Optimal. Leaf size=27 \[ \text {Int}\left (\frac {\text {ArcSin}(a x)^n}{x \sqrt {1-a^2 x^2}},x\right ) \]
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Rubi [A]
time = 0.07, 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 {\text {ArcSin}(a x)^n}{x \sqrt {1-a^2 x^2}} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\sin ^{-1}(a x)^n}{x \sqrt {1-a^2 x^2}} \, dx &=\int \frac {\sin ^{-1}(a x)^n}{x \sqrt {1-a^2 x^2}} \, dx\\ \end {align*}
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Mathematica [A]
time = 2.35, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\text {ArcSin}(a x)^n}{x \sqrt {1-a^2 x^2}} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.15, size = 0, normalized size = 0.00 \[\int \frac {\arcsin \left (a x \right )^{n}}{x \sqrt {-a^{2} x^{2}+1}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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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.
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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\operatorname {asin}^{n}{\left (a x \right )}}{x \sqrt {- \left (a x - 1\right ) \left (a x + 1\right )}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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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.
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Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\mathrm {asin}\left (a\,x\right )}^n}{x\,\sqrt {1-a^2\,x^2}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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