1,0,0,0,0.000000," ","integrate(F**(c*(b*x+a))*sin(e*x+d)**n,x)","\int F^{c \left(a + b x\right)} \sin^{n}{\left(d + e x \right)}\, dx"," ",0,"Integral(F**(c*(a + b*x))*sin(d + e*x)**n, x)","F",0
2,-1,0,0,0.000000," ","integrate(F**(c*(b*x+a))*sin(e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3,1,627,0,34.888677," ","integrate(F**(c*(b*x+a))*sin(e*x+d)**2,x)","\begin{cases} \frac{x \sin^{2}{\left(d + e x \right)}}{2} + \frac{x \cos^{2}{\left(d + e x \right)}}{2} - \frac{\sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{2 e} & \text{for}\: F = 1 \\\tilde{\infty} e^{2} \left(e^{- \frac{2 i e}{b c}}\right)^{a c} \left(e^{- \frac{2 i e}{b c}}\right)^{b c x} \sin^{2}{\left(d + e x \right)} + \tilde{\infty} e^{2} \left(e^{- \frac{2 i e}{b c}}\right)^{a c} \left(e^{- \frac{2 i e}{b c}}\right)^{b c x} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)} + \tilde{\infty} e^{2} \left(e^{- \frac{2 i e}{b c}}\right)^{a c} \left(e^{- \frac{2 i e}{b c}}\right)^{b c x} \cos^{2}{\left(d + e x \right)} & \text{for}\: F = e^{- \frac{2 i e}{b c}} \\\tilde{\infty} e^{2} \left(e^{\frac{2 i e}{b c}}\right)^{a c} \left(e^{\frac{2 i e}{b c}}\right)^{b c x} \sin^{2}{\left(d + e x \right)} + \tilde{\infty} e^{2} \left(e^{\frac{2 i e}{b c}}\right)^{a c} \left(e^{\frac{2 i e}{b c}}\right)^{b c x} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)} + \tilde{\infty} e^{2} \left(e^{\frac{2 i e}{b c}}\right)^{a c} \left(e^{\frac{2 i e}{b c}}\right)^{b c x} \cos^{2}{\left(d + e x \right)} & \text{for}\: F = e^{\frac{2 i e}{b c}} \\F^{a c} \left(\frac{x \sin^{2}{\left(d + e x \right)}}{2} + \frac{x \cos^{2}{\left(d + e x \right)}}{2} - \frac{\sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{2 e}\right) & \text{for}\: b = 0 \\\frac{x \sin^{2}{\left(d + e x \right)}}{2} + \frac{x \cos^{2}{\left(d + e x \right)}}{2} - \frac{\sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{2 e} & \text{for}\: c = 0 \\\frac{F^{a c} F^{b c x} b^{2} c^{2} \log{\left(F \right)}^{2} \sin^{2}{\left(d + e x \right)}}{b^{3} c^{3} \log{\left(F \right)}^{3} + 4 b c e^{2} \log{\left(F \right)}} - \frac{2 F^{a c} F^{b c x} b c e \log{\left(F \right)} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{b^{3} c^{3} \log{\left(F \right)}^{3} + 4 b c e^{2} \log{\left(F \right)}} + \frac{2 F^{a c} F^{b c x} e^{2} \sin^{2}{\left(d + e x \right)}}{b^{3} c^{3} \log{\left(F \right)}^{3} + 4 b c e^{2} \log{\left(F \right)}} + \frac{2 F^{a c} F^{b c x} e^{2} \cos^{2}{\left(d + e x \right)}}{b^{3} c^{3} \log{\left(F \right)}^{3} + 4 b c e^{2} \log{\left(F \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(d + e*x)**2/2 + x*cos(d + e*x)**2/2 - sin(d + e*x)*cos(d + e*x)/(2*e), Eq(F, 1)), (zoo*e**2*exp(-2*I*e/(b*c))**(a*c)*exp(-2*I*e/(b*c))**(b*c*x)*sin(d + e*x)**2 + zoo*e**2*exp(-2*I*e/(b*c))**(a*c)*exp(-2*I*e/(b*c))**(b*c*x)*sin(d + e*x)*cos(d + e*x) + zoo*e**2*exp(-2*I*e/(b*c))**(a*c)*exp(-2*I*e/(b*c))**(b*c*x)*cos(d + e*x)**2, Eq(F, exp(-2*I*e/(b*c)))), (zoo*e**2*exp(2*I*e/(b*c))**(a*c)*exp(2*I*e/(b*c))**(b*c*x)*sin(d + e*x)**2 + zoo*e**2*exp(2*I*e/(b*c))**(a*c)*exp(2*I*e/(b*c))**(b*c*x)*sin(d + e*x)*cos(d + e*x) + zoo*e**2*exp(2*I*e/(b*c))**(a*c)*exp(2*I*e/(b*c))**(b*c*x)*cos(d + e*x)**2, Eq(F, exp(2*I*e/(b*c)))), (F**(a*c)*(x*sin(d + e*x)**2/2 + x*cos(d + e*x)**2/2 - sin(d + e*x)*cos(d + e*x)/(2*e)), Eq(b, 0)), (x*sin(d + e*x)**2/2 + x*cos(d + e*x)**2/2 - sin(d + e*x)*cos(d + e*x)/(2*e), Eq(c, 0)), (F**(a*c)*F**(b*c*x)*b**2*c**2*log(F)**2*sin(d + e*x)**2/(b**3*c**3*log(F)**3 + 4*b*c*e**2*log(F)) - 2*F**(a*c)*F**(b*c*x)*b*c*e*log(F)*sin(d + e*x)*cos(d + e*x)/(b**3*c**3*log(F)**3 + 4*b*c*e**2*log(F)) + 2*F**(a*c)*F**(b*c*x)*e**2*sin(d + e*x)**2/(b**3*c**3*log(F)**3 + 4*b*c*e**2*log(F)) + 2*F**(a*c)*F**(b*c*x)*e**2*cos(d + e*x)**2/(b**3*c**3*log(F)**3 + 4*b*c*e**2*log(F)), True))","A",0
4,1,326,0,7.836972," ","integrate(F**(c*(b*x+a))*sin(e*x+d),x)","\begin{cases} \frac{\left(-1\right)^{a c} \left(-1\right)^{\frac{e x}{\pi}} x \sin{\left(d + e x \right)}}{2} + \frac{\left(-1\right)^{a c} \left(-1\right)^{\frac{e x}{\pi}} i x \cos{\left(d + e x \right)}}{2} - \frac{\left(-1\right)^{a c} \left(-1\right)^{\frac{e x}{\pi}} \cos{\left(d + e x \right)}}{2 e} & \text{for}\: F = -1 \wedge b = \frac{e}{\pi c} \\x \sin{\left(d \right)} & \text{for}\: F = 1 \wedge e = 0 \\\tilde{\infty} e \left(e^{- \frac{i e}{b c}}\right)^{a c} \left(e^{- \frac{i e}{b c}}\right)^{b c x} \sin{\left(d + e x \right)} + \tilde{\infty} e \left(e^{- \frac{i e}{b c}}\right)^{a c} \left(e^{- \frac{i e}{b c}}\right)^{b c x} \cos{\left(d + e x \right)} & \text{for}\: F = e^{- \frac{i e}{b c}} \\\tilde{\infty} e \left(e^{\frac{i e}{b c}}\right)^{a c} \left(e^{\frac{i e}{b c}}\right)^{b c x} \sin{\left(d + e x \right)} + \tilde{\infty} e \left(e^{\frac{i e}{b c}}\right)^{a c} \left(e^{\frac{i e}{b c}}\right)^{b c x} \cos{\left(d + e x \right)} & \text{for}\: F = e^{\frac{i e}{b c}} \\\frac{F^{a c} F^{b c x} b c \log{\left(F \right)} \sin{\left(d + e x \right)}}{b^{2} c^{2} \log{\left(F \right)}^{2} + e^{2}} - \frac{F^{a c} F^{b c x} e \cos{\left(d + e x \right)}}{b^{2} c^{2} \log{\left(F \right)}^{2} + e^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-1)**(a*c)*(-1)**(e*x/pi)*x*sin(d + e*x)/2 + (-1)**(a*c)*(-1)**(e*x/pi)*I*x*cos(d + e*x)/2 - (-1)**(a*c)*(-1)**(e*x/pi)*cos(d + e*x)/(2*e), Eq(F, -1) & Eq(b, e/(pi*c))), (x*sin(d), Eq(F, 1) & Eq(e, 0)), (zoo*e*exp(-I*e/(b*c))**(a*c)*exp(-I*e/(b*c))**(b*c*x)*sin(d + e*x) + zoo*e*exp(-I*e/(b*c))**(a*c)*exp(-I*e/(b*c))**(b*c*x)*cos(d + e*x), Eq(F, exp(-I*e/(b*c)))), (zoo*e*exp(I*e/(b*c))**(a*c)*exp(I*e/(b*c))**(b*c*x)*sin(d + e*x) + zoo*e*exp(I*e/(b*c))**(a*c)*exp(I*e/(b*c))**(b*c*x)*cos(d + e*x), Eq(F, exp(I*e/(b*c)))), (F**(a*c)*F**(b*c*x)*b*c*log(F)*sin(d + e*x)/(b**2*c**2*log(F)**2 + e**2) - F**(a*c)*F**(b*c*x)*e*cos(d + e*x)/(b**2*c**2*log(F)**2 + e**2), True))","A",0
5,0,0,0,0.000000," ","integrate(F**(c*(b*x+a))*csc(e*x+d),x)","\int F^{c \left(a + b x\right)} \csc{\left(d + e x \right)}\, dx"," ",0,"Integral(F**(c*(a + b*x))*csc(d + e*x), x)","F",0
6,0,0,0,0.000000," ","integrate(F**(c*(b*x+a))*csc(e*x+d)**2,x)","\int F^{c \left(a + b x\right)} \csc^{2}{\left(d + e x \right)}\, dx"," ",0,"Integral(F**(c*(a + b*x))*csc(d + e*x)**2, x)","F",0
7,0,0,0,0.000000," ","integrate(F**(c*(b*x+a))*csc(e*x+d)**3,x)","\int F^{c \left(a + b x\right)} \csc^{3}{\left(d + e x \right)}\, dx"," ",0,"Integral(F**(c*(a + b*x))*csc(d + e*x)**3, x)","F",0
8,-1,0,0,0.000000," ","integrate(F**(c*(b*x+a))*csc(e*x+d)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
9,1,70,0,3.738960," ","integrate(exp(x)*sin(x)**4,x)","\frac{41 e^{x} \sin^{4}{\left(x \right)}}{85} - \frac{44 e^{x} \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{85} + \frac{12 e^{x} \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{17} - \frac{24 e^{x} \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{85} + \frac{24 e^{x} \cos^{4}{\left(x \right)}}{85}"," ",0,"41*exp(x)*sin(x)**4/85 - 44*exp(x)*sin(x)**3*cos(x)/85 + 12*exp(x)*sin(x)**2*cos(x)**2/17 - 24*exp(x)*sin(x)*cos(x)**3/85 + 24*exp(x)*cos(x)**4/85","A",0
10,0,0,0,0.000000," ","integrate(F**(c*(b*x+a))*cos(e*x+d)**n,x)","\int F^{c \left(a + b x\right)} \cos^{n}{\left(d + e x \right)}\, dx"," ",0,"Integral(F**(c*(a + b*x))*cos(d + e*x)**n, x)","F",0
11,-1,0,0,0.000000," ","integrate(F**(c*(b*x+a))*cos(e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
12,1,627,0,34.782563," ","integrate(F**(c*(b*x+a))*cos(e*x+d)**2,x)","\begin{cases} \frac{x \sin^{2}{\left(d + e x \right)}}{2} + \frac{x \cos^{2}{\left(d + e x \right)}}{2} + \frac{\sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{2 e} & \text{for}\: F = 1 \\\tilde{\infty} e^{2} \left(e^{- \frac{2 i e}{b c}}\right)^{a c} \left(e^{- \frac{2 i e}{b c}}\right)^{b c x} \sin^{2}{\left(d + e x \right)} + \tilde{\infty} e^{2} \left(e^{- \frac{2 i e}{b c}}\right)^{a c} \left(e^{- \frac{2 i e}{b c}}\right)^{b c x} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)} + \tilde{\infty} e^{2} \left(e^{- \frac{2 i e}{b c}}\right)^{a c} \left(e^{- \frac{2 i e}{b c}}\right)^{b c x} \cos^{2}{\left(d + e x \right)} & \text{for}\: F = e^{- \frac{2 i e}{b c}} \\\tilde{\infty} e^{2} \left(e^{\frac{2 i e}{b c}}\right)^{a c} \left(e^{\frac{2 i e}{b c}}\right)^{b c x} \sin^{2}{\left(d + e x \right)} + \tilde{\infty} e^{2} \left(e^{\frac{2 i e}{b c}}\right)^{a c} \left(e^{\frac{2 i e}{b c}}\right)^{b c x} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)} + \tilde{\infty} e^{2} \left(e^{\frac{2 i e}{b c}}\right)^{a c} \left(e^{\frac{2 i e}{b c}}\right)^{b c x} \cos^{2}{\left(d + e x \right)} & \text{for}\: F = e^{\frac{2 i e}{b c}} \\F^{a c} \left(\frac{x \sin^{2}{\left(d + e x \right)}}{2} + \frac{x \cos^{2}{\left(d + e x \right)}}{2} + \frac{\sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{2 e}\right) & \text{for}\: b = 0 \\\frac{x \sin^{2}{\left(d + e x \right)}}{2} + \frac{x \cos^{2}{\left(d + e x \right)}}{2} + \frac{\sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{2 e} & \text{for}\: c = 0 \\\frac{F^{a c} F^{b c x} b^{2} c^{2} \log{\left(F \right)}^{2} \cos^{2}{\left(d + e x \right)}}{b^{3} c^{3} \log{\left(F \right)}^{3} + 4 b c e^{2} \log{\left(F \right)}} + \frac{2 F^{a c} F^{b c x} b c e \log{\left(F \right)} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{b^{3} c^{3} \log{\left(F \right)}^{3} + 4 b c e^{2} \log{\left(F \right)}} + \frac{2 F^{a c} F^{b c x} e^{2} \sin^{2}{\left(d + e x \right)}}{b^{3} c^{3} \log{\left(F \right)}^{3} + 4 b c e^{2} \log{\left(F \right)}} + \frac{2 F^{a c} F^{b c x} e^{2} \cos^{2}{\left(d + e x \right)}}{b^{3} c^{3} \log{\left(F \right)}^{3} + 4 b c e^{2} \log{\left(F \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(d + e*x)**2/2 + x*cos(d + e*x)**2/2 + sin(d + e*x)*cos(d + e*x)/(2*e), Eq(F, 1)), (zoo*e**2*exp(-2*I*e/(b*c))**(a*c)*exp(-2*I*e/(b*c))**(b*c*x)*sin(d + e*x)**2 + zoo*e**2*exp(-2*I*e/(b*c))**(a*c)*exp(-2*I*e/(b*c))**(b*c*x)*sin(d + e*x)*cos(d + e*x) + zoo*e**2*exp(-2*I*e/(b*c))**(a*c)*exp(-2*I*e/(b*c))**(b*c*x)*cos(d + e*x)**2, Eq(F, exp(-2*I*e/(b*c)))), (zoo*e**2*exp(2*I*e/(b*c))**(a*c)*exp(2*I*e/(b*c))**(b*c*x)*sin(d + e*x)**2 + zoo*e**2*exp(2*I*e/(b*c))**(a*c)*exp(2*I*e/(b*c))**(b*c*x)*sin(d + e*x)*cos(d + e*x) + zoo*e**2*exp(2*I*e/(b*c))**(a*c)*exp(2*I*e/(b*c))**(b*c*x)*cos(d + e*x)**2, Eq(F, exp(2*I*e/(b*c)))), (F**(a*c)*(x*sin(d + e*x)**2/2 + x*cos(d + e*x)**2/2 + sin(d + e*x)*cos(d + e*x)/(2*e)), Eq(b, 0)), (x*sin(d + e*x)**2/2 + x*cos(d + e*x)**2/2 + sin(d + e*x)*cos(d + e*x)/(2*e), Eq(c, 0)), (F**(a*c)*F**(b*c*x)*b**2*c**2*log(F)**2*cos(d + e*x)**2/(b**3*c**3*log(F)**3 + 4*b*c*e**2*log(F)) + 2*F**(a*c)*F**(b*c*x)*b*c*e*log(F)*sin(d + e*x)*cos(d + e*x)/(b**3*c**3*log(F)**3 + 4*b*c*e**2*log(F)) + 2*F**(a*c)*F**(b*c*x)*e**2*sin(d + e*x)**2/(b**3*c**3*log(F)**3 + 4*b*c*e**2*log(F)) + 2*F**(a*c)*F**(b*c*x)*e**2*cos(d + e*x)**2/(b**3*c**3*log(F)**3 + 4*b*c*e**2*log(F)), True))","A",0
