3.99 \(\int \frac {\text {Ci}(a+b x)^2}{x^3} \, dx\)

Optimal. Leaf size=15 \[ \text {Int}\left (\frac {\text {Ci}(a+b x)^2}{x^3},x\right ) \]

[Out]

CannotIntegrate(Ci(b*x+a)^2/x^3,x)

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Rubi [A]  time = 0.03, 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 = {} \[ \int \frac {\text {CosIntegral}(a+b x)^2}{x^3} \, dx \]

Verification is Not applicable to the result.

[In]

Int[CosIntegral[a + b*x]^2/x^3,x]

[Out]

Defer[Int][CosIntegral[a + b*x]^2/x^3, x]

Rubi steps

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

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Mathematica [A]  time = 2.75, size = 0, normalized size = 0.00 \[ \int \frac {\text {Ci}(a+b x)^2}{x^3} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[CosIntegral[a + b*x]^2/x^3,x]

[Out]

Integrate[CosIntegral[a + b*x]^2/x^3, x]

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fricas [A]  time = 1.12, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\operatorname {Ci}\left (b x + a\right )^{2}}{x^{3}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(Ci(b*x+a)^2/x^3,x, algorithm="fricas")

[Out]

integral(cos_integral(b*x + a)^2/x^3, x)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\rm Ci}\left (b x + a\right )^{2}}{x^{3}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(Ci(b*x+a)^2/x^3,x, algorithm="giac")

[Out]

integrate(Ci(b*x + a)^2/x^3, x)

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maple [A]  time = 0.02, size = 0, normalized size = 0.00 \[ \int \frac {\Ci \left (b x +a \right )^{2}}{x^{3}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(Ci(b*x+a)^2/x^3,x)

[Out]

int(Ci(b*x+a)^2/x^3,x)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\rm Ci}\left (b x + a\right )^{2}}{x^{3}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(Ci(b*x+a)^2/x^3,x, algorithm="maxima")

[Out]

integrate(Ci(b*x + a)^2/x^3, x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.07 \[ \int \frac {{\mathrm {cosint}\left (a+b\,x\right )}^2}{x^3} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(cosint(a + b*x)^2/x^3,x)

[Out]

int(cosint(a + b*x)^2/x^3, x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {Ci}^{2}{\left (a + b x \right )}}{x^{3}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(Ci(b*x+a)**2/x**3,x)

[Out]

Integral(Ci(a + b*x)**2/x**3, x)

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