\(\int \frac {1}{x \text {arccosh}(a x)^{5/2}} \, dx\) [108]

Optimal result

Integrand size = 12, antiderivative size = 12 \[ \int \frac {1}{x \text {arccosh}(a x)^{5/2}} \, dx=\text {Int}\left (\frac {1}{x \text {arccosh}(a x)^{5/2}},x\right ) \]

[Out]

Unintegrable(1/x/arccosh(a*x)^(5/2),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 = {} \[ \int \frac {1}{x \text {arccosh}(a x)^{5/2}} \, dx=\int \frac {1}{x \text {arccosh}(a x)^{5/2}} \, dx \]

[In]

Int[1/(x*ArcCosh[a*x]^(5/2)),x]

[Out]

Defer[Int][1/(x*ArcCosh[a*x]^(5/2)), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{x \text {arccosh}(a x)^{5/2}} \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 0.17 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {1}{x \text {arccosh}(a x)^{5/2}} \, dx=\int \frac {1}{x \text {arccosh}(a x)^{5/2}} \, dx \]

[In]

Integrate[1/(x*ArcCosh[a*x]^(5/2)),x]

[Out]

Integrate[1/(x*ArcCosh[a*x]^(5/2)), x]

Maple [N/A] (verified)

Not integrable

Time = 0.20 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83

\[\int \frac {1}{x \operatorname {arccosh}\left (a x \right )^{\frac {5}{2}}}d x\]

[In]

int(1/x/arccosh(a*x)^(5/2),x)

[Out]

int(1/x/arccosh(a*x)^(5/2),x)

Fricas [F(-2)]

Exception generated. \[ \int \frac {1}{x \text {arccosh}(a x)^{5/2}} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(1/x/arccosh(a*x)^(5/2),x, algorithm="fricas")

[Out]

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

Sympy [N/A]

Not integrable

Time = 58.73 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x \text {arccosh}(a x)^{5/2}} \, dx=\int \frac {1}{x \operatorname {acosh}^{\frac {5}{2}}{\left (a x \right )}}\, dx \]

[In]

integrate(1/x/acosh(a*x)**(5/2),x)

[Out]

Integral(1/(x*acosh(a*x)**(5/2)), x)

Maxima [N/A]

Not integrable

Time = 0.50 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x \text {arccosh}(a x)^{5/2}} \, dx=\int { \frac {1}{x \operatorname {arcosh}\left (a x\right )^{\frac {5}{2}}} \,d x } \]

[In]

integrate(1/x/arccosh(a*x)^(5/2),x, algorithm="maxima")

[Out]

integrate(1/(x*arccosh(a*x)^(5/2)), x)

Giac [N/A]

Not integrable

Time = 0.30 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x \text {arccosh}(a x)^{5/2}} \, dx=\int { \frac {1}{x \operatorname {arcosh}\left (a x\right )^{\frac {5}{2}}} \,d x } \]

[In]

integrate(1/x/arccosh(a*x)^(5/2),x, algorithm="giac")

[Out]

integrate(1/(x*arccosh(a*x)^(5/2)), x)

Mupad [N/A]

Not integrable

Time = 2.74 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x \text {arccosh}(a x)^{5/2}} \, dx=\int \frac {1}{x\,{\mathrm {acosh}\left (a\,x\right )}^{5/2}} \,d x \]

[In]

int(1/(x*acosh(a*x)^(5/2)),x)

[Out]

int(1/(x*acosh(a*x)^(5/2)), x)