log[f]]*Sin[3*d] + (-1)^(1/4)*c^3*E^((((9*I)/4)*e^2)/(3*f + I*c*Log[f]))*Erfi[((-1)^(3/4)*(3*e + 6*f*x + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]^3*Sqrt[3*f + I*c*Log[f]]*Sin[3*d]))/(16*(f - I*c*Log[f])*(3*f - I*c*Log[f])*(f + I*c*Log[f])*(3*f + I*c*Log[f]))","B",0
125,1,151,172,0.325099,"\int f^{a+b x+c x^2} \cos (d+e x) \, dx","Integrate[f^(a + b*x + c*x^2)*Cos[d + e*x],x]","\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} e^{\frac{e (e-2 i b \log (f))}{4 c \log (f)}} \left(e^{\frac{i b e}{c}} (\cos (d)-i \sin (d)) \text{erfi}\left(\frac{\log (f) (b+2 c x)-i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+(\cos (d)+i \sin (d)) \text{erfi}\left(\frac{\log (f) (b+2 c x)+i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)\right)}{4 \sqrt{c} \sqrt{\log (f)}}","\frac{\sqrt{\pi } f^a e^{\frac{(e-i b \log (f))^2}{4 c \log (f)}+i d} \text{erfi}\left(\frac{b \log (f)+2 c x \log (f)+i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}-\frac{\sqrt{\pi } f^a e^{\frac{(e+i b \log (f))^2}{4 c \log (f)}-i d} \text{erfi}\left(\frac{-b \log (f)-2 c x \log (f)+i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}",1,"(E^((e*(e - (2*I)*b*Log[f]))/(4*c*Log[f]))*f^(a - b^2/(4*c))*Sqrt[Pi]*(E^((I*b*e)/c)*Erfi[((-I)*e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cos[d] - I*Sin[d]) + Erfi[(I*e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cos[d] + I*Sin[d])))/(4*Sqrt[c]*Sqrt[Log[f]])","A",1
126,1,204,231,0.6118287,"\int f^{a+b x+c x^2} \cos ^2(d+e x) \, dx","Integrate[f^(a + b*x + c*x^2)*Cos[d + e*x]^2,x]","\frac{\sqrt{\pi } e^{-\frac{i b e}{c}} f^{a-\frac{b^2}{4 c}} \left((\cos (2 d)+i \sin (2 d)) e^{\frac{e^2}{c \log (f)}} \text{erfi}\left(\frac{\log (f) (b+2 c x)+2 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+(\cos (2 d)-i \sin (2 d)) e^{\frac{e (e+2 i b \log (f))}{c \log (f)}} \text{erfi}\left(\frac{\log (f) (b+2 c x)-2 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+2 e^{\frac{i b e}{c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)\right)}{8 \sqrt{c} \sqrt{\log (f)}}","\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}-\frac{\sqrt{\pi } f^a e^{\frac{(2 e+i b \log (f))^2}{4 c \log (f)}-2 i d} \text{erfi}\left(\frac{-b \log (f)-2 c x \log (f)+2 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{8 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a e^{2 i d-\frac{(b \log (f)+2 i e)^2}{4 c \log (f)}} \text{erfi}\left(\frac{b \log (f)+2 c x \log (f)+2 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{8 \sqrt{c} \sqrt{\log (f)}}",1,"(f^(a - b^2/(4*c))*Sqrt[Pi]*(2*E^((I*b*e)/c)*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])] + E^((e*(e + (2*I)*b*Log[f]))/(c*Log[f]))*Erfi[((-2*I)*e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cos[2*d] - I*Sin[2*d]) + E^(e^2/(c*Log[f]))*Erfi[((2*I)*e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cos[2*d] + I*Sin[2*d])))/(8*Sqrt[c]*E^((I*b*e)/c)*Sqrt[Log[f]])","A",1
127,1,386,346,0.9467107,"\int f^{a+b x+c x^2} \cos ^3(d+e x) \, dx","Integrate[f^(a + b*x + c*x^2)*Cos[d + e*x]^3,x]","\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} e^{\frac{e (e-6 i b \log (f))}{4 c \log (f)}} \left(i \sin (3 d) e^{\frac{2 e^2}{c \log (f)}} \text{erfi}\left(\frac{\log (f) (b+2 c x)+3 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+\cos (3 d) e^{\frac{2 e^2}{c \log (f)}} \text{erfi}\left(\frac{\log (f) (b+2 c x)+3 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)-i \sin (3 d) e^{\frac{e (2 e+3 i b \log (f))}{c \log (f)}} \text{erfi}\left(\frac{\log (f) (b+2 c x)-3 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+\cos (3 d) e^{\frac{e (2 e+3 i b \log (f))}{c \log (f)}} \text{erfi}\left(\frac{\log (f) (b+2 c x)-3 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+3 e^{\frac{2 i b e}{c}} (\cos (d)-i \sin (d)) \text{erfi}\left(\frac{\log (f) (b+2 c x)-i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+3 e^{\frac{i b e}{c}} (\cos (d)+i \sin (d)) \text{erfi}\left(\frac{\log (f) (b+2 c x)+i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)\right)}{16 \sqrt{c} \sqrt{\log (f)}}","-\frac{3 \sqrt{\pi } f^a e^{\frac{(e+i b \log (f))^2}{4 c \log (f)}-i d} \text{erfi}\left(\frac{-b \log (f)-2 c x \log (f)+i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}-\frac{\sqrt{\pi } f^a e^{\frac{(3 e+i b \log (f))^2}{4 c \log (f)}-3 i d} \text{erfi}\left(\frac{-b \log (f)-2 c x \log (f)+3 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}+\frac{3 \sqrt{\pi } f^a e^{\frac{(e-i b \log (f))^2}{4 c \log (f)}+i d} \text{erfi}\left(\frac{b \log (f)+2 c x \log (f)+i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a e^{3 i d-\frac{(b \log (f)+3 i e)^2}{4 c \log (f)}} \text{erfi}\left(\frac{b \log (f)+2 c x \log (f)+3 i e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}",1,"(E^((e*(e - (6*I)*b*Log[f]))/(4*c*Log[f]))*f^(a - b^2/(4*c))*Sqrt[Pi]*(E^((e*(2*e + (3*I)*b*Log[f]))/(c*Log[f]))*Cos[3*d]*Erfi[((-3*I)*e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])] + E^((2*e^2)/(c*Log[f]))*Cos[3*d]*Erfi[((3*I)*e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])] + 3*E^(((2*I)*b*e)/c)*Erfi[((-I)*e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cos[d] - I*Sin[d]) + 3*E^((I*b*e)/c)*Erfi[(I*e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cos[d] + I*Sin[d]) - I*E^((e*(2*e + (3*I)*b*Log[f]))/(c*Log[f]))*Erfi[((-3*I)*e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*Sin[3*d] + I*E^((2*e^2)/(c*Log[f]))*Erfi[((3*I)*e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*Sin[3*d]))/(16*Sqrt[c]*Sqrt[Log[f]])","A",1
