\(\int x^m \text {arccosh}(a x)^{3/2} \, dx\) [122]

Optimal result

Integrand size = 12, antiderivative size = 12 \[ \int x^m \text {arccosh}(a x)^{3/2} \, dx=\text {Int}\left (x^m \text {arccosh}(a x)^{3/2},x\right ) \]

[Out]

Unintegrable(x^m*arccosh(a*x)^(3/2),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 = {} \[ \int x^m \text {arccosh}(a x)^{3/2} \, dx=\int x^m \text {arccosh}(a x)^{3/2} \, dx \]

[In]

Int[x^m*ArcCosh[a*x]^(3/2),x]

[Out]

Defer[Int][x^m*ArcCosh[a*x]^(3/2), x]

Rubi steps \begin{align*} \text {integral}& = \int x^m \text {arccosh}(a x)^{3/2} \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 0.93 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int x^m \text {arccosh}(a x)^{3/2} \, dx=\int x^m \text {arccosh}(a x)^{3/2} \, dx \]

[In]

Integrate[x^m*ArcCosh[a*x]^(3/2),x]

[Out]

Integrate[x^m*ArcCosh[a*x]^(3/2), x]

Maple [N/A] (verified)

Not integrable

Time = 0.27 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83

\[\int x^{m} \operatorname {arccosh}\left (a x \right )^{\frac {3}{2}}d x\]

[In]

int(x^m*arccosh(a*x)^(3/2),x)

[Out]

int(x^m*arccosh(a*x)^(3/2),x)

Fricas [F(-2)]

Exception generated. \[ \int x^m \text {arccosh}(a x)^{3/2} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(x^m*arccosh(a*x)^(3/2),x, algorithm="fricas")

[Out]

Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (co
nstant residues)

Sympy [F(-1)]

Timed out. \[ \int x^m \text {arccosh}(a x)^{3/2} \, dx=\text {Timed out} \]

[In]

integrate(x**m*acosh(a*x)**(3/2),x)

[Out]

Timed out

Maxima [N/A]

Not integrable

Time = 0.57 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int x^m \text {arccosh}(a x)^{3/2} \, dx=\int { x^{m} \operatorname {arcosh}\left (a x\right )^{\frac {3}{2}} \,d x } \]

[In]

integrate(x^m*arccosh(a*x)^(3/2),x, algorithm="maxima")

[Out]

integrate(x^m*arccosh(a*x)^(3/2), x)

Giac [F(-1)]

Timed out. \[ \int x^m \text {arccosh}(a x)^{3/2} \, dx=\text {Timed out} \]

[In]

integrate(x^m*arccosh(a*x)^(3/2),x, algorithm="giac")

[Out]

Timed out

Mupad [N/A]

Not integrable

Time = 2.63 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int x^m \text {arccosh}(a x)^{3/2} \, dx=\int x^m\,{\mathrm {acosh}\left (a\,x\right )}^{3/2} \,d x \]

[In]

int(x^m*acosh(a*x)^(3/2),x)

[Out]

int(x^m*acosh(a*x)^(3/2), x)