\(\int \operatorname {FresnelC}(b x)^n \sin (\frac {1}{2} b^2 \pi x^2) \, dx\) [199]

Optimal result

Integrand size = 19, antiderivative size = 19 \[ \int \operatorname {FresnelC}(b x)^n \sin \left (\frac {1}{2} b^2 \pi x^2\right ) \, dx=\text {Int}\left (\operatorname {FresnelC}(b x)^n \sin \left (\frac {1}{2} b^2 \pi x^2\right ),x\right ) \]

[Out]

Unintegrable(FresnelC(b*x)^n*sin(1/2*b^2*Pi*x^2),x)

Rubi [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \operatorname {FresnelC}(b x)^n \sin \left (\frac {1}{2} b^2 \pi x^2\right ) \, dx=\int \operatorname {FresnelC}(b x)^n \sin \left (\frac {1}{2} b^2 \pi x^2\right ) \, dx \]

[In]

Int[FresnelC[b*x]^n*Sin[(b^2*Pi*x^2)/2],x]

[Out]

Defer[Int][FresnelC[b*x]^n*Sin[(b^2*Pi*x^2)/2], x]

Rubi steps \begin{align*} \text {integral}& = \int \operatorname {FresnelC}(b x)^n \sin \left (\frac {1}{2} b^2 \pi x^2\right ) \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 0.05 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.11 \[ \int \operatorname {FresnelC}(b x)^n \sin \left (\frac {1}{2} b^2 \pi x^2\right ) \, dx=\int \operatorname {FresnelC}(b x)^n \sin \left (\frac {1}{2} b^2 \pi x^2\right ) \, dx \]

[In]

Integrate[FresnelC[b*x]^n*Sin[(b^2*Pi*x^2)/2],x]

[Out]

Integrate[FresnelC[b*x]^n*Sin[(b^2*Pi*x^2)/2], x]

Maple [N/A] (verified)

Not integrable

Time = 0.13 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.89

\[\int \operatorname {FresnelC}\left (b x \right )^{n} \sin \left (\frac {b^{2} \pi \,x^{2}}{2}\right )d x\]

[In]

int(FresnelC(b*x)^n*sin(1/2*b^2*Pi*x^2),x)

[Out]

int(FresnelC(b*x)^n*sin(1/2*b^2*Pi*x^2),x)

Fricas [N/A]

Not integrable

Time = 0.26 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00 \[ \int \operatorname {FresnelC}(b x)^n \sin \left (\frac {1}{2} b^2 \pi x^2\right ) \, dx=\int { \operatorname {C}\left (b x\right )^{n} \sin \left (\frac {1}{2} \, \pi b^{2} x^{2}\right ) \,d x } \]

[In]

integrate(fresnel_cos(b*x)^n*sin(1/2*b^2*pi*x^2),x, algorithm="fricas")

[Out]

integral(fresnel_cos(b*x)^n*sin(1/2*pi*b^2*x^2), x)

Sympy [N/A]

Not integrable

Time = 1.13 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00 \[ \int \operatorname {FresnelC}(b x)^n \sin \left (\frac {1}{2} b^2 \pi x^2\right ) \, dx=\int \sin {\left (\frac {\pi b^{2} x^{2}}{2} \right )} C^{n}\left (b x\right )\, dx \]

[In]

integrate(fresnelc(b*x)**n*sin(1/2*b**2*pi*x**2),x)

[Out]

Integral(sin(pi*b**2*x**2/2)*fresnelc(b*x)**n, x)

Maxima [N/A]

Not integrable

Time = 0.28 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00 \[ \int \operatorname {FresnelC}(b x)^n \sin \left (\frac {1}{2} b^2 \pi x^2\right ) \, dx=\int { \operatorname {C}\left (b x\right )^{n} \sin \left (\frac {1}{2} \, \pi b^{2} x^{2}\right ) \,d x } \]

[In]

integrate(fresnel_cos(b*x)^n*sin(1/2*b^2*pi*x^2),x, algorithm="maxima")

[Out]

integrate(fresnel_cos(b*x)^n*sin(1/2*pi*b^2*x^2), x)

Giac [N/A]

Not integrable

Time = 0.31 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00 \[ \int \operatorname {FresnelC}(b x)^n \sin \left (\frac {1}{2} b^2 \pi x^2\right ) \, dx=\int { \operatorname {C}\left (b x\right )^{n} \sin \left (\frac {1}{2} \, \pi b^{2} x^{2}\right ) \,d x } \]

[In]

integrate(fresnel_cos(b*x)^n*sin(1/2*b^2*pi*x^2),x, algorithm="giac")

[Out]

integrate(fresnel_cos(b*x)^n*sin(1/2*pi*b^2*x^2), x)

Mupad [N/A]

Not integrable

Time = 4.70 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00 \[ \int \operatorname {FresnelC}(b x)^n \sin \left (\frac {1}{2} b^2 \pi x^2\right ) \, dx=\int {\mathrm {FresnelC}\left (b\,x\right )}^n\,\sin \left (\frac {\Pi \,b^2\,x^2}{2}\right ) \,d x \]

[In]

int(FresnelC(b*x)^n*sin((Pi*b^2*x^2)/2),x)

[Out]

int(FresnelC(b*x)^n*sin((Pi*b^2*x^2)/2), x)