128,1,231,189,1.0039493,"\int f^{a+b x+c x^2} \cos \left(d+f x^2\right) \, dx","Integrate[f^(a + b*x + c*x^2)*Cos[d + f*x^2],x]","-\frac{(-1)^{3/4} \sqrt{\pi } f^a e^{\frac{b^2 \log ^2(f)}{-4 c \log (f)+4 i f}} \left(\sqrt{f-i c \log (f)} (f+i c \log (f)) (\cos (d)+i \sin (d)) e^{\frac{i b^2 f \log ^2(f)}{2 \left(c^2 \log ^2(f)+f^2\right)}} \text{erfi}\left(\frac{\sqrt[4]{-1} (2 f x-i \log (f) (b+2 c x))}{2 \sqrt{f-i c \log (f)}}\right)+(f-i c \log (f)) \sqrt{f+i c \log (f)} (-\sin (d)-i \cos (d)) \text{erfi}\left(\frac{(-1)^{3/4} (2 f x+i \log (f) (b+2 c x))}{2 \sqrt{f+i c \log (f)}}\right)\right)}{4 \left(c^2 \log ^2(f)+f^2\right)}","\frac{\sqrt{\pi } f^a e^{i d-\frac{b^2 \log ^2(f)}{4 c \log (f)+4 i f}} \text{erfi}\left(\frac{b \log (f)+2 x (c \log (f)+i f)}{2 \sqrt{c \log (f)+i f}}\right)}{4 \sqrt{c \log (f)+i f}}-\frac{\sqrt{\pi } f^a e^{\frac{b^2 \log ^2(f)}{-4 c \log (f)+4 i f}-i d} \text{erf}\left(\frac{b \log (f)-2 x (-c \log (f)+i f)}{2 \sqrt{-c \log (f)+i f}}\right)}{4 \sqrt{-c \log (f)+i f}}",1,"-1/4*((-1)^(3/4)*E^((b^2*Log[f]^2)/((4*I)*f - 4*c*Log[f]))*f^a*Sqrt[Pi]*(Erfi[((-1)^(3/4)*(2*f*x + I*(b + 2*c*x)*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*(f - I*c*Log[f])*Sqrt[f + I*c*Log[f]]*((-I)*Cos[d] - Sin[d]) + E^(((I/2)*b^2*f*Log[f]^2)/(f^2 + c^2*Log[f]^2))*Erfi[((-1)^(1/4)*(2*f*x - I*(b + 2*c*x)*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Sqrt[f - I*c*Log[f]]*(f + I*c*Log[f])*(Cos[d] + I*Sin[d])))/(f^2 + c^2*Log[f]^2)","A",1
129,1,301,245,3.096579,"\int f^{a+b x+c x^2} \cos ^2\left(d+f x^2\right) \, dx","Integrate[f^(a + b*x + c*x^2)*Cos[d + f*x^2]^2,x]","\frac{1}{8} \sqrt{\pi } f^a \left(\frac{2 f^{-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{\sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt[4]{-1} e^{\frac{b^2 \log ^2(f)}{-4 c \log (f)+8 i f}} \left(\sqrt{2 f-i c \log (f)} (2 f+i c \log (f)) (\sin (2 d)-i \cos (2 d)) e^{\frac{i b^2 f \log ^2(f)}{c^2 \log ^2(f)+4 f^2}} \text{erfi}\left(\frac{\sqrt[4]{-1} (4 f x-i \log (f) (b+2 c x))}{2 \sqrt{2 f-i c \log (f)}}\right)-(2 f-i c \log (f)) \sqrt{2 f+i c \log (f)} (\cos (2 d)-i \sin (2 d)) \text{erfi}\left(\frac{(-1)^{3/4} (4 f x+i \log (f) (b+2 c x))}{2 \sqrt{2 f+i c \log (f)}}\right)\right)}{c^2 \log ^2(f)+4 f^2}\right)","-\frac{\sqrt{\pi } f^a e^{\frac{b^2 \log ^2(f)}{-4 c \log (f)+8 i f}-2 i d} \text{erf}\left(\frac{b \log (f)-2 x (-c \log (f)+2 i f)}{2 \sqrt{-c \log (f)+2 i f}}\right)}{8 \sqrt{-c \log (f)+2 i f}}+\frac{\sqrt{\pi } f^a e^{2 i d-\frac{b^2 \log ^2(f)}{4 c \log (f)+8 i f}} \text{erfi}\left(\frac{b \log (f)+2 x (c \log (f)+2 i f)}{2 \sqrt{c \log (f)+2 i f}}\right)}{8 \sqrt{c \log (f)+2 i f}}+\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}",1,"(f^a*Sqrt[Pi]*((2*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])])/(Sqrt[c]*f^(b^2/(4*c))*Sqrt[Log[f]]) + ((-1)^(1/4)*E^((b^2*Log[f]^2)/((8*I)*f - 4*c*Log[f]))*(-(Erfi[((-1)^(3/4)*(4*f*x + I*(b + 2*c*x)*Log[f]))/(2*Sqrt[2*f + I*c*Log[f]])]*(2*f - I*c*Log[f])*Sqrt[2*f + I*c*Log[f]]*(Cos[2*d] - I*Sin[2*d])) + E^((I*b^2*f*Log[f]^2)/(4*f^2 + c^2*Log[f]^2))*Erfi[((-1)^(1/4)*(4*f*x - I*(b + 2*c*x)*Log[f]))/(2*Sqrt[2*f - I*c*Log[f]])]*Sqrt[2*f - I*c*Log[f]]*(2*f + I*c*Log[f])*((-I)*Cos[2*d] + Sin[2*d])))/(4*f^2 + c^2*Log[f]^2)))/8","A",0
130,1,3285,378,7.0018238,"\int f^{a+b x+c x^2} \cos ^3\left(d+f x^2\right) \, dx","Integrate[f^(a + b*x + c*x^2)*Cos[d + f*x^2]^3,x]","\text{Result too large to show}","-\frac{3 \sqrt{\pi } f^a e^{\frac{b^2 \log ^2(f)}{-4 c \log (f)+4 i f}-i d} \text{erf}\left(\frac{b \log (f)-2 x (-c \log (f)+i f)}{2 \sqrt{-c \log (f)+i f}}\right)}{16 \sqrt{-c \log (f)+i f}}-\frac{\sqrt{\pi } f^a e^{\frac{b^2 \log ^2(f)}{-4 c \log (f)+12 i f}-3 i d} \text{erf}\left(\frac{b \log (f)-2 x (-c \log (f)+3 i f)}{2 \sqrt{-c \log (f)+3 i f}}\right)}{16 \sqrt{-c \log (f)+3 i f}}+\frac{\sqrt{\pi } f^a \exp \left(3 i d-\frac{b^2 \log ^2(f)}{4 (c \log (f)+3 i f)}\right) \text{erfi}\left(\frac{b \log (f)+2 x (c \log (f)+3 i f)}{2 \sqrt{c \log (f)+3 i f}}\right)}{16 \sqrt{c \log (f)+3 i f}}+\frac{3 \sqrt{\pi } f^a e^{i d-\frac{b^2 \log ^2(f)}{4 c \log (f)+4 i f}} \text{erfi}\left(\frac{b \log (f)+2 x (c \log (f)+i f)}{2 \sqrt{c \log (f)+i f}}\right)}{16 \sqrt{c \log (f)+i f}}",1,"(f^a*Sqrt[Pi]*(-27*(-1)^(3/4)*E^(((I/4)*b^2*Log[f]^2)/(f - I*c*Log[f]))*f^3*Cos[d]*Erfi[((-1)^(1/4)*(2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Sqrt[f - I*c*Log[f]] + 27*(-1)^(1/4)*c*E^(((I/4)*b^2*Log[f]^2)/(f - I*c*Log[f]))*f^2*Cos[d]*Erfi[((-1)^(1/4)*(2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]*Sqrt[f - I*c*Log[f]] - 3*(-1)^(3/4)*c^2*E^(((I/4)*b^2*Log[f]^2)/(f - I*c*Log[f]))*f*Cos[d]*Erfi[((-1)^(1/4)*(2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]^2*Sqrt[f - I*c*Log[f]] + 3*(-1)^(1/4)*c^3*E^(((I/4)*b^2*Log[f]^2)/(f - I*c*Log[f]))*Cos[d]*Erfi[((-1)^(1/4)*(2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]^3*Sqrt[f - I*c*Log[f]] - 3*(-1)^(3/4)*E^(((I/4)*b^2*Log[f]^2)/(3*f - I*c*Log[f]))*f^3*Cos[3*d]*Erfi[((-1)^(1/4)*(6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Sqrt[3*f - I*c*Log[f]] + (-1)^(1/4)*c*E^(((I/4)*b^2*Log[f]^2)/(3*f - I*c*Log[f]))*f^2*Cos[3*d]*Erfi[((-1)^(1/4)*(6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]*Sqrt[3*f - I*c*Log[f]] - 3*(-1)^(3/4)*c^2*E^(((I/4)*b^2*Log[f]^2)/(3*f - I*c*Log[f]))*f*Cos[3*d]*Erfi[((-1)^(1/4)*(6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]^2*Sqrt[3*f - I*c*Log[f]] + (-1)^(1/4)*c^3*E^(((I/4)*b^2*Log[f]^2)/(3*f - I*c*Log[f]))*Cos[3*d]*Erfi[((-1)^(1/4)*(6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]^3*Sqrt[3*f - I*c*Log[f]] - (27*(-1)^(1/4)*f^3*Cos[d]*Erfi[((-1)^(3/4)*(2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Sqrt[f + I*c*Log[f]])/E^(((I/4)*b^2*Log[f]^2)/(f + I*c*Log[f])) + (27*(-1)^(3/4)*c*f^2*Cos[d]*Erfi[((-1)^(3/4)*(2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]*Sqrt[f + I*c*Log[f]])/E^(((I/4)*b^2*Log[f]^2)/(f + I*c*Log[f])) - (3*(-1)^(1/4)*c^2*f*Cos[d]*Erfi[((-1)^(3/4)*(2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]^2*Sqrt[f + I*c*Log[f]])/E^(((I/4)*b^2*Log[f]^2)/(f + I*c*Log[f])) + (3*(-1)^(3/4)*c^3*Cos[d]*Erfi[((-1)^(3/4)*(2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]^3*Sqrt[f + I*c*Log[f]])/E^(((I/4)*b^2*Log[f]^2)/(f + I*c*Log[f])) - (3*(-1)^(1/4)*f^3*Cos[3*d]*Erfi[((-1)^(3/4)*(6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Sqrt[3*f + I*c*Log[f]])/E^(((I/4)*b^2*Log[f]^2)/(3*f + I*c*Log[f])) + ((-1)^(3/4)*c*f^2*Cos[3*d]*Erfi[((-1)^(3/4)*(6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]*Sqrt[3*f + I*c*Log[f]])/E^(((I/4)*b^2*Log[f]^2)/(3*f + I*c*Log[f])) - (3*(-1)^(1/4)*c^2*f*Cos[3*d]*Erfi[((-1)^(3/4)*(6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]^2*Sqrt[3*f + I*c*Log[f]])/E^(((I/4)*b^2*Log[f]^2)/(3*f + I*c*Log[f])) + ((-1)^(3/4)*c^3*Cos[3*d]*Erfi[((-1)^(3/4)*(6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]^3*Sqrt[3*f + I*c*Log[f]])/E^(((I/4)*b^2*Log[f]^2)/(3*f + I*c*Log[f])) + 27*(-1)^(1/4)*E^(((I/4)*b^2*Log[f]^2)/(f - I*c*Log[f]))*f^3*Erfi[((-1)^(1/4)*(2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Sqrt[f - I*c*Log[f]]*Sin[d] + 27*(-1)^(3/4)*c*E^(((I/4)*b^2*Log[f]^2)/(f - I*c*Log[f]))*f^2*Erfi[((-1)^(1/4)*(2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]*Sqrt[f - I*c*Log[f]]*Sin[d] + 3*(-1)^(1/4)*c^2*E^(((I/4)*b^2*Log[f]^2)/(f - I*c*Log[f]))*f*Erfi[((-1)^(1/4)*(2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]^2*Sqrt[f - I*c*Log[f]]*Sin[d] + 3*(-1)^(3/4)*c^3*E^(((I/4)*b^2*Log[f]^2)/(f - I*c*Log[f]))*Erfi[((-1)^(1/4)*(2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]^3*Sqrt[f - I*c*Log[f]]*Sin[d] + (27*(-1)^(3/4)*f^3*Erfi[((-1)^(3/4)*(2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Sqrt[f + I*c*Log[f]]*Sin[d])/E^(((I/4)*b^2*Log[f]^2)/(f + I*c*Log[f])) + (27*(-1)^(1/4)*c*f^2*Erfi[((-1)^(3/4)*(2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]*Sqrt[f + I*c*Log[f]]*Sin[d])/E^(((I/4)*b^2*Log[f]^2)/(f + I*c*Log[f])) + (3*(-1)^(3/4)*c^2*f*Erfi[((-1)^(3/4)*(2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]^2*Sqrt[f + I*c*Log[f]]*Sin[d])/E^(((I/4)*b^2*Log[f]^2)/(f + I*c*Log[f])) + (3*(-1)^(1/4)*c^3*Erfi[((-1)^(3/4)*(2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]^3*Sqrt[f + I*c*Log[f]]*Sin[d])/E^(((I/4)*b^2*Log[f]^2)/(f + I*c*Log[f])) + 3*(-1)^(1/4)*E^(((I/4)*b^2*Log[f]^2)/(3*f - I*c*Log[f]))*f^3*Erfi[((-1)^(1/4)*(6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Sqrt[3*f - I*c*Log[f]]*Sin[3*d] + (-1)^(3/4)*c*E^(((I/4)*b^2*Log[f]^2)/(3*f - I*c*Log[f]))*f^2*Erfi[((-1)^(1/4)*(6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]*Sqrt[3*f - I*c*Log[f]]*Sin[3*d] + 3*(-1)^(1/4)*c^2*E^(((I/4)*b^2*Log[f]^2)/(3*f - I*c*Log[f]))*f*Erfi[((-1)^(1/4)*(6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]^2*Sqrt[3*f - I*c*Log[f]]*Sin[3*d] + (-1)^(3/4)*c^3*E^(((I/4)*b^2*Log[f]^2)/(3*f - I*c*Log[f]))*Erfi[((-1)^(1/4)*(6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]^3*Sqrt[3*f - I*c*Log[f]]*Sin[3*d] + (3*(-1)^(3/4)*f^3*Erfi[((-1)^(3/4)*(6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Sqrt[3*f + I*c*Log[f]]*Sin[3*d])/E^(((I/4)*b^2*Log[f]^2)/(3*f + I*c*Log[f])) + ((-1)^(1/4)*c*f^2*Erfi[((-1)^(3/4)*(6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]*Sqrt[3*f + I*c*Log[f]]*Sin[3*d])/E^(((I/4)*b^2*Log[f]^2)/(3*f + I*c*Log[f])) + (3*(-1)^(3/4)*c^2*f*Erfi[((-1)^(3/4)*(6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]^2*Sqrt[3*f + I*c*Log[f]]*Sin[3*d])/E^(((I/4)*b^2*Log[f]^2)/(3*f + I*c*Log[f])) + ((-1)^(1/4)*c^3*Erfi[((-1)^(3/4)*(6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]^3*Sqrt[3*f + I*c*Log[f]]*Sin[3*d])/E^(((I/4)*b^2*Log[f]^2)/(3*f + I*c*Log[f]))))/(16*(f - I*c*Log[f])*(3*f - I*c*Log[f])*(f + I*c*Log[f])*(3*f + I*c*Log[f]))","B",1
