Optimal. Leaf size=50 \[ \text {Int}\left (\frac {\left (a+b F^{\frac {c \sqrt {d+e x}}{\sqrt {d f-e f x}}}\right )^n}{d^2-e^2 x^2},x\right ) \]
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Rubi [A]
time = 0.15, 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 {\left (a+b F^{\frac {c \sqrt {d+e x}}{\sqrt {d f-e f x}}}\right )^n}{d^2-e^2 x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\left (a+b F^{\frac {c \sqrt {d+e x}}{\sqrt {d f-e f x}}}\right )^n}{d^2-e^2 x^2} \, dx &=\int \frac {\left (a+b F^{\frac {c \sqrt {d+e x}}{\sqrt {d f-e f x}}}\right )^n}{d^2-e^2 x^2} \, dx\\ \end {align*}
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Mathematica [A]
time = 0.49, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (a+b F^{\frac {c \sqrt {d+e x}}{\sqrt {d f-e f x}}}\right )^n}{d^2-e^2 x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.01, size = 0, normalized size = 0.00 \[\int \frac {\left (a +b \,F^{\frac {c \sqrt {e x +d}}{\sqrt {-e f x +d f}}}\right )^{n}}{-e^{2} x^{2}+d^{2}}\, dx\]
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 [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}
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 \begin {gather*} - \int \frac {\left (F^{\frac {c \sqrt {d + e x}}{\sqrt {d f - e f x}}} b + a\right )^{n}}{- d^{2} + e^{2} x^{2}}\, dx \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 = -0.02 \begin {gather*} \int \frac {{\left (a+b\,{\mathrm {e}}^{\frac {c\,\ln \left (F\right )\,\sqrt {d+e\,x}}{\sqrt {d\,f-e\,f\,x}}}\right )}^n}{d^2-e^2\,x^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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