Optimal. Leaf size=17 \[ \text {Int}\left (\frac {\sin ^{-1}(a x)^n}{(b x)^{3/2}},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, 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 = {} \[ \int \frac {\sin ^{-1}(a x)^n}{(b x)^{3/2}} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {\sin ^{-1}(a x)^n}{(b x)^{3/2}} \, dx &=\int \frac {\sin ^{-1}(a x)^n}{(b x)^{3/2}} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 1.93, size = 0, normalized size = 0.00 \[ \int \frac {\sin ^{-1}(a x)^n}{(b x)^{3/2}} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.45, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\sqrt {b x} \arcsin \left (a x\right )^{n}}{b^{2} x^{2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\arcsin \left (a x\right )^{n}}{\left (b x\right )^{\frac {3}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.10, size = 0, normalized size = 0.00 \[ \int \frac {\arcsin \left (a x \right )^{n}}{\left (b x \right )^{\frac {3}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: RuntimeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.06 \[ \int \frac {{\mathrm {asin}\left (a\,x\right )}^n}{{\left (b\,x\right )}^{3/2}} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {asin}^{n}{\left (a x \right )}}{\left (b x\right )^{\frac {3}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________