3.1.16 \(\int \frac {\text {Si}(b x)^2}{x^3} \, dx\) [16]

Optimal. Leaf size=13 \[ \text {Int}\left (\frac {\text {Si}(b x)^2}{x^3},x\right ) \]

[Out]

CannotIntegrate(Si(b*x)^2/x^3,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 {Si}(b x)^2}{x^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[SinIntegral[b*x]^2/x^3,x]

[Out]

Defer[Int][SinIntegral[b*x]^2/x^3, x]

Rubi steps

\begin {align*} \int \frac {\text {Si}(b x)^2}{x^3} \, dx &=\int \frac {\text {Si}(b x)^2}{x^3} \, dx\\ \end {align*}

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Mathematica [A]
time = 0.36, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\text {Si}(b x)^2}{x^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[SinIntegral[b*x]^2/x^3,x]

[Out]

Integrate[SinIntegral[b*x]^2/x^3, x]

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Maple [A]
time = 0.14, size = 0, normalized size = 0.00 \[\int \frac {\sinIntegral \left (b x \right )^{2}}{x^{3}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(Si(b*x)^2/x^3,x)

[Out]

int(Si(b*x)^2/x^3,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(sin_integral(b*x)^2/x^3,x, algorithm="maxima")

[Out]

integrate(sin_integral(b*x)^2/x^3, x)

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Fricas [A] Leaf count of result is larger than twice the leaf count of optimal. 87 vs. \(2 (12) = 24\).
time = 0.37, size = 87, normalized size = 6.69 \begin {gather*} \frac {2 \, b^{2} x^{2} \operatorname {Ci}\left (2 \, b x\right ) + 2 \, b^{2} x^{2} \operatorname {Ci}\left (-2 \, b x\right ) - 2 \, b x \cos \left (b x\right ) \operatorname {Si}\left (b x\right ) - {\left (b^{2} x^{2} + 2\right )} \operatorname {Si}\left (b x\right )^{2} + \cos \left (b x\right )^{2} - 2 \, {\left (2 \, b x \cos \left (b x\right ) + \operatorname {Si}\left (b x\right )\right )} \sin \left (b x\right ) - 1}{4 \, x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sin_integral(b*x)^2/x^3,x, algorithm="fricas")

[Out]

1/4*(2*b^2*x^2*cos_integral(2*b*x) + 2*b^2*x^2*cos_integral(-2*b*x) - 2*b*x*cos(b*x)*sin_integral(b*x) - (b^2*
x^2 + 2)*sin_integral(b*x)^2 + cos(b*x)^2 - 2*(2*b*x*cos(b*x) + sin_integral(b*x))*sin(b*x) - 1)/x^2

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\operatorname {Si}^{2}{\left (b x \right )}}{x^{3}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(Si(b*x)**2/x**3,x)

[Out]

Integral(Si(b*x)**2/x**3, 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(sin_integral(b*x)^2/x^3,x, algorithm="giac")

[Out]

integrate(sin_integral(b*x)^2/x^3, x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.08 \begin {gather*} \int \frac {{\mathrm {sinint}\left (b\,x\right )}^2}{x^3} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(sinint(b*x)^2/x^3,x)

[Out]

int(sinint(b*x)^2/x^3, x)

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