13,1,352,0,7.857772," ","integrate(F**(c*(b*x+a))*cos(e*x+d),x)","\begin{cases} - \frac{\left(-1\right)^{a c} \left(-1\right)^{\frac{e x}{\pi}} i x \sin{\left(d + e x \right)}}{2} + \frac{\left(-1\right)^{a c} \left(-1\right)^{\frac{e x}{\pi}} x \cos{\left(d + e x \right)}}{2} + \frac{\left(-1\right)^{a c} \left(-1\right)^{\frac{e x}{\pi}} \sin{\left(d + e x \right)}}{e} + \frac{\left(-1\right)^{a c} \left(-1\right)^{\frac{e x}{\pi}} i \cos{\left(d + e x \right)}}{2 e} & \text{for}\: F = -1 \wedge b = \frac{e}{\pi c} \\x \cos{\left(d \right)} & \text{for}\: F = 1 \wedge e = 0 \\\tilde{\infty} e \left(e^{- \frac{i e}{b c}}\right)^{a c} \left(e^{- \frac{i e}{b c}}\right)^{b c x} \sin{\left(d + e x \right)} + \tilde{\infty} e \left(e^{- \frac{i e}{b c}}\right)^{a c} \left(e^{- \frac{i e}{b c}}\right)^{b c x} \cos{\left(d + e x \right)} & \text{for}\: F = e^{- \frac{i e}{b c}} \\\tilde{\infty} e \left(e^{\frac{i e}{b c}}\right)^{a c} \left(e^{\frac{i e}{b c}}\right)^{b c x} \sin{\left(d + e x \right)} + \tilde{\infty} e \left(e^{\frac{i e}{b c}}\right)^{a c} \left(e^{\frac{i e}{b c}}\right)^{b c x} \cos{\left(d + e x \right)} & \text{for}\: F = e^{\frac{i e}{b c}} \\\frac{F^{a c} F^{b c x} b c \log{\left(F \right)} \cos{\left(d + e x \right)}}{b^{2} c^{2} \log{\left(F \right)}^{2} + e^{2}} + \frac{F^{a c} F^{b c x} e \sin{\left(d + e x \right)}}{b^{2} c^{2} \log{\left(F \right)}^{2} + e^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-(-1)**(a*c)*(-1)**(e*x/pi)*I*x*sin(d + e*x)/2 + (-1)**(a*c)*(-1)**(e*x/pi)*x*cos(d + e*x)/2 + (-1)**(a*c)*(-1)**(e*x/pi)*sin(d + e*x)/e + (-1)**(a*c)*(-1)**(e*x/pi)*I*cos(d + e*x)/(2*e), Eq(F, -1) & Eq(b, e/(pi*c))), (x*cos(d), Eq(F, 1) & Eq(e, 0)), (zoo*e*exp(-I*e/(b*c))**(a*c)*exp(-I*e/(b*c))**(b*c*x)*sin(d + e*x) + zoo*e*exp(-I*e/(b*c))**(a*c)*exp(-I*e/(b*c))**(b*c*x)*cos(d + e*x), Eq(F, exp(-I*e/(b*c)))), (zoo*e*exp(I*e/(b*c))**(a*c)*exp(I*e/(b*c))**(b*c*x)*sin(d + e*x) + zoo*e*exp(I*e/(b*c))**(a*c)*exp(I*e/(b*c))**(b*c*x)*cos(d + e*x), Eq(F, exp(I*e/(b*c)))), (F**(a*c)*F**(b*c*x)*b*c*log(F)*cos(d + e*x)/(b**2*c**2*log(F)**2 + e**2) + F**(a*c)*F**(b*c*x)*e*sin(d + e*x)/(b**2*c**2*log(F)**2 + e**2), True))","A",0
14,0,0,0,0.000000," ","integrate(F**(c*(b*x+a))*sec(e*x+d),x)","\int F^{c \left(a + b x\right)} \sec{\left(d + e x \right)}\, dx"," ",0,"Integral(F**(c*(a + b*x))*sec(d + e*x), x)","F",0
15,0,0,0,0.000000," ","integrate(F**(c*(b*x+a))*sec(e*x+d)**2,x)","\int F^{c \left(a + b x\right)} \sec^{2}{\left(d + e x \right)}\, dx"," ",0,"Integral(F**(c*(a + b*x))*sec(d + e*x)**2, x)","F",0
16,-1,0,0,0.000000," ","integrate(F**(c*(b*x+a))*sec(e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
17,-1,0,0,0.000000," ","integrate(F**(c*(b*x+a))*sec(e*x+d)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
18,1,70,0,3.711835," ","integrate(exp(x)*cos(x)**4,x)","\frac{24 e^{x} \sin^{4}{\left(x \right)}}{85} + \frac{24 e^{x} \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{85} + \frac{12 e^{x} \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{17} + \frac{44 e^{x} \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{85} + \frac{41 e^{x} \cos^{4}{\left(x \right)}}{85}"," ",0,"24*exp(x)*sin(x)**4/85 + 24*exp(x)*sin(x)**3*cos(x)/85 + 12*exp(x)*sin(x)**2*cos(x)**2/17 + 44*exp(x)*sin(x)*cos(x)**3/85 + 41*exp(x)*cos(x)**4/85","A",0
19,0,0,0,0.000000," ","integrate(exp(c*(b*x+a))*tan(e*x+d)**3,x)","e^{a c} \int e^{b c x} \tan^{3}{\left(d + e x \right)}\, dx"," ",0,"exp(a*c)*Integral(exp(b*c*x)*tan(d + e*x)**3, x)","F",0
20,0,0,0,0.000000," ","integrate(exp(c*(b*x+a))*tan(e*x+d)**2,x)","e^{a c} \int e^{b c x} \tan^{2}{\left(d + e x \right)}\, dx"," ",0,"exp(a*c)*Integral(exp(b*c*x)*tan(d + e*x)**2, x)","F",0
21,0,0,0,0.000000," ","integrate(exp(c*(b*x+a))*tan(e*x+d),x)","e^{a c} \int e^{b c x} \tan{\left(d + e x \right)}\, dx"," ",0,"exp(a*c)*Integral(exp(b*c*x)*tan(d + e*x), x)","F",0
22,0,0,0,0.000000," ","integrate(exp(c*(b*x+a))*cot(e*x+d),x)","e^{a c} \int e^{b c x} \cot{\left(d + e x \right)}\, dx"," ",0,"exp(a*c)*Integral(exp(b*c*x)*cot(d + e*x), x)","F",0
23,0,0,0,0.000000," ","integrate(exp(c*(b*x+a))*cot(e*x+d)**2,x)","e^{a c} \int e^{b c x} \cot^{2}{\left(d + e x \right)}\, dx"," ",0,"exp(a*c)*Integral(exp(b*c*x)*cot(d + e*x)**2, x)","F",0
24,0,0,0,0.000000," ","integrate(exp(c*(b*x+a))*cot(e*x+d)**3,x)","e^{a c} \int e^{b c x} \cot^{3}{\left(d + e x \right)}\, dx"," ",0,"exp(a*c)*Integral(exp(b*c*x)*cot(d + e*x)**3, x)","F",0
25,0,0,0,0.000000," ","integrate(F**(b*x+a)*cot(1/2*c+1/4*pi+1/2*d*x),x)","\int F^{a + b x} \cot{\left(\frac{c}{2} + \frac{d x}{2} + \frac{\pi}{4} \right)}\, dx"," ",0,"Integral(F**(a + b*x)*cot(c/2 + d*x/2 + pi/4), x)","F",0
26,0,0,0,0.000000," ","integrate(F**(c*(b*x+a))*sec(e*x+d)**n,x)","\int F^{c \left(a + b x\right)} \sec^{n}{\left(d + e x \right)}\, dx"," ",0,"Integral(F**(c*(a + b*x))*sec(d + e*x)**n, x)","F",0
27,0,0,0,0.000000," ","integrate(F**(c*(b*x+a))*csc(e*x+d)**n,x)","\int F^{c \left(a + b x\right)} \csc^{n}{\left(d + e x \right)}\, dx"," ",0,"Integral(F**(c*(a + b*x))*csc(d + e*x)**n, x)","F",0
28,0,0,0,0.000000," ","integrate(F**(c*(b*x+a))*(f*x)**m*sin(e*x+d),x)","\int F^{c \left(a + b x\right)} \left(f x\right)^{m} \sin{\left(d + e x \right)}\, dx"," ",0,"Integral(F**(c*(a + b*x))*(f*x)**m*sin(d + e*x), x)","F",0
29,0,0,0,0.000000," ","integrate(F**(c*(b*x+a))*(f*x)**m/sin(e*x+d),x)","\int \frac{F^{c \left(a + b x\right)} \left(f x\right)^{m}}{\sin{\left(d + e x \right)}}\, dx"," ",0,"Integral(F**(c*(a + b*x))*(f*x)**m/sin(d + e*x), x)","F",0
30,0,0,0,0.000000," ","integrate(F**(c*(b*x+a))*(f*x)**m/sin(e*x+d)**2,x)","\int \frac{F^{c \left(a + b x\right)} \left(f x\right)^{m}}{\sin^{2}{\left(d + e x \right)}}\, dx"," ",0,"Integral(F**(c*(a + b*x))*(f*x)**m/sin(d + e*x)**2, x)","F",0
31,-1,0,0,0.000000," ","integrate(f*F**(c*(b*x+a))*(f*x)**(-2+m)*(e*x*cos(e*x+d)+(-1+m+b*c*x*ln(F))*sin(e*x+d)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
32,-1,0,0,0.000000," ","integrate(f*F**(c*(b*x+a))*(f*x)**m*(e*x*cos(e*x+d)+(1+m+b*c*x*ln(F))*sin(e*x+d)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
33,-1,0,0,0.000000," ","integrate(F**(c*(b*x+a))*(f*x)**m*(e*x*cos(e*x+d)+(m+b*c*x*ln(F))*sin(e*x+d))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
34,1,19,0,7.556657," ","integrate(F**(c*(b*x+a))*(e*x*cos(e*x+d)+(1+b*c*x*ln(F))*sin(e*x+d)),x)","F^{a c} F^{b c x} x \sin{\left(d + e x \right)}"," ",0,"F**(a*c)*F**(b*c*x)*x*sin(d + e*x)","A",0
35,1,17,0,1.632443," ","integrate(F**(c*(b*x+a))*(e*cos(e*x+d)+b*c*ln(F)*sin(e*x+d)),x)","F^{a c} F^{b c x} \sin{\left(d + e x \right)}"," ",0,"F**(a*c)*F**(b*c*x)*sin(d + e*x)","A",0
36,0,0,0,0.000000," ","integrate(F**(c*(b*x+a))*(e*x*cos(e*x+d)+(-1+b*c*x*ln(F))*sin(e*x+d))/x**2,x)","\int \frac{F^{c \left(a + b x\right)} \left(b c x \log{\left(F \right)} \sin{\left(d + e x \right)} + e x \cos{\left(d + e x \right)} - \sin{\left(d + e x \right)}\right)}{x^{2}}\, dx"," ",0,"Integral(F**(c*(a + b*x))*(b*c*x*log(F)*sin(d + e*x) + e*x*cos(d + e*x) - sin(d + e*x))/x**2, x)","F",0
37,0,0,0,0.000000," ","integrate(F**(c*(b*x+a))*(e*x*cos(e*x+d)+(-2+b*c*x*ln(F))*sin(e*x+d))/x**3,x)","\int \frac{F^{c \left(a + b x\right)} \left(b c x \log{\left(F \right)} \sin{\left(d + e x \right)} + e x \cos{\left(d + e x \right)} - 2 \sin{\left(d + e x \right)}\right)}{x^{3}}\, dx"," ",0,"Integral(F**(c*(a + b*x))*(b*c*x*log(F)*sin(d + e*x) + e*x*cos(d + e*x) - 2*sin(d + e*x))/x**3, x)","F",0
38,1,325,0,8.518840," ","integrate(exp(b*x+a)*cos(d*x+c)*sin(d*x+c),x)","\begin{cases} x e^{a} \sin{\left(c \right)} \cos{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\\frac{i x e^{a} e^{- 2 i d x} \sin^{2}{\left(c + d x \right)}}{4} + \frac{x e^{a} e^{- 2 i d x} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2} - \frac{i x e^{a} e^{- 2 i d x} \cos^{2}{\left(c + d x \right)}}{4} + \frac{i e^{a} e^{- 2 i d x} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} & \text{for}\: b = - 2 i d \\- \frac{i x e^{a} e^{2 i d x} \sin^{2}{\left(c + d x \right)}}{4} + \frac{x e^{a} e^{2 i d x} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2} + \frac{i x e^{a} e^{2 i d x} \cos^{2}{\left(c + d x \right)}}{4} - \frac{i e^{a} e^{2 i d x} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} & \text{for}\: b = 2 i d \\\frac{b e^{a} e^{b x} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{b^{2} + 4 d^{2}} + \frac{d e^{a} e^{b x} \sin^{2}{\left(c + d x \right)}}{b^{2} + 4 d^{2}} - \frac{d e^{a} e^{b x} \cos^{2}{\left(c + d x \right)}}{b^{2} + 4 d^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*exp(a)*sin(c)*cos(c), Eq(b, 0) & Eq(d, 0)), (I*x*exp(a)*exp(-2*I*d*x)*sin(c + d*x)**2/4 + x*exp(a)*exp(-2*I*d*x)*sin(c + d*x)*cos(c + d*x)/2 - I*x*exp(a)*exp(-2*I*d*x)*cos(c + d*x)**2/4 + I*exp(a)*exp(-2*I*d*x)*sin(c + d*x)*cos(c + d*x)/(4*d), Eq(b, -2*I*d)), (-I*x*exp(a)*exp(2*I*d*x)*sin(c + d*x)**2/4 + x*exp(a)*exp(2*I*d*x)*sin(c + d*x)*cos(c + d*x)/2 + I*x*exp(a)*exp(2*I*d*x)*cos(c + d*x)**2/4 - I*exp(a)*exp(2*I*d*x)*sin(c + d*x)*cos(c + d*x)/(4*d), Eq(b, 2*I*d)), (b*exp(a)*exp(b*x)*sin(c + d*x)*cos(c + d*x)/(b**2 + 4*d**2) + d*exp(a)*exp(b*x)*sin(c + d*x)**2/(b**2 + 4*d**2) - d*exp(a)*exp(b*x)*cos(c + d*x)**2/(b**2 + 4*d**2), True))","A",0
