Optimal. Leaf size=27 \[ \frac {1}{4} x^4 \left (a+b \log \left (c x^n\right )\right )-\frac {1}{16} b n x^4 \]
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Rubi [A] time = 0.01, antiderivative size = 27, 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} \[ \frac {1}{4} x^4 \left (a+b \log \left (c x^n\right )\right )-\frac {1}{16} b n x^4 \]
Antiderivative was successfully verified.
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Rule 2304
Rubi steps
\begin {align*} \int x^3 \left (a+b \log \left (c x^n\right )\right ) \, dx &=-\frac {1}{16} b n x^4+\frac {1}{4} x^4 \left (a+b \log \left (c x^n\right )\right )\\ \end {align*}
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Mathematica [A] time = 0.00, size = 32, normalized size = 1.19 \[ \frac {a x^4}{4}+\frac {1}{4} b x^4 \log \left (c x^n\right )-\frac {1}{16} b n x^4 \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 30, normalized size = 1.11 \[ \frac {1}{4} \, b n x^{4} \log \relax (x) + \frac {1}{4} \, b x^{4} \log \relax (c) - \frac {1}{16} \, {\left (b n - 4 \, a\right )} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 31, normalized size = 1.15 \[ \frac {1}{4} \, b n x^{4} \log \relax (x) - \frac {1}{16} \, b n x^{4} + \frac {1}{4} \, b x^{4} \log \relax (c) + \frac {1}{4} \, a x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.22, size = 112, normalized size = 4.15 \[ \frac {b \,x^{4} \ln \left (x^{n}\right )}{4}+\frac {\left (-2 i \pi b \,\mathrm {csgn}\left (i c \right ) \mathrm {csgn}\left (i x^{n}\right ) \mathrm {csgn}\left (i c \,x^{n}\right )+2 i \pi b \,\mathrm {csgn}\left (i c \right ) \mathrm {csgn}\left (i c \,x^{n}\right )^{2}+2 i \pi b \,\mathrm {csgn}\left (i x^{n}\right ) \mathrm {csgn}\left (i c \,x^{n}\right )^{2}-2 i \pi b \mathrm {csgn}\left (i c \,x^{n}\right )^{3}-b n +4 b \ln \relax (c )+4 a \right ) x^{4}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 26, normalized size = 0.96 \[ -\frac {1}{16} \, b n x^{4} + \frac {1}{4} \, b x^{4} \log \left (c x^{n}\right ) + \frac {1}{4} \, a x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.59, size = 25, normalized size = 0.93 \[ x^4\,\left (\frac {a}{4}-\frac {b\,n}{16}\right )+\frac {b\,x^4\,\ln \left (c\,x^n\right )}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.36, size = 36, normalized size = 1.33 \[ \frac {a x^{4}}{4} + \frac {b n x^{4} \log {\relax (x )}}{4} - \frac {b n x^{4}}{16} + \frac {b x^{4} \log {\relax (c )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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