Optimal. Leaf size=26 \[ \frac{\text{Unintegrable}\left (\frac{1}{(c+d x) \left (a+b \sin ^{-1}(c+d x)\right )},x\right )}{e} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0638499, 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 = {} \[ \int \frac{1}{(c e+d e x) \left (a+b \sin ^{-1}(c+d x)\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{1}{(c e+d e x) \left (a+b \sin ^{-1}(c+d x)\right )} \, dx &=\frac{\operatorname{Subst}\left (\int \frac{1}{e x \left (a+b \sin ^{-1}(x)\right )} \, dx,x,c+d x\right )}{d}\\ &=\frac{\operatorname{Subst}\left (\int \frac{1}{x \left (a+b \sin ^{-1}(x)\right )} \, dx,x,c+d x\right )}{d e}\\ \end{align*}
Mathematica [A] time = 0.7783, size = 0, normalized size = 0. \[ \int \frac{1}{(c e+d e x) \left (a+b \sin ^{-1}(c+d x)\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.095, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ( dex+ce \right ) \left ( a+b\arcsin \left ( dx+c \right ) \right ) }}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (d e x + c e\right )}{\left (b \arcsin \left (d x + c\right ) + a\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{a d e x + a c e +{\left (b d e x + b c e\right )} \arcsin \left (d x + c\right )}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \frac{\int \frac{1}{a c + a d x + b c \operatorname{asin}{\left (c + d x \right )} + b d x \operatorname{asin}{\left (c + d x \right )}}\, dx}{e} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (d e x + c e\right )}{\left (b \arcsin \left (d x + c\right ) + a\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]