Optimal. Leaf size=28 \[ \text {Int}\left (\frac {(f x)^m \left (a+b \log \left (c x^n\right )\right )}{d+e x^r},x\right ) \]
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Rubi [A] time = 0.07, 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 = {} \[ \int \frac {(f x)^m \left (a+b \log \left (c x^n\right )\right )}{d+e x^r} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {(f x)^m \left (a+b \log \left (c x^n\right )\right )}{d+e x^r} \, dx &=\int \frac {(f x)^m \left (a+b \log \left (c x^n\right )\right )}{d+e x^r} \, dx\\ \end {align*}
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Mathematica [A] time = 0.16, size = 111, normalized size = 3.96 \[ \frac {x (f x)^m \left ((m+1) \left (a+b \log \left (c x^n\right )\right ) \, _2F_1\left (1,\frac {m+1}{r};\frac {m+r+1}{r};-\frac {e x^r}{d}\right )-b n \, _3F_2\left (1,\frac {m}{r}+\frac {1}{r},\frac {m}{r}+\frac {1}{r};\frac {m}{r}+\frac {1}{r}+1,\frac {m}{r}+\frac {1}{r}+1;-\frac {e x^r}{d}\right )\right )}{d (m+1)^2} \]
Warning: Unable to verify antiderivative.
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fricas [A] time = 0.79, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\left (f x\right )^{m} b \log \left (c x^{n}\right ) + \left (f x\right )^{m} a}{e x^{r} + d}, x\right ) \]
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 \[ \int \frac {{\left (b \log \left (c x^{n}\right ) + a\right )} \left (f x\right )^{m}}{e x^{r} + d}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 1.10, size = 0, normalized size = 0.00 \[ \int \frac {\left (b \ln \left (c \,x^{n}\right )+a \right ) \left (f x \right )^{m}}{e \,x^{r}+d}\, dx \]
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 \[ \int \frac {{\left (b \log \left (c x^{n}\right ) + a\right )} \left (f x\right )^{m}}{e x^{r} + d}\,{d x} \]
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 \[ \int \frac {{\left (f\,x\right )}^m\,\left (a+b\,\ln \left (c\,x^n\right )\right )}{d+e\,x^r} \,d x \]
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 \[ \int \frac {\left (f x\right )^{m} \left (a + b \log {\left (c x^{n} \right )}\right )}{d + e x^{r}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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