Optimal. Leaf size=29 \[ \text {Int}\left (\frac {\left (a+b x^n+c x^{2 n}\right )^p}{\left (d+e x^n\right )^3},x\right ) \]
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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 = {} \[ \int \frac {\left (a+b x^n+c x^{2 n}\right )^p}{\left (d+e x^n\right )^3} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\left (a+b x^n+c x^{2 n}\right )^p}{\left (d+e x^n\right )^3} \, dx &=\int \frac {\left (a+b x^n+c x^{2 n}\right )^p}{\left (d+e x^n\right )^3} \, dx\\ \end {align*}
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Mathematica [A] time = 0.73, size = 0, normalized size = 0.00 \[ \int \frac {\left (a+b x^n+c x^{2 n}\right )^p}{\left (d+e x^n\right )^3} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 1.15, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\left (c x^{2 \, n} + b x^{n} + a\right )}^{p}}{e^{3} x^{3 \, n} + 3 \, d e^{2} x^{2 \, n} + 3 \, d^{2} e x^{n} + d^{3}}, x\right ) \]
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 \[ \int \frac {{\left (c x^{2 \, n} + b x^{n} + a\right )}^{p}}{{\left (e x^{n} + d\right )}^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 0, normalized size = 0.00 \[ \int \frac {\left (b \,x^{n}+c \,x^{2 n}+a \right )^{p}}{\left (e \,x^{n}+d \right )^{3}}\, dx \]
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 \[ \int \frac {{\left (c x^{2 \, n} + b x^{n} + a\right )}^{p}}{{\left (e x^{n} + d\right )}^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {{\left (a+b\,x^n+c\,x^{2\,n}\right )}^p}{{\left (d+e\,x^n\right )}^3} \,d x \]
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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