Optimal. Leaf size=26 \[ \text {Int}\left (\frac {a+b \log \left (c x^n\right )}{x^3 \left (d+e x^r\right )},x\right ) \]
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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 = {} \[ \int \frac {a+b \log \left (c x^n\right )}{x^3 \left (d+e x^r\right )} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {a+b \log \left (c x^n\right )}{x^3 \left (d+e x^r\right )} \, dx &=\int \frac {a+b \log \left (c x^n\right )}{x^3 \left (d+e x^r\right )} \, dx\\ \end {align*}
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Mathematica [A] time = 0.12, size = 86, normalized size = 3.31 \[ -\frac {b n \, _3F_2\left (1,-\frac {2}{r},-\frac {2}{r};1-\frac {2}{r},1-\frac {2}{r};-\frac {e x^r}{d}\right )+2 \, _2F_1\left (1,-\frac {2}{r};\frac {r-2}{r};-\frac {e x^r}{d}\right ) \left (a+b \log \left (c x^n\right )\right )}{4 d x^2} \]
Warning: Unable to verify antiderivative.
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fricas [A] time = 0.45, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {b \log \left (c x^{n}\right ) + a}{e x^{3} x^{r} + d x^{3}}, x\right ) \]
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 \[ \int \frac {b \log \left (c x^{n}\right ) + a}{{\left (e x^{r} + d\right )} x^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.76, size = 0, normalized size = 0.00 \[ \int \frac {b \ln \left (c \,x^{n}\right )+a}{\left (e \,x^{r}+d \right ) x^{3}}\, dx \]
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 \[ \int \frac {b \log \left (c x^{n}\right ) + a}{{\left (e x^{r} + d\right )} x^{3}}\,{d x} \]
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 \[ \int \frac {a+b\,\ln \left (c\,x^n\right )}{x^3\,\left (d+e\,x^r\right )} \,d x \]
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 \[ \int \frac {a + b \log {\left (c x^{n} \right )}}{x^{3} \left (d + e x^{r}\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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