Optimal. Leaf size=34 \[ \text {Int}\left (\frac {(f x)^m \left (a+b x^n+c x^{2 n}\right )^p}{d+e x^n},x\right ) \]
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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 = {}
\begin {gather*} \int \frac {(f x)^m \left (a+b x^n+c x^{2 n}\right )^p}{d+e x^n} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {(f x)^m \left (a+b x^n+c x^{2 n}\right )^p}{d+e x^n} \, dx &=\int \frac {(f x)^m \left (a+b x^n+c x^{2 n}\right )^p}{d+e x^n} \, dx\\ \end {align*}
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Mathematica [A]
time = 0.24, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(f x)^m \left (a+b x^n+c x^{2 n}\right )^p}{d+e x^n} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.05, size = 0, normalized size = 0.00 \[\int \frac {\left (f x \right )^{m} \left (a +b \,x^{n}+c \,x^{2 n}\right )^{p}}{d +e \,x^{n}}\, dx\]
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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
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 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \int \frac {{\left (f\,x\right )}^m\,{\left (a+b\,x^n+c\,x^{2\,n}\right )}^p}{d+e\,x^n} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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