Optimal. Leaf size=27 \[ x C(b x)-\frac {\sin \left (\frac {1}{2} \pi b^2 x^2\right )}{\pi b} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {6419} \[ x \text {FresnelC}(b x)-\frac {\sin \left (\frac {1}{2} \pi b^2 x^2\right )}{\pi b} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 6419
Rubi steps
\begin {align*} \int C(b x) \, dx &=x C(b x)-\frac {\sin \left (\frac {1}{2} b^2 \pi x^2\right )}{b \pi }\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 27, normalized size = 1.00 \[ x C(b x)-\frac {\sin \left (\frac {1}{2} \pi b^2 x^2\right )}{\pi b} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [F] time = 0.45, size = 0, normalized size = 0.00 \[ {\rm integral}\left ({\rm fresnelc}\left (b x\right ), x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\rm fresnelc}\left (b x\right )\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 28, normalized size = 1.04 \[ \frac {b x \FresnelC \left (b x \right )-\frac {\sin \left (\frac {b^{2} \pi \,x^{2}}{2}\right )}{\pi }}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\rm fresnelc}\left (b x\right )\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.04 \[ \int \mathrm {FresnelC}\left (b\,x\right ) \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [B] time = 0.70, size = 44, normalized size = 1.63 \[ \frac {x C\left (b x\right ) \Gamma \left (\frac {1}{4}\right )}{4 \Gamma \left (\frac {5}{4}\right )} - \frac {\sin {\left (\frac {\pi b^{2} x^{2}}{2} \right )} \Gamma \left (\frac {1}{4}\right )}{4 \pi b \Gamma \left (\frac {5}{4}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________