Optimal. Leaf size=21 \[ \text {Int}\left ((c+d x)^m (a+a \tanh (e+f x)),x\right ) \]
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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 = {}
\begin {gather*} \int (c+d x)^m (a+a \tanh (e+f x)) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int (c+d x)^m (a+a \tanh (e+f x)) \, dx &=\int (c+d x)^m (a+a \tanh (e+f x)) \, dx\\ \end {align*}
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Mathematica [A]
time = 10.54, size = 0, normalized size = 0.00 \begin {gather*} \int (c+d x)^m (a+a \tanh (e+f x)) \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 180.00, size = 0, normalized size = 0.00 \[\int \left (d x +c \right )^{m} \left (a +a \tanh \left (f x +e \right )\right )\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} a \left (\int \left (c + d x\right )^{m} \tanh {\left (e + f x \right )}\, dx + \int \left (c + d x\right )^{m}\, dx\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \int \left (a+a\,\mathrm {tanh}\left (e+f\,x\right )\right )\,{\left (c+d\,x\right )}^m \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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