Optimal. Leaf size=23 \[ \text {Int}\left (\frac {\log \left (e \left (f^{c (a+b x)}\right )^n+1\right )}{x},x\right ) \]
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Rubi [A] time = 0.06, 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 = {} \[ \int \frac {\log \left (1+e \left (f^{c (a+b x)}\right )^n\right )}{x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\log \left (1+e \left (f^{c (a+b x)}\right )^n\right )}{x} \, dx &=\int \frac {\log \left (1+e \left (f^{c (a+b x)}\right )^n\right )}{x} \, dx\\ \end {align*}
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Mathematica [A] time = 0.31, size = 0, normalized size = 0.00 \[ \int \frac {\log \left (1+e \left (f^{c (a+b x)}\right )^n\right )}{x} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.56, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\log \left (e {\left (f^{b c x + a c}\right )}^{n} + 1\right )}{x}, x\right ) \]
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 \[ \int \frac {\log \left (e {\left (f^{{\left (b x + a\right )} c}\right )}^{n} + 1\right )}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.24, size = 0, normalized size = 0.00 \[ \int \frac {\ln \left (e \left (f^{\left (b x +a \right ) c}\right )^{n}+1\right )}{x}\, dx \]
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 \[ \int \frac {\log \left (e f^{{\left (b x + a\right )} c n} + 1\right )}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {\ln \left (e\,{\left (f^{c\,\left (a+b\,x\right )}\right )}^n+1\right )}{x} \,d x \]
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 \[ \int \frac {\log {\left (e \left (f^{a c} f^{b c x}\right )^{n} + 1 \right )}}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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