131,1,348,208,2.10031,"\int f^{a+b x+c x^2} \cos \left(d+e x+f x^2\right) \, dx","Integrate[f^(a + b*x + c*x^2)*Cos[d + e*x + f*x^2],x]","\frac{\sqrt[4]{-1} \sqrt{\pi } f^{\frac{f (a f-b e)+a c^2 \log ^2(f)}{c^2 \log ^2(f)+f^2}} \exp \left(-\frac{1}{4} i \left(\frac{b^2 \log ^2(f)}{f+i c \log (f)}+\frac{e^2}{f-i c \log (f)}\right)\right) \left(\sqrt{f-i c \log (f)} (f+i c \log (f)) (\sin (d)-i \cos (d)) e^{\frac{i b^2 f \log ^2(f)}{2 \left(c^2 \log ^2(f)+f^2\right)}} f^{\frac{b e}{2 f+2 i c \log (f)}} \text{erfi}\left(\frac{\sqrt[4]{-1} (-i \log (f) (b+2 c x)+e+2 f x)}{2 \sqrt{f-i c \log (f)}}\right)-(f-i c \log (f)) \sqrt{f+i c \log (f)} (\cos (d)-i \sin (d)) e^{\frac{i e^2 f}{2 \left(c^2 \log ^2(f)+f^2\right)}} f^{\frac{b e}{2 f-2 i c \log (f)}} \text{erfi}\left(\frac{(-1)^{3/4} (i \log (f) (b+2 c x)+e+2 f x)}{2 \sqrt{f+i c \log (f)}}\right)\right)}{4 \left(c^2 \log ^2(f)+f^2\right)}","\frac{\sqrt{\pi } f^a \exp \left(-\frac{(e+i b \log (f))^2}{-4 c \log (f)+4 i f}-i d\right) \text{erf}\left(\frac{-b \log (f)+2 x (-c \log (f)+i f)+i e}{2 \sqrt{-c \log (f)+i f}}\right)}{4 \sqrt{-c \log (f)+i f}}+\frac{\sqrt{\pi } f^a \exp \left(\frac{(e-i b \log (f))^2}{4 c \log (f)+4 i f}+i d\right) \text{erfi}\left(\frac{b \log (f)+2 x (c \log (f)+i f)+i e}{2 \sqrt{c \log (f)+i f}}\right)}{4 \sqrt{c \log (f)+i f}}",1,"((-1)^(1/4)*f^((f*(-(b*e) + a*f) + a*c^2*Log[f]^2)/(f^2 + c^2*Log[f]^2))*Sqrt[Pi]*(-(E^(((I/2)*e^2*f)/(f^2 + c^2*Log[f]^2))*f^((b*e)/(2*f - (2*I)*c*Log[f]))*Erfi[((-1)^(3/4)*(e + 2*f*x + I*(b + 2*c*x)*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*(f - I*c*Log[f])*Sqrt[f + I*c*Log[f]]*(Cos[d] - I*Sin[d])) + E^(((I/2)*b^2*f*Log[f]^2)/(f^2 + c^2*Log[f]^2))*f^((b*e)/(2*f + (2*I)*c*Log[f]))*Erfi[((-1)^(1/4)*(e + 2*f*x - I*(b + 2*c*x)*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Sqrt[f - I*c*Log[f]]*(f + I*c*Log[f])*((-I)*Cos[d] + Sin[d])))/(4*E^((I/4)*(e^2/(f - I*c*Log[f]) + (b^2*Log[f]^2)/(f + I*c*Log[f])))*(f^2 + c^2*Log[f]^2))","A",0
132,1,1118,268,6.7392553,"\int f^{a+b x+c x^2} \cos ^2\left(d+e x+f x^2\right) \, dx","Integrate[f^(a + b*x + c*x^2)*Cos[d + e*x + f*x^2]^2,x]","\frac{f^a \sqrt{\pi } \left(8 \sqrt{c} \text{erfi}\left(\frac{(b+2 c x) \sqrt{\log (f)}}{2 \sqrt{c}}\right) \sqrt{\log (f)} f^{2-\frac{b^2}{4 c}}+2 c^{5/2} \text{erfi}\left(\frac{(b+2 c x) \sqrt{\log (f)}}{2 \sqrt{c}}\right) \log ^{\frac{5}{2}}(f) f^{-\frac{b^2}{4 c}}+2 \sqrt[4]{-1} c e^{\frac{i \left(-4 e^2+4 i b \log (f) e+b^2 \log ^2(f)\right)}{4 (2 f-i c \log (f))}} \text{erfi}\left(\frac{\sqrt[4]{-1} (2 e+4 f x-i b \log (f)-2 i c x \log (f))}{2 \sqrt{2 f-i c \log (f)}}\right) \log (f) \sqrt{2 f-i c \log (f)} \sin (2 d) f+2 (-1)^{3/4} c e^{-\frac{i \left(-4 e^2-4 i b \log (f) e+b^2 \log ^2(f)\right)}{4 (2 f+i c \log (f))}} \text{erfi}\left(\frac{(-1)^{3/4} (2 e+4 f x+i b \log (f)+2 i c x \log (f))}{2 \sqrt{2 f+i c \log (f)}}\right) \log (f) \sqrt{2 f+i c \log (f)} \sin (2 d) f-2 (-1)^{3/4} c e^{\frac{i \left(-4 e^2+4 i b \log (f) e+b^2 \log ^2(f)\right)}{4 (2 f-i c \log (f))}} \cos (2 d) \text{erfi}\left(\frac{\sqrt[4]{-1} (2 e+4 f x-i b \log (f)-2 i c x \log (f))}{2 \sqrt{2 f-i c \log (f)}}\right) \log (f) \sqrt{2 f-i c \log (f)} f-2 \sqrt[4]{-1} c e^{-\frac{i \left(-4 e^2-4 i b \log (f) e+b^2 \log ^2(f)\right)}{4 (2 f+i c \log (f))}} \cos (2 d) \text{erfi}\left(\frac{(-1)^{3/4} (2 e+4 f x+i b \log (f)+2 i c x \log (f))}{2 \sqrt{2 f+i c \log (f)}}\right) \log (f) \sqrt{2 f+i c \log (f)} f+(-1)^{3/4} c^2 e^{\frac{i \left(-4 e^2+4 i b \log (f) e+b^2 \log ^2(f)\right)}{4 (2 f-i c \log (f))}} \text{erfi}\left(\frac{\sqrt[4]{-1} (2 e+4 f x-i b \log (f)-2 i c x \log (f))}{2 \sqrt{2 f-i c \log (f)}}\right) \log ^2(f) \sqrt{2 f-i c \log (f)} \sin (2 d)+\sqrt[4]{-1} c^2 e^{-\frac{i \left(-4 e^2-4 i b \log (f) e+b^2 \log ^2(f)\right)}{4 (2 f+i c \log (f))}} \text{erfi}\left(\frac{(-1)^{3/4} (2 e+4 f x+i b \log (f)+2 i c x \log (f))}{2 \sqrt{2 f+i c \log (f)}}\right) \log ^2(f) \sqrt{2 f+i c \log (f)} \sin (2 d)+\sqrt[4]{-1} c^2 e^{\frac{i \left(-4 e^2+4 i b \log (f) e+b^2 \log ^2(f)\right)}{4 (2 f-i c \log (f))}} \cos (2 d) \text{erfi}\left(\frac{\sqrt[4]{-1} (2 e+4 f x-i b \log (f)-2 i c x \log (f))}{2 \sqrt{2 f-i c \log (f)}}\right) \log ^2(f) \sqrt{2 f-i c \log (f)}+(-1)^{3/4} c^2 e^{-\frac{i \left(-4 e^2-4 i b \log (f) e+b^2 \log ^2(f)\right)}{4 (2 f+i c \log (f))}} \cos (2 d) \text{erfi}\left(\frac{(-1)^{3/4} (2 e+4 f x+i b \log (f)+2 i c x \log (f))}{2 \sqrt{2 f+i c \log (f)}}\right) \log ^2(f) \sqrt{2 f+i c \log (f)}\right)}{8 c \log (f) (2 f-i c \log (f)) (2 f+i c \log (f))}","\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a \exp \left(-\frac{(2 e+i b \log (f))^2}{-4 c \log (f)+8 i f}-2 i d\right) \text{erf}\left(\frac{-b \log (f)+2 x (-c \log (f)+2 i f)+2 i e}{2 \sqrt{-c \log (f)+2 i f}}\right)}{8 \sqrt{-c \log (f)+2 i f}}+\frac{\sqrt{\pi } f^a \exp \left(\frac{(2 e-i b \log (f))^2}{4 c \log (f)+8 i f}+2 i d\right) \text{erfi}\left(\frac{b \log (f)+2 x (c \log (f)+2 i f)+2 i e}{2 \sqrt{c \log (f)+2 i f}}\right)}{8 \sqrt{c \log (f)+2 i f}}",1,"(f^a*Sqrt[Pi]*(8*Sqrt[c]*f^(2 - b^2/(4*c))*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])]*Sqrt[Log[f]] + (2*c^(5/2)*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])]*Log[f]^(5/2))/f^(b^2/(4*c)) - 