Optimal. Leaf size=18 \[ \text{Unintegrable}\left (\sec ^2(a+b x) (c+d x)^m,x\right ) \]
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Rubi [A] time = 0.0354351, 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 = {} \[ \int (c+d x)^m \sec ^2(a+b x) \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int (c+d x)^m \sec ^2(a+b x) \, dx &=\int (c+d x)^m \sec ^2(a+b x) \, dx\\ \end{align*}
Mathematica [A] time = 0.825649, size = 0, normalized size = 0. \[ \int (c+d x)^m \sec ^2(a+b x) \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.194, size = 0, normalized size = 0. \begin{align*} \int \left ( dx+c \right ) ^{m} \left ( \sec \left ( bx+a \right ) \right ) ^{2}\, 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 (d x + c\right )}^{m} \sec \left (b x + a\right )^{2}\,{d x} \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 (d x + c\right )}^{m} \sec \left (b x + a\right )^{2}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \left (c + d x\right )^{m} \sec ^{2}{\left (a + b x \right )}\, dx \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 (d x + c\right )}^{m} \sec \left (b x + a\right )^{2}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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