39,1,1030,0,44.425783," ","integrate(exp(b*x+a)*cos(d*x+c)*sin(d*x+c)**2,x)","\begin{cases} x e^{a} \sin^{2}{\left(c \right)} \cos{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\\frac{i x e^{a} e^{- 3 i d x} \sin^{3}{\left(c + d x \right)}}{8} + \frac{3 x e^{a} e^{- 3 i d x} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8} - \frac{3 i x e^{a} e^{- 3 i d x} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} - \frac{x e^{a} e^{- 3 i d x} \cos^{3}{\left(c + d x \right)}}{8} + \frac{e^{a} e^{- 3 i d x} \sin^{3}{\left(c + d x \right)}}{24 d} - \frac{e^{a} e^{- 3 i d x} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} + \frac{i e^{a} e^{- 3 i d x} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: b = - 3 i d \\\frac{i x e^{a} e^{- i d x} \sin^{3}{\left(c + d x \right)}}{8} + \frac{x e^{a} e^{- i d x} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8} + \frac{i x e^{a} e^{- i d x} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{x e^{a} e^{- i d x} \cos^{3}{\left(c + d x \right)}}{8} + \frac{e^{a} e^{- i d x} \sin^{3}{\left(c + d x \right)}}{8 d} - \frac{e^{a} e^{- i d x} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} + \frac{i e^{a} e^{- i d x} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: b = - i d \\- \frac{i x e^{a} e^{i d x} \sin^{3}{\left(c + d x \right)}}{8} + \frac{x e^{a} e^{i d x} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8} - \frac{i x e^{a} e^{i d x} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{x e^{a} e^{i d x} \cos^{3}{\left(c + d x \right)}}{8} + \frac{e^{a} e^{i d x} \sin^{3}{\left(c + d x \right)}}{8 d} - \frac{e^{a} e^{i d x} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} - \frac{i e^{a} e^{i d x} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: b = i d \\- \frac{i x e^{a} e^{3 i d x} \sin^{3}{\left(c + d x \right)}}{8} + \frac{3 x e^{a} e^{3 i d x} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8} + \frac{3 i x e^{a} e^{3 i d x} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} - \frac{x e^{a} e^{3 i d x} \cos^{3}{\left(c + d x \right)}}{8} + \frac{e^{a} e^{3 i d x} \sin^{3}{\left(c + d x \right)}}{24 d} - \frac{e^{a} e^{3 i d x} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} - \frac{i e^{a} e^{3 i d x} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: b = 3 i d \\\frac{b^{3} e^{a} e^{b x} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{b^{4} + 10 b^{2} d^{2} + 9 d^{4}} + \frac{b^{2} d e^{a} e^{b x} \sin^{3}{\left(c + d x \right)}}{b^{4} + 10 b^{2} d^{2} + 9 d^{4}} - \frac{2 b^{2} d e^{a} e^{b x} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{b^{4} + 10 b^{2} d^{2} + 9 d^{4}} + \frac{3 b d^{2} e^{a} e^{b x} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{b^{4} + 10 b^{2} d^{2} + 9 d^{4}} + \frac{2 b d^{2} e^{a} e^{b x} \cos^{3}{\left(c + d x \right)}}{b^{4} + 10 b^{2} d^{2} + 9 d^{4}} + \frac{3 d^{3} e^{a} e^{b x} \sin^{3}{\left(c + d x \right)}}{b^{4} + 10 b^{2} d^{2} + 9 d^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*exp(a)*sin(c)**2*cos(c), Eq(b, 0) & Eq(d, 0)), (I*x*exp(a)*exp(-3*I*d*x)*sin(c + d*x)**3/8 + 3*x*exp(a)*exp(-3*I*d*x)*sin(c + d*x)**2*cos(c + d*x)/8 - 3*I*x*exp(a)*exp(-3*I*d*x)*sin(c + d*x)*cos(c + d*x)**2/8 - x*exp(a)*exp(-3*I*d*x)*cos(c + d*x)**3/8 + exp(a)*exp(-3*I*d*x)*sin(c + d*x)**3/(24*d) - exp(a)*exp(-3*I*d*x)*sin(c + d*x)*cos(c + d*x)**2/(4*d) + I*exp(a)*exp(-3*I*d*x)*cos(c + d*x)**3/(8*d), Eq(b, -3*I*d)), (I*x*exp(a)*exp(-I*d*x)*sin(c + d*x)**3/8 + x*exp(a)*exp(-I*d*x)*sin(c + d*x)**2*cos(c + d*x)/8 + I*x*exp(a)*exp(-I*d*x)*sin(c + d*x)*cos(c + d*x)**2/8 + x*exp(a)*exp(-I*d*x)*cos(c + d*x)**3/8 + exp(a)*exp(-I*d*x)*sin(c + d*x)**3/(8*d) - exp(a)*exp(-I*d*x)*sin(c + d*x)*cos(c + d*x)**2/(4*d) + I*exp(a)*exp(-I*d*x)*cos(c + d*x)**3/(8*d), Eq(b, -I*d)), (-I*x*exp(a)*exp(I*d*x)*sin(c + d*x)**3/8 + x*exp(a)*exp(I*d*x)*sin(c + d*x)**2*cos(c + d*x)/8 - I*x*exp(a)*exp(I*d*x)*sin(c + d*x)*cos(c + d*x)**2/8 + x*exp(a)*exp(I*d*x)*cos(c + d*x)**3/8 + exp(a)*exp(I*d*x)*sin(c + d*x)**3/(8*d) - exp(a)*exp(I*d*x)*sin(c + d*x)*cos(c + d*x)**2/(4*d) - I*exp(a)*exp(I*d*x)*cos(c + d*x)**3/(8*d), Eq(b, I*d)), (-I*x*exp(a)*exp(3*I*d*x)*sin(c + d*x)**3/8 + 3*x*exp(a)*exp(3*I*d*x)*sin(c + d*x)**2*cos(c + d*x)/8 + 3*I*x*exp(a)*exp(3*I*d*x)*sin(c + d*x)*cos(c + d*x)**2/8 - x*exp(a)*exp(3*I*d*x)*cos(c + d*x)**3/8 + exp(a)*exp(3*I*d*x)*sin(c + d*x)**3/(24*d) - exp(a)*exp(3*I*d*x)*sin(c + d*x)*cos(c + d*x)**2/(4*d) - I*exp(a)*exp(3*I*d*x)*cos(c + d*x)**3/(8*d), Eq(b, 3*I*d)), (b**3*exp(a)*exp(b*x)*sin(c + d*x)**2*cos(c + d*x)/(b**4 + 10*b**2*d**2 + 9*d**4) + b**2*d*exp(a)*exp(b*x)*sin(c + d*x)**3/(b**4 + 10*b**2*d**2 + 9*d**4) - 2*b**2*d*exp(a)*exp(b*x)*sin(c + d*x)*cos(c + d*x)**2/(b**4 + 10*b**2*d**2 + 9*d**4) + 3*b*d**2*exp(a)*exp(b*x)*sin(c + d*x)**2*cos(c + d*x)/(b**4 + 10*b**2*d**2 + 9*d**4) + 2*b*d**2*exp(a)*exp(b*x)*cos(c + d*x)**3/(b**4 + 10*b**2*d**2 + 9*d**4) + 3*d**3*exp(a)*exp(b*x)*sin(c + d*x)**3/(b**4 + 10*b**2*d**2 + 9*d**4), True))","A",0
40,1,1353,0,147.998152," ","integrate(exp(b*x+a)*cos(d*x+c)*sin(d*x+c)**3,x)","\begin{cases} x e^{a} \sin^{3}{\left(c \right)} \cos{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\\frac{i x e^{a} e^{- 4 i d x} \sin^{4}{\left(c + d x \right)}}{16} + \frac{x e^{a} e^{- 4 i d x} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4} - \frac{3 i x e^{a} e^{- 4 i d x} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} - \frac{x e^{a} e^{- 4 i d x} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4} + \frac{i x e^{a} e^{- 4 i d x} \cos^{4}{\left(c + d x \right)}}{16} - \frac{e^{a} e^{- 4 i d x} \sin^{4}{\left(c + d x \right)}}{24 d} + \frac{11 i e^{a} e^{- 4 i d x} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{48 d} + \frac{5 i e^{a} e^{- 4 i d x} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{48 d} + \frac{e^{a} e^{- 4 i d x} \cos^{4}{\left(c + d x \right)}}{24 d} & \text{for}\: b = - 4 i d \\\frac{i x e^{a} e^{- 2 i d x} \sin^{4}{\left(c + d x \right)}}{8} + \frac{x e^{a} e^{- 2 i d x} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4} + \frac{x e^{a} e^{- 2 i d x} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4} - \frac{i x e^{a} e^{- 2 i d x} \cos^{4}{\left(c + d x \right)}}{8} + \frac{e^{a} e^{- 2 i d x} \sin^{4}{\left(c + d x \right)}}{16 d} - \frac{e^{a} e^{- 2 i d x} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} + \frac{i e^{a} e^{- 2 i d x} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{e^{a} e^{- 2 i d x} \cos^{4}{\left(c + d x \right)}}{48 d} & \text{for}\: b = - 2 i d \\- \frac{i x e^{a} e^{2 i d x} \sin^{4}{\left(c + d x \right)}}{8} + \frac{x e^{a} e^{2 i d x} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4} + \frac{x e^{a} e^{2 i d x} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4} + \frac{i x e^{a} e^{2 i d x} \cos^{4}{\left(c + d x \right)}}{8} + \frac{e^{a} e^{2 i d x} \sin^{4}{\left(c + d x \right)}}{16 d} - \frac{e^{a} e^{2 i d x} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} - \frac{i e^{a} e^{2 i d x} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{e^{a} e^{2 i d x} \cos^{4}{\left(c + d x \right)}}{48 d} & \text{for}\: b = 2 i d \\- \frac{i x e^{a} e^{4 i d x} \sin^{4}{\left(c + d x \right)}}{16} + \frac{x e^{a} e^{4 i d x} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4} + \frac{3 i x e^{a} e^{4 i d x} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} - \frac{x e^{a} e^{4 i d x} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4} - \frac{i x e^{a} e^{4 i d x} \cos^{4}{\left(c + d x \right)}}{16} - \frac{e^{a} e^{4 i d x} \sin^{4}{\left(c + d x \right)}}{24 d} - \frac{11 i e^{a} e^{4 i d x} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{48 d} - \frac{5 i e^{a} e^{4 i d x} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{48 d} + \frac{e^{a} e^{4 i d x} \cos^{4}{\left(c + d x \right)}}{24 d} & \text{for}\: b = 4 i d \\\frac{b^{3} e^{a} e^{b x} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{b^{4} + 20 b^{2} d^{2} + 64 d^{4}} + \frac{b^{2} d e^{a} e^{b x} \sin^{4}{\left(c + d x \right)}}{b^{4} + 20 b^{2} d^{2} + 64 d^{4}} - \frac{3 b^{2} d e^{a} e^{b x} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{b^{4} + 20 b^{2} d^{2} + 64 d^{4}} + \frac{10 b d^{2} e^{a} e^{b x} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{b^{4} + 20 b^{2} d^{2} + 64 d^{4}} + \frac{6 b d^{2} e^{a} e^{b x} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{b^{4} + 20 b^{2} d^{2} + 64 d^{4}} + \frac{10 d^{3} e^{a} e^{b x} \sin^{4}{\left(c + d x \right)}}{b^{4} + 20 b^{2} d^{2} + 64 d^{4}} - \frac{12 d^{3} e^{a} e^{b x} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{b^{4} + 20 b^{2} d^{2} + 64 d^{4}} - \frac{6 d^{3} e^{a} e^{b x} \cos^{4}{\left(c + d x \right)}}{b^{4} + 20 b^{2} d^{2} + 64 d^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*exp(a)*sin(c)**3*cos(c), Eq(b, 0) & Eq(d, 0)), (I*x*exp(a)*exp(-4*I*d*x)*sin(c + d*x)**4/16 + x*exp(a)*exp(-4*I*d*x)*sin(c + d*x)**3*cos(c + d*x)/4 - 3*I*x*exp(a)*exp(-4*I*d*x)*sin(c + d*x)**2*cos(c + d*x)**2/8 - x*exp(a)*exp(-4*I*d*x)*sin(c + d*x)*cos(c + d*x)**3/4 + I*x*exp(a)*exp(-4*I*d*x)*cos(c + d*x)**4/16 - exp(a)*exp(-4*I*d*x)*sin(c + d*x)**4/(24*d) + 11*I*exp(a)*exp(-4*I*d*x)*sin(c + d*x)**3*cos(c + d*x)/(48*d) + 5*I*exp(a)*exp(-4*I*d*x)*sin(c + d*x)*cos(c + d*x)**3/(48*d) + exp(a)*exp(-4*I*d*x)*cos(c + d*x)**4/(24*d), Eq(b, -4*I*d)), (I*x*exp(a)*exp(-2*I*d*x)*sin(c + d*x)**4/8 + x*exp(a)*exp(-2*I*d*x)*sin(c + d*x)**3*cos(c + d*x)/4 + x*exp(a)*exp(-2*I*d*x)*sin(c + d*x)*cos(c + d*x)**3/4 - I*x*exp(a)*exp(-2*I*d*x)*cos(c + d*x)**4/8 + exp(a)*exp(-2*I*d*x)*sin(c + d*x)**4/(16*d) - exp(a)*exp(-2*I*d*x)*sin(c + d*x)**2*cos(c + d*x)**2/(4*d) + I*exp(a)*exp(-2*I*d*x)*sin(c + d*x)*cos(c + d*x)**3/(6*d) + exp(a)*exp(-2*I*d*x)*cos(c + d*x)**4/(48*d), Eq(b, -2*I*d)), (-I*x*exp(a)*exp(2*I*d*x)*sin(c + d*x)**4/8 + x*exp(a)*exp(2*I*d*x)*sin(c + d*x)**3*cos(c + d*x)/4 + x*exp(a)*exp(2*I*d*x)*sin(c + d*x)*cos(c + d*x)**3/4 + I*x*exp(a)*exp(2*I*d*x)*cos(c + d*x)**4/8 + exp(a)*exp(2*I*d*x)*sin(c + d*x)**4/(16*d) - exp(a)*exp(2*I*d*x)*sin(c + d*x)**2*cos(c + d*x)**2/(4*d) - I*exp(a)*exp(2*I*d*x)*sin(c + d*x)*cos(c + d*x)**3/(6*d) + exp(a)*exp(2*I*d*x)*cos(c + d*x)**4/(48*d), Eq(b, 2*I*d)), (-I*x*exp(a)*exp(4*I*d*x)*sin(c + d*x)**4/16 + x*exp(a)*exp(4*I*d*x)*sin(c + d*x)**3*cos(c + d*x)/4 + 3*I*x*exp(a)*exp(4*I*d*x)*sin(c + d*x)**2*cos(c + d*x)**2/8 - x*exp(a)*exp(4*I*d*x)*sin(c + d*x)*cos(c + d*x)**3/4 - I*x*exp(a)*exp(4*I*d*x)*cos(c + d*x)**4/16 - exp(a)*exp(4*I*d*x)*sin(c + d*x)**4/(24*d) - 11*I*exp(a)*exp(4*I*d*x)*sin(c + d*x)**3*cos(c + d*x)/(48*d) - 5*I*exp(a)*exp(4*I*d*x)*sin(c + d*x)*cos(c + d*x)**3/(48*d) + exp(a)*exp(4*I*d*x)*cos(c + d*x)**4/(24*d), Eq(b, 4*I*d)), (b**3*exp(a)*exp(b*x)*sin(c + d*x)**3*cos(c + d*x)/(b**4 + 20*b**2*d**2 + 64*d**4) + b**2*d*exp(a)*exp(b*x)*sin(c + d*x)**4/(b**4 + 20*b**2*d**2 + 64*d**4) - 3*b**2*d*exp(a)*exp(b*x)*sin(c + d*x)**2*cos(c + d*x)**2/(b**4 + 20*b**2*d**2 + 64*d**4) + 10*b*d**2*exp(a)*exp(b*x)*sin(c + d*x)**3*cos(c + d*x)/(b**4 + 20*b**2*d**2 + 64*d**4) + 6*b*d**2*exp(a)*exp(b*x)*sin(c + d*x)*cos(c + d*x)**3/(b**4 + 20*b**2*d**2 + 64*d**4) + 10*d**3*exp(a)*exp(b*x)*sin(c + d*x)**4/(b**4 + 20*b**2*d**2 + 64*d**4) - 12*d**3*exp(a)*exp(b*x)*sin(c + d*x)**2*cos(c + d*x)**2/(b**4 + 20*b**2*d**2 + 64*d**4) - 6*d**3*exp(a)*exp(b*x)*cos(c + d*x)**4/(b**4 + 20*b**2*d**2 + 64*d**4), True))","A",0
