Integrand size = 12, antiderivative size = 12 \[ \int x \sqrt {\cos (a+b x)} \, dx=\text {Int}\left (x \sqrt {\cos (a+b x)},x\right ) \]
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Not integrable
Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int x \sqrt {\cos (a+b x)} \, dx=\int x \sqrt {\cos (a+b x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int x \sqrt {\cos (a+b x)} \, dx \\ \end{align*}
Not integrable
Time = 26.26 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int x \sqrt {\cos (a+b x)} \, dx=\int x \sqrt {\cos (a+b x)} \, dx \]
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Not integrable
Time = 0.12 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83
\[\int x \left (\sqrt {\cos }\left (b x +a \right )\right )d x\]
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Exception generated. \[ \int x \sqrt {\cos (a+b x)} \, dx=\text {Exception raised: TypeError} \]
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Not integrable
Time = 6.36 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int x \sqrt {\cos (a+b x)} \, dx=\int x \sqrt {\cos {\left (a + b x \right )}}\, dx \]
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Not integrable
Time = 0.70 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int x \sqrt {\cos (a+b x)} \, dx=\int { x \sqrt {\cos \left (b x + a\right )} \,d x } \]
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Not integrable
Time = 0.33 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int x \sqrt {\cos (a+b x)} \, dx=\int { x \sqrt {\cos \left (b x + a\right )} \,d x } \]
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Not integrable
Time = 13.31 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int x \sqrt {\cos (a+b x)} \, dx=\int x\,\sqrt {\cos \left (a+b\,x\right )} \,d x \]
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