Optimal. Leaf size=27 \[ \text {Int}\left (\frac {F^{c+d x}}{\left (a+b F^{c+d x}\right ) x},x\right ) \]
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Rubi [A]
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 = {}
\begin {gather*} \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right ) x} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right ) x} \, dx &=\int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right ) x} \, dx\\ \end {align*}
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Mathematica [A]
time = 0.26, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right ) x} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.01, size = 0, normalized size = 0.00 \[\int \frac {F^{d x +c}}{\left (a +b \,F^{d x +c}\right ) x}\, dx\]
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 \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*} \int \frac {F^{c + d x}}{x \left (F^{c} F^{d x} b + a\right )}\, dx \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 = -0.04 \begin {gather*} \int \frac {F^{c+d\,x}}{x\,\left (a+F^{c+d\,x}\,b\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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