41,1,1040,0,44.752412," ","integrate(exp(b*x+a)*cos(d*x+c)**2*sin(d*x+c),x)","\begin{cases} x e^{a} \sin{\left(c \right)} \cos^{2}{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\- \frac{x e^{a} e^{- 3 i d x} \sin^{3}{\left(c + d x \right)}}{8} + \frac{3 i x e^{a} e^{- 3 i d x} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8} + \frac{3 x e^{a} e^{- 3 i d x} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} - \frac{i x e^{a} e^{- 3 i d x} \cos^{3}{\left(c + d x \right)}}{8} + \frac{i e^{a} e^{- 3 i d x} \sin^{3}{\left(c + d x \right)}}{24 d} + \frac{i e^{a} e^{- 3 i d x} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} + \frac{e^{a} e^{- 3 i d x} \cos^{3}{\left(c + d x \right)}}{24 d} & \text{for}\: b = - 3 i d \\\frac{x e^{a} e^{- i d x} \sin^{3}{\left(c + d x \right)}}{8} - \frac{i x e^{a} e^{- i d x} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8} + \frac{x e^{a} e^{- i d x} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} - \frac{i x e^{a} e^{- i d x} \cos^{3}{\left(c + d x \right)}}{8} - \frac{i e^{a} e^{- i d x} \sin^{3}{\left(c + d x \right)}}{8 d} - \frac{i e^{a} e^{- i d x} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} - \frac{3 e^{a} e^{- i d x} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: b = - i d \\\frac{x e^{a} e^{i d x} \sin^{3}{\left(c + d x \right)}}{8} + \frac{i x e^{a} e^{i d x} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8} + \frac{x e^{a} e^{i d x} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{i x e^{a} e^{i d x} \cos^{3}{\left(c + d x \right)}}{8} + \frac{i e^{a} e^{i d x} \sin^{3}{\left(c + d x \right)}}{8 d} + \frac{i e^{a} e^{i d x} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} - \frac{3 e^{a} e^{i d x} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: b = i d \\- \frac{x e^{a} e^{3 i d x} \sin^{3}{\left(c + d x \right)}}{8} - \frac{3 i x e^{a} e^{3 i d x} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8} + \frac{3 x e^{a} e^{3 i d x} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{i x e^{a} e^{3 i d x} \cos^{3}{\left(c + d x \right)}}{8} - \frac{i e^{a} e^{3 i d x} \sin^{3}{\left(c + d x \right)}}{24 d} - \frac{i e^{a} e^{3 i d x} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} + \frac{e^{a} e^{3 i d x} \cos^{3}{\left(c + d x \right)}}{24 d} & \text{for}\: b = 3 i d \\\frac{b^{3} e^{a} e^{b x} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{b^{4} + 10 b^{2} d^{2} + 9 d^{4}} + \frac{2 b^{2} d e^{a} e^{b x} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{b^{4} + 10 b^{2} d^{2} + 9 d^{4}} - \frac{b^{2} d e^{a} e^{b x} \cos^{3}{\left(c + d x \right)}}{b^{4} + 10 b^{2} d^{2} + 9 d^{4}} + \frac{2 b d^{2} e^{a} e^{b x} \sin^{3}{\left(c + d x \right)}}{b^{4} + 10 b^{2} d^{2} + 9 d^{4}} + \frac{3 b d^{2} e^{a} e^{b x} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{b^{4} + 10 b^{2} d^{2} + 9 d^{4}} - \frac{3 d^{3} e^{a} e^{b x} \cos^{3}{\left(c + d x \right)}}{b^{4} + 10 b^{2} d^{2} + 9 d^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*exp(a)*sin(c)*cos(c)**2, Eq(b, 0) & Eq(d, 0)), (-x*exp(a)*exp(-3*I*d*x)*sin(c + d*x)**3/8 + 3*I*x*exp(a)*exp(-3*I*d*x)*sin(c + d*x)**2*cos(c + d*x)/8 + 3*x*exp(a)*exp(-3*I*d*x)*sin(c + d*x)*cos(c + d*x)**2/8 - I*x*exp(a)*exp(-3*I*d*x)*cos(c + d*x)**3/8 + I*exp(a)*exp(-3*I*d*x)*sin(c + d*x)**3/(24*d) + I*exp(a)*exp(-3*I*d*x)*sin(c + d*x)*cos(c + d*x)**2/(4*d) + exp(a)*exp(-3*I*d*x)*cos(c + d*x)**3/(24*d), Eq(b, -3*I*d)), (x*exp(a)*exp(-I*d*x)*sin(c + d*x)**3/8 - I*x*exp(a)*exp(-I*d*x)*sin(c + d*x)**2*cos(c + d*x)/8 + x*exp(a)*exp(-I*d*x)*sin(c + d*x)*cos(c + d*x)**2/8 - I*x*exp(a)*exp(-I*d*x)*cos(c + d*x)**3/8 - I*exp(a)*exp(-I*d*x)*sin(c + d*x)**3/(8*d) - I*exp(a)*exp(-I*d*x)*sin(c + d*x)*cos(c + d*x)**2/(4*d) - 3*exp(a)*exp(-I*d*x)*cos(c + d*x)**3/(8*d), Eq(b, -I*d)), (x*exp(a)*exp(I*d*x)*sin(c + d*x)**3/8 + I*x*exp(a)*exp(I*d*x)*sin(c + d*x)**2*cos(c + d*x)/8 + x*exp(a)*exp(I*d*x)*sin(c + d*x)*cos(c + d*x)**2/8 + I*x*exp(a)*exp(I*d*x)*cos(c + d*x)**3/8 + I*exp(a)*exp(I*d*x)*sin(c + d*x)**3/(8*d) + I*exp(a)*exp(I*d*x)*sin(c + d*x)*cos(c + d*x)**2/(4*d) - 3*exp(a)*exp(I*d*x)*cos(c + d*x)**3/(8*d), Eq(b, I*d)), (-x*exp(a)*exp(3*I*d*x)*sin(c + d*x)**3/8 - 3*I*x*exp(a)*exp(3*I*d*x)*sin(c + d*x)**2*cos(c + d*x)/8 + 3*x*exp(a)*exp(3*I*d*x)*sin(c + d*x)*cos(c + d*x)**2/8 + I*x*exp(a)*exp(3*I*d*x)*cos(c + d*x)**3/8 - I*exp(a)*exp(3*I*d*x)*sin(c + d*x)**3/(24*d) - I*exp(a)*exp(3*I*d*x)*sin(c + d*x)*cos(c + d*x)**2/(4*d) + exp(a)*exp(3*I*d*x)*cos(c + d*x)**3/(24*d), Eq(b, 3*I*d)), (b**3*exp(a)*exp(b*x)*sin(c + d*x)*cos(c + d*x)**2/(b**4 + 10*b**2*d**2 + 9*d**4) + 2*b**2*d*exp(a)*exp(b*x)*sin(c + d*x)**2*cos(c + d*x)/(b**4 + 10*b**2*d**2 + 9*d**4) - b**2*d*exp(a)*exp(b*x)*cos(c + d*x)**3/(b**4 + 10*b**2*d**2 + 9*d**4) + 2*b*d**2*exp(a)*exp(b*x)*sin(c + d*x)**3/(b**4 + 10*b**2*d**2 + 9*d**4) + 3*b*d**2*exp(a)*exp(b*x)*sin(c + d*x)*cos(c + d*x)**2/(b**4 + 10*b**2*d**2 + 9*d**4) - 3*d**3*exp(a)*exp(b*x)*cos(c + d*x)**3/(b**4 + 10*b**2*d**2 + 9*d**4), True))","A",0
42,1,850,0,94.597070," ","integrate(exp(b*x+a)*cos(d*x+c)**2*sin(d*x+c)**2,x)","\begin{cases} x e^{a} \sin^{2}{\left(c \right)} \cos^{2}{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\\left(\frac{x \sin^{4}{\left(c + d x \right)}}{8} + \frac{x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{x \cos^{4}{\left(c + d x \right)}}{8} + \frac{\sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{\sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d}\right) e^{a} & \text{for}\: b = 0 \\- \frac{x e^{a} e^{- 4 i d x} \sin^{4}{\left(c + d x \right)}}{16} + \frac{i x e^{a} e^{- 4 i d x} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4} + \frac{3 x e^{a} e^{- 4 i d x} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} - \frac{i x e^{a} e^{- 4 i d x} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4} - \frac{x e^{a} e^{- 4 i d x} \cos^{4}{\left(c + d x \right)}}{16} + \frac{i e^{a} e^{- 4 i d x} \sin^{4}{\left(c + d x \right)}}{24 d} + \frac{5 e^{a} e^{- 4 i d x} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{48 d} - \frac{5 e^{a} e^{- 4 i d x} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{48 d} + \frac{i e^{a} e^{- 4 i d x} \cos^{4}{\left(c + d x \right)}}{24 d} & \text{for}\: b = - 4 i d \\- \frac{x e^{a} e^{4 i d x} \sin^{4}{\left(c + d x \right)}}{16} - \frac{i x e^{a} e^{4 i d x} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4} + \frac{3 x e^{a} e^{4 i d x} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{i x e^{a} e^{4 i d x} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4} - \frac{x e^{a} e^{4 i d x} \cos^{4}{\left(c + d x \right)}}{16} - \frac{i e^{a} e^{4 i d x} \sin^{4}{\left(c + d x \right)}}{24 d} + \frac{5 e^{a} e^{4 i d x} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{48 d} - \frac{5 e^{a} e^{4 i d x} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{48 d} - \frac{i e^{a} e^{4 i d x} \cos^{4}{\left(c + d x \right)}}{24 d} & \text{for}\: b = 4 i d \\\frac{b^{2} e^{a} e^{b x} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{b^{3} + 16 b d^{2}} + \frac{2 b d e^{a} e^{b x} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{b^{3} + 16 b d^{2}} - \frac{2 b d e^{a} e^{b x} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{b^{3} + 16 b d^{2}} + \frac{2 d^{2} e^{a} e^{b x} \sin^{4}{\left(c + d x \right)}}{b^{3} + 16 b d^{2}} + \frac{4 d^{2} e^{a} e^{b x} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{b^{3} + 16 b d^{2}} + \frac{2 d^{2} e^{a} e^{b x} \cos^{4}{\left(c + d x \right)}}{b^{3} + 16 b d^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*exp(a)*sin(c)**2*cos(c)**2, Eq(b, 0) & Eq(d, 0)), ((x*sin(c + d*x)**4/8 + x*sin(c + d*x)**2*cos(c + d*x)**2/4 + x*cos(c + d*x)**4/8 + sin(c + d*x)**3*cos(c + d*x)/(8*d) - sin(c + d*x)*cos(c + d*x)**3/(8*d))*exp(a), Eq(b, 0)), (-x*exp(a)*exp(-4*I*d*x)*sin(c + d*x)**4/16 + I*x*exp(a)*exp(-4*I*d*x)*sin(c + d*x)**3*cos(c + d*x)/4 + 3*x*exp(a)*exp(-4*I*d*x)*sin(c + d*x)**2*cos(c + d*x)**2/8 - I*x*exp(a)*exp(-4*I*d*x)*sin(c + d*x)*cos(c + d*x)**3/4 - x*exp(a)*exp(-4*I*d*x)*cos(c + d*x)**4/16 + I*exp(a)*exp(-4*I*d*x)*sin(c + d*x)**4/(24*d) + 5*exp(a)*exp(-4*I*d*x)*sin(c + d*x)**3*cos(c + d*x)/(48*d) - 5*exp(a)*exp(-4*I*d*x)*sin(c + d*x)*cos(c + d*x)**3/(48*d) + I*exp(a)*exp(-4*I*d*x)*cos(c + d*x)**4/(24*d), Eq(b, -4*I*d)), (-x*exp(a)*exp(4*I*d*x)*sin(c + d*x)**4/16 - I*x*exp(a)*exp(4*I*d*x)*sin(c + d*x)**3*cos(c + d*x)/4 + 3*x*exp(a)*exp(4*I*d*x)*sin(c + d*x)**2*cos(c + d*x)**2/8 + I*x*exp(a)*exp(4*I*d*x)*sin(c + d*x)*cos(c + d*x)**3/4 - x*exp(a)*exp(4*I*d*x)*cos(c + d*x)**4/16 - I*exp(a)*exp(4*I*d*x)*sin(c + d*x)**4/(24*d) + 5*exp(a)*exp(4*I*d*x)*sin(c + d*x)**3*cos(c + d*x)/(48*d) - 5*exp(a)*exp(4*I*d*x)*sin(c + d*x)*cos(c + d*x)**3/(48*d) - I*exp(a)*exp(4*I*d*x)*cos(c + d*x)**4/(24*d), Eq(b, 4*I*d)), (b**2*exp(a)*exp(b*x)*sin(c + d*x)**2*cos(c + d*x)**2/(b**3 + 16*b*d**2) + 2*b*d*exp(a)*exp(b*x)*sin(c + d*x)**3*cos(c + d*x)/(b**3 + 16*b*d**2) - 2*b*d*exp(a)*exp(b*x)*sin(c + d*x)*cos(c + d*x)**3/(b**3 + 16*b*d**2) + 2*d**2*exp(a)*exp(b*x)*sin(c + d*x)**4/(b**3 + 16*b*d**2) + 4*d**2*exp(a)*exp(b*x)*sin(c + d*x)**2*cos(c + d*x)**2/(b**3 + 16*b*d**2) + 2*d**2*exp(a)*exp(b*x)*cos(c + d*x)**4/(b**3 + 16*b*d**2), True))","A",0
43,-1,0,0,0.000000," ","integrate(exp(b*x+a)*cos(d*x+c)**2*sin(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
44,1,1357,0,146.899384," ","integrate(exp(b*x+a)*cos(d*x+c)**3*sin(d*x+c),x)","\begin{cases} x e^{a} \sin{\left(c \right)} \cos^{3}{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\- \frac{i x e^{a} e^{- 4 i d x} \sin^{4}{\left(c + d x \right)}}{16} - \frac{x e^{a} e^{- 4 i d x} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4} + \frac{3 i x e^{a} e^{- 4 i d x} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{x e^{a} e^{- 4 i d x} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4} - \frac{i x e^{a} e^{- 4 i d x} \cos^{4}{\left(c + d x \right)}}{16} - \frac{e^{a} e^{- 4 i d x} \sin^{4}{\left(c + d x \right)}}{24 d} + \frac{5 i e^{a} e^{- 4 i d x} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{48 d} + \frac{11 i e^{a} e^{- 4 i d x} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{48 d} + \frac{e^{a} e^{- 4 i d x} \cos^{4}{\left(c + d x \right)}}{24 d} & \text{for}\: b = - 4 i d \\\frac{i x e^{a} e^{- 2 i d x} \sin^{4}{\left(c + d x \right)}}{8} + \frac{x e^{a} e^{- 2 i d x} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4} + \frac{x e^{a} e^{- 2 i d x} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4} - \frac{i x e^{a} e^{- 2 i d x} \cos^{4}{\left(c + d x \right)}}{8} + \frac{e^{a} e^{- 2 i d x} \sin^{4}{\left(c + d x \right)}}{16 d} + \frac{e^{a} e^{- 2 i d x} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} - \frac{i e^{a} e^{- 2 i d x} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} - \frac{7 e^{a} e^{- 2 i d x} \cos^{4}{\left(c + d x \right)}}{48 d} & \text{for}\: b = - 2 i d \\- \frac{i x e^{a} e^{2 i d x} \sin^{4}{\left(c + d x \right)}}{8} + \frac{x e^{a} e^{2 i d x} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4} + \frac{x e^{a} e^{2 i d x} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4} + \frac{i x e^{a} e^{2 i d x} \cos^{4}{\left(c + d x \right)}}{8} + \frac{e^{a} e^{2 i d x} \sin^{4}{\left(c + d x \right)}}{16 d} + \frac{e^{a} e^{2 i d x} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} + \frac{i e^{a} e^{2 i d x} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} - \frac{7 e^{a} e^{2 i d x} \cos^{4}{\left(c + d x \right)}}{48 d} & \text{for}\: b = 2 i d \\\frac{i x e^{a} e^{4 i d x} \sin^{4}{\left(c + d x \right)}}{16} - \frac{x e^{a} e^{4 i d x} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4} - \frac{3 i x e^{a} e^{4 i d x} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{x e^{a} e^{4 i d x} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4} + \frac{i x e^{a} e^{4 i d x} \cos^{4}{\left(c + d x \right)}}{16} - \frac{e^{a} e^{4 i d x} \sin^{4}{\left(c + d x \right)}}{24 d} - \frac{5 i e^{a} e^{4 i d x} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{48 d} - \frac{11 i e^{a} e^{4 i d x} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{48 d} + \frac{e^{a} e^{4 i d x} \cos^{4}{\left(c + d x \right)}}{24 d} & \text{for}\: b = 4 i d \\\frac{b^{3} e^{a} e^{b x} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{b^{4} + 20 b^{2} d^{2} + 64 d^{4}} + \frac{3 b^{2} d e^{a} e^{b x} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{b^{4} + 20 b^{2} d^{2} + 64 d^{4}} - \frac{b^{2} d e^{a} e^{b x} \cos^{4}{\left(c + d x \right)}}{b^{4} + 20 b^{2} d^{2} + 64 d^{4}} + \frac{6 b d^{2} e^{a} e^{b x} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{b^{4} + 20 b^{2} d^{2} + 64 d^{4}} + \frac{10 b d^{2} e^{a} e^{b x} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{b^{4} + 20 b^{2} d^{2} + 64 d^{4}} + \frac{6 d^{3} e^{a} e^{b x} \sin^{4}{\left(c + d x \right)}}{b^{4} + 20 b^{2} d^{2} + 64 d^{4}} + \frac{12 d^{3} e^{a} e^{b x} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{b^{4} + 20 b^{2} d^{2} + 64 d^{4}} - \frac{10 d^{3} e^{a} e^{b x} \cos^{4}{\left(c + d x \right)}}{b^{4} + 20 b^{2} d^{2} + 64 d^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*exp(a)*sin(c)*cos(c)**3, Eq(b, 0) & Eq(d, 0)), (-I*x*exp(a)*exp(-4*I*d*x)*sin(c + d*x)**4/16 - x*exp(a)*exp(-4*I*d*x)*sin(c + d*x)**3*cos(c + d*x)/4 + 3*I*x*exp(a)*exp(-4*I*d*x)*sin(c + d*x)**2*cos(c + d*x)**2/8 + x*exp(a)*exp(-4*I*d*x)*sin(c + d*x)*cos(c + d*x)**3/4 - I*x*exp(a)*exp(-4*I*d*x)*cos(c + d*x)**4/16 - exp(a)*exp(-4*I*d*x)*sin(c + d*x)**4/(24*d) + 5*I*exp(a)*exp(-4*I*d*x)*sin(c + d*x)**3*cos(c + d*x)/(48*d) + 11*I*exp(a)*exp(-4*I*d*x)*sin(c + d*x)*cos(c + d*x)**3/(48*d) + exp(a)*exp(-4*I*d*x)*cos(c + d*x)**4/(24*d), Eq(b, -4*I*d)), (I*x*exp(a)*exp(-2*I*d*x)*sin(c + d*x)**4/8 + x*exp(a)*exp(-2*I*d*x)*sin(c + d*x)**3*cos(c + d*x)/4 + x*exp(a)*exp(-2*I*d*x)*sin(c + d*x)*cos(c + d*x)**3/4 - I*x*exp(a)*exp(-2*I*d*x)*cos(c + d*x)**4/8 + exp(a)*exp(-2*I*d*x)*sin(c + d*x)**4/(16*d) + exp(a)*exp(-2*I*d*x)*sin(c + d*x)**2*cos(c + d*x)**2/(4*d) - I*exp(a)*exp(-2*I*d*x)*sin(c + d*x)*cos(c + d*x)**3/(6*d) - 7*exp(a)*exp(-2*I*d*x)*cos(c + d*x)**4/(48*d), Eq(b, -2*I*d)), (-I*x*exp(a)*exp(2*I*d*x)*sin(c + d*x)**4/8 + x*exp(a)*exp(2*I*d*x)*sin(c + d*x)**3*cos(c + d*x)/4 + x*exp(a)*exp(2*I*d*x)*sin(c + d*x)*cos(c + d*x)**3/4 + I*x*exp(a)*exp(2*I*d*x)*cos(c + d*x)**4/8 + exp(a)*exp(2*I*d*x)*sin(c + d*x)**4/(16*d) + exp(a)*exp(2*I*d*x)*sin(c + d*x)**2*cos(c + d*x)**2/(4*d) + I*exp(a)*exp(2*I*d*x)*sin(c + d*x)*cos(c + d*x)**3/(6*d) - 7*exp(a)*exp(2*I*d*x)*cos(c + d*x)**4/(48*d), Eq(b, 2*I*d)), (I*x*exp(a)*exp(4*I*d*x)*sin(c + d*x)**4/16 - x*exp(a)*exp(4*I*d*x)*sin(c + d*x)**3*cos(c + d*x)/4 - 3*I*x*exp(a)*exp(4*I*d*x)*sin(c + d*x)**2*cos(c + d*x)**2/8 + x*exp(a)*exp(4*I*d*x)*sin(c + d*x)*cos(c + d*x)**3/4 + I*x*exp(a)*exp(4*I*d*x)*cos(c + d*x)**4/16 - exp(a)*exp(4*I*d*x)*sin(c + d*x)**4/(24*d) - 5*I*exp(a)*exp(4*I*d*x)*sin(c + d*x)**3*cos(c + d*x)/(48*d) - 11*I*exp(a)*exp(4*I*d*x)*sin(c + d*x)*cos(c + d*x)**3/(48*d) + exp(a)*exp(4*I*d*x)*cos(c + d*x)**4/(24*d), Eq(b, 4*I*d)), (b**3*exp(a)*exp(b*x)*sin(c + d*x)*cos(c + d*x)**3/(b**4 + 20*b**2*d**2 + 64*d**4) + 3*b**2*d*exp(a)*exp(b*x)*sin(c + d*x)**2*cos(c + d*x)**2/(b**4 + 20*b**2*d**2 + 64*d**4) - b**2*d*exp(a)*exp(b*x)*cos(c + d*x)**4/(b**4 + 20*b**2*d**2 + 64*d**4) + 6*b*d**2*exp(a)*exp(b*x)*sin(c + d*x)**3*cos(c + d*x)/(b**4 + 20*b**2*d**2 + 64*d**4) + 10*b*d**2*exp(a)*exp(b*x)*sin(c + d*x)*cos(c + d*x)**3/(b**4 + 20*b**2*d**2 + 64*d**4) + 6*d**3*exp(a)*exp(b*x)*sin(c + d*x)**4/(b**4 + 20*b**2*d**2 + 64*d**4) + 12*d**3*exp(a)*exp(b*x)*sin(c + d*x)**2*cos(c + d*x)**2/(b**4 + 20*b**2*d**2 + 64*d**4) - 10*d**3*exp(a)*exp(b*x)*cos(c + d*x)**4/(b**4 + 20*b**2*d**2 + 64*d**4), True))","A",0
45,-1,0,0,0.000000," ","integrate(exp(b*x+a)*cos(d*x+c)**3*sin(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
46,-1,0,0,0.000000," ","integrate(exp(b*x+a)*cos(d*x+c)**3*sin(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
47,1,27,0,0.637772," ","integrate(exp(x)*x*sin(x),x)","\frac{x e^{x} \sin{\left(x \right)}}{2} - \frac{x e^{x} \cos{\left(x \right)}}{2} + \frac{e^{x} \cos{\left(x \right)}}{2}"," ",0,"x*exp(x)*sin(x)/2 - x*exp(x)*cos(x)/2 + exp(x)*cos(x)/2","A",0
48,1,48,0,1.555791," ","integrate(exp(x)*x**2*sin(x),x)","\frac{x^{2} e^{x} \sin{\left(x \right)}}{2} - \frac{x^{2} e^{x} \cos{\left(x \right)}}{2} + x e^{x} \cos{\left(x \right)} - \frac{e^{x} \sin{\left(x \right)}}{2} - \frac{e^{x} \cos{\left(x \right)}}{2}"," ",0,"x**2*exp(x)*sin(x)/2 - x**2*exp(x)*cos(x)/2 + x*exp(x)*cos(x) - exp(x)*sin(x)/2 - exp(x)*cos(x)/2","A",0
49,1,27,0,0.625428," ","integrate(exp(x)*x*cos(x),x)","\frac{x e^{x} \sin{\left(x \right)}}{2} + \frac{x e^{x} \cos{\left(x \right)}}{2} - \frac{e^{x} \sin{\left(x \right)}}{2}"," ",0,"x*exp(x)*sin(x)/2 + x*exp(x)*cos(x)/2 - exp(x)*sin(x)/2","A",0
50,1,48,0,1.557270," ","integrate(exp(x)*x**2*cos(x),x)","\frac{x^{2} e^{x} \sin{\left(x \right)}}{2} + \frac{x^{2} e^{x} \cos{\left(x \right)}}{2} - x e^{x} \sin{\left(x \right)} + \frac{e^{x} \sin{\left(x \right)}}{2} - \frac{e^{x} \cos{\left(x \right)}}{2}"," ",0,"x**2*exp(x)*sin(x)/2 + x**2*exp(x)*cos(x)/2 - x*exp(x)*sin(x) + exp(x)*sin(x)/2 - exp(x)*cos(x)/2","A",0
51,1,27,0,0.247985," ","integrate(exp(3*x)*(-5*cos(4*x)+2*sin(4*x)),x)","- \frac{14 e^{3 x} \sin{\left(4 x \right)}}{25} - \frac{23 e^{3 x} \cos{\left(4 x \right)}}{25}"," ",0,"-14*exp(3*x)*sin(4*x)/25 - 23*exp(3*x)*cos(4*x)/25","A",0
52,1,32,0,0.466392," ","integrate(sin(x)/exp(x)+exp(x)*sin(x),x)","\frac{e^{x} \sin{\left(x \right)}}{2} - \frac{e^{x} \cos{\left(x \right)}}{2} - \frac{e^{- x} \sin{\left(x \right)}}{2} - \frac{e^{- x} \cos{\left(x \right)}}{2}"," ",0,"exp(x)*sin(x)/2 - exp(x)*cos(x)/2 - exp(-x)*sin(x)/2 - exp(-x)*cos(x)/2","A",0
53,0,0,0,0.000000," ","integrate(F**(b*x+a)*cos(d*x+c)/(e+e*sin(d*x+c)),x)","\frac{\int \frac{F^{a} F^{b x} \cos{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{e}"," ",0,"Integral(F**a*F**(b*x)*cos(c + d*x)/(sin(c + d*x) + 1), x)/e","F",0
54,0,0,0,0.000000," ","integrate(F**(b*x+a)*cos(d*x+c)/(e-e*sin(d*x+c)),x)","- \frac{\int \frac{F^{a} F^{b x} \cos{\left(c + d x \right)}}{\sin{\left(c + d x \right)} - 1}\, dx}{e}"," ",0,"-Integral(F**a*F**(b*x)*cos(c + d*x)/(sin(c + d*x) - 1), x)/e","F",0
55,0,0,0,0.000000," ","integrate(F**(b*x+a)*sin(d*x+c)/(e+e*cos(d*x+c)),x)","\frac{\int \frac{F^{a} F^{b x} \sin{\left(c + d x \right)}}{\cos{\left(c + d x \right)} + 1}\, dx}{e}"," ",0,"Integral(F**a*F**(b*x)*sin(c + d*x)/(cos(c + d*x) + 1), x)/e","F",0
56,0,0,0,0.000000," ","integrate(F**(b*x+a)*sin(d*x+c)/(e-e*cos(d*x+c)),x)","- \frac{\int \frac{F^{a} F^{b x} \sin{\left(c + d x \right)}}{\cos{\left(c + d x \right)} - 1}\, dx}{e}"," ",0,"-Integral(F**a*F**(b*x)*sin(c + d*x)/(cos(c + d*x) - 1), x)/e","F",0
57,0,0,0,0.000000," ","integrate(exp(x**2)*sin(b*x),x)","\int e^{x^{2}} \sin{\left(b x \right)}\, dx"," ",0,"Integral(exp(x**2)*sin(b*x), x)","F",0
58,0,0,0,0.000000," ","integrate(exp(x**2)*cos(b*x),x)","\int e^{x^{2}} \cos{\left(b x \right)}\, dx"," ",0,"Integral(exp(x**2)*cos(b*x), x)","F",0
59,0,0,0,0.000000," ","integrate(exp(x**2)*sin(b*x+a),x)","\int e^{x^{2}} \sin{\left(a + b x \right)}\, dx"," ",0,"Integral(exp(x**2)*sin(a + b*x), x)","F",0
60,0,0,0,0.000000," ","integrate(exp(x**2)*cos(b*x+a),x)","\int e^{x^{2}} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral(exp(x**2)*cos(a + b*x), x)","F",0
61,1,29,0,6.225310," ","integrate(exp(2*x**2)*x*cos(2*x**2),x)","\frac{e^{2 x^{2}} \sin{\left(2 x^{2} \right)}}{8} + \frac{e^{2 x^{2}} \cos{\left(2 x^{2} \right)}}{8}"," ",0,"exp(2*x**2)*sin(2*x**2)/8 + exp(2*x**2)*cos(2*x**2)/8","A",0
62,1,5,0,0.229998," ","integrate(exp(x)*sin(exp(x)),x)","- \cos{\left(e^{x} \right)}"," ",0,"-cos(exp(x))","A",0
63,0,0,0,0.000000," ","integrate(exp(x)*csc(exp(x))*sec(exp(x)),x)","\int e^{x} \csc{\left(e^{x} \right)} \sec{\left(e^{x} \right)}\, dx"," ",0,"Integral(exp(x)*csc(exp(x))*sec(exp(x)), x)","F",0
64,1,3,0,0.225653," ","integrate(exp(x)*cos(exp(x)),x)","\sin{\left(e^{x} \right)}"," ",0,"sin(exp(x))","A",0
65,1,7,0,0.236709," ","integrate(exp(2*x)*cos(exp(2*x)),x)","\frac{\sin{\left(e^{2 x} \right)}}{2}"," ",0,"sin(exp(2*x))/2","A",0
66,1,10,0,0.372652," ","integrate(cos(exp(-2*x))/exp(2*x),x)","- \frac{\sin{\left(e^{- 2 x} \right)}}{2}"," ",0,"-sin(exp(-2*x))/2","A",0
67,1,12,0,10.677608," ","integrate(exp(2*x)*cos(exp(x)),x)","e^{x} \sin{\left(e^{x} \right)} + \cos{\left(e^{x} \right)}"," ",0,"exp(x)*sin(exp(x)) + cos(exp(x))","A",0
68,-1,0,0,0.000000," ","integrate(exp(-1+3*x)*cos(exp(-1+3*x))*sin(1+exp(-1+3*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
69,1,10,0,0.164380," ","integrate(exp(x)*tan(exp(x)),x)","\frac{\log{\left(\tan^{2}{\left(e^{x} \right)} + 1 \right)}}{2}"," ",0,"log(tan(exp(x))**2 + 1)/2","A",0
70,1,10,0,1.021290," ","integrate(exp(x)*sec(exp(x)),x)","\log{\left(\tan{\left(e^{x} \right)} + \sec{\left(e^{x} \right)} \right)}"," ",0,"log(tan(exp(x)) + sec(exp(x)))","A",0
71,1,3,0,0.602884," ","integrate(exp(x)*sec(exp(x))*tan(exp(x)),x)","\sec{\left(e^{x} \right)}"," ",0,"sec(exp(x))","A",0
72,1,5,0,0.805080," ","integrate(exp(x)*csc(exp(x))**2,x)","- \cot{\left(e^{x} \right)}"," ",0,"-cot(exp(x))","A",0
73,1,116,0,0.785113," ","integrate(exp(x)*sin(b*x+a),x)","\begin{cases} \frac{x e^{x} \sin{\left(a - i x \right)}}{2} + \frac{i x e^{x} \cos{\left(a - i x \right)}}{2} - \frac{i e^{x} \cos{\left(a - i x \right)}}{2} & \text{for}\: b = - i \\\frac{x e^{x} \sin{\left(a + i x \right)}}{2} - \frac{i x e^{x} \cos{\left(a + i x \right)}}{2} + \frac{i e^{x} \cos{\left(a + i x \right)}}{2} & \text{for}\: b = i \\- \frac{b e^{x} \cos{\left(a + b x \right)}}{b^{2} + 1} + \frac{e^{x} \sin{\left(a + b x \right)}}{b^{2} + 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*exp(x)*sin(a - I*x)/2 + I*x*exp(x)*cos(a - I*x)/2 - I*exp(x)*cos(a - I*x)/2, Eq(b, -I)), (x*exp(x)*sin(a + I*x)/2 - I*x*exp(x)*cos(a + I*x)/2 + I*exp(x)*cos(a + I*x)/2, Eq(b, I)), (-b*exp(x)*cos(a + b*x)/(b**2 + 1) + exp(x)*sin(a + b*x)/(b**2 + 1), True))","A",0
74,0,0,0,0.000000," ","integrate(exp(x)*sin(c*x**2+a),x)","\int e^{x} \sin{\left(a + c x^{2} \right)}\, dx"," ",0,"Integral(exp(x)*sin(a + c*x**2), x)","F",0
