\(\int \frac {\text {arccosh}(a x)^{5/2}}{x} \, dx\) [89]

Optimal result

Integrand size = 12, antiderivative size = 12 \[ \int \frac {\text {arccosh}(a x)^{5/2}}{x} \, dx=\text {Int}\left (\frac {\text {arccosh}(a x)^{5/2}}{x},x\right ) \]

[Out]

Unintegrable(arccosh(a*x)^(5/2)/x,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 = {} \[ \int \frac {\text {arccosh}(a x)^{5/2}}{x} \, dx=\int \frac {\text {arccosh}(a x)^{5/2}}{x} \, dx \]

[In]

Int[ArcCosh[a*x]^(5/2)/x,x]

[Out]

Defer[Int][ArcCosh[a*x]^(5/2)/x, x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {\text {arccosh}(a x)^{5/2}}{x} \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 0.15 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\text {arccosh}(a x)^{5/2}}{x} \, dx=\int \frac {\text {arccosh}(a x)^{5/2}}{x} \, dx \]

[In]

Integrate[ArcCosh[a*x]^(5/2)/x,x]

[Out]

Integrate[ArcCosh[a*x]^(5/2)/x, x]

Maple [N/A] (verified)

Not integrable

Time = 0.16 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83

\[\int \frac {\operatorname {arccosh}\left (a x \right )^{\frac {5}{2}}}{x}d x\]

[In]

int(arccosh(a*x)^(5/2)/x,x)

[Out]

int(arccosh(a*x)^(5/2)/x,x)

Fricas [F(-2)]

Exception generated. \[ \int \frac {\text {arccosh}(a x)^{5/2}}{x} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(arccosh(a*x)^(5/2)/x,x, algorithm="fricas")

[Out]

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

Sympy [F(-1)]

Timed out. \[ \int \frac {\text {arccosh}(a x)^{5/2}}{x} \, dx=\text {Timed out} \]

[In]

integrate(acosh(a*x)**(5/2)/x,x)

[Out]

Timed out

Maxima [N/A]

Not integrable

Time = 0.49 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {\text {arccosh}(a x)^{5/2}}{x} \, dx=\int { \frac {\operatorname {arcosh}\left (a x\right )^{\frac {5}{2}}}{x} \,d x } \]

[In]

integrate(arccosh(a*x)^(5/2)/x,x, algorithm="maxima")

[Out]

integrate(arccosh(a*x)^(5/2)/x, x)

Giac [N/A]

Not integrable

Time = 3.60 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {\text {arccosh}(a x)^{5/2}}{x} \, dx=\int { \frac {\operatorname {arcosh}\left (a x\right )^{\frac {5}{2}}}{x} \,d x } \]

[In]

integrate(arccosh(a*x)^(5/2)/x,x, algorithm="giac")

[Out]

integrate(arccosh(a*x)^(5/2)/x, x)

Mupad [N/A]

Not integrable

Time = 2.74 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {\text {arccosh}(a x)^{5/2}}{x} \, dx=\int \frac {{\mathrm {acosh}\left (a\,x\right )}^{5/2}}{x} \,d x \]

[In]

int(acosh(a*x)^(5/2)/x,x)

[Out]

int(acosh(a*x)^(5/2)/x, x)