Optimal. Leaf size=22 \[ \frac {\left (a+b \log \left (c x^n\right )\right )^2}{2 b n} \]
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Rubi [A] time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {2301} \[ \frac {\left (a+b \log \left (c x^n\right )\right )^2}{2 b n} \]
Antiderivative was successfully verified.
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Rule 2301
Rubi steps
\begin {align*} \int \frac {a+b \log \left (c x^n\right )}{x} \, dx &=\frac {\left (a+b \log \left (c x^n\right )\right )^2}{2 b n}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 21, normalized size = 0.95 \[ a \log (x)+\frac {b \log ^2\left (c x^n\right )}{2 n} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.45, size = 18, normalized size = 0.82 \[ \frac {1}{2} \, b n \log \relax (x)^{2} + {\left (b \log \relax (c) + a\right )} \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 19, normalized size = 0.86 \[ \frac {1}{2} \, b n \log \relax (x)^{2} + b \log \relax (c) \log \relax (x) + a \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 27, normalized size = 1.23 \[ \frac {b \ln \left (c \,x^{n}\right )^{2}}{2 n}+\frac {a \ln \left (c \,x^{n}\right )}{n} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 20, normalized size = 0.91 \[ \frac {{\left (b \log \left (c x^{n}\right ) + a\right )}^{2}}{2 \, b n} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.41, size = 19, normalized size = 0.86 \[ a\,\ln \relax (x)+\frac {b\,{\ln \left (c\,x^n\right )}^2}{2\,n} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 8.60, size = 34, normalized size = 1.55 \[ \begin {cases} a \log {\relax (x )} & \text {for}\: b = 0 \\- \left (- a - b \log {\relax (c )}\right ) \log {\relax (x )} & \text {for}\: n = 0 \\\frac {\left (- a - b \log {\left (c x^{n} \right )}\right )^{2}}{2 b n} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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