Optimal. Leaf size=30 \[ \text {Int}\left (\frac {x^m \left (a+b \sin ^{-1}(c x)\right )^2}{d-c^2 d x^2},x\right ) \]
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Rubi [A] time = 0.09, 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 = {} \[ \int \frac {x^m \left (a+b \sin ^{-1}(c x)\right )^2}{d-c^2 d x^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {x^m \left (a+b \sin ^{-1}(c x)\right )^2}{d-c^2 d x^2} \, dx &=\int \frac {x^m \left (a+b \sin ^{-1}(c x)\right )^2}{d-c^2 d x^2} \, dx\\ \end {align*}
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Mathematica [A] time = 7.50, size = 0, normalized size = 0.00 \[ \int \frac {x^m \left (a+b \sin ^{-1}(c x)\right )^2}{d-c^2 d x^2} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.46, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-\frac {{\left (b^{2} \arcsin \left (c x\right )^{2} + 2 \, a b \arcsin \left (c x\right ) + a^{2}\right )} x^{m}}{c^{2} d x^{2} - d}, x\right ) \]
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 \[ \int -\frac {{\left (b \arcsin \left (c x\right ) + a\right )}^{2} x^{m}}{c^{2} d x^{2} - d}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.59, size = 0, normalized size = 0.00 \[ \int \frac {x^{m} \left (a +b \arcsin \left (c x \right )\right )^{2}}{-c^{2} d \,x^{2}+d}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ -\int \frac {{\left (b \arcsin \left (c x\right ) + a\right )}^{2} x^{m}}{c^{2} d x^{2} - d}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {x^m\,{\left (a+b\,\mathrm {asin}\left (c\,x\right )\right )}^2}{d-c^2\,d\,x^2} \,d x \]
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 \[ - \frac {\int \frac {a^{2} x^{m}}{c^{2} x^{2} - 1}\, dx + \int \frac {b^{2} x^{m} \operatorname {asin}^{2}{\left (c x \right )}}{c^{2} x^{2} - 1}\, dx + \int \frac {2 a b x^{m} \operatorname {asin}{\left (c x \right )}}{c^{2} x^{2} - 1}\, dx}{d} \]
Verification of antiderivative is not currently implemented for this CAS.
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