Optimal. Leaf size=26 \[ \text {Int}\left (\frac {a+b \log \left (c x^n\right )}{x^2 \left (d+e x^r\right )^2},x\right ) \]
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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 = {}
\begin {gather*} \int \frac {a+b \log \left (c x^n\right )}{x^2 \left (d+e x^r\right )^2} \, dx \end {gather*}
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^2 \left (d+e x^r\right )^2} \, dx &=\int \frac {a+b \log \left (c x^n\right )}{x^2 \left (d+e x^r\right )^2} \, dx\\ \end {align*}
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Mathematica [A] Leaf count is larger than twice the leaf count of optimal. \(135\) vs. \(2(26)=52\).
time = 0.13, size = 135, normalized size = 5.19 \begin {gather*} \frac {-b n (1+r) \left (d+e x^r\right ) \, _3F_2\left (1,-\frac {1}{r},-\frac {1}{r};1-\frac {1}{r},1-\frac {1}{r};-\frac {e x^r}{d}\right )+d \left (a+b \log \left (c x^n\right )\right )-\left (d+e x^r\right ) \, _2F_1\left (1,-\frac {1}{r};\frac {-1+r}{r};-\frac {e x^r}{d}\right ) \left (a-b n+a r+b (1+r) \log \left (c x^n\right )\right )}{d^2 r x \left (d+e x^r\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 0, normalized size = 0.00 \[\int \frac {a +b \ln \left (c \,x^{n}\right )}{x^{2} \left (d +e \,x^{r}\right )^{2}}\, dx\]
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 {a + b \log {\left (c x^{n} \right )}}{x^{2} \left (d + e x^{r}\right )^{2}}\, 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 {a+b\,\ln \left (c\,x^n\right )}{x^2\,{\left (d+e\,x^r\right )}^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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