\(\int \cos (a+b x) \text {Si}(c+d x) \, dx\) [67]

Optimal result

Integrand size = 13, antiderivative size = 153 \[ \int \cos (a+b x) \text {Si}(c+d x) \, dx=-\frac {\cos \left (a-\frac {b c}{d}\right ) \operatorname {CosIntegral}\left (\frac {c (b-d)}{d}+(b-d) x\right )}{2 b}+\frac {\cos \left (a-\frac {b c}{d}\right ) \operatorname {CosIntegral}\left (\frac {c (b+d)}{d}+(b+d) x\right )}{2 b}+\frac {\sin \left (a-\frac {b c}{d}\right ) \text {Si}\left (\frac {c (b-d)}{d}+(b-d) x\right )}{2 b}+\frac {\sin (a+b x) \text {Si}(c+d x)}{b}-\frac {\sin \left (a-\frac {b c}{d}\right ) \text {Si}\left (\frac {c (b+d)}{d}+(b+d) x\right )}{2 b} \]

[Out]

-1/2*Ci(c*(b-d)/d+(b-d)*x)*cos(a-b*c/d)/b+1/2*Ci(c*(b+d)/d+(b+d)*x)*cos(a-b*c/d)/b+1/2*Si(c*(b-d)/d+(b-d)*x)*s
in(a-b*c/d)/b-1/2*Si(c*(b+d)/d+(b+d)*x)*sin(a-b*c/d)/b+Si(d*x+c)*sin(b*x+a)/b

Rubi [A] (verified)

Time = 0.17 (sec) , antiderivative size = 153, normalized size of antiderivative = 1.00, number of steps used = 9, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.385, Rules used = {6652, 4513, 3384, 3380, 3383} \[ \int \cos (a+b x) \text {Si}(c+d x) \, dx=-\frac {\cos \left (a-\frac {b c}{d}\right ) \operatorname {CosIntegral}\left (x (b-d)+\frac {c (b-d)}{d}\right )}{2 b}+\frac {\cos \left (a-\frac {b c}{d}\right ) \operatorname {CosIntegral}\left (x (b+d)+\frac {c (b+d)}{d}\right )}{2 b}+\frac {\sin \left (a-\frac {b c}{d}\right ) \text {Si}\left (x (b-d)+\frac {c (b-d)}{d}\right )}{2 b}+\frac {\sin (a+b x) \text {Si}(c+d x)}{b}-\frac {\sin \left (a-\frac {b c}{d}\right ) \text {Si}\left (x (b+d)+\frac {c (b+d)}{d}\right )}{2 b} \]

[In]

Int[Cos[a + b*x]*SinIntegral[c + d*x],x]

[Out]

-1/2*(Cos[a - (b*c)/d]*CosIntegral[(c*(b - d))/d + (b - d)*x])/b + (Cos[a - (b*c)/d]*CosIntegral[(c*(b + d))/d
+ (b + d)*x])/(2*b) + (Sin[a - (b*c)/d]*SinIntegral[(c*(b - d))/d + (b - d)*x])/(2*b) + (Sin[a + b*x]*SinInte
gral[c + d*x])/b - (Sin[a - (b*c)/d]*SinIntegral[(c*(b + d))/d + (b + d)*x])/(2*b)

Rule 3380

Int[sin[(e_.) + (f_.)*(x_)]/((c_.) + (d_.)*(x_)), x_Symbol] :> Simp[SinIntegral[e + f*x]/d, x] /; FreeQ[{c, d,
e, f}, x] && EqQ[d*e - c*f, 0]

Rule 3383

Int[sin[(e_.) + (f_.)*(x_)]/((c_.) + (d_.)*(x_)), x_Symbol] :> Simp[CosIntegral[e - Pi/2 + f*x]/d, x] /; FreeQ
[{c, d, e, f}, x] && EqQ[d*(e - Pi/2) - c*f, 0]

Rule 3384

Int[sin[(e_.) + (f_.)*(x_)]/((c_.) + (d_.)*(x_)), x_Symbol] :> Dist[Cos[(d*e - c*f)/d], Int[Sin[c*(f/d) + f*x]
/(c + d*x), x], x] + Dist[Sin[(d*e - c*f)/d], Int[Cos[c*(f/d) + f*x]/(c + d*x), x], x] /; FreeQ[{c, d, e, f},
x] && NeQ[d*e - c*f, 0]

Rule 4513

Int[((e_.) + (f_.)*(x_))^(m_.)*Sin[(a_.) + (b_.)*(x_)]^(p_.)*Sin[(c_.) + (d_.)*(x_)]^(q_.), x_Symbol] :> Int[E
xpandTrigReduce[(e + f*x)^m, Sin[a + b*x]^p*Sin[c + d*x]^q, x], x] /; FreeQ[{a, b, c, d, e, f}, x] && IGtQ[p,
0] && IGtQ[q, 0] && IntegerQ[m]

