Optimal. Leaf size=21 \[ \text {Int}\left ((a+b x)^2 \sqrt {\tan ^{-1}(a+b x)},x\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int (a+b x)^2 \sqrt {\tan ^{-1}(a+b x)} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int (a+b x)^2 \sqrt {\tan ^{-1}(a+b x)} \, dx &=\int (a+b x)^2 \sqrt {\tan ^{-1}(a+b x)} \, dx\\ \end {align*}
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Mathematica [A] time = 6.11, size = 0, normalized size = 0.00 \[ \int (a+b x)^2 \sqrt {\tan ^{-1}(a+b x)} \, dx \]
Verification is Not applicable to the result.
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fricas [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 3.23, size = 0, normalized size = 0.00 \[ \int \left (b x +a \right )^{2} \sqrt {\arctan \left (b x +a \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: RuntimeError} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.05 \[ \int \sqrt {\mathrm {atan}\left (a+b\,x\right )}\,{\left (a+b\,x\right )}^2 \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (a + b x\right )^{2} \sqrt {\operatorname {atan}{\left (a + b x \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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