Optimal. Leaf size=24 \[ \text{Unintegrable}\left (\frac{(e (c+d x))^m}{a+b \sin ^{-1}(c+d x)},x\right ) \]
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Rubi [A] time = 0.0579832, 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 = {} \[ \int \frac{(c e+d e x)^m}{a+b \sin ^{-1}(c+d x)} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{(c e+d e x)^m}{a+b \sin ^{-1}(c+d x)} \, dx &=\frac{\operatorname{Subst}\left (\int \frac{(e x)^m}{a+b \sin ^{-1}(x)} \, dx,x,c+d x\right )}{d}\\ \end{align*}
Mathematica [A] time = 1.44408, size = 0, normalized size = 0. \[ \int \frac{(c e+d e x)^m}{a+b \sin ^{-1}(c+d x)} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.767, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( dex+ce \right ) ^{m}}{a+b\arcsin \left ( dx+c \right ) }}\, 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 (d e x + c e\right )}^{m}}{b \arcsin \left (d x + c\right ) + a}\,{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{{\left (d e x + c e\right )}^{m}}{b \arcsin \left (d x + c\right ) + a}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\left (e \left (c + d x\right )\right )^{m}}{a + b \operatorname{asin}{\left (c + d x \right )}}\, dx \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 (d e x + c e\right )}^{m}}{b \arcsin \left (d x + c\right ) + a}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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