Rule 6652

Int[Cos[(a_.) + (b_.)*(x_)]*SinIntegral[(c_.) + (d_.)*(x_)], x_Symbol] :> Simp[Sin[a + b*x]*(SinIntegral[c + d
*x]/b), x] - Dist[d/b, Int[Sin[a + b*x]*(Sin[c + d*x]/(c + d*x)), x], x] /; FreeQ[{a, b, c, d}, x]

Rubi steps \begin{align*} \text {integral}& = \frac {\sin (a+b x) \text {Si}(c+d x)}{b}-\frac {d \int \frac {\sin (a+b x) \sin (c+d x)}{c+d x} \, dx}{b} \\ & = \frac {\sin (a+b x) \text {Si}(c+d x)}{b}-\frac {d \int \left (\frac {\cos (a-c+(b-d) x)}{2 (c+d x)}-\frac {\cos (a+c+(b+d) x)}{2 (c+d x)}\right ) \, dx}{b} \\ & = \frac {\sin (a+b x) \text {Si}(c+d x)}{b}-\frac {d \int \frac {\cos (a-c+(b-d) x)}{c+d x} \, dx}{2 b}+\frac {d \int \frac {\cos (a+c+(b+d) x)}{c+d x} \, dx}{2 b} \\ & = \frac {\sin (a+b x) \text {Si}(c+d x)}{b}-\frac {\left (d \cos \left (a-\frac {b c}{d}\right )\right ) \int \frac {\cos \left (\frac {c (b-d)}{d}+(b-d) x\right )}{c+d x} \, dx}{2 b}+\frac {\left (d \cos \left (a-\frac {b c}{d}\right )\right ) \int \frac {\cos \left (\frac {c (b+d)}{d}+(b+d) x\right )}{c+d x} \, dx}{2 b}+\frac {\left (d \sin \left (a-\frac {b c}{d}\right )\right ) \int \frac {\sin \left (\frac {c (b-d)}{d}+(b-d) x\right )}{c+d x} \, dx}{2 b}-\frac {\left (d \sin \left (a-\frac {b c}{d}\right )\right ) \int \frac {\sin \left (\frac {c (b+d)}{d}+(b+d) x\right )}{c+d x} \, dx}{2 b} \\ & = -\frac {\cos \left (a-\frac {b c}{d}\right ) \operatorname {CosIntegral}\left (\frac {c (b-d)}{d}+(b-d) x\right )}{2 b}+\frac {\cos \left (a-\frac {b c}{d}\right ) \operatorname {CosIntegral}\left (\frac {c (b+d)}{d}+(b+d) x\right )}{2 b}+\frac {\sin \left (a-\frac {b c}{d}\right ) \text {Si}\left (\frac {c (b-d)}{d}+(b-d) x\right )}{2 b}+\frac {\sin (a+b x) \text {Si}(c+d x)}{b}-\frac {\sin \left (a-\frac {b c}{d}\right ) \text {Si}\left (\frac {c (b+d)}{d}+(b+d) x\right )}{2 b} \\ \end{align*}

Mathematica [C] (verified)

Result contains complex when optimal does not.

Time = 1.03 (sec) , antiderivative size = 164, normalized size of antiderivative = 1.07 \[ \int \cos (a+b x) \text {Si}(c+d x) \, dx=\frac {e^{-\frac {i (b c+a d)}{d}} \left (-e^{\frac {2 i b c}{d}} \operatorname {ExpIntegralEi}\left (-\frac {i (b-d) (c+d x)}{d}\right )-e^{2 i a} \operatorname {ExpIntegralEi}\left (\frac {i (b-d) (c+d x)}{d}\right )+e^{\frac {2 i b c}{d}} \operatorname {ExpIntegralEi}\left (-\frac {i (b+d) (c+d x)}{d}\right )+e^{2 i a} \operatorname {ExpIntegralEi}\left (\frac {i (b+d) (c+d x)}{d}\right )+4 e^{\frac {i (b c+a d)}{d}} \sin (a+b x) \text {Si}(c+d x)\right )}{4 b} \]

[In]

Integrate[Cos[a + b*x]*SinIntegral[c + d*x],x]

[Out]

(-(E^(((2*I)*b*c)/d)*ExpIntegralEi[((-I)*(b - d)*(c + d*x))/d]) - E^((2*I)*a)*ExpIntegralEi[(I*(b - d)*(c + d*
x))/d] + E^(((2*I)*b*c)/d)*ExpIntegralEi[((-I)*(b + d)*(c + d*x))/d] + E^((2*I)*a)*ExpIntegralEi[(I*(b + d)*(c
+ d*x))/d] + 4*E^((I*(b*c + a*d))/d)*Sin[a + b*x]*SinIntegral[c + d*x])/(4*b*E^((I*(b*c + a*d))/d))

Maple [A] (verified)

