Optimal. Leaf size=30 \[ \text{Unintegrable}\left ((f x)^m \left (c^2 d x^2+d\right )^q \left (a+b \tan ^{-1}(c x)\right )^p,x\right ) \]
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Rubi [A] time = 0.0986459, 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 = {} \[ \int (f x)^m \left (d+c^2 d x^2\right )^q \left (a+b \tan ^{-1}(c x)\right )^p \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int (f x)^m \left (d+c^2 d x^2\right )^q \left (a+b \tan ^{-1}(c x)\right )^p \, dx &=\int (f x)^m \left (d+c^2 d x^2\right )^q \left (a+b \tan ^{-1}(c x)\right )^p \, dx\\ \end{align*}
Mathematica [A] time = 0.630113, size = 0, normalized size = 0. \[ \int (f x)^m \left (d+c^2 d x^2\right )^q \left (a+b \tan ^{-1}(c x)\right )^p \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 5.934, size = 0, normalized size = 0. \begin{align*} \int \left ( fx \right ) ^{m} \left ({c}^{2}d{x}^{2}+d \right ) ^{q} \left ( a+b\arctan \left ( cx \right ) \right ) ^{p}\, 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*} \int{\left (c^{2} d x^{2} + d\right )}^{q} \left (f x\right )^{m}{\left (b \arctan \left (c x\right ) + a\right )}^{p}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \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 (c^{2} d x^{2} + d\right )}^{q} \left (f x\right )^{m}{\left (b \arctan \left (c x\right ) + a\right )}^{p}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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