Optimal. Leaf size=27 \[ -\frac {1}{9} n p x^3+\frac {1}{3} x^3 \log \left (c \left (b x^n\right )^p\right ) \]
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Rubi [A]
time = 0.02, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {2341, 2495}
\begin {gather*} \frac {1}{3} x^3 \log \left (c \left (b x^n\right )^p\right )-\frac {1}{9} n p x^3 \end {gather*}
Antiderivative was successfully verified.
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Rule 2341
Rule 2495
Rubi steps
\begin {align*} \int x^2 \log \left (c \left (b x^n\right )^p\right ) \, dx &=\text {Subst}\left (\int x^2 \log \left (b^p c x^{n p}\right ) \, dx,b^p c x^{n p},c \left (b x^n\right )^p\right )\\ &=-\frac {1}{9} n p x^3+\frac {1}{3} x^3 \log \left (c \left (b x^n\right )^p\right )\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 27, normalized size = 1.00 \begin {gather*} -\frac {1}{9} n p x^3+\frac {1}{3} x^3 \log \left (c \left (b x^n\right )^p\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.02, size = 0, normalized size = 0.00 \[\int x^{2} \ln \left (c \left (b \,x^{n}\right )^{p}\right )\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 23, normalized size = 0.85 \begin {gather*} -\frac {1}{9} \, n p x^{3} + \frac {1}{3} \, x^{3} \log \left (\left (b x^{n}\right )^{p} c\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 32, normalized size = 1.19 \begin {gather*} \frac {1}{3} \, n p x^{3} \log \left (x\right ) - \frac {1}{9} \, n p x^{3} + \frac {1}{3} \, p x^{3} \log \left (b\right ) + \frac {1}{3} \, x^{3} \log \left (c\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.41, size = 22, normalized size = 0.81 \begin {gather*} - \frac {n p x^{3}}{9} + \frac {x^{3} \log {\left (c \left (b x^{n}\right )^{p} \right )}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.53, size = 32, normalized size = 1.19 \begin {gather*} \frac {1}{3} \, n p x^{3} \log \left (x\right ) - \frac {1}{9} \, n p x^{3} + \frac {1}{3} \, p x^{3} \log \left (b\right ) + \frac {1}{3} \, x^{3} \log \left (c\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.84, size = 23, normalized size = 0.85 \begin {gather*} \frac {x^3\,\ln \left (c\,{\left (b\,x^n\right )}^p\right )}{3}-\frac {n\,p\,x^3}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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