Optimal. Leaf size=24 \[ \text {Int}\left (\frac {x \left (a+b \log \left (c x^n\right )\right )}{d+e x^r},x\right ) \]
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Rubi [A] time = 0.04, 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 = {} \[ \int \frac {x \left (a+b \log \left (c x^n\right )\right )}{d+e x^r} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {x \left (a+b \log \left (c x^n\right )\right )}{d+e x^r} \, dx &=\int \frac {x \left (a+b \log \left (c x^n\right )\right )}{d+e x^r} \, dx\\ \end {align*}
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Mathematica [A] time = 0.11, size = 87, normalized size = 3.62 \[ \frac {x^2 \left (2 \, _2F_1\left (1,\frac {2}{r};\frac {r+2}{r};-\frac {e x^r}{d}\right ) \left (a+b \log \left (c x^n\right )\right )-b n \, _3F_2\left (1,\frac {2}{r},\frac {2}{r};1+\frac {2}{r},1+\frac {2}{r};-\frac {e x^r}{d}\right )\right )}{4 d} \]
Warning: Unable to verify antiderivative.
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fricas [A] time = 0.40, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {b x \log \left (c x^{n}\right ) + a x}{e x^{r} + d}, x\right ) \]
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 \[ \int \frac {{\left (b \log \left (c x^{n}\right ) + a\right )} x}{e x^{r} + d}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.69, size = 0, normalized size = 0.00 \[ \int \frac {\left (b \ln \left (c \,x^{n}\right )+a \right ) x}{e \,x^{r}+d}\, dx \]
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 \[ \int \frac {{\left (b \log \left (c x^{n}\right ) + a\right )} x}{e x^{r} + d}\,{d x} \]
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 \[ \int \frac {x\,\left (a+b\,\ln \left (c\,x^n\right )\right )}{d+e\,x^r} \,d x \]
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 \[ \int \frac {x \left (a + b \log {\left (c x^{n} \right )}\right )}{d + e x^{r}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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