Optimal. Leaf size=28 \[ \frac{\text{Unintegrable}\left (\frac{\sqrt{a+b \sin ^{-1}(c+d x)}}{c+d x},x\right )}{e} \]
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Rubi [A] time = 0.0825867, 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 = {} \[ \int \frac{\sqrt{a+b \sin ^{-1}(c+d x)}}{c e+d e x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\sqrt{a+b \sin ^{-1}(c+d x)}}{c e+d e x} \, dx &=\frac{\operatorname{Subst}\left (\int \frac{\sqrt{a+b \sin ^{-1}(x)}}{e x} \, dx,x,c+d x\right )}{d}\\ &=\frac{\operatorname{Subst}\left (\int \frac{\sqrt{a+b \sin ^{-1}(x)}}{x} \, dx,x,c+d x\right )}{d e}\\ \end{align*}
Mathematica [A] time = 2.31972, size = 0, normalized size = 0. \[ \int \frac{\sqrt{a+b \sin ^{-1}(c+d x)}}{c e+d e x} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.091, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{dex+ce}\sqrt{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{\sqrt{b \arcsin \left (d x + c\right ) + a}}{d e x + c e}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \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*} \frac{\int \frac{\sqrt{a + b \operatorname{asin}{\left (c + d x \right )}}}{c + d x}\, dx}{e} \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{\sqrt{b \arcsin \left (d x + c\right ) + a}}{d e x + c e}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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