Time = 2.29 (sec) , antiderivative size = 272, normalized size of antiderivative = 1.78

method	result	size
default	\(\frac {\frac {\operatorname {Si}\left (d x +c \right ) d \sin \left (\frac {b \left (d x +c \right )}{d}+\frac {a d -b c}{d}\right )}{b}-\frac {d \left (\frac {d \left (-\frac {\operatorname {Si}\left (-\left (-1+\frac {b}{d}\right ) \left (d x +c \right )-a +\frac {b c}{d}-\frac {-a d +b c}{d}\right ) \sin \left (\frac {-a d +b c}{d}\right )}{d}+\frac {\operatorname {Ci}\left (\left (-1+\frac {b}{d}\right ) \left (d x +c \right )+a -\frac {b c}{d}+\frac {-a d +b c}{d}\right ) \cos \left (\frac {-a d +b c}{d}\right )}{d}\right )}{2}-\frac {d \left (-\frac {\operatorname {Si}\left (-\left (1+\frac {b}{d}\right ) \left (d x +c \right )-a +\frac {b c}{d}-\frac {-a d +b c}{d}\right ) \sin \left (\frac {-a d +b c}{d}\right )}{d}+\frac {\operatorname {Ci}\left (\left (1+\frac {b}{d}\right ) \left (d x +c \right )+a -\frac {b c}{d}+\frac {-a d +b c}{d}\right ) \cos \left (\frac {-a d +b c}{d}\right )}{d}\right )}{2}\right )}{b}}{d}\)	\(272\)

[In]

int(cos(b*x+a)*Si(d*x+c),x,method=_RETURNVERBOSE)

[Out]

(Si(d*x+c)/b*d*sin(1/d*b*(d*x+c)+(a*d-b*c)/d)-1/b*d*(1/2*d*(-Si(-(-1+b/d)*(d*x+c)-a+b*c/d-(-a*d+b*c)/d)*sin((-
a*d+b*c)/d)/d+Ci((-1+b/d)*(d*x+c)+a-b*c/d+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d)-1/2*d*(-Si(-(1+b/d)*(d*x+c)-a+b*c
/d-(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d+Ci((1+b/d)*(d*x+c)+a-b*c/d+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d)))/d

Fricas [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 147, normalized size of antiderivative = 0.96 \[ \int \cos (a+b x) \text {Si}(c+d x) \, dx=\frac {{\left (\operatorname {Ci}\left (\frac {b c + c d + {\left (b d + d^{2}\right )} x}{d}\right ) - \operatorname {Ci}\left (-\frac {b c - c d + {\left (b d - d^{2}\right )} x}{d}\right )\right )} \cos \left (-\frac {b c - a d}{d}\right ) - {\left (\operatorname {Si}\left (\frac {b c + c d + {\left (b d + d^{2}\right )} x}{d}\right ) + \operatorname {Si}\left (-\frac {b c - c d + {\left (b d - d^{2}\right )} x}{d}\right )\right )} \sin \left (-\frac {b c - a d}{d}\right ) + 2 \, \sin \left (b x + a\right ) \operatorname {Si}\left (d x + c\right )}{2 \, b} \]

[In]

integrate(cos(b*x+a)*sin_integral(d*x+c),x, algorithm="fricas")

[Out]

1/2*((cos_integral((b*c + c*d + (b*d + d^2)*x)/d) - cos_integral(-(b*c - c*d + (b*d - d^2)*x)/d))*cos(-(b*c -
a*d)/d) - (sin_integral((b*c + c*d + (b*d + d^2)*x)/d) + sin_integral(-(b*c - c*d + (b*d - d^2)*x)/d))*sin(-(b
*c - a*d)/d) + 2*sin(b*x + a)*sin_integral(d*x + c))/b

Sympy [F]

\[ \int \cos (a+b x) \text {Si}(c+d x) \, dx=\int \cos {\left (a + b x \right )} \operatorname {Si}{\left (c + d x \right )}\, dx \]

[In]

integrate(cos(b*x+a)*Si(d*x+c),x)

[Out]

Integral(cos(a + b*x)*Si(c + d*x), x)

Maxima [F]

\[ \int \cos (a+b x) \text {Si}(c+d x) \, dx=\int { \cos \left (b x + a\right ) \operatorname {Si}\left (d x + c\right ) \,d x } \]

[In]

integrate(cos(b*x+a)*sin_integral(d*x+c),x, algorithm="maxima")

[Out]

integrate(cos(b*x + a)*sin_integral(d*x + c), x)

Giac [C] (verification not implemented)

Result contains higher order function than in optimal. Order 9 vs. order 4.

Time = 0.56 (sec) , antiderivative size = 9214, normalized size of antiderivative = 60.22 \[ \int \cos (a+b x) \text {Si}(c+d x) \, dx=\text {Too large to display} \]

[In]

integrate(cos(b*x+a)*sin_integral(d*x+c),x, algorithm="giac")

[Out]