2*(-1)^(3/4)*c*E^(((I/4)*(-4*e^2 + (4*I)*b*e*Log[f] + b^2*Log[f]^2))/(2*f - I*c*Log[f]))*f*Cos[2*d]*Erfi[((-1)^(1/4)*(2*e + 4*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[2*f - I*c*Log[f]])]*Log[f]*Sqrt[2*f - I*c*Log[f]] + (-1)^(1/4)*c^2*E^(((I/4)*(-4*e^2 + (4*I)*b*e*Log[f] + b^2*Log[f]^2))/(2*f - I*c*Log[f]))*Cos[2*d]*Erfi[((-1)^(1/4)*(2*e + 4*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[2*f - I*c*Log[f]])]*Log[f]^2*Sqrt[2*f - I*c*Log[f]] - (2*(-1)^(1/4)*c*f*Cos[2*d]*Erfi[((-1)^(3/4)*(2*e + 4*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[2*f + I*c*Log[f]])]*Log[f]*Sqrt[2*f + I*c*Log[f]])/E^(((I/4)*(-4*e^2 - (4*I)*b*e*Log[f] + b^2*Log[f]^2))/(2*f + I*c*Log[f])) + ((-1)^(3/4)*c^2*Cos[2*d]*Erfi[((-1)^(3/4)*(2*e + 4*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[2*f + I*c*Log[f]])]*Log[f]^2*Sqrt[2*f + I*c*Log[f]])/E^(((I/4)*(-4*e^2 - (4*I)*b*e*Log[f] + b^2*Log[f]^2))/(2*f + I*c*Log[f])) + 2*(-1)^(1/4)*c*E^(((I/4)*(-4*e^2 + (4*I)*b*e*Log[f] + b^2*Log[f]^2))/(2*f - I*c*Log[f]))*f*Erfi[((-1)^(1/4)*(2*e + 4*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[2*f - I*c*Log[f]])]*Log[f]*Sqrt[2*f - I*c*Log[f]]*Sin[2*d] + (-1)^(3/4)*c^2*E^(((I/4)*(-4*e^2 + (4*I)*b*e*Log[f] + b^2*Log[f]^2))/(2*f - I*c*Log[f]))*Erfi[((-1)^(1/4)*(2*e + 4*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[2*f - I*c*Log[f]])]*Log[f]^2*Sqrt[2*f - I*c*Log[f]]*Sin[2*d] + (2*(-1)^(3/4)*c*f*Erfi[((-1)^(3/4)*(2*e + 4*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[2*f + I*c*Log[f]])]*Log[f]*Sqrt[2*f + I*c*Log[f]]*Sin[2*d])/E^(((I/4)*(-4*e^2 - (4*I)*b*e*Log[f] + b^2*Log[f]^2))/(2*f + I*c*Log[f])) + ((-1)^(1/4)*c^2*Erfi[((-1)^(3/4)*(2*e + 4*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[2*f + I*c*Log[f]])]*Log[f]^2*Sqrt[2*f + I*c*Log[f]]*Sin[2*d])/E^(((I/4)*(-4*e^2 - (4*I)*b*e*Log[f] + b^2*Log[f]^2))/(2*f + I*c*Log[f]))))/(8*c*Log[f]*(2*f - I*c*Log[f])*(2*f + I*c*Log[f]))","B",0
133,1,3829,422,7.2842886,"\int f^{a+b x+c x^2} \cos ^3\left(d+e x+f x^2\right) \, dx","Integrate[f^(a + b*x + c*x^2)*Cos[d + e*x + f*x^2]^3,x]","\text{Result too large to show}","\frac{3 \sqrt{\pi } f^a \exp \left(-\frac{(e+i b \log (f))^2}{-4 c \log (f)+4 i f}-i d\right) \text{erf}\left(\frac{-b \log (f)+2 x (-c \log (f)+i f)+i e}{2 \sqrt{-c \log (f)+i f}}\right)}{16 \sqrt{-c \log (f)+i f}}+\frac{\sqrt{\pi } f^a \exp \left(-\frac{(3 e+i b \log (f))^2}{4 (-c \log (f)+3 i f)}-3 i d\right) \text{erf}\left(\frac{-b \log (f)+2 x (-c \log (f)+3 i f)+3 i e}{2 \sqrt{-c \log (f)+3 i f}}\right)}{16 \sqrt{-c \log (f)+3 i f}}+\frac{3 \sqrt{\pi } f^a \exp \left(\frac{(e-i b \log (f))^2}{4 c \log (f)+4 i f}+i d\right) \text{erfi}\left(\frac{b \log (f)+2 x (c \log (f)+i f)+i e}{2 \sqrt{c \log (f)+i f}}\right)}{16 \sqrt{c \log (f)+i f}}+\frac{\sqrt{\pi } f^a \exp \left(3 i d-\frac{(b \log (f)+3 i e)^2}{4 (c \log (f)+3 i f)}\right) \text{erfi}\left(\frac{b \log (f)+2 x (c \log (f)+3 i f)+3 i e}{2 \sqrt{c \log (f)+3 i f}}\right)}{16 \sqrt{c \log (f)+3 i f}}",1,"(f^a*Sqrt[Pi]*(-27*(-1)^(3/4)*E^(((I/4)*(-e^2 + (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f - I*c*Log[f]))*f^3*Cos[d]*Erfi[((-1)^(1/4)*(e + 2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Sqrt[f - I*c*Log[f]] + 27*(-1)^(1/4)*c*E^(((I/4)*(-e^2 + (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f - I*c*Log[f]))*f^2*Cos[d]*Erfi[((-1)^(1/4)*(e + 2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]*Sqrt[f - I*c*Log[f]] - 3*(-1)^(3/4)*c^2*E^(((I/4)*(-e^2 + (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f - I*c*Log[f]))*f*Cos[d]*Erfi[((-1)^(1/4)*(e + 2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]^2*Sqrt[f - I*c*Log[f]] + 3*(-1)^(1/4)*c^3*E^(((I/4)*(-e^2 + (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f - I*c*Log[f]))*Cos[d]*Erfi[((-1)^(1/4)*(e + 2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]^3*Sqrt[f - I*c*Log[f]] - 3*(-1)^(3/4)*E^(((I/4)*(-9*e^2 + (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f - I*c*Log[f]))*f^3*Cos[3*d]*Erfi[((-1)^(1/4)*(3*e + 6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Sqrt[3*f - I*c*Log[f]] + (-1)^(1/4)*c*E^(((I/4)*(-9*e^2 + (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f - I*c*Log[f]))*f^2*Cos[3*d]*Erfi[((-1)^(1/4)*(3*e + 6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]*Sqrt[3*f - I*c*Log[f]] - 3*(-1)^(3/4)*c^2*E^(((I/4)*(-9*e^2 + (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f - I*c*Log[f]))*f*Cos[3*d]*Erfi[((-1)^(1/4)*(3*e + 6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]^2*Sqrt[3*f - I*c*Log[f]] + (-1)^(1/4)*c^3*E^(((I/4)*(-9*e^2 + (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f - I*c*Log[f]))*Cos[3*d]*Erfi[((-1)^(1/4)*(3*e + 6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]^3*Sqrt[3*f - I*c*Log[f]] - (27*(-1)^(1/4)*f^3*Cos[d]*Erfi[((-1)^(3/4)*(e + 2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Sqrt[f + I*c*Log[f]])/E^(((I/4)*(-e^2 - (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f + I*c*Log[f])) + (27*(-1)^(3/4)*c*f^2*Cos[d]*Erfi[((-1)^(3/4)*(e + 2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]*Sqrt[f + I*c*Log[f]])/E^(((I/4)*(-e^2 - (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f + I*c*Log[f])) - (3*(-1)^(1/4)*c^2*f*Cos[d]*Erfi[((-1)^(3/4)*(e + 2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]^2*Sqrt[f + I*c*Log[f]])/E^(((I/4)*(-e^2 - (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f + I*c*Log[f])) + (3*(-1)^(3/4)*c^3*Cos[d]*Erfi[((-1)^(3/4)*(e + 2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]^3*Sqrt[f + I*c*Log[f]])/E^(((I/4)*(-e^2 - (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f + I*c*Log[f])) - (3*(-1)^(1/4)*f^3*Cos[3*d]*Erfi[((-1)^(3/4)*(3*e + 6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Sqrt[3*f + I*c*Log[f]])/E^(((I/4)*(-9*e^2 - (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f + I*c*Log[f])) + ((-1)^(3/4)*c*f^2*Cos[3*d]*Erfi[((-1)^(3/4)*(3*e + 6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]*Sqrt[3*f + I*c*Log[f]])/E^(((I/4)*(-9*e^2 - (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f + I*c*Log[f])) - (3*(-1)^(1/4)*c^2*f*Cos[3*d]*Erfi[((-1)^(3/4)*(3*e + 6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]^2*Sqrt[3*f + I*c*Log[f]])/E^(((I/4)*(-9*e^2 - (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f + I*c*Log[f])) + ((-1)^(3/4)*c^3*Cos[3*d]*Erfi[((-1)^(3/4)*(3*e + 6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]^3*Sqrt[3*f + I*c*Log[f]])/E^(((I/4)*(-9*e^2 - (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f + I*c*Log[f])) + 27*(-1)^(1/4)*E^(((I/4)*(-e^2 + (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f - I*c*Log[f]))*f^3*Erfi[((-1)^(1/4)*(e + 2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Sqrt[f - I*c*Log[f]]*Sin[d] + 27*(-1)^(3/4)*c*E^(((I/4)*(-e^2 + (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f - I*c*Log[f]))*f^2*Erfi[((-1)^(1/4)*(e + 2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]*Sqrt[f - I*c*Log[f]]*Sin[d] + 3*(-1)^(1/4)*c^2*E^(((I/4)*(-e^2 + (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f - I*c*Log[f]))*f*Erfi[((-1)^(1/4)*(e + 2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]^2*Sqrt[f - I*c*Log[f]]*Sin[d] + 3*(-1)^(3/4)*c^3*E^(((I/4)*(-e^2 + (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f - I*c*Log[f]))*Erfi[((-1)^(1/4)*(e + 2*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[f - I*c*Log[f]])]*Log[f]^3*Sqrt[f - I*c*Log[f]]*Sin[d] + (27*(-1)^(3/4)*f^3*Erfi[((-1)^(3/4)*(e + 2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Sqrt[f + I*c*Log[f]]*Sin[d])/E^(((I/4)*(-e^2 - (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f + I*c*Log[f])) + (27*(-1)^(1/4)*c*f^2*Erfi[((-1)^(3/4)*(e + 2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]*Sqrt[f + I*c*Log[f]]*Sin[d])/E^(((I/4)*(-e^2 - (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f + I*c*Log[f])) + (3*(-1)^(3/4)*c^2*f*Erfi[((-1)^(3/4)*(e + 2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]^2*Sqrt[f + I*c*Log[f]]*Sin[d])/E^(((I/4)*(-e^2 - (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f + I*c*Log[f])) + (3*(-1)^(1/4)*c^3*Erfi[((-1)^(3/4)*(e + 2*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[f + I*c*Log[f]])]*Log[f]^3*Sqrt[f + I*c*Log[f]]*Sin[d])/E^(((I/4)*(-e^2 - (2*I)*b*e*Log[f] + b^2*Log[f]^2))/(f + I*c*Log[f])) + 3*(-1)^(1/4)*E^(((I/4)*(-9*e^2 + (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f - I*c*Log[f]))*f^3*Erfi[((-1)^(1/4)*(3*e + 6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Sqrt[3*f - I*c*Log[f]]*Sin[3*d] + (-1)^(3/4)*c*E^(((I/4)*(-9*e^2 + (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f - I*c*Log[f]))*f^2*Erfi[((-1)^(1/4)*(3*e + 6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]*Sqrt[3*f - I*c*Log[f]]*Sin[3*d] + 3*(-1)^(1/4)*c^2*E^(((I/4)*(-9*e^2 + (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f - I*c*Log[f]))*f*Erfi[((-1)^(1/4)*(3*e + 6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]^2*Sqrt[3*f - I*c*Log[f]]*Sin[3*d] + (-1)^(3/4)*c^3*E^(((I/4)*(-9*e^2 + (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f - I*c*Log[f]))*Erfi[((-1)^(1/4)*(3*e + 6*f*x - I*b*Log[f] - (2*I)*c*x*Log[f]))/(2*Sqrt[3*f - I*c*Log[f]])]*Log[f]^3*Sqrt[3*f - I*c*Log[f]]*Sin[3*d] + (3*(-1)^(3/4)*f^3*Erfi[((-1)^(3/4)*(3*e + 6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Sqrt[3*f + I*c*Log[f]]*Sin[3*d])/E^(((I/4)*(-9*e^2 - (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f + I*c*Log[f])) + ((-1)^(1/4)*c*f^2*Erfi[((-1)^(3/4)*(3*e + 6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]*Sqrt[3*f + I*c*Log[f]]*Sin[3*d])/E^(((I/4)*(-9*e^2 - (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f + I*c*Log[f])) + (3*(-1)^(3/4)*c^2*f*Erfi[((-1)^(3/4)*(3*e + 6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]^2*Sqrt[3*f + I*c*Log[f]]*Sin[3*d])/E^(((I/4)*(-9*e^2 - (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f + I*c*Log[f])) + ((-1)^(1/4)*c^3*Erfi[((-1)^(3/4)*(3*e + 6*f*x + I*b*Log[f] + (2*I)*c*x*Log[f]))/(2*Sqrt[3*f + I*c*Log[f]])]*Log[f]^3*Sqrt[3*f + I*c*Log[f]]*Sin[3*d])/E^(((I/4)*(-9*e^2 - (6*I)*b*e*Log[f] + b^2*Log[f]^2))/(3*f + I*c*Log[f]))))/(16*(f - I*c*Log[f])*(3*f - I*c*Log[f])*(f + I*c*Log[f])*(3*f + I*c*Log[f]))","B",0
