Optimal. Leaf size=15 \[ \text {Int}\left (\frac {1}{x \sin ^{-1}(a+b x)^3},x\right ) \]
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Rubi [A] time = 0.04, 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 = {} \[ \int \frac {1}{x \sin ^{-1}(a+b x)^3} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{x \sin ^{-1}(a+b x)^3} \, dx &=\frac {\operatorname {Subst}\left (\int \frac {1}{\left (-\frac {a}{b}+\frac {x}{b}\right ) \sin ^{-1}(x)^3} \, dx,x,a+b x\right )}{b}\\ \end {align*}
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Mathematica [A] time = 2.71, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \sin ^{-1}(a+b x)^3} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.44, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{x \arcsin \left (b x + a\right )^{3}}, x\right ) \]
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 \[ \int \frac {1}{x \arcsin \left (b x + a\right )^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 1.49, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \arcsin \left (b x +a \right )^{3}}\, dx \]
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 \[ -\frac {x^{2} \arctan \left (b x + a, \sqrt {b x + a + 1} \sqrt {-b x - a + 1}\right )^{2} \int \frac {a b x + 2 \, a^{2} - 2}{x^{3} \arctan \left (b x + a, \sqrt {b x + a + 1} \sqrt {-b x - a + 1}\right )}\,{d x} + \sqrt {b x + a + 1} \sqrt {-b x - a + 1} b x + {\left (a b x + a^{2} - 1\right )} \arctan \left (b x + a, \sqrt {b x + a + 1} \sqrt {-b x - a + 1}\right )}{2 \, b^{2} x^{2} \arctan \left (b x + a, \sqrt {b x + a + 1} \sqrt {-b x - a + 1}\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.07 \[ \int \frac {1}{x\,{\mathrm {asin}\left (a+b\,x\right )}^3} \,d x \]
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 \[ \int \frac {1}{x \operatorname {asin}^{3}{\left (a + b x \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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