Optimal. Leaf size=31 \[ \text {Int}\left (\frac {\sqrt {1-c^2 x^2}}{x^4 (a+b \text {ArcSin}(c x))^2},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.08, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {\sqrt {1-c^2 x^2}}{x^4 (a+b \text {ArcSin}(c x))^2} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {\sqrt {1-c^2 x^2}}{x^4 \left (a+b \sin ^{-1}(c x)\right )^2} \, dx &=\int \frac {\sqrt {1-c^2 x^2}}{x^4 \left (a+b \sin ^{-1}(c x)\right )^2} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 2.54, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sqrt {1-c^2 x^2}}{x^4 (a+b \text {ArcSin}(c x))^2} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 4.62, size = 0, normalized size = 0.00 \[\int \frac {\sqrt {-c^{2} x^{2}+1}}{x^{4} \left (a +b \arcsin \left (c x \right )\right )^{2}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sqrt {- \left (c x - 1\right ) \left (c x + 1\right )}}{x^{4} \left (a + b \operatorname {asin}{\left (c x \right )}\right )^{2}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [A]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {\sqrt {1-c^2\,x^2}}{x^4\,{\left (a+b\,\mathrm {asin}\left (c\,x\right )\right )}^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________