Optimal. Leaf size=22 \[ \text {Int}\left (\text {FresnelC}(b x)^n \sin \left (\frac {1}{2} b^2 \pi x^2\right ),x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, 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 \text {FresnelC}(b x)^n \sin \left (\frac {1}{2} b^2 \pi x^2\right ) \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int C(b x)^n \sin \left (\frac {1}{2} b^2 \pi x^2\right ) \, dx &=\int C(b x)^n \sin \left (\frac {1}{2} b^2 \pi x^2\right ) \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.05, size = 0, normalized size = 0.00 \begin {gather*} \int \text {FresnelC}(b x)^n \sin \left (\frac {1}{2} b^2 \pi x^2\right ) \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.04, size = 0, normalized size = 0.00 \[\int \FresnelC \left (b x \right )^{n} \sin \left (\frac {b^{2} \pi \,x^{2}}{2}\right )\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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]
[Out]
________________________________________________________________________________________
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]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \sin {\left (\frac {\pi b^{2} x^{2}}{2} \right )} C^{n}\left (b x\right )\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
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]
[Out]
________________________________________________________________________________________
Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int {\mathrm {FresnelC}\left (b\,x\right )}^n\,\sin \left (\frac {\Pi \,b^2\,x^2}{2}\right ) \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________