Optimal. Leaf size=61 \[ x \left (1-e^{2 a} x^4\right )^{-p} \left (e^{2 a} x^4-1\right )^p F_1\left (\frac{1}{4};-p,p;\frac{5}{4};e^{2 a} x^4,-e^{2 a} x^4\right ) \]
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Rubi [F] time = 0.0108366, 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 = {} \[ \int \tanh ^p(a+2 \log (x)) \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \tanh ^p(a+2 \log (x)) \, dx &=\int \tanh ^p(a+2 \log (x)) \, dx\\ \end{align*}
Mathematica [B] time = 1.77489, size = 171, normalized size = 2.8 \[ \frac{5 x \left (\frac{e^{2 a} x^4-1}{e^{2 a} x^4+1}\right )^p F_1\left (\frac{1}{4};-p,p;\frac{5}{4};e^{2 a} x^4,-e^{2 a} x^4\right )}{5 F_1\left (\frac{1}{4};-p,p;\frac{5}{4};e^{2 a} x^4,-e^{2 a} x^4\right )-4 e^{2 a} p x^4 \left (F_1\left (\frac{5}{4};1-p,p;\frac{9}{4};e^{2 a} x^4,-e^{2 a} x^4\right )+F_1\left (\frac{5}{4};-p,p+1;\frac{9}{4};e^{2 a} x^4,-e^{2 a} x^4\right )\right )} \]
Warning: Unable to verify antiderivative.
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Maple [F] time = 0.046, size = 0, normalized size = 0. \begin{align*} \int \left ( \tanh \left ( a+2\,\ln \left ( x \right ) \right ) \right ) ^{p}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \tanh \left (a + 2 \, \log \left (x\right )\right )^{p}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\tanh \left (a + 2 \, \log \left (x\right )\right )^{p}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \tanh ^{p}{\left (a + 2 \log{\left (x \right )} \right )}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \tanh \left (a + 2 \, \log \left (x\right )\right )^{p}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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