3.150 \(\int \frac {C(b x)^2}{x^3} \, dx\)

Optimal. Leaf size=39 \[ b \text {Int}\left (\frac {C(b x) \cos \left (\frac {1}{2} \pi b^2 x^2\right )}{x^2},x\right )-\frac {C(b x)^2}{2 x^2} \]

[Out]

-1/2*FresnelC(b*x)^2/x^2+b*Unintegrable(cos(1/2*b^2*Pi*x^2)*FresnelC(b*x)/x^2,x)

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Rubi [A]  time = 0.04, 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 = {} \[ \int \frac {\text {FresnelC}(b x)^2}{x^3} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

-FresnelC[b*x]^2/(2*x^2) + b*Defer[Int][(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x^2, x]

Rubi steps

\begin {align*} \int \frac {C(b x)^2}{x^3} \, dx &=-\frac {C(b x)^2}{2 x^2}+b \int \frac {\cos \left (\frac {1}{2} b^2 \pi x^2\right ) C(b x)}{x^2} \, dx\\ \end {align*}

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Mathematica [A]  time = 0.02, size = 0, normalized size = 0.00 \[ \int \frac {C(b x)^2}{x^3} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

Integrate[FresnelC[b*x]^2/x^3, x]

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fricas [A]  time = 0.47, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\rm fresnelc}\left (b x\right )^{2}}{x^{3}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(fresnelc(b*x)^2/x^3, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(fresnelc(b*x)^2/x^3,x, algorithm="giac")

[Out]

integrate(fresnelc(b*x)^2/x^3, x)

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maple [A]  time = 0.01, size = 0, normalized size = 0.00 \[ \int \frac {\FresnelC \left (b x \right )^{2}}{x^{3}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(fresnelc(b*x)^2/x^3,x, algorithm="maxima")

[Out]

integrate(fresnelc(b*x)^2/x^3, x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {{\mathrm {FresnelC}\left (b\,x\right )}^2}{x^3} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int(FresnelC(b*x)^2/x^3, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(fresnelc(b*x)**2/x**3, x)

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