3.135 \(\int \cos (a+b x) \text {Ci}(c+d x) \, dx\)

Optimal. Leaf size=153 \[ -\frac {\sin \left (a-\frac {b c}{d}\right ) \text {Ci}\left (x (b-d)+\frac {c (b-d)}{d}\right )}{2 b}-\frac {\sin \left (a-\frac {b c}{d}\right ) \text {Ci}\left (x (b+d)+\frac {c (b+d)}{d}\right )}{2 b}+\frac {\sin (a+b x) \text {Ci}(c+d x)}{b}-\frac {\cos \left (a-\frac {b c}{d}\right ) \text {Si}\left (x (b-d)+\frac {c (b-d)}{d}\right )}{2 b}-\frac {\cos \left (a-\frac {b c}{d}\right ) \text {Si}\left (x (b+d)+\frac {c (b+d)}{d}\right )}{2 b} \]

[Out]

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

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Rubi [A]  time = 0.22, antiderivative size = 153, normalized size of antiderivative = 1.00, number of steps used = 9, number of rules used = 5, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.385, Rules used = {6512, 4430, 3303, 3299, 3302} \[ -\frac {\sin \left (a-\frac {b c}{d}\right ) \text {CosIntegral}\left (\frac {c (b-d)}{d}+x (b-d)\right )}{2 b}-\frac {\sin \left (a-\frac {b c}{d}\right ) \text {CosIntegral}\left (\frac {c (b+d)}{d}+x (b+d)\right )}{2 b}+\frac {\sin (a+b x) \text {CosIntegral}(c+d x)}{b}-\frac {\cos \left (a-\frac {b c}{d}\right ) \text {Si}\left (x (b-d)+\frac {c (b-d)}{d}\right )}{2 b}-\frac {\cos \left (a-\frac {b c}{d}\right ) \text {Si}\left (x (b+d)+\frac {c (b+d)}{d}\right )}{2 b} \]

Antiderivative was successfully verified.

[In]

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

[Out]

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

Rule 3299

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 3302

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 3303

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 4430

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

Rule 6512

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

Rubi steps

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

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Mathematica [C]  time = 1.43, size = 153, normalized size = 1.00 \[ \frac {4 \sin (a+b x) \text {Ci}(c+d x)+i e^{-\frac {i (a d+b c)}{d}} \left (e^{2 i a} \text {Ei}\left (\frac {i (b-d) (c+d x)}{d}\right )+e^{2 i a} \text {Ei}\left (\frac {i (b+d) (c+d x)}{d}\right )-e^{\frac {2 i b c}{d}} \text {Ei}\left (-\frac {i (b-d) (c+d x)}{d}\right )-e^{\frac {2 i b c}{d}} \text {Ei}\left (-\frac {i (b+d) (c+d x)}{d}\right )\right )}{4 b} \]

Antiderivative was successfully verified.

[In]

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

[Out]

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

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fricas [F]  time = 0.87, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\cos \left (b x + a\right ) \operatorname {Ci}\left (d x + c\right ), x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(cos(b*x + a)*cos_integral(d*x + c), x)

