Optimal. Leaf size=22 \[ \text{Unintegrable}\left ((e+f x)^m \left (a+b \tan ^{-1}(c+d x)\right )^3,x\right ) \]
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Rubi [A] time = 0.0564118, 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 = {} \[ \int (e+f x)^m \left (a+b \tan ^{-1}(c+d x)\right )^3 \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int (e+f x)^m \left (a+b \tan ^{-1}(c+d x)\right )^3 \, dx &=\frac{\operatorname{Subst}\left (\int \left (\frac{d e-c f}{d}+\frac{f x}{d}\right )^m \left (a+b \tan ^{-1}(x)\right )^3 \, dx,x,c+d x\right )}{d}\\ \end{align*}
Mathematica [A] time = 0.405131, size = 0, normalized size = 0. \[ \int (e+f x)^m \left (a+b \tan ^{-1}(c+d x)\right )^3 \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 1.097, size = 0, normalized size = 0. \begin{align*} \int \left ( fx+e \right ) ^{m} \left ( a+b\arctan \left ( dx+c \right ) \right ) ^{3}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \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 ({\left (b^{3} \arctan \left (d x + c\right )^{3} + 3 \, a b^{2} \arctan \left (d x + c\right )^{2} + 3 \, a^{2} b \arctan \left (d x + c\right ) + a^{3}\right )}{\left (f x + e\right )}^{m}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \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{\left (b \arctan \left (d x + c\right ) + a\right )}^{3}{\left (f x + e\right )}^{m}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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