3.2.33 \(\int \frac {\text {CosIntegral}(c+d x) \sin (a+b x)}{x} \, dx\) [133]

Optimal. Leaf size=19 \[ \text {Int}\left (\frac {\text {CosIntegral}(c+d x) \sin (a+b x)}{x},x\right ) \]

[Out]

CannotIntegrate(Ci(d*x+c)*sin(b*x+a)/x,x)

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Rubi [A]
time = 0.11, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {\text {CosIntegral}(c+d x) \sin (a+b x)}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(CosIntegral[c + d*x]*Sin[a + b*x])/x,x]

[Out]

Defer[Int][(CosIntegral[c + d*x]*Sin[a + b*x])/x, x]

Rubi steps

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

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Mathematica [A]
time = 21.64, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\text {CosIntegral}(c+d x) \sin (a+b x)}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(CosIntegral[c + d*x]*Sin[a + b*x])/x,x]

[Out]

Integrate[(CosIntegral[c + d*x]*Sin[a + b*x])/x, x]

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Maple [A]
time = 0.12, size = 0, normalized size = 0.00 \[\int \frac {\cosineIntegral \left (d x +c \right ) \sin \left (b x +a \right )}{x}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(fresnel_cos(d*x+c)*sin(b*x+a)/x,x, algorithm="maxima")

[Out]

integrate(fresnel_cos(d*x + c)*sin(b*x + a)/x, x)

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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(fresnel_cos(d*x+c)*sin(b*x+a)/x,x, algorithm="fricas")

[Out]

integral(fresnel_cos(d*x + c)*sin(b*x + a)/x, x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sin {\left (a + b x \right )} \operatorname {Ci}{\left (c + d x \right )}}{x}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(sin(a + b*x)*Ci(c + d*x)/x, x)

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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(fresnel_cos(d*x+c)*sin(b*x+a)/x,x, algorithm="giac")

[Out]

integrate(fresnel_cos(d*x + c)*sin(b*x + a)/x, x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {\mathrm {cosint}\left (c+d\,x\right )\,\sin \left (a+b\,x\right )}{x} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((cosint(c + d*x)*sin(a + b*x))/x,x)

[Out]

int((cosint(c + d*x)*sin(a + b*x))/x, x)

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