Optimal. Leaf size=19 \[ \text {Int}\left (x^m \left (a+b \sin ^{-1}(c+d x)\right )^n,x\right ) \]
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Rubi [A] time = 0.05, 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 = {} \[ \int x^m \left (a+b \sin ^{-1}(c+d x)\right )^n \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int x^m \left (a+b \sin ^{-1}(c+d x)\right )^n \, dx &=\frac {\operatorname {Subst}\left (\int \left (-\frac {c}{d}+\frac {x}{d}\right )^m \left (a+b \sin ^{-1}(x)\right )^n \, dx,x,c+d x\right )}{d}\\ \end {align*}
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Mathematica [A] time = 0.54, size = 0, normalized size = 0.00 \[ \int x^m \left (a+b \sin ^{-1}(c+d x)\right )^n \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.46, size = 0, normalized size = 0.00 \[ {\rm integral}\left ({\left (b \arcsin \left (d x + c\right ) + a\right )}^{n} x^{m}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 2.12, size = 0, normalized size = 0.00 \[ \int x^{m} \left (a +b \arcsin \left (d x +c \right )\right )^{n}\, dx \]
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 \[ \int {\left (b \arcsin \left (d x + c\right ) + a\right )}^{n} x^{m}\,{d x} \]
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 \[ \int x^m\,{\left (a+b\,\mathrm {asin}\left (c+d\,x\right )\right )}^n \,d x \]
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 \[ \int x^{m} \left (a + b \operatorname {asin}{\left (c + d x \right )}\right )^{n}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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