Optimal. Leaf size=15 \[ \frac {\log \left (2 x^n+3\right )}{2 n} \]
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Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {1593, 260} \begin {gather*} \frac {\log \left (2 x^n+3\right )}{2 n} \end {gather*}
Antiderivative was successfully verified.
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Rule 260
Rule 1593
Rubi steps
\begin {align*} \int \frac {1}{2 x+3 x^{1-n}} \, dx &=\int \frac {x^{-1+n}}{3+2 x^n} \, dx\\ &=\frac {\log \left (3+2 x^n\right )}{2 n}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} \frac {\log \left (2 x^n+3\right )}{2 n} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 18, normalized size = 1.20 \begin {gather*} \frac {\log \left (2 n x^n+3 n\right )}{2 n} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 26, normalized size = 1.73 \begin {gather*} \frac {{\left (n - 1\right )} \log \relax (x) + \log \left (3 \, x^{-n + 1} + 2 \, x\right )}{2 \, n} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{3 \, x^{-n + 1} + 2 \, x}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.05, size = 34, normalized size = 2.27 \begin {gather*} \frac {\ln \relax (x )}{2}-\frac {\ln \relax (x )}{2 n}+\frac {\ln \left (2 x +3 \,{\mathrm e}^{\left (-n +1\right ) \ln \relax (x )}\right )}{2 n} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.32, size = 11, normalized size = 0.73 \begin {gather*} \frac {\log \left (x^{n} + \frac {3}{2}\right )}{2 \, n} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.20, size = 28, normalized size = 1.87 \begin {gather*} \frac {\ln \left (\frac {2\,x}{3}+x^{1-n}\right )}{2\,n}+\frac {\ln \relax (x)\,\left (n-1\right )}{2\,n} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.70, size = 22, normalized size = 1.47 \begin {gather*} \begin {cases} \frac {\log {\relax (x )}}{2} + \frac {\log {\left (\frac {2}{3} + x^{- n} \right )}}{2 n} & \text {for}\: n \neq 0 \\\frac {\log {\relax (x )}}{5} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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