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

Optimal. Leaf size=370 \[ \frac{\sin \left (a-\frac{b c}{d}\right ) \text{CosIntegral}\left (\frac{c (b-d)}{d}+x (b-d)\right )}{2 b^2}-\frac{\sin \left (a-\frac{b c}{d}\right ) \text{CosIntegral}\left (\frac{c (b+d)}{d}+x (b+d)\right )}{2 b^2}+\frac{\cos \left (a-\frac{b c}{d}\right ) \text{Si}\left (x (b-d)+\frac{c (b-d)}{d}\right )}{2 b^2}+\frac{\cos (a+b x) \text{Si}(c+d x)}{b^2}-\frac{\cos \left (a-\frac{b c}{d}\right ) \text{Si}\left (x (b+d)+\frac{c (b+d)}{d}\right )}{2 b^2}+\frac{c \cos \left (a-\frac{b c}{d}\right ) \text{CosIntegral}\left (\frac{c (b-d)}{d}+x (b-d)\right )}{2 b d}-\frac{c \cos \left (a-\frac{b c}{d}\right ) \text{CosIntegral}\left (\frac{c (b+d)}{d}+x (b+d)\right )}{2 b d}-\frac{c \sin \left (a-\frac{b c}{d}\right ) \text{Si}\left (x (b-d)+\frac{c (b-d)}{d}\right )}{2 b d}+\frac{x \sin (a+b x) \text{Si}(c+d x)}{b}+\frac{c \sin \left (a-\frac{b c}{d}\right ) \text{Si}\left (x (b+d)+\frac{c (b+d)}{d}\right )}{2 b d}-\frac{\sin (a+x (b-d)-c)}{2 b (b-d)}+\frac{\sin (a+x (b+d)+c)}{2 b (b+d)} \]

[Out]

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

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Rubi [A]  time = 1.24023, antiderivative size = 370, normalized size of antiderivative = 1., number of steps used = 24, number of rules used = 9, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.643, Rules used = {6519, 4608, 6742, 2637, 3303, 3299, 3302, 6511, 4430} \[ \frac{\sin \left (a-\frac{b c}{d}\right ) \text{CosIntegral}\left (\frac{c (b-d)}{d}+x (b-d)\right )}{2 b^2}-\frac{\sin \left (a-\frac{b c}{d}\right ) \text{CosIntegral}\left (\frac{c (b+d)}{d}+x (b+d)\right )}{2 b^2}+\frac{\cos \left (a-\frac{b c}{d}\right ) \text{Si}\left (x (b-d)+\frac{c (b-d)}{d}\right )}{2 b^2}+\frac{\cos (a+b x) \text{Si}(c+d x)}{b^2}-\frac{\cos \left (a-\frac{b c}{d}\right ) \text{Si}\left (x (b+d)+\frac{c (b+d)}{d}\right )}{2 b^2}+\frac{c \cos \left (a-\frac{b c}{d}\right ) \text{CosIntegral}\left (\frac{c (b-d)}{d}+x (b-d)\right )}{2 b d}-\frac{c \cos \left (a-\frac{b c}{d}\right ) \text{CosIntegral}\left (\frac{c (b+d)}{d}+x (b+d)\right )}{2 b d}-\frac{c \sin \left (a-\frac{b c}{d}\right ) \text{Si}\left (x (b-d)+\frac{c (b-d)}{d}\right )}{2 b d}+\frac{x \sin (a+b x) \text{Si}(c+d x)}{b}+\frac{c \sin \left (a-\frac{b c}{d}\right ) \text{Si}\left (x (b+d)+\frac{c (b+d)}{d}\right )}{2 b d}-\frac{\sin (a+x (b-d)-c)}{2 b (b-d)}+\frac{\sin (a+x (b+d)+c)}{2 b (b+d)} \]

Antiderivative was successfully verified.

[In]

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

[Out]

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

Rule 6519

Int[Cos[(a_.) + (b_.)*(x_)]*((e_.) + (f_.)*(x_))^(m_.)*SinIntegral[(c_.) + (d_.)*(x_)], x_Symbol] :> Simp[((e
+ f*x)^m*Sin[a + b*x]*SinIntegral[c + d*x])/b, x] + (-Dist[d/b, Int[((e + f*x)^m*Sin[a + b*x]*Sin[c + d*x])/(c
+ d*x), x], x] - Dist[(f*m)/b, Int[(e + f*x)^(m - 1)*Sin[a + b*x]*SinIntegral[c + d*x], x], x]) /; FreeQ[{a,
b, c, d, e, f}, x] && IGtQ[m, 0]

Rule 4608

Int[(u_.)*Sin[(a_.) + (b_.)*(x_)]^(m_.)*Sin[(c_.) + (d_.)*(x_)]^(n_.), x_Symbol] :> Int[ExpandTrigReduce[u, Si
n[a + b*x]^m*Sin[c + d*x]^n, x], x] /; FreeQ[{a, b, c, d}, x] && IGtQ[m, 0] && IGtQ[n, 0]

Rule 6742

Int[u_, x_Symbol] :> With[{v = ExpandIntegrand[u, x]}, Int[v, x] /; SumQ[v]]

Rule 2637

Int[sin[Pi/2 + (c_.) + (d_.)*(x_)], x_Symbol] :> Simp[Sin[c + d*x]/d, x] /; FreeQ[{c, d}, x]

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 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 6511

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

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]

