Optimal. Leaf size=21 \[ \text {Int}\left (\frac {x^2}{\log ^3\left (c \left (a+b x^2\right )^p\right )},x\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {x^2}{\log ^3\left (c \left (a+b x^2\right )^p\right )} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {x^2}{\log ^3\left (c \left (a+b x^2\right )^p\right )} \, dx &=\int \frac {x^2}{\log ^3\left (c \left (a+b x^2\right )^p\right )} \, dx\\ \end {align*}
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Mathematica [A] time = 0.56, size = 0, normalized size = 0.00 \[ \int \frac {x^2}{\log ^3\left (c \left (a+b x^2\right )^p\right )} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.44, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {x^{2}}{\log \left ({\left (b x^{2} + a\right )}^{p} c\right )^{3}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{2}}{\log \left ({\left (b x^{2} + a\right )}^{p} c\right )^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 3.65, size = 0, normalized size = 0.00 \[ \int \frac {x^{2}}{\ln \left (c \left (b \,x^{2}+a \right )^{p}\right )^{3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ -\frac {b^{2} {\left (2 \, p + 3 \, \log \relax (c)\right )} x^{4} + 2 \, a b {\left (p + 2 \, \log \relax (c)\right )} x^{2} + a^{2} \log \relax (c) + {\left (3 \, b^{2} p x^{4} + 4 \, a b p x^{2} + a^{2} p\right )} \log \left (b x^{2} + a\right )}{8 \, {\left (b^{2} p^{4} x \log \left (b x^{2} + a\right )^{2} + 2 \, b^{2} p^{3} x \log \left (b x^{2} + a\right ) \log \relax (c) + b^{2} p^{2} x \log \relax (c)^{2}\right )}} + \int \frac {9 \, b^{2} x^{4} + 4 \, a b x^{2} - a^{2}}{8 \, {\left (b^{2} p^{3} x^{2} \log \left (b x^{2} + a\right ) + b^{2} p^{2} x^{2} \log \relax (c)\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {x^2}{{\ln \left (c\,{\left (b\,x^2+a\right )}^p\right )}^3} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{2}}{\log {\left (c \left (a + b x^{2}\right )^{p} \right )}^{3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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