Optimal. Leaf size=29 \[ \text{Unintegrable}\left (\frac{(a+b \sin (e+f x))^m}{(c+d \sin (e+f x))^{5/2}},x\right ) \]
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Rubi [A] time = 0.0777509, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{(a+b \sin (e+f x))^m}{(c+d \sin (e+f x))^{5/2}} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{(a+b \sin (e+f x))^m}{(c+d \sin (e+f x))^{5/2}} \, dx &=\int \frac{(a+b \sin (e+f x))^m}{(c+d \sin (e+f x))^{5/2}} \, dx\\ \end{align*}
Mathematica [A] time = 9.8531, size = 0, normalized size = 0. \[ \int \frac{(a+b \sin (e+f x))^m}{(c+d \sin (e+f x))^{5/2}} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.155, size = 0, normalized size = 0. \begin{align*} \int{ \left ( a+b\sin \left ( fx+e \right ) \right ) ^{m} \left ( c+d\sin \left ( fx+e \right ) \right ) ^{-{\frac{5}{2}}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (b \sin \left (f x + e\right ) + a\right )}^{m}}{{\left (d \sin \left (f x + e\right ) + c\right )}^{\frac{5}{2}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (-\frac{\sqrt{d \sin \left (f x + e\right ) + c}{\left (b \sin \left (f x + e\right ) + a\right )}^{m}}{3 \, c d^{2} \cos \left (f x + e\right )^{2} - c^{3} - 3 \, c d^{2} +{\left (d^{3} \cos \left (f x + e\right )^{2} - 3 \, c^{2} d - d^{3}\right )} \sin \left (f x + e\right )}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (b \sin \left (f x + e\right ) + a\right )}^{m}}{{\left (d \sin \left (f x + e\right ) + c\right )}^{\frac{5}{2}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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