134,1,325,209,1.8133777,"\int f^{a+b x+c x^2} \cos \left(a+b x+e x^2\right) \, dx","Integrate[f^(a + b*x + c*x^2)*Cos[a + b*x + e*x^2],x]","-\frac{i \sqrt{\pi } e^{-\frac{b^2 c \log ^3(f)}{2 \left(c^2 \log ^2(f)+e^2\right)}} f^{a-\frac{b^2}{2 (e-i c \log (f))}} \left((\cos (a)+i \sin (a)) (e+i c \log (f)) \sqrt{c \log (f)+i e} \exp \left(\frac{1}{4} b^2 \left(\frac{\log ^2(f)}{c \log (f)-i e}+\frac{1}{c \log (f)+i e}\right)\right) \text{erfi}\left(\frac{\log (f) (b+2 c x)+i (b+2 e x)}{2 \sqrt{c \log (f)+i e}}\right)-(\cos (a)-i \sin (a)) (e-i c \log (f)) \sqrt{c \log (f)-i e} f^{\frac{i b^2 c \log (f)}{c^2 \log ^2(f)+e^2}} \exp \left(\frac{1}{4} b^2 \left(\frac{\log ^2(f)}{c \log (f)+i e}+\frac{1}{c \log (f)-i e}\right)\right) \text{erfi}\left(\frac{\log (f) (b+2 c x)-i (b+2 e x)}{2 \sqrt{c \log (f)-i e}}\right)\right)}{4 \left(c^2 \log ^2(f)+e^2\right)}","\frac{\sqrt{\pi } \exp \left(-\left((-\log (f)+i) \left(a-\frac{b^2 (-\log (f)+i)}{-4 c \log (f)+4 i e}\right)\right)\right) \text{erf}\left(\frac{b (-\log (f)+i)+2 x (-c \log (f)+i e)}{2 \sqrt{-c \log (f)+i e}}\right)}{4 \sqrt{-c \log (f)+i e}}+\frac{\sqrt{\pi } \exp \left((\log (f)+i) \left(a-\frac{b^2 (\log (f)+i)}{4 c \log (f)+4 i e}\right)\right) \text{erfi}\left(\frac{b (\log (f)+i)+2 x (c \log (f)+i e)}{2 \sqrt{c \log (f)+i e}}\right)}{4 \sqrt{c \log (f)+i e}}",1,"((-1/4*I)*f^(a - b^2/(2*(e - I*c*Log[f])))*Sqrt[Pi]*(-(E^((b^2*(((-I)*e + c*Log[f])^(-1) + Log[f]^2/(I*e + c*Log[f])))/4)*f^((I*b^2*c*Log[f])/(e^2 + c^2*Log[f]^2))*Erfi[((-I)*(b + 2*e*x) + (b + 2*c*x)*Log[f])/(2*Sqrt[(-I)*e + c*Log[f]])]*(e - I*c*Log[f])*Sqrt[(-I)*e + c*Log[f]]*(Cos[a] - I*Sin[a])) + E^((b^2*(Log[f]^2/((-I)*e + c*Log[f]) + (I*e + c*Log[f])^(-1)))/4)*Erfi[(I*(b + 2*e*x) + (b + 2*c*x)*Log[f])/(2*Sqrt[I*e + c*Log[f]])]*(e + I*c*Log[f])*Sqrt[I*e + c*Log[f]]*(Cos[a] + I*Sin[a])))/(E^((b^2*c*Log[f]^3)/(2*(e^2 + c^2*Log[f]^2)))*(e^2 + c^2*Log[f]^2))","A",0
135,1,180,245,1.6283526,"\int F^{c (a+b x)} (f+f \sin (d+e x))^2 \, dx","Integrate[F^(c*(a + b*x))*(f + f*Sin[d + e*x])^2,x]","\frac{f^2 (\sin (d+e x)+1)^2 F^{c (a+b x)} \left(\frac{4 b c \log (F) \sin (d+e x)}{b^2 c^2 \log ^2(F)+e^2}-\frac{2 e \sin (2 (d+e x))}{b^2 c^2 \log ^2(F)+4 e^2}-\frac{4 e \cos (d+e x)}{b^2 c^2 \log ^2(F)+e^2}-\frac{b c \log (F) \cos (2 (d+e x))}{b^2 c^2 \log ^2(F)+4 e^2}+\frac{3}{b c \log (F)}\right)}{2 \left(\sin \left(\frac{1}{2} (d+e x)\right)+\cos \left(\frac{1}{2} (d+e x)\right)\right)^4}","\frac{b c f^2 \log (F) \sin ^2(d+e x) F^{a c+b c x}}{b^2 c^2 \log ^2(F)+4 e^2}+\frac{2 b c f^2 \log (F) \sin (d+e x) F^{a c+b c x}}{b^2 c^2 \log ^2(F)+e^2}-\frac{2 e f^2 \cos (d+e x) F^{a c+b c x}}{b^2 c^2 \log ^2(F)+e^2}-\frac{2 e f^2 \sin (d+e x) \cos (d+e x) F^{a c+b c x}}{b^2 c^2 \log ^2(F)+4 e^2}+\frac{2 e^2 f^2 F^{a c+b c x}}{b c \log (F) \left(b^2 c^2 \log ^2(F)+4 e^2\right)}+\frac{f^2 F^{a c+b c x}}{b c \log (F)}",1,"(f^2*F^(c*(a + b*x))*(1 + Sin[d + e*x])^2*(3/(b*c*Log[F]) - (4*e*Cos[d + e*x])/(e^2 + b^2*c^2*Log[F]^2) - (b*c*Cos[2*(d + e*x)]*Log[F])/(4*e^2 + b^2*c^2*Log[F]^2) + (4*b*c*Log[F]*Sin[d + e*x])/(e^2 + b^2*c^2*Log[F]^2) - (2*e*Sin[2*(d + e*x)])/(4*e^2 + b^2*c^2*Log[F]^2)))/(2*(Cos[(d + e*x)/2] + Sin[(d + e*x)/2])^4)","A",1
136,1,83,99,0.5698139,"\int F^{c (a+b x)} (f+f \sin (d+e x)) \, dx","Integrate[F^(c*(a + b*x))*(f + f*Sin[d + e*x]),x]","\frac{f F^{c (a+b x)} \left(b^2 c^2 \log ^2(F) \sin (d+e x)+b^2 c^2 \log ^2(F)-b c e \log (F) \cos (d+e x)+e^2\right)}{b c \log (F) \left(b^2 c^2 \log ^2(F)+e^2\right)}","\frac{b c f \log (F) \sin (d+e x) F^{a c+b c x}}{b^2 c^2 \log ^2(F)+e^2}-\frac{e f \cos (d+e x) F^{a c+b c x}}{b^2 c^2 \log ^2(F)+e^2}+\frac{f F^{a c+b c x}}{b c \log (F)}",1,"(f*F^(c*(a + b*x))*(e^2 - b*c*e*Cos[d + e*x]*Log[F] + b^2*c^2*Log[F]^2 + b^2*c^2*Log[F]^2*Sin[d + e*x]))/(b*c*Log[F]*(e^2 + b^2*c^2*Log[F]^2))","A",1
137,1,128,80,1.6941817,"\int \frac{F^{c (a+b x)}}{f+f \sin (d+e x)} \, dx","Integrate[F^(c*(a + b*x))/(f + f*Sin[d + e*x]),x]","\frac{2 F^{c (a+b x)} \left(-i \, _2F_1\left(1,-\frac{i b c \log (F)}{e};1-\frac{i b c \log (F)}{e};i \cos (d+e x)-\sin (d+e x)\right)+\frac{\sin \left(\frac{e x}{2}\right)}{\left(\sin \left(\frac{d}{2}\right)+\cos \left(\frac{d}{2}\right)\right) \left(\sin \left(\frac{1}{2} (d+e x)\right)+\cos \left(\frac{1}{2} (d+e x)\right)\right)}-\frac{1}{\cos (d)+i (\sin (d)+1)}\right)}{e f}","-\frac{2 e^{i (d+e x)} F^{c (a+b x)} \, _2F_1\left(2,1-\frac{i b c \log (F)}{e};2-\frac{i b c \log (F)}{e};i e^{i (d+e x)}\right)}{f (e-i b c \log (F))}",1,"(2*F^(c*(a + b*x))*((-I)*Hypergeometric2F1[1, ((-I)*b*c*Log[F])/e, 1 - (I*b*c*Log[F])/e, I*Cos[d + e*x] - Sin[d + e*x]] - (Cos[d] + I*(1 + Sin[d]))^(-1) + Sin[(e*x)/2]/((Cos[d/2] + Sin[d/2])*(Cos[(d + e*x)/2] + Sin[(d + e*x)/2]))))/(e*f)","A",1
