Optimal. Leaf size=37 \[ \text{Unintegrable}\left (\frac{\log \left (h (f+g x)^m\right )}{\sqrt{1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.193949, 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 = {} \[ \int \frac{\log \left (h (f+g x)^m\right )}{\sqrt{1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{\log \left (h (f+g x)^m\right )}{\sqrt{1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )} \, dx &=\int \frac{\log \left (h (f+g x)^m\right )}{\sqrt{1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )} \, dx\\ \end{align*}
Mathematica [A] time = 0.205206, size = 0, normalized size = 0. \[ \int \frac{\log \left (h (f+g x)^m\right )}{\sqrt{1-c^2 x^2} \left (a+b \sin ^{-1}(c x)\right )} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 2.396, size = 0, normalized size = 0. \begin{align*} \int{\frac{\ln \left ( h \left ( gx+f \right ) ^{m} \right ) }{a+b\arcsin \left ( cx \right ) }{\frac{1}{\sqrt{-{c}^{2}{x}^{2}+1}}}}\, 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{\log \left ({\left (g x + f\right )}^{m} h\right )}{\sqrt{-c^{2} x^{2} + 1}{\left (b \arcsin \left (c x\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{\sqrt{-c^{2} x^{2} + 1} \log \left ({\left (g x + f\right )}^{m} h\right )}{a c^{2} x^{2} +{\left (b c^{2} x^{2} - b\right )} \arcsin \left (c x\right ) - a}, 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*} \int \frac{\log{\left (h \left (f + g x\right )^{m} \right )}}{\sqrt{- \left (c x - 1\right ) \left (c x + 1\right )} \left (a + b \operatorname{asin}{\left (c x \right )}\right )}\, dx \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{\log \left ({\left (g x + f\right )}^{m} h\right )}{\sqrt{-c^{2} x^{2} + 1}{\left (b \arcsin \left (c x\right ) + a\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]