Optimal. Leaf size=19 \[ \text {Int}\left (\frac {(a+b \text {ArcSin}(c+d x))^n}{x},x\right ) \]
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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 = {}
\begin {gather*} \int \frac {(a+b \text {ArcSin}(c+d x))^n}{x} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\left (a+b \sin ^{-1}(c+d x)\right )^n}{x} \, dx &=\frac {\text {Subst}\left (\int \frac {\left (a+b \sin ^{-1}(x)\right )^n}{-\frac {c}{d}+\frac {x}{d}} \, dx,x,c+d x\right )}{d}\\ \end {align*}
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Mathematica [A]
time = 0.13, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(a+b \text {ArcSin}(c+d x))^n}{x} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.20, size = 0, normalized size = 0.00 \[\int \frac {\left (a +b \arcsin \left (d x +c \right )\right )^{n}}{x}\, dx\]
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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \int \frac {\left (a + b \operatorname {asin}{\left (c + d x \right )}\right )^{n}}{x}\, dx \end {gather*}
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 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \int \frac {{\left (a+b\,\mathrm {asin}\left (c+d\,x\right )\right )}^n}{x} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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