Optimal. Leaf size=30 \[ \frac{\log (x)}{2}-\frac{1}{2} \text{Unintegrable}\left (\frac{\cos \left (2 x^2+2 x+\frac{1}{2}\right )}{x},x\right ) \]
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Rubi [A] time = 0.0275321, 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 = {} \[ \int \frac{\sin ^2\left (\frac{1}{4}+x+x^2\right )}{x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\sin ^2\left (\frac{1}{4}+x+x^2\right )}{x} \, dx &=\int \left (\frac{1}{2 x}-\frac{\cos \left (\frac{1}{2}+2 x+2 x^2\right )}{2 x}\right ) \, dx\\ &=\frac{\log (x)}{2}-\frac{1}{2} \int \frac{\cos \left (\frac{1}{2}+2 x+2 x^2\right )}{x} \, dx\\ \end{align*}
Mathematica [A] time = 10.9925, size = 0, normalized size = 0. \[ \int \frac{\sin ^2\left (\frac{1}{4}+x+x^2\right )}{x} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.106, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{x} \left ( \sin \left ({\frac{1}{4}}+x+{x}^{2} \right ) \right ) ^{2}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} -\frac{1}{2} \, \int \frac{\cos \left (2 \, x^{2} + 2 \, x + \frac{1}{2}\right )}{x}\,{d x} + \frac{1}{2} \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (-\frac{\cos \left (x^{2} + x + \frac{1}{4}\right )^{2} - 1}{x}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sin ^{2}{\left (x^{2} + x + \frac{1}{4} \right )}}{x}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sin \left (x^{2} + x + \frac{1}{4}\right )^{2}}{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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