Optimal. Leaf size=21 \[ \text {Int}\left (\frac {1}{(d+e x) \left (a+b \sin ^{-1}(c x)\right )},x\right ) \]
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Rubi [A] time = 0.03, 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 = {} \[ \int \frac {1}{(d+e x) \left (a+b \sin ^{-1}(c x)\right )} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{(d+e x) \left (a+b \sin ^{-1}(c x)\right )} \, dx &=\int \frac {1}{(d+e x) \left (a+b \sin ^{-1}(c x)\right )} \, dx\\ \end {align*}
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Mathematica [A] time = 0.21, size = 0, normalized size = 0.00 \[ \int \frac {1}{(d+e x) \left (a+b \sin ^{-1}(c x)\right )} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.73, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{a e x + a d + {\left (b e x + b d\right )} \arcsin \left (c x\right )}, x\right ) \]
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 \[ \int \frac {1}{{\left (e x + d\right )} {\left (b \arcsin \left (c x\right ) + a\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 3.15, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (e x +d \right ) \left (a +b \arcsin \left (c x \right )\right )}\, dx \]
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 \[ \int \frac {1}{{\left (e x + d\right )} {\left (b \arcsin \left (c x\right ) + a\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {1}{\left (a+b\,\mathrm {asin}\left (c\,x\right )\right )\,\left (d+e\,x\right )} \,d x \]
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 \[ \int \frac {1}{\left (a + b \operatorname {asin}{\left (c x \right )}\right ) \left (d + e x\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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