1/4*(real_part(cos_integral(b*x + d*x + c + b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c
*d)/d)^2*tan(1/2*(b*c - c*d)/d)^2 - real_part(cos_integral(b*x - d*x - c + b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/
2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d)^2 - real_part(cos_integral(-b*x + d*x + c - b*c
/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d)^2 + real_part(c
os_integral(-b*x - d*x - c - b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2*tan(1/
2*(b*c - c*d)/d)^2 + 2*imag_part(cos_integral(b*x - d*x - c + b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)^
2*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d) - 2*imag_part(cos_integral(-b*x + d*x + c - b*c/d))*tan(1/2*
a + 1/2*c)^2*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d) + 4*sin_integral((b*d*x - d^
2*x + b*c - c*d)/d)*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d)
- 2*imag_part(cos_integral(b*x + d*x + c + b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*
d)/d)*tan(1/2*(b*c - c*d)/d)^2 + 2*imag_part(cos_integral(-b*x - d*x - c - b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/
2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)*tan(1/2*(b*c - c*d)/d)^2 - 4*sin_integral((b*d*x + d^2*x + b*c + c*d)/d)
*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)*tan(1/2*(b*c - c*d)/d)^2 - 2*imag_part(cos_i
ntegral(b*x - d*x - c + b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c
- c*d)/d)^2 + 2*imag_part(cos_integral(-b*x + d*x + c - b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)*tan(1/
2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d)^2 - 4*sin_integral((b*d*x - d^2*x + b*c - c*d)/d)*tan(1/2*a + 1/2*c)
^2*tan(1/2*a - 1/2*c)*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d)^2 + 2*imag_part(cos_integral(b*x + d*x +
c + b*c/d))*tan(1/2*a + 1/2*c)*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d)^2 - 2*ima
g_part(cos_integral(-b*x - d*x - c - b*c/d))*tan(1/2*a + 1/2*c)*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2*
tan(1/2*(b*c - c*d)/d)^2 + 4*sin_integral((b*d*x + d^2*x + b*c + c*d)/d)*tan(1/2*a + 1/2*c)*tan(1/2*a - 1/2*c)
^2*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d)^2 + real_part(cos_integral(b*x + d*x + c + b*c/d))*tan(1/2*
a + 1/2*c)^2*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2 + real_part(cos_integral(b*x - d*x - c + b*c/d))*ta
n(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2 + real_part(cos_integral(-b*x + d*x + c - b*c
/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2 + real_part(cos_integral(-b*x - d*x -
c - b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2 - 4*real_part(cos_integral(b*x
- d*x - c + b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d) -
4*real_part(cos_integral(-b*x + d*x + c - b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)*tan(1/2*(b*c + c*d)/
d)^2*tan(1/2*(b*c - c*d)/d) - real_part(cos_integral(b*x + d*x + c + b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*a -
1/2*c)^2*tan(1/2*(b*c - c*d)/d)^2 - real_part(cos_integral(b*x - d*x - c + b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/
2*a - 1/2*c)^2*tan(1/2*(b*c - c*d)/d)^2 - real_part(cos_integral(-b*x + d*x + c - b*c/d))*tan(1/2*a + 1/2*c)^2
*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c - c*d)/d)^2 - real_part(cos_integral(-b*x - d*x - c - b*c/d))*tan(1/2*a + 1
/2*c)^2*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c - c*d)/d)^2 + 4*real_part(cos_integral(b*x + d*x + c + b*c/d))*tan(1
/2*a + 1/2*c)*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)*tan(1/2*(b*c - c*d)/d)^2 + 4*real_part(cos_integral(
-b*x - d*x - c - b*c/d))*tan(1/2*a + 1/2*c)*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)*tan(1/2*(b*c - c*d)/d)
^2 + real_part(cos_integral(b*x + d*x + c + b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c
- c*d)/d)^2 + real_part(cos_integral(b*x - d*x - c + b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2*ta
n(1/2*(b*c - c*d)/d)^2 + real_part(cos_integral(-b*x + d*x + c - b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*(b*c + c
