3.2.9 \(\int \frac {\text {CosIntegral}(b x) \sin (b x)}{x} \, dx\) [109]

Optimal. Leaf size=15 \[ \text {Int}\left (\frac {\text {CosIntegral}(b x) \sin (b x)}{x},x\right ) \]

[Out]

CannotIntegrate(Ci(b*x)*sin(b*x)/x,x)

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Rubi [A]
time = 0.02, 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}(b x) \sin (b x)}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(CosIntegral[b*x]*Sin[b*x])/x,x]

[Out]

Defer[Int][(CosIntegral[b*x]*Sin[b*x])/x, x]

Rubi steps

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

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Mathematica [A]
time = 1.43, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\text {CosIntegral}(b x) \sin (b x)}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(CosIntegral[b*x]*Sin[b*x])/x,x]

[Out]

Integrate[(CosIntegral[b*x]*Sin[b*x])/x, x]

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Maple [A]
time = 0.10, size = 0, normalized size = 0.00 \[\int \frac {\cosineIntegral \left (b x \right ) \sin \left (b x \right )}{x}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(Ci(b*x)*sin(b*x)/x,x)

[Out]

int(Ci(b*x)*sin(b*x)/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(b*x)*sin(b*x)/x,x, algorithm="maxima")

[Out]

integrate(fresnel_cos(b*x)*sin(b*x)/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(b*x)*sin(b*x)/x,x, algorithm="fricas")

[Out]

integral(fresnel_cos(b*x)*sin(b*x)/x, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(Ci(b*x)*sin(b*x)/x,x)

[Out]

Integral(sin(b*x)*Ci(b*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(b*x)*sin(b*x)/x,x, algorithm="giac")

[Out]

integrate(fresnel_cos(b*x)*sin(b*x)/x, x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.07 \begin {gather*} \int \frac {\mathrm {cosint}\left (b\,x\right )\,\sin \left (b\,x\right )}{x} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((cosint(b*x)*sin(b*x))/x,x)

[Out]

int((cosint(b*x)*sin(b*x))/x, x)

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