Integrand size = 16, antiderivative size = 16 \[ \int \frac {(a+b \arcsin (c+d x))^n}{x} \, dx=\text {Int}\left (\frac {(a+b \arcsin (c+d x))^n}{x},x\right ) \]
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Not integrable
Time = 0.04 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {(a+b \arcsin (c+d x))^n}{x} \, dx=\int \frac {(a+b \arcsin (c+d x))^n}{x} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \frac {\text {Subst}\left (\int \frac {(a+b \arcsin (x))^n}{-\frac {c}{d}+\frac {x}{d}} \, dx,x,c+d x\right )}{d} \\ \end{align*}
Not integrable
Time = 0.34 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {(a+b \arcsin (c+d x))^n}{x} \, dx=\int \frac {(a+b \arcsin (c+d x))^n}{x} \, dx \]
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Not integrable
Time = 0.46 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00
\[\int \frac {\left (a +b \arcsin \left (d x +c \right )\right )^{n}}{x}d x\]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {(a+b \arcsin (c+d x))^n}{x} \, dx=\int { \frac {{\left (b \arcsin \left (d x + c\right ) + a\right )}^{n}}{x} \,d x } \]
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Not integrable
Time = 0.62 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \frac {(a+b \arcsin (c+d x))^n}{x} \, dx=\int \frac {\left (a + b \operatorname {asin}{\left (c + d x \right )}\right )^{n}}{x}\, dx \]
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Not integrable
Time = 0.95 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {(a+b \arcsin (c+d x))^n}{x} \, dx=\int { \frac {{\left (b \arcsin \left (d x + c\right ) + a\right )}^{n}}{x} \,d x } \]
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Not integrable
Time = 0.50 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {(a+b \arcsin (c+d x))^n}{x} \, dx=\int { \frac {{\left (b \arcsin \left (d x + c\right ) + a\right )}^{n}}{x} \,d x } \]
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Not integrable
Time = 0.23 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {(a+b \arcsin (c+d x))^n}{x} \, dx=\int \frac {{\left (a+b\,\mathrm {asin}\left (c+d\,x\right )\right )}^n}{x} \,d x \]
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