*d)/d)^2*tan(1/2*(b*c - c*d)/d)^2 + real_part(cos_integral(-b*x - d*x - c - b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1
/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d)^2 - real_part(cos_integral(b*x + d*x + c + b*c/d))*tan(1/2*a - 1/2*
c)^2*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d)^2 - real_part(cos_integral(b*x - d*x - c + b*c/d))*tan(1/
2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d)^2 - real_part(cos_integral(-b*x + d*x + c - b*c
/d))*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d)^2 - real_part(cos_integral(-b*x - d*
x - c - b*c/d))*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d)^2 - 2*imag_part(cos_integ
ral(b*x + d*x + c + b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d) + 2*imag_part(cos
_integral(-b*x - d*x - c - b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d) - 4*sin_in
tegral((b*d*x + d^2*x + b*c + c*d)/d)*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d) + 2*ima
g_part(cos_integral(b*x - d*x - c + b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)*tan(1/2*(b*c + c*d)/d)^2 -
2*imag_part(cos_integral(-b*x + d*x + c - b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)*tan(1/2*(b*c + c*d)
/d)^2 + 4*sin_integral((b*d*x - d^2*x + b*c - c*d)/d)*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)*tan(1/2*(b*c + c
*d)/d)^2 + 2*imag_part(cos_integral(b*x + d*x + c + b*c/d))*tan(1/2*a + 1/2*c)*tan(1/2*a - 1/2*c)^2*tan(1/2*(b
*c + c*d)/d)^2 - 2*imag_part(cos_integral(-b*x - d*x - c - b*c/d))*tan(1/2*a + 1/2*c)*tan(1/2*a - 1/2*c)^2*tan
(1/2*(b*c + c*d)/d)^2 + 4*sin_integral((b*d*x + d^2*x + b*c + c*d)/d)*tan(1/2*a + 1/2*c)*tan(1/2*a - 1/2*c)^2*
tan(1/2*(b*c + c*d)/d)^2 + 2*imag_part(cos_integral(b*x - d*x - c + b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1
/2*c)^2*tan(1/2*(b*c - c*d)/d) - 2*imag_part(cos_integral(-b*x + d*x + c - b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/
2*a - 1/2*c)^2*tan(1/2*(b*c - c*d)/d) + 4*sin_integral((b*d*x - d^2*x + b*c - c*d)/d)*tan(1/2*a + 1/2*c)^2*tan
(1/2*a - 1/2*c)^2*tan(1/2*(b*c - c*d)/d) - 2*imag_part(cos_integral(b*x - d*x - c + b*c/d))*tan(1/2*a + 1/2*c)
^2*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d) + 2*imag_part(cos_integral(-b*x + d*x + c - b*c/d))*tan(1/2
*a + 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d) - 4*sin_integral((b*d*x - d^2*x + b*c - c*d)/d)*
tan(1/2*a + 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d) + 2*imag_part(cos_integral(b*x - d*x - c
+ b*c/d))*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d) - 2*imag_part(cos_integral(-b*x
+ d*x + c - b*c/d))*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d) + 4*sin_integral((b*
d*x - d^2*x + b*c - c*d)/d)*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d) - 2*imag_part
(cos_integral(b*x - d*x - c + b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)*tan(1/2*(b*c - c*d)/d)^2 + 2*ima
g_part(cos_integral(-b*x + d*x + c - b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)*tan(1/2*(b*c - c*d)/d)^2
- 4*sin_integral((b*d*x - d^2*x + b*c - c*d)/d)*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)*tan(1/2*(b*c - c*d)/d)
^2 - 2*imag_part(cos_integral(b*x + d*x + c + b*c/d))*tan(1/2*a + 1/2*c)*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c - c
*d)/d)^2 + 2*imag_part(cos_integral(-b*x - d*x - c - b*c/d))*tan(1/2*a + 1/2*c)*tan(1/2*a - 1/2*c)^2*tan(1/2*(
b*c - c*d)/d)^2 - 4*sin_integral((b*d*x + d^2*x + b*c + c*d)/d)*tan(1/2*a + 1/2*c)*tan(1/2*a - 1/2*c)^2*tan(1/
2*(b*c - c*d)/d)^2 - 2*imag_part(cos_integral(b*x + d*x + c + b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*(b*c + c*d)
/d)*tan(1/2*(b*c - c*d)/d)^2 + 2*imag_part(cos_integral(-b*x - d*x - c - b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*
(b*c + c*d)/d)*tan(1/2*(b*c - c*d)/d)^2 - 4*sin_integral((b*d*x + d^2*x + b*c + c*d)/d)*tan(1/2*a + 1/2*c)^2*t
an(1/2*(b*c + c*d)/d)*tan(1/2*(b*c - c*d)/d)^2 + 2*imag_part(cos_integral(b*x + d*x + c + b*c/d))*tan(1/2*a -