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giac [C]  time = 0.66, size = 9540, normalized size = 62.35 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/4*(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)^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)^2 + 2*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 + 2*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 + 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(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*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)*tan(1/2*(b*c - c*d)/d)^2 - 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)*tan(1/2*(b*c + c*d)/d)^2*tan(1/2*
(b*c - c*d)/d)^2 - 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)*t
an(1/2*(b*c + c*d)/d)^2*tan(1/2*(b*c - c*d)/d)^2 - 2*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)^2*tan(1/2*(b*c - c*d)/d)^2 - 2*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)^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 - 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)^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 + 2*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 - 2*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 + 4*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) - 4*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) + 8*sin_integ
ral((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) - 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)^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)^2 - 2*sin_integral((b*d*x + d^2*x + b*c + c*d)/d)*tan(1/2*a + 1/2*c)^2*ta
n(1/2*a - 1/2*c)^2*tan(1/2*(b*c - c*d)/d)^2 + 2*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 + 4*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)*tan(1/2*(b*c - c*d)/d)^2 - 4*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)*tan(1/2*(b*c - c*d)/d)^2 +
8*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)*t
an(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)^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)^2 + 2*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 - 2*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)^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)^2 - 2*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 + 2*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 + 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)*tan(1/2*(b*c + c*d)/d)^2 + 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)*tan(1/2*(b*c + c*d)/d)^2 - 2*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)^2 - 2*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)^2 + 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_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*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*a - 1/2*c)*t
an(1/2*(b*c - c*d)/d)^2 - 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)*tan(1/2*(b*c - c*d)/d)^2 + 2*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)^2 + 2*real_part(cos_integral(-b*x - d*x - c - b*c/d))*tan(1/2*a + 1/2*c)*ta
n(1/2*a - 1/2*c)^2*tan(1/2*(b*c - c*d)/d)^2 + 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)*tan(1/2*(b*c - c*d)/d)^2 + 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)*tan(1/2*(b*c - c*d)/d)^2 - 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)*tan(1/2*(b*c - c*d)/d)^2 - 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)*tan(1/2*(b*c - c*d)/d)^2 - 2*real_part(cos_integr
al(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*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)^2 - 2
*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)^2 - 2*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)^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*tan(1/2*a - 1/2*c)^2 + imag_part(cos_inte
gral(-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*tan(1/2*a - 1/2*c)^2 - 2*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 - 2*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 + 4*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) - 4*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) + 8*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) + 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)^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_inte
gral(-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 + 2*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 + 2*sin_integral((b*d*x - d^2*x + b*c - c*d)/d)*ta
n(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)^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)^2 - 2*sin_integr
al((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 - 2*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 + 4*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) - 4*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) + 8*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) + 4*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) - 4*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) + 8*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) - imag_part(co
s_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)^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)^2 - 2*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 - 2*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_pa
rt(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)^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 + 2*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 + 2*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 + 4*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)*tan(1/2*(b*c - c*d)/d)^2 - 4*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)*tan(1/2*(b*c - c*d)/d)^2 + 8*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)*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)^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)^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)^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)^2 - 2*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 - 2*si
n_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 + 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_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*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 + 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_pa
rt(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)*tan(1/2*(b*c + c*d)/d)^2 - 2*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 + 2*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 + 2*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 - 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*(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*a + 1/2*
c)*tan(1/2*(b*c - c*d)/d)^2 + 2*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 - 2*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 -
2*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 - 2*real_part(c
os_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*real_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 - 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)^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)^2 - 2*sin_integral((b*d*x + d^2*x + b*c + c*d)/d)*tan(1/2*a + 1/2*c)^2 + 2*sin_integra
l((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)^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)^2 + 2*sin_integral((b*d*x + d^2*x + b*c + c*d)/d)*tan(1/2*a - 1/2*c)^2 - 2*sin_integral((b*d*x - d^2*x + b
*c - c*d)/d)*tan(1/2*a - 1/2*c)^2 + 4*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) - 4*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)
+ 8*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) - imag_part(cos_int
egral(b*x + d*x + c + b*c/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_integral(-b*x + d*x + c - b*c/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 - 2*sin_integral((b*d*x + d^2*x + b*c + c*d)/d)*tan
(1/2*(b*c + c*d)/d)^2 + 2*sin_integral((b*d*x - d^2*x + b*c - c*d)/d)*tan(1/2*(b*c + c*d)/d)^2 + 4*imag_part(c
os_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*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) + 8*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) + imag_part(cos_integral(b*x + d*x + c + b*c/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_integral(-b*x
+ d*x + c - b*c/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 + 2*sin_integral((b*d*x + d^2*x + b*c + c*d)/d)*tan(1/2*(b*c - c*d)/d)^2 - 2*sin_integral((b*d*x - d
^2*x + b*c - c*d)/d)*tan(1/2*(b*c - c*d)/d)^2 + 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*(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*real_part(cos_integral(-b*x + d*x + c - b*c/d))*tan(1/2*(b*c - c*d)/d) + imag_part(cos_integral(b*x + d*x
+ c + b*c/d)) + imag_part(cos_integral(b*x - d*x - c + b*c/d)) - imag_part(cos_integral(-b*x + d*x + c - b*c/
d)) - imag_part(cos_integral(-b*x - d*x - c - b*c/d)) + 2*sin_integral((b*d*x + d^2*x + b*c + c*d)/d) + 2*sin_
integral((b*d*x - d^2*x + b*c - c*d)/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*t
an(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) + cos
_integral(d*x + c)*sin(b*x + a)/b

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maple [A]  time = 0.04, size = 282, normalized size = 1.84 \[ \frac {\frac {\Ci \left (d x +c \right ) \sin \left (\frac {b \left (d x +c \right )}{d}+\frac {a d -b c}{d}\right ) d}{b}-\frac {d \left (\frac {d \left (\frac {\Si \left (\frac {\left (b -d \right ) \left (d x +c \right )}{d}+\frac {a d -b c}{d}+\frac {-a d +b c}{d}\right ) \cos \left (\frac {-a d +b c}{d}\right )}{d}-\frac {\Ci \left (\frac {\left (b -d \right ) \left (d x +c \right )}{d}+\frac {a d -b c}{d}+\frac {-a d +b c}{d}\right ) \sin \left (\frac {-a d +b c}{d}\right )}{d}\right )}{2}+\frac {d \left (\frac {\Si \left (\frac {\left (b +d \right ) \left (d x +c \right )}{d}+\frac {a d -b c}{d}+\frac {-a d +b c}{d}\right ) \cos \left (\frac {-a d +b c}{d}\right )}{d}-\frac {\Ci \left (\frac {\left (b +d \right ) \left (d x +c \right )}{d}+\frac {a d -b c}{d}+\frac {-a d +b c}{d}\right ) \sin \left (\frac {-a d +b c}{d}\right )}{d}\right )}{2}\right )}{b}}{d} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(Ci(d*x+c)*cos(b*x+a),x)

[Out]

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

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \int {\rm Ci}\left (d x + c\right ) \cos \left (b x + a\right )\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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mupad [F]  time = 0.00, size = -1, normalized size = -0.01 \[ \int \mathrm {cosint}\left (c+d\,x\right )\,\cos \left (a+b\,x\right ) \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(cosint(c + d*x)*cos(a + b*x),x)

[Out]

int(cosint(c + d*x)*cos(a + b*x), x)

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sympy [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \cos {\left (a + b x \right )} \operatorname {Ci}{\left (c + d x \right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(cos(a + b*x)*Ci(c + d*x), x)

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