Rubi steps

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

Mathematica [C]  time = 4.21426, size = 393, normalized size = 1.06 \[ \frac{e^{-\frac{i (d (a-d x)+b (c+d x))}{d}} \left (-\left (b^2-d^2\right ) (b c-i d) e^{i (2 a+x (b-d))} \text{ExpIntegralEi}\left (\frac{i (b+d) (c+d x)}{d}\right )-i b d e^{\frac{i c (b+d)}{d}} \left (-d e^{2 i (a+b x)}+b e^{2 i (a+b x)}+b+d\right )+\left (b^2-d^2\right ) (b c+i d) e^{i b \left (\frac{2 c}{d}+x\right )-i d x} \text{ExpIntegralEi}\left (-\frac{i (b-d) (c+d x)}{d}\right )\right )}{4 b^2 d (b-d) (b+d)}-\frac{e^{-i (a+c)} \left ((-b c+i d) e^{\frac{i (d (2 a+c)-b c)}{d}} \text{ExpIntegralEi}\left (\frac{i (b-d) (c+d x)}{d}\right )-i b d \left (\frac{e^{i (2 a+x (b-d))}}{b-d}+\frac{e^{-i x (b+d)}}{b+d}\right )+(b c+i d) e^{\frac{i c (b+d)}{d}} \text{ExpIntegralEi}\left (-\frac{i (b+d) (c+d x)}{d}\right )\right )}{4 b^2 d}+\frac{\text{Si}(c+d x) (b x \sin (a+b x)+\cos (a+b x))}{b^2} \]

Warning: Unable to verify antiderivative.

[In]

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

[Out]

-((-I)*b*d*(1/((b + d)*E^(I*(b + d)*x)) + E^(I*(2*a + (b - d)*x))/(b - d)) + (-(b*c) + I*d)*E^((I*(-(b*c) + (2
*a + c)*d))/d)*ExpIntegralEi[(I*(b - d)*(c + d*x))/d] + (b*c + I*d)*E^((I*c*(b + d))/d)*ExpIntegralEi[((-I)*(b
+ d)*(c + d*x))/d])/(4*b^2*d*E^(I*(a + c))) + ((-I)*b*d*E^((I*c*(b + d))/d)*(b + d + b*E^((2*I)*(a + b*x)) -
d*E^((2*I)*(a + b*x))) + (b*c + I*d)*(b^2 - d^2)*E^((-I)*d*x + I*b*((2*c)/d + x))*ExpIntegralEi[((-I)*(b - d)*
(c + d*x))/d] - (b*c - I*d)*(b^2 - d^2)*E^(I*(2*a + (b - d)*x))*ExpIntegralEi[(I*(b + d)*(c + d*x))/d])/(4*b^2
*(b - d)*d*(b + d)*E^((I*(d*(a - d*x) + b*(c + d*x)))/d)) + ((Cos[a + b*x] + b*x*Sin[a + b*x])*SinIntegral[c +
d*x])/b^2

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Maple [B]  time = 0.107, size = 1208, normalized size = 3.3 \begin{align*} \text{result too large to display} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(Si(d*x+c)/b*(1/b*d*(sin(b/d*(d*x+c)+(a*d-b*c)/d)*(b/d*(d*x+c)+(a*d-b*c)/d)+cos(b/d*(d*x+c)+(a*d-b*c)/d))-a*d/
b*sin(b/d*(d*x+c)+(a*d-b*c)/d))-1/b*(1/2/(b-d)*d*sin((b-d)/d*(d*x+c)+(a*d-b*c)/d)+1/2*(a*d-b*c)*d/(b-d)*(Si((b
-d)/d*(d*x+c)+(a*d-b*c)/d+(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d+Ci((b-d)/d*(d*x+c)+(a*d-b*c)/d+(-a*d+b*c)/d)*cos((
-a*d+b*c)/d)/d)-1/2/(b-d)*d^2*a*(Si((b-d)/d*(d*x+c)+(a*d-b*c)/d+(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d+Ci((b-d)/d*(
d*x+c)+(a*d-b*c)/d+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d)+1/2/(b-d)*c*d^2*(Si((b-d)/d*(d*x+c)+(a*d-b*c)/d+(-a*d+b*
c)/d)*sin((-a*d+b*c)/d)/d+Ci((b-d)/d*(d*x+c)+(a*d-b*c)/d+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d)-1/2/(b+d)*d*sin((b
+d)/d*(d*x+c)+(a*d-b*c)/d)-1/2*(a*d-b*c)*d/(b+d)*(Si((b+d)/d*(d*x+c)+(a*d-b*c)/d+(-a*d+b*c)/d)*sin((-a*d+b*c)/
d)/d+Ci((b+d)/d*(d*x+c)+(a*d-b*c)/d+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d)+1/2/(b+d)*d^2*a*(Si((b+d)/d*(d*x+c)+(a*
d-b*c)/d+(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d+Ci((b+d)/d*(d*x+c)+(a*d-b*c)/d+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d)+1
/2/(b+d)*c*d^2*(Si((b+d)/d*(d*x+c)+(a*d-b*c)/d+(-a*d+b*c)/d)*sin((-a*d+b*c)/d)/d+Ci((b+d)/d*(d*x+c)+(a*d-b*c)/
d+(-a*d+b*c)/d)*cos((-a*d+b*c)/d)/d)-1/2/b*d^2*(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/b*d^2*(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., size = 0, normalized size = 0. \begin{align*} \int x{\rm Si}\left (d x + c\right ) \cos \left (b x + a\right )\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Fricas [F]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (x \cos \left (b x + a\right ) \operatorname{Si}\left (d x + c\right ), x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Sympy [F]  time = 0., size = 0, normalized size = 0. \begin{align*} \int x \cos{\left (a + b x \right )} \operatorname{Si}{\left (c + d x \right )}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Giac [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out