1/2*c)^2*tan(1/2*(b*c + c*d)/d)*tan(1/2*(b*c - c*d)/d)^2 - 2*imag_part(cos_integral(-b*x - d*x - c - b*c/d))*t
an(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)*tan(1/2*(b*c - c*d)/d)^2 + 4*sin_integral((b*d*x + d^2*x + b*c + c*
d)/d)*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)*tan(1/2*(b*c - c*d)/d)^2 + 2*imag_part(cos_integral(b*x + d*
x + c + b*c/d))*tan(1/2*a + 1/2*c)*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d)^2 - 2*imag_part(cos_integra
l(-b*x - d*x - c - b*c/d))*tan(1/2*a + 1/2*c)*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d)^2 + 4*sin_integr
al((b*d*x + d^2*x + b*c + c*d)/d)*tan(1/2*a + 1/2*c)*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d)^2 - 2*ima
g_part(cos_integral(b*x - d*x - c + b*c/d))*tan(1/2*a - 1/2*c)*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d)
^2 + 2*imag_part(cos_integral(-b*x + d*x + c - b*c/d))*tan(1/2*a - 1/2*c)*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*
c - c*d)/d)^2 - 4*sin_integral((b*d*x - d^2*x + b*c - c*d)/d)*tan(1/2*a - 1/2*c)*tan(1/2*(b*c + c*d)/d)^2*tan(
1/2*(b*c - c*d)/d)^2 - real_part(cos_integral(b*x + d*x + c + b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)^
2 + real_part(cos_integral(b*x - d*x - c + b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)^2 + real_part(cos_i
ntegral(-b*x + d*x + c - b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)^2 - real_part(cos_integral(-b*x - d*x
- c - b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)^2 + 4*real_part(cos_integral(b*x + d*x + c + b*c/d))*ta
n(1/2*a + 1/2*c)*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d) + 4*real_part(cos_integral(-b*x - d*x - c - b*c/d
))*tan(1/2*a + 1/2*c)*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d) + real_part(cos_integral(b*x + d*x + c + b*c
/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2 - real_part(cos_integral(b*x - d*x - c + b*c/d))*tan(1/2*a
+ 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2 - real_part(cos_integral(-b*x + d*x + c - b*c/d))*tan(1/2*a + 1/2*c)^2*tan
(1/2*(b*c + c*d)/d)^2 + real_part(cos_integral(-b*x - d*x - c - b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*(b*c + c*
d)/d)^2 - real_part(cos_integral(b*x + d*x + c + b*c/d))*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2 + real_
part(cos_integral(b*x - d*x - c + b*c/d))*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2 + real_part(cos_integr
al(-b*x + d*x + c - b*c/d))*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2 - real_part(cos_integral(-b*x - d*x
- c - b*c/d))*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2 - 4*real_part(cos_integral(b*x - d*x - c + b*c/d))
*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)*tan(1/2*(b*c - c*d)/d) - 4*real_part(cos_integral(-b*x + d*x + c - b*
c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)*tan(1/2*(b*c - c*d)/d) - 4*real_part(cos_integral(b*x - d*x - c
+ b*c/d))*tan(1/2*a - 1/2*c)*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d) - 4*real_part(cos_integral(-b*x +
d*x + c - b*c/d))*tan(1/2*a - 1/2*c)*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d) - real_part(cos_integral
(b*x + d*x + c + b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*(b*c - c*d)/d)^2 + real_part(cos_integral(b*x - d*x - c
+ b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*(b*c - c*d)/d)^2 + real_part(cos_integral(-b*x + d*x + c - b*c/d))*tan(
1/2*a + 1/2*c)^2*tan(1/2*(b*c - c*d)/d)^2 - real_part(cos_integral(-b*x - d*x - c - b*c/d))*tan(1/2*a + 1/2*c)
^2*tan(1/2*(b*c - c*d)/d)^2 + real_part(cos_integral(b*x + d*x + c + b*c/d))*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c
- c*d)/d)^2 - real_part(cos_integral(b*x - d*x - c + b*c/d))*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c - c*d)/d)^2 -
real_part(cos_integral(-b*x + d*x + c - b*c/d))*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c - c*d)/d)^2 + real_part(cos_
integral(-b*x - d*x - c - b*c/d))*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c - c*d)/d)^2 + 4*real_part(cos_integral(b*x
