Optimal. Leaf size=27 \[ \text {Int}\left (\frac {\left (a+b x^4+c x^2\right )^p}{c+e x^2},x\right ) \]
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Rubi [A] time = 0.01, 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 = {} \[ \int \frac {\left (a+c x^2+b x^4\right )^p}{c+e x^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\left (a+c x^2+b x^4\right )^p}{c+e x^2} \, dx &=\int \frac {\left (a+c x^2+b x^4\right )^p}{c+e x^2} \, dx\\ \end {align*}
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Mathematica [A] time = 0.13, size = 0, normalized size = 0.00 \[ \int \frac {\left (a+c x^2+b x^4\right )^p}{c+e x^2} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.45, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\left (b x^{4} + c x^{2} + a\right )}^{p}}{e x^{2} + c}, x\right ) \]
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 \[ \int \frac {{\left (b x^{4} + c x^{2} + a\right )}^{p}}{e x^{2} + c}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 0, normalized size = 0.00 \[ \int \frac {\left (b \,x^{4}+c \,x^{2}+a \right )^{p}}{e \,x^{2}+c}\, dx \]
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 \[ \int \frac {{\left (b x^{4} + c x^{2} + a\right )}^{p}}{e x^{2} + c}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {{\left (b\,x^4+c\,x^2+a\right )}^p}{e\,x^2+c} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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