Optimal. Leaf size=32 \[ \frac{1}{2} \text{Unintegrable}\left (\frac{\cos \left (2 a+2 b x-2 c x^2\right )}{x},x\right )+\frac{\log (x)}{2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0293602, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{\cos ^2\left (a+b x-c x^2\right )}{x} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{\cos ^2\left (a+b x-c x^2\right )}{x} \, dx &=\int \left (\frac{1}{2 x}+\frac{\cos \left (2 a+2 b x-2 c x^2\right )}{2 x}\right ) \, dx\\ &=\frac{\log (x)}{2}+\frac{1}{2} \int \frac{\cos \left (2 a+2 b x-2 c x^2\right )}{x} \, dx\\ \end{align*}
Mathematica [A] time = 3.42087, size = 0, normalized size = 0. \[ \int \frac{\cos ^2\left (a+b x-c x^2\right )}{x} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.135, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( \cos \left ( -c{x}^{2}+bx+a \right ) \right ) ^{2}}{x}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} \frac{1}{2} \, \int \frac{\cos \left (2 \, c x^{2} - 2 \, b x - 2 \, a\right )}{x}\,{d x} + \frac{1}{2} \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\cos \left (c x^{2} - b x - a\right )^{2}}{x}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\cos ^{2}{\left (a + b x - c x^{2} \right )}}{x}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\cos \left (-c x^{2} + b x + a\right )^{2}}{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]