Optimal. Leaf size=17 \[ \text {Int}\left (\frac {1}{x^2 \left (a+b \sin ^{-1}(c x)\right )^3},x\right ) \]
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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 = {} \[ \int \frac {1}{x^2 \left (a+b \sin ^{-1}(c x)\right )^3} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{x^2 \left (a+b \sin ^{-1}(c x)\right )^3} \, dx &=\int \frac {1}{x^2 \left (a+b \sin ^{-1}(c x)\right )^3} \, dx\\ \end {align*}
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Mathematica [A] time = 19.12, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^2 \left (a+b \sin ^{-1}(c x)\right )^3} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.52, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{b^{3} x^{2} \arcsin \left (c x\right )^{3} + 3 \, a b^{2} x^{2} \arcsin \left (c x\right )^{2} + 3 \, a^{2} b x^{2} \arcsin \left (c x\right ) + a^{3} x^{2}}, x\right ) \]
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 \[ \int \frac {1}{{\left (b \arcsin \left (c x\right ) + a\right )}^{3} x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.61, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^{2} \left (a +b \arcsin \left (c x \right )\right )^{3}}\, dx \]
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 \[ -\frac {a c^{2} x^{2} + \sqrt {c x + 1} \sqrt {-c x + 1} b c x + {\left (b c^{2} x^{2} - 2 \, b\right )} \arctan \left (c x, \sqrt {c x + 1} \sqrt {-c x + 1}\right ) + {\left (b^{4} c^{2} x^{3} \arctan \left (c x, \sqrt {c x + 1} \sqrt {-c x + 1}\right )^{2} + 2 \, a b^{3} c^{2} x^{3} \arctan \left (c x, \sqrt {c x + 1} \sqrt {-c x + 1}\right ) + a^{2} b^{2} c^{2} x^{3}\right )} \int \frac {c^{2} x^{2} - 6}{b^{3} c^{2} x^{4} \arctan \left (c x, \sqrt {c x + 1} \sqrt {-c x + 1}\right ) + a b^{2} c^{2} x^{4}}\,{d x} - 2 \, a}{2 \, {\left (b^{4} c^{2} x^{3} \arctan \left (c x, \sqrt {c x + 1} \sqrt {-c x + 1}\right )^{2} + 2 \, a b^{3} c^{2} x^{3} \arctan \left (c x, \sqrt {c x + 1} \sqrt {-c x + 1}\right ) + a^{2} b^{2} c^{2} x^{3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.06 \[ \int \frac {1}{x^2\,{\left (a+b\,\mathrm {asin}\left (c\,x\right )\right )}^3} \,d x \]
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 \[ \int \frac {1}{x^{2} \left (a + b \operatorname {asin}{\left (c x \right )}\right )^{3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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