Optimal. Leaf size=23 \[ -\frac {a+b \log \left (c x^n\right )}{x}-\frac {b n}{x} \]
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Rubi [A] time = 0.01, antiderivative size = 23, 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 = {2304} \[ -\frac {a+b \log \left (c x^n\right )}{x}-\frac {b n}{x} \]
Antiderivative was successfully verified.
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Rule 2304
Rubi steps
\begin {align*} \int \frac {a+b \log \left (c x^n\right )}{x^2} \, dx &=-\frac {b n}{x}-\frac {a+b \log \left (c x^n\right )}{x}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 26, normalized size = 1.13 \[ -\frac {a}{x}-\frac {b \log \left (c x^n\right )}{x}-\frac {b n}{x} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 19, normalized size = 0.83 \[ -\frac {b n \log \relax (x) + b n + b \log \relax (c) + a}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.25, size = 24, normalized size = 1.04 \[ -\frac {b n \log \relax (x)}{x} - \frac {b n + b \log \relax (c) + a}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.12, size = 112, normalized size = 4.87 \[ -\frac {b \ln \left (x^{n}\right )}{x}-\frac {-i \pi b \,\mathrm {csgn}\left (i c \right ) \mathrm {csgn}\left (i x^{n}\right ) \mathrm {csgn}\left (i c \,x^{n}\right )+i \pi b \,\mathrm {csgn}\left (i c \right ) \mathrm {csgn}\left (i c \,x^{n}\right )^{2}+i \pi b \,\mathrm {csgn}\left (i x^{n}\right ) \mathrm {csgn}\left (i c \,x^{n}\right )^{2}-i \pi b \mathrm {csgn}\left (i c \,x^{n}\right )^{3}+2 b n +2 b \ln \relax (c )+2 a}{2 x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 26, normalized size = 1.13 \[ -\frac {b n}{x} - \frac {b \log \left (c x^{n}\right )}{x} - \frac {a}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.56, size = 23, normalized size = 1.00 \[ -\frac {a+b\,n}{x}-\frac {b\,\ln \left (c\,x^n\right )}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.46, size = 24, normalized size = 1.04 \[ - \frac {a}{x} - \frac {b n \log {\relax (x )}}{x} - \frac {b n}{x} - \frac {b \log {\relax (c )}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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