Integrand size = 10, antiderivative size = 10 \[ \int x \sqrt {\arctan (a x)} \, dx=\text {Int}\left (x \sqrt {\arctan (a x)},x\right ) \]
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Not integrable
Time = 0.01 (sec) , antiderivative size = 10, 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 = {} \[ \int x \sqrt {\arctan (a x)} \, dx=\int x \sqrt {\arctan (a x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int x \sqrt {\arctan (a x)} \, dx \\ \end{align*}
Not integrable
Time = 1.48 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int x \sqrt {\arctan (a x)} \, dx=\int x \sqrt {\arctan (a x)} \, dx \]
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Not integrable
Time = 2.09 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80
\[\int x \sqrt {\arctan \left (a x \right )}d x\]
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Exception generated. \[ \int x \sqrt {\arctan (a x)} \, dx=\text {Exception raised: TypeError} \]
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Not integrable
Time = 0.40 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int x \sqrt {\arctan (a x)} \, dx=\int x \sqrt {\operatorname {atan}{\left (a x \right )}}\, dx \]
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Exception generated. \[ \int x \sqrt {\arctan (a x)} \, dx=\text {Exception raised: RuntimeError} \]
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Not integrable
Time = 53.54 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.30 \[ \int x \sqrt {\arctan (a x)} \, dx=\int { x \sqrt {\arctan \left (a x\right )} \,d x } \]
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Not integrable
Time = 0.31 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int x \sqrt {\arctan (a x)} \, dx=\int x\,\sqrt {\mathrm {atan}\left (a\,x\right )} \,d x \]
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