75,0,0,0,0.000000," ","integrate(exp(x)*sin(c*x**2+b*x+a),x)","\int e^{x} \sin{\left(a + b x + c x^{2} \right)}\, dx"," ",0,"Integral(exp(x)*sin(a + b*x + c*x**2), x)","F",0
76,0,0,0,0.000000," ","integrate(exp(x**2)*sin(b*x+a),x)","\int e^{x^{2}} \sin{\left(a + b x \right)}\, dx"," ",0,"Integral(exp(x**2)*sin(a + b*x), x)","F",0
77,0,0,0,0.000000," ","integrate(exp(x**2)*sin(c*x**2+a),x)","\int e^{x^{2}} \sin{\left(a + c x^{2} \right)}\, dx"," ",0,"Integral(exp(x**2)*sin(a + c*x**2), x)","F",0
78,0,0,0,0.000000," ","integrate(exp(x**2)*sin(c*x**2+b*x+a),x)","\int e^{x^{2}} \sin{\left(a + b x + c x^{2} \right)}\, dx"," ",0,"Integral(exp(x**2)*sin(a + b*x + c*x**2), x)","F",0
79,0,0,0,0.000000," ","integrate(f**(b*x+a)*sin(f*x**2+d),x)","\int f^{a + b x} \sin{\left(d + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + b*x)*sin(d + f*x**2), x)","F",0
80,0,0,0,0.000000," ","integrate(f**(b*x+a)*sin(f*x**2+d)**2,x)","\int f^{a + b x} \sin^{2}{\left(d + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + b*x)*sin(d + f*x**2)**2, x)","F",0
81,0,0,0,0.000000," ","integrate(f**(b*x+a)*sin(f*x**2+d)**3,x)","\int f^{a + b x} \sin^{3}{\left(d + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + b*x)*sin(d + f*x**2)**3, x)","F",0
82,0,0,0,0.000000," ","integrate(f**(b*x+a)*sin(f*x**2+e*x+d),x)","\int f^{a + b x} \sin{\left(d + e x + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + b*x)*sin(d + e*x + f*x**2), x)","F",0
83,0,0,0,0.000000," ","integrate(f**(b*x+a)*sin(f*x**2+e*x+d)**2,x)","\int f^{a + b x} \sin^{2}{\left(d + e x + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + b*x)*sin(d + e*x + f*x**2)**2, x)","F",0
84,-1,0,0,0.000000," ","integrate(f**(b*x+a)*sin(f*x**2+e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
85,0,0,0,0.000000," ","integrate(f**(c*x**2+a)*sin(e*x+d),x)","\int f^{a + c x^{2}} \sin{\left(d + e x \right)}\, dx"," ",0,"Integral(f**(a + c*x**2)*sin(d + e*x), x)","F",0
86,0,0,0,0.000000," ","integrate(f**(c*x**2+a)*sin(e*x+d)**2,x)","\int f^{a + c x^{2}} \sin^{2}{\left(d + e x \right)}\, dx"," ",0,"Integral(f**(a + c*x**2)*sin(d + e*x)**2, x)","F",0
87,0,0,0,0.000000," ","integrate(f**(c*x**2+a)*sin(e*x+d)**3,x)","\int f^{a + c x^{2}} \sin^{3}{\left(d + e x \right)}\, dx"," ",0,"Integral(f**(a + c*x**2)*sin(d + e*x)**3, x)","F",0
88,0,0,0,0.000000," ","integrate(f**(c*x**2+a)*sin(f*x**2+d),x)","\int f^{a + c x^{2}} \sin{\left(d + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + c*x**2)*sin(d + f*x**2), x)","F",0
89,0,0,0,0.000000," ","integrate(f**(c*x**2+a)*sin(f*x**2+d)**2,x)","\int f^{a + c x^{2}} \sin^{2}{\left(d + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + c*x**2)*sin(d + f*x**2)**2, x)","F",0
90,0,0,0,0.000000," ","integrate(f**(c*x**2+a)*sin(f*x**2+d)**3,x)","\int f^{a + c x^{2}} \sin^{3}{\left(d + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + c*x**2)*sin(d + f*x**2)**3, x)","F",0
91,0,0,0,0.000000," ","integrate(f**(c*x**2+a)*sin(f*x**2+e*x+d),x)","\int f^{a + c x^{2}} \sin{\left(d + e x + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + c*x**2)*sin(d + e*x + f*x**2), x)","F",0
92,0,0,0,0.000000," ","integrate(f**(c*x**2+a)*sin(f*x**2+e*x+d)**2,x)","\int f^{a + c x^{2}} \sin^{2}{\left(d + e x + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + c*x**2)*sin(d + e*x + f*x**2)**2, x)","F",0
93,-1,0,0,0.000000," ","integrate(f**(c*x**2+a)*sin(f*x**2+e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
94,0,0,0,0.000000," ","integrate(f**(c*x**2+b*x+a)*sin(e*x+d),x)","\int f^{a + b x + c x^{2}} \sin{\left(d + e x \right)}\, dx"," ",0,"Integral(f**(a + b*x + c*x**2)*sin(d + e*x), x)","F",0
95,0,0,0,0.000000," ","integrate(f**(c*x**2+b*x+a)*sin(e*x+d)**2,x)","\int f^{a + b x + c x^{2}} \sin^{2}{\left(d + e x \right)}\, dx"," ",0,"Integral(f**(a + b*x + c*x**2)*sin(d + e*x)**2, x)","F",0
96,-1,0,0,0.000000," ","integrate(f**(c*x**2+b*x+a)*sin(e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,0,0,0,0.000000," ","integrate(f**(c*x**2+b*x+a)*sin(f*x**2+d),x)","\int f^{a + b x + c x^{2}} \sin{\left(d + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + b*x + c*x**2)*sin(d + f*x**2), x)","F",0
98,0,0,0,0.000000," ","integrate(f**(c*x**2+b*x+a)*sin(f*x**2+d)**2,x)","\int f^{a + b x + c x^{2}} \sin^{2}{\left(d + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + b*x + c*x**2)*sin(d + f*x**2)**2, x)","F",0
99,-1,0,0,0.000000," ","integrate(f**(c*x**2+b*x+a)*sin(f*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,0,0,0,0.000000," ","integrate(f**(c*x**2+b*x+a)*sin(f*x**2+e*x+d),x)","\int f^{a + b x + c x^{2}} \sin{\left(d + e x + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + b*x + c*x**2)*sin(d + e*x + f*x**2), x)","F",0
101,-1,0,0,0.000000," ","integrate(f**(c*x**2+b*x+a)*sin(f*x**2+e*x+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
102,-1,0,0,0.000000," ","integrate(f**(c*x**2+b*x+a)*sin(f*x**2+e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
103,0,0,0,0.000000," ","integrate(f**(c*x**2+b*x+a)*sin(e*x**2+b*x+a),x)","\int f^{a + b x + c x^{2}} \sin{\left(a + b x + e x^{2} \right)}\, dx"," ",0,"Integral(f**(a + b*x + c*x**2)*sin(a + b*x + e*x**2), x)","F",0
104,1,112,0,0.773581," ","integrate(exp(x)*cos(b*x+a),x)","\begin{cases} - \frac{i x e^{x} \sin{\left(a - i x \right)}}{2} + \frac{x e^{x} \cos{\left(a - i x \right)}}{2} + \frac{e^{x} \cos{\left(a - i x \right)}}{2} & \text{for}\: b = - i \\\frac{i x e^{x} \sin{\left(a + i x \right)}}{2} + \frac{x e^{x} \cos{\left(a + i x \right)}}{2} + \frac{e^{x} \cos{\left(a + i x \right)}}{2} & \text{for}\: b = i \\\frac{b e^{x} \sin{\left(a + b x \right)}}{b^{2} + 1} + \frac{e^{x} \cos{\left(a + b x \right)}}{b^{2} + 1} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*x*exp(x)*sin(a - I*x)/2 + x*exp(x)*cos(a - I*x)/2 + exp(x)*cos(a - I*x)/2, Eq(b, -I)), (I*x*exp(x)*sin(a + I*x)/2 + x*exp(x)*cos(a + I*x)/2 + exp(x)*cos(a + I*x)/2, Eq(b, I)), (b*exp(x)*sin(a + b*x)/(b**2 + 1) + exp(x)*cos(a + b*x)/(b**2 + 1), True))","A",0
105,0,0,0,0.000000," ","integrate(exp(x)*cos(c*x**2+a),x)","\int e^{x} \cos{\left(a + c x^{2} \right)}\, dx"," ",0,"Integral(exp(x)*cos(a + c*x**2), x)","F",0
106,0,0,0,0.000000," ","integrate(exp(x)*cos(c*x**2+b*x+a),x)","\int e^{x} \cos{\left(a + b x + c x^{2} \right)}\, dx"," ",0,"Integral(exp(x)*cos(a + b*x + c*x**2), x)","F",0
107,0,0,0,0.000000," ","integrate(exp(x**2)*cos(b*x+a),x)","\int e^{x^{2}} \cos{\left(a + b x \right)}\, dx"," ",0,"Integral(exp(x**2)*cos(a + b*x), x)","F",0
108,0,0,0,0.000000," ","integrate(exp(x**2)*cos(c*x**2+a),x)","\int e^{x^{2}} \cos{\left(a + c x^{2} \right)}\, dx"," ",0,"Integral(exp(x**2)*cos(a + c*x**2), x)","F",0
109,0,0,0,0.000000," ","integrate(exp(x**2)*cos(c*x**2+b*x+a),x)","\int e^{x^{2}} \cos{\left(a + b x + c x^{2} \right)}\, dx"," ",0,"Integral(exp(x**2)*cos(a + b*x + c*x**2), x)","F",0
110,0,0,0,0.000000," ","integrate(f**(b*x+a)*cos(f*x**2+d),x)","\int f^{a + b x} \cos{\left(d + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + b*x)*cos(d + f*x**2), x)","F",0
111,0,0,0,0.000000," ","integrate(f**(b*x+a)*cos(f*x**2+d)**2,x)","\int f^{a + b x} \cos^{2}{\left(d + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + b*x)*cos(d + f*x**2)**2, x)","F",0
112,0,0,0,0.000000," ","integrate(f**(b*x+a)*cos(f*x**2+d)**3,x)","\int f^{a + b x} \cos^{3}{\left(d + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + b*x)*cos(d + f*x**2)**3, x)","F",0
113,0,0,0,0.000000," ","integrate(f**(b*x+a)*cos(f*x**2+e*x+d),x)","\int f^{a + b x} \cos{\left(d + e x + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + b*x)*cos(d + e*x + f*x**2), x)","F",0
114,0,0,0,0.000000," ","integrate(f**(b*x+a)*cos(f*x**2+e*x+d)**2,x)","\int f^{a + b x} \cos^{2}{\left(d + e x + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + b*x)*cos(d + e*x + f*x**2)**2, x)","F",0
115,0,0,0,0.000000," ","integrate(f**(b*x+a)*cos(f*x**2+e*x+d)**3,x)","\int f^{a + b x} \cos^{3}{\left(d + e x + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + b*x)*cos(d + e*x + f*x**2)**3, x)","F",0
116,0,0,0,0.000000," ","integrate(f**(c*x**2+a)*cos(e*x+d),x)","\int f^{a + c x^{2}} \cos{\left(d + e x \right)}\, dx"," ",0,"Integral(f**(a + c*x**2)*cos(d + e*x), x)","F",0
117,0,0,0,0.000000," ","integrate(f**(c*x**2+a)*cos(e*x+d)**2,x)","\int f^{a + c x^{2}} \cos^{2}{\left(d + e x \right)}\, dx"," ",0,"Integral(f**(a + c*x**2)*cos(d + e*x)**2, x)","F",0
118,0,0,0,0.000000," ","integrate(f**(c*x**2+a)*cos(e*x+d)**3,x)","\int f^{a + c x^{2}} \cos^{3}{\left(d + e x \right)}\, dx"," ",0,"Integral(f**(a + c*x**2)*cos(d + e*x)**3, x)","F",0
119,0,0,0,0.000000," ","integrate(f**(c*x**2+a)*cos(f*x**2+d),x)","\int f^{a + c x^{2}} \cos{\left(d + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + c*x**2)*cos(d + f*x**2), x)","F",0
120,0,0,0,0.000000," ","integrate(f**(c*x**2+a)*cos(f*x**2+d)**2,x)","\int f^{a + c x^{2}} \cos^{2}{\left(d + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + c*x**2)*cos(d + f*x**2)**2, x)","F",0
121,0,0,0,0.000000," ","integrate(f**(c*x**2+a)*cos(f*x**2+d)**3,x)","\int f^{a + c x^{2}} \cos^{3}{\left(d + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + c*x**2)*cos(d + f*x**2)**3, x)","F",0
122,0,0,0,0.000000," ","integrate(f**(c*x**2+a)*cos(f*x**2+e*x+d),x)","\int f^{a + c x^{2}} \cos{\left(d + e x + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + c*x**2)*cos(d + e*x + f*x**2), x)","F",0
123,0,0,0,0.000000," ","integrate(f**(c*x**2+a)*cos(f*x**2+e*x+d)**2,x)","\int f^{a + c x^{2}} \cos^{2}{\left(d + e x + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + c*x**2)*cos(d + e*x + f*x**2)**2, x)","F",0
124,-1,0,0,0.000000," ","integrate(f**(c*x**2+a)*cos(f*x**2+e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
125,0,0,0,0.000000," ","integrate(f**(c*x**2+b*x+a)*cos(e*x+d),x)","\int f^{a + b x + c x^{2}} \cos{\left(d + e x \right)}\, dx"," ",0,"Integral(f**(a + b*x + c*x**2)*cos(d + e*x), x)","F",0
126,0,0,0,0.000000," ","integrate(f**(c*x**2+b*x+a)*cos(e*x+d)**2,x)","\int f^{a + b x + c x^{2}} \cos^{2}{\left(d + e x \right)}\, dx"," ",0,"Integral(f**(a + b*x + c*x**2)*cos(d + e*x)**2, x)","F",0
127,-1,0,0,0.000000," ","integrate(f**(c*x**2+b*x+a)*cos(e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
128,0,0,0,0.000000," ","integrate(f**(c*x**2+b*x+a)*cos(f*x**2+d),x)","\int f^{a + b x + c x^{2}} \cos{\left(d + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + b*x + c*x**2)*cos(d + f*x**2), x)","F",0
129,0,0,0,0.000000," ","integrate(f**(c*x**2+b*x+a)*cos(f*x**2+d)**2,x)","\int f^{a + b x + c x^{2}} \cos^{2}{\left(d + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + b*x + c*x**2)*cos(d + f*x**2)**2, x)","F",0
130,-1,0,0,0.000000," ","integrate(f**(c*x**2+b*x+a)*cos(f*x**2+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
