Optimal. Leaf size=158 \[ \frac {e^{-6 a} 2^{-p} \left (2 p^2+1\right ) \left (e^{2 a} \sqrt [3]{x}-1\right )^{p+1} \, _2F_1\left (p,p+1;p+2;\frac {1}{2} \left (1-e^{2 a} \sqrt [3]{x}\right )\right )}{p+1}-e^{-6 a} p \left (e^{2 a} \sqrt [3]{x}-1\right )^{p+1} \left (e^{2 a} \sqrt [3]{x}+1\right )^{1-p}+e^{-4 a} \sqrt [3]{x} \left (e^{2 a} \sqrt [3]{x}-1\right )^{p+1} \left (e^{2 a} \sqrt [3]{x}+1\right )^{1-p} \]
[Out]
________________________________________________________________________________________
Rubi [F] time = 0.05, 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 = {} \[ \int \tanh ^p\left (a+\frac {\log (x)}{6}\right ) \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \tanh ^p\left (a+\frac {\log (x)}{6}\right ) \, dx &=\int \tanh ^p\left (\frac {1}{6} (6 a+\log (x))\right ) \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [C] time = 4.28, size = 177, normalized size = 1.12 \[ \frac {4 x \left (\frac {e^{2 a} \sqrt [3]{x}-1}{e^{2 a} \sqrt [3]{x}+1}\right )^p F_1\left (3;-p,p;4;e^{2 a} \sqrt [3]{x},-e^{2 a} \sqrt [3]{x}\right )}{4 F_1\left (3;-p,p;4;e^{2 a} \sqrt [3]{x},-e^{2 a} \sqrt [3]{x}\right )-e^{2 a} p \sqrt [3]{x} \left (F_1\left (4;1-p,p;5;e^{2 a} \sqrt [3]{x},-e^{2 a} \sqrt [3]{x}\right )+F_1\left (4;-p,p+1;5;e^{2 a} \sqrt [3]{x},-e^{2 a} \sqrt [3]{x}\right )\right )} \]
Warning: Unable to verify antiderivative.
[In]
[Out]
________________________________________________________________________________________
fricas [F] time = 1.53, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\tanh \left (a + \frac {1}{6} \, \log \relax (x)\right )^{p}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \tanh \left (a + \frac {1}{6} \, \log \relax (x)\right )^{p}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [F] time = 0.12, size = 0, normalized size = 0.00 \[ \int \tanh ^{p}\left (a +\frac {\ln \relax (x )}{6}\right )\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \tanh \left (a + \frac {1}{6} \, \log \relax (x)\right )^{p}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.01 \[ \int {\mathrm {tanh}\left (a+\frac {\ln \relax (x)}{6}\right )}^p \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \tanh ^{p}{\left (a + \frac {\log {\relax (x )}}{6} \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________