Optimal. Leaf size=162 \[ \frac {(e x)^{m+1} \left (1-e^{2 i a} x^{2 i b}\right )^{-p} \left (\frac {i \left (1-e^{2 i a} x^{2 i b}\right )}{1+e^{2 i a} x^{2 i b}}\right )^p \left (1+e^{2 i a} x^{2 i b}\right )^p F_1\left (-\frac {i (m+1)}{2 b};-p,p;1-\frac {i (m+1)}{2 b};e^{2 i a} x^{2 i b},-e^{2 i a} x^{2 i b}\right )}{e (m+1)} \]
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Rubi [F] time = 0.13, 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 = {} \[ \int (e x)^m \tan ^p(a+b \log (x)) \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int (e x)^m \tan ^p(a+b \log (x)) \, dx &=\int (e x)^m \tan ^p(a+b \log (x)) \, dx\\ \end {align*}
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Mathematica [A] time = 0.67, size = 157, normalized size = 0.97 \[ \frac {x (e x)^m \left (1-e^{2 i a} x^{2 i b}\right )^{-p} \left (-\frac {i \left (-1+e^{2 i a} x^{2 i b}\right )}{1+e^{2 i a} x^{2 i b}}\right )^p \left (1+e^{2 i a} x^{2 i b}\right )^p F_1\left (-\frac {i (m+1)}{2 b};-p,p;1-\frac {i (m+1)}{2 b};e^{2 i a} x^{2 i b},-e^{2 i a} x^{2 i b}\right )}{m+1} \]
Antiderivative was successfully verified.
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fricas [F] time = 0.50, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\left (e x\right )^{m} \tan \left (b \log \relax (x) + a\right )^{p}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.35, size = 0, normalized size = 0.00 \[ \int \left (e x \right )^{m} \left (\tan ^{p}\left (a +b \ln \relax (x )\right )\right )\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (e x\right )^{m} \tan \left (b \log \relax (x) + a\right )^{p}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.01 \[ \int {\mathrm {tan}\left (a+b\,\ln \relax (x)\right )}^p\,{\left (e\,x\right )}^m \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (e x\right )^{m} \tan ^{p}{\left (a + b \log {\relax (x )} \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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