Optimal. Leaf size=28 \[ \frac {x^{-n} (c x)^n \log \left (a+b x^n\right )}{b c n} \]
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Rubi [A] time = 0.01, antiderivative size = 28, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {268, 260} \[ \frac {x^{-n} (c x)^n \log \left (a+b x^n\right )}{b c n} \]
Antiderivative was successfully verified.
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Rule 260
Rule 268
Rubi steps
\begin {align*} \int \frac {(c x)^{-1+n}}{a+b x^n} \, dx &=\frac {\left (x^{-n} (c x)^n\right ) \int \frac {x^{-1+n}}{a+b x^n} \, dx}{c}\\ &=\frac {x^{-n} (c x)^n \log \left (a+b x^n\right )}{b c n}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 29, normalized size = 1.04 \[ \frac {x^{1-n} (c x)^{n-1} \log \left (a+b x^n\right )}{b n} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 20, normalized size = 0.71 \[ \frac {c^{n - 1} \log \left (b x^{n} + a\right )}{b n} \]
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 \[ \int \frac {\left (c x\right )^{n - 1}}{b x^{n} + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.29, size = 0, normalized size = 0.00 \[ \int \frac {\left (c x \right )^{n -1}}{b \,x^{n}+a}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.70, size = 24, normalized size = 0.86 \[ \frac {c^{n - 1} \log \left (\frac {b x^{n} + a}{b}\right )}{b n} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {{\left (c\,x\right )}^{n-1}}{a+b\,x^n} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 4.80, size = 17, normalized size = 0.61 \[ \frac {c^{n} \log {\left (1 + \frac {b x^{n}}{a} \right )}}{b c n} \]
Verification of antiderivative is not currently implemented for this CAS.
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