+ d*x + c + b*c/d))*tan(1/2*a + 1/2*c)*tan(1/2*(b*c + c*d)/d)*tan(1/2*(b*c - c*d)/d)^2 + 4*real_part(cos_inte
gral(-b*x - d*x - c - b*c/d))*tan(1/2*a + 1/2*c)*tan(1/2*(b*c + c*d)/d)*tan(1/2*(b*c - c*d)/d)^2 - real_part(c
os_integral(b*x + d*x + c + b*c/d))*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d)^2 + real_part(cos_integral
(b*x - d*x - c + b*c/d))*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d)^2 + real_part(cos_integral(-b*x + d*x
+ c - b*c/d))*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d)^2 - real_part(cos_integral(-b*x - d*x - c - b*c
/d))*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d)^2 + 2*imag_part(cos_integral(b*x - d*x - c + b*c/d))*tan(
1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c) - 2*imag_part(cos_integral(-b*x + d*x + c - b*c/d))*tan(1/2*a + 1/2*c)^2*t
an(1/2*a - 1/2*c) + 4*sin_integral((b*d*x - d^2*x + b*c - c*d)/d)*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c) - 2*
imag_part(cos_integral(b*x + d*x + c + b*c/d))*tan(1/2*a + 1/2*c)*tan(1/2*a - 1/2*c)^2 + 2*imag_part(cos_integ
ral(-b*x - d*x - c - b*c/d))*tan(1/2*a + 1/2*c)*tan(1/2*a - 1/2*c)^2 - 4*sin_integral((b*d*x + d^2*x + b*c + c
*d)/d)*tan(1/2*a + 1/2*c)*tan(1/2*a - 1/2*c)^2 - 2*imag_part(cos_integral(b*x + d*x + c + b*c/d))*tan(1/2*a +
1/2*c)^2*tan(1/2*(b*c + c*d)/d) + 2*imag_part(cos_integral(-b*x - d*x - c - b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1
/2*(b*c + c*d)/d) - 4*sin_integral((b*d*x + d^2*x + b*c + c*d)/d)*tan(1/2*a + 1/2*c)^2*tan(1/2*(b*c + c*d)/d)
+ 2*imag_part(cos_integral(b*x + d*x + c + b*c/d))*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d) - 2*imag_part(c
os_integral(-b*x - d*x - c - b*c/d))*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d) + 4*sin_integral((b*d*x + d^2
*x + b*c + c*d)/d)*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d) + 2*imag_part(cos_integral(b*x + d*x + c + b*c/
d))*tan(1/2*a + 1/2*c)*tan(1/2*(b*c + c*d)/d)^2 - 2*imag_part(cos_integral(-b*x - d*x - c - b*c/d))*tan(1/2*a
+ 1/2*c)*tan(1/2*(b*c + c*d)/d)^2 + 4*sin_integral((b*d*x + d^2*x + b*c + c*d)/d)*tan(1/2*a + 1/2*c)*tan(1/2*(
b*c + c*d)/d)^2 + 2*imag_part(cos_integral(b*x - d*x - c + b*c/d))*tan(1/2*a - 1/2*c)*tan(1/2*(b*c + c*d)/d)^2
- 2*imag_part(cos_integral(-b*x + d*x + c - b*c/d))*tan(1/2*a - 1/2*c)*tan(1/2*(b*c + c*d)/d)^2 + 4*sin_integ
ral((b*d*x - d^2*x + b*c - c*d)/d)*tan(1/2*a - 1/2*c)*tan(1/2*(b*c + c*d)/d)^2 - 2*imag_part(cos_integral(b*x
- d*x - c + b*c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*(b*c - c*d)/d) + 2*imag_part(cos_integral(-b*x + d*x + c - b*
c/d))*tan(1/2*a + 1/2*c)^2*tan(1/2*(b*c - c*d)/d) - 4*sin_integral((b*d*x - d^2*x + b*c - c*d)/d)*tan(1/2*a +
1/2*c)^2*tan(1/2*(b*c - c*d)/d) + 2*imag_part(cos_integral(b*x - d*x - c + b*c/d))*tan(1/2*a - 1/2*c)^2*tan(1/
2*(b*c - c*d)/d) - 2*imag_part(cos_integral(-b*x + d*x + c - b*c/d))*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c - c*d)/
d) + 4*sin_integral((b*d*x - d^2*x + b*c - c*d)/d)*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c - c*d)/d) - 2*imag_part(c
os_integral(b*x - d*x - c + b*c/d))*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d) + 2*imag_part(cos_integral
(-b*x + d*x + c - b*c/d))*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d) - 4*sin_integral((b*d*x - d^2*x + b*
c - c*d)/d)*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d) - 2*imag_part(cos_integral(b*x + d*x + c + b*c/d))
*tan(1/2*a + 1/2*c)*tan(1/2*(b*c - c*d)/d)^2 + 2*imag_part(cos_integral(-b*x - d*x - c - b*c/d))*tan(1/2*a + 1
/2*c)*tan(1/2*(b*c - c*d)/d)^2 - 4*sin_integral((b*d*x + d^2*x + b*c + c*d)/d)*tan(1/2*a + 1/2*c)*tan(1/2*(b*c
- c*d)/d)^2 - 2*imag_part(cos_integral(b*x - d*x - c + b*c/d))*tan(1/2*a - 1/2*c)*tan(1/2*(b*c - c*d)/d)^2 +
2*imag_part(cos_integral(-b*x + d*x + c - b*c/d))*tan(1/2*a - 1/2*c)*tan(1/2*(b*c - c*d)/d)^2 - 4*sin_integral
((b*d*x - d^2*x + b*c - c*d)/d)*tan(1/2*a - 1/2*c)*tan(1/2*(b*c - c*d)/d)^2 + 2*imag_part(cos_integral(b*x + d
