Optimal. Leaf size=9 \[ \frac {\log (C(b x))}{b} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {6441, 29} \[ \frac {\log (\text {FresnelC}(b x))}{b} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 29
Rule 6441
Rubi steps
\begin {align*} \int \frac {\cos \left (\frac {1}{2} b^2 \pi x^2\right )}{C(b x)} \, dx &=\frac {\operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,C(b x)\right )}{b}\\ &=\frac {\log (C(b x))}{b}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 9, normalized size = 1.00 \[ \frac {\log (C(b x))}{b} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [F] time = 0.40, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\cos \left (\frac {1}{2} \, \pi b^{2} x^{2}\right )}{{\rm fresnelc}\left (b x\right )}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\cos \left (\frac {1}{2} \, \pi b^{2} x^{2}\right )}{{\rm fresnelc}\left (b x\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.08, size = 10, normalized size = 1.11 \[ \frac {\ln \left (\FresnelC \left (b x \right )\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\cos \left (\frac {1}{2} \, \pi b^{2} x^{2}\right )}{{\rm fresnelc}\left (b x\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.11 \[ \int \frac {\cos \left (\frac {\Pi \,b^2\,x^2}{2}\right )}{\mathrm {FresnelC}\left (b\,x\right )} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.24, size = 10, normalized size = 1.11 \[ \begin {cases} \frac {\log {\left (C\left (b x\right ) \right )}}{b} & \text {for}\: b \neq 0 \\\tilde {\infty } x & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________