\(\int x^m \sqrt {\text {arccosh}(a x)} \, dx\) [123]

Optimal result

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

[Out]

Unintegrable(x^m*arccosh(a*x)^(1/2),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 = {} \[ \int x^m \sqrt {\text {arccosh}(a x)} \, dx=\int x^m \sqrt {\text {arccosh}(a x)} \, dx \]

[In]

Int[x^m*Sqrt[ArcCosh[a*x]],x]

[Out]

Defer[Int][x^m*Sqrt[ArcCosh[a*x]], x]

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

Mathematica [N/A]

Not integrable

Time = 1.02 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int x^m \sqrt {\text {arccosh}(a x)} \, dx=\int x^m \sqrt {\text {arccosh}(a x)} \, dx \]

[In]

Integrate[x^m*Sqrt[ArcCosh[a*x]],x]

[Out]

Integrate[x^m*Sqrt[ArcCosh[a*x]], x]

Maple [N/A] (verified)

Not integrable

Time = 0.26 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83

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

[In]

int(x^m*arccosh(a*x)^(1/2),x)

[Out]

int(x^m*arccosh(a*x)^(1/2),x)

Fricas [F(-2)]

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

[In]

integrate(x^m*arccosh(a*x)^(1/2),x, algorithm="fricas")

[Out]

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

Sympy [N/A]

Not integrable

Time = 3.25 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int x^m \sqrt {\text {arccosh}(a x)} \, dx=\int x^{m} \sqrt {\operatorname {acosh}{\left (a x \right )}}\, dx \]

[In]

integrate(x**m*acosh(a*x)**(1/2),x)

[Out]

Integral(x**m*sqrt(acosh(a*x)), x)

Maxima [N/A]

Not integrable

Time = 0.50 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int x^m \sqrt {\text {arccosh}(a x)} \, dx=\int { x^{m} \sqrt {\operatorname {arcosh}\left (a x\right )} \,d x } \]

[In]

integrate(x^m*arccosh(a*x)^(1/2),x, algorithm="maxima")

[Out]

integrate(x^m*sqrt(arccosh(a*x)), x)

Giac [F(-1)]

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

[In]

integrate(x^m*arccosh(a*x)^(1/2),x, algorithm="giac")

[Out]

Timed out

Mupad [N/A]

Not integrable

Time = 2.80 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int x^m \sqrt {\text {arccosh}(a x)} \, dx=\int x^m\,\sqrt {\mathrm {acosh}\left (a\,x\right )} \,d x \]

[In]

int(x^m*acosh(a*x)^(1/2),x)

[Out]

int(x^m*acosh(a*x)^(1/2), x)