131,0,0,0,0.000000," ","integrate(f**(c*x**2+b*x+a)*cos(f*x**2+e*x+d),x)","\int f^{a + b x + c x^{2}} \cos{\left(d + e x + f x^{2} \right)}\, dx"," ",0,"Integral(f**(a + b*x + c*x**2)*cos(d + e*x + f*x**2), x)","F",0
132,-1,0,0,0.000000," ","integrate(f**(c*x**2+b*x+a)*cos(f*x**2+e*x+d)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
133,-1,0,0,0.000000," ","integrate(f**(c*x**2+b*x+a)*cos(f*x**2+e*x+d)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
134,0,0,0,0.000000," ","integrate(f**(c*x**2+b*x+a)*cos(e*x**2+b*x+a),x)","\int f^{a + b x + c x^{2}} \cos{\left(a + b x + e x^{2} \right)}\, dx"," ",0,"Integral(f**(a + b*x + c*x**2)*cos(a + b*x + e*x**2), x)","F",0
135,1,1760,0,58.623770," ","integrate(F**(c*(b*x+a))*(f+f*sin(e*x+d))**2,x)","\begin{cases} \frac{f^{2} x \sin^{2}{\left(d + e x \right)}}{2} + \frac{f^{2} x \cos^{2}{\left(d + e x \right)}}{2} + f^{2} x - \frac{f^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{2 e} - \frac{2 f^{2} \cos{\left(d + e x \right)}}{e} & \text{for}\: F = 1 \\\tilde{\infty} e^{4} f^{2} \left(e^{- \frac{2 i e}{b c}}\right)^{a c} \left(e^{- \frac{2 i e}{b c}}\right)^{b c x} \sin^{2}{\left(d + e x \right)} + \tilde{\infty} e^{4} f^{2} \left(e^{- \frac{2 i e}{b c}}\right)^{a c} \left(e^{- \frac{2 i e}{b c}}\right)^{b c x} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)} + \tilde{\infty} e^{4} f^{2} \left(e^{- \frac{2 i e}{b c}}\right)^{a c} \left(e^{- \frac{2 i e}{b c}}\right)^{b c x} \cos^{2}{\left(d + e x \right)} & \text{for}\: F = e^{- \frac{2 i e}{b c}} \\\tilde{\infty} e^{4} f^{2} \left(e^{- \frac{i e}{b c}}\right)^{a c} \left(e^{- \frac{i e}{b c}}\right)^{b c x} \sin{\left(d + e x \right)} + \tilde{\infty} e^{4} f^{2} \left(e^{- \frac{i e}{b c}}\right)^{a c} \left(e^{- \frac{i e}{b c}}\right)^{b c x} \cos{\left(d + e x \right)} & \text{for}\: F = e^{- \frac{i e}{b c}} \\\tilde{\infty} e^{4} f^{2} \left(e^{\frac{i e}{b c}}\right)^{a c} \left(e^{\frac{i e}{b c}}\right)^{b c x} \sin{\left(d + e x \right)} + \tilde{\infty} e^{4} f^{2} \left(e^{\frac{i e}{b c}}\right)^{a c} \left(e^{\frac{i e}{b c}}\right)^{b c x} \cos{\left(d + e x \right)} & \text{for}\: F = e^{\frac{i e}{b c}} \\\tilde{\infty} e^{4} f^{2} \left(e^{\frac{2 i e}{b c}}\right)^{a c} \left(e^{\frac{2 i e}{b c}}\right)^{b c x} \sin^{2}{\left(d + e x \right)} + \tilde{\infty} e^{4} f^{2} \left(e^{\frac{2 i e}{b c}}\right)^{a c} \left(e^{\frac{2 i e}{b c}}\right)^{b c x} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)} + \tilde{\infty} e^{4} f^{2} \left(e^{\frac{2 i e}{b c}}\right)^{a c} \left(e^{\frac{2 i e}{b c}}\right)^{b c x} \cos^{2}{\left(d + e x \right)} & \text{for}\: F = e^{\frac{2 i e}{b c}} \\F^{a c} \left(\frac{f^{2} x \sin^{2}{\left(d + e x \right)}}{2} + \frac{f^{2} x \cos^{2}{\left(d + e x \right)}}{2} + f^{2} x - \frac{f^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{2 e} - \frac{2 f^{2} \cos{\left(d + e x \right)}}{e}\right) & \text{for}\: b = 0 \\\frac{f^{2} x \sin^{2}{\left(d + e x \right)}}{2} + \frac{f^{2} x \cos^{2}{\left(d + e x \right)}}{2} + f^{2} x - \frac{f^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{2 e} - \frac{2 f^{2} \cos{\left(d + e x \right)}}{e} & \text{for}\: c = 0 \\\frac{F^{a c} F^{b c x} b^{4} c^{4} f^{2} \log{\left(F \right)}^{4} \sin^{2}{\left(d + e x \right)}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} + \frac{2 F^{a c} F^{b c x} b^{4} c^{4} f^{2} \log{\left(F \right)}^{4} \sin{\left(d + e x \right)}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} + \frac{F^{a c} F^{b c x} b^{4} c^{4} f^{2} \log{\left(F \right)}^{4}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} - \frac{2 F^{a c} F^{b c x} b^{3} c^{3} e f^{2} \log{\left(F \right)}^{3} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} - \frac{2 F^{a c} F^{b c x} b^{3} c^{3} e f^{2} \log{\left(F \right)}^{3} \cos{\left(d + e x \right)}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} + \frac{3 F^{a c} F^{b c x} b^{2} c^{2} e^{2} f^{2} \log{\left(F \right)}^{2} \sin^{2}{\left(d + e x \right)}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} + \frac{8 F^{a c} F^{b c x} b^{2} c^{2} e^{2} f^{2} \log{\left(F \right)}^{2} \sin{\left(d + e x \right)}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} + \frac{2 F^{a c} F^{b c x} b^{2} c^{2} e^{2} f^{2} \log{\left(F \right)}^{2} \cos^{2}{\left(d + e x \right)}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} + \frac{5 F^{a c} F^{b c x} b^{2} c^{2} e^{2} f^{2} \log{\left(F \right)}^{2}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} - \frac{2 F^{a c} F^{b c x} b c e^{3} f^{2} \log{\left(F \right)} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} - \frac{8 F^{a c} F^{b c x} b c e^{3} f^{2} \log{\left(F \right)} \cos{\left(d + e x \right)}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} + \frac{2 F^{a c} F^{b c x} e^{4} f^{2} \sin^{2}{\left(d + e x \right)}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} + \frac{2 F^{a c} F^{b c x} e^{4} f^{2} \cos^{2}{\left(d + e x \right)}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} + \frac{4 F^{a c} F^{b c x} e^{4} f^{2}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((f**2*x*sin(d + e*x)**2/2 + f**2*x*cos(d + e*x)**2/2 + f**2*x - f**2*sin(d + e*x)*cos(d + e*x)/(2*e) - 2*f**2*cos(d + e*x)/e, Eq(F, 1)), (zoo*e**4*f**2*exp(-2*I*e/(b*c))**(a*c)*exp(-2*I*e/(b*c))**(b*c*x)*sin(d + e*x)**2 + zoo*e**4*f**2*exp(-2*I*e/(b*c))**(a*c)*exp(-2*I*e/(b*c))**(b*c*x)*sin(d + e*x)*cos(d + e*x) + zoo*e**4*f**2*exp(-2*I*e/(b*c))**(a*c)*exp(-2*I*e/(b*c))**(b*c*x)*cos(d + e*x)**2, Eq(F, exp(-2*I*e/(b*c)))), (zoo*e**4*f**2*exp(-I*e/(b*c))**(a*c)*exp(-I*e/(b*c))**(b*c*x)*sin(d + e*x) + zoo*e**4*f**2*exp(-I*e/(b*c))**(a*c)*exp(-I*e/(b*c))**(b*c*x)*cos(d + e*x), Eq(F, exp(-I*e/(b*c)))), (zoo*e**4*f**2*exp(I*e/(b*c))**(a*c)*exp(I*e/(b*c))**(b*c*x)*sin(d + e*x) + zoo*e**4*f**2*exp(I*e/(b*c))**(a*c)*exp(I*e/(b*c))**(b*c*x)*cos(d + e*x), Eq(F, exp(I*e/(b*c)))), (zoo*e**4*f**2*exp(2*I*e/(b*c))**(a*c)*exp(2*I*e/(b*c))**(b*c*x)*sin(d + e*x)**2 + zoo*e**4*f**2*exp(2*I*e/(b*c))**(a*c)*exp(2*I*e/(b*c))**(b*c*x)*sin(d + e*x)*cos(d + e*x) + zoo*e**4*f**2*exp(2*I*e/(b*c))**(a*c)*exp(2*I*e/(b*c))**(b*c*x)*cos(d + e*x)**2, Eq(F, exp(2*I*e/(b*c)))), (F**(a*c)*(f**2*x*sin(d + e*x)**2/2 + f**2*x*cos(d + e*x)**2/2 + f**2*x - f**2*sin(d + e*x)*cos(d + e*x)/(2*e) - 2*f**2*cos(d + e*x)/e), Eq(b, 0)), (f**2*x*sin(d + e*x)**2/2 + f**2*x*cos(d + e*x)**2/2 + f**2*x - f**2*sin(d + e*x)*cos(d + e*x)/(2*e) - 2*f**2*cos(d + e*x)/e, Eq(c, 0)), (F**(a*c)*F**(b*c*x)*b**4*c**4*f**2*log(F)**4*sin(d + e*x)**2/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)) + 2*F**(a*c)*F**(b*c*x)*b**4*c**4*f**2*log(F)**4*sin(d + e*x)/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)) + F**(a*c)*F**(b*c*x)*b**4*c**4*f**2*log(F)**4/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)) - 2*F**(a*c)*F**(b*c*x)*b**3*c**3*e*f**2*log(F)**3*sin(d + e*x)*cos(d + e*x)/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)) - 2*F**(a*c)*F**(b*c*x)*b**3*c**3*e*f**2*log(F)**3*cos(d + e*x)/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)) + 3*F**(a*c)*F**(b*c*x)*b**2*c**2*e**2*f**2*log(F)**2*sin(d + e*x)**2/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)) + 8*F**(a*c)*F**(b*c*x)*b**2*c**2*e**2*f**2*log(F)**2*sin(d + e*x)/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)) + 2*F**(a*c)*F**(b*c*x)*b**2*c**2*e**2*f**2*log(F)**2*cos(d + e*x)**2/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)) + 5*F**(a*c)*F**(b*c*x)*b**2*c**2*e**2*f**2*log(F)**2/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)) - 2*F**(a*c)*F**(b*c*x)*b*c*e**3*f**2*log(F)*sin(d + e*x)*cos(d + e*x)/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)) - 8*F**(a*c)*F**(b*c*x)*b*c*e**3*f**2*log(F)*cos(d + e*x)/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)) + 2*F**(a*c)*F**(b*c*x)*e**4*f**2*sin(d + e*x)**2/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)) + 2*F**(a*c)*F**(b*c*x)*e**4*f**2*cos(d + e*x)**2/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)) + 4*F**(a*c)*F**(b*c*x)*e**4*f**2/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)), True))","A",0
136,1,408,0,7.368784," ","integrate(F**(c*(b*x+a))*(f+f*sin(e*x+d)),x)","\begin{cases} f x - \frac{f \cos{\left(d + e x \right)}}{e} & \text{for}\: F = 1 \\\tilde{\infty} e^{2} f \left(e^{- \frac{i e}{b c}}\right)^{a c} \left(e^{- \frac{i e}{b c}}\right)^{b c x} \sin{\left(d + e x \right)} + \tilde{\infty} e^{2} f \left(e^{- \frac{i e}{b c}}\right)^{a c} \left(e^{- \frac{i e}{b c}}\right)^{b c x} \cos{\left(d + e x \right)} & \text{for}\: F = e^{- \frac{i e}{b c}} \\\tilde{\infty} e^{2} f \left(e^{\frac{i e}{b c}}\right)^{a c} \left(e^{\frac{i e}{b c}}\right)^{b c x} \sin{\left(d + e x \right)} + \tilde{\infty} e^{2} f \left(e^{\frac{i e}{b c}}\right)^{a c} \left(e^{\frac{i e}{b c}}\right)^{b c x} \cos{\left(d + e x \right)} & \text{for}\: F = e^{\frac{i e}{b c}} \\F^{a c} \left(f x - \frac{f \cos{\left(d + e x \right)}}{e}\right) & \text{for}\: b = 0 \\f x - \frac{f \cos{\left(d + e x \right)}}{e} & \text{for}\: c = 0 \\\frac{F^{a c} F^{b c x} b^{2} c^{2} f \log{\left(F \right)}^{2} \sin{\left(d + e x \right)}}{b^{3} c^{3} \log{\left(F \right)}^{3} + b c e^{2} \log{\left(F \right)}} + \frac{F^{a c} F^{b c x} b^{2} c^{2} f \log{\left(F \right)}^{2}}{b^{3} c^{3} \log{\left(F \right)}^{3} + b c e^{2} \log{\left(F \right)}} - \frac{F^{a c} F^{b c x} b c e f \log{\left(F \right)} \cos{\left(d + e x \right)}}{b^{3} c^{3} \log{\left(F \right)}^{3} + b c e^{2} \log{\left(F \right)}} + \frac{F^{a c} F^{b c x} e^{2} f}{b^{3} c^{3} \log{\left(F \right)}^{3} + b c e^{2} \log{\left(F \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((f*x - f*cos(d + e*x)/e, Eq(F, 1)), (zoo*e**2*f*exp(-I*e/(b*c))**(a*c)*exp(-I*e/(b*c))**(b*c*x)*sin(d + e*x) + zoo*e**2*f*exp(-I*e/(b*c))**(a*c)*exp(-I*e/(b*c))**(b*c*x)*cos(d + e*x), Eq(F, exp(-I*e/(b*c)))), (zoo*e**2*f*exp(I*e/(b*c))**(a*c)*exp(I*e/(b*c))**(b*c*x)*sin(d + e*x) + zoo*e**2*f*exp(I*e/(b*c))**(a*c)*exp(I*e/(b*c))**(b*c*x)*cos(d + e*x), Eq(F, exp(I*e/(b*c)))), (F**(a*c)*(f*x - f*cos(d + e*x)/e), Eq(b, 0)), (f*x - f*cos(d + e*x)/e, Eq(c, 0)), (F**(a*c)*F**(b*c*x)*b**2*c**2*f*log(F)**2*sin(d + e*x)/(b**3*c**3*log(F)**3 + b*c*e**2*log(F)) + F**(a*c)*F**(b*c*x)*b**2*c**2*f*log(F)**2/(b**3*c**3*log(F)**3 + b*c*e**2*log(F)) - F**(a*c)*F**(b*c*x)*b*c*e*f*log(F)*cos(d + e*x)/(b**3*c**3*log(F)**3 + b*c*e**2*log(F)) + F**(a*c)*F**(b*c*x)*e**2*f/(b**3*c**3*log(F)**3 + b*c*e**2*log(F)), True))","A",0
137,0,0,0,0.000000," ","integrate(F**(c*(b*x+a))/(f+f*sin(e*x+d)),x)","\frac{\int \frac{F^{a c} F^{b c x}}{\sin{\left(d + e x \right)} + 1}\, dx}{f}"," ",0,"Integral(F**(a*c)*F**(b*c*x)/(sin(d + e*x) + 1), x)/f","F",0
