Optimal. Leaf size=18 \[ \text{Unintegrable}\left ((d x)^m \left (a+b \sec ^{-1}(c x)\right )^3,x\right ) \]
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Rubi [A] time = 0.0220289, 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 = {} \[ \int (d x)^m \left (a+b \sec ^{-1}(c x)\right )^3 \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int (d x)^m \left (a+b \sec ^{-1}(c x)\right )^3 \, dx &=\int (d x)^m \left (a+b \sec ^{-1}(c x)\right )^3 \, dx\\ \end{align*}
Mathematica [A] time = 4.39341, size = 0, normalized size = 0. \[ \int (d x)^m \left (a+b \sec ^{-1}(c x)\right )^3 \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 1.964, size = 0, normalized size = 0. \begin{align*} \int \left ( dx \right ) ^{m} \left ( a+b{\rm arcsec} \left (cx\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} \operatorname{arcsec}\left (c x\right )^{3} + 3 \, a b^{2} \operatorname{arcsec}\left (c x\right )^{2} + 3 \, a^{2} b \operatorname{arcsec}\left (c x\right ) + a^{3}\right )} \left (d x\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 \operatorname{arcsec}\left (c x\right ) + a\right )}^{3} \left (d x\right )^{m}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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