138,1,240,184,3.1980941,"\int \frac{F^{c (a+b x)}}{(f+f \sin (d+e x))^2} \, dx","Integrate[F^(c*(a + b*x))/(f + f*Sin[d + e*x])^2,x]","\frac{F^{c (a+b x)} \left(\sin \left(\frac{1}{2} (d+e x)\right)+\cos \left(\frac{1}{2} (d+e x)\right)\right) \left((-1+i) \left(b^2 c^2 \log ^2(F)+e^2\right) \left(\sin \left(\frac{1}{2} (d+e x)\right)+\cos \left(\frac{1}{2} (d+e x)\right)\right)^3 \left(1-(1-i) \, _2F_1\left(1,-\frac{i b c \log (F)}{e};1-\frac{i b c \log (F)}{e};i \cos (d+e x)-\sin (d+e x)\right)\right)+2 \sin \left(\frac{1}{2} (d+e x)\right) \left(b^2 c^2 \log ^2(F)+e^2\right) \left(\sin \left(\frac{1}{2} (d+e x)\right)+\cos \left(\frac{1}{2} (d+e x)\right)\right)^2-e (b c \log (F)+e) \left(\sin \left(\frac{1}{2} (d+e x)\right)+\cos \left(\frac{1}{2} (d+e x)\right)\right)+2 e^2 \sin \left(\frac{1}{2} (d+e x)\right)\right)}{3 e^3 f^2 (\sin (d+e x)+1)^2}","-\frac{2 e^{i (d+e x)} F^{c (a+b x)} (e+i b c \log (F)) \, _2F_1\left(2,1-\frac{i b c \log (F)}{e};2-\frac{i b c \log (F)}{e};i e^{i (d+e x)}\right)}{3 e^2 f^2}-\frac{b c \log (F) \csc ^2\left(\frac{d}{2}+\frac{e x}{2}+\frac{\pi }{4}\right) F^{c (a+b x)}}{6 e^2 f^2}-\frac{\cot \left(\frac{d}{2}+\frac{e x}{2}+\frac{\pi }{4}\right) \csc ^2\left(\frac{d}{2}+\frac{e x}{2}+\frac{\pi }{4}\right) F^{c (a+b x)}}{6 e f^2}",1,"(F^(c*(a + b*x))*(Cos[(d + e*x)/2] + Sin[(d + e*x)/2])*(2*e^2*Sin[(d + e*x)/2] - e*(e + b*c*Log[F])*(Cos[(d + e*x)/2] + Sin[(d + e*x)/2]) + 2*(e^2 + b^2*c^2*Log[F]^2)*Sin[(d + e*x)/2]*(Cos[(d + e*x)/2] + Sin[(d + e*x)/2])^2 - (1 - I)*(1 - (1 - I)*Hypergeometric2F1[1, ((-I)*b*c*Log[F])/e, 1 - (I*b*c*Log[F])/e, I*Cos[d + e*x] - Sin[d + e*x]])*(e^2 + b^2*c^2*Log[F]^2)*(Cos[(d + e*x)/2] + Sin[(d + e*x)/2])^3))/(3*e^3*f^2*(1 + Sin[d + e*x])^2)","A",1
139,1,228,245,0.6371016,"\int F^{c (a+b x)} (f+f \cos (d+e x))^2 \, dx","Integrate[F^(c*(a + b*x))*(f + f*Cos[d + e*x])^2,x]","\frac{f^2 F^{c (a+b x)} \left(3 b^4 c^4 \log ^4(F)+4 b^3 c^3 e \log ^3(F) \sin (d+e x)+2 b^3 c^3 e \log ^3(F) \sin (2 (d+e x))+b^2 c^2 \log ^2(F) \cos (2 (d+e x)) \left(b^2 c^2 \log ^2(F)+e^2\right)+4 b^2 c^2 \log ^2(F) \cos (d+e x) \left(b^2 c^2 \log ^2(F)+4 e^2\right)+15 b^2 c^2 e^2 \log ^2(F)+16 b c e^3 \log (F) \sin (d+e x)+2 b c e^3 \log (F) \sin (2 (d+e x))+12 e^4\right)}{2 \left(b^5 c^5 \log ^5(F)+5 b^3 c^3 e^2 \log ^3(F)+4 b c e^4 \log (F)\right)}","\frac{2 e f^2 \sin (d+e x) F^{a c+b c x}}{b^2 c^2 \log ^2(F)+e^2}+\frac{b c f^2 \log (F) \cos ^2(d+e x) F^{a c+b c x}}{b^2 c^2 \log ^2(F)+4 e^2}+\frac{2 b c f^2 \log (F) \cos (d+e x) F^{a c+b c x}}{b^2 c^2 \log ^2(F)+e^2}+\frac{2 e f^2 \sin (d+e x) \cos (d+e x) F^{a c+b c x}}{b^2 c^2 \log ^2(F)+4 e^2}+\frac{2 e^2 f^2 F^{a c+b c x}}{b c \log (F) \left(b^2 c^2 \log ^2(F)+4 e^2\right)}+\frac{f^2 F^{a c+b c x}}{b c \log (F)}",1,"(f^2*F^(c*(a + b*x))*(12*e^4 + 15*b^2*c^2*e^2*Log[F]^2 + 3*b^4*c^4*Log[F]^4 + b^2*c^2*Cos[2*(d + e*x)]*Log[F]^2*(e^2 + b^2*c^2*Log[F]^2) + 4*b^2*c^2*Cos[d + e*x]*Log[F]^2*(4*e^2 + b^2*c^2*Log[F]^2) + 16*b*c*e^3*Log[F]*Sin[d + e*x] + 4*b^3*c^3*e*Log[F]^3*Sin[d + e*x] + 2*b*c*e^3*Log[F]*Sin[2*(d + e*x)] + 2*b^3*c^3*e*Log[F]^3*Sin[2*(d + e*x)]))/(2*(4*b*c*e^4*Log[F] + 5*b^3*c^3*e^2*Log[F]^3 + b^5*c^5*Log[F]^5))","A",1
140,1,82,98,0.2402702,"\int F^{c (a+b x)} (f+f \cos (d+e x)) \, dx","Integrate[F^(c*(a + b*x))*(f + f*Cos[d + e*x]),x]","\frac{f F^{c (a+b x)} \left(b^2 c^2 \log ^2(F) \cos (d+e x)+b^2 c^2 \log ^2(F)+b c e \log (F) \sin (d+e x)+e^2\right)}{b c \log (F) \left(b^2 c^2 \log ^2(F)+e^2\right)}","\frac{e f \sin (d+e x) F^{a c+b c x}}{b^2 c^2 \log ^2(F)+e^2}+\frac{b c f \log (F) \cos (d+e x) F^{a c+b c x}}{b^2 c^2 \log ^2(F)+e^2}+\frac{f F^{a c+b c x}}{b c \log (F)}",1,"(f*F^(c*(a + b*x))*(e^2 + b^2*c^2*Log[F]^2 + b^2*c^2*Cos[d + e*x]*Log[F]^2 + b*c*e*Log[F]*Sin[d + e*x]))/(b*c*Log[F]*(e^2 + b^2*c^2*Log[F]^2))","A",1
141,1,80,79,0.0493872,"\int \frac{F^{c (a+b x)}}{f+f \cos (d+e x)} \, dx","Integrate[F^(c*(a + b*x))/(f + f*Cos[d + e*x]),x]","-\frac{2 i e^{i (d+e x)} F^{c (a+b x)} \, _2F_1\left(2,1-\frac{i b c \log (F)}{e};2-\frac{i b c \log (F)}{e};-e^{i (d+e x)}\right)}{f (e-i b c \log (F))}","\frac{2 e^{i (d+e x)} F^{c (a+b x)} \, _2F_1\left(2,1-\frac{i b c \log (F)}{e};2-\frac{i b c \log (F)}{e};-e^{i (d+e x)}\right)}{f (b c \log (F)+i e)}",1,"((-2*I)*E^(I*(d + e*x))*F^(c*(a + b*x))*Hypergeometric2F1[2, 1 - (I*b*c*Log[F])/e, 2 - (I*b*c*Log[F])/e, -E^(I*(d + e*x))])/(f*(e - I*b*c*Log[F]))","A",1
142,1,145,169,0.3935707,"\int \frac{F^{c (a+b x)}}{(f+f \cos (d+e x))^2} \, dx","Integrate[F^(c*(a + b*x))/(f + f*Cos[d + e*x])^2,x]","\frac{2 \cos \left(\frac{1}{2} (d+e x)\right) F^{c (a+b x)} \left(4 e^{i (d+e x)} \cos ^3\left(\frac{1}{2} (d+e x)\right) (b c \log (F)-i e) \, _2F_1\left(2,1-\frac{i b c \log (F)}{e};2-\frac{i b c \log (F)}{e};-e^{i (d+e x)}\right)-b c \log (F) \cos \left(\frac{1}{2} (d+e x)\right)+e \sin \left(\frac{1}{2} (d+e x)\right)\right)}{3 e^2 f^2 (\cos (d+e x)+1)^2}","-\frac{2 e^{i (d+e x)} F^{c (a+b x)} (-b c \log (F)+i e) \, _2F_1\left(2,1-\frac{i b c \log (F)}{e};2-\frac{i b c \log (F)}{e};-e^{i (d+e x)}\right)}{3 e^2 f^2}-\frac{b c \log (F) \sec ^2\left(\frac{d}{2}+\frac{e x}{2}\right) F^{c (a+b x)}}{6 e^2 f^2}+\frac{\tan \left(\frac{d}{2}+\frac{e x}{2}\right) \sec ^2\left(\frac{d}{2}+\frac{e x}{2}\right) F^{c (a+b x)}}{6 e f^2}",1,"(2*F^(c*(a + b*x))*Cos[(d + e*x)/2]*(-(b*c*Cos[(d + e*x)/2]*Log[F]) + 4*E^(I*(d + e*x))*Cos[(d + e*x)/2]^3*Hypergeometric2F1[2, 1 - (I*b*c*Log[F])/e, 2 - (I*b*c*Log[F])/e, -E^(I*(d + e*x))]*((-I)*e + b*c*Log[F]) + e*Sin[(d + e*x)/2]))/(3*e^2*f^2*(1 + Cos[d + e*x])^2)","A",1