138,0,0,0,0.000000," ","integrate(F**(c*(b*x+a))/(f+f*sin(e*x+d))**2,x)","\frac{\int \frac{F^{a c} F^{b c x}}{\sin^{2}{\left(d + e x \right)} + 2 \sin{\left(d + e x \right)} + 1}\, dx}{f^{2}}"," ",0,"Integral(F**(a*c)*F**(b*c*x)/(sin(d + e*x)**2 + 2*sin(d + e*x) + 1), x)/f**2","F",0
139,1,1760,0,58.625030," ","integrate(F**(c*(b*x+a))*(f+f*cos(e*x+d))**2,x)","\begin{cases} \frac{f^{2} x \sin^{2}{\left(d + e x \right)}}{2} + \frac{f^{2} x \cos^{2}{\left(d + e x \right)}}{2} + f^{2} x + \frac{f^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{2 e} + \frac{2 f^{2} \sin{\left(d + e x \right)}}{e} & \text{for}\: F = 1 \\\tilde{\infty} e^{4} f^{2} \left(e^{- \frac{2 i e}{b c}}\right)^{a c} \left(e^{- \frac{2 i e}{b c}}\right)^{b c x} \sin^{2}{\left(d + e x \right)} + \tilde{\infty} e^{4} f^{2} \left(e^{- \frac{2 i e}{b c}}\right)^{a c} \left(e^{- \frac{2 i e}{b c}}\right)^{b c x} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)} + \tilde{\infty} e^{4} f^{2} \left(e^{- \frac{2 i e}{b c}}\right)^{a c} \left(e^{- \frac{2 i e}{b c}}\right)^{b c x} \cos^{2}{\left(d + e x \right)} & \text{for}\: F = e^{- \frac{2 i e}{b c}} \\\tilde{\infty} e^{4} f^{2} \left(e^{- \frac{i e}{b c}}\right)^{a c} \left(e^{- \frac{i e}{b c}}\right)^{b c x} \sin{\left(d + e x \right)} + \tilde{\infty} e^{4} f^{2} \left(e^{- \frac{i e}{b c}}\right)^{a c} \left(e^{- \frac{i e}{b c}}\right)^{b c x} \cos{\left(d + e x \right)} & \text{for}\: F = e^{- \frac{i e}{b c}} \\\tilde{\infty} e^{4} f^{2} \left(e^{\frac{i e}{b c}}\right)^{a c} \left(e^{\frac{i e}{b c}}\right)^{b c x} \sin{\left(d + e x \right)} + \tilde{\infty} e^{4} f^{2} \left(e^{\frac{i e}{b c}}\right)^{a c} \left(e^{\frac{i e}{b c}}\right)^{b c x} \cos{\left(d + e x \right)} & \text{for}\: F = e^{\frac{i e}{b c}} \\\tilde{\infty} e^{4} f^{2} \left(e^{\frac{2 i e}{b c}}\right)^{a c} \left(e^{\frac{2 i e}{b c}}\right)^{b c x} \sin^{2}{\left(d + e x \right)} + \tilde{\infty} e^{4} f^{2} \left(e^{\frac{2 i e}{b c}}\right)^{a c} \left(e^{\frac{2 i e}{b c}}\right)^{b c x} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)} + \tilde{\infty} e^{4} f^{2} \left(e^{\frac{2 i e}{b c}}\right)^{a c} \left(e^{\frac{2 i e}{b c}}\right)^{b c x} \cos^{2}{\left(d + e x \right)} & \text{for}\: F = e^{\frac{2 i e}{b c}} \\F^{a c} \left(\frac{f^{2} x \sin^{2}{\left(d + e x \right)}}{2} + \frac{f^{2} x \cos^{2}{\left(d + e x \right)}}{2} + f^{2} x + \frac{f^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{2 e} + \frac{2 f^{2} \sin{\left(d + e x \right)}}{e}\right) & \text{for}\: b = 0 \\\frac{f^{2} x \sin^{2}{\left(d + e x \right)}}{2} + \frac{f^{2} x \cos^{2}{\left(d + e x \right)}}{2} + f^{2} x + \frac{f^{2} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{2 e} + \frac{2 f^{2} \sin{\left(d + e x \right)}}{e} & \text{for}\: c = 0 \\\frac{F^{a c} F^{b c x} b^{4} c^{4} f^{2} \log{\left(F \right)}^{4} \cos^{2}{\left(d + e x \right)}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} + \frac{2 F^{a c} F^{b c x} b^{4} c^{4} f^{2} \log{\left(F \right)}^{4} \cos{\left(d + e x \right)}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} + \frac{F^{a c} F^{b c x} b^{4} c^{4} f^{2} \log{\left(F \right)}^{4}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} + \frac{2 F^{a c} F^{b c x} b^{3} c^{3} e f^{2} \log{\left(F \right)}^{3} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} + \frac{2 F^{a c} F^{b c x} b^{3} c^{3} e f^{2} \log{\left(F \right)}^{3} \sin{\left(d + e x \right)}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} + \frac{2 F^{a c} F^{b c x} b^{2} c^{2} e^{2} f^{2} \log{\left(F \right)}^{2} \sin^{2}{\left(d + e x \right)}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} + \frac{3 F^{a c} F^{b c x} b^{2} c^{2} e^{2} f^{2} \log{\left(F \right)}^{2} \cos^{2}{\left(d + e x \right)}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} + \frac{8 F^{a c} F^{b c x} b^{2} c^{2} e^{2} f^{2} \log{\left(F \right)}^{2} \cos{\left(d + e x \right)}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} + \frac{5 F^{a c} F^{b c x} b^{2} c^{2} e^{2} f^{2} \log{\left(F \right)}^{2}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} + \frac{2 F^{a c} F^{b c x} b c e^{3} f^{2} \log{\left(F \right)} \sin{\left(d + e x \right)} \cos{\left(d + e x \right)}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} + \frac{8 F^{a c} F^{b c x} b c e^{3} f^{2} \log{\left(F \right)} \sin{\left(d + e x \right)}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} + \frac{2 F^{a c} F^{b c x} e^{4} f^{2} \sin^{2}{\left(d + e x \right)}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} + \frac{2 F^{a c} F^{b c x} e^{4} f^{2} \cos^{2}{\left(d + e x \right)}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} + \frac{4 F^{a c} F^{b c x} e^{4} f^{2}}{b^{5} c^{5} \log{\left(F \right)}^{5} + 5 b^{3} c^{3} e^{2} \log{\left(F \right)}^{3} + 4 b c e^{4} \log{\left(F \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((f**2*x*sin(d + e*x)**2/2 + f**2*x*cos(d + e*x)**2/2 + f**2*x + f**2*sin(d + e*x)*cos(d + e*x)/(2*e) + 2*f**2*sin(d + e*x)/e, Eq(F, 1)), (zoo*e**4*f**2*exp(-2*I*e/(b*c))**(a*c)*exp(-2*I*e/(b*c))**(b*c*x)*sin(d + e*x)**2 + zoo*e**4*f**2*exp(-2*I*e/(b*c))**(a*c)*exp(-2*I*e/(b*c))**(b*c*x)*sin(d + e*x)*cos(d + e*x) + zoo*e**4*f**2*exp(-2*I*e/(b*c))**(a*c)*exp(-2*I*e/(b*c))**(b*c*x)*cos(d + e*x)**2, Eq(F, exp(-2*I*e/(b*c)))), (zoo*e**4*f**2*exp(-I*e/(b*c))**(a*c)*exp(-I*e/(b*c))**(b*c*x)*sin(d + e*x) + zoo*e**4*f**2*exp(-I*e/(b*c))**(a*c)*exp(-I*e/(b*c))**(b*c*x)*cos(d + e*x), Eq(F, exp(-I*e/(b*c)))), (zoo*e**4*f**2*exp(I*e/(b*c))**(a*c)*exp(I*e/(b*c))**(b*c*x)*sin(d + e*x) + zoo*e**4*f**2*exp(I*e/(b*c))**(a*c)*exp(I*e/(b*c))**(b*c*x)*cos(d + e*x), Eq(F, exp(I*e/(b*c)))), (zoo*e**4*f**2*exp(2*I*e/(b*c))**(a*c)*exp(2*I*e/(b*c))**(b*c*x)*sin(d + e*x)**2 + zoo*e**4*f**2*exp(2*I*e/(b*c))**(a*c)*exp(2*I*e/(b*c))**(b*c*x)*sin(d + e*x)*cos(d + e*x) + zoo*e**4*f**2*exp(2*I*e/(b*c))**(a*c)*exp(2*I*e/(b*c))**(b*c*x)*cos(d + e*x)**2, Eq(F, exp(2*I*e/(b*c)))), (F**(a*c)*(f**2*x*sin(d + e*x)**2/2 + f**2*x*cos(d + e*x)**2/2 + f**2*x + f**2*sin(d + e*x)*cos(d + e*x)/(2*e) + 2*f**2*sin(d + e*x)/e), Eq(b, 0)), (f**2*x*sin(d + e*x)**2/2 + f**2*x*cos(d + e*x)**2/2 + f**2*x + f**2*sin(d + e*x)*cos(d + e*x)/(2*e) + 2*f**2*sin(d + e*x)/e, Eq(c, 0)), (F**(a*c)*F**(b*c*x)*b**4*c**4*f**2*log(F)**4*cos(d + e*x)**2/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)) + 2*F**(a*c)*F**(b*c*x)*b**4*c**4*f**2*log(F)**4*cos(d + e*x)/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)) + F**(a*c)*F**(b*c*x)*b**4*c**4*f**2*log(F)**4/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)) + 2*F**(a*c)*F**(b*c*x)*b**3*c**3*e*f**2*log(F)**3*sin(d + e*x)*cos(d + e*x)/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)) + 2*F**(a*c)*F**(b*c*x)*b**3*c**3*e*f**2*log(F)**3*sin(d + e*x)/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)) + 2*F**(a*c)*F**(b*c*x)*b**2*c**2*e**2*f**2*log(F)**2*sin(d + e*x)**2/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)) + 3*F**(a*c)*F**(b*c*x)*b**2*c**2*e**2*f**2*log(F)**2*cos(d + e*x)**2/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)) + 8*F**(a*c)*F**(b*c*x)*b**2*c**2*e**2*f**2*log(F)**2*cos(d + e*x)/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)) + 5*F**(a*c)*F**(b*c*x)*b**2*c**2*e**2*f**2*log(F)**2/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)) + 2*F**(a*c)*F**(b*c*x)*b*c*e**3*f**2*log(F)*sin(d + e*x)*cos(d + e*x)/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)) + 8*F**(a*c)*F**(b*c*x)*b*c*e**3*f**2*log(F)*sin(d + e*x)/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)) + 2*F**(a*c)*F**(b*c*x)*e**4*f**2*sin(d + e*x)**2/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)) + 2*F**(a*c)*F**(b*c*x)*e**4*f**2*cos(d + e*x)**2/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)) + 4*F**(a*c)*F**(b*c*x)*e**4*f**2/(b**5*c**5*log(F)**5 + 5*b**3*c**3*e**2*log(F)**3 + 4*b*c*e**4*log(F)), True))","A",0
140,1,408,0,7.315541," ","integrate(F**(c*(b*x+a))*(f+f*cos(e*x+d)),x)","\begin{cases} f x + \frac{f \sin{\left(d + e x \right)}}{e} & \text{for}\: F = 1 \\\tilde{\infty} e^{2} f \left(e^{- \frac{i e}{b c}}\right)^{a c} \left(e^{- \frac{i e}{b c}}\right)^{b c x} \sin{\left(d + e x \right)} + \tilde{\infty} e^{2} f \left(e^{- \frac{i e}{b c}}\right)^{a c} \left(e^{- \frac{i e}{b c}}\right)^{b c x} \cos{\left(d + e x \right)} & \text{for}\: F = e^{- \frac{i e}{b c}} \\\tilde{\infty} e^{2} f \left(e^{\frac{i e}{b c}}\right)^{a c} \left(e^{\frac{i e}{b c}}\right)^{b c x} \sin{\left(d + e x \right)} + \tilde{\infty} e^{2} f \left(e^{\frac{i e}{b c}}\right)^{a c} \left(e^{\frac{i e}{b c}}\right)^{b c x} \cos{\left(d + e x \right)} & \text{for}\: F = e^{\frac{i e}{b c}} \\F^{a c} \left(f x + \frac{f \sin{\left(d + e x \right)}}{e}\right) & \text{for}\: b = 0 \\f x + \frac{f \sin{\left(d + e x \right)}}{e} & \text{for}\: c = 0 \\\frac{F^{a c} F^{b c x} b^{2} c^{2} f \log{\left(F \right)}^{2} \cos{\left(d + e x \right)}}{b^{3} c^{3} \log{\left(F \right)}^{3} + b c e^{2} \log{\left(F \right)}} + \frac{F^{a c} F^{b c x} b^{2} c^{2} f \log{\left(F \right)}^{2}}{b^{3} c^{3} \log{\left(F \right)}^{3} + b c e^{2} \log{\left(F \right)}} + \frac{F^{a c} F^{b c x} b c e f \log{\left(F \right)} \sin{\left(d + e x \right)}}{b^{3} c^{3} \log{\left(F \right)}^{3} + b c e^{2} \log{\left(F \right)}} + \frac{F^{a c} F^{b c x} e^{2} f}{b^{3} c^{3} \log{\left(F \right)}^{3} + b c e^{2} \log{\left(F \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((f*x + f*sin(d + e*x)/e, Eq(F, 1)), (zoo*e**2*f*exp(-I*e/(b*c))**(a*c)*exp(-I*e/(b*c))**(b*c*x)*sin(d + e*x) + zoo*e**2*f*exp(-I*e/(b*c))**(a*c)*exp(-I*e/(b*c))**(b*c*x)*cos(d + e*x), Eq(F, exp(-I*e/(b*c)))), (zoo*e**2*f*exp(I*e/(b*c))**(a*c)*exp(I*e/(b*c))**(b*c*x)*sin(d + e*x) + zoo*e**2*f*exp(I*e/(b*c))**(a*c)*exp(I*e/(b*c))**(b*c*x)*cos(d + e*x), Eq(F, exp(I*e/(b*c)))), (F**(a*c)*(f*x + f*sin(d + e*x)/e), Eq(b, 0)), (f*x + f*sin(d + e*x)/e, Eq(c, 0)), (F**(a*c)*F**(b*c*x)*b**2*c**2*f*log(F)**2*cos(d + e*x)/(b**3*c**3*log(F)**3 + b*c*e**2*log(F)) + F**(a*c)*F**(b*c*x)*b**2*c**2*f*log(F)**2/(b**3*c**3*log(F)**3 + b*c*e**2*log(F)) + F**(a*c)*F**(b*c*x)*b*c*e*f*log(F)*sin(d + e*x)/(b**3*c**3*log(F)**3 + b*c*e**2*log(F)) + F**(a*c)*F**(b*c*x)*e**2*f/(b**3*c**3*log(F)**3 + b*c*e**2*log(F)), True))","A",0
141,0,0,0,0.000000," ","integrate(F**(c*(b*x+a))/(f+f*cos(e*x+d)),x)","\frac{\int \frac{F^{a c} F^{b c x}}{\cos{\left(d + e x \right)} + 1}\, dx}{f}"," ",0,"Integral(F**(a*c)*F**(b*c*x)/(cos(d + e*x) + 1), x)/f","F",0
142,0,0,0,0.000000," ","integrate(F**(c*(b*x+a))/(f+f*cos(e*x+d))**2,x)","\frac{\int \frac{F^{a c} F^{b c x}}{\cos^{2}{\left(d + e x \right)} + 2 \cos{\left(d + e x \right)} + 1}\, dx}{f^{2}}"," ",0,"Integral(F**(a*c)*F**(b*c*x)/(cos(d + e*x)**2 + 2*cos(d + e*x) + 1), x)/f**2","F",0