*x + c + b*c/d))*tan(1/2*(b*c + c*d)/d)*tan(1/2*(b*c - c*d)/d)^2 - 2*imag_part(cos_integral(-b*x - d*x - c - b
*c/d))*tan(1/2*(b*c + c*d)/d)*tan(1/2*(b*c - c*d)/d)^2 + 4*sin_integral((b*d*x + d^2*x + b*c + c*d)/d)*tan(1/2
*(b*c + c*d)/d)*tan(1/2*(b*c - c*d)/d)^2 - real_part(cos_integral(b*x + d*x + c + b*c/d))*tan(1/2*a + 1/2*c)^2
- real_part(cos_integral(b*x - d*x - c + b*c/d))*tan(1/2*a + 1/2*c)^2 - real_part(cos_integral(-b*x + d*x + c
- b*c/d))*tan(1/2*a + 1/2*c)^2 - real_part(cos_integral(-b*x - d*x - c - b*c/d))*tan(1/2*a + 1/2*c)^2 + real_
part(cos_integral(b*x + d*x + c + b*c/d))*tan(1/2*a - 1/2*c)^2 + real_part(cos_integral(b*x - d*x - c + b*c/d)
)*tan(1/2*a - 1/2*c)^2 + real_part(cos_integral(-b*x + d*x + c - b*c/d))*tan(1/2*a - 1/2*c)^2 + real_part(cos_
integral(-b*x - d*x - c - b*c/d))*tan(1/2*a - 1/2*c)^2 + 4*real_part(cos_integral(b*x + d*x + c + b*c/d))*tan(
1/2*a + 1/2*c)*tan(1/2*(b*c + c*d)/d) + 4*real_part(cos_integral(-b*x - d*x - c - b*c/d))*tan(1/2*a + 1/2*c)*t
an(1/2*(b*c + c*d)/d) - real_part(cos_integral(b*x + d*x + c + b*c/d))*tan(1/2*(b*c + c*d)/d)^2 - real_part(co
s_integral(b*x - d*x - c + b*c/d))*tan(1/2*(b*c + c*d)/d)^2 - real_part(cos_integral(-b*x + d*x + c - b*c/d))*
tan(1/2*(b*c + c*d)/d)^2 - real_part(cos_integral(-b*x - d*x - c - b*c/d))*tan(1/2*(b*c + c*d)/d)^2 - 4*real_p
art(cos_integral(b*x - d*x - c + b*c/d))*tan(1/2*a - 1/2*c)*tan(1/2*(b*c - c*d)/d) - 4*real_part(cos_integral(
-b*x + d*x + c - b*c/d))*tan(1/2*a - 1/2*c)*tan(1/2*(b*c - c*d)/d) + real_part(cos_integral(b*x + d*x + c + b*
c/d))*tan(1/2*(b*c - c*d)/d)^2 + real_part(cos_integral(b*x - d*x - c + b*c/d))*tan(1/2*(b*c - c*d)/d)^2 + rea
l_part(cos_integral(-b*x + d*x + c - b*c/d))*tan(1/2*(b*c - c*d)/d)^2 + real_part(cos_integral(-b*x - d*x - c
- b*c/d))*tan(1/2*(b*c - c*d)/d)^2 - 2*imag_part(cos_integral(b*x + d*x + c + b*c/d))*tan(1/2*a + 1/2*c) + 2*i
mag_part(cos_integral(-b*x - d*x - c - b*c/d))*tan(1/2*a + 1/2*c) - 4*sin_integral((b*d*x + d^2*x + b*c + c*d)
/d)*tan(1/2*a + 1/2*c) + 2*imag_part(cos_integral(b*x - d*x - c + b*c/d))*tan(1/2*a - 1/2*c) - 2*imag_part(cos
_integral(-b*x + d*x + c - b*c/d))*tan(1/2*a - 1/2*c) + 4*sin_integral((b*d*x - d^2*x + b*c - c*d)/d)*tan(1/2*
a - 1/2*c) + 2*imag_part(cos_integral(b*x + d*x + c + b*c/d))*tan(1/2*(b*c + c*d)/d) - 2*imag_part(cos_integra
l(-b*x - d*x - c - b*c/d))*tan(1/2*(b*c + c*d)/d) + 4*sin_integral((b*d*x + d^2*x + b*c + c*d)/d)*tan(1/2*(b*c
+ c*d)/d) - 2*imag_part(cos_integral(b*x - d*x - c + b*c/d))*tan(1/2*(b*c - c*d)/d) + 2*imag_part(cos_integra
l(-b*x + d*x + c - b*c/d))*tan(1/2*(b*c - c*d)/d) - 4*sin_integral((b*d*x - d^2*x + b*c - c*d)/d)*tan(1/2*(b*c
- c*d)/d) + real_part(cos_integral(b*x + d*x + c + b*c/d)) - real_part(cos_integral(b*x - d*x - c + b*c/d)) -
real_part(cos_integral(-b*x + d*x + c - b*c/d)) + real_part(cos_integral(-b*x - d*x - c - b*c/d)))*d/(b*d*tan
(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d)^2 + b*d*tan(1/2*a + 1/2
*c)^2*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2 + b*d*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)^2*tan(1/2*(b
*c - c*d)/d)^2 + b*d*tan(1/2*a + 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d)^2 + b*d*tan(1/2*a -
1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d)^2 + b*d*tan(1/2*a + 1/2*c)^2*tan(1/2*a - 1/2*c)^2 + b
*d*tan(1/2*a + 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2 + b*d*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c + c*d)/d)^2 + b*d*tan
(1/2*a + 1/2*c)^2*tan(1/2*(b*c - c*d)/d)^2 + b*d*tan(1/2*a - 1/2*c)^2*tan(1/2*(b*c - c*d)/d)^2 + b*d*tan(1/2*(
b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d)^2 + b*d*tan(1/2*a + 1/2*c)^2 + b*d*tan(1/2*a - 1/2*c)^2 + b*d*tan(1/2*(
b*c + c*d)/d)^2 + b*d*tan(1/2*(b*c - c*d)/d)^2 + b*d) + sin(b*x + a)*sin_integral(d*x + c)/b

Mupad [F(-1)]

Timed out. \[ \int \cos (a+b x) \text {Si}(c+d x) \, dx=\int \mathrm {sinint}\left (c+d\,x\right )\,\cos \left (a+b\,x\right ) \,d x \]

[In]

int(sinint(c + d*x)*cos(a + b*x),x)

[Out]

int(sinint(c + d*x)*cos(a + b*x), x)