\(\int (b x)^m \arcsin (a x)^n \, dx\) [129]

Optimal result

Integrand size = 12, antiderivative size = 12 \[ \int (b x)^m \arcsin (a x)^n \, dx=\text {Int}\left ((b x)^m \arcsin (a x)^n,x\right ) \]

[Out]

Unintegrable((b*x)^m*arcsin(a*x)^n,x)

Rubi [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 12, 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 = {} \[ \int (b x)^m \arcsin (a x)^n \, dx=\int (b x)^m \arcsin (a x)^n \, dx \]

[In]

Int[(b*x)^m*ArcSin[a*x]^n,x]

[Out]

Defer[Int][(b*x)^m*ArcSin[a*x]^n, x]

Rubi steps \begin{align*} \text {integral}& = \int (b x)^m \arcsin (a x)^n \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 0.44 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int (b x)^m \arcsin (a x)^n \, dx=\int (b x)^m \arcsin (a x)^n \, dx \]

[In]

Integrate[(b*x)^m*ArcSin[a*x]^n,x]

[Out]

Integrate[(b*x)^m*ArcSin[a*x]^n, x]

Maple [N/A] (verified)

Not integrable

Time = 0.61 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00

\[\int \left (b x \right )^{m} \arcsin \left (a x \right )^{n}d x\]

[In]

int((b*x)^m*arcsin(a*x)^n,x)

[Out]

int((b*x)^m*arcsin(a*x)^n,x)

Fricas [N/A]

Not integrable

Time = 0.26 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int (b x)^m \arcsin (a x)^n \, dx=\int { \left (b x\right )^{m} \arcsin \left (a x\right )^{n} \,d x } \]

[In]

integrate((b*x)^m*arcsin(a*x)^n,x, algorithm="fricas")

[Out]

integral((b*x)^m*arcsin(a*x)^n, x)

Sympy [N/A]

Not integrable

Time = 3.49 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int (b x)^m \arcsin (a x)^n \, dx=\int \left (b x\right )^{m} \operatorname {asin}^{n}{\left (a x \right )}\, dx \]

[In]

integrate((b*x)**m*asin(a*x)**n,x)

[Out]

Integral((b*x)**m*asin(a*x)**n, x)

Maxima [F(-2)]

Exception generated. \[ \int (b x)^m \arcsin (a x)^n \, dx=\text {Exception raised: RuntimeError} \]

[In]

integrate((b*x)^m*arcsin(a*x)^n,x, algorithm="maxima")

[Out]

Exception raised: RuntimeError >> ECL says: expt: undefined: 0 to a negative exponent.

Giac [N/A]

Not integrable

Time = 0.82 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int (b x)^m \arcsin (a x)^n \, dx=\int { \left (b x\right )^{m} \arcsin \left (a x\right )^{n} \,d x } \]

[In]

integrate((b*x)^m*arcsin(a*x)^n,x, algorithm="giac")

[Out]

integrate((b*x)^m*arcsin(a*x)^n, x)

Mupad [N/A]

Not integrable

Time = 0.04 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int (b x)^m \arcsin (a x)^n \, dx=\int {\mathrm {asin}\left (a\,x\right )}^n\,{\left (b\,x\right )}^m \,d x \]

[In]

int(asin(a*x)^n*(b*x)^m,x)

[Out]

int(asin(